Finite Group Databasebeta

← C61×#62889 #29566322

Subgroups — C61×#62889 #29566322

Order 15616.

6186 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3564C218yesmaximal, complemented
2C61×#3563C218yesmaximal, complemented
3C61×#3563C218yesmaximal, complemented
4C61×#3557C214yesmaximal, complemented
5C61×#3556C214yesmaximal, complemented
6C61×#3555C218yesmaximal, complemented
7C61×#3555C218yesmaximal, complemented
8C61×#3509C212yesmaximal, complemented
9C61×#3507C212yesmaximal, complemented
10C61×#3504C212yesmaximal, complemented
11C61×#3502C212yesmaximal, complemented
12C61×#3495C214yesmaximal, complemented
13C61×#3458C211yesmaximal, characteristic, complemented
14C61×#3455C211yesmaximal, characteristic
15C2×C61×#541C211yesmaximal, characteristic, complemented
16C61×#564C22116yescomplemented
17C61×#563C22116yes—
18C61×#563C22116yes—
19C61×#563C22116yescomplemented
20C61×#559C2214yescomplemented
21Q82×C61C2214yescomplemented
22Q82×C61C2214yescomplemented
23C61×#557C2214yescomplemented
24C61×#557C22116yescomplemented
25C61×#557C2218yescomplemented
26C61×#557C2218yescomplemented
27C61×#557C2218yescomplemented
28C61×#557C2214yescomplemented
29C61×#557C2218yescomplemented
30C61×#557C2214yescomplemented
31C61×#556C22116yes—
32C61×#556C2218yes—
33C61×#556C2214yescomplemented
34C61×#556C2218yescomplemented
35C61×#556C2218yescomplemented
36C61×#554C2218yes—
37C61×#554C22116yes—
38C61×#554C2218yescomplemented
39C61×#554C2214yescomplemented
40C61×#552C22116yes—
41C61×#552C2218yes—
42C61×#552C2218yes—
43C61×#552C22116yes—
44C61×#552C22116yes—
45C61×#552C2218yescomplemented
46C61×#552C22116yescomplemented
47C61×#551C22116yes—
48C61×#544C2214yes—
49C61×#544C2214yes—
50C61×#544C2214yes—
51C61×#544C2218yes—
52C61×#544C2214yes—
53C61×#544C22116yescomplemented
54C61×#544C2218yescomplemented
55C61×#543C2214yes—
56C61×#542C2214yes—
57C61×#542C22116yes—
58C61×#542C2218yes—
59C61×#541C2214yes—
60C61×#541C22116yes—
61C61×#541C2218yes—
62C61×#541C2218yes—
63C61×#541C2212yes—
64C61×#541C2214yes—
65C61×#541C22116yes—
66C61×#541C22116yescomplemented
67C61×#541C22116yescomplemented
68C61×#541C2214yescomplemented
69C61×#541C22116yescomplemented
70C61×#541C2214yescomplemented
71C61×#540C2212yes—
72C61×#539C22116yes—
73C61×#539C2214yes—
74C61×#539C2218yes—
75C61×#538C2214yes—
76C61×#536C2214yes—
77C61×#533C2214yes—
78C61×#533C2218yes—
79C61×#533C2214yes—
80C61×#533C2218yes—
81C61×#533C2211yescharacteristic
82C61×#533C2212yes—
83C61×#533C2212yes—
84C61×#533C2214yescomplemented
85C61×#533C2218yescomplemented
86C61×#532C2211yescharacteristic
87C2×C4⋊Q8×C61C2211yescharacteristic
88C61×#529C2218yes—
89C61×#529C2218yes—
90C61×#529C2218yes—
91C2×#126×C61C2214yes—
92C2×#125×C61C2214yes—
93C2×#125×C61C2211yescharacteristic
94C2×#125×C61C2214yescomplemented
95C61×#525C2212yes—
96C2×C22⋊Q8×C61C2212yes—
97C61×#520C2214yes—
98C61×#519C2214yes—
99C4×#41×C61C2212yes—
100C2×C4×Q8×C61C2212yes—
101C2×#117×C61C2211yescharacteristic
102C2×#117×C61C2212yes—
103C2×#41×C61C2312yes—
104C22×Q8×C61C2312yes—
105C23×C4×C61C2311yescharacteristic
106C4⋊Q8×C61C2314yes—
107C4⋊Q8×C61C2314yes—
108C4⋊Q8×C61C2311yescharacteristic
109C4⋊Q8×C61C2314yes—
110C4⋊Q8×C61C2318yes—
111C4⋊Q8×C61C2318yes—
112C4⋊Q8×C61C2318yes—
113C4⋊Q8×C61C2312yes—
114C4⋊Q8×C61C2318yes—
115C4⋊Q8×C61C2312yes—
116C4⋊Q8×C61C2312yes—
117C4⋊Q8×C61C2318yes—
118C4⋊Q8×C61C2318yes—
119C4⋊Q8×C61C2318yes—
120C4⋊Q8×C61C23116yes—
121C4⋊Q8×C61C23116yes—
122C4⋊Q8×C61C23116yes—
123#127×C61C2311yescharacteristic
124#126×C61C2318yes—
125#126×C61C23116yes—
126#126×C61C2318yes—
127#126×C61C23116yes—
128#126×C61C23116yes—
129#126×C61C23116yes—
130#126×C61C23116yes—
131#126×C61C23116yes—
132#126×C61C23116yes—
133#126×C61C23116yes—
134#126×C61C23116yes—
135#126×C61C23116yes—
136#125×C61C2312yes—
137#125×C61C23116yes—
138#125×C61C2312yes—
139#125×C61C2318yes—
140#125×C61C2312yes—
141#125×C61C23116yes—
142#125×C61C2314yes—
143#125×C61C2318yes—
144#125×C61C2314yes—
145#125×C61C23116yes—
146#125×C61C23116yes—
147#125×C61C23116yes—
148#125×C61C2318yes—
149#125×C61C23116yes—
150#125×C61C23116yes—
151#125×C61C2314yes—
152#125×C61C2318yes—
153#125×C61C23116yes—
154#125×C61C23116yes—
155#125×C61C23116yes—
156#125×C61C23116yes—
157#125×C61C23116yes—
158#125×C61C23116yes—
159#125×C61C2318yes—
160#125×C61C23116yes—
161#125×C61C2318yes—
162#124×C61C2312yes—
163#124×C61C2318yes—
164#124×C61C2318yes—
165#124×C61C23116yes—
166#124×C61C2318yes—
167#123×C61C23116yes—
168#123×C61C2318yes—
169#123×C61C23116yes—
170#123×C61C23116yes—
171#123×C61C2314yes—
172#123×C61C2318yes—
173#123×C61C23116yes—
174C22⋊Q8×C61C2314yes—
175C22⋊Q8×C61C2314yes—
176C22⋊Q8×C61C2314yes—
177C22⋊Q8×C61C2318yes—
178C22⋊Q8×C61C2318yes—
179C22⋊Q8×C61C2318yes—
180C22⋊Q8×C61C23116yes—
181C22⋊Q8×C61C2314yes—
182C22⋊Q8×C61C2318yes—
183C22⋊Q8×C61C2318yes—
184C22⋊Q8×C61C2318yes—
185C22⋊Q8×C61C23116yes—
186C22⋊Q8×C61C2318yes—
187C22⋊Q8×C61C2318yes—
188C22⋊Q8×C61C23116yes—
189C22⋊Q8×C61C23116yes—
190C22⋊Q8×C61C2318yes—
191C22⋊Q8×C61C23116yes—
192C22⋊Q8×C61C23116yes—
193C22⋊Q8×C61C2318yes—
194C22⋊Q8×C61C23116yes—
195C22⋊Q8×C61C23116yes—
196#121×C61C2314yes—
197#121×C61C2318yes—
198#121×C61C2314yes—
199#120×C61C2314yes—
200C4×Q8×C61C2318yes—
201C4×Q8×C61C2314yes—
202C4×Q8×C61C2314yes—
203C4×Q8×C61C23116yes—
204C4×Q8×C61C2318yes—
205C4×Q8×C61C2318yes—
206C4×Q8×C61C23116yes—
207C4×Q8×C61C2318yes—
208C4×Q8×C61C2318yes—
209C4×Q8×C61C2314yes—
210C4×Q8×C61C23116yes—
211C4×Q8×C61C23116yes—
212C4×Q8×C61C2318yes—
213C4×Q8×C61C2318yes—
214C4×Q8×C61C2314yes—
215C4×Q8×C61C2314yes—
216C4×Q8×C61C2314yes—
217C4×Q8×C61C2318yes—
218C4×Q8×C61C2314yes—
219C4×Q8×C61C2314yes—
220C4×Q8×C61C2318yes—
221C4×D4×C61C2314yes—
222C4×D4×C61C2318yes—
223C4×D4×C61C2318yes—
224C4×D4×C61C23116yes—
225C4×D4×C61C23116yes—
226C4×D4×C61C2314yes—
227C4×D4×C61C2318yes—
228C4×D4×C61C2318yes—
229#117×C61C2314yes—
230#117×C61C2312yes—
231#117×C61C2312yes—
232#117×C61C2314yes—
233#117×C61C23116yes—
234#117×C61C2312yes—
235#117×C61C23116yes—
236#117×C61C23116yes—
237#117×C61C2318yes—
238#117×C61C2314yes—
239#117×C61C2314yes—
240#117×C61C23116yes—
241#117×C61C23116yes—
242#117×C61C2312yes—
243#117×C61C2314yes—
244#117×C61C2312yes—
245C2×C4⋊C4×C61C2314yes—
246C2×C4⋊C4×C61C2312yes—
247C2×C4⋊C4×C61C2314yes—
248C2×C4⋊C4×C61C23116yes—
249C2×C4⋊C4×C61C2314yes—
250C2×C4⋊C4×C61C2312yes—
251C2×C4⋊C4×C61C2318yes—
252C2×C4⋊C4×C61C2314yes—
253C2×C4⋊C4×C61C2314yes—
254C2×C22⋊C4×C61C2312yes—
255C2×C22⋊C4×C61C2314yes—
256C2×C22⋊C4×C61C2314yes—
257C2×C42×C61C2311yescharacteristic
258C2×C42×C61C2311yescharacteristic
259C2×C42×C61C2314yes—
260C2×C42×C61C2314yes—
261C2×C42×C61C2314yes—
262C24×C61C2411yescharacteristic
263#41×C61—28no—
264C2×Q8×C61—28no—
265C2×Q8×C61C2414yes—
266C2×Q8×C61C2414yes—
267C2×Q8×C61C2412yes—
268C2×Q8×C61C2418yes—
269C2×Q8×C61C2414yes—
270C2×Q8×C61C24116yes—
271C2×Q8×C61C2414yes—
272C2×Q8×C61C2414yes—
273C2×D4×C61C2414yes—
274C2×D4×C61C2412yes—
275C2×D4×C61C2418yes—
276C2×D4×C61C2414yes—
277C22×C4×C61—24no—
278C22×C4×C61C2412yes—
279C22×C4×C61C2414yes—
280C22×C4×C61C2414yes—
281C22×C4×C61C2411yescharacteristic
282C22×C4×C61C2412yes—
283C22×C4×C61C2412yes—
284C22×C4×C61C2412yes—
285C22×C4×C61C2414yes—
286C22×C4×C61C2418yes—
287C22×C4×C61C2418yes—
288C22×C4×C61C24116yes—
289C22×C4×C61C2411yescharacteristic
290C4⋊C4×C61C2414yes—
291C4⋊C4×C61C2414yes—
292C4⋊C4×C61C2418yes—
293C4⋊C4×C61C24116yes—
294C4⋊C4×C61C2414yes—
295C4⋊C4×C61C2414yes—
296C4⋊C4×C61C2418yes—
297C4⋊C4×C61C2414yes—
298C4⋊C4×C61C24116yes—
299C4⋊C4×C61C24116yes—
300C4⋊C4×C61C24116yes—
301C4⋊C4×C61C24116yes—
302C4⋊C4×C61C2414yes—
303C4⋊C4×C61C24116yes—
304C4⋊C4×C61C2418yes—
305C4⋊C4×C61C2418yes—
306C4⋊C4×C61C2418yes—
307C4⋊C4×C61C2418yes—
308C4⋊C4×C61C24116yes—
309C4⋊C4×C61C2414yes—
310C4⋊C4×C61C2418yes—
311C4⋊C4×C61C24116yes—
312C4⋊C4×C61C24116yes—
313C4⋊C4×C61C2414yes—
314C4⋊C4×C61C2414yes—
315C4⋊C4×C61C24116yes—
316C4⋊C4×C61C2418yes—
317C4⋊C4×C61C2418yes—
318C4⋊C4×C61C2418yes—
319C4⋊C4×C61C2418yes—
320C4⋊C4×C61C2414yes—
321C4⋊C4×C61C24116yes—
322C4⋊C4×C61C2414yes—
323C22⋊C4×C61C2418yes—
324C22⋊C4×C61C2414yes—
325C22⋊C4×C61C2414yes—
326C22⋊C4×C61C2414yes—
327C22⋊C4×C61C2414yes—
328C22⋊C4×C61C24116yes—
329C22⋊C4×C61C2414yes—
330C22⋊C4×C61C2418yes—
331C22⋊C4×C61C2418yes—
332C22⋊C4×C61C2418yes—
333C22⋊C4×C61C24116yes—
334C22⋊C4×C61C24116yes—
335C22⋊C4×C61C2418yes—
336C22⋊C4×C61C24116yes—
337C42×C61C2412yes—
338C42×C61C2414yes—
339C42×C61C2412yes—
340C42×C61C2414yes—
341C42×C61C2412yes—
342C42×C61C2418yes—
343C42×C61C2411yescharacteristic
344C42×C61C2411yescharacteristic
345C42×C61C2418yes—
346C42×C61C2414yes—
347C42×C61C2418yes—
348C42×C61C2418yes—
349C42×C61C24116yes—
350C42×C61C24116yes—
351C42×C61C24116yes—
352C23×C61—22no—
353C23×C61—42no—
354C23×C61C2512yes—
355C23×C61C2514yes—
356C23×C61C2511yescharacteristic
357Q8×C61—28no—
358Q8×C61—28no—
359Q8×C61—24no—
360Q8×C61—48no—
361Q8×C61—44no—
362Q8×C61—416no—
363Q8×C61—44no—
364Q8×C61—44no—
365D4×C61—28no—
366D4×C61—24no—
367D4×C61—44no—
368D4×C61—48no—
369C2×C4×C61—22no—
370C2×C4×C61—28no—
371C2×C4×C61—24no—
372C2×C4×C61—24no—
373C2×C4×C61—28no—
374C2×C4×C61—42no—
375C2×C4×C61—44no—
376C2×C4×C61—416no—
377C2×C4×C61—48no—
378C2×C4×C61—48no—
379C2×C4×C61—42no—
380C2×C4×C612−1+414yes—
381C2×C4×C61C2518yes—
382C2×C4×C61C2512yes—
383C2×C4×C61C2518yes—
384C2×C4×C61C2514yes—
385C2×C4×C61C2518yes—
386C2×C4×C61C2512yes—
387C2×C4×C61C2512yes—
388C2×C4×C61C2514yes—
389C2×C4×C61C2518yes—
390C2×C4×C61C2518yes—
391C2×C4×C61C2511yescharacteristic
392C2×C4×C61C2511yescharacteristic
393#62889C6111yesmaximal, characteristic, direct product factor, Sylow
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—24no—
397C22×C61—28no—
398C22×C61—24no—
399C22×C61—82no—
400C22×C61C2×2−1+412yes—
401C22×C61C2611yescharacteristic
402C4×C61—22no—
403C4×C61—24no—
404C4×C61—28no—
405C4×C61—28no—
406C4×C61—24no—
407C4×C61—28no—
408C4×C61—22no—
409C4×C61—28no—
410C4×C61—28no—
411C4×C61—22no—
412C4×C61C2×2−1+412yes—
413C4×C61C2×2−1+412yes—
414#3564C2×C6118yescomplemented
415#3563C2×C6118yescomplemented
416#3563C2×C6118yescomplemented
417#3557C2×C6114yescomplemented
418#3556C2×C6114yescomplemented
419#3555C2×C6118yescomplemented
420#3555C2×C6118yescomplemented
421#3509C2×C6112yescomplemented
422#3507C2×C6112yescomplemented
423#3504C2×C6112yescomplemented
424#3502C2×C6112yescomplemented
425#3495C2×C6114yescomplemented
426#3458C2×C6111yescharacteristic, complemented
427#3455C2×C6111yescharacteristic
428C2×#541C2×C6111yescharacteristic, complemented
429C2×C61—22no—
430C2×C61—44no—
431C2×C61—42no—
432C2×C61C22×2−1+411yescharacteristic
433C2×C612−1+612yes—
434#564C22×C61116yescomplemented
435#563C22×C61116yes—
436#563C22×C61116yes—
437#563C22×C61116yescomplemented
438#559C22×C6114yescomplemented
439Q82C22×C6114yescomplemented
440Q82C22×C6114yescomplemented
441#557C22×C6114yescomplemented
442#557C22×C6118yescomplemented
443#557C22×C6118yescomplemented
444#557C22×C6114yescomplemented
445#557C22×C6118yescomplemented
446#557C22×C6114yescomplemented
447#557C22×C6118yescomplemented
448#557C22×C61116yescomplemented
449#556C22×C6118yes—
450#556C22×C61116yes—
451#556C22×C6114yescomplemented
452#556C22×C6118yescomplemented
453#556C22×C6118yescomplemented
454#554C22×C6118yes—
455#554C22×C61116yes—
456#554C22×C6118yescomplemented
457#554C22×C6114yescomplemented
458#552C22×C6118yes—
459#552C22×C6118yes—
460#552C22×C61116yes—
461#552C22×C61116yes—
462#552C22×C61116yes—
463#552C22×C6118yescomplemented
464#552C22×C61116yescomplemented
465#551C22×C61116yes—
466#544C22×C6114yes—
467#544C22×C6114yes—
468#544C22×C6114yes—
469#544C22×C6114yes—
470#544C22×C6118yes—
471#544C22×C6118yescomplemented
472#544C22×C61116yescomplemented
473#543C22×C6114yes—
474#542C22×C6114yes—
475#542C22×C6118yes—
476#542C22×C61116yes—
477#541C22×C6114yes—
478#541C22×C6118yes—
479#541C22×C6114yes—
480#541C22×C6112yes—
481#541C22×C6118yes—
482#541C22×C61116yes—
483#541C22×C61116yes—
484#541C22×C6114yescomplemented
485#541C22×C6114yescomplemented
486#541C22×C61116yescomplemented
487#541C22×C61116yescomplemented
488#541C22×C61116yescomplemented
489#540C22×C6112yes—
490#539C22×C6114yes—
491#539C22×C6118yes—
492#539C22×C61116yes—
493#538C22×C6114yes—
494#536C22×C6114yes—
495#533C22×C6111yescharacteristic
496#533C22×C6112yes—
497#533C22×C6112yes—
498#533C22×C6114yes—
499#533C22×C6114yes—
500#533C22×C6118yes—
501#533C22×C6118yes—
502#533C22×C6114yescomplemented
503#533C22×C6118yescomplemented
504#532C22×C6111yescharacteristic
505C2×C4⋊Q8C22×C6111yescharacteristic
506#529C22×C6118yes—
507#529C22×C6118yes—
508#529C22×C6118yes—
509C2×#126C22×C6114yes—
510C2×#125C22×C6111yescharacteristic
511C2×#125C22×C6114yes—
512C2×#125C22×C6114yescomplemented
513#525C22×C6112yes—
514C2×C22⋊Q8C22×C6112yes—
515#520C22×C6114yes—
516#519C22×C6114yes—
517C4×#41C22×C6112yes—
518C2×C4×Q8C22×C6112yes—
519C2×#117C22×C6111yescharacteristic
520C2×#117C22×C6112yes—
521C61#6288911yescharacteristic, direct product factor, Sylow
522C2×#41C23×C6112yes—
523C22×Q8C23×C6112yes—
524C23×C4C23×C6111yescharacteristic
525C4⋊Q8C23×C6114yes—
526C4⋊Q8C23×C6114yes—
527C4⋊Q8C23×C6111yescharacteristic
528C4⋊Q8C23×C6114yes—
529C4⋊Q8C23×C6118yes—
530C4⋊Q8C23×C6118yes—
531C4⋊Q8C23×C6118yes—
532C4⋊Q8C23×C6112yes—
533C4⋊Q8C23×C6118yes—
534C4⋊Q8C23×C6112yes—
535C4⋊Q8C23×C6112yes—
536C4⋊Q8C23×C6118yes—
537C4⋊Q8C23×C6118yes—
538C4⋊Q8C23×C6118yes—
539C4⋊Q8C23×C61116yes—
540C4⋊Q8C23×C61116yes—
541C4⋊Q8C23×C61116yes—
542#127C23×C6111yescharacteristic
543#126C23×C61116yes—
544#126C23×C61116yes—
545#126C23×C6118yes—
546#126C23×C6118yes—
547#126C23×C61116yes—
548#126C23×C61116yes—
549#126C23×C61116yes—
550#126C23×C61116yes—
551#126C23×C61116yes—
552#126C23×C61116yes—
553#126C23×C61116yes—
554#126C23×C61116yes—
555#125C23×C6114yes—
556#125C23×C61116yes—
557#125C23×C61116yes—
558#125C23×C6114yes—
559#125C23×C6112yes—
560#125C23×C61116yes—
561#125C23×C6118yes—
562#125C23×C6118yes—
563#125C23×C6118yes—
564#125C23×C6118yes—
565#125C23×C6112yes—
566#125C23×C61116yes—
567#125C23×C6112yes—
568#125C23×C6118yes—
569#125C23×C61116yes—
570#125C23×C6114yes—
571#125C23×C6118yes—
572#125C23×C61116yes—
573#125C23×C61116yes—
574#125C23×C61116yes—
575#125C23×C61116yes—
576#125C23×C61116yes—
577#125C23×C61116yes—
578#125C23×C61116yes—
579#125C23×C61116yes—
580#125C23×C61116yes—
581#124C23×C6118yes—
582#124C23×C6118yes—
583#124C23×C6118yes—
584#124C23×C6112yes—
585#124C23×C61116yes—
586#123C23×C6114yes—
587#123C23×C61116yes—
588#123C23×C6118yes—
589#123C23×C6118yes—
590#123C23×C61116yes—
591#123C23×C61116yes—
592#123C23×C61116yes—
593C22⋊Q8C23×C6118yes—
594C22⋊Q8C23×C6118yes—
595C22⋊Q8C23×C6114yes—
596C22⋊Q8C23×C6114yes—
597C22⋊Q8C23×C6118yes—
598C22⋊Q8C23×C6114yes—
599C22⋊Q8C23×C6114yes—
600C22⋊Q8C23×C6118yes—
601C22⋊Q8C23×C6118yes—
602C22⋊Q8C23×C61116yes—
603C22⋊Q8C23×C6118yes—
604C22⋊Q8C23×C6118yes—
605C22⋊Q8C23×C6118yes—
606C22⋊Q8C23×C61116yes—
607C22⋊Q8C23×C6118yes—
608C22⋊Q8C23×C6118yes—
609C22⋊Q8C23×C61116yes—
610C22⋊Q8C23×C61116yes—
611C22⋊Q8C23×C61116yes—
612C22⋊Q8C23×C61116yes—
613C22⋊Q8C23×C61116yes—
614C22⋊Q8C23×C61116yes—
615#121C23×C6114yes—
616#121C23×C6114yes—
617#121C23×C6118yes—
618#120C23×C6114yes—
619C4×Q8C23×C6114yes—
620C4×Q8C23×C6114yes—
621C4×Q8C23×C6114yes—
622C4×Q8C23×C6114yes—
623C4×Q8C23×C6114yes—
624C4×Q8C23×C6118yes—
625C4×Q8C23×C6118yes—
626C4×Q8C23×C6118yes—
627C4×Q8C23×C6118yes—
628C4×Q8C23×C6118yes—
629C4×Q8C23×C6114yes—
630C4×Q8C23×C6118yes—
631C4×Q8C23×C6118yes—
632C4×Q8C23×C6114yes—
633C4×Q8C23×C6114yes—
634C4×Q8C23×C61116yes—
635C4×Q8C23×C6118yes—
636C4×Q8C23×C61116yes—
637C4×Q8C23×C6118yes—
638C4×Q8C23×C61116yes—
639C4×Q8C23×C61116yes—
640C4×D4C23×C6118yes—
641C4×D4C23×C6114yes—
642C4×D4C23×C61116yes—
643C4×D4C23×C6118yes—
644C4×D4C23×C6118yes—
645C4×D4C23×C6114yes—
646C4×D4C23×C6118yes—
647C4×D4C23×C61116yes—
648#117C23×C6114yes—
649#117C23×C6114yes—
650#117C23×C6112yes—
651#117C23×C6112yes—
652#117C23×C6114yes—
653#117C23×C6112yes—
654#117C23×C6114yes—
655#117C23×C6112yes—
656#117C23×C6112yes—
657#117C23×C6114yes—
658#117C23×C61116yes—
659#117C23×C6118yes—
660#117C23×C61116yes—
661#117C23×C61116yes—
662#117C23×C61116yes—
663#117C23×C61116yes—
664C2×C4⋊C4C23×C6112yes—
665C2×C4⋊C4C23×C6114yes—
666C2×C4⋊C4C23×C6112yes—
667C2×C4⋊C4C23×C6114yes—
668C2×C4⋊C4C23×C6118yes—
669C2×C4⋊C4C23×C6114yes—
670C2×C4⋊C4C23×C6114yes—
671C2×C4⋊C4C23×C6114yes—
672C2×C4⋊C4C23×C61116yes—
673C2×C22⋊C4C23×C6112yes—
674C2×C22⋊C4C23×C6114yes—
675C2×C22⋊C4C23×C6114yes—
676C2×C42C23×C6111yescharacteristic
677C2×C42C23×C6111yescharacteristic
678C2×C42C23×C6114yes—
679C2×C42C23×C6114yes—
680C2×C42C23×C6114yes—
681C24C24×C6111yescharacteristic
682#41—28no—
683C2×Q8—28no—
684C2×Q8C24×C6114yes—
685C2×Q8C24×C6114yes—
686C2×Q8C24×C6112yes—
687C2×Q8C24×C6118yes—
688C2×Q8C24×C6114yes—
689C2×Q8C24×C61116yes—
690C2×Q8C24×C6114yes—
691C2×Q8C24×C6114yes—
692C2×D4C24×C6114yes—
693C2×D4C24×C6112yes—
694C2×D4C24×C6118yes—
695C2×D4C24×C6114yes—
696C22×C4—24no—
697C22×C4C24×C6112yes—
698C22×C4C24×C6114yes—
699C22×C4C24×C6114yes—
700C22×C4C24×C6111yescharacteristic
701C22×C4C24×C6112yes—
702C22×C4C24×C6112yes—
703C22×C4C24×C6112yes—
704C22×C4C24×C6114yes—
705C22×C4C24×C6118yes—
706C22×C4C24×C6118yes—
707C22×C4C24×C61116yes—
708C22×C4C24×C6111yescharacteristic
709C4⋊C4C24×C6114yes—
710C4⋊C4C24×C6114yes—
711C4⋊C4C24×C61116yes—
712C4⋊C4C24×C6118yes—
713C4⋊C4C24×C6114yes—
714C4⋊C4C24×C6114yes—
715C4⋊C4C24×C6118yes—
716C4⋊C4C24×C6114yes—
717C4⋊C4C24×C61116yes—
718C4⋊C4C24×C61116yes—
719C4⋊C4C24×C61116yes—
720C4⋊C4C24×C61116yes—
721C4⋊C4C24×C6114yes—
722C4⋊C4C24×C61116yes—
723C4⋊C4C24×C6118yes—
724C4⋊C4C24×C6118yes—
725C4⋊C4C24×C6118yes—
726C4⋊C4C24×C6118yes—
727C4⋊C4C24×C61116yes—
728C4⋊C4C24×C6114yes—
729C4⋊C4C24×C6118yes—
730C4⋊C4C24×C61116yes—
731C4⋊C4C24×C61116yes—
732C4⋊C4C24×C6114yes—
733C4⋊C4C24×C6114yes—
734C4⋊C4C24×C61116yes—
735C4⋊C4C24×C6118yes—
736C4⋊C4C24×C6118yes—
737C4⋊C4C24×C6118yes—
738C4⋊C4C24×C6118yes—
739C4⋊C4C24×C6114yes—
740C4⋊C4C24×C61116yes—
741C4⋊C4C24×C6114yes—
742C22⋊C4C24×C6118yes—
743C22⋊C4C24×C6114yes—
744C22⋊C4C24×C6114yes—
745C22⋊C4C24×C6114yes—
746C22⋊C4C24×C6114yes—
747C22⋊C4C24×C61116yes—
748C22⋊C4C24×C6114yes—
749C22⋊C4C24×C6118yes—
750C22⋊C4C24×C6118yes—
751C22⋊C4C24×C6118yes—
752C22⋊C4C24×C61116yes—
753C22⋊C4C24×C61116yes—
754C22⋊C4C24×C6118yes—
755C22⋊C4C24×C61116yes—
756C42C24×C6112yes—
757C42C24×C6114yes—
758C42C24×C6112yes—
759C42C24×C6114yes—
760C42C24×C6112yes—
761C42C24×C6118yes—
762C42C24×C6111yescharacteristic
763C42C24×C6111yescharacteristic
764C42C24×C6118yes—
765C42C24×C6114yes—
766C42C24×C6118yes—
767C42C24×C6118yes—
768C42C24×C61116yes—
769C42C24×C61116yes—
770C42C24×C61116yes—
771C23—22no—
772C23—42no—
773C23C25×C6112yes—
774C23C25×C6114yes—
775C23C25×C6111yescharacteristic
776Q8—28no—
777Q8—28no—
778Q8—24no—
779Q8—48no—
780Q8—44no—
781Q8—416no—
782Q8—44no—
783Q8—44no—
784D4—28no—
785D4—24no—
786D4—44no—
787D4—48no—
788C2×C4—22no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—416no—
796C2×C4—48no—
797C2×C4—48no—
798C2×C4—42no—
799C2×C42−1+4×C6114yes—
800C2×C4C25×C6118yes—
801C2×C4C25×C6112yes—
802C2×C4C25×C6118yes—
803C2×C4C25×C6114yes—
804C2×C4C25×C6118yes—
805C2×C4C25×C6112yes—
806C2×C4C25×C6112yes—
807C2×C4C25×C6114yes—
808C2×C4C25×C6118yes—
809C2×C4C25×C6118yes—
810C2×C4C25×C6111yescharacteristic
811C2×C4C25×C6111yescharacteristic
812C22—22no—
813C22—22no—
814C22—24no—
815C22—28no—
816C22—24no—
817C22—82no—
818C22C2×2−1+4×C6112yes—
819C22C26×C6111yescharacteristic
820C4—22no—
821C4—24no—
822C4—28no—
823C4—28no—
824C4—24no—
825C4—28no—
826C4—22no—
827C4—28no—
828C4—28no—
829C4—22no—
830C4C2×2−1+4×C6112yes—
831C4C2×2−1+4×C6112yes—
832C2—22no—
833C2—42no—
834C2—44no—
835C2C22×2−1+4×C6111yescharacteristic
836C2C61×2−1+612yes—
subgroupG/H
center, socleC22×C61C26
commutator, Frattini, cosocleC22C26×C61
prime radicalC61×#3455C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3564C2semidirect
2. C61×#3563C2semidirect
3. C61×#3563C2semidirect
4. C61×#3557C2semidirect
5. C61×#3556C2semidirect
6. C61×#3555C2semidirect
7. C61×#3555C2semidirect
8. C61×#3509C2semidirect
9. C61×#3507C2semidirect
10. C61×#3504C2semidirect
11. C61×#3502C2semidirect
12. C61×#3495C2semidirect
13. C61×#3458C2semidirect
15. C2×C61×#541C2semidirect
16. C61×#564C22semidirect
19. C61×#563C22semidirect
20. C61×#559C22semidirect
21. Q82×C61C22semidirect
22. Q82×C61C22semidirect
23. C61×#557C22semidirect
24. C61×#557C22semidirect
25. C61×#557C22semidirect
26. C61×#557C22semidirect
27. C61×#557C22semidirect
28. C61×#557C22semidirect
29. C61×#557C22semidirect
30. C61×#557C22semidirect
33. C61×#556C22semidirect
34. C61×#556C22semidirect
35. C61×#556C22semidirect
38. C61×#554C22semidirect
39. C61×#554C22semidirect
45. C61×#552C22semidirect
46. C61×#552C22semidirect
53. C61×#544C22semidirect
54. C61×#544C22semidirect
66. C61×#541C22semidirect
67. C61×#541C22semidirect
68. C61×#541C22semidirect
69. C61×#541C22semidirect
70. C61×#541C22semidirect
84. C61×#533C22semidirect
85. C61×#533C22semidirect
94. C2×#125×C61C22semidirect
393. #62889C61direct (N × H)
414. #3564C2×C61semidirect
415. #3563C2×C61semidirect
416. #3563C2×C61semidirect
417. #3557C2×C61semidirect
418. #3556C2×C61semidirect
419. #3555C2×C61semidirect
420. #3555C2×C61semidirect
421. #3509C2×C61semidirect
422. #3507C2×C61semidirect
423. #3504C2×C61semidirect
424. #3502C2×C61semidirect
425. #3495C2×C61semidirect
426. #3458C2×C61semidirect
428. C2×#541C2×C61semidirect
434. #564C22×C61semidirect
437. #563C22×C61semidirect
438. #559C22×C61semidirect
439. Q82C22×C61semidirect
440. Q82C22×C61semidirect
441. #557C22×C61semidirect
442. #557C22×C61semidirect
443. #557C22×C61semidirect
444. #557C22×C61semidirect
445. #557C22×C61semidirect
446. #557C22×C61semidirect
447. #557C22×C61semidirect
448. #557C22×C61semidirect
451. #556C22×C61semidirect
452. #556C22×C61semidirect
453. #556C22×C61semidirect
456. #554C22×C61semidirect
457. #554C22×C61semidirect
463. #552C22×C61semidirect
464. #552C22×C61semidirect
471. #544C22×C61semidirect
472. #544C22×C61semidirect
484. #541C22×C61semidirect
485. #541C22×C61semidirect
486. #541C22×C61semidirect
487. #541C22×C61semidirect
488. #541C22×C61semidirect
502. #533C22×C61semidirect
503. #533C22×C61semidirect
512. C2×#125C22×C61semidirect
521. C61#62889direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35642
C61×#35632
C61×#35572
C61×#35562
C61×#35552
C61×#35092
C61×#35072
C61×#35042
C61×#35022
C61×#34952
C61×#34582
C61×#34552
C2×C61×#5412
#6288961