Finite Group Databasebeta

← C61×#63034 #29566467

Subgroups — C61×#63034 #29566467

Order 15616.

6508 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3565C2112yesmaximal, complemented
2C61×#3554C216yesmaximal, complemented
3C61×#3550C213yesmaximal, complemented
4C61×#3547C216yesmaximal, complemented
5C61×#3524C214yesmaximal, complemented
6C61×#3518C216yesmaximal, complemented
7C61×#3518C212yesmaximal, complemented
8C61×#3511C213yesmaximal, complemented
9C61×#3509C213yesmaximal, complemented
10C61×#3507C216yesmaximal, complemented
11C61×#3503C211yesmaximal, characteristic, complemented
12C61×#3502C212yesmaximal, complemented
13C61×#3483C211yesmaximal, characteristic, complemented
14C61×#3482C213yesmaximal, complemented
15C61×#3482C211yesmaximal, characteristic, complemented
16C61×#3480C212yesmaximal, complemented
17Q8×#41×C61C212yesmaximal, complemented
18C61×#563C22112yes—
19C61×#562C22124yes—
20C61×#559C2216yes—
21C61×#559C22112yes—
22Q82×C61C2216yes—
23Q82×C61C2212yes—
24Q82×C61C2211yescharacteristic
25C61×#557C2216yes—
26C61×#557C22112yes—
27C61×#557C2211yescharacteristic
28C61×#557C2214yes—
29C61×#557C2212yes—
30C61×#557C2213yes—
31C61×#556C2216yes—
32C61×#556C2216yes—
33C61×#556C22124yes—
34C61×#556C22112yes—
35C61×#556C2216yes—
36C61×#556C2211yescharacteristic
37C61×#556C2213yes—
38C61×#556C2216yes—
39C61×#555C2216yes—
40C61×#555C22112yes—
41C61×#555C2216yes—
42C61×#555C2213yes—
43C61×#554C2216yes—
44C61×#554C22112yes—
45C61×#554C2216yes—
46C61×#553C22112yes—
47C61×#553C22112yes—
48C61×#552C22112yes—
49C61×#552C22112yes—
50C61×#552C2216yes—
51C61×#552C22112yes—
52C61×#552C2216yes—
53C61×#550C2213yes—
54C61×#550C2211yescharacteristic
55C61×#550C2212yes—
56D4×Q8×C61C2216yes—
57D4×Q8×C61C2213yes—
58D4×Q8×C61C2216yes—
59D4×Q8×C61C2211yescharacteristic
60C61×#548C2216yes—
61C61×#548C22112yes—
62C61×#548C2214yes—
63C61×#548C2212yes—
64C61×#547C2213yes—
65C61×#547C2216yes—
66C61×#547C2213yes—
67C61×#544C22112yes—
68C61×#544C2216yes—
69C61×#542C22124yes—
70C61×#542C22112yes—
71C61×#542C22112yes—
72C61×#542C22112yes—
73C61×#542C22112yes—
74C61×#541C22112yes—
75C61×#540C22112yes—
76C61×#539C22124yes—
77C61×#537C2216yes—
78C61×#536C22112yes—
79C61×#536C2216yes—
80C61×#533C2216yes—
81C61×#533C2213yes—
82C61×#533C2213yes—
83C61×#533C2216yes—
84C61×#533C22112yes—
85C61×#533C2216yes—
86C61×#533C2216yes—
87C61×#532C2216yes—
88C61×#532C2213yes—
89C61×#532C2216yes—
90C2×C4⋊Q8×C61C2213yes—
91C61×#529C2216yes—
92C61×#529C2216yes—
93C61×#529C22112yes—
94C61×#529C22112yes—
95C61×#529C22112yes—
96C61×#520C2212yes—
97C61×#520C2216yes—
98C61×#519C2214yes—
99C61×#519C2216yes—
100C4×#41×C61C2214yes—
101C4×#41×C61C2212yes—
102C4×#41×C61C2216yes—
103C4×#41×C61C2213yes—
104C4×#41×C61C2211yescharacteristic
105C4×#41×C61C2213yes—
106C2×C4×Q8×C61C2216yes—
107C2×C4×Q8×C61C2212yes—
108C2×#41×C61C2312yes—
109C2×#41×C61C2311yescharacteristic
110C2×#41×C61C2316yes—
111C2×#41×C61C2316yes—
112C2×#41×C61C2313yes—
113C2×#41×C61C2313yes—
114C22×Q8×C61C2312yes—
115C22×Q8×C61C2316yes—
116C22×Q8×C61C2316yes—
117C4⋊Q8×C61C2313yes—
118C4⋊Q8×C61C2316yes—
119C4⋊Q8×C61C2316yes—
120C4⋊Q8×C61C2316yes—
121C4⋊Q8×C61C2313yes—
122C4⋊Q8×C61C2316yes—
123C4⋊Q8×C61C2313yes—
124C4⋊Q8×C61C2311yescharacteristic
125C4⋊Q8×C61C2313yes—
126C4⋊Q8×C61C2316yes—
127C4⋊Q8×C61C2316yes—
128C4⋊Q8×C61C23112yes—
129C4⋊Q8×C61C23112yes—
130C4⋊Q8×C61C23124yes—
131#127×C61C2313yes—
132#127×C61C2316yes—
133#126×C61C23112yes—
134#126×C61C23124yes—
135#126×C61C23124yes—
136#126×C61C23124yes—
137#126×C61C23112yes—
138#126×C61C2314yes—
139#126×C61C23112yes—
140#125×C61C2316yes—
141#125×C61C2316yes—
142#125×C61C23112yes—
143#125×C61C23112yes—
144#125×C61C23112yes—
145#125×C61C2316yes—
146#125×C61C2316yes—
147#125×C61C23124yes—
148#125×C61C23112yes—
149#125×C61C23112yes—
150#124×C61C23112yes—
151#124×C61C23112yes—
152#124×C61C2316yes—
153#124×C61C23124yes—
154#124×C61C23124yes—
155#124×C61C23112yes—
156#124×C61C23112yes—
157#124×C61C2312yes—
158#124×C61C2316yes—
159#123×C61C23124yes—
160#123×C61C23124yes—
161#123×C61C23124yes—
162#123×C61C23112yes—
163#123×C61C23112yes—
164#123×C61C23112yes—
165#123×C61C23112yes—
166C22⋊Q8×C61C2312yes—
167C22⋊Q8×C61C2316yes—
168C22⋊Q8×C61C2316yes—
169C22⋊Q8×C61C2316yes—
170C22⋊Q8×C61C23112yes—
171C22⋊Q8×C61C23112yes—
172C22⋊Q8×C61C23112yes—
173C22⋊Q8×C61C23112yes—
174C22⋊Q8×C61C23124yes—
175C22⋊Q8×C61C2316yes—
176C22⋊Q8×C61C2316yes—
177C22⋊Q8×C61C23124yes—
178C22⋊Q8×C61C23112yes—
179C22⋊Q8×C61C23112yes—
180C22⋊Q8×C61C2316yes—
181C22⋊Q8×C61C23124yes—
182C22⋊Q8×C61C2316yes—
183C22⋊Q8×C61C23112yes—
184#121×C61C23112yes—
185#121×C61C23112yes—
186#121×C61C23112yes—
187#121×C61C2316yes—
188#121×C61C2316yes—
189#121×C61C2316yes—
190#121×C61C2316yes—
191#121×C61C2316yes—
192#121×C61C23124yes—
193#121×C61C2316yes—
194#121×C61C23112yes—
195C4×Q8×C61C23112yes—
196C4×Q8×C61C2316yes—
197C4×Q8×C61C2313yes—
198C4×Q8×C61C2316yes—
199C4×Q8×C61C2313yes—
200C4×Q8×C61C23112yes—
201C4×Q8×C61C23112yes—
202C4×Q8×C61C23112yes—
203C4×Q8×C61C23112yes—
204C4×Q8×C61C23112yes—
205C4×Q8×C61C2316yes—
206C4×Q8×C61C23112yes—
207C4×Q8×C61C2316yes—
208C4×Q8×C61C23112yes—
209C4×Q8×C61C2312yes—
210C4×Q8×C61C2314yes—
211C4×Q8×C61C2311yescharacteristic
212C4×Q8×C61C2311yescharacteristic
213C4×Q8×C61C2312yes—
214C4×Q8×C61C2312yes—
215C4×Q8×C61C2316yes—
216C4×Q8×C61C2313yes—
217C4×Q8×C61C2316yes—
218C4×Q8×C61C2311yescharacteristic
219C4×D4×C61C2313yes—
220C4×D4×C61C2313yes—
221C4×D4×C61C2316yes—
222C4×D4×C61C2316yes—
223C4×D4×C61C23112yes—
224C4×D4×C61C23112yes—
225C4×D4×C61C23124yes—
226C4×D4×C61C23112yes—
227C4×D4×C61C23112yes—
228C4×D4×C61C2316yes—
229C4×D4×C61C23112yes—
230C4×D4×C61C2316yes—
231C4×D4×C61C2311yescharacteristic
232C4×D4×C61C2316yes—
233C4×D4×C61C2313yes—
234C4×D4×C61C2316yes—
235C4×D4×C61C23112yes—
236C4×D4×C61C2313yes—
237C4×D4×C61C2316yes—
238C4×D4×C61C2313yes—
239#117×C61C23112yes—
240#117×C61C2316yes—
241#117×C61C2316yes—
242#117×C61C23112yes—
243#117×C61C23112yes—
244#117×C61C2316yes—
245#117×C61C23112yes—
246#117×C61C2316yes—
247#117×C61C2316yes—
248#117×C61C23124yes—
249#117×C61C2313yes—
250#117×C61C2313yes—
251#117×C61C23112yes—
252#117×C61C2313yes—
253#117×C61C2312yes—
254C2×C4⋊C4×C61C2316yes—
255C2×C4⋊C4×C61C2316yes—
256C2×C4⋊C4×C61C23112yes—
257C2×C4⋊C4×C61C2316yes—
258C2×C4⋊C4×C61C2316yes—
259C2×C42×C61C2313yes—
260C2×C42×C61C2316yes—
261C2×C42×C61C2316yes—
262C2×C42×C61C23112yes—
263#41×C61—28no—
264#41×C61—24no—
265#41×C61—412no—
266#41×C61—46no—
267#41×C61—412no—
268#41×C61—46no—
269C2×Q8×C61—28no—
270C2×Q8×C61—412no—
271C2×Q8×C61—412no—
272C2×Q8×C61C2416yes—
273C2×Q8×C61C2412yes—
274C2×Q8×C61C2413yes—
275C2×Q8×C61C2416yes—
276C2×Q8×C61C2411yescharacteristic
277C2×Q8×C61C24112yes—
278C2×Q8×C61C24112yes—
279C2×Q8×C61C2416yes—
280C2×Q8×C61C2411yescharacteristic
281C2×D4×C61C2413yes—
282C2×D4×C61C2416yes—
283C2×D4×C61C2411yescharacteristic
284C2×D4×C61C2413yes—
285C2×D4×C61C24112yes—
286C2×D4×C61C2416yes—
287C2×D4×C61C2416yes—
288C2×D4×C61C24112yes—
289C2×D4×C61C2416yes—
290C22×C4×C61C2416yes—
291C22×C4×C61C2412yes—
292C22×C4×C61C2413yes—
293C22×C4×C61C2413yes—
294C22×C4×C61C2416yes—
295C22×C4×C61C2416yes—
296C22×C4×C61C2413yes—
297C22×C4×C61C24112yes—
298C22×C4×C61C2416yes—
299C22×C4×C61C2416yes—
300C22×C4×C61C24112yes—
301C22×C4×C61C24112yes—
302C4⋊C4×C61C2411yescharacteristic
303C4⋊C4×C61C2416yes—
304C4⋊C4×C61C2414yes—
305C4⋊C4×C61C2413yes—
306C4⋊C4×C61C2416yes—
307C4⋊C4×C61C2416yes—
308C4⋊C4×C61C24112yes—
309C4⋊C4×C61C2416yes—
310C4⋊C4×C61C24112yes—
311C4⋊C4×C61C24112yes—
312C4⋊C4×C61C24112yes—
313C4⋊C4×C61C24112yes—
314C4⋊C4×C61C24112yes—
315C4⋊C4×C61C2411yescharacteristic
316C4⋊C4×C61C2413yes—
317C4⋊C4×C61C2413yes—
318C4⋊C4×C61C2412yes—
319C4⋊C4×C61C2416yes—
320C4⋊C4×C61C24112yes—
321C4⋊C4×C61C2412yes—
322C4⋊C4×C61C2412yes—
323C4⋊C4×C61C2413yes—
324C4⋊C4×C61C2416yes—
325C4⋊C4×C61C24112yes—
326C4⋊C4×C61C2416yes—
327C4⋊C4×C61C24124yes—
328C4⋊C4×C61C2416yes—
329C4⋊C4×C61C2416yes—
330C4⋊C4×C61C24112yes—
331C4⋊C4×C61C24112yes—
332C22⋊C4×C61C2416yes—
333C22⋊C4×C61C2416yes—
334C22⋊C4×C61C2412yes—
335C22⋊C4×C61C2414yes—
336C22⋊C4×C61C24112yes—
337C22⋊C4×C61C24112yes—
338C22⋊C4×C61C2416yes—
339C22⋊C4×C61C2414yes—
340C22⋊C4×C61C2416yes—
341C22⋊C4×C61C24124yes—
342C22⋊C4×C61C24112yes—
343C22⋊C4×C61C2416yes—
344C22⋊C4×C61C24112yes—
345C22⋊C4×C61C24124yes—
346C22⋊C4×C61C2416yes—
347C22⋊C4×C61C24112yes—
348C42×C61C2414yes—
349C42×C61C2411yescharacteristic
350C42×C61C2413yes—
351C42×C61C2412yes—
352C42×C61C2416yes—
353C42×C61C2413yes—
354C42×C61C2413yes—
355C42×C61C2416yes—
356C42×C61C24112yes—
357C42×C61C2416yes—
358C42×C61C24112yes—
359C42×C61C2416yes—
360C42×C61C2416yes—
361C42×C61C24124yes—
362C23×C61C2512yes—
363C23×C61C2513yes—
364C23×C61C2516yes—
365Q8×C61—212no—
366Q8×C61—24no—
367Q8×C61—26no—
368Q8×C61—212no—
369Q8×C61—22no—
370Q8×C61—412no—
371Q8×C61—412no—
372Q8×C61—46no—
373Q8×C612−1+414yes—
374D4×C61—26no—
375D4×C61—212no—
376D4×C61—22no—
377D4×C61—26no—
378D4×C61—46no—
379D4×C61—412no—
380D4×C61—46no—
381D4×C61—412no—
382D4×C61—46no—
383C2×C4×C61—212no—
384C2×C4×C61—212no—
385C2×C4×C61—26no—
386C2×C4×C61—26no—
387C2×C4×C61—212no—
388C2×C4×C61—24no—
389C2×C4×C61—26no—
390C2×C4×C61—412no—
391C2×C4×C61—412no—
392C2×C4×C61—412no—
393C2×C4×C61—46no—
394C2×C4×C61—46no—
395C2×C4×C61C2512yes—
396C2×C4×C61C2512yes—
397C2×C4×C61C2516yes—
398C2×C4×C61C2516yes—
399C2×C4×C61C2511yescharacteristic
400C2×C4×C61C2513yes—
401C2×C4×C61C2514yes—
402C2×C4×C61C2516yes—
403C2×C4×C61C25112yes—
404C2×C4×C61C2513yes—
405C2×C4×C61C2512yes—
406C2×C4×C61C2513yes—
407C2×C4×C61C2511yescharacteristic
408C2×C4×C61C2511yescharacteristic
409#63034C6111yesmaximal, characteristic, direct product factor, Sylow
410C22×C61—22no—
411C22×C61—23no—
412C22×C61—26no—
413C22×C61—23no—
414C22×C61—26no—
415C22×C61—22no—
416C22×C61—23no—
417C22×C61—22no—
418C22×C61—26no—
419C22×C61C2611yescharacteristic
420C4×C61—22no—
421C4×C61—21no—
422C4×C61—26no—
423C4×C61—22no—
424C4×C61—23no—
425C4×C61—23no—
426C4×C61—26no—
427C4×C61—22no—
428C4×C61—212no—
429C4×C61—26no—
430C4×C61—24no—
431C4×C61C2×2−1+416yes—
432C4×C61#58512yes—
433C4×C61#58512yes—
434#3565C2×C61112yescomplemented
435#3554C2×C6116yescomplemented
436#3550C2×C6113yescomplemented
437#3547C2×C6116yescomplemented
438#3524C2×C6114yescomplemented
439#3518C2×C6112yescomplemented
440#3518C2×C6116yescomplemented
441#3511C2×C6113yescomplemented
442#3509C2×C6113yescomplemented
443#3507C2×C6116yescomplemented
444#3503C2×C6111yescharacteristic, complemented
445#3502C2×C6112yescomplemented
446#3483C2×C6111yescharacteristic, complemented
447#3482C2×C6113yescomplemented
448#3482C2×C6111yescharacteristic, complemented
449#3480C2×C6112yescomplemented
450Q8×#41C2×C6112yescomplemented
451C2×C61—42no—
452C2×C61—43no—
453C2×C61—46no—
454C2×C61C22×2−1+411yescharacteristic
455C2×C61C2×#58511yescharacteristic
456C2×C61C2×#58511yescharacteristic
457#563C22×C61112yes—
458#562C22×C61124yes—
459#559C22×C6116yes—
460#559C22×C61112yes—
461Q82C22×C6112yes—
462Q82C22×C6111yescharacteristic
463Q82C22×C6116yes—
464#557C22×C6111yescharacteristic
465#557C22×C6114yes—
466#557C22×C6112yes—
467#557C22×C6113yes—
468#557C22×C61112yes—
469#557C22×C6116yes—
470#556C22×C6116yes—
471#556C22×C6111yescharacteristic
472#556C22×C6113yes—
473#556C22×C6116yes—
474#556C22×C6116yes—
475#556C22×C61124yes—
476#556C22×C6116yes—
477#556C22×C61112yes—
478#555C22×C6113yes—
479#555C22×C6116yes—
480#555C22×C6116yes—
481#555C22×C61112yes—
482#554C22×C6116yes—
483#554C22×C61112yes—
484#554C22×C6116yes—
485#553C22×C61112yes—
486#553C22×C61112yes—
487#552C22×C6116yes—
488#552C22×C61112yes—
489#552C22×C6116yes—
490#552C22×C61112yes—
491#552C22×C61112yes—
492#550C22×C6111yescharacteristic
493#550C22×C6112yes—
494#550C22×C6113yes—
495D4×Q8C22×C6116yes—
496D4×Q8C22×C6111yescharacteristic
497D4×Q8C22×C6113yes—
498D4×Q8C22×C6116yes—
499#548C22×C6114yes—
500#548C22×C6112yes—
501#548C22×C6116yes—
502#548C22×C61112yes—
503#547C22×C6113yes—
504#547C22×C6113yes—
505#547C22×C6116yes—
506#544C22×C61112yes—
507#544C22×C6116yes—
508#542C22×C61112yes—
509#542C22×C61124yes—
510#542C22×C61112yes—
511#542C22×C61112yes—
512#542C22×C61112yes—
513#541C22×C61112yes—
514#540C22×C61112yes—
515#539C22×C61124yes—
516#537C22×C6116yes—
517#536C22×C61112yes—
518#536C22×C6116yes—
519#533C22×C6116yes—
520#533C22×C61112yes—
521#533C22×C6116yes—
522#533C22×C6113yes—
523#533C22×C6113yes—
524#533C22×C6116yes—
525#533C22×C6116yes—
526#532C22×C6116yes—
527#532C22×C6116yes—
528#532C22×C6113yes—
529C2×C4⋊Q8C22×C6113yes—
530#529C22×C61112yes—
531#529C22×C6116yes—
532#529C22×C6116yes—
533#529C22×C61112yes—
534#529C22×C61112yes—
535#520C22×C6112yes—
536#520C22×C6116yes—
537#519C22×C6114yes—
538#519C22×C6116yes—
539C4×#41C22×C6114yes—
540C4×#41C22×C6112yes—
541C4×#41C22×C6116yes—
542C4×#41C22×C6113yes—
543C4×#41C22×C6111yescharacteristic
544C4×#41C22×C6113yes—
545C2×C4×Q8C22×C6116yes—
546C2×C4×Q8C22×C6112yes—
547C61#6303411yescharacteristic, direct product factor, Sylow
548C2×#41C23×C6112yes—
549C2×#41C23×C6111yescharacteristic
550C2×#41C23×C6116yes—
551C2×#41C23×C6113yes—
552C2×#41C23×C6113yes—
553C2×#41C23×C6116yes—
554C22×Q8C23×C6112yes—
555C22×Q8C23×C6116yes—
556C22×Q8C23×C6116yes—
557C4⋊Q8C23×C6113yes—
558C4⋊Q8C23×C6116yes—
559C4⋊Q8C23×C6116yes—
560C4⋊Q8C23×C6116yes—
561C4⋊Q8C23×C6113yes—
562C4⋊Q8C23×C6116yes—
563C4⋊Q8C23×C6113yes—
564C4⋊Q8C23×C6111yescharacteristic
565C4⋊Q8C23×C6113yes—
566C4⋊Q8C23×C6116yes—
567C4⋊Q8C23×C6116yes—
568C4⋊Q8C23×C61112yes—
569C4⋊Q8C23×C61112yes—
570C4⋊Q8C23×C61124yes—
571#127C23×C6113yes—
572#127C23×C6116yes—
573#126C23×C6114yes—
574#126C23×C61112yes—
575#126C23×C61112yes—
576#126C23×C61124yes—
577#126C23×C61112yes—
578#126C23×C61124yes—
579#126C23×C61124yes—
580#125C23×C6116yes—
581#125C23×C6116yes—
582#125C23×C61112yes—
583#125C23×C61112yes—
584#125C23×C61112yes—
585#125C23×C61112yes—
586#125C23×C61112yes—
587#125C23×C6116yes—
588#125C23×C6116yes—
589#125C23×C61124yes—
590#124C23×C6112yes—
591#124C23×C6116yes—
592#124C23×C61112yes—
593#124C23×C61112yes—
594#124C23×C61112yes—
595#124C23×C61112yes—
596#124C23×C6116yes—
597#124C23×C61124yes—
598#124C23×C61124yes—
599#123C23×C61124yes—
600#123C23×C61124yes—
601#123C23×C61112yes—
602#123C23×C61112yes—
603#123C23×C61112yes—
604#123C23×C61112yes—
605#123C23×C61124yes—
606C22⋊Q8C23×C61112yes—
607C22⋊Q8C23×C6116yes—
608C22⋊Q8C23×C6116yes—
609C22⋊Q8C23×C61112yes—
610C22⋊Q8C23×C6112yes—
611C22⋊Q8C23×C6116yes—
612C22⋊Q8C23×C6116yes—
613C22⋊Q8C23×C6116yes—
614C22⋊Q8C23×C61112yes—
615C22⋊Q8C23×C61112yes—
616C22⋊Q8C23×C61112yes—
617C22⋊Q8C23×C61112yes—
618C22⋊Q8C23×C61124yes—
619C22⋊Q8C23×C6116yes—
620C22⋊Q8C23×C6116yes—
621C22⋊Q8C23×C61124yes—
622C22⋊Q8C23×C61112yes—
623C22⋊Q8C23×C61124yes—
624#121C23×C6116yes—
625#121C23×C6116yes—
626#121C23×C6116yes—
627#121C23×C6116yes—
628#121C23×C61112yes—
629#121C23×C61112yes—
630#121C23×C61112yes—
631#121C23×C61112yes—
632#121C23×C6116yes—
633#121C23×C6116yes—
634#121C23×C61124yes—
635C4×Q8C23×C6112yes—
636C4×Q8C23×C6111yescharacteristic
637C4×Q8C23×C6113yes—
638C4×Q8C23×C6112yes—
639C4×Q8C23×C6116yes—
640C4×Q8C23×C6116yes—
641C4×Q8C23×C61112yes—
642C4×Q8C23×C6116yes—
643C4×Q8C23×C6116yes—
644C4×Q8C23×C61112yes—
645C4×Q8C23×C6111yescharacteristic
646C4×Q8C23×C6111yescharacteristic
647C4×Q8C23×C6112yes—
648C4×Q8C23×C6116yes—
649C4×Q8C23×C6114yes—
650C4×Q8C23×C6113yes—
651C4×Q8C23×C6116yes—
652C4×Q8C23×C6113yes—
653C4×Q8C23×C61112yes—
654C4×Q8C23×C61112yes—
655C4×Q8C23×C61112yes—
656C4×Q8C23×C61112yes—
657C4×Q8C23×C61112yes—
658C4×Q8C23×C61112yes—
659C4×D4C23×C6111yescharacteristic
660C4×D4C23×C6113yes—
661C4×D4C23×C6116yes—
662C4×D4C23×C6113yes—
663C4×D4C23×C6116yes—
664C4×D4C23×C61112yes—
665C4×D4C23×C6113yes—
666C4×D4C23×C6116yes—
667C4×D4C23×C61112yes—
668C4×D4C23×C6113yes—
669C4×D4C23×C6113yes—
670C4×D4C23×C6116yes—
671C4×D4C23×C6116yes—
672C4×D4C23×C61112yes—
673C4×D4C23×C6116yes—
674C4×D4C23×C61112yes—
675C4×D4C23×C6116yes—
676C4×D4C23×C61112yes—
677C4×D4C23×C61124yes—
678C4×D4C23×C61112yes—
679#117C23×C6112yes—
680#117C23×C6113yes—
681#117C23×C6113yes—
682#117C23×C61112yes—
683#117C23×C61112yes—
684#117C23×C6116yes—
685#117C23×C6116yes—
686#117C23×C6116yes—
687#117C23×C6113yes—
688#117C23×C6116yes—
689#117C23×C61112yes—
690#117C23×C61124yes—
691#117C23×C61112yes—
692#117C23×C6116yes—
693#117C23×C61112yes—
694C2×C4⋊C4C23×C6116yes—
695C2×C4⋊C4C23×C61112yes—
696C2×C4⋊C4C23×C6116yes—
697C2×C4⋊C4C23×C6116yes—
698C2×C4⋊C4C23×C6116yes—
699C2×C42C23×C61112yes—
700C2×C42C23×C6116yes—
701C2×C42C23×C6116yes—
702C2×C42C23×C6113yes—
703#41—28no—
704#41—24no—
705#41—412no—
706#41—46no—
707#41—412no—
708#41—46no—
709C2×Q8—28no—
710C2×Q8—412no—
711C2×Q8—412no—
712C2×Q8C24×C6116yes—
713C2×Q8C24×C6112yes—
714C2×Q8C24×C6113yes—
715C2×Q8C24×C6116yes—
716C2×Q8C24×C6111yescharacteristic
717C2×Q8C24×C61112yes—
718C2×Q8C24×C61112yes—
719C2×Q8C24×C6116yes—
720C2×Q8C24×C6111yescharacteristic
721C2×D4C24×C6113yes—
722C2×D4C24×C6116yes—
723C2×D4C24×C6111yescharacteristic
724C2×D4C24×C6113yes—
725C2×D4C24×C6116yes—
726C2×D4C24×C61112yes—
727C2×D4C24×C6116yes—
728C2×D4C24×C61112yes—
729C2×D4C24×C6116yes—
730C22×C4C24×C6116yes—
731C22×C4C24×C6112yes—
732C22×C4C24×C6113yes—
733C22×C4C24×C6113yes—
734C22×C4C24×C6116yes—
735C22×C4C24×C6116yes—
736C22×C4C24×C6113yes—
737C22×C4C24×C61112yes—
738C22×C4C24×C6116yes—
739C22×C4C24×C6116yes—
740C22×C4C24×C61112yes—
741C22×C4C24×C61112yes—
742C4⋊C4C24×C6111yescharacteristic
743C4⋊C4C24×C6116yes—
744C4⋊C4C24×C6114yes—
745C4⋊C4C24×C6113yes—
746C4⋊C4C24×C6116yes—
747C4⋊C4C24×C6116yes—
748C4⋊C4C24×C6116yes—
749C4⋊C4C24×C61112yes—
750C4⋊C4C24×C61112yes—
751C4⋊C4C24×C61112yes—
752C4⋊C4C24×C61112yes—
753C4⋊C4C24×C61112yes—
754C4⋊C4C24×C61112yes—
755C4⋊C4C24×C6111yescharacteristic
756C4⋊C4C24×C6113yes—
757C4⋊C4C24×C6113yes—
758C4⋊C4C24×C6112yes—
759C4⋊C4C24×C6116yes—
760C4⋊C4C24×C61112yes—
761C4⋊C4C24×C6112yes—
762C4⋊C4C24×C6112yes—
763C4⋊C4C24×C6113yes—
764C4⋊C4C24×C6116yes—
765C4⋊C4C24×C61112yes—
766C4⋊C4C24×C6116yes—
767C4⋊C4C24×C61124yes—
768C4⋊C4C24×C6116yes—
769C4⋊C4C24×C6116yes—
770C4⋊C4C24×C61112yes—
771C4⋊C4C24×C61112yes—
772C22⋊C4C24×C6116yes—
773C22⋊C4C24×C6116yes—
774C22⋊C4C24×C6112yes—
775C22⋊C4C24×C6114yes—
776C22⋊C4C24×C61112yes—
777C22⋊C4C24×C61112yes—
778C22⋊C4C24×C6116yes—
779C22⋊C4C24×C6114yes—
780C22⋊C4C24×C6116yes—
781C22⋊C4C24×C61124yes—
782C22⋊C4C24×C61112yes—
783C22⋊C4C24×C6116yes—
784C22⋊C4C24×C61112yes—
785C22⋊C4C24×C61124yes—
786C22⋊C4C24×C61112yes—
787C22⋊C4C24×C6116yes—
788C42C24×C6114yes—
789C42C24×C6111yescharacteristic
790C42C24×C6113yes—
791C42C24×C6112yes—
792C42C24×C6116yes—
793C42C24×C6113yes—
794C42C24×C6113yes—
795C42C24×C6116yes—
796C42C24×C61112yes—
797C42C24×C6116yes—
798C42C24×C61112yes—
799C42C24×C6116yes—
800C42C24×C6116yes—
801C42C24×C61124yes—
802C23C25×C6112yes—
803C23C25×C6113yes—
804C23C25×C6116yes—
805Q8—212no—
806Q8—24no—
807Q8—26no—
808Q8—212no—
809Q8—22no—
810Q8—412no—
811Q8—412no—
812Q8—46no—
813Q82−1+4×C6114yes—
814D4—26no—
815D4—212no—
816D4—22no—
817D4—26no—
818D4—46no—
819D4—412no—
820D4—46no—
821D4—46no—
822D4—412no—
823C2×C4—212no—
824C2×C4—212no—
825C2×C4—26no—
826C2×C4—26no—
827C2×C4—212no—
828C2×C4—24no—
829C2×C4—26no—
830C2×C4—412no—
831C2×C4—412no—
832C2×C4—412no—
833C2×C4—46no—
834C2×C4—46no—
835C2×C4C25×C6112yes—
836C2×C4C25×C6112yes—
837C2×C4C25×C6116yes—
838C2×C4C25×C6116yes—
839C2×C4C25×C6111yescharacteristic
840C2×C4C25×C6113yes—
841C2×C4C25×C6114yes—
842C2×C4C25×C6116yes—
843C2×C4C25×C61112yes—
844C2×C4C25×C6113yes—
845C2×C4C25×C6112yes—
846C2×C4C25×C6113yes—
847C2×C4C25×C6111yescharacteristic
848C2×C4C25×C6111yescharacteristic
849C22—22no—
850C22—23no—
851C22—26no—
852C22—23no—
853C22—26no—
854C22—22no—
855C22—23no—
856C22—22no—
857C22—26no—
858C22C26×C6111yescharacteristic
859C4—22no—
860C4—21no—
861C4—26no—
862C4—22no—
863C4—23no—
864C4—23no—
865C4—26no—
866C4—22no—
867C4—212no—
868C4—26no—
869C4—24no—
870C4C2×2−1+4×C6116yes—
871C4C61×#58512yes—
872C4C61×#58512yes—
873C2—42no—
874C2—43no—
875C2—46no—
876C2C22×2−1+4×C6111yescharacteristic
877C2C2×C61×#58511yescharacteristic
878C2C2×C61×#58511yescharacteristic
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×#3554C2semidirect
3. C61×#3550C2semidirect
4. C61×#3547C2semidirect
5. C61×#3524C2semidirect
6. C61×#3518C2semidirect
7. C61×#3518C2semidirect
8. C61×#3511C2semidirect
9. C61×#3509C2semidirect
10. C61×#3507C2semidirect
11. C61×#3503C2semidirect
12. C61×#3502C2semidirect
13. C61×#3483C2semidirect
14. C61×#3482C2semidirect
15. C61×#3482C2semidirect
16. C61×#3480C2semidirect
17. Q8×#41×C61C2semidirect
409. #63034C61direct (N × H)
434. #3565C2×C61semidirect
435. #3554C2×C61semidirect
436. #3550C2×C61semidirect
437. #3547C2×C61semidirect
438. #3524C2×C61semidirect
439. #3518C2×C61semidirect
440. #3518C2×C61semidirect
441. #3511C2×C61semidirect
442. #3509C2×C61semidirect
443. #3507C2×C61semidirect
444. #3503C2×C61semidirect
445. #3502C2×C61semidirect
446. #3483C2×C61semidirect
447. #3482C2×C61semidirect
448. #3482C2×C61semidirect
449. #3480C2×C61semidirect
450. Q8×#41C2×C61semidirect
547. C61#63034direct (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×#35542
C61×#35502
C61×#35472
C61×#35242
C61×#35182
C61×#35112
C61×#35092
C61×#35072
C61×#35032
C61×#35022
C61×#34832
C61×#34822
C61×#34802
Q8×#41×C612
#6303461