Finite Group Databasebeta

← C61×#62959 #29566392

Subgroups — C61×#62959 #29566392

Order 15616.

6354 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3565C218yesmaximal, complemented
2C61×#3564C218yesmaximal, complemented
3C61×#3561C214yesmaximal, complemented
4C61×#3555C218yesmaximal, complemented
5C61×#3555C214yesmaximal, complemented
6C61×#3552C214yesmaximal, complemented
7C61×#3523C214yesmaximal, complemented
8C61×#3518C214yesmaximal, complemented
9C61×#3509C214yesmaximal, complemented
10C61×#3503C212yesmaximal, complemented
11C61×#3502C211yesmaximal, characteristic, complemented
12C61×#3495C214yesmaximal, complemented
13C61×#3493C212yesmaximal, complemented
14C61×#3475C212yesmaximal, complemented
15C2×C61×#556C211yesmaximal, characteristic, complemented
16C61×#3461C211yesmaximal, characteristic, complemented
17C61×#3458C212yesmaximal, complemented
18C61×#563C2218yes—
19C61×#563C22116yescomplemented
20C61×#563C22116yescomplemented
21C61×#562C2218yes—
22Q82×C61C2214yescomplemented
23Q82×C61C2214yescomplemented
24C61×#557C2214yescomplemented
25C61×#557C2218yescomplemented
26C61×#557C2214yescomplemented
27C61×#557C2218yescomplemented
28C61×#557C2214yescomplemented
29C61×#557C2214yescomplemented
30C61×#556C2214yes—
31C61×#556C2218yes—
32C61×#556C2218yes—
33C61×#556C2214yes—
34C61×#556C2212yes—
35C61×#556C2218yescomplemented
36C61×#556C22116yescomplemented
37C61×#556C2218yescomplemented
38C61×#556C2218yescomplemented
39C61×#556C2214yescomplemented
40C61×#555C2212yes—
41C61×#555C2218yescomplemented
42C61×#554C2212yes—
43C61×#554C2218yes—
44C61×#554C2218yescomplemented
45C61×#554C2214yescomplemented
46C61×#553C2214yes—
47C61×#553C2218yescomplemented
48C61×#552C2214yes—
49C61×#552C22116yes—
50C61×#552C2214yes—
51C61×#552C2218yescomplemented
52C61×#552C2218yescomplemented
53C61×#552C22116yescomplemented
54C61×#552C2218yescomplemented
55C61×#551C22116yes—
56C61×#551C2218yes—
57D4×Q8×C61C2218yes—
58D4×Q8×C61C2214yescomplemented
59D4×Q8×C61C2214yescomplemented
60C61×#548C2218yes—
61C61×#547C2212yes—
62C61×#546C2214yes—
63C61×#544C2214yes—
64C61×#544C2211yescharacteristic
65C61×#544C2212yes—
66C61×#544C2214yes—
67C61×#544C2218yescomplemented
68C61×#544C2218yescomplemented
69C61×#544C2218yescomplemented
70C61×#543C2218yes—
71C61×#542C22116yes—
72C61×#542C2218yes—
73C61×#542C2218yescomplemented
74C61×#542C22116yescomplemented
75C61×#542C2214yescomplemented
76C61×#541C2218yescomplemented
77C61×#541C22116yescomplemented
78C61×#541C2214yescomplemented
79C61×#541C2218yescomplemented
80C61×#541C22116yescomplemented
81C61×#541C22116yescomplemented
82C61×#539C2214yes—
83C61×#539C22116yescomplemented
84C61×#538C2218yes—
85C61×#537C2211yescharacteristic
86C61×#536C2218yes—
87C61×#536C2212yes—
88C61×#533C2214yes—
89C61×#533C2218yes—
90C61×#533C2212yes—
91C61×#533C2218yescomplemented
92C61×#533C2214yescomplemented
93C61×#533C2218yescomplemented
94C61×#533C2214yescomplemented
95C61×#533C2218yescomplemented
96C2×C4⋊Q8×C61C2211yescharacteristic
97C2×C4⋊Q8×C61C2214yescomplemented
98C61×#529C2214yes—
99C61×#529C2218yes—
100C61×#529C2214yes—
101C61×#529C2218yes—
102C61×#529C2214yescomplemented
103C61×#529C2218yescomplemented
104C2×#126×C61C2214yes—
105C2×#124×C61C2212yes—
106C61×#525C2214yes—
107C2×C22⋊Q8×C61C2212yes—
108C61×#520C2214yes—
109C61×#519C2212yes—
110C61×#519C2218yescomplemented
111C4×#41×C61C2212yes—
112C4×#41×C61C2214yes—
113C2×C4×Q8×C61C2211yescharacteristic
114C2×C4×Q8×C61C2212yes—
115C2×C4×D4×C61C2211yescharacteristic
116C2×#117×C61C2212yes—
117C2×#117×C61C2214yes—
118C2×#41×C61C2312yes—
119C2×#41×C61C2314yes—
120C22×Q8×C61C2311yescharacteristic
121C22×Q8×C61C2312yes—
122C22×Q8×C61C2318yes—
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61C2312yes—
125C4⋊Q8×C61C2314yes—
126C4⋊Q8×C61C2314yes—
127C4⋊Q8×C61C2312yes—
128C4⋊Q8×C61C2318yes—
129C4⋊Q8×C61C2318yes—
130C4⋊Q8×C61C2318yes—
131C4⋊Q8×C61C2312yes—
132C4⋊Q8×C61C2314yes—
133C4⋊Q8×C61C2314yes—
134C4⋊Q8×C61C2318yes—
135C4⋊Q8×C61C2318yes—
136C4⋊Q8×C61C2314yes—
137C4⋊Q8×C61C2314yes—
138C4⋊Q8×C61C2318yes—
139C4⋊Q8×C61C2318yes—
140C4⋊Q8×C61C23116yes—
141C4⋊Q8×C61C23116yes—
142#126×C61C23116yes—
143#126×C61C2318yes—
144#126×C61C23116yes—
145#126×C61C23116yes—
146#126×C61C2318yes—
147#126×C61C23116yes—
148#126×C61C23116yes—
149#126×C61C2318yes—
150#126×C61C2318yes—
151#126×C61C2318yes—
152#126×C61C23116yes—
153#126×C61C23116yes—
154#126×C61C23116yes—
155#125×C61C23116yes—
156#125×C61C2318yes—
157#125×C61C2314yes—
158#125×C61C2314yes—
159#125×C61C2318yes—
160#125×C61C2318yes—
161#125×C61C23116yes—
162#125×C61C2318yes—
163#125×C61C2318yes—
164#125×C61C23116yes—
165#125×C61C23116yes—
166#125×C61C23116yes—
167#125×C61C23116yes—
168#125×C61C2318yes—
169#125×C61C2314yes—
170#125×C61C2318yes—
171#125×C61C2314yes—
172#124×C61C2314yes—
173#124×C61C2318yes—
174#124×C61C2314yes—
175#124×C61C23116yes—
176#124×C61C2318yes—
177#124×C61C23116yes—
178#124×C61C2318yes—
179#124×C61C2318yes—
180#124×C61C2314yes—
181#123×C61C23116yes—
182#123×C61C2318yes—
183#123×C61C23116yes—
184#123×C61C2318yes—
185#123×C61C2318yes—
186#123×C61C2318yes—
187#123×C61C2318yes—
188#123×C61C23116yes—
189#123×C61C2318yes—
190C22⋊Q8×C61C2314yes—
191C22⋊Q8×C61C2318yes—
192C22⋊Q8×C61C2314yes—
193C22⋊Q8×C61C23116yes—
194C22⋊Q8×C61C2314yes—
195C22⋊Q8×C61C2314yes—
196C22⋊Q8×C61C23116yes—
197C22⋊Q8×C61C23116yes—
198C22⋊Q8×C61C2314yes—
199C22⋊Q8×C61C2314yes—
200C22⋊Q8×C61C2318yes—
201C22⋊Q8×C61C23116yes—
202C22⋊Q8×C61C2318yes—
203C22⋊Q8×C61C2318yes—
204C22⋊Q8×C61C23116yes—
205C22⋊Q8×C61C23116yes—
206C22⋊Q8×C61C2318yes—
207C22⋊Q8×C61C2314yes—
208C22⋊Q8×C61C23116yes—
209C22⋊Q8×C61C23116yes—
210C22⋊Q8×C61C2314yes—
211C22⋊Q8×C61C2318yes—
212C22⋊Q8×C61C2314yes—
213C22⋊Q8×C61C23116yes—
214C22⋊Q8×C61C2318yes—
215#121×C61C2314yes—
216#121×C61C2314yes—
217#121×C61C23116yes—
218#121×C61C2314yes—
219#121×C61C2318yes—
220#121×C61C2314yes—
221#121×C61C2314yes—
222#120×C61C2318yes—
223C4×Q8×C61C23116yes—
224C4×Q8×C61C2318yes—
225C4×Q8×C61C2318yes—
226C4×Q8×C61C2318yes—
227C4×Q8×C61C2318yes—
228C4×Q8×C61C2314yes—
229C4×Q8×C61C2314yes—
230C4×Q8×C61C2312yes—
231C4×Q8×C61C2314yes—
232C4×Q8×C61C2318yes—
233C4×Q8×C61C23116yes—
234C4×Q8×C61C2318yes—
235C4×Q8×C61C2318yes—
236C4×Q8×C61C2318yes—
237C4×Q8×C61C2314yes—
238C4×Q8×C61C2314yes—
239C4×Q8×C61C2312yes—
240C4×Q8×C61C2318yes—
241C4×Q8×C61C2318yes—
242C4×Q8×C61C2314yes—
243C4×Q8×C61C2318yes—
244C4×Q8×C61C2314yes—
245C4×Q8×C61C2314yes—
246C4×D4×C61C23116yes—
247C4×D4×C61C2314yes—
248C4×D4×C61C2318yes—
249C4×D4×C61C23116yes—
250C4×D4×C61C2314yes—
251C4×D4×C61C2318yes—
252C4×D4×C61C2312yes—
253C4×D4×C61C2318yes—
254C4×D4×C61C2314yes—
255C4×D4×C61C2312yes—
256C4×D4×C61C2312yes—
257C4×D4×C61C2314yes—
258C4×D4×C61C2314yes—
259C4×D4×C61C2318yes—
260C4×D4×C61C2318yes—
261C4×D4×C61C2312yes—
262#117×C61C2318yes—
263#117×C61C2314yes—
264#117×C61C2318yes—
265#117×C61C2314yes—
266#117×C61C2314yes—
267#117×C61C2318yes—
268#117×C61C2318yes—
269#117×C61C23116yes—
270#117×C61C2318yes—
271#117×C61C2312yes—
272#117×C61C2318yes—
273#117×C61C2318yes—
274#117×C61C2314yes—
275#117×C61C23116yes—
276#117×C61C23116yes—
277#117×C61C2318yes—
278#117×C61C2314yes—
279C2×C4⋊C4×C61C2312yes—
280C2×C4⋊C4×C61C2312yes—
281C2×C4⋊C4×C61C2318yes—
282C2×C4⋊C4×C61C2318yes—
283C2×C4⋊C4×C61C2311yescharacteristic
284C2×C4⋊C4×C61C2312yes—
285C2×C4⋊C4×C61C2314yes—
286C2×C4⋊C4×C61C2314yes—
287C2×C4⋊C4×C61C2311yescharacteristic
288C2×C4⋊C4×C61C2314yes—
289C2×C22⋊C4×C61C2314yes—
290C2×C22⋊C4×C61C2318yes—
291C2×C22⋊C4×C61C2312yes—
292C2×C22⋊C4×C61C2314yes—
293C2×C42×C61C2311yescharacteristic
294C2×C42×C61C2314yes—
295C2×C42×C61C2314yes—
296C2×C42×C61C2312yes—
297C2×C42×C61C2318yes—
298C24×C61C2412yes—
299#41×C61—28no—
300#41×C61—48no—
301C2×Q8×C61—24no—
302C2×Q8×C61—44no—
303C2×Q8×C61—416no—
304C2×Q8×C61C2414yes—
305C2×Q8×C61C2412yes—
306C2×Q8×C61C2414yes—
307C2×Q8×C61C2414yes—
308C2×Q8×C61C2414yes—
309C2×Q8×C61C2414yes—
310C2×Q8×C61C2418yes—
311C2×Q8×C61C24116yes—
312C2×Q8×C61C2414yes—
313C2×D4×C61—42no—
314C2×D4×C61C2414yes—
315C2×D4×C61C2412yes—
316C2×D4×C61C2412yes—
317C2×D4×C61C2418yes—
318C2×D4×C61C2414yes—
319C2×D4×C61C2418yes—
320C2×D4×C61C2412yes—
321C22×C4×C61—28no—
322C22×C4×C61C2411yescharacteristic
323C22×C4×C61C2412yes—
324C22×C4×C61C2414yes—
325C22×C4×C61C2412yes—
326C22×C4×C61C2414yes—
327C22×C4×C61C2414yes—
328C22×C4×C61C2414yes—
329C22×C4×C61C2412yes—
330C22×C4×C61C2411yescharacteristic
331C22×C4×C61C2414yes—
332C22×C4×C61C2418yes—
333C22×C4×C61C2418yes—
334C22×C4×C61C2414yes—
335C22×C4×C61C24116yes—
336C22×C4×C61C2411yescharacteristic
337C4⋊C4×C61C2414yes—
338C4⋊C4×C61C2412yes—
339C4⋊C4×C61C2418yes—
340C4⋊C4×C61C2412yes—
341C4⋊C4×C61C2418yes—
342C4⋊C4×C61C2414yes—
343C4⋊C4×C61C2411yescharacteristic
344C4⋊C4×C61C2414yes—
345C4⋊C4×C61C2414yes—
346C4⋊C4×C61C2418yes—
347C4⋊C4×C61C2418yes—
348C4⋊C4×C61C2418yes—
349C4⋊C4×C61C24116yes—
350C4⋊C4×C61C2411yescharacteristic
351C4⋊C4×C61C2412yes—
352C4⋊C4×C61C24116yes—
353C4⋊C4×C61C2418yes—
354C4⋊C4×C61C2418yes—
355C4⋊C4×C61C2418yes—
356C4⋊C4×C61C2418yes—
357C4⋊C4×C61C2414yes—
358C4⋊C4×C61C2414yes—
359C4⋊C4×C61C2418yes—
360C4⋊C4×C61C2414yes—
361C4⋊C4×C61C24116yes—
362C4⋊C4×C61C2418yes—
363C4⋊C4×C61C24116yes—
364C4⋊C4×C61C2418yes—
365C4⋊C4×C61C2418yes—
366C4⋊C4×C61C2418yes—
367C4⋊C4×C61C24116yes—
368C4⋊C4×C61C2414yes—
369C4⋊C4×C61C2418yes—
370C4⋊C4×C61C2418yes—
371C4⋊C4×C61C2418yes—
372C4⋊C4×C61C2414yes—
373C22⋊C4×C61C2414yes—
374C22⋊C4×C61C2418yes—
375C22⋊C4×C61C2414yes—
376C22⋊C4×C61C2418yes—
377C22⋊C4×C61C24116yes—
378C22⋊C4×C61C2418yes—
379C22⋊C4×C61C24116yes—
380C22⋊C4×C61C2414yes—
381C22⋊C4×C61C2418yes—
382C22⋊C4×C61C2418yes—
383C22⋊C4×C61C2418yes—
384C22⋊C4×C61C2418yes—
385C22⋊C4×C61C2418yes—
386C22⋊C4×C61C2414yes—
387C22⋊C4×C61C24116yes—
388C22⋊C4×C61C2414yes—
389C22⋊C4×C61C2418yes—
390C22⋊C4×C61C2418yes—
391C42×C61C2414yes—
392C42×C61C2412yes—
393C42×C61C2418yes—
394C42×C61C2418yes—
395C42×C61C2418yes—
396C42×C61C2418yes—
397C42×C61C2412yes—
398C42×C61C2414yes—
399C42×C61C2414yes—
400C42×C61C2414yes—
401C42×C61C2418yes—
402C42×C61C2414yes—
403C42×C61C24116yes—
404C42×C61C24116yes—
405C23×C61—24no—
406C23×C61—42no—
407C23×C61—42no—
408C23×C61C2514yes—
409C23×C61C2514yes—
410C23×C61C2511yescharacteristic
411Q8×C61—28no—
412Q8×C61—24no—
413Q8×C61—28no—
414Q8×C61—28no—
415Q8×C61—416no—
416Q8×C61—44no—
417Q8×C61—44no—
418Q8×C61—44no—
419Q8×C61—48no—
420D4×C61—28no—
421D4×C61—24no—
422D4×C61—24no—
423D4×C61—42no—
424D4×C61—48no—
425D4×C61—44no—
426D4×C61—48no—
427C2×C4×C61—24no—
428C2×C4×C61—24no—
429C2×C4×C61—28no—
430C2×C4×C61—28no—
431C2×C4×C61—28no—
432C2×C4×C61—22no—
433C2×C4×C61—28no—
434C2×C4×C61—41no—
435C2×C4×C61—44no—
436C2×C4×C61—48no—
437C2×C4×C61—42no—
438C2×C4×C61—416no—
439C2×C4×C61—44no—
440C2×C4×C61—48no—
441C2×C4×C612−1+414yes—
442C2×C4×C61C2512yes—
443C2×C4×C61C2514yes—
444C2×C4×C61C2514yes—
445C2×C4×C61C2514yes—
446C2×C4×C61C2518yes—
447C2×C4×C61C2511yescharacteristic
448C2×C4×C61C2512yes—
449C2×C4×C61C2514yes—
450C2×C4×C61C2512yes—
451C2×C4×C61C2514yes—
452C2×C4×C61C2518yes—
453C2×C4×C61C2518yes—
454C2×C4×C61C2512yes—
455C2×C4×C61C2511yescharacteristic
456#62959C6111yesmaximal, characteristic, direct product factor, Sylow
457C22×C61—21no—
458C22×C61—21no—
459C22×C61—24no—
460C22×C61—24no—
461C22×C61—24no—
462C22×C61—24no—
463C22×C61—24no—
464C22×C61—24no—
465C22×C61—84no—
466C22×C61C2×2−1+412yes—
467C22×C61C2611yescharacteristic
468C4×C61—22no—
469C4×C61—22no—
470C4×C61—24no—
471C4×C61—24no—
472C4×C61—24no—
473C4×C61—21no—
474C4×C61—28no—
475C4×C61—28no—
476C4×C61—22no—
477C4×C61—24no—
478C4×C61—28no—
479C4×C61—24no—
480C4×C61C2×2−1+414yes—
481C4×C61#58512yes—
482#3565C2×C6118yescomplemented
483#3564C2×C6118yescomplemented
484#3561C2×C6114yescomplemented
485#3555C2×C6118yescomplemented
486#3555C2×C6114yescomplemented
487#3552C2×C6114yescomplemented
488#3523C2×C6114yescomplemented
489#3518C2×C6114yescomplemented
490#3509C2×C6114yescomplemented
491#3503C2×C6112yescomplemented
492#3502C2×C6111yescharacteristic, complemented
493#3495C2×C6114yescomplemented
494#3493C2×C6112yescomplemented
495#3475C2×C6112yescomplemented
496C2×#556C2×C6111yescharacteristic, complemented
497#3461C2×C6111yescharacteristic, complemented
498#3458C2×C6112yescomplemented
499C2×C61—22no—
500C2×C61—44no—
501C2×C61—44no—
502C2×C61C22×2−1+411yescharacteristic
503C2×C61C2×#58511yescharacteristic
504C2×C612−1+611yescharacteristic
505#563C22×C6118yes—
506#563C22×C61116yescomplemented
507#563C22×C61116yescomplemented
508#562C22×C6118yes—
509Q82C22×C6114yescomplemented
510Q82C22×C6114yescomplemented
511#557C22×C6114yescomplemented
512#557C22×C6118yescomplemented
513#557C22×C6114yescomplemented
514#557C22×C6114yescomplemented
515#557C22×C6114yescomplemented
516#557C22×C6118yescomplemented
517#556C22×C6114yes—
518#556C22×C6114yes—
519#556C22×C6118yes—
520#556C22×C6112yes—
521#556C22×C6118yes—
522#556C22×C6118yescomplemented
523#556C22×C6118yescomplemented
524#556C22×C6114yescomplemented
525#556C22×C61116yescomplemented
526#556C22×C6118yescomplemented
527#555C22×C6112yes—
528#555C22×C6118yescomplemented
529#554C22×C6112yes—
530#554C22×C6118yes—
531#554C22×C6118yescomplemented
532#554C22×C6114yescomplemented
533#553C22×C6114yes—
534#553C22×C6118yescomplemented
535#552C22×C6114yes—
536#552C22×C6114yes—
537#552C22×C61116yes—
538#552C22×C6118yescomplemented
539#552C22×C6118yescomplemented
540#552C22×C6118yescomplemented
541#552C22×C61116yescomplemented
542#551C22×C6118yes—
543#551C22×C61116yes—
544D4×Q8C22×C6118yes—
545D4×Q8C22×C6114yescomplemented
546D4×Q8C22×C6114yescomplemented
547#548C22×C6118yes—
548#547C22×C6112yes—
549#546C22×C6114yes—
550#544C22×C6111yescharacteristic
551#544C22×C6112yes—
552#544C22×C6114yes—
553#544C22×C6114yes—
554#544C22×C6118yescomplemented
555#544C22×C6118yescomplemented
556#544C22×C6118yescomplemented
557#543C22×C6118yes—
558#542C22×C6118yes—
559#542C22×C61116yes—
560#542C22×C6114yescomplemented
561#542C22×C6118yescomplemented
562#542C22×C61116yescomplemented
563#541C22×C6114yescomplemented
564#541C22×C6118yescomplemented
565#541C22×C61116yescomplemented
566#541C22×C6118yescomplemented
567#541C22×C61116yescomplemented
568#541C22×C61116yescomplemented
569#539C22×C6114yes—
570#539C22×C61116yescomplemented
571#538C22×C6118yes—
572#537C22×C6111yescharacteristic
573#536C22×C6112yes—
574#536C22×C6118yes—
575#533C22×C6118yes—
576#533C22×C6112yes—
577#533C22×C6114yes—
578#533C22×C6118yescomplemented
579#533C22×C6118yescomplemented
580#533C22×C6114yescomplemented
581#533C22×C6118yescomplemented
582#533C22×C6114yescomplemented
583C2×C4⋊Q8C22×C6111yescharacteristic
584C2×C4⋊Q8C22×C6114yescomplemented
585#529C22×C6114yes—
586#529C22×C6114yes—
587#529C22×C6118yes—
588#529C22×C6118yes—
589#529C22×C6114yescomplemented
590#529C22×C6118yescomplemented
591C2×#126C22×C6114yes—
592C2×#124C22×C6112yes—
593#525C22×C6114yes—
594C2×C22⋊Q8C22×C6112yes—
595#520C22×C6114yes—
596#519C22×C6112yes—
597#519C22×C6118yescomplemented
598C4×#41C22×C6112yes—
599C4×#41C22×C6114yes—
600C2×C4×Q8C22×C6111yescharacteristic
601C2×C4×Q8C22×C6112yes—
602C2×C4×D4C22×C6111yescharacteristic
603C2×#117C22×C6112yes—
604C2×#117C22×C6114yes—
605C61#6295911yescharacteristic, direct product factor, Sylow
606C2×#41C23×C6112yes—
607C2×#41C23×C6114yes—
608C22×Q8C23×C6111yescharacteristic
609C22×Q8C23×C6112yes—
610C22×Q8C23×C6118yes—
611C22×D4C23×C6111yescharacteristic
612C23×C4C23×C6112yes—
613C4⋊Q8C23×C6114yes—
614C4⋊Q8C23×C6114yes—
615C4⋊Q8C23×C6112yes—
616C4⋊Q8C23×C6118yes—
617C4⋊Q8C23×C6118yes—
618C4⋊Q8C23×C6118yes—
619C4⋊Q8C23×C6112yes—
620C4⋊Q8C23×C6114yes—
621C4⋊Q8C23×C6114yes—
622C4⋊Q8C23×C6118yes—
623C4⋊Q8C23×C6118yes—
624C4⋊Q8C23×C6114yes—
625C4⋊Q8C23×C6114yes—
626C4⋊Q8C23×C6118yes—
627C4⋊Q8C23×C6118yes—
628C4⋊Q8C23×C61116yes—
629C4⋊Q8C23×C61116yes—
630#126C23×C61116yes—
631#126C23×C61116yes—
632#126C23×C6118yes—
633#126C23×C6118yes—
634#126C23×C6118yes—
635#126C23×C6118yes—
636#126C23×C61116yes—
637#126C23×C6118yes—
638#126C23×C61116yes—
639#126C23×C61116yes—
640#126C23×C61116yes—
641#126C23×C61116yes—
642#126C23×C61116yes—
643#125C23×C6118yes—
644#125C23×C6114yes—
645#125C23×C6118yes—
646#125C23×C6114yes—
647#125C23×C6114yes—
648#125C23×C6118yes—
649#125C23×C61116yes—
650#125C23×C6118yes—
651#125C23×C6114yes—
652#125C23×C6118yes—
653#125C23×C61116yes—
654#125C23×C6118yes—
655#125C23×C6118yes—
656#125C23×C61116yes—
657#125C23×C61116yes—
658#125C23×C61116yes—
659#125C23×C61116yes—
660#124C23×C6118yes—
661#124C23×C6118yes—
662#124C23×C6114yes—
663#124C23×C6118yes—
664#124C23×C6118yes—
665#124C23×C6114yes—
666#124C23×C6114yes—
667#124C23×C61116yes—
668#124C23×C61116yes—
669#123C23×C6118yes—
670#123C23×C6118yes—
671#123C23×C6118yes—
672#123C23×C6118yes—
673#123C23×C6118yes—
674#123C23×C6118yes—
675#123C23×C61116yes—
676#123C23×C61116yes—
677#123C23×C61116yes—
678C22⋊Q8C23×C6118yes—
679C22⋊Q8C23×C6118yes—
680C22⋊Q8C23×C6114yes—
681C22⋊Q8C23×C6114yes—
682C22⋊Q8C23×C6118yes—
683C22⋊Q8C23×C6114yes—
684C22⋊Q8C23×C6114yes—
685C22⋊Q8C23×C6118yes—
686C22⋊Q8C23×C6114yes—
687C22⋊Q8C23×C6114yes—
688C22⋊Q8C23×C61116yes—
689C22⋊Q8C23×C6114yes—
690C22⋊Q8C23×C61116yes—
691C22⋊Q8C23×C61116yes—
692C22⋊Q8C23×C6114yes—
693C22⋊Q8C23×C6114yes—
694C22⋊Q8C23×C6118yes—
695C22⋊Q8C23×C61116yes—
696C22⋊Q8C23×C6118yes—
697C22⋊Q8C23×C6118yes—
698C22⋊Q8C23×C61116yes—
699C22⋊Q8C23×C61116yes—
700C22⋊Q8C23×C61116yes—
701C22⋊Q8C23×C61116yes—
702C22⋊Q8C23×C61116yes—
703#121C23×C6114yes—
704#121C23×C6114yes—
705#121C23×C6114yes—
706#121C23×C6114yes—
707#121C23×C6118yes—
708#121C23×C6114yes—
709#121C23×C61116yes—
710#120C23×C6118yes—
711C4×Q8C23×C6114yes—
712C4×Q8C23×C6114yes—
713C4×Q8C23×C6114yes—
714C4×Q8C23×C6118yes—
715C4×Q8C23×C6114yes—
716C4×Q8C23×C6114yes—
717C4×Q8C23×C6114yes—
718C4×Q8C23×C6112yes—
719C4×Q8C23×C6112yes—
720C4×Q8C23×C6118yes—
721C4×Q8C23×C6118yes—
722C4×Q8C23×C61116yes—
723C4×Q8C23×C6118yes—
724C4×Q8C23×C61116yes—
725C4×Q8C23×C6118yes—
726C4×Q8C23×C6118yes—
727C4×Q8C23×C6114yes—
728C4×Q8C23×C6114yes—
729C4×Q8C23×C6118yes—
730C4×Q8C23×C6118yes—
731C4×Q8C23×C6118yes—
732C4×Q8C23×C6118yes—
733C4×Q8C23×C6118yes—
734C4×D4C23×C6112yes—
735C4×D4C23×C6112yes—
736C4×D4C23×C6114yes—
737C4×D4C23×C6118yes—
738C4×D4C23×C6114yes—
739C4×D4C23×C6112yes—
740C4×D4C23×C6114yes—
741C4×D4C23×C6114yes—
742C4×D4C23×C6118yes—
743C4×D4C23×C6112yes—
744C4×D4C23×C61116yes—
745C4×D4C23×C6118yes—
746C4×D4C23×C6118yes—
747C4×D4C23×C6114yes—
748C4×D4C23×C6118yes—
749C4×D4C23×C61116yes—
750#117C23×C6112yes—
751#117C23×C6114yes—
752#117C23×C6118yes—
753#117C23×C6118yes—
754#117C23×C6114yes—
755#117C23×C6114yes—
756#117C23×C6118yes—
757#117C23×C6118yes—
758#117C23×C6114yes—
759#117C23×C6114yes—
760#117C23×C6118yes—
761#117C23×C6118yes—
762#117C23×C6118yes—
763#117C23×C61116yes—
764#117C23×C61116yes—
765#117C23×C6118yes—
766#117C23×C61116yes—
767C2×C4⋊C4C23×C6111yescharacteristic
768C2×C4⋊C4C23×C6112yes—
769C2×C4⋊C4C23×C6114yes—
770C2×C4⋊C4C23×C6114yes—
771C2×C4⋊C4C23×C6111yescharacteristic
772C2×C4⋊C4C23×C6114yes—
773C2×C4⋊C4C23×C6112yes—
774C2×C4⋊C4C23×C6118yes—
775C2×C4⋊C4C23×C6112yes—
776C2×C4⋊C4C23×C6118yes—
777C2×C22⋊C4C23×C6114yes—
778C2×C22⋊C4C23×C6118yes—
779C2×C22⋊C4C23×C6112yes—
780C2×C22⋊C4C23×C6114yes—
781C2×C42C23×C6114yes—
782C2×C42C23×C6118yes—
783C2×C42C23×C6111yescharacteristic
784C2×C42C23×C6112yes—
785C2×C42C23×C6114yes—
786C24C24×C6112yes—
787#41—28no—
788#41—48no—
789C2×Q8—24no—
790C2×Q8—44no—
791C2×Q8—416no—
792C2×Q8C24×C6114yes—
793C2×Q8C24×C6112yes—
794C2×Q8C24×C6114yes—
795C2×Q8C24×C6114yes—
796C2×Q8C24×C6114yes—
797C2×Q8C24×C6114yes—
798C2×Q8C24×C6118yes—
799C2×Q8C24×C61116yes—
800C2×Q8C24×C6114yes—
801C2×D4—42no—
802C2×D4C24×C6114yes—
803C2×D4C24×C6112yes—
804C2×D4C24×C6112yes—
805C2×D4C24×C6118yes—
806C2×D4C24×C6114yes—
807C2×D4C24×C6118yes—
808C2×D4C24×C6112yes—
809C22×C4—28no—
810C22×C4C24×C6111yescharacteristic
811C22×C4C24×C6112yes—
812C22×C4C24×C6114yes—
813C22×C4C24×C6112yes—
814C22×C4C24×C6114yes—
815C22×C4C24×C6114yes—
816C22×C4C24×C6114yes—
817C22×C4C24×C6112yes—
818C22×C4C24×C6111yescharacteristic
819C22×C4C24×C6114yes—
820C22×C4C24×C6118yes—
821C22×C4C24×C6118yes—
822C22×C4C24×C6114yes—
823C22×C4C24×C61116yes—
824C22×C4C24×C6111yescharacteristic
825C4⋊C4C24×C6114yes—
826C4⋊C4C24×C6112yes—
827C4⋊C4C24×C6118yes—
828C4⋊C4C24×C6112yes—
829C4⋊C4C24×C6118yes—
830C4⋊C4C24×C6114yes—
831C4⋊C4C24×C6111yescharacteristic
832C4⋊C4C24×C6114yes—
833C4⋊C4C24×C6114yes—
834C4⋊C4C24×C6118yes—
835C4⋊C4C24×C6118yes—
836C4⋊C4C24×C6118yes—
837C4⋊C4C24×C61116yes—
838C4⋊C4C24×C6111yescharacteristic
839C4⋊C4C24×C6112yes—
840C4⋊C4C24×C61116yes—
841C4⋊C4C24×C6118yes—
842C4⋊C4C24×C6118yes—
843C4⋊C4C24×C6118yes—
844C4⋊C4C24×C6118yes—
845C4⋊C4C24×C6114yes—
846C4⋊C4C24×C6114yes—
847C4⋊C4C24×C6118yes—
848C4⋊C4C24×C6114yes—
849C4⋊C4C24×C61116yes—
850C4⋊C4C24×C6118yes—
851C4⋊C4C24×C61116yes—
852C4⋊C4C24×C6118yes—
853C4⋊C4C24×C6118yes—
854C4⋊C4C24×C6118yes—
855C4⋊C4C24×C6114yes—
856C4⋊C4C24×C61116yes—
857C4⋊C4C24×C6118yes—
858C4⋊C4C24×C6118yes—
859C4⋊C4C24×C6118yes—
860C4⋊C4C24×C6114yes—
861C22⋊C4C24×C6114yes—
862C22⋊C4C24×C6118yes—
863C22⋊C4C24×C6114yes—
864C22⋊C4C24×C6118yes—
865C22⋊C4C24×C61116yes—
866C22⋊C4C24×C6118yes—
867C22⋊C4C24×C61116yes—
868C22⋊C4C24×C6114yes—
869C22⋊C4C24×C6118yes—
870C22⋊C4C24×C6118yes—
871C22⋊C4C24×C6118yes—
872C22⋊C4C24×C6118yes—
873C22⋊C4C24×C6118yes—
874C22⋊C4C24×C6114yes—
875C22⋊C4C24×C61116yes—
876C22⋊C4C24×C6114yes—
877C22⋊C4C24×C6118yes—
878C22⋊C4C24×C6118yes—
879C42C24×C6114yes—
880C42C24×C6112yes—
881C42C24×C6118yes—
882C42C24×C6118yes—
883C42C24×C6118yes—
884C42C24×C6118yes—
885C42C24×C6112yes—
886C42C24×C6114yes—
887C42C24×C6114yes—
888C42C24×C6114yes—
889C42C24×C6118yes—
890C42C24×C6114yes—
891C42C24×C61116yes—
892C42C24×C61116yes—
893C23—24no—
894C23—42no—
895C23—42no—
896C23C25×C6114yes—
897C23C25×C6114yes—
898C23C25×C6111yescharacteristic
899Q8—28no—
900Q8—24no—
901Q8—28no—
902Q8—28no—
903Q8—416no—
904Q8—44no—
905Q8—44no—
906Q8—44no—
907Q8—48no—
908D4—28no—
909D4—24no—
910D4—24no—
911D4—42no—
912D4—48no—
913D4—44no—
914D4—48no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—28no—
920C2×C4—22no—
921C2×C4—28no—
922C2×C4—41no—
923C2×C4—44no—
924C2×C4—48no—
925C2×C4—42no—
926C2×C4—416no—
927C2×C4—44no—
928C2×C4—48no—
929C2×C42−1+4×C6114yes—
930C2×C4C25×C6112yes—
931C2×C4C25×C6114yes—
932C2×C4C25×C6114yes—
933C2×C4C25×C6114yes—
934C2×C4C25×C6118yes—
935C2×C4C25×C6111yescharacteristic
936C2×C4C25×C6112yes—
937C2×C4C25×C6114yes—
938C2×C4C25×C6112yes—
939C2×C4C25×C6114yes—
940C2×C4C25×C6118yes—
941C2×C4C25×C6118yes—
942C2×C4C25×C6112yes—
943C2×C4C25×C6111yescharacteristic
944C22—21no—
945C22—21no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—84no—
953C22C2×2−1+4×C6112yes—
954C22C26×C6111yescharacteristic
955C4—22no—
956C4—22no—
957C4—24no—
958C4—24no—
959C4—24no—
960C4—21no—
961C4—28no—
962C4—28no—
963C4—22no—
964C4—24no—
965C4—28no—
966C4—24no—
967C4C2×2−1+4×C6114yes—
968C4C61×#58512yes—
969C2—22no—
970C2—44no—
971C2—44no—
972C2C22×2−1+4×C6111yescharacteristic
973C2C2×C61×#58511yescharacteristic
974C2C61×2−1+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×#3564C2semidirect
3. C61×#3561C2semidirect
4. C61×#3555C2semidirect
5. C61×#3555C2semidirect
6. C61×#3552C2semidirect
7. C61×#3523C2semidirect
8. C61×#3518C2semidirect
9. C61×#3509C2semidirect
10. C61×#3503C2semidirect
11. C61×#3502C2semidirect
12. C61×#3495C2semidirect
13. C61×#3493C2semidirect
14. C61×#3475C2semidirect
15. C2×C61×#556C2semidirect
16. C61×#3461C2semidirect
17. C61×#3458C2semidirect
19. C61×#563C22semidirect
20. C61×#563C22semidirect
22. Q82×C61C22semidirect
23. Q82×C61C22semidirect
24. C61×#557C22semidirect
25. C61×#557C22semidirect
26. C61×#557C22semidirect
27. C61×#557C22semidirect
28. C61×#557C22semidirect
29. C61×#557C22semidirect
35. C61×#556C22semidirect
36. C61×#556C22semidirect
37. C61×#556C22semidirect
38. C61×#556C22semidirect
39. C61×#556C22semidirect
41. C61×#555C22semidirect
44. C61×#554C22semidirect
45. C61×#554C22semidirect
47. C61×#553C22semidirect
51. C61×#552C22semidirect
52. C61×#552C22semidirect
53. C61×#552C22semidirect
54. C61×#552C22semidirect
58. D4×Q8×C61C22semidirect
59. D4×Q8×C61C22semidirect
67. C61×#544C22semidirect
68. C61×#544C22semidirect
69. C61×#544C22semidirect
73. C61×#542C22semidirect
74. C61×#542C22semidirect
75. C61×#542C22semidirect
76. C61×#541C22semidirect
77. C61×#541C22semidirect
78. C61×#541C22semidirect
79. C61×#541C22semidirect
80. C61×#541C22semidirect
81. C61×#541C22semidirect
83. C61×#539C22semidirect
91. C61×#533C22semidirect
92. C61×#533C22semidirect
93. C61×#533C22semidirect
94. C61×#533C22semidirect
95. C61×#533C22semidirect
97. C2×C4⋊Q8×C61C22semidirect
102. C61×#529C22semidirect
103. C61×#529C22semidirect
110. C61×#519C22semidirect
456. #62959C61direct (N × H)
482. #3565C2×C61semidirect
483. #3564C2×C61semidirect
484. #3561C2×C61semidirect
485. #3555C2×C61semidirect
486. #3555C2×C61semidirect
487. #3552C2×C61semidirect
488. #3523C2×C61semidirect
489. #3518C2×C61semidirect
490. #3509C2×C61semidirect
491. #3503C2×C61semidirect
492. #3502C2×C61semidirect
493. #3495C2×C61semidirect
494. #3493C2×C61semidirect
495. #3475C2×C61semidirect
496. C2×#556C2×C61semidirect
497. #3461C2×C61semidirect
498. #3458C2×C61semidirect
506. #563C22×C61semidirect
507. #563C22×C61semidirect
509. Q82C22×C61semidirect
510. Q82C22×C61semidirect
511. #557C22×C61semidirect
512. #557C22×C61semidirect
513. #557C22×C61semidirect
514. #557C22×C61semidirect
515. #557C22×C61semidirect
516. #557C22×C61semidirect
522. #556C22×C61semidirect
523. #556C22×C61semidirect
524. #556C22×C61semidirect
525. #556C22×C61semidirect
526. #556C22×C61semidirect
528. #555C22×C61semidirect
531. #554C22×C61semidirect
532. #554C22×C61semidirect
534. #553C22×C61semidirect
538. #552C22×C61semidirect
539. #552C22×C61semidirect
540. #552C22×C61semidirect
541. #552C22×C61semidirect
545. D4×Q8C22×C61semidirect
546. D4×Q8C22×C61semidirect
554. #544C22×C61semidirect
555. #544C22×C61semidirect
556. #544C22×C61semidirect
560. #542C22×C61semidirect
561. #542C22×C61semidirect
562. #542C22×C61semidirect
563. #541C22×C61semidirect
564. #541C22×C61semidirect
565. #541C22×C61semidirect
566. #541C22×C61semidirect
567. #541C22×C61semidirect
568. #541C22×C61semidirect
570. #539C22×C61semidirect
578. #533C22×C61semidirect
579. #533C22×C61semidirect
580. #533C22×C61semidirect
581. #533C22×C61semidirect
582. #533C22×C61semidirect
584. C2×C4⋊Q8C22×C61semidirect
589. #529C22×C61semidirect
590. #529C22×C61semidirect
597. #519C22×C61semidirect
605. C61#62959direct (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×#35642
C61×#35612
C61×#35552
C61×#35522
C61×#35232
C61×#35182
C61×#35092
C61×#35032
C61×#35022
C61×#34952
C61×#34932
C61×#34752
C2×C61×#5562
C61×#34612
C61×#34582
#6295961