Finite Group Databasebeta

← C61×#62877 #29566310

Subgroups — C61×#62877 #29566310

Order 15616.

6394 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3565C214yesmaximal, complemented
2C61×#3565C214yesmaximal, complemented
3C61×#3563C214yesmaximal, complemented
4C61×#3559C214yesmaximal, complemented
5C61×#3555C214yesmaximal, complemented
6C61×#3553C214yesmaximal, complemented
7C61×#3552C214yesmaximal, complemented
8C61×#3552C214yesmaximal, complemented
9C61×#3547C214yesmaximal, complemented
10C61×#3544C214yesmaximal, complemented
11C61×#3541C218yesmaximal, complemented
12C61×#3512C212yesmaximal, complemented
13C61×#3511C212yesmaximal, complemented
14C61×#3504C212yesmaximal, complemented
15C61×#3503C212yesmaximal, complemented
16C61×#3493C211yesmaximal, characteristic, complemented
17C61×#3493C211yesmaximal, characteristic, complemented
18C61×#3492C212yesmaximal, complemented
19C2×C61×#544C211yesmaximal, characteristic, complemented
20C61×#3455C212yesmaximal, complemented
21C61×#564C2214yescomplemented
22C61×#563C2218yes—
23C61×#563C2218yes—
24C61×#563C2214yescomplemented
25C61×#563C2218yescomplemented
26C61×#563C2218yescomplemented
27C61×#563C2214yescomplemented
28C61×#562C2218yes—
29C61×#562C2218yes—
30C61×#562C2214yescomplemented
31Q82×C61C2214yescomplemented
32C61×#557C2214yescomplemented
33C61×#557C2214yescomplemented
34C61×#557C2214yescomplemented
35C61×#557C2214yescomplemented
36C61×#556C2214yes—
37C61×#556C2214yes—
38C61×#556C2218yes—
39C61×#556C2214yescomplemented
40C61×#556C2214yescomplemented
41C61×#555C2214yes—
42C61×#555C2214yes—
43C61×#555C2214yescomplemented
44C61×#554C2214yes—
45C61×#554C2214yes—
46C61×#554C2218yes—
47C61×#554C2218yes—
48C61×#554C2218yes—
49C61×#554C2214yescomplemented
50C61×#554C2214yescomplemented
51C61×#554C2214yescomplemented
52C61×#554C2214yescomplemented
53C61×#553C2214yes—
54C61×#553C2214yes—
55C61×#553C2218yes—
56C61×#553C2218yes—
57C61×#553C2218yes—
58C61×#553C2214yes—
59C61×#553C2214yes—
60C61×#553C2214yescomplemented
61C61×#553C2214yescomplemented
62C61×#552C2214yes—
63C61×#552C2214yes—
64C61×#552C2214yes—
65C61×#552C2214yes—
66C61×#552C2218yes—
67C61×#552C2218yescomplemented
68C61×#552C2214yescomplemented
69C61×#552C2218yescomplemented
70C61×#552C2214yescomplemented
71D4×Q8×C61C2218yes—
72D4×Q8×C61C2214yescomplemented
73D4×Q8×C61C2214yescomplemented
74C61×#548C2218yes—
75C61×#548C2218yes—
76C61×#547C2214yes—
77C61×#547C2218yes—
78C61×#547C2214yes—
79C61×#547C2214yescomplemented
80C61×#547C2214yescomplemented
81C61×#544C2214yes—
82C61×#544C2214yes—
83C61×#544C2214yes—
84C61×#544C2214yes—
85C61×#544C2212yes—
86C61×#544C2211yescharacteristic
87C61×#544C2211yescharacteristic
88C61×#544C2218yescomplemented
89C61×#544C2214yescomplemented
90C61×#544C2214yescomplemented
91C61×#544C2214yescomplemented
92C61×#544C2214yescomplemented
93C61×#542C2212yes—
94C61×#542C2218yes—
95C61×#542C2218yes—
96C61×#542C2212yes—
97C61×#542C2212yes—
98C61×#542C2212yes—
99C61×#542C2218yes—
100C61×#542C2214yescomplemented
101C61×#542C2218yescomplemented
102C61×#542C2214yescomplemented
103C61×#541C2212yes—
104C61×#541C2218yes—
105C61×#541C2212yes—
106C61×#541C2218yescomplemented
107C61×#541C2218yescomplemented
108C61×#541C2218yescomplemented
109C61×#541C2214yescomplemented
110C61×#540C2212yes—
111C61×#540C2212yes—
112C61×#540C2214yescomplemented
113C61×#539C2214yes—
114C61×#539C2218yes—
115C61×#539C2218yes—
116C61×#539C2214yes—
117C61×#539C2218yes—
118C61×#539C2218yescomplemented
119C61×#539C2218yescomplemented
120C61×#538C2214yes—
121C61×#538C2214yes—
122C61×#538C2214yes—
123C61×#538C2214yes—
124C61×#537C2218yes—
125C61×#537C2212yes—
126C61×#537C2211yescharacteristic
127C61×#537C2211yescharacteristic
128C61×#536C2218yes—
129C61×#536C2218yescomplemented
130C61×#533C2212yes—
131C61×#533C2214yescomplemented
132C61×#533C2214yescomplemented
133C61×#533C2214yescomplemented
134C61×#532C2212yes—
135C61×#532C2214yescomplemented
136C2×C4⋊Q8×C61C2212yes—
137C2×C4⋊Q8×C61C2212yes—
138C2×C4⋊Q8×C61C2214yescomplemented
139C61×#529C2214yes—
140C61×#529C2214yes—
141C61×#529C2214yes—
142C61×#529C2214yes—
143C61×#529C2214yes—
144C61×#529C2214yes—
145C61×#529C2214yescomplemented
146C61×#529C2214yescomplemented
147C2×#125×C61C2212yes—
148C2×#125×C61C2212yes—
149C2×#125×C61C2214yescomplemented
150C61×#525C2212yes—
151C61×#525C2212yes—
152C61×#525C2218yes—
153C2×C22⋊Q8×C61C2214yes—
154C61×#520C2212yes—
155C61×#520C2212yes—
156C61×#520C2212yes—
157C61×#520C2212yes—
158C4×#41×C61C2212yes—
159C4×#41×C61C2212yes—
160C2×#117×C61C2211yescharacteristic
161C2×#117×C61C2211yescharacteristic
162C22×C4⋊C4×C61C2211yescharacteristic
163C2×#41×C61C2312yes—
164C2×#41×C61C2312yes—
165C2×#41×C61C2318yes—
166C2×#41×C61C2318yes—
167C22×Q8×C61C2314yes—
168C22×Q8×C61C2318yes—
169C23×C4×C61C2311yescharacteristic
170C23×C4×C61C2312yes—
171C4⋊Q8×C61C2314yes—
172C4⋊Q8×C61C2314yes—
173C4⋊Q8×C61C2318yes—
174C4⋊Q8×C61C2314yes—
175C4⋊Q8×C61C2314yes—
176C4⋊Q8×C61C2314yes—
177C4⋊Q8×C61C2314yes—
178C4⋊Q8×C61C2312yes—
179C4⋊Q8×C61C2318yes—
180C4⋊Q8×C61C2318yes—
181C4⋊Q8×C61C2314yes—
182C4⋊Q8×C61C2314yes—
183C4⋊Q8×C61C2312yes—
184C4⋊Q8×C61C2312yes—
185C4⋊Q8×C61C2314yes—
186C4⋊Q8×C61C2314yes—
187C4⋊Q8×C61C2318yes—
188C4⋊Q8×C61C2318yes—
189C4⋊Q8×C61C2318yes—
190C4⋊Q8×C61C2318yes—
191#127×C61C2312yes—
192#126×C61C2314yes—
193#126×C61C2318yes—
194#126×C61C2314yes—
195#126×C61C2318yes—
196#126×C61C2314yes—
197#126×C61C2314yes—
198#126×C61C2314yes—
199#126×C61C2318yes—
200#126×C61C2314yes—
201#126×C61C2318yes—
202#126×C61C2318yes—
203#126×C61C2318yes—
204#126×C61C2314yes—
205#126×C61C2314yes—
206#126×C61C2318yes—
207#126×C61C2318yes—
208#126×C61C2318yes—
209#126×C61C2318yes—
210#126×C61C2318yes—
211#126×C61C2318yes—
212#125×C61C2312yes—
213#125×C61C2312yes—
214#125×C61C2314yes—
215#125×C61C2318yes—
216#125×C61C2314yes—
217#125×C61C2314yes—
218#125×C61C2318yes—
219#125×C61C2318yes—
220#125×C61C2314yes—
221#125×C61C2314yes—
222#125×C61C2314yes—
223#125×C61C2314yes—
224#125×C61C2318yes—
225#125×C61C2318yes—
226#125×C61C2318yes—
227#125×C61C2318yes—
228#125×C61C2318yes—
229#125×C61C2318yes—
230#125×C61C2318yes—
231#125×C61C2318yes—
232#125×C61C2318yes—
233#125×C61C2314yes—
234#125×C61C2314yes—
235#125×C61C2314yes—
236#125×C61C2314yes—
237#125×C61C2314yes—
238#125×C61C2314yes—
239#125×C61C2314yes—
240#125×C61C2314yes—
241#125×C61C2314yes—
242#124×C61C2312yes—
243#124×C61C2312yes—
244#124×C61C2318yes—
245#124×C61C2314yes—
246#124×C61C2318yes—
247#124×C61C2314yes—
248#124×C61C2318yes—
249#124×C61C2314yes—
250#124×C61C2318yes—
251#124×C61C2314yes—
252#124×C61C2314yes—
253#124×C61C2318yes—
254#124×C61C2314yes—
255#123×C61C2314yes—
256#123×C61C2318yes—
257#123×C61C2318yes—
258#123×C61C2318yes—
259#123×C61C2314yes—
260#123×C61C2318yes—
261#123×C61C2318yes—
262#123×C61C2314yes—
263#123×C61C2318yes—
264#123×C61C2314yes—
265#123×C61C2314yes—
266#123×C61C2314yes—
267#123×C61C2314yes—
268#123×C61C2318yes—
269#123×C61C2314yes—
270#123×C61C2318yes—
271#123×C61C2318yes—
272#123×C61C2318yes—
273#123×C61C2314yes—
274#123×C61C2314yes—
275#123×C61C2318yes—
276#123×C61C2318yes—
277C22⋊Q8×C61C2314yes—
278C22⋊Q8×C61C2314yes—
279C22⋊Q8×C61C2318yes—
280C22⋊Q8×C61C2314yes—
281C22⋊Q8×C61C2314yes—
282C22⋊Q8×C61C2318yes—
283C22⋊Q8×C61C2318yes—
284C22⋊Q8×C61C2318yes—
285C22⋊Q8×C61C2318yes—
286C22⋊Q8×C61C2318yes—
287C22⋊Q8×C61C2318yes—
288C22⋊Q8×C61C2318yes—
289C22⋊Q8×C61C2318yes—
290C22⋊Q8×C61C2314yes—
291C22⋊Q8×C61C2318yes—
292C22⋊Q8×C61C2318yes—
293C22⋊Q8×C61C2318yes—
294C22⋊Q8×C61C2318yes—
295C22⋊Q8×C61C2314yes—
296C22⋊Q8×C61C2314yes—
297C22⋊Q8×C61C2318yes—
298C22⋊Q8×C61C2314yes—
299C22⋊Q8×C61C2314yes—
300C22⋊Q8×C61C2314yes—
301C22⋊Q8×C61C2318yes—
302C22⋊Q8×C61C2318yes—
303C22⋊Q8×C61C2318yes—
304C22⋊Q8×C61C2314yes—
305C22⋊Q8×C61C2314yes—
306C22⋊Q8×C61C2318yes—
307C22⋊Q8×C61C2318yes—
308C22⋊Q8×C61C2312yes—
309C22⋊Q8×C61C2312yes—
310C22⋊Q8×C61C2312yes—
311C22⋊Q8×C61C2312yes—
312C22⋊Q8×C61C2318yes—
313C22⋊Q8×C61C2318yes—
314C22⋊Q8×C61C2318yes—
315C22⋊Q8×C61C2318yes—
316#121×C61C2314yes—
317#121×C61C2314yes—
318#121×C61C2318yes—
319#121×C61C2314yes—
320#121×C61C2314yes—
321#121×C61C2314yes—
322#121×C61C2314yes—
323#121×C61C2318yes—
324#121×C61C2318yes—
325#121×C61C2314yes—
326#121×C61C2314yes—
327#121×C61C2318yes—
328#121×C61C2318yes—
329#121×C61C2318yes—
330#121×C61C2314yes—
331#121×C61C2314yes—
332#121×C61C2318yes—
333#121×C61C2314yes—
334#121×C61C2314yes—
335#121×C61C2312yes—
336#121×C61C2312yes—
337#121×C61C2312yes—
338#121×C61C2312yes—
339#120×C61C2314yes—
340#120×C61C2314yes—
341C4×Q8×C61C2314yes—
342C4×Q8×C61C2314yes—
343C4×Q8×C61C2318yes—
344C4×Q8×C61C2318yes—
345C4×Q8×C61C2318yes—
346C4×Q8×C61C2318yes—
347C4×Q8×C61C2318yes—
348C4×Q8×C61C2314yes—
349C4×Q8×C61C2314yes—
350C4×Q8×C61C2312yes—
351C4×Q8×C61C2312yes—
352C4×Q8×C61C2312yes—
353C4×Q8×C61C2312yes—
354C4×Q8×C61C2314yes—
355C4×Q8×C61C2314yes—
356C4×Q8×C61C2314yes—
357C4×Q8×C61C2314yes—
358C4×D4×C61C2314yes—
359C4×D4×C61C2314yes—
360C4×D4×C61C2318yes—
361C4×D4×C61C2314yes—
362C4×D4×C61C2314yes—
363C4×D4×C61C2314yes—
364C4×D4×C61C2314yes—
365C4×D4×C61C2314yes—
366C4×D4×C61C2314yes—
367C4×D4×C61C2318yes—
368C4×D4×C61C2318yes—
369C4×D4×C61C2318yes—
370C4×D4×C61C2318yes—
371C4×D4×C61C2318yes—
372C4×D4×C61C2318yes—
373C4×D4×C61C2318yes—
374C4×D4×C61C2314yes—
375C4×D4×C61C2314yes—
376C4×D4×C61C2318yes—
377C4×D4×C61C2312yes—
378C4×D4×C61C2312yes—
379C4×D4×C61C2312yes—
380C4×D4×C61C2312yes—
381C4×D4×C61C2314yes—
382C4×D4×C61C2314yes—
383C4×D4×C61C2314yes—
384C4×D4×C61C2314yes—
385C4×D4×C61C2314yes—
386C4×D4×C61C2314yes—
387#117×C61C2312yes—
388#117×C61C2312yes—
389#117×C61C2318yes—
390#117×C61C2314yes—
391#117×C61C2314yes—
392#117×C61C2314yes—
393#117×C61C2314yes—
394#117×C61C2318yes—
395#117×C61C2318yes—
396#117×C61C2312yes—
397#117×C61C2312yes—
398#117×C61C2314yes—
399#117×C61C2318yes—
400#117×C61C2312yes—
401#117×C61C2312yes—
402#117×C61C2318yes—
403#117×C61C2314yes—
404#117×C61C2318yes—
405#117×C61C2314yes—
406#117×C61C2314yes—
407C2×C4⋊C4×C61C2311yescharacteristic
408C2×C4⋊C4×C61C2311yescharacteristic
409C2×C4⋊C4×C61C2312yes—
410C2×C4⋊C4×C61C2312yes—
411C2×C4⋊C4×C61C2314yes—
412C2×C4⋊C4×C61C2314yes—
413C2×C4⋊C4×C61C2318yes—
414C2×C4⋊C4×C61C2314yes—
415C2×C4⋊C4×C61C2314yes—
416C2×C4⋊C4×C61C2318yes—
417C2×C4⋊C4×C61C2311yescharacteristic
418C2×C4⋊C4×C61C2311yescharacteristic
419C2×C4⋊C4×C61C2318yes—
420C2×C4⋊C4×C61C2314yes—
421C2×C4⋊C4×C61C2314yes—
422C2×C4⋊C4×C61C2314yes—
423C2×C4⋊C4×C61C2314yes—
424C2×C4⋊C4×C61C2314yes—
425C2×C22⋊C4×C61C2312yes—
426C2×C22⋊C4×C61C2312yes—
427C2×C42×C61C2312yes—
428C2×C42×C61C2312yes—
429C2×C42×C61C2314yes—
430C2×C42×C61C2314yes—
431C24×C61C2411yescharacteristic
432#41×C61—28no—
433#41×C61—28no—
434#41×C61—88no—
435#41×C61—88no—
436C2×Q8×C61—84no—
437C2×Q8×C61—88no—
438C2×Q8×C61C2412yes—
439C2×Q8×C61C2412yes—
440C2×Q8×C61C2414yes—
441C2×Q8×C61C2414yes—
442C2×Q8×C61C2418yes—
443C2×Q8×C61C2414yes—
444C2×Q8×C61C2418yes—
445C2×Q8×C61C2418yes—
446C2×Q8×C61C2414yes—
447C2×D4×C61C2414yes—
448C2×D4×C61C2414yes—
449C2×D4×C61C2412yes—
450C2×D4×C61C2412yes—
451C2×D4×C61C2414yes—
452C2×D4×C61C2414yes—
453C2×D4×C61C2414yes—
454C2×D4×C61C2414yes—
455C2×D4×C61C2414yes—
456C2×D4×C61C2414yes—
457C2×D4×C61C2418yes—
458C2×D4×C61C2414yes—
459C2×D4×C61C2414yes—
460C22×C4×C61—24no—
461C22×C4×C61—82no—
462C22×C4×C61C2411yescharacteristic
463C22×C4×C61C2414yes—
464C22×C4×C61C2414yes—
465C22×C4×C61C2412yes—
466C22×C4×C61C2412yes—
467C22×C4×C61C2412yes—
468C22×C4×C61C2412yes—
469C22×C4×C61C2412yes—
470C22×C4×C61C2412yes—
471C22×C4×C61C2414yes—
472C22×C4×C61C2414yes—
473C22×C4×C61C2414yes—
474C22×C4×C61C2414yes—
475C22×C4×C61C2414yes—
476C22×C4×C61C2418yes—
477C22×C4×C61C2418yes—
478C22×C4×C61C2418yes—
479C22×C4×C61C2418yes—
480C22×C4×C61C2418yes—
481C22×C4×C61C2411yescharacteristic
482C4⋊C4×C61C2414yes—
483C4⋊C4×C61C2414yes—
484C4⋊C4×C61C2412yes—
485C4⋊C4×C61C2414yes—
486C4⋊C4×C61C2414yes—
487C4⋊C4×C61C2414yes—
488C4⋊C4×C61C2412yes—
489C4⋊C4×C61C2414yes—
490C4⋊C4×C61C2412yes—
491C4⋊C4×C61C2418yes—
492C4⋊C4×C61C2414yes—
493C4⋊C4×C61C2414yes—
494C4⋊C4×C61C2418yes—
495C4⋊C4×C61C2418yes—
496C4⋊C4×C61C2414yes—
497C4⋊C4×C61C2418yes—
498C4⋊C4×C61C2414yes—
499C4⋊C4×C61C2411yescharacteristic
500C4⋊C4×C61C2411yescharacteristic
501C4⋊C4×C61C2412yes—
502C4⋊C4×C61C2412yes—
503C4⋊C4×C61C2411yescharacteristic
504C4⋊C4×C61C2411yescharacteristic
505C4⋊C4×C61C2418yes—
506C4⋊C4×C61C2418yes—
507C4⋊C4×C61C2418yes—
508C4⋊C4×C61C2418yes—
509C4⋊C4×C61C2418yes—
510C4⋊C4×C61C2418yes—
511C4⋊C4×C61C2418yes—
512C4⋊C4×C61C2418yes—
513C4⋊C4×C61C2418yes—
514C4⋊C4×C61C2418yes—
515C4⋊C4×C61C2412yes—
516C4⋊C4×C61C2414yes—
517C4⋊C4×C61C2414yes—
518C4⋊C4×C61C2414yes—
519C4⋊C4×C61C2418yes—
520C4⋊C4×C61C2414yes—
521C4⋊C4×C61C2414yes—
522C4⋊C4×C61C2414yes—
523C4⋊C4×C61C2414yes—
524C4⋊C4×C61C2414yes—
525C4⋊C4×C61C2414yes—
526C4⋊C4×C61C2414yes—
527C4⋊C4×C61C2418yes—
528C4⋊C4×C61C2414yes—
529C4⋊C4×C61C2414yes—
530C4⋊C4×C61C2414yes—
531C4⋊C4×C61C2414yes—
532C4⋊C4×C61C2414yes—
533C4⋊C4×C61C2414yes—
534C22⋊C4×C61C2412yes—
535C22⋊C4×C61C2412yes—
536C22⋊C4×C61C2412yes—
537C22⋊C4×C61C2418yes—
538C22⋊C4×C61C2412yes—
539C22⋊C4×C61C2414yes—
540C22⋊C4×C61C2414yes—
541C22⋊C4×C61C2418yes—
542C22⋊C4×C61C2418yes—
543C22⋊C4×C61C2418yes—
544C22⋊C4×C61C2414yes—
545C22⋊C4×C61C2414yes—
546C22⋊C4×C61C2414yes—
547C22⋊C4×C61C2414yes—
548C22⋊C4×C61C2414yes—
549C22⋊C4×C61C2414yes—
550C22⋊C4×C61C2414yes—
551C22⋊C4×C61C2414yes—
552C22⋊C4×C61C2418yes—
553C22⋊C4×C61C2418yes—
554C22⋊C4×C61C2418yes—
555C22⋊C4×C61C2418yes—
556C22⋊C4×C61C2414yes—
557C22⋊C4×C61C2414yes—
558C22⋊C4×C61C2414yes—
559C22⋊C4×C61C2414yes—
560C22⋊C4×C61C2418yes—
561C22⋊C4×C61C2414yes—
562C22⋊C4×C61C2414yes—
563C22⋊C4×C61C2414yes—
564C22⋊C4×C61C2414yes—
565C42×C61C2412yes—
566C42×C61C2412yes—
567C42×C61C2414yes—
568C42×C61C2414yes—
569C42×C61C2412yes—
570C42×C61C2412yes—
571C42×C61C2414yes—
572C42×C61C2414yes—
573C42×C61C2414yes—
574C42×C61C2414yes—
575C42×C61C2414yes—
576C42×C61C2414yes—
577C42×C61C2418yes—
578C42×C61C2418yes—
579C42×C61C2418yes—
580C42×C61C2418yes—
581C23×C61—22no—
582C23×C61—41no—
583C23×C61—41no—
584C23×C61C2512yes—
585C23×C61C2514yes—
586C23×C61C2514yes—
587C23×C61C2511yescharacteristic
588Q8×C61—24no—
589Q8×C61—24no—
590Q8×C61—48no—
591Q8×C61—44no—
592Q8×C61—44no—
593Q8×C61—48no—
594Q8×C61—48no—
595Q8×C61—44no—
596Q8×C61—44no—
597D4×C61—28no—
598D4×C61—28no—
599D4×C61—24no—
600D4×C61—24no—
601D4×C61—44no—
602D4×C61—44no—
603D4×C61—44no—
604D4×C61—44no—
605D4×C61—44no—
606D4×C61—48no—
607D4×C61—44no—
608D4×C61—44no—
609D4×C61—44no—
610C2×C4×C61—22no—
611C2×C4×C61—24no—
612C2×C4×C61—24no—
613C2×C4×C61—28no—
614C2×C4×C61—28no—
615C2×C4×C61—44no—
616C2×C4×C61—48no—
617C2×C4×C61—42no—
618C2×C4×C61—44no—
619C2×C4×C61—42no—
620C2×C4×C61—48no—
621C2×C4×C61—44no—
622C2×C4×C61—42no—
623C2×C4×C61—42no—
624C2×C4×C61—44no—
625C2×C4×C61—48no—
626C2×C4×C61—48no—
627C2×C4×C61—48no—
628C2×C4×C61—44no—
629C2×C4×C612−1+414yes—
630C2×C4×C61C2514yes—
631C2×C4×C61C2514yes—
632C2×C4×C61C2514yes—
633C2×C4×C61C2511yescharacteristic
634C2×C4×C61C2511yescharacteristic
635C2×C4×C61C2512yes—
636C2×C4×C61C2512yes—
637C2×C4×C61C2514yes—
638C2×C4×C61C2514yes—
639C2×C4×C61C2514yes—
640C2×C4×C61C2514yes—
641C2×C4×C61C2512yes—
642C2×C4×C61C2512yes—
643C2×C4×C61C2514yes—
644C2×C4×C61C2518yes—
645C2×C4×C61C2512yes—
646#62877C6111yesmaximal, characteristic, direct product factor, Sylow
647C22×C61—21no—
648C22×C61—21no—
649C22×C61—22no—
650C22×C61—24no—
651C22×C61—24no—
652C22×C61—24no—
653C22×C61—22no—
654C22×C61—24no—
655C22×C61—24no—
656C22×C61—24no—
657C22×C61—22no—
658C22×C61—44no—
659C22×C61C2×2−1+412yes—
660C22×C61C2611yescharacteristic
661C4×C61—21no—
662C4×C61—21no—
663C4×C61—24no—
664C4×C61—24no—
665C4×C61—28no—
666C4×C61—24no—
667C4×C61—22no—
668C4×C61—24no—
669C4×C61—24no—
670C4×C61—22no—
671C4×C61—22no—
672C4×C61—24no—
673C4×C61—24no—
674C4×C61—22no—
675C4×C61—24no—
676C4×C61C2×2−1+414yes—
677#3565C2×C6114yescomplemented
678#3565C2×C6114yescomplemented
679#3563C2×C6114yescomplemented
680#3559C2×C6114yescomplemented
681#3555C2×C6114yescomplemented
682#3553C2×C6114yescomplemented
683#3552C2×C6114yescomplemented
684#3552C2×C6114yescomplemented
685#3547C2×C6114yescomplemented
686#3544C2×C6114yescomplemented
687#3541C2×C6118yescomplemented
688#3512C2×C6112yescomplemented
689#3511C2×C6112yescomplemented
690#3504C2×C6112yescomplemented
691#3503C2×C6112yescomplemented
692#3493C2×C6111yescharacteristic, complemented
693#3493C2×C6111yescharacteristic, complemented
694#3492C2×C6112yescomplemented
695C2×#544C2×C6111yescharacteristic, complemented
696#3455C2×C6112yescomplemented
697C2×C61—22no—
698C2×C61—44no—
699C2×C61—44no—
700C2×C61—42no—
701C2×C61C22×2−1+411yescharacteristic
702C2×C61H(7,𝔽2)11yescharacteristic
703C2×C612−1+611yescharacteristic
704#564C22×C6114yescomplemented
705#563C22×C6118yes—
706#563C22×C6118yes—
707#563C22×C6114yescomplemented
708#563C22×C6118yescomplemented
709#563C22×C6118yescomplemented
710#563C22×C6114yescomplemented
711#562C22×C6118yes—
712#562C22×C6118yes—
713#562C22×C6114yescomplemented
714Q82C22×C6114yescomplemented
715#557C22×C6114yescomplemented
716#557C22×C6114yescomplemented
717#557C22×C6114yescomplemented
718#557C22×C6114yescomplemented
719#556C22×C6114yes—
720#556C22×C6114yes—
721#556C22×C6118yes—
722#556C22×C6114yescomplemented
723#556C22×C6114yescomplemented
724#555C22×C6114yes—
725#555C22×C6114yes—
726#555C22×C6114yescomplemented
727#554C22×C6114yes—
728#554C22×C6114yes—
729#554C22×C6118yes—
730#554C22×C6118yes—
731#554C22×C6118yes—
732#554C22×C6114yescomplemented
733#554C22×C6114yescomplemented
734#554C22×C6114yescomplemented
735#554C22×C6114yescomplemented
736#553C22×C6114yes—
737#553C22×C6114yes—
738#553C22×C6114yes—
739#553C22×C6114yes—
740#553C22×C6118yes—
741#553C22×C6118yes—
742#553C22×C6118yes—
743#553C22×C6114yescomplemented
744#553C22×C6114yescomplemented
745#552C22×C6114yes—
746#552C22×C6114yes—
747#552C22×C6114yes—
748#552C22×C6114yes—
749#552C22×C6118yes—
750#552C22×C6114yescomplemented
751#552C22×C6114yescomplemented
752#552C22×C6118yescomplemented
753#552C22×C6118yescomplemented
754D4×Q8C22×C6118yes—
755D4×Q8C22×C6114yescomplemented
756D4×Q8C22×C6114yescomplemented
757#548C22×C6118yes—
758#548C22×C6118yes—
759#547C22×C6114yes—
760#547C22×C6114yes—
761#547C22×C6118yes—
762#547C22×C6114yescomplemented
763#547C22×C6114yescomplemented
764#544C22×C6114yes—
765#544C22×C6114yes—
766#544C22×C6114yes—
767#544C22×C6114yes—
768#544C22×C6112yes—
769#544C22×C6111yescharacteristic
770#544C22×C6111yescharacteristic
771#544C22×C6114yescomplemented
772#544C22×C6114yescomplemented
773#544C22×C6114yescomplemented
774#544C22×C6114yescomplemented
775#544C22×C6118yescomplemented
776#542C22×C6112yes—
777#542C22×C6112yes—
778#542C22×C6112yes—
779#542C22×C6112yes—
780#542C22×C6118yes—
781#542C22×C6118yes—
782#542C22×C6118yes—
783#542C22×C6114yescomplemented
784#542C22×C6114yescomplemented
785#542C22×C6118yescomplemented
786#541C22×C6112yes—
787#541C22×C6112yes—
788#541C22×C6118yes—
789#541C22×C6114yescomplemented
790#541C22×C6118yescomplemented
791#541C22×C6118yescomplemented
792#541C22×C6118yescomplemented
793#540C22×C6112yes—
794#540C22×C6112yes—
795#540C22×C6114yescomplemented
796#539C22×C6114yes—
797#539C22×C6114yes—
798#539C22×C6118yes—
799#539C22×C6118yes—
800#539C22×C6118yes—
801#539C22×C6118yescomplemented
802#539C22×C6118yescomplemented
803#538C22×C6114yes—
804#538C22×C6114yes—
805#538C22×C6114yes—
806#538C22×C6114yes—
807#537C22×C6112yes—
808#537C22×C6111yescharacteristic
809#537C22×C6111yescharacteristic
810#537C22×C6118yes—
811#536C22×C6118yes—
812#536C22×C6118yescomplemented
813#533C22×C6112yes—
814#533C22×C6114yescomplemented
815#533C22×C6114yescomplemented
816#533C22×C6114yescomplemented
817#532C22×C6112yes—
818#532C22×C6114yescomplemented
819C2×C4⋊Q8C22×C6112yes—
820C2×C4⋊Q8C22×C6112yes—
821C2×C4⋊Q8C22×C6114yescomplemented
822#529C22×C6114yes—
823#529C22×C6114yes—
824#529C22×C6114yes—
825#529C22×C6114yes—
826#529C22×C6114yes—
827#529C22×C6114yes—
828#529C22×C6114yescomplemented
829#529C22×C6114yescomplemented
830C2×#125C22×C6112yes—
831C2×#125C22×C6112yes—
832C2×#125C22×C6114yescomplemented
833#525C22×C6112yes—
834#525C22×C6112yes—
835#525C22×C6118yes—
836C2×C22⋊Q8C22×C6114yes—
837#520C22×C6112yes—
838#520C22×C6112yes—
839#520C22×C6112yes—
840#520C22×C6112yes—
841C4×#41C22×C6112yes—
842C4×#41C22×C6112yes—
843C2×#117C22×C6111yescharacteristic
844C2×#117C22×C6111yescharacteristic
845C22×C4⋊C4C22×C6111yescharacteristic
846C61#6287711yescharacteristic, direct product factor, Sylow
847C2×#41C23×C6112yes—
848C2×#41C23×C6112yes—
849C2×#41C23×C6118yes—
850C2×#41C23×C6118yes—
851C22×Q8C23×C6114yes—
852C22×Q8C23×C6118yes—
853C23×C4C23×C6111yescharacteristic
854C23×C4C23×C6112yes—
855C4⋊Q8C23×C6114yes—
856C4⋊Q8C23×C6114yes—
857C4⋊Q8C23×C6118yes—
858C4⋊Q8C23×C6114yes—
859C4⋊Q8C23×C6114yes—
860C4⋊Q8C23×C6114yes—
861C4⋊Q8C23×C6114yes—
862C4⋊Q8C23×C6112yes—
863C4⋊Q8C23×C6118yes—
864C4⋊Q8C23×C6118yes—
865C4⋊Q8C23×C6114yes—
866C4⋊Q8C23×C6114yes—
867C4⋊Q8C23×C6112yes—
868C4⋊Q8C23×C6112yes—
869C4⋊Q8C23×C6114yes—
870C4⋊Q8C23×C6114yes—
871C4⋊Q8C23×C6118yes—
872C4⋊Q8C23×C6118yes—
873C4⋊Q8C23×C6118yes—
874C4⋊Q8C23×C6118yes—
875#127C23×C6112yes—
876#126C23×C6114yes—
877#126C23×C6114yes—
878#126C23×C6114yes—
879#126C23×C6114yes—
880#126C23×C6114yes—
881#126C23×C6114yes—
882#126C23×C6114yes—
883#126C23×C6114yes—
884#126C23×C6118yes—
885#126C23×C6118yes—
886#126C23×C6118yes—
887#126C23×C6118yes—
888#126C23×C6118yes—
889#126C23×C6118yes—
890#126C23×C6118yes—
891#126C23×C6118yes—
892#126C23×C6118yes—
893#126C23×C6118yes—
894#126C23×C6118yes—
895#126C23×C6118yes—
896#125C23×C6114yes—
897#125C23×C6114yes—
898#125C23×C6118yes—
899#125C23×C6114yes—
900#125C23×C6114yes—
901#125C23×C6114yes—
902#125C23×C6114yes—
903#125C23×C6112yes—
904#125C23×C6118yes—
905#125C23×C6118yes—
906#125C23×C6114yes—
907#125C23×C6114yes—
908#125C23×C6114yes—
909#125C23×C6114yes—
910#125C23×C6114yes—
911#125C23×C6114yes—
912#125C23×C6114yes—
913#125C23×C6114yes—
914#125C23×C6112yes—
915#125C23×C6118yes—
916#125C23×C6114yes—
917#125C23×C6114yes—
918#125C23×C6118yes—
919#125C23×C6118yes—
920#125C23×C6118yes—
921#125C23×C6118yes—
922#125C23×C6118yes—
923#125C23×C6118yes—
924#125C23×C6118yes—
925#125C23×C6118yes—
926#124C23×C6114yes—
927#124C23×C6114yes—
928#124C23×C6114yes—
929#124C23×C6114yes—
930#124C23×C6114yes—
931#124C23×C6114yes—
932#124C23×C6112yes—
933#124C23×C6112yes—
934#124C23×C6118yes—
935#124C23×C6118yes—
936#124C23×C6118yes—
937#124C23×C6118yes—
938#124C23×C6118yes—
939#123C23×C6114yes—
940#123C23×C6114yes—
941#123C23×C6118yes—
942#123C23×C6118yes—
943#123C23×C6114yes—
944#123C23×C6114yes—
945#123C23×C6114yes—
946#123C23×C6114yes—
947#123C23×C6114yes—
948#123C23×C6114yes—
949#123C23×C6114yes—
950#123C23×C6114yes—
951#123C23×C6118yes—
952#123C23×C6118yes—
953#123C23×C6118yes—
954#123C23×C6118yes—
955#123C23×C6118yes—
956#123C23×C6118yes—
957#123C23×C6118yes—
958#123C23×C6118yes—
959#123C23×C6118yes—
960#123C23×C6118yes—
961C22⋊Q8C23×C6118yes—
962C22⋊Q8C23×C6118yes—
963C22⋊Q8C23×C6118yes—
964C22⋊Q8C23×C6118yes—
965C22⋊Q8C23×C6118yes—
966C22⋊Q8C23×C6118yes—
967C22⋊Q8C23×C6112yes—
968C22⋊Q8C23×C6112yes—
969C22⋊Q8C23×C6112yes—
970C22⋊Q8C23×C6112yes—
971C22⋊Q8C23×C6114yes—
972C22⋊Q8C23×C6114yes—
973C22⋊Q8C23×C6114yes—
974C22⋊Q8C23×C6114yes—
975C22⋊Q8C23×C6114yes—
976C22⋊Q8C23×C6114yes—
977C22⋊Q8C23×C6114yes—
978C22⋊Q8C23×C6114yes—
979C22⋊Q8C23×C6114yes—
980C22⋊Q8C23×C6114yes—
981C22⋊Q8C23×C6118yes—
982C22⋊Q8C23×C6114yes—
983C22⋊Q8C23×C6114yes—
984C22⋊Q8C23×C6118yes—
985C22⋊Q8C23×C6118yes—
986C22⋊Q8C23×C6118yes—
987C22⋊Q8C23×C6118yes—
988C22⋊Q8C23×C6118yes—
989C22⋊Q8C23×C6118yes—
990C22⋊Q8C23×C6118yes—
991C22⋊Q8C23×C6118yes—
992C22⋊Q8C23×C6118yes—
993C22⋊Q8C23×C6118yes—
994C22⋊Q8C23×C6118yes—
995C22⋊Q8C23×C6118yes—
996C22⋊Q8C23×C6118yes—
997C22⋊Q8C23×C6118yes—
998C22⋊Q8C23×C6118yes—
999C22⋊Q8C23×C6118yes—
1000#121C23×C6118yes—
1001#121C23×C6118yes—
1002#121C23×C6112yes—
1003#121C23×C6112yes—
1004#121C23×C6112yes—
1005#121C23×C6112yes—
1006#121C23×C6114yes—
1007#121C23×C6114yes—
1008#121C23×C6114yes—
1009#121C23×C6114yes—
1010#121C23×C6114yes—
1011#121C23×C6114yes—
1012#121C23×C6114yes—
1013#121C23×C6114yes—
1014#121C23×C6114yes—
1015#121C23×C6114yes—
1016#121C23×C6118yes—
1017#121C23×C6114yes—
1018#121C23×C6114yes—
1019#121C23×C6118yes—
1020#121C23×C6118yes—
1021#121C23×C6118yes—
1022#121C23×C6118yes—
1023#120C23×C6114yes—
1024#120C23×C6114yes—
1025C4×Q8C23×C6112yes—
1026C4×Q8C23×C6112yes—
1027C4×Q8C23×C6112yes—
1028C4×Q8C23×C6112yes—
1029C4×Q8C23×C6114yes—
1030C4×Q8C23×C6114yes—
1031C4×Q8C23×C6114yes—
1032C4×Q8C23×C6114yes—
1033C4×Q8C23×C6114yes—
1034C4×Q8C23×C6114yes—
1035C4×Q8C23×C6114yes—
1036C4×Q8C23×C6114yes—
1037C4×Q8C23×C6118yes—
1038C4×Q8C23×C6118yes—
1039C4×Q8C23×C6118yes—
1040C4×Q8C23×C6118yes—
1041C4×Q8C23×C6118yes—
1042C4×D4C23×C6114yes—
1043C4×D4C23×C6114yes—
1044C4×D4C23×C6114yes—
1045C4×D4C23×C6114yes—
1046C4×D4C23×C6112yes—
1047C4×D4C23×C6112yes—
1048C4×D4C23×C6112yes—
1049C4×D4C23×C6112yes—
1050C4×D4C23×C6118yes—
1051C4×D4C23×C6118yes—
1052C4×D4C23×C6118yes—
1053C4×D4C23×C6118yes—
1054C4×D4C23×C6114yes—
1055C4×D4C23×C6114yes—
1056C4×D4C23×C6114yes—
1057C4×D4C23×C6114yes—
1058C4×D4C23×C6114yes—
1059C4×D4C23×C6114yes—
1060C4×D4C23×C6114yes—
1061C4×D4C23×C6114yes—
1062C4×D4C23×C6118yes—
1063C4×D4C23×C6118yes—
1064C4×D4C23×C6114yes—
1065C4×D4C23×C6114yes—
1066C4×D4C23×C6114yes—
1067C4×D4C23×C6114yes—
1068C4×D4C23×C6118yes—
1069C4×D4C23×C6118yes—
1070C4×D4C23×C6118yes—
1071#117C23×C6112yes—
1072#117C23×C6112yes—
1073#117C23×C6112yes—
1074#117C23×C6112yes—
1075#117C23×C6114yes—
1076#117C23×C6114yes—
1077#117C23×C6112yes—
1078#117C23×C6112yes—
1079#117C23×C6114yes—
1080#117C23×C6114yes—
1081#117C23×C6114yes—
1082#117C23×C6114yes—
1083#117C23×C6114yes—
1084#117C23×C6114yes—
1085#117C23×C6118yes—
1086#117C23×C6118yes—
1087#117C23×C6118yes—
1088#117C23×C6118yes—
1089#117C23×C6118yes—
1090#117C23×C6118yes—
1091C2×C4⋊C4C23×C6112yes—
1092C2×C4⋊C4C23×C6112yes—
1093C2×C4⋊C4C23×C6114yes—
1094C2×C4⋊C4C23×C6114yes—
1095C2×C4⋊C4C23×C6111yescharacteristic
1096C2×C4⋊C4C23×C6111yescharacteristic
1097C2×C4⋊C4C23×C6111yescharacteristic
1098C2×C4⋊C4C23×C6111yescharacteristic
1099C2×C4⋊C4C23×C6114yes—
1100C2×C4⋊C4C23×C6114yes—
1101C2×C4⋊C4C23×C6114yes—
1102C2×C4⋊C4C23×C6114yes—
1103C2×C4⋊C4C23×C6114yes—
1104C2×C4⋊C4C23×C6114yes—
1105C2×C4⋊C4C23×C6114yes—
1106C2×C4⋊C4C23×C6118yes—
1107C2×C4⋊C4C23×C6118yes—
1108C2×C4⋊C4C23×C6118yes—
1109C2×C22⋊C4C23×C6112yes—
1110C2×C22⋊C4C23×C6112yes—
1111C2×C42C23×C6112yes—
1112C2×C42C23×C6112yes—
1113C2×C42C23×C6114yes—
1114C2×C42C23×C6114yes—
1115C24C24×C6111yescharacteristic
1116#41—28no—
1117#41—28no—
1118#41—88no—
1119#41—88no—
1120C2×Q8—84no—
1121C2×Q8—88no—
1122C2×Q8C24×C6112yes—
1123C2×Q8C24×C6112yes—
1124C2×Q8C24×C6114yes—
1125C2×Q8C24×C6114yes—
1126C2×Q8C24×C6118yes—
1127C2×Q8C24×C6114yes—
1128C2×Q8C24×C6118yes—
1129C2×Q8C24×C6118yes—
1130C2×Q8C24×C6114yes—
1131C2×D4C24×C6114yes—
1132C2×D4C24×C6114yes—
1133C2×D4C24×C6112yes—
1134C2×D4C24×C6112yes—
1135C2×D4C24×C6114yes—
1136C2×D4C24×C6114yes—
1137C2×D4C24×C6114yes—
1138C2×D4C24×C6114yes—
1139C2×D4C24×C6114yes—
1140C2×D4C24×C6114yes—
1141C2×D4C24×C6118yes—
1142C2×D4C24×C6114yes—
1143C2×D4C24×C6114yes—
1144C22×C4—24no—
1145C22×C4—82no—
1146C22×C4C24×C6111yescharacteristic
1147C22×C4C24×C6114yes—
1148C22×C4C24×C6114yes—
1149C22×C4C24×C6112yes—
1150C22×C4C24×C6112yes—
1151C22×C4C24×C6112yes—
1152C22×C4C24×C6112yes—
1153C22×C4C24×C6112yes—
1154C22×C4C24×C6112yes—
1155C22×C4C24×C6114yes—
1156C22×C4C24×C6114yes—
1157C22×C4C24×C6114yes—
1158C22×C4C24×C6114yes—
1159C22×C4C24×C6114yes—
1160C22×C4C24×C6118yes—
1161C22×C4C24×C6118yes—
1162C22×C4C24×C6118yes—
1163C22×C4C24×C6118yes—
1164C22×C4C24×C6118yes—
1165C22×C4C24×C6111yescharacteristic
1166C4⋊C4C24×C6114yes—
1167C4⋊C4C24×C6114yes—
1168C4⋊C4C24×C6112yes—
1169C4⋊C4C24×C6114yes—
1170C4⋊C4C24×C6114yes—
1171C4⋊C4C24×C6114yes—
1172C4⋊C4C24×C6112yes—
1173C4⋊C4C24×C6114yes—
1174C4⋊C4C24×C6112yes—
1175C4⋊C4C24×C6114yes—
1176C4⋊C4C24×C6118yes—
1177C4⋊C4C24×C6118yes—
1178C4⋊C4C24×C6114yes—
1179C4⋊C4C24×C6118yes—
1180C4⋊C4C24×C6114yes—
1181C4⋊C4C24×C6118yes—
1182C4⋊C4C24×C6114yes—
1183C4⋊C4C24×C6111yescharacteristic
1184C4⋊C4C24×C6111yescharacteristic
1185C4⋊C4C24×C6112yes—
1186C4⋊C4C24×C6112yes—
1187C4⋊C4C24×C6111yescharacteristic
1188C4⋊C4C24×C6111yescharacteristic
1189C4⋊C4C24×C6118yes—
1190C4⋊C4C24×C6118yes—
1191C4⋊C4C24×C6118yes—
1192C4⋊C4C24×C6118yes—
1193C4⋊C4C24×C6118yes—
1194C4⋊C4C24×C6118yes—
1195C4⋊C4C24×C6118yes—
1196C4⋊C4C24×C6118yes—
1197C4⋊C4C24×C6118yes—
1198C4⋊C4C24×C6118yes—
1199C4⋊C4C24×C6112yes—
1200C4⋊C4C24×C6114yes—
1201C4⋊C4C24×C6114yes—
1202C4⋊C4C24×C6114yes—
1203C4⋊C4C24×C6118yes—
1204C4⋊C4C24×C6114yes—
1205C4⋊C4C24×C6114yes—
1206C4⋊C4C24×C6114yes—
1207C4⋊C4C24×C6114yes—
1208C4⋊C4C24×C6114yes—
1209C4⋊C4C24×C6114yes—
1210C4⋊C4C24×C6114yes—
1211C4⋊C4C24×C6118yes—
1212C4⋊C4C24×C6114yes—
1213C4⋊C4C24×C6114yes—
1214C4⋊C4C24×C6114yes—
1215C4⋊C4C24×C6114yes—
1216C4⋊C4C24×C6114yes—
1217C4⋊C4C24×C6114yes—
1218C22⋊C4C24×C6112yes—
1219C22⋊C4C24×C6112yes—
1220C22⋊C4C24×C6112yes—
1221C22⋊C4C24×C6118yes—
1222C22⋊C4C24×C6112yes—
1223C22⋊C4C24×C6114yes—
1224C22⋊C4C24×C6114yes—
1225C22⋊C4C24×C6118yes—
1226C22⋊C4C24×C6118yes—
1227C22⋊C4C24×C6118yes—
1228C22⋊C4C24×C6114yes—
1229C22⋊C4C24×C6114yes—
1230C22⋊C4C24×C6114yes—
1231C22⋊C4C24×C6114yes—
1232C22⋊C4C24×C6114yes—
1233C22⋊C4C24×C6114yes—
1234C22⋊C4C24×C6114yes—
1235C22⋊C4C24×C6114yes—
1236C22⋊C4C24×C6118yes—
1237C22⋊C4C24×C6118yes—
1238C22⋊C4C24×C6118yes—
1239C22⋊C4C24×C6118yes—
1240C22⋊C4C24×C6114yes—
1241C22⋊C4C24×C6114yes—
1242C22⋊C4C24×C6114yes—
1243C22⋊C4C24×C6114yes—
1244C22⋊C4C24×C6118yes—
1245C22⋊C4C24×C6114yes—
1246C22⋊C4C24×C6114yes—
1247C22⋊C4C24×C6114yes—
1248C22⋊C4C24×C6114yes—
1249C42C24×C6112yes—
1250C42C24×C6112yes—
1251C42C24×C6114yes—
1252C42C24×C6114yes—
1253C42C24×C6112yes—
1254C42C24×C6112yes—
1255C42C24×C6114yes—
1256C42C24×C6114yes—
1257C42C24×C6114yes—
1258C42C24×C6114yes—
1259C42C24×C6114yes—
1260C42C24×C6114yes—
1261C42C24×C6118yes—
1262C42C24×C6118yes—
1263C42C24×C6118yes—
1264C42C24×C6118yes—
1265C23—22no—
1266C23—41no—
1267C23—41no—
1268C23C25×C6112yes—
1269C23C25×C6114yes—
1270C23C25×C6114yes—
1271C23C25×C6111yescharacteristic
1272Q8—24no—
1273Q8—24no—
1274Q8—48no—
1275Q8—44no—
1276Q8—44no—
1277Q8—48no—
1278Q8—48no—
1279Q8—44no—
1280Q8—44no—
1281D4—28no—
1282D4—28no—
1283D4—24no—
1284D4—24no—
1285D4—44no—
1286D4—44no—
1287D4—44no—
1288D4—44no—
1289D4—44no—
1290D4—48no—
1291D4—44no—
1292D4—44no—
1293D4—44no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—28no—
1298C2×C4—28no—
1299C2×C4—44no—
1300C2×C4—48no—
1301C2×C4—42no—
1302C2×C4—44no—
1303C2×C4—42no—
1304C2×C4—48no—
1305C2×C4—44no—
1306C2×C4—42no—
1307C2×C4—42no—
1308C2×C4—44no—
1309C2×C4—48no—
1310C2×C4—48no—
1311C2×C4—48no—
1312C2×C4—44no—
1313C2×C42−1+4×C6114yes—
1314C2×C4C25×C6114yes—
1315C2×C4C25×C6114yes—
1316C2×C4C25×C6114yes—
1317C2×C4C25×C6111yescharacteristic
1318C2×C4C25×C6111yescharacteristic
1319C2×C4C25×C6112yes—
1320C2×C4C25×C6112yes—
1321C2×C4C25×C6114yes—
1322C2×C4C25×C6114yes—
1323C2×C4C25×C6114yes—
1324C2×C4C25×C6114yes—
1325C2×C4C25×C6112yes—
1326C2×C4C25×C6112yes—
1327C2×C4C25×C6114yes—
1328C2×C4C25×C6118yes—
1329C2×C4C25×C6112yes—
1330C22—21no—
1331C22—21no—
1332C22—22no—
1333C22—24no—
1334C22—24no—
1335C22—24no—
1336C22—22no—
1337C22—24no—
1338C22—24no—
1339C22—24no—
1340C22—22no—
1341C22—44no—
1342C22C2×2−1+4×C6112yes—
1343C22C26×C6111yescharacteristic
1344C4—21no—
1345C4—21no—
1346C4—24no—
1347C4—24no—
1348C4—28no—
1349C4—24no—
1350C4—22no—
1351C4—24no—
1352C4—24no—
1353C4—22no—
1354C4—22no—
1355C4—24no—
1356C4—24no—
1357C4—22no—
1358C4—24no—
1359C4C2×2−1+4×C6114yes—
1360C2—22no—
1361C2—42no—
1362C2—44no—
1363C2—44no—
1364C2C22×2−1+4×C6111yescharacteristic
1365C2C61×H(7,𝔽2)11yescharacteristic
1366C2C61×2−1+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×#3565C2semidirect
2. C61×#3565C2semidirect
3. C61×#3563C2semidirect
4. C61×#3559C2semidirect
5. C61×#3555C2semidirect
6. C61×#3553C2semidirect
7. C61×#3552C2semidirect
8. C61×#3552C2semidirect
9. C61×#3547C2semidirect
10. C61×#3544C2semidirect
11. C61×#3541C2semidirect
12. C61×#3512C2semidirect
13. C61×#3511C2semidirect
14. C61×#3504C2semidirect
15. C61×#3503C2semidirect
16. C61×#3493C2semidirect
17. C61×#3493C2semidirect
18. C61×#3492C2semidirect
19. C2×C61×#544C2semidirect
20. C61×#3455C2semidirect
21. C61×#564C22semidirect
24. C61×#563C22semidirect
25. C61×#563C22semidirect
26. C61×#563C22semidirect
27. C61×#563C22semidirect
30. C61×#562C22semidirect
31. Q82×C61C22semidirect
32. C61×#557C22semidirect
33. C61×#557C22semidirect
34. C61×#557C22semidirect
35. C61×#557C22semidirect
39. C61×#556C22semidirect
40. C61×#556C22semidirect
43. C61×#555C22semidirect
49. C61×#554C22semidirect
50. C61×#554C22semidirect
51. C61×#554C22semidirect
52. C61×#554C22semidirect
60. C61×#553C22semidirect
61. C61×#553C22semidirect
67. C61×#552C22semidirect
68. C61×#552C22semidirect
69. C61×#552C22semidirect
70. C61×#552C22semidirect
72. D4×Q8×C61C22semidirect
73. D4×Q8×C61C22semidirect
79. C61×#547C22semidirect
80. C61×#547C22semidirect
88. C61×#544C22semidirect
89. C61×#544C22semidirect
90. C61×#544C22semidirect
91. C61×#544C22semidirect
92. C61×#544C22semidirect
100. C61×#542C22semidirect
101. C61×#542C22semidirect
102. C61×#542C22semidirect
106. C61×#541C22semidirect
107. C61×#541C22semidirect
108. C61×#541C22semidirect
109. C61×#541C22semidirect
112. C61×#540C22semidirect
118. C61×#539C22semidirect
119. C61×#539C22semidirect
129. C61×#536C22semidirect
131. C61×#533C22semidirect
132. C61×#533C22semidirect
133. C61×#533C22semidirect
135. C61×#532C22semidirect
138. C2×C4⋊Q8×C61C22semidirect
145. C61×#529C22semidirect
146. C61×#529C22semidirect
149. C2×#125×C61C22semidirect
646. #62877C61direct (N × H)
677. #3565C2×C61semidirect
678. #3565C2×C61semidirect
679. #3563C2×C61semidirect
680. #3559C2×C61semidirect
681. #3555C2×C61semidirect
682. #3553C2×C61semidirect
683. #3552C2×C61semidirect
684. #3552C2×C61semidirect
685. #3547C2×C61semidirect
686. #3544C2×C61semidirect
687. #3541C2×C61semidirect
688. #3512C2×C61semidirect
689. #3511C2×C61semidirect
690. #3504C2×C61semidirect
691. #3503C2×C61semidirect
692. #3493C2×C61semidirect
693. #3493C2×C61semidirect
694. #3492C2×C61semidirect
695. C2×#544C2×C61semidirect
696. #3455C2×C61semidirect
704. #564C22×C61semidirect
707. #563C22×C61semidirect
708. #563C22×C61semidirect
709. #563C22×C61semidirect
710. #563C22×C61semidirect
713. #562C22×C61semidirect
714. Q82C22×C61semidirect
715. #557C22×C61semidirect
716. #557C22×C61semidirect
717. #557C22×C61semidirect
718. #557C22×C61semidirect
722. #556C22×C61semidirect
723. #556C22×C61semidirect
726. #555C22×C61semidirect
732. #554C22×C61semidirect
733. #554C22×C61semidirect
734. #554C22×C61semidirect
735. #554C22×C61semidirect
743. #553C22×C61semidirect
744. #553C22×C61semidirect
750. #552C22×C61semidirect
751. #552C22×C61semidirect
752. #552C22×C61semidirect
753. #552C22×C61semidirect
755. D4×Q8C22×C61semidirect
756. D4×Q8C22×C61semidirect
762. #547C22×C61semidirect
763. #547C22×C61semidirect
771. #544C22×C61semidirect
772. #544C22×C61semidirect
773. #544C22×C61semidirect
774. #544C22×C61semidirect
775. #544C22×C61semidirect
783. #542C22×C61semidirect
784. #542C22×C61semidirect
785. #542C22×C61semidirect
789. #541C22×C61semidirect
790. #541C22×C61semidirect
791. #541C22×C61semidirect
792. #541C22×C61semidirect
795. #540C22×C61semidirect
801. #539C22×C61semidirect
802. #539C22×C61semidirect
812. #536C22×C61semidirect
814. #533C22×C61semidirect
815. #533C22×C61semidirect
816. #533C22×C61semidirect
818. #532C22×C61semidirect
821. C2×C4⋊Q8C22×C61semidirect
828. #529C22×C61semidirect
829. #529C22×C61semidirect
832. C2×#125C22×C61semidirect
846. C61#62877direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35652
C61×#35632
C61×#35592
C61×#35552
C61×#35532
C61×#35522
C61×#35472
C61×#35442
C61×#35412
C61×#35122
C61×#35112
C61×#35042
C61×#35032
C61×#34932
C61×#34922
C2×C61×#5442
C61×#34552
#6287761