Finite Group Databasebeta

← C61×#62927 #29566360

Subgroups — C61×#62927 #29566360

Order 15616.

7096 conjugacy classes of subgroups.

The subgroup lattice has 1584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3560C214yesmaximal, complemented
2C61×#3559C214yesmaximal, complemented
3C61×#3551C214yesmaximal, complemented
4C61×#3547C214yesmaximal, complemented
5C61×#3542C214yesmaximal, complemented
6C61×#3541C214yesmaximal, complemented
7C61×#3539C214yesmaximal, complemented
8C61×#3538C214yesmaximal, complemented
9C61×#3534C214yesmaximal, complemented
10C61×#3520C214yesmaximal, complemented
11C61×#3512C212yesmaximal, complemented
12C61×#3505C214yesmaximal, complemented
13C61×#3497C211yesmaximal, characteristic, complemented
14C61×#3494C214yesmaximal, complemented
15C61×#3493C211yesmaximal, characteristic, complemented
16C61×#3492C211yesmaximal, characteristic, complemented
17C61×#3489C212yesmaximal, complemented
18C61×#3489C212yesmaximal, complemented
19C2×C61×#552C211yesmaximal, characteristic, complemented
20D4×#41×C61C212yesmaximal, complemented
21C61×#3461C211yesmaximal, characteristic, complemented
22C61×#3449C211yesmaximal, characteristic, complemented
23C2×C61×#537C211yesmaximal, characteristic, complemented
24C2×2−1+4×C61C2212yescomplemented
25C22×#41×C61C2212yescomplemented
26C22×#41×C61C2212yescomplemented
27C61×#563C2218yescomplemented
28C61×#563C2218yescomplemented
29C61×#562C2218yescomplemented
30C61×#562C2218yescomplemented
31C61×#560C2218yescomplemented
32C61×#560C2218yescomplemented
33C61×#556C2214yescomplemented
34C61×#555C2218yescomplemented
35C61×#555C2214yescomplemented
36C61×#554C2214yescomplemented
37C61×#554C2218yescomplemented
38C61×#553C2218yescomplemented
39C61×#553C2214yescomplemented
40C61×#553C2214yescomplemented
41C61×#553C2218yescomplemented
42C61×#553C2218yescomplemented
43C61×#553C2218yescomplemented
44C61×#553C2214yescomplemented
45C61×#553C2218yescomplemented
46C61×#553C2214yescomplemented
47C61×#552C2214yescomplemented
48C61×#552C2214yescomplemented
49C61×#552C2214yescomplemented
50C61×#552C2214yescomplemented
51C61×#552C2214yescomplemented
52C61×#552C2214yescomplemented
53C61×#552C2214yescomplemented
54C61×#552C2214yescomplemented
55C61×#551C2218yescomplemented
56C61×#551C2218yescomplemented
57C61×#551C2218yescomplemented
58C61×#551C2218yescomplemented
59C61×#550C2212yescomplemented
60C61×#550C2214yescomplemented
61D4×Q8×C61C2214yescomplemented
62D4×Q8×C61C2212yescomplemented
63D4×Q8×C61C2214yescomplemented
64D4×Q8×C61C2214yescomplemented
65C61×#548C2212yes—
66C61×#548C2212yescomplemented
67C61×#548C2214yescomplemented
68C61×#548C2214yescomplemented
69C61×#548C2214yescomplemented
70C61×#548C2214yescomplemented
71C61×#547C2214yescomplemented
72C61×#547C2214yescomplemented
73C61×#547C2218yescomplemented
74C61×#547C2218yescomplemented
75C61×#547C2212yescomplemented
76C61×#547C2214yescomplemented
77C61×#547C2214yescomplemented
78C61×#546C2212yes—
79C61×#546C2212yescomplemented
80C61×#546C2214yescomplemented
81C61×#546C2214yescomplemented
82C61×#546C2218yescomplemented
83C61×#546C2214yescomplemented
84C61×#546C2218yescomplemented
85C61×#546C2214yescomplemented
86C61×#546C2218yescomplemented
87D42×C61C2214yes—
88D42×C61C2212yescomplemented
89C61×#544C2218yescomplemented
90C61×#544C2211yescharacteristic, complemented
91C61×#544C2214yescomplemented
92C61×#542C2214yescomplemented
93C61×#542C2218yescomplemented
94C61×#542C2214yescomplemented
95C61×#542C2214yescomplemented
96C61×#541C2214yescomplemented
97C61×#541C2214yescomplemented
98C61×#540C2218yescomplemented
99C61×#540C2214yescomplemented
100C61×#540C2218yescomplemented
101C61×#540C2214yescomplemented
102C61×#540C2214yescomplemented
103C61×#539C2214yescomplemented
104C61×#539C2214yescomplemented
105C61×#539C2218yescomplemented
106C61×#539C2218yescomplemented
107C61×#539C2218yescomplemented
108C61×#539C2218yescomplemented
109C61×#538C2218yescomplemented
110C61×#538C2218yescomplemented
111C61×#538C2214yescomplemented
112C61×#538C2218yescomplemented
113C61×#537C2211yescharacteristic
114C61×#537C2214yescomplemented
115C61×#537C2214yescomplemented
116C61×#537C2214yescomplemented
117C61×#537C2214yescomplemented
118C61×#537C2214yescomplemented
119C61×#537C2214yescomplemented
120C61×#537C2212yescomplemented
121C61×#537C2211yescharacteristic, complemented
122C61×#537C2212yescomplemented
123C61×#537C2211yescharacteristic, complemented
124C61×#536C2214yescomplemented
125C61×#536C2214yescomplemented
126C61×#536C2214yescomplemented
127C61×#536C2212yescomplemented
128C61×#535C2214yescomplemented
129C61×#535C2214yescomplemented
130C61×#534C2214yescomplemented
131C61×#534C2218yescomplemented
132C61×#533C2214yescomplemented
133C61×#532C2214yescomplemented
134C61×#532C2214yescomplemented
135C61×#532C2214yescomplemented
136C61×#532C2212yescomplemented
137C61×#529C2214yescomplemented
138C61×#529C2214yescomplemented
139C61×#529C2214yescomplemented
140C61×#529C2214yescomplemented
141C61×#529C2214yescomplemented
142C2×#126×C61C2212yescomplemented
143C2×#125×C61C2212yescomplemented
144C2×#125×C61C2211yescharacteristic, complemented
145C61×#525C2214yes—
146C61×#525C2214yescomplemented
147C61×#525C2214yescomplemented
148C61×#525C2212yescomplemented
149C61×#525C2212yescomplemented
150C61×#525C2214yescomplemented
151C61×#525C2214yescomplemented
152C61×#525C2214yescomplemented
153C61×#525C2214yescomplemented
154C2×#123×C61C2212yes—
155C2×C22⋊Q8×C61C2214yescomplemented
156C2×C22⋊Q8×C61C2211yescharacteristic, complemented
157C2×C22⋊Q8×C61C2211yescharacteristic, complemented
158C2×C22⋊Q8×C61C2214yescomplemented
159C2×C22⋊Q8×C61C2214yescomplemented
160C2×#121×C61C2214yescomplemented
161C2×#121×C61C2214yescomplemented
162C61×#520C2212yescomplemented
163C61×#520C2212yescomplemented
164C61×#520C2214yescomplemented
165C61×#518C2214yescomplemented
166C4×#41×C61C2212yescomplemented
167C2×C4×Q8×C61C2211yescharacteristic, complemented
168C2×C4×D4×C61C2211yescharacteristic
169C2×C4×D4×C61C2214yescomplemented
170C2×#117×C61C2211yescharacteristic, complemented
171C2×#117×C61C2212yescomplemented
172C22×C4⋊C4×C61C2211yescharacteristic, complemented
1732−1+4×C61—48no—
174C2×#41×C61—48no—
175C2×#41×C61—48no—
176C2×#41×C61C2312yes—
177C2×#41×C61C2312yes—
178C2×#41×C61C2312yes—
179C2×#41×C61C2314yes—
180C2×#41×C61C2314yes—
181C2×#41×C61C2314yes—
182C2×#41×C61C2318yes—
183C2×#41×C61C2314yes—
184C2×#41×C61C2314yes—
185C2×#41×C61C2312yes—
186C2×#41×C61C2312yes—
187C2×#41×C61C2314yes—
188C2×#41×C61C2314yes—
189C2×#41×C61C2312yes—
190C2×#41×C61C2312yes—
191C22×Q8×C61C2311yescharacteristic
192C22×Q8×C61C2312yes—
193C22×Q8×C61C2314yes—
194C22×Q8×C61C2314yes—
195C22×Q8×C61C2312yes—
196C22×D4×C61C2314yes—
197C22×D4×C61C2314yes—
198C22×D4×C61C2314yes—
199C22×D4×C61C2312yes—
200C22×D4×C61C2311yescharacteristic
201C22×D4×C61C2314yes—
202C22×D4×C61C2312yes—
203C23×C4×C61C2311yescharacteristic
204C23×C4×C61C2311yescharacteristic
205C23×C4×C61C2314yes—
206C23×C4×C61C2314yes—
207C23×C4×C61C2312yes—
208C4⋊Q8×C61C2314yes—
209C4⋊Q8×C61C2312yes—
210C4⋊Q8×C61C2314yes—
211C4⋊Q8×C61C2314yes—
212C4⋊Q8×C61C2314yes—
213C4⋊Q8×C61C2314yes—
214C4⋊Q8×C61C2318yes—
215C4⋊Q8×C61C2318yes—
216#127×C61C2314yes—
217#127×C61C2314yes—
218#127×C61C2314yes—
219#127×C61C2312yes—
220#126×C61C2318yes—
221#126×C61C2318yes—
222#126×C61C2318yes—
223#126×C61C2318yes—
224#126×C61C2318yes—
225#126×C61C2318yes—
226#126×C61C2318yes—
227#126×C61C2318yes—
228#126×C61C2318yes—
229#126×C61C2318yes—
230#126×C61C2318yes—
231#125×C61C2318yes—
232#125×C61C2314yes—
233#125×C61C2318yes—
234#125×C61C2318yes—
235#125×C61C2318yes—
236#125×C61C2318yes—
237#125×C61C2314yes—
238#125×C61C2318yes—
239#125×C61C2314yes—
240#125×C61C2314yes—
241#125×C61C2314yes—
242#124×C61C2318yes—
243#124×C61C2318yes—
244#124×C61C2314yes—
245#124×C61C2314yes—
246#124×C61C2312yes—
247#124×C61C2312yes—
248#124×C61C2314yes—
249#124×C61C2314yes—
250#124×C61C2318yes—
251#124×C61C2318yes—
252#124×C61C2314yes—
253#124×C61C2318yes—
254#123×C61C2318yes—
255#123×C61C2318yes—
256#123×C61C2318yes—
257#123×C61C2318yes—
258#123×C61C2318yes—
259#123×C61C2318yes—
260#123×C61C2318yes—
261#123×C61C2318yes—
262#123×C61C2318yes—
263#123×C61C2318yes—
264#123×C61C2318yes—
265#123×C61C2318yes—
266#123×C61C2314yes—
267#123×C61C2318yes—
268#123×C61C2318yes—
269#123×C61C2318yes—
270#123×C61C2314yes—
271#123×C61C2314yes—
272#123×C61C2318yes—
273#123×C61C2318yes—
274#123×C61C2318yes—
275#123×C61C2318yes—
276#123×C61C2314yes—
277#123×C61C2314yes—
278#123×C61C2314yes—
279C22⋊Q8×C61C2314yes—
280C22⋊Q8×C61C2314yes—
281C22⋊Q8×C61C2318yes—
282C22⋊Q8×C61C2314yes—
283C22⋊Q8×C61C2314yes—
284C22⋊Q8×C61C2312yes—
285C22⋊Q8×C61C2312yes—
286C22⋊Q8×C61C2314yes—
287C22⋊Q8×C61C2314yes—
288C22⋊Q8×C61C2314yes—
289C22⋊Q8×C61C2314yes—
290C22⋊Q8×C61C2314yes—
291C22⋊Q8×C61C2318yes—
292C22⋊Q8×C61C2314yes—
293C22⋊Q8×C61C2314yes—
294C22⋊Q8×C61C2318yes—
295C22⋊Q8×C61C2318yes—
296C22⋊Q8×C61C2318yes—
297C22⋊Q8×C61C2318yes—
298C22⋊Q8×C61C2318yes—
299C22⋊Q8×C61C2314yes—
300C22⋊Q8×C61C2318yes—
301C22⋊Q8×C61C2318yes—
302C22⋊Q8×C61C2314yes—
303C22⋊Q8×C61C2314yes—
304C22⋊Q8×C61C2318yes—
305C22⋊Q8×C61C2318yes—
306C22⋊Q8×C61C2318yes—
307C22⋊Q8×C61C2314yes—
308C22⋊Q8×C61C2314yes—
309C22⋊Q8×C61C2314yes—
310C22⋊Q8×C61C2312yes—
311C22⋊Q8×C61C2314yes—
312C22⋊Q8×C61C2312yes—
313C22⋊Q8×C61C2314yes—
314#121×C61C2314yes—
315#121×C61C2314yes—
316#121×C61C2314yes—
317#121×C61C2318yes—
318#121×C61C2314yes—
319#121×C61C2314yes—
320#121×C61C2314yes—
321#121×C61C2314yes—
322#121×C61C2314yes—
323#121×C61C2314yes—
324#121×C61C2318yes—
325#121×C61C2318yes—
326#121×C61C2318yes—
327#121×C61C2318yes—
328#121×C61C2314yes—
329#121×C61C2314yes—
330#121×C61C2318yes—
331#121×C61C2314yes—
332#121×C61C2314yes—
333#121×C61C2318yes—
334#121×C61C2314yes—
335#121×C61C2318yes—
336#121×C61C2314yes—
337#121×C61C2314yes—
338#121×C61C2312yes—
339#121×C61C2318yes—
340#121×C61C2314yes—
341#121×C61C2312yes—
342#121×C61C2314yes—
343#121×C61C2318yes—
344#121×C61C2318yes—
345#121×C61C2318yes—
346#121×C61C2318yes—
347#121×C61C2318yes—
348#121×C61C2318yes—
349#121×C61C2318yes—
350#121×C61C2314yes—
351#121×C61C2314yes—
352#121×C61C2314yes—
353#121×C61C2314yes—
354#121×C61C2314yes—
355#121×C61C2312yes—
356#121×C61C2312yes—
357#120×C61C2318yes—
358#120×C61C2314yes—
359#120×C61C2318yes—
360#120×C61C2318yes—
361#120×C61C2318yes—
362#120×C61C2314yes—
363#120×C61C2314yes—
364#120×C61C2314yes—
365#120×C61C2314yes—
366#120×C61C2314yes—
367C4×Q8×C61C2314yes—
368C4×Q8×C61C2312yes—
369C4×Q8×C61C2314yes—
370C4×Q8×C61C2312yes—
371C4×Q8×C61C2314yes—
372C4×Q8×C61C2314yes—
373C4×Q8×C61C2314yes—
374C4×Q8×C61C2314yes—
375C4×D4×C61C2312yes—
376C4×D4×C61C2314yes—
377C4×D4×C61C2318yes—
378C4×D4×C61C2314yes—
379C4×D4×C61C2314yes—
380C4×D4×C61C2314yes—
381C4×D4×C61C2314yes—
382C4×D4×C61C2314yes—
383C4×D4×C61C2314yes—
384C4×D4×C61C2314yes—
385C4×D4×C61C2318yes—
386C4×D4×C61C2314yes—
387C4×D4×C61C2318yes—
388C4×D4×C61C2318yes—
389C4×D4×C61C2318yes—
390C4×D4×C61C2318yes—
391C4×D4×C61C2318yes—
392C4×D4×C61C2314yes—
393C4×D4×C61C2314yes—
394C4×D4×C61C2314yes—
395C4×D4×C61C2318yes—
396C4×D4×C61C2318yes—
397C4×D4×C61C2318yes—
398C4×D4×C61C2318yes—
399C4×D4×C61C2314yes—
400C4×D4×C61C2314yes—
401C4×D4×C61C2314yes—
402C4×D4×C61C2312yes—
403C4×D4×C61C2314yes—
404C4×D4×C61C2312yes—
405C4×D4×C61C2312yes—
406C4×D4×C61C2312yes—
407C4×D4×C61C2314yes—
408C4×D4×C61C2314yes—
409C4×D4×C61C2314yes—
410C4×D4×C61C2314yes—
411C4×D4×C61C2312yes—
412#117×C61C2318yes—
413#117×C61C2314yes—
414#117×C61C2314yes—
415#117×C61C2312yes—
416#117×C61C2314yes—
417#117×C61C2314yes—
418#117×C61C2314yes—
419#117×C61C2314yes—
420#117×C61C2314yes—
421#117×C61C2318yes—
422#117×C61C2318yes—
423#117×C61C2318yes—
424#117×C61C2314yes—
425#117×C61C2314yes—
426#117×C61C2314yes—
427C2×C4⋊C4×C61C2311yescharacteristic
428C2×C4⋊C4×C61C2312yes—
429C2×C4⋊C4×C61C2312yes—
430C2×C4⋊C4×C61C2314yes—
431C2×C4⋊C4×C61C2311yescharacteristic
432C2×C4⋊C4×C61C2311yescharacteristic
433C2×C4⋊C4×C61C2314yes—
434C2×C4⋊C4×C61C2314yes—
435C2×C4⋊C4×C61C2314yes—
436C2×C4⋊C4×C61C2314yes—
437C2×C4⋊C4×C61C2318yes—
438C2×C4⋊C4×C61C2318yes—
439C2×C4⋊C4×C61C2312yes—
440C2×C4⋊C4×C61C2311yescharacteristic
441C2×C4⋊C4×C61C2312yes—
442C2×C4⋊C4×C61C2314yes—
443C2×C4⋊C4×C61C2312yes—
444C2×C4⋊C4×C61C2312yes—
445C2×C22⋊C4×C61C2312yes—
446C2×C22⋊C4×C61C2318yes—
447C2×C22⋊C4×C61C2318yes—
448C2×C22⋊C4×C61C2314yes—
449C2×C22⋊C4×C61C2314yes—
450C2×C22⋊C4×C61C2311yescharacteristic
451C2×C22⋊C4×C61C2312yes—
452C2×C22⋊C4×C61C2311yescharacteristic
453C2×C22⋊C4×C61C2312yes—
454C2×C22⋊C4×C61C2318yes—
455C2×C42×C61C2312yes—
456C2×C42×C61C2312yes—
457C2×C42×C61C2311yescharacteristic
458C2×C42×C61C2314yes—
459C24×C61C2411yescharacteristic
460C24×C61C2411yescharacteristic
461C24×C61C2414yes—
462C24×C61C2414yes—
463#41×C61—28no—
464#41×C61—28no—
465#41×C61—28no—
466#41×C61—48no—
467#41×C61—48no—
468#41×C61—48no—
469#41×C61—48no—
470#41×C61—48no—
471#41×C61—416no—
472#41×C61—44no—
473#41×C61—44no—
474#41×C61—44no—
475#41×C61—44no—
476#41×C61—48no—
477#41×C61—48no—
478C2×Q8×C61—24no—
479C2×Q8×C61—44no—
480C2×Q8×C61—44no—
481C2×Q8×C61—48no—
482C2×Q8×C61—48no—
483C2×Q8×C61C2414yes—
484C2×Q8×C61C2412yes—
485C2×Q8×C61C2412yes—
486C2×Q8×C61C2412yes—
487C2×Q8×C61C2414yes—
488C2×Q8×C61C2414yes—
489C2×Q8×C61C2418yes—
490C2×Q8×C61C2414yes—
491C2×D4×C61—44no—
492C2×D4×C61—44no—
493C2×D4×C61—48no—
494C2×D4×C61—42no—
495C2×D4×C61—48no—
496C2×D4×C61—48no—
497C2×D4×C61—48no—
498C2×D4×C61C2414yes—
499C2×D4×C61C2412yes—
500C2×D4×C61C2414yes—
501C2×D4×C61C2414yes—
502C2×D4×C61C2414yes—
503C2×D4×C61C2412yes—
504C2×D4×C61C2412yes—
505C2×D4×C61C2412yes—
506C2×D4×C61C2414yes—
507C2×D4×C61C2418yes—
508C2×D4×C61C2414yes—
509C2×D4×C61C2414yes—
510C2×D4×C61C2414yes—
511C2×D4×C61C2414yes—
512C2×D4×C61C2414yes—
513C2×D4×C61C2412yes—
514C2×D4×C61C2418yes—
515C2×D4×C61C2414yes—
516C2×D4×C61C2414yes—
517C2×D4×C61C2414yes—
518C2×D4×C61C2418yes—
519C2×D4×C61C2414yes—
520C2×D4×C61C2414yes—
521C2×D4×C61C2414yes—
522C2×D4×C61C2414yes—
523C2×D4×C61C2414yes—
524C22×C4×C61—24no—
525C22×C4×C61—24no—
526C22×C4×C61—48no—
527C22×C4×C61—48no—
528C22×C4×C61—44no—
529C22×C4×C61C2411yescharacteristic
530C22×C4×C61C2412yes—
531C22×C4×C61C2414yes—
532C22×C4×C61C2414yes—
533C22×C4×C61C2411yescharacteristic
534C22×C4×C61C2412yes—
535C22×C4×C61C2412yes—
536C22×C4×C61C2414yes—
537C22×C4×C61C2414yes—
538C22×C4×C61C2412yes—
539C22×C4×C61C2412yes—
540C22×C4×C61C2411yescharacteristic
541C22×C4×C61C2412yes—
542C22×C4×C61C2412yes—
543C22×C4×C61C2414yes—
544C22×C4×C61C2411yescharacteristic
545C22×C4×C61C2414yes—
546C22×C4×C61C2414yes—
547C22×C4×C61C2412yes—
548C22×C4×C61C2418yes—
549C22×C4×C61C2418yes—
550C22×C4×C61C2414yes—
551C22×C4×C61C2418yes—
552C22×C4×C61C2418yes—
553C22×C4×C61C2414yes—
554C22×C4×C61C2414yes—
555C22×C4×C61C2414yes—
556C22×C4×C61C2414yes—
557C22×C4×C61C2414yes—
558C22×C4×C61C2411yescharacteristic
559C4⋊C4×C61C2414yes—
560C4⋊C4×C61C2414yes—
561C4⋊C4×C61C2414yes—
562C4⋊C4×C61C2412yes—
563C4⋊C4×C61C2414yes—
564C4⋊C4×C61C2418yes—
565C4⋊C4×C61C2414yes—
566C4⋊C4×C61C2412yes—
567C4⋊C4×C61C2412yes—
568C4⋊C4×C61C2418yes—
569C4⋊C4×C61C2414yes—
570C4⋊C4×C61C2418yes—
571C4⋊C4×C61C2414yes—
572C4⋊C4×C61C2414yes—
573C4⋊C4×C61C2414yes—
574C4⋊C4×C61C2418yes—
575C4⋊C4×C61C2418yes—
576C4⋊C4×C61C2418yes—
577C4⋊C4×C61C2414yes—
578C4⋊C4×C61C2412yes—
579C4⋊C4×C61C2414yes—
580C4⋊C4×C61C2414yes—
581C4⋊C4×C61C2414yes—
582C4⋊C4×C61C2418yes—
583C4⋊C4×C61C2418yes—
584C4⋊C4×C61C2418yes—
585C4⋊C4×C61C2418yes—
586C4⋊C4×C61C2414yes—
587C4⋊C4×C61C2418yes—
588C4⋊C4×C61C2414yes—
589C4⋊C4×C61C2414yes—
590C4⋊C4×C61C2414yes—
591C4⋊C4×C61C2414yes—
592C4⋊C4×C61C2414yes—
593C22⋊C4×C61C2411yescharacteristic
594C22⋊C4×C61C2414yes—
595C22⋊C4×C61C2414yes—
596C22⋊C4×C61C2412yes—
597C22⋊C4×C61C2418yes—
598C22⋊C4×C61C2414yes—
599C22⋊C4×C61C2418yes—
600C22⋊C4×C61C2411yescharacteristic
601C22⋊C4×C61C2411yescharacteristic
602C22⋊C4×C61C2411yescharacteristic
603C22⋊C4×C61C2414yes—
604C22⋊C4×C61C2418yes—
605C22⋊C4×C61C2414yes—
606C22⋊C4×C61C2418yes—
607C22⋊C4×C61C2418yes—
608C22⋊C4×C61C2418yes—
609C22⋊C4×C61C2418yes—
610C22⋊C4×C61C2414yes—
611C22⋊C4×C61C2414yes—
612C22⋊C4×C61C2412yes—
613C22⋊C4×C61C2414yes—
614C22⋊C4×C61C2418yes—
615C22⋊C4×C61C2418yes—
616C22⋊C4×C61C2414yes—
617C22⋊C4×C61C2414yes—
618C22⋊C4×C61C2414yes—
619C22⋊C4×C61C2414yes—
620C22⋊C4×C61C2414yes—
621C22⋊C4×C61C2414yes—
622C22⋊C4×C61C2418yes—
623C22⋊C4×C61C2418yes—
624C22⋊C4×C61C2418yes—
625C22⋊C4×C61C2414yes—
626C22⋊C4×C61C2418yes—
627C22⋊C4×C61C2414yes—
628C22⋊C4×C61C2414yes—
629C42×C61C2412yes—
630C42×C61C2414yes—
631C42×C61C2414yes—
632C42×C61C2414yes—
633C42×C61C2414yes—
634C42×C61C2414yes—
635C42×C61C2412yes—
636C42×C61C2414yes—
637C42×C61C2414yes—
638C42×C61C2418yes—
639C42×C61C2418yes—
640C23×C61—22no—
641C23×C61—22no—
642C23×C61—22no—
643C23×C61—28no—
644C23×C61—41no—
645C23×C61—44no—
646C23×C61—44no—
647C23×C61—41no—
648C23×C61—44no—
649C23×C61—41no—
650C23×C61—44no—
651C23×C61—44no—
652C23×C61C2512yes—
653C23×C61C2514yes—
654C23×C61C2511yescharacteristic
655C23×C61C2514yes—
656C23×C61C2514yes—
657C23×C61C2511yescharacteristic
658C23×C61C2511yescharacteristic
659Q8×C61—28no—
660Q8×C61—24no—
661Q8×C61—24no—
662Q8×C61—24no—
663Q8×C61—48no—
664Q8×C61—44no—
665Q8×C61—44no—
666Q8×C61—44no—
667D4×C61—28no—
668D4×C61—28no—
669D4×C61—28no—
670D4×C61—24no—
671D4×C61—28no—
672D4×C61—24no—
673D4×C61—24no—
674D4×C61—24no—
675D4×C61—48no—
676D4×C61—44no—
677D4×C61—44no—
678D4×C61—42no—
679D4×C61—44no—
680D4×C61—44no—
681D4×C61—44no—
682D4×C61—44no—
683D4×C61—44no—
684D4×C61—44no—
685D4×C61—44no—
686D4×C61—44no—
687D4×C61—44no—
688D4×C61—48no—
689D4×C61—44no—
690D4×C61—44no—
691D4×C61—44no—
692D4×C61—48no—
693C2×C4×C61—22no—
694C2×C4×C61—22no—
695C2×C4×C61—24no—
696C2×C4×C61—28no—
697C2×C4×C61—24no—
698C2×C4×C61—24no—
699C2×C4×C61—24no—
700C2×C4×C61—24no—
701C2×C4×C61—28no—
702C2×C4×C61—28no—
703C2×C4×C61—28no—
704C2×C4×C61—42no—
705C2×C4×C61—44no—
706C2×C4×C61—42no—
707C2×C4×C61—44no—
708C2×C4×C61—44no—
709C2×C4×C61—44no—
710C2×C4×C61—44no—
711C2×C4×C61—44no—
712C2×C4×C61—44no—
713C2×C4×C61—44no—
714C2×C4×C61—41no—
715C2×C4×C61—42no—
716C2×C4×C61—48no—
717C2×C4×C61—41no—
718C2×C4×C61—44no—
719C2×C4×C61—48no—
720C2×C4×C61—48no—
721C2×C4×C61—48no—
722C2×C4×C61H(5,𝔽2)14yes—
723C2×C4×C61C2511yescharacteristic
724C2×C4×C61C2511yescharacteristic
725C2×C4×C61C2514yes—
726C2×C4×C61C2514yes—
727C2×C4×C61C2514yes—
728C2×C4×C61C2514yes—
729C2×C4×C61C2512yes—
730C2×C4×C61C2511yescharacteristic
731C2×C4×C61C2511yescharacteristic
732C2×C4×C61C2514yes—
733C2×C4×C61C2514yes—
734C2×C4×C61C2514yes—
735C2×C4×C61C2514yes—
736C2×C4×C61C2514yes—
737C2×C4×C61C2512yes—
738C2×C4×C61C2512yes—
739#62927C6111yesmaximal, characteristic, direct product factor, Sylow
740C22×C61—21no—
741C22×C61—21no—
742C22×C61—21no—
743C22×C61—21no—
744C22×C61—22no—
745C22×C61—21no—
746C22×C61—24no—
747C22×C61—24no—
748C22×C61—24no—
749C22×C61—21no—
750C22×C61—24no—
751C22×C61—24no—
752C22×C61—22no—
753C22×C61—24no—
754C22×C61—24no—
755C22×C61—24no—
756C22×C61—21no—
757C22×C61—24no—
758C22×C61—22no—
759C22×C61—44no—
760C22×C61—88no—
761C22×C61—82no—
762C22×C61—88no—
763C22×C61C2×H(5,𝔽2)12yes—
764C22×C61#58512yes—
765C22×C61C2611yescharacteristic
766C4×C61—21no—
767C4×C61—22no—
768C4×C61—21no—
769C4×C61—24no—
770C4×C61—24no—
771C4×C61—24no—
772C4×C61—24no—
773C4×C61—24no—
774C4×C61—24no—
775C4×C61—22no—
776C4×C61—24no—
777C4×C61—21no—
778C4×C61—24no—
779C4×C61—24no—
780C4×C61—21no—
781C4×C61C2×H(5,𝔽2)14yes—
782#3560C2×C6114yescomplemented
783#3559C2×C6114yescomplemented
784#3551C2×C6114yescomplemented
785#3547C2×C6114yescomplemented
786#3542C2×C6114yescomplemented
787#3541C2×C6114yescomplemented
788#3539C2×C6114yescomplemented
789#3538C2×C6114yescomplemented
790#3534C2×C6114yescomplemented
791#3520C2×C6114yescomplemented
792#3512C2×C6112yescomplemented
793#3505C2×C6114yescomplemented
794#3497C2×C6111yescharacteristic, complemented
795#3494C2×C6114yescomplemented
796#3493C2×C6111yescharacteristic, complemented
797#3492C2×C6111yescharacteristic, complemented
798#3489C2×C6112yescomplemented
799#3489C2×C6112yescomplemented
800C2×#552C2×C6111yescharacteristic, complemented
801D4×#41C2×C6112yescomplemented
802#3461C2×C6111yescharacteristic, complemented
803#3449C2×C6111yescharacteristic, complemented
804C2×#537C2×C6111yescharacteristic, complemented
805C2×C61—22no—
806C2×C61—22no—
807C2×C61—41no—
808C2×C61—44no—
809C2×C61—44no—
810C2×C61—44no—
811C2×C61—42no—
812C2×C61C22×H(5,𝔽2)11yescharacteristic
813C2×C61C2×#58511yescharacteristic
814C2×C612−1+611yescharacteristic
815C2×2−1+4C22×C6112yescomplemented
816C22×#41C22×C6112yescomplemented
817C22×#41C22×C6112yescomplemented
818#563C22×C6118yescomplemented
819#563C22×C6118yescomplemented
820#562C22×C6118yescomplemented
821#562C22×C6118yescomplemented
822#560C22×C6118yescomplemented
823#560C22×C6118yescomplemented
824#556C22×C6114yescomplemented
825#555C22×C6114yescomplemented
826#555C22×C6118yescomplemented
827#554C22×C6114yescomplemented
828#554C22×C6118yescomplemented
829#553C22×C6114yescomplemented
830#553C22×C6114yescomplemented
831#553C22×C6118yescomplemented
832#553C22×C6118yescomplemented
833#553C22×C6114yescomplemented
834#553C22×C6118yescomplemented
835#553C22×C6118yescomplemented
836#553C22×C6118yescomplemented
837#553C22×C6114yescomplemented
838#552C22×C6114yescomplemented
839#552C22×C6114yescomplemented
840#552C22×C6114yescomplemented
841#552C22×C6114yescomplemented
842#552C22×C6114yescomplemented
843#552C22×C6114yescomplemented
844#552C22×C6114yescomplemented
845#552C22×C6114yescomplemented
846#551C22×C6118yescomplemented
847#551C22×C6118yescomplemented
848#551C22×C6118yescomplemented
849#551C22×C6118yescomplemented
850#550C22×C6112yescomplemented
851#550C22×C6114yescomplemented
852D4×Q8C22×C6112yescomplemented
853D4×Q8C22×C6114yescomplemented
854D4×Q8C22×C6114yescomplemented
855D4×Q8C22×C6114yescomplemented
856#548C22×C6112yes—
857#548C22×C6112yescomplemented
858#548C22×C6114yescomplemented
859#548C22×C6114yescomplemented
860#548C22×C6114yescomplemented
861#548C22×C6114yescomplemented
862#547C22×C6112yescomplemented
863#547C22×C6114yescomplemented
864#547C22×C6118yescomplemented
865#547C22×C6114yescomplemented
866#547C22×C6114yescomplemented
867#547C22×C6118yescomplemented
868#547C22×C6114yescomplemented
869#546C22×C6112yes—
870#546C22×C6114yescomplemented
871#546C22×C6112yescomplemented
872#546C22×C6114yescomplemented
873#546C22×C6118yescomplemented
874#546C22×C6114yescomplemented
875#546C22×C6118yescomplemented
876#546C22×C6114yescomplemented
877#546C22×C6118yescomplemented
878D42C22×C6114yes—
879D42C22×C6112yescomplemented
880#544C22×C6111yescharacteristic, complemented
881#544C22×C6114yescomplemented
882#544C22×C6118yescomplemented
883#542C22×C6114yescomplemented
884#542C22×C6114yescomplemented
885#542C22×C6114yescomplemented
886#542C22×C6118yescomplemented
887#541C22×C6114yescomplemented
888#541C22×C6114yescomplemented
889#540C22×C6114yescomplemented
890#540C22×C6114yescomplemented
891#540C22×C6114yescomplemented
892#540C22×C6118yescomplemented
893#540C22×C6118yescomplemented
894#539C22×C6114yescomplemented
895#539C22×C6114yescomplemented
896#539C22×C6118yescomplemented
897#539C22×C6118yescomplemented
898#539C22×C6118yescomplemented
899#539C22×C6118yescomplemented
900#538C22×C6114yescomplemented
901#538C22×C6118yescomplemented
902#538C22×C6118yescomplemented
903#538C22×C6118yescomplemented
904#537C22×C6111yescharacteristic
905#537C22×C6112yescomplemented
906#537C22×C6111yescharacteristic, complemented
907#537C22×C6114yescomplemented
908#537C22×C6114yescomplemented
909#537C22×C6114yescomplemented
910#537C22×C6112yescomplemented
911#537C22×C6111yescharacteristic, complemented
912#537C22×C6114yescomplemented
913#537C22×C6114yescomplemented
914#537C22×C6114yescomplemented
915#536C22×C6114yescomplemented
916#536C22×C6112yescomplemented
917#536C22×C6114yescomplemented
918#536C22×C6114yescomplemented
919#535C22×C6114yescomplemented
920#535C22×C6114yescomplemented
921#534C22×C6114yescomplemented
922#534C22×C6118yescomplemented
923#533C22×C6114yescomplemented
924#532C22×C6114yescomplemented
925#532C22×C6112yescomplemented
926#532C22×C6114yescomplemented
927#532C22×C6114yescomplemented
928#529C22×C6114yescomplemented
929#529C22×C6114yescomplemented
930#529C22×C6114yescomplemented
931#529C22×C6114yescomplemented
932#529C22×C6114yescomplemented
933C2×#126C22×C6112yescomplemented
934C2×#125C22×C6111yescharacteristic, complemented
935C2×#125C22×C6112yescomplemented
936#525C22×C6114yes—
937#525C22×C6114yescomplemented
938#525C22×C6114yescomplemented
939#525C22×C6112yescomplemented
940#525C22×C6112yescomplemented
941#525C22×C6114yescomplemented
942#525C22×C6114yescomplemented
943#525C22×C6114yescomplemented
944#525C22×C6114yescomplemented
945C2×#123C22×C6112yes—
946C2×C22⋊Q8C22×C6114yescomplemented
947C2×C22⋊Q8C22×C6111yescharacteristic, complemented
948C2×C22⋊Q8C22×C6111yescharacteristic, complemented
949C2×C22⋊Q8C22×C6114yescomplemented
950C2×C22⋊Q8C22×C6114yescomplemented
951C2×#121C22×C6114yescomplemented
952C2×#121C22×C6114yescomplemented
953#520C22×C6112yescomplemented
954#520C22×C6112yescomplemented
955#520C22×C6114yescomplemented
956#518C22×C6114yescomplemented
957C4×#41C22×C6112yescomplemented
958C2×C4×Q8C22×C6111yescharacteristic, complemented
959C2×C4×D4C22×C6111yescharacteristic
960C2×C4×D4C22×C6114yescomplemented
961C2×#117C22×C6111yescharacteristic, complemented
962C2×#117C22×C6112yescomplemented
963C22×C4⋊C4C22×C6111yescharacteristic, complemented
964C61#6292711yescharacteristic, direct product factor, Sylow
9652−1+4—48no—
966C2×#41—48no—
967C2×#41—48no—
968C2×#41C23×C6112yes—
969C2×#41C23×C6112yes—
970C2×#41C23×C6112yes—
971C2×#41C23×C6114yes—
972C2×#41C23×C6114yes—
973C2×#41C23×C6112yes—
974C2×#41C23×C6112yes—
975C2×#41C23×C6114yes—
976C2×#41C23×C6114yes—
977C2×#41C23×C6114yes—
978C2×#41C23×C6114yes—
979C2×#41C23×C6118yes—
980C2×#41C23×C6114yes—
981C2×#41C23×C6112yes—
982C2×#41C23×C6112yes—
983C22×Q8C23×C6111yescharacteristic
984C22×Q8C23×C6112yes—
985C22×Q8C23×C6114yes—
986C22×Q8C23×C6114yes—
987C22×Q8C23×C6112yes—
988C22×D4C23×C6111yescharacteristic
989C22×D4C23×C6114yes—
990C22×D4C23×C6114yes—
991C22×D4C23×C6114yes—
992C22×D4C23×C6112yes—
993C22×D4C23×C6114yes—
994C22×D4C23×C6112yes—
995C23×C4C23×C6111yescharacteristic
996C23×C4C23×C6111yescharacteristic
997C23×C4C23×C6112yes—
998C23×C4C23×C6114yes—
999C23×C4C23×C6114yes—
1000C4⋊Q8C23×C6114yes—
1001C4⋊Q8C23×C6112yes—
1002C4⋊Q8C23×C6114yes—
1003C4⋊Q8C23×C6114yes—
1004C4⋊Q8C23×C6114yes—
1005C4⋊Q8C23×C6114yes—
1006C4⋊Q8C23×C6118yes—
1007C4⋊Q8C23×C6118yes—
1008#127C23×C6114yes—
1009#127C23×C6114yes—
1010#127C23×C6114yes—
1011#127C23×C6112yes—
1012#126C23×C6118yes—
1013#126C23×C6118yes—
1014#126C23×C6118yes—
1015#126C23×C6118yes—
1016#126C23×C6118yes—
1017#126C23×C6118yes—
1018#126C23×C6118yes—
1019#126C23×C6118yes—
1020#126C23×C6118yes—
1021#126C23×C6118yes—
1022#126C23×C6118yes—
1023#125C23×C6114yes—
1024#125C23×C6118yes—
1025#125C23×C6114yes—
1026#125C23×C6118yes—
1027#125C23×C6114yes—
1028#125C23×C6114yes—
1029#125C23×C6114yes—
1030#125C23×C6118yes—
1031#125C23×C6118yes—
1032#125C23×C6118yes—
1033#125C23×C6118yes—
1034#124C23×C6112yes—
1035#124C23×C6112yes—
1036#124C23×C6114yes—
1037#124C23×C6114yes—
1038#124C23×C6114yes—
1039#124C23×C6118yes—
1040#124C23×C6118yes—
1041#124C23×C6114yes—
1042#124C23×C6114yes—
1043#124C23×C6118yes—
1044#124C23×C6118yes—
1045#124C23×C6118yes—
1046#123C23×C6118yes—
1047#123C23×C6118yes—
1048#123C23×C6114yes—
1049#123C23×C6114yes—
1050#123C23×C6114yes—
1051#123C23×C6118yes—
1052#123C23×C6118yes—
1053#123C23×C6118yes—
1054#123C23×C6114yes—
1055#123C23×C6114yes—
1056#123C23×C6118yes—
1057#123C23×C6118yes—
1058#123C23×C6114yes—
1059#123C23×C6118yes—
1060#123C23×C6118yes—
1061#123C23×C6118yes—
1062#123C23×C6118yes—
1063#123C23×C6118yes—
1064#123C23×C6118yes—
1065#123C23×C6118yes—
1066#123C23×C6118yes—
1067#123C23×C6118yes—
1068#123C23×C6118yes—
1069#123C23×C6118yes—
1070#123C23×C6118yes—
1071C22⋊Q8C23×C6112yes—
1072C22⋊Q8C23×C6114yes—
1073C22⋊Q8C23×C6112yes—
1074C22⋊Q8C23×C6114yes—
1075C22⋊Q8C23×C6114yes—
1076C22⋊Q8C23×C6114yes—
1077C22⋊Q8C23×C6114yes—
1078C22⋊Q8C23×C6114yes—
1079C22⋊Q8C23×C6114yes—
1080C22⋊Q8C23×C6114yes—
1081C22⋊Q8C23×C6114yes—
1082C22⋊Q8C23×C6118yes—
1083C22⋊Q8C23×C6114yes—
1084C22⋊Q8C23×C6114yes—
1085C22⋊Q8C23×C6118yes—
1086C22⋊Q8C23×C6118yes—
1087C22⋊Q8C23×C6118yes—
1088C22⋊Q8C23×C6118yes—
1089C22⋊Q8C23×C6118yes—
1090C22⋊Q8C23×C6114yes—
1091C22⋊Q8C23×C6114yes—
1092C22⋊Q8C23×C6114yes—
1093C22⋊Q8C23×C6112yes—
1094C22⋊Q8C23×C6112yes—
1095C22⋊Q8C23×C6114yes—
1096C22⋊Q8C23×C6114yes—
1097C22⋊Q8C23×C6114yes—
1098C22⋊Q8C23×C6114yes—
1099C22⋊Q8C23×C6114yes—
1100C22⋊Q8C23×C6118yes—
1101C22⋊Q8C23×C6118yes—
1102C22⋊Q8C23×C6118yes—
1103C22⋊Q8C23×C6118yes—
1104C22⋊Q8C23×C6118yes—
1105C22⋊Q8C23×C6118yes—
1106#121C23×C6114yes—
1107#121C23×C6114yes—
1108#121C23×C6114yes—
1109#121C23×C6114yes—
1110#121C23×C6118yes—
1111#121C23×C6114yes—
1112#121C23×C6114yes—
1113#121C23×C6118yes—
1114#121C23×C6114yes—
1115#121C23×C6114yes—
1116#121C23×C6118yes—
1117#121C23×C6118yes—
1118#121C23×C6114yes—
1119#121C23×C6114yes—
1120#121C23×C6112yes—
1121#121C23×C6112yes—
1122#121C23×C6114yes—
1123#121C23×C6114yes—
1124#121C23×C6114yes—
1125#121C23×C6114yes—
1126#121C23×C6112yes—
1127#121C23×C6112yes—
1128#121C23×C6114yes—
1129#121C23×C6114yes—
1130#121C23×C6114yes—
1131#121C23×C6114yes—
1132#121C23×C6118yes—
1133#121C23×C6114yes—
1134#121C23×C6114yes—
1135#121C23×C6114yes—
1136#121C23×C6114yes—
1137#121C23×C6114yes—
1138#121C23×C6118yes—
1139#121C23×C6118yes—
1140#121C23×C6118yes—
1141#121C23×C6118yes—
1142#121C23×C6118yes—
1143#121C23×C6118yes—
1144#121C23×C6118yes—
1145#121C23×C6118yes—
1146#121C23×C6118yes—
1147#121C23×C6118yes—
1148#121C23×C6118yes—
1149#120C23×C6114yes—
1150#120C23×C6114yes—
1151#120C23×C6114yes—
1152#120C23×C6118yes—
1153#120C23×C6118yes—
1154#120C23×C6118yes—
1155#120C23×C6118yes—
1156#120C23×C6114yes—
1157#120C23×C6114yes—
1158#120C23×C6114yes—
1159C4×Q8C23×C6114yes—
1160C4×Q8C23×C6114yes—
1161C4×Q8C23×C6112yes—
1162C4×Q8C23×C6112yes—
1163C4×Q8C23×C6114yes—
1164C4×Q8C23×C6114yes—
1165C4×Q8C23×C6114yes—
1166C4×Q8C23×C6114yes—
1167C4×D4C23×C6112yes—
1168C4×D4C23×C6112yes—
1169C4×D4C23×C6112yes—
1170C4×D4C23×C6112yes—
1171C4×D4C23×C6114yes—
1172C4×D4C23×C6114yes—
1173C4×D4C23×C6114yes—
1174C4×D4C23×C6114yes—
1175C4×D4C23×C6114yes—
1176C4×D4C23×C6114yes—
1177C4×D4C23×C6114yes—
1178C4×D4C23×C6112yes—
1179C4×D4C23×C6114yes—
1180C4×D4C23×C6114yes—
1181C4×D4C23×C6112yes—
1182C4×D4C23×C6114yes—
1183C4×D4C23×C6118yes—
1184C4×D4C23×C6114yes—
1185C4×D4C23×C6118yes—
1186C4×D4C23×C6114yes—
1187C4×D4C23×C6114yes—
1188C4×D4C23×C6114yes—
1189C4×D4C23×C6118yes—
1190C4×D4C23×C6118yes—
1191C4×D4C23×C6118yes—
1192C4×D4C23×C6114yes—
1193C4×D4C23×C6114yes—
1194C4×D4C23×C6114yes—
1195C4×D4C23×C6114yes—
1196C4×D4C23×C6114yes—
1197C4×D4C23×C6114yes—
1198C4×D4C23×C6118yes—
1199C4×D4C23×C6118yes—
1200C4×D4C23×C6118yes—
1201C4×D4C23×C6118yes—
1202C4×D4C23×C6118yes—
1203C4×D4C23×C6118yes—
1204#117C23×C6114yes—
1205#117C23×C6114yes—
1206#117C23×C6114yes—
1207#117C23×C6114yes—
1208#117C23×C6114yes—
1209#117C23×C6114yes—
1210#117C23×C6112yes—
1211#117C23×C6114yes—
1212#117C23×C6114yes—
1213#117C23×C6114yes—
1214#117C23×C6114yes—
1215#117C23×C6118yes—
1216#117C23×C6118yes—
1217#117C23×C6118yes—
1218#117C23×C6118yes—
1219C2×C4⋊C4C23×C6111yescharacteristic
1220C2×C4⋊C4C23×C6111yescharacteristic
1221C2×C4⋊C4C23×C6114yes—
1222C2×C4⋊C4C23×C6112yes—
1223C2×C4⋊C4C23×C6114yes—
1224C2×C4⋊C4C23×C6111yescharacteristic
1225C2×C4⋊C4C23×C6112yes—
1226C2×C4⋊C4C23×C6112yes—
1227C2×C4⋊C4C23×C6111yescharacteristic
1228C2×C4⋊C4C23×C6114yes—
1229C2×C4⋊C4C23×C6112yes—
1230C2×C4⋊C4C23×C6114yes—
1231C2×C4⋊C4C23×C6114yes—
1232C2×C4⋊C4C23×C6114yes—
1233C2×C4⋊C4C23×C6118yes—
1234C2×C4⋊C4C23×C6112yes—
1235C2×C4⋊C4C23×C6118yes—
1236C2×C4⋊C4C23×C6112yes—
1237C2×C22⋊C4C23×C6111yescharacteristic
1238C2×C22⋊C4C23×C6112yes—
1239C2×C22⋊C4C23×C6112yes—
1240C2×C22⋊C4C23×C6111yescharacteristic
1241C2×C22⋊C4C23×C6114yes—
1242C2×C22⋊C4C23×C6114yes—
1243C2×C22⋊C4C23×C6118yes—
1244C2×C22⋊C4C23×C6118yes—
1245C2×C22⋊C4C23×C6112yes—
1246C2×C22⋊C4C23×C6118yes—
1247C2×C42C23×C6112yes—
1248C2×C42C23×C6112yes—
1249C2×C42C23×C6111yescharacteristic
1250C2×C42C23×C6114yes—
1251C24C24×C6111yescharacteristic
1252C24C24×C6111yescharacteristic
1253C24C24×C6114yes—
1254C24C24×C6114yes—
1255#41—28no—
1256#41—28no—
1257#41—28no—
1258#41—48no—
1259#41—48no—
1260#41—48no—
1261#41—48no—
1262#41—416no—
1263#41—48no—
1264#41—44no—
1265#41—44no—
1266#41—44no—
1267#41—44no—
1268#41—48no—
1269#41—48no—
1270C2×Q8—24no—
1271C2×Q8—44no—
1272C2×Q8—44no—
1273C2×Q8—48no—
1274C2×Q8—48no—
1275C2×Q8C24×C6114yes—
1276C2×Q8C24×C6112yes—
1277C2×Q8C24×C6112yes—
1278C2×Q8C24×C6112yes—
1279C2×Q8C24×C6114yes—
1280C2×Q8C24×C6114yes—
1281C2×Q8C24×C6118yes—
1282C2×Q8C24×C6114yes—
1283C2×D4—44no—
1284C2×D4—44no—
1285C2×D4—48no—
1286C2×D4—48no—
1287C2×D4—48no—
1288C2×D4—42no—
1289C2×D4—48no—
1290C2×D4C24×C6114yes—
1291C2×D4C24×C6112yes—
1292C2×D4C24×C6114yes—
1293C2×D4C24×C6114yes—
1294C2×D4C24×C6114yes—
1295C2×D4C24×C6112yes—
1296C2×D4C24×C6112yes—
1297C2×D4C24×C6112yes—
1298C2×D4C24×C6114yes—
1299C2×D4C24×C6118yes—
1300C2×D4C24×C6114yes—
1301C2×D4C24×C6114yes—
1302C2×D4C24×C6114yes—
1303C2×D4C24×C6114yes—
1304C2×D4C24×C6114yes—
1305C2×D4C24×C6112yes—
1306C2×D4C24×C6118yes—
1307C2×D4C24×C6114yes—
1308C2×D4C24×C6114yes—
1309C2×D4C24×C6114yes—
1310C2×D4C24×C6118yes—
1311C2×D4C24×C6114yes—
1312C2×D4C24×C6114yes—
1313C2×D4C24×C6114yes—
1314C2×D4C24×C6114yes—
1315C2×D4C24×C6114yes—
1316C22×C4—24no—
1317C22×C4—24no—
1318C22×C4—48no—
1319C22×C4—48no—
1320C22×C4—44no—
1321C22×C4C24×C6111yescharacteristic
1322C22×C4C24×C6112yes—
1323C22×C4C24×C6114yes—
1324C22×C4C24×C6114yes—
1325C22×C4C24×C6111yescharacteristic
1326C22×C4C24×C6112yes—
1327C22×C4C24×C6112yes—
1328C22×C4C24×C6114yes—
1329C22×C4C24×C6114yes—
1330C22×C4C24×C6112yes—
1331C22×C4C24×C6112yes—
1332C22×C4C24×C6111yescharacteristic
1333C22×C4C24×C6112yes—
1334C22×C4C24×C6112yes—
1335C22×C4C24×C6114yes—
1336C22×C4C24×C6111yescharacteristic
1337C22×C4C24×C6114yes—
1338C22×C4C24×C6114yes—
1339C22×C4C24×C6112yes—
1340C22×C4C24×C6118yes—
1341C22×C4C24×C6118yes—
1342C22×C4C24×C6114yes—
1343C22×C4C24×C6118yes—
1344C22×C4C24×C6118yes—
1345C22×C4C24×C6114yes—
1346C22×C4C24×C6114yes—
1347C22×C4C24×C6114yes—
1348C22×C4C24×C6114yes—
1349C22×C4C24×C6114yes—
1350C22×C4C24×C6111yescharacteristic
1351C4⋊C4C24×C6114yes—
1352C4⋊C4C24×C6114yes—
1353C4⋊C4C24×C6114yes—
1354C4⋊C4C24×C6112yes—
1355C4⋊C4C24×C6114yes—
1356C4⋊C4C24×C6118yes—
1357C4⋊C4C24×C6114yes—
1358C4⋊C4C24×C6112yes—
1359C4⋊C4C24×C6112yes—
1360C4⋊C4C24×C6118yes—
1361C4⋊C4C24×C6118yes—
1362C4⋊C4C24×C6114yes—
1363C4⋊C4C24×C6114yes—
1364C4⋊C4C24×C6114yes—
1365C4⋊C4C24×C6114yes—
1366C4⋊C4C24×C6118yes—
1367C4⋊C4C24×C6118yes—
1368C4⋊C4C24×C6118yes—
1369C4⋊C4C24×C6114yes—
1370C4⋊C4C24×C6112yes—
1371C4⋊C4C24×C6114yes—
1372C4⋊C4C24×C6114yes—
1373C4⋊C4C24×C6114yes—
1374C4⋊C4C24×C6118yes—
1375C4⋊C4C24×C6118yes—
1376C4⋊C4C24×C6118yes—
1377C4⋊C4C24×C6118yes—
1378C4⋊C4C24×C6114yes—
1379C4⋊C4C24×C6118yes—
1380C4⋊C4C24×C6114yes—
1381C4⋊C4C24×C6114yes—
1382C4⋊C4C24×C6114yes—
1383C4⋊C4C24×C6114yes—
1384C4⋊C4C24×C6114yes—
1385C22⋊C4C24×C6111yescharacteristic
1386C22⋊C4C24×C6114yes—
1387C22⋊C4C24×C6114yes—
1388C22⋊C4C24×C6112yes—
1389C22⋊C4C24×C6118yes—
1390C22⋊C4C24×C6114yes—
1391C22⋊C4C24×C6118yes—
1392C22⋊C4C24×C6111yescharacteristic
1393C22⋊C4C24×C6111yescharacteristic
1394C22⋊C4C24×C6111yescharacteristic
1395C22⋊C4C24×C6114yes—
1396C22⋊C4C24×C6118yes—
1397C22⋊C4C24×C6114yes—
1398C22⋊C4C24×C6118yes—
1399C22⋊C4C24×C6118yes—
1400C22⋊C4C24×C6118yes—
1401C22⋊C4C24×C6118yes—
1402C22⋊C4C24×C6114yes—
1403C22⋊C4C24×C6114yes—
1404C22⋊C4C24×C6112yes—
1405C22⋊C4C24×C6114yes—
1406C22⋊C4C24×C6118yes—
1407C22⋊C4C24×C6118yes—
1408C22⋊C4C24×C6114yes—
1409C22⋊C4C24×C6114yes—
1410C22⋊C4C24×C6114yes—
1411C22⋊C4C24×C6114yes—
1412C22⋊C4C24×C6114yes—
1413C22⋊C4C24×C6114yes—
1414C22⋊C4C24×C6118yes—
1415C22⋊C4C24×C6118yes—
1416C22⋊C4C24×C6118yes—
1417C22⋊C4C24×C6114yes—
1418C22⋊C4C24×C6118yes—
1419C22⋊C4C24×C6114yes—
1420C22⋊C4C24×C6114yes—
1421C42C24×C6112yes—
1422C42C24×C6114yes—
1423C42C24×C6114yes—
1424C42C24×C6114yes—
1425C42C24×C6114yes—
1426C42C24×C6114yes—
1427C42C24×C6112yes—
1428C42C24×C6114yes—
1429C42C24×C6114yes—
1430C42C24×C6118yes—
1431C42C24×C6118yes—
1432C23—22no—
1433C23—22no—
1434C23—22no—
1435C23—28no—
1436C23—41no—
1437C23—44no—
1438C23—44no—
1439C23—41no—
1440C23—44no—
1441C23—41no—
1442C23—44no—
1443C23—44no—
1444C23C25×C6112yes—
1445C23C25×C6114yes—
1446C23C25×C6111yescharacteristic
1447C23C25×C6114yes—
1448C23C25×C6114yes—
1449C23C25×C6111yescharacteristic
1450C23C25×C6111yescharacteristic
1451Q8—28no—
1452Q8—24no—
1453Q8—24no—
1454Q8—24no—
1455Q8—48no—
1456Q8—44no—
1457Q8—44no—
1458Q8—44no—
1459D4—28no—
1460D4—28no—
1461D4—28no—
1462D4—24no—
1463D4—28no—
1464D4—24no—
1465D4—24no—
1466D4—24no—
1467D4—48no—
1468D4—44no—
1469D4—44no—
1470D4—42no—
1471D4—44no—
1472D4—44no—
1473D4—44no—
1474D4—44no—
1475D4—44no—
1476D4—44no—
1477D4—44no—
1478D4—44no—
1479D4—44no—
1480D4—48no—
1481D4—44no—
1482D4—44no—
1483D4—44no—
1484D4—48no—
1485C2×C4—22no—
1486C2×C4—22no—
1487C2×C4—24no—
1488C2×C4—28no—
1489C2×C4—24no—
1490C2×C4—24no—
1491C2×C4—24no—
1492C2×C4—24no—
1493C2×C4—28no—
1494C2×C4—28no—
1495C2×C4—28no—
1496C2×C4—42no—
1497C2×C4—44no—
1498C2×C4—42no—
1499C2×C4—44no—
1500C2×C4—44no—
1501C2×C4—44no—
1502C2×C4—44no—
1503C2×C4—44no—
1504C2×C4—44no—
1505C2×C4—44no—
1506C2×C4—41no—
1507C2×C4—42no—
1508C2×C4—48no—
1509C2×C4—41no—
1510C2×C4—44no—
1511C2×C4—48no—
1512C2×C4—48no—
1513C2×C4—48no—
1514C2×C4H(5,𝔽2)×C6114yes—
1515C2×C4C25×C6111yescharacteristic
1516C2×C4C25×C6111yescharacteristic
1517C2×C4C25×C6114yes—
1518C2×C4C25×C6114yes—
1519C2×C4C25×C6114yes—
1520C2×C4C25×C6114yes—
1521C2×C4C25×C6112yes—
1522C2×C4C25×C6111yescharacteristic
1523C2×C4C25×C6111yescharacteristic
1524C2×C4C25×C6114yes—
1525C2×C4C25×C6114yes—
1526C2×C4C25×C6114yes—
1527C2×C4C25×C6114yes—
1528C2×C4C25×C6114yes—
1529C2×C4C25×C6112yes—
1530C2×C4C25×C6112yes—
1531C22—21no—
1532C22—21no—
1533C22—21no—
1534C22—21no—
1535C22—22no—
1536C22—21no—
1537C22—24no—
1538C22—24no—
1539C22—24no—
1540C22—21no—
1541C22—24no—
1542C22—24no—
1543C22—22no—
1544C22—24no—
1545C22—24no—
1546C22—24no—
1547C22—21no—
1548C22—24no—
1549C22—22no—
1550C22—44no—
1551C22—88no—
1552C22—82no—
1553C22—88no—
1554C22C2×H(5,𝔽2)×C6112yes—
1555C22C61×#58512yes—
1556C22C26×C6111yescharacteristic
1557C4—21no—
1558C4—22no—
1559C4—21no—
1560C4—24no—
1561C4—24no—
1562C4—24no—
1563C4—24no—
1564C4—24no—
1565C4—24no—
1566C4—22no—
1567C4—24no—
1568C4—21no—
1569C4—24no—
1570C4—24no—
1571C4—21no—
1572C4C2×H(5,𝔽2)×C6114yes—
1573C2—22no—
1574C2—22no—
1575C2—41no—
1576C2—42no—
1577C2—44no—
1578C2—44no—
1579C2—44no—
1580C2C22×H(5,𝔽2)×C6111yescharacteristic
1581C2C2×C61×#58511yescharacteristic
1582C2C61×2−1+611yescharacteristic
subgroupG/H
center, socleC22×C61C26
commutator, Frattini, cosocleC22C26×C61
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C61×#3560C2semidirect
2. C61×#3559C2semidirect
3. C61×#3551C2semidirect
4. C61×#3547C2semidirect
5. C61×#3542C2semidirect
6. C61×#3541C2semidirect
7. C61×#3539C2semidirect
8. C61×#3538C2semidirect
9. C61×#3534C2semidirect
10. C61×#3520C2semidirect
11. C61×#3512C2semidirect
12. C61×#3505C2semidirect
13. C61×#3497C2semidirect
14. C61×#3494C2semidirect
15. C61×#3493C2semidirect
16. C61×#3492C2semidirect
17. C61×#3489C2semidirect
18. C61×#3489C2semidirect
19. C2×C61×#552C2semidirect
20. D4×#41×C61C2semidirect
21. C61×#3461C2semidirect
22. C61×#3449C2semidirect
23. C2×C61×#537C2semidirect
24. C2×2−1+4×C61C22semidirect
25. C22×#41×C61C22semidirect
26. C22×#41×C61C22semidirect
27. C61×#563C22semidirect
28. C61×#563C22semidirect
29. C61×#562C22semidirect
30. C61×#562C22semidirect
31. C61×#560C22semidirect
32. C61×#560C22semidirect
33. C61×#556C22semidirect
34. C61×#555C22semidirect
35. C61×#555C22semidirect
36. C61×#554C22semidirect
37. C61×#554C22semidirect
38. C61×#553C22semidirect
39. C61×#553C22semidirect
40. C61×#553C22semidirect
41. C61×#553C22semidirect
42. C61×#553C22semidirect
43. C61×#553C22semidirect
44. C61×#553C22semidirect
45. C61×#553C22semidirect
46. C61×#553C22semidirect
47. C61×#552C22semidirect
48. C61×#552C22semidirect
49. C61×#552C22semidirect
50. C61×#552C22semidirect
51. C61×#552C22semidirect
52. C61×#552C22semidirect
53. C61×#552C22semidirect
54. C61×#552C22semidirect
55. C61×#551C22semidirect
56. C61×#551C22semidirect
57. C61×#551C22semidirect
58. C61×#551C22semidirect
59. C61×#550C22semidirect
60. C61×#550C22semidirect
61. D4×Q8×C61C22semidirect
62. D4×Q8×C61C22semidirect
63. D4×Q8×C61C22semidirect
64. D4×Q8×C61C22semidirect
66. C61×#548C22semidirect
67. C61×#548C22semidirect
68. C61×#548C22semidirect
69. C61×#548C22semidirect
70. C61×#548C22semidirect
71. C61×#547C22semidirect
72. C61×#547C22semidirect
73. C61×#547C22semidirect
74. C61×#547C22semidirect
75. C61×#547C22semidirect
76. C61×#547C22semidirect
77. C61×#547C22semidirect
79. C61×#546C22semidirect
80. C61×#546C22semidirect
81. C61×#546C22semidirect
82. C61×#546C22semidirect
83. C61×#546C22semidirect
84. C61×#546C22semidirect
85. C61×#546C22semidirect
86. C61×#546C22semidirect
88. D42×C61C22semidirect
89. C61×#544C22semidirect
90. C61×#544C22semidirect
91. C61×#544C22semidirect
92. C61×#542C22semidirect
93. C61×#542C22semidirect
94. C61×#542C22semidirect
95. C61×#542C22semidirect
96. C61×#541C22semidirect
97. C61×#541C22semidirect
98. C61×#540C22semidirect
99. C61×#540C22semidirect
100. C61×#540C22semidirect
101. C61×#540C22semidirect
102. C61×#540C22semidirect
103. C61×#539C22semidirect
104. C61×#539C22semidirect
105. C61×#539C22semidirect
106. C61×#539C22semidirect
107. C61×#539C22semidirect
108. C61×#539C22semidirect
109. C61×#538C22semidirect
110. C61×#538C22semidirect
111. C61×#538C22semidirect
112. C61×#538C22semidirect
114. C61×#537C22semidirect
115. C61×#537C22semidirect
116. C61×#537C22semidirect
117. C61×#537C22semidirect
118. C61×#537C22semidirect
119. C61×#537C22semidirect
120. C61×#537C22semidirect
121. C61×#537C22semidirect
122. C61×#537C22semidirect
123. C61×#537C22semidirect
124. C61×#536C22semidirect
125. C61×#536C22semidirect
126. C61×#536C22semidirect
127. C61×#536C22semidirect
128. C61×#535C22semidirect
129. C61×#535C22semidirect
130. C61×#534C22semidirect
131. C61×#534C22semidirect
132. C61×#533C22semidirect
133. C61×#532C22semidirect
134. C61×#532C22semidirect
135. C61×#532C22semidirect
136. C61×#532C22semidirect
137. C61×#529C22semidirect
138. C61×#529C22semidirect
139. C61×#529C22semidirect
140. C61×#529C22semidirect
141. C61×#529C22semidirect
142. C2×#126×C61C22semidirect
143. C2×#125×C61C22semidirect
144. C2×#125×C61C22semidirect
146. C61×#525C22semidirect
147. C61×#525C22semidirect
148. C61×#525C22semidirect
149. C61×#525C22semidirect
150. C61×#525C22semidirect
151. C61×#525C22semidirect
152. C61×#525C22semidirect
153. C61×#525C22semidirect
155. C2×C22⋊Q8×C61C22semidirect
156. C2×C22⋊Q8×C61C22semidirect
157. C2×C22⋊Q8×C61C22semidirect
158. C2×C22⋊Q8×C61C22semidirect
159. C2×C22⋊Q8×C61C22semidirect
160. C2×#121×C61C22semidirect
161. C2×#121×C61C22semidirect
162. C61×#520C22semidirect
163. C61×#520C22semidirect
164. C61×#520C22semidirect
165. C61×#518C22semidirect
166. C4×#41×C61C22semidirect
167. C2×C4×Q8×C61C22semidirect
169. C2×C4×D4×C61C22semidirect
170. C2×#117×C61C22semidirect
171. C2×#117×C61C22semidirect
172. C22×C4⋊C4×C61C22semidirect
739. #62927C61direct (N × H)
782. #3560C2×C61semidirect
783. #3559C2×C61semidirect
784. #3551C2×C61semidirect
785. #3547C2×C61semidirect
786. #3542C2×C61semidirect
787. #3541C2×C61semidirect
788. #3539C2×C61semidirect
789. #3538C2×C61semidirect
790. #3534C2×C61semidirect
791. #3520C2×C61semidirect
792. #3512C2×C61semidirect
793. #3505C2×C61semidirect
794. #3497C2×C61semidirect
795. #3494C2×C61semidirect
796. #3493C2×C61semidirect
797. #3492C2×C61semidirect
798. #3489C2×C61semidirect
799. #3489C2×C61semidirect
800. C2×#552C2×C61semidirect
801. D4×#41C2×C61semidirect
802. #3461C2×C61semidirect
803. #3449C2×C61semidirect
804. C2×#537C2×C61semidirect
815. C2×2−1+4C22×C61semidirect
816. C22×#41C22×C61semidirect
817. C22×#41C22×C61semidirect
818. #563C22×C61semidirect
819. #563C22×C61semidirect
820. #562C22×C61semidirect
821. #562C22×C61semidirect
822. #560C22×C61semidirect
823. #560C22×C61semidirect
824. #556C22×C61semidirect
825. #555C22×C61semidirect
826. #555C22×C61semidirect
827. #554C22×C61semidirect
828. #554C22×C61semidirect
829. #553C22×C61semidirect
830. #553C22×C61semidirect
831. #553C22×C61semidirect
832. #553C22×C61semidirect
833. #553C22×C61semidirect
834. #553C22×C61semidirect
835. #553C22×C61semidirect
836. #553C22×C61semidirect
837. #553C22×C61semidirect
838. #552C22×C61semidirect
839. #552C22×C61semidirect
840. #552C22×C61semidirect
841. #552C22×C61semidirect
842. #552C22×C61semidirect
843. #552C22×C61semidirect
844. #552C22×C61semidirect
845. #552C22×C61semidirect
846. #551C22×C61semidirect
847. #551C22×C61semidirect
848. #551C22×C61semidirect
849. #551C22×C61semidirect
850. #550C22×C61semidirect
851. #550C22×C61semidirect
852. D4×Q8C22×C61semidirect
853. D4×Q8C22×C61semidirect
854. D4×Q8C22×C61semidirect
855. D4×Q8C22×C61semidirect
857. #548C22×C61semidirect
858. #548C22×C61semidirect
859. #548C22×C61semidirect
860. #548C22×C61semidirect
861. #548C22×C61semidirect
862. #547C22×C61semidirect
863. #547C22×C61semidirect
864. #547C22×C61semidirect
865. #547C22×C61semidirect
866. #547C22×C61semidirect
867. #547C22×C61semidirect
868. #547C22×C61semidirect
870. #546C22×C61semidirect
871. #546C22×C61semidirect
872. #546C22×C61semidirect
873. #546C22×C61semidirect
874. #546C22×C61semidirect
875. #546C22×C61semidirect
876. #546C22×C61semidirect
877. #546C22×C61semidirect
879. D42C22×C61semidirect
880. #544C22×C61semidirect
881. #544C22×C61semidirect
882. #544C22×C61semidirect
883. #542C22×C61semidirect
884. #542C22×C61semidirect
885. #542C22×C61semidirect
886. #542C22×C61semidirect
887. #541C22×C61semidirect
888. #541C22×C61semidirect
889. #540C22×C61semidirect
890. #540C22×C61semidirect
891. #540C22×C61semidirect
892. #540C22×C61semidirect
893. #540C22×C61semidirect
894. #539C22×C61semidirect
895. #539C22×C61semidirect
896. #539C22×C61semidirect
897. #539C22×C61semidirect
898. #539C22×C61semidirect
899. #539C22×C61semidirect
900. #538C22×C61semidirect
901. #538C22×C61semidirect
902. #538C22×C61semidirect
903. #538C22×C61semidirect
905. #537C22×C61semidirect
906. #537C22×C61semidirect
907. #537C22×C61semidirect
908. #537C22×C61semidirect
909. #537C22×C61semidirect
910. #537C22×C61semidirect
911. #537C22×C61semidirect
912. #537C22×C61semidirect
913. #537C22×C61semidirect
914. #537C22×C61semidirect
915. #536C22×C61semidirect
916. #536C22×C61semidirect
917. #536C22×C61semidirect
918. #536C22×C61semidirect
919. #535C22×C61semidirect
920. #535C22×C61semidirect
921. #534C22×C61semidirect
922. #534C22×C61semidirect
923. #533C22×C61semidirect
924. #532C22×C61semidirect
925. #532C22×C61semidirect
926. #532C22×C61semidirect
927. #532C22×C61semidirect
928. #529C22×C61semidirect
929. #529C22×C61semidirect
930. #529C22×C61semidirect
931. #529C22×C61semidirect
932. #529C22×C61semidirect
933. C2×#126C22×C61semidirect
934. C2×#125C22×C61semidirect
935. C2×#125C22×C61semidirect
937. #525C22×C61semidirect
938. #525C22×C61semidirect
939. #525C22×C61semidirect
940. #525C22×C61semidirect
941. #525C22×C61semidirect
942. #525C22×C61semidirect
943. #525C22×C61semidirect
944. #525C22×C61semidirect
946. C2×C22⋊Q8C22×C61semidirect
947. C2×C22⋊Q8C22×C61semidirect
948. C2×C22⋊Q8C22×C61semidirect
949. C2×C22⋊Q8C22×C61semidirect
950. C2×C22⋊Q8C22×C61semidirect
951. C2×#121C22×C61semidirect
952. C2×#121C22×C61semidirect
953. #520C22×C61semidirect
954. #520C22×C61semidirect
955. #520C22×C61semidirect
956. #518C22×C61semidirect
957. C4×#41C22×C61semidirect
958. C2×C4×Q8C22×C61semidirect
960. C2×C4×D4C22×C61semidirect
961. C2×#117C22×C61semidirect
962. C2×#117C22×C61semidirect
963. C22×C4⋊C4C22×C61semidirect
964. C61#62927direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C61×#35602
C61×#35592
C61×#35512
C61×#35472
C61×#35422
C61×#35412
C61×#35392
C61×#35382
C61×#35342
C61×#35202
C61×#35122
C61×#35052
C61×#34972
C61×#34942
C61×#34932
C61×#34922
C61×#34892
C2×C61×#5522
D4×#41×C612
C61×#34612
C61×#34492
C2×C61×#5372
#6292761