Finite Group Databasebeta

← C61×#62949 #29566382

Subgroups — C61×#62949 #29566382

Order 15616.

6346 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3565C216yesmaximal, complemented
2C61×#3563C216yesmaximal, complemented
3C61×#3563C213yesmaximal, complemented
4C61×#3559C213yesmaximal, complemented
5C61×#3557C216yesmaximal, complemented
6C61×#3555C216yesmaximal, complemented
7C61×#3544C216yesmaximal, complemented
8C61×#3524C212yesmaximal, complemented
9C61×#3523C211yesmaximal, characteristic, complemented
10C61×#3522C211yesmaximal, characteristic, complemented
11C61×#3516C212yesmaximal, complemented
12C61×#3516C212yesmaximal, complemented
13C61×#3515C216yesmaximal, complemented
14C61×#3507C213yesmaximal, complemented
15C61×#3504C212yesmaximal, complemented
16C61×#3502C212yesmaximal, complemented
17C61×#3482C212yesmaximal, complemented
18C2×C61×#557C211yesmaximal, characteristic, complemented
19C61×#3461C213yesmaximal, complemented
20C61×#564C2216yes—
21C61×#563C22112yes—
22C61×#563C22112yes—
23C61×#563C2216yes—
24C61×#563C2216yes—
25C61×#562C2216yes—
26C61×#559C2213yes—
27C61×#559C2216yes—
28Q82×C61C2216yes—
29Q82×C61C2211yescharacteristic
30C61×#557C2213yes—
31C61×#557C2216yes—
32C61×#557C2216yes—
33C61×#557C2216yes—
34C61×#557C2216yes—
35C61×#557C2216yes—
36C61×#557C2212yes—
37C61×#557C2212yes—
38C61×#557C2212yes—
39C61×#557C2212yes—
40C61×#557C2211yescharacteristic
41C61×#556C2216yes—
42C61×#556C2216yes—
43C61×#556C22112yes—
44C61×#556C2216yes—
45C61×#556C2213yes—
46C61×#555C2216yes—
47C61×#554C2216yes—
48C61×#554C2216yes—
49C61×#554C2216yes—
50C61×#554C2216yes—
51C61×#554C2213yes—
52C61×#554C2216yes—
53C61×#554C2216yes—
54C61×#553C2216yes—
55C61×#553C2216yes—
56C61×#553C2216yes—
57C61×#552C2216yes—
58C61×#552C22112yes—
59C61×#552C2216yes—
60C61×#552C22112yes—
61C61×#552C22112yes—
62C61×#552C2216yes—
63C61×#552C2216yes—
64C61×#552C22112yes—
65C61×#552C2216yes—
66C61×#552C2216yes—
67C61×#550C2211yescharacteristic
68D4×Q8×C61C2212yes—
69D4×Q8×C61C2211yescharacteristic
70C61×#548C2212yes—
71C61×#548C2212yes—
72C61×#548C2212yes—
73C61×#547C2216yes—
74C61×#547C22112yes—
75C61×#547C2216yes—
76C61×#544C22112yes—
77C61×#544C2216yes—
78C61×#544C2216yes—
79C61×#544C2216yes—
80C61×#544C2213yes—
81C61×#544C2216yes—
82C61×#542C2216yes—
83C61×#542C22112yes—
84C61×#542C2216yes—
85C61×#542C2216yes—
86C61×#542C2216yes—
87C61×#542C2216yes—
88C61×#542C2216yes—
89C61×#541C2216yes—
90C61×#541C22112yes—
91C61×#541C22112yes—
92C61×#541C2216yes—
93C61×#541C2216yes—
94C61×#541C2216yes—
95C61×#541C2216yes—
96C61×#540C2216yes—
97C61×#539C22112yes—
98C61×#539C22112yes—
99C61×#539C2216yes—
100C61×#539C2211yescharacteristic
101C61×#539C2213yes—
102C61×#539C2216yes—
103C61×#537C2213yes—
104C61×#536C2216yes—
105C61×#536C2216yes—
106C61×#533C2216yes—
107C61×#533C2216yes—
108C61×#533C2216yes—
109C61×#533C2213yes—
110C61×#533C2216yes—
111C61×#532C2213yes—
112C2×C4⋊Q8×C61C2213yes—
113C61×#529C2216yes—
114C61×#529C2216yes—
115C61×#529C2216yes—
116C61×#529C2216yes—
117C61×#529C2216yes—
118C61×#529C2213yes—
119C61×#529C2213yes—
120C61×#529C2216yes—
121C61×#529C2216yes—
122C61×#529C2216yes—
123C2×#125×C61C2213yes—
124C2×#125×C61C2216yes—
125C2×#125×C61C2213yes—
126C61×#520C2212yes—
127C61×#520C2212yes—
128C61×#520C2216yes—
129C61×#519C2212yes—
130C61×#519C2212yes—
131C4×#41×C61C2216yes—
132C4×#41×C61C2212yes—
133C2×C4×Q8×C61C2213yes—
134C2×C4×Q8×C61C2211yescharacteristic
135C2×C4×Q8×C61C2211yescharacteristic
136C2×C4×Q8×C61C2211yescharacteristic
137C2×C4×Q8×C61C2212yes—
138C2×#41×C61C2312yes—
139C2×#41×C61C2316yes—
140C2×#41×C61C2316yes—
141C22×Q8×C61C2311yescharacteristic
142C22×Q8×C61C2312yes—
143C22×Q8×C61C2313yes—
144C4⋊Q8×C61C2316yes—
145C4⋊Q8×C61C2316yes—
146C4⋊Q8×C61C23112yes—
147C4⋊Q8×C61C2313yes—
148C4⋊Q8×C61C2316yes—
149C4⋊Q8×C61C2316yes—
150C4⋊Q8×C61C2316yes—
151C4⋊Q8×C61C2313yes—
152C4⋊Q8×C61C2316yes—
153C4⋊Q8×C61C2316yes—
154C4⋊Q8×C61C2316yes—
155C4⋊Q8×C61C2316yes—
156C4⋊Q8×C61C2316yes—
157C4⋊Q8×C61C2313yes—
158C4⋊Q8×C61C23112yes—
159C4⋊Q8×C61C23112yes—
160#127×C61C2313yes—
161#126×C61C2316yes—
162#126×C61C2312yes—
163#126×C61C2316yes—
164#126×C61C23112yes—
165#126×C61C23112yes—
166#126×C61C23112yes—
167#126×C61C2316yes—
168#126×C61C23112yes—
169#126×C61C2316yes—
170#126×C61C2316yes—
171#126×C61C23112yes—
172#126×C61C2316yes—
173#126×C61C23112yes—
174#126×C61C23112yes—
175#126×C61C23112yes—
176#126×C61C2316yes—
177#125×C61C2312yes—
178#125×C61C2316yes—
179#125×C61C2316yes—
180#125×C61C2316yes—
181#125×C61C2316yes—
182#125×C61C23112yes—
183#125×C61C2316yes—
184#125×C61C2316yes—
185#125×C61C23112yes—
186#125×C61C2316yes—
187#125×C61C23112yes—
188#125×C61C23112yes—
189#125×C61C2316yes—
190#125×C61C2316yes—
191#125×C61C2316yes—
192#125×C61C23112yes—
193#125×C61C23112yes—
194#125×C61C23112yes—
195#125×C61C2313yes—
196#125×C61C2316yes—
197#125×C61C2313yes—
198#125×C61C2316yes—
199#125×C61C2316yes—
200#125×C61C2316yes—
201#125×C61C2316yes—
202#125×C61C23112yes—
203#125×C61C2316yes—
204#125×C61C2316yes—
205#125×C61C2316yes—
206#124×C61C2316yes—
207#124×C61C2316yes—
208#124×C61C23112yes—
209#124×C61C2316yes—
210#124×C61C2316yes—
211#124×C61C2316yes—
212#124×C61C2316yes—
213#124×C61C2313yes—
214#124×C61C2313yes—
215#124×C61C2316yes—
216#123×C61C2312yes—
217#123×C61C2316yes—
218#123×C61C2316yes—
219#123×C61C2316yes—
220#123×C61C23112yes—
221#123×C61C2316yes—
222#123×C61C23112yes—
223#123×C61C23112yes—
224#123×C61C23112yes—
225#123×C61C2312yes—
226#123×C61C23112yes—
227#123×C61C23112yes—
228#123×C61C2316yes—
229#123×C61C2316yes—
230#123×C61C23112yes—
231C22⋊Q8×C61C2316yes—
232C22⋊Q8×C61C2312yes—
233C22⋊Q8×C61C2313yes—
234C22⋊Q8×C61C2316yes—
235C22⋊Q8×C61C2316yes—
236C22⋊Q8×C61C2316yes—
237C22⋊Q8×C61C2316yes—
238C22⋊Q8×C61C2316yes—
239C22⋊Q8×C61C2316yes—
240C22⋊Q8×C61C23112yes—
241C22⋊Q8×C61C2316yes—
242C22⋊Q8×C61C2316yes—
243C22⋊Q8×C61C23112yes—
244C22⋊Q8×C61C2316yes—
245C22⋊Q8×C61C2316yes—
246C22⋊Q8×C61C2316yes—
247C22⋊Q8×C61C23112yes—
248C22⋊Q8×C61C23112yes—
249C22⋊Q8×C61C23112yes—
250C22⋊Q8×C61C23112yes—
251C22⋊Q8×C61C23112yes—
252C22⋊Q8×C61C23112yes—
253C22⋊Q8×C61C2311yescharacteristic
254C22⋊Q8×C61C2316yes—
255C22⋊Q8×C61C2316yes—
256C22⋊Q8×C61C23112yes—
257C22⋊Q8×C61C2316yes—
258C22⋊Q8×C61C2316yes—
259#121×C61C2313yes—
260#121×C61C2316yes—
261#121×C61C2311yescharacteristic
262#121×C61C2316yes—
263#121×C61C2316yes—
264#121×C61C2316yes—
265#121×C61C23112yes—
266#121×C61C2316yes—
267#121×C61C2316yes—
268#121×C61C2316yes—
269C4×Q8×C61C2316yes—
270C4×Q8×C61C2313yes—
271C4×Q8×C61C2316yes—
272C4×Q8×C61C2316yes—
273C4×Q8×C61C2313yes—
274C4×Q8×C61C2316yes—
275C4×Q8×C61C23112yes—
276C4×Q8×C61C23112yes—
277C4×Q8×C61C2316yes—
278C4×Q8×C61C2316yes—
279C4×Q8×C61C2316yes—
280C4×Q8×C61C2316yes—
281C4×Q8×C61C2316yes—
282C4×Q8×C61C2313yes—
283C4×Q8×C61C2316yes—
284C4×Q8×C61C2316yes—
285C4×Q8×C61C2316yes—
286C4×Q8×C61C2316yes—
287C4×Q8×C61C2316yes—
288C4×Q8×C61C2316yes—
289C4×Q8×C61C2313yes—
290C4×Q8×C61C2316yes—
291C4×Q8×C61C2312yes—
292C4×Q8×C61C2312yes—
293C4×Q8×C61C2312yes—
294C4×Q8×C61C2311yescharacteristic
295C4×Q8×C61C2312yes—
296C4×Q8×C61C2311yescharacteristic
297C4×D4×C61C2316yes—
298C4×D4×C61C2316yes—
299C4×D4×C61C2312yes—
300C4×D4×C61C2316yes—
301C4×D4×C61C2316yes—
302C4×D4×C61C23112yes—
303C4×D4×C61C23112yes—
304C4×D4×C61C23112yes—
305C4×D4×C61C2316yes—
306C4×D4×C61C2316yes—
307C4×D4×C61C2316yes—
308C4×D4×C61C2316yes—
309C4×D4×C61C2316yes—
310C4×D4×C61C2316yes—
311C4×D4×C61C2316yes—
312C4×D4×C61C2316yes—
313C4×D4×C61C2313yes—
314C4×D4×C61C2313yes—
315C4×D4×C61C2316yes—
316#117×C61C2316yes—
317#117×C61C2316yes—
318#117×C61C2316yes—
319#117×C61C2316yes—
320#117×C61C2316yes—
321#117×C61C2316yes—
322#117×C61C2316yes—
323#117×C61C23112yes—
324#117×C61C2316yes—
325#117×C61C2316yes—
326#117×C61C2316yes—
327#117×C61C23112yes—
328#117×C61C23112yes—
329#117×C61C23112yes—
330#117×C61C2316yes—
331C2×C4⋊C4×C61C2313yes—
332C2×C4⋊C4×C61C2313yes—
333C2×C4⋊C4×C61C2316yes—
334C2×C4⋊C4×C61C2313yes—
335C2×C4⋊C4×C61C2311yescharacteristic
336C2×C4⋊C4×C61C2313yes—
337C2×C4⋊C4×C61C23112yes—
338C2×C4⋊C4×C61C23112yes—
339C2×C4⋊C4×C61C2316yes—
340C2×C4⋊C4×C61C2316yes—
341C2×C4⋊C4×C61C2316yes—
342C2×C4⋊C4×C61C2313yes—
343C2×C42×C61C2313yes—
344C2×C42×C61C2313yes—
345C2×C42×C61C2316yes—
346C2×C42×C61C2316yes—
347C2×C42×C61C2313yes—
348#41×C61—28no—
349#41×C61—412no—
350#41×C61—412no—
351C2×Q8×C61—24no—
352C2×Q8×C61—28no—
353C2×Q8×C61—46no—
354C2×Q8×C61C2416yes—
355C2×Q8×C61C2413yes—
356C2×Q8×C61C2416yes—
357C2×Q8×C61C2413yes—
358C2×Q8×C61C2411yescharacteristic
359C2×Q8×C61C2416yes—
360C2×Q8×C61C2416yes—
361C2×Q8×C61C2416yes—
362C2×Q8×C61C2416yes—
363C2×Q8×C61C2411yescharacteristic
364C2×D4×C61C2416yes—
365C2×D4×C61C2412yes—
366C2×D4×C61C2416yes—
367C2×D4×C61C2416yes—
368C2×D4×C61C2411yescharacteristic
369C2×D4×C61C2413yes—
370C2×D4×C61C2416yes—
371C2×D4×C61C2416yes—
372C22×C4×C61C2413yes—
373C22×C4×C61C2411yescharacteristic
374C22×C4×C61C2413yes—
375C22×C4×C61C2413yes—
376C22×C4×C61C2416yes—
377C22×C4×C61C2416yes—
378C22×C4×C61C2411yescharacteristic
379C22×C4×C61C2411yescharacteristic
380C22×C4×C61C2412yes—
381C22×C4×C61C2413yes—
382C22×C4×C61C2416yes—
383C22×C4×C61C2416yes—
384C22×C4×C61C2416yes—
385C22×C4×C61C24112yes—
386C22×C4×C61C24112yes—
387C4⋊C4×C61C2416yes—
388C4⋊C4×C61C2413yes—
389C4⋊C4×C61C2416yes—
390C4⋊C4×C61C2416yes—
391C4⋊C4×C61C2416yes—
392C4⋊C4×C61C2416yes—
393C4⋊C4×C61C2416yes—
394C4⋊C4×C61C2416yes—
395C4⋊C4×C61C2416yes—
396C4⋊C4×C61C24112yes—
397C4⋊C4×C61C2416yes—
398C4⋊C4×C61C2416yes—
399C4⋊C4×C61C2416yes—
400C4⋊C4×C61C2413yes—
401C4⋊C4×C61C24112yes—
402C4⋊C4×C61C24112yes—
403C4⋊C4×C61C2416yes—
404C4⋊C4×C61C24112yes—
405C4⋊C4×C61C2412yes—
406C4⋊C4×C61C2412yes—
407C4⋊C4×C61C2416yes—
408C4⋊C4×C61C2416yes—
409C4⋊C4×C61C2416yes—
410C4⋊C4×C61C2416yes—
411C4⋊C4×C61C2416yes—
412C4⋊C4×C61C24112yes—
413C4⋊C4×C61C2412yes—
414C4⋊C4×C61C2416yes—
415C4⋊C4×C61C2412yes—
416C4⋊C4×C61C2412yes—
417C4⋊C4×C61C2416yes—
418C4⋊C4×C61C2416yes—
419C4⋊C4×C61C24112yes—
420C4⋊C4×C61C2416yes—
421C4⋊C4×C61C2416yes—
422C4⋊C4×C61C2416yes—
423C4⋊C4×C61C2416yes—
424C4⋊C4×C61C2416yes—
425C4⋊C4×C61C2416yes—
426C4⋊C4×C61C2416yes—
427C4⋊C4×C61C2416yes—
428C4⋊C4×C61C2411yescharacteristic
429C4⋊C4×C61C2413yes—
430C4⋊C4×C61C2413yes—
431C4⋊C4×C61C2411yescharacteristic
432C4⋊C4×C61C2412yes—
433C4⋊C4×C61C2416yes—
434C22⋊C4×C61C2416yes—
435C22⋊C4×C61C2412yes—
436C22⋊C4×C61C2412yes—
437C22⋊C4×C61C2416yes—
438C22⋊C4×C61C2412yes—
439C22⋊C4×C61C2416yes—
440C22⋊C4×C61C2416yes—
441C22⋊C4×C61C2412yes—
442C22⋊C4×C61C2416yes—
443C22⋊C4×C61C24112yes—
444C22⋊C4×C61C24112yes—
445C22⋊C4×C61C2416yes—
446C22⋊C4×C61C2416yes—
447C22⋊C4×C61C2416yes—
448C22⋊C4×C61C24112yes—
449C22⋊C4×C61C24112yes—
450C22⋊C4×C61C2416yes—
451C22⋊C4×C61C2416yes—
452C22⋊C4×C61C2416yes—
453C22⋊C4×C61C2416yes—
454C22⋊C4×C61C2416yes—
455C22⋊C4×C61C2412yes—
456C42×C61C2416yes—
457C42×C61C2412yes—
458C42×C61C2416yes—
459C42×C61C2416yes—
460C42×C61C2416yes—
461C42×C61C2413yes—
462C42×C61C2416yes—
463C42×C61C2416yes—
464C42×C61C2416yes—
465C42×C61C2413yes—
466C42×C61C2416yes—
467C42×C61C2416yes—
468C42×C61C2413yes—
469C42×C61C2413yes—
470C42×C61C24112yes—
471C42×C61C24112yes—
472C23×C61C2512yes—
473C23×C61C2516yes—
474C23×C61C2511yescharacteristic
475Q8×C61—26no—
476Q8×C61—212no—
477Q8×C61—46no—
478Q8×C61—46no—
479Q8×C61—46no—
480Q8×C61—43no—
481Q8×C61—41no—
482Q8×C61—46no—
483Q8×C61—46no—
484Q8×C612−1+414yes—
485D4×C61—24no—
486D4×C61—212no—
487D4×C61—212no—
488D4×C61—46no—
489D4×C61—43no—
490D4×C61—41no—
491D4×C61—46no—
492D4×C61—46no—
493C2×C4×C61—22no—
494C2×C4×C61—26no—
495C2×C4×C61—26no—
496C2×C4×C61—26no—
497C2×C4×C61—212no—
498C2×C4×C61—212no—
499C2×C4×C61—41no—
500C2×C4×C61—46no—
501C2×C4×C61—42no—
502C2×C4×C61—43no—
503C2×C4×C61—412no—
504C2×C4×C61—41no—
505C2×C4×C61—412no—
506C2×C4×C61—46no—
507C2×C4×C61—46no—
508C2×C4×C61C2512yes—
509C2×C4×C61C2513yes—
510C2×C4×C61C2516yes—
511C2×C4×C61C2512yes—
512C2×C4×C61C2512yes—
513C2×C4×C61C2511yescharacteristic
514C2×C4×C61C2513yes—
515C2×C4×C61C2511yescharacteristic
516C2×C4×C61C2512yes—
517C2×C4×C61C2516yes—
518C2×C4×C61C2516yes—
519C2×C4×C61C2516yes—
520C2×C4×C61C2512yes—
521C2×C4×C61C2516yes—
522C2×C4×C61C2513yes—
523C2×C4×C61C2513yes—
524#62949C6111yesmaximal, characteristic, direct product factor, Sylow
525C22×C61—21no—
526C22×C61—21no—
527C22×C61—22no—
528C22×C61—26no—
529C22×C61—22no—
530C22×C61—26no—
531C22×C61—26no—
532C22×C61—22no—
533C22×C61#58512yes—
534C22×C61C2611yescharacteristic
535C4×C61—22no—
536C4×C61—23no—
537C4×C61—26no—
538C4×C61—23no—
539C4×C61—26no—
540C4×C61—23no—
541C4×C61—22no—
542C4×C61—26no—
543C4×C61—22no—
544C4×C61—22no—
545C4×C61—26no—
546C4×C61—26no—
547C4×C61—21no—
548C4×C61—21no—
549C4×C61—22no—
550C4×C61C2×2−1+416yes—
551#3565C2×C6116yescomplemented
552#3563C2×C6113yescomplemented
553#3563C2×C6116yescomplemented
554#3559C2×C6113yescomplemented
555#3557C2×C6116yescomplemented
556#3555C2×C6116yescomplemented
557#3544C2×C6116yescomplemented
558#3524C2×C6112yescomplemented
559#3523C2×C6111yescharacteristic, complemented
560#3522C2×C6111yescharacteristic, complemented
561#3516C2×C6112yescomplemented
562#3516C2×C6112yescomplemented
563#3515C2×C6116yescomplemented
564#3507C2×C6113yescomplemented
565#3504C2×C6112yescomplemented
566#3502C2×C6112yescomplemented
567#3482C2×C6112yescomplemented
568C2×#557C2×C6111yescharacteristic, complemented
569#3461C2×C6113yescomplemented
570C2×C61—22no—
571C2×C61—42no—
572C2×C61—46no—
573C2×C61C22×2−1+411yescharacteristic
574C2×C61C2×#58511yescharacteristic
575C2×C612−1+611yescharacteristic
576#564C22×C6116yes—
577#563C22×C61112yes—
578#563C22×C61112yes—
579#563C22×C6116yes—
580#563C22×C6116yes—
581#562C22×C6116yes—
582#559C22×C6116yes—
583#559C22×C6113yes—
584Q82C22×C6111yescharacteristic
585Q82C22×C6116yes—
586#557C22×C6112yes—
587#557C22×C6112yes—
588#557C22×C6116yes—
589#557C22×C6116yes—
590#557C22×C6112yes—
591#557C22×C6112yes—
592#557C22×C6116yes—
593#557C22×C6116yes—
594#557C22×C6116yes—
595#557C22×C6111yescharacteristic
596#557C22×C6113yes—
597#556C22×C6116yes—
598#556C22×C6116yes—
599#556C22×C61112yes—
600#556C22×C6116yes—
601#556C22×C6113yes—
602#555C22×C6116yes—
603#554C22×C6116yes—
604#554C22×C6116yes—
605#554C22×C6116yes—
606#554C22×C6116yes—
607#554C22×C6116yes—
608#554C22×C6116yes—
609#554C22×C6113yes—
610#553C22×C6116yes—
611#553C22×C6116yes—
612#553C22×C6116yes—
613#552C22×C6116yes—
614#552C22×C6116yes—
615#552C22×C61112yes—
616#552C22×C6116yes—
617#552C22×C6116yes—
618#552C22×C61112yes—
619#552C22×C61112yes—
620#552C22×C61112yes—
621#552C22×C6116yes—
622#552C22×C6116yes—
623#550C22×C6111yescharacteristic
624D4×Q8C22×C6112yes—
625D4×Q8C22×C6111yescharacteristic
626#548C22×C6112yes—
627#548C22×C6112yes—
628#548C22×C6112yes—
629#547C22×C6116yes—
630#547C22×C6116yes—
631#547C22×C61112yes—
632#544C22×C6113yes—
633#544C22×C6116yes—
634#544C22×C6116yes—
635#544C22×C6116yes—
636#544C22×C6116yes—
637#544C22×C61112yes—
638#542C22×C6116yes—
639#542C22×C6116yes—
640#542C22×C6116yes—
641#542C22×C6116yes—
642#542C22×C6116yes—
643#542C22×C6116yes—
644#542C22×C61112yes—
645#541C22×C6116yes—
646#541C22×C6116yes—
647#541C22×C61112yes—
648#541C22×C6116yes—
649#541C22×C6116yes—
650#541C22×C6116yes—
651#541C22×C61112yes—
652#540C22×C6116yes—
653#539C22×C6111yescharacteristic
654#539C22×C6113yes—
655#539C22×C6116yes—
656#539C22×C6116yes—
657#539C22×C61112yes—
658#539C22×C61112yes—
659#537C22×C6113yes—
660#536C22×C6116yes—
661#536C22×C6116yes—
662#533C22×C6116yes—
663#533C22×C6116yes—
664#533C22×C6116yes—
665#533C22×C6116yes—
666#533C22×C6113yes—
667#532C22×C6113yes—
668C2×C4⋊Q8C22×C6113yes—
669#529C22×C6116yes—
670#529C22×C6116yes—
671#529C22×C6113yes—
672#529C22×C6113yes—
673#529C22×C6116yes—
674#529C22×C6116yes—
675#529C22×C6116yes—
676#529C22×C6116yes—
677#529C22×C6116yes—
678#529C22×C6116yes—
679C2×#125C22×C6113yes—
680C2×#125C22×C6113yes—
681C2×#125C22×C6116yes—
682#520C22×C6112yes—
683#520C22×C6112yes—
684#520C22×C6116yes—
685#519C22×C6112yes—
686#519C22×C6112yes—
687C4×#41C22×C6116yes—
688C4×#41C22×C6112yes—
689C2×C4×Q8C22×C6113yes—
690C2×C4×Q8C22×C6111yescharacteristic
691C2×C4×Q8C22×C6111yescharacteristic
692C2×C4×Q8C22×C6111yescharacteristic
693C2×C4×Q8C22×C6112yes—
694C61#6294911yescharacteristic, direct product factor, Sylow
695C2×#41C23×C6112yes—
696C2×#41C23×C6116yes—
697C2×#41C23×C6116yes—
698C22×Q8C23×C6111yescharacteristic
699C22×Q8C23×C6112yes—
700C22×Q8C23×C6113yes—
701C4⋊Q8C23×C6116yes—
702C4⋊Q8C23×C6116yes—
703C4⋊Q8C23×C61112yes—
704C4⋊Q8C23×C6113yes—
705C4⋊Q8C23×C6116yes—
706C4⋊Q8C23×C6116yes—
707C4⋊Q8C23×C6116yes—
708C4⋊Q8C23×C6113yes—
709C4⋊Q8C23×C6116yes—
710C4⋊Q8C23×C6116yes—
711C4⋊Q8C23×C6116yes—
712C4⋊Q8C23×C6116yes—
713C4⋊Q8C23×C6116yes—
714C4⋊Q8C23×C6113yes—
715C4⋊Q8C23×C61112yes—
716C4⋊Q8C23×C61112yes—
717#127C23×C6113yes—
718#126C23×C6112yes—
719#126C23×C6116yes—
720#126C23×C6116yes—
721#126C23×C6116yes—
722#126C23×C61112yes—
723#126C23×C6116yes—
724#126C23×C6116yes—
725#126C23×C6116yes—
726#126C23×C61112yes—
727#126C23×C61112yes—
728#126C23×C61112yes—
729#126C23×C6116yes—
730#126C23×C61112yes—
731#126C23×C61112yes—
732#126C23×C61112yes—
733#126C23×C61112yes—
734#125C23×C6116yes—
735#125C23×C6116yes—
736#125C23×C6116yes—
737#125C23×C6116yes—
738#125C23×C6116yes—
739#125C23×C61112yes—
740#125C23×C6116yes—
741#125C23×C6116yes—
742#125C23×C6116yes—
743#125C23×C6116yes—
744#125C23×C6116yes—
745#125C23×C61112yes—
746#125C23×C6116yes—
747#125C23×C6116yes—
748#125C23×C6113yes—
749#125C23×C6113yes—
750#125C23×C6116yes—
751#125C23×C6116yes—
752#125C23×C6116yes—
753#125C23×C6112yes—
754#125C23×C6116yes—
755#125C23×C6116yes—
756#125C23×C6116yes—
757#125C23×C61112yes—
758#125C23×C61112yes—
759#125C23×C61112yes—
760#125C23×C61112yes—
761#125C23×C61112yes—
762#125C23×C61112yes—
763#124C23×C6116yes—
764#124C23×C6116yes—
765#124C23×C6116yes—
766#124C23×C6116yes—
767#124C23×C6116yes—
768#124C23×C6116yes—
769#124C23×C6113yes—
770#124C23×C6113yes—
771#124C23×C6116yes—
772#124C23×C61112yes—
773#123C23×C6112yes—
774#123C23×C6116yes—
775#123C23×C6116yes—
776#123C23×C6112yes—
777#123C23×C6116yes—
778#123C23×C6116yes—
779#123C23×C61112yes—
780#123C23×C61112yes—
781#123C23×C6116yes—
782#123C23×C6116yes—
783#123C23×C61112yes—
784#123C23×C61112yes—
785#123C23×C61112yes—
786#123C23×C61112yes—
787#123C23×C61112yes—
788C22⋊Q8C23×C6111yescharacteristic
789C22⋊Q8C23×C6116yes—
790C22⋊Q8C23×C6113yes—
791C22⋊Q8C23×C6116yes—
792C22⋊Q8C23×C6116yes—
793C22⋊Q8C23×C6116yes—
794C22⋊Q8C23×C6116yes—
795C22⋊Q8C23×C6116yes—
796C22⋊Q8C23×C6116yes—
797C22⋊Q8C23×C6116yes—
798C22⋊Q8C23×C6112yes—
799C22⋊Q8C23×C6116yes—
800C22⋊Q8C23×C6116yes—
801C22⋊Q8C23×C6116yes—
802C22⋊Q8C23×C6116yes—
803C22⋊Q8C23×C6116yes—
804C22⋊Q8C23×C6116yes—
805C22⋊Q8C23×C61112yes—
806C22⋊Q8C23×C6116yes—
807C22⋊Q8C23×C6116yes—
808C22⋊Q8C23×C61112yes—
809C22⋊Q8C23×C61112yes—
810C22⋊Q8C23×C61112yes—
811C22⋊Q8C23×C61112yes—
812C22⋊Q8C23×C61112yes—
813C22⋊Q8C23×C61112yes—
814C22⋊Q8C23×C61112yes—
815C22⋊Q8C23×C61112yes—
816#121C23×C6111yescharacteristic
817#121C23×C6116yes—
818#121C23×C6113yes—
819#121C23×C6116yes—
820#121C23×C6116yes—
821#121C23×C6116yes—
822#121C23×C6116yes—
823#121C23×C6116yes—
824#121C23×C6116yes—
825#121C23×C61112yes—
826C4×Q8C23×C6112yes—
827C4×Q8C23×C6111yescharacteristic
828C4×Q8C23×C6112yes—
829C4×Q8C23×C6112yes—
830C4×Q8C23×C6111yescharacteristic
831C4×Q8C23×C6116yes—
832C4×Q8C23×C6116yes—
833C4×Q8C23×C6116yes—
834C4×Q8C23×C6116yes—
835C4×Q8C23×C6113yes—
836C4×Q8C23×C6116yes—
837C4×Q8C23×C6116yes—
838C4×Q8C23×C6116yes—
839C4×Q8C23×C6116yes—
840C4×Q8C23×C6113yes—
841C4×Q8C23×C6112yes—
842C4×Q8C23×C6116yes—
843C4×Q8C23×C6116yes—
844C4×Q8C23×C6116yes—
845C4×Q8C23×C6116yes—
846C4×Q8C23×C6116yes—
847C4×Q8C23×C6116yes—
848C4×Q8C23×C61112yes—
849C4×Q8C23×C6113yes—
850C4×Q8C23×C6116yes—
851C4×Q8C23×C6113yes—
852C4×Q8C23×C6116yes—
853C4×Q8C23×C61112yes—
854C4×D4C23×C6112yes—
855C4×D4C23×C6116yes—
856C4×D4C23×C6116yes—
857C4×D4C23×C6116yes—
858C4×D4C23×C6116yes—
859C4×D4C23×C6116yes—
860C4×D4C23×C6116yes—
861C4×D4C23×C6116yes—
862C4×D4C23×C61112yes—
863C4×D4C23×C61112yes—
864C4×D4C23×C6116yes—
865C4×D4C23×C6116yes—
866C4×D4C23×C6116yes—
867C4×D4C23×C6116yes—
868C4×D4C23×C6116yes—
869C4×D4C23×C6113yes—
870C4×D4C23×C6113yes—
871C4×D4C23×C61112yes—
872C4×D4C23×C6116yes—
873#117C23×C6116yes—
874#117C23×C6116yes—
875#117C23×C6116yes—
876#117C23×C6116yes—
877#117C23×C6116yes—
878#117C23×C6116yes—
879#117C23×C6116yes—
880#117C23×C6116yes—
881#117C23×C6116yes—
882#117C23×C6116yes—
883#117C23×C61112yes—
884#117C23×C6116yes—
885#117C23×C61112yes—
886#117C23×C61112yes—
887#117C23×C61112yes—
888C2×C4⋊C4C23×C6111yescharacteristic
889C2×C4⋊C4C23×C6113yes—
890C2×C4⋊C4C23×C6113yes—
891C2×C4⋊C4C23×C6113yes—
892C2×C4⋊C4C23×C6113yes—
893C2×C4⋊C4C23×C6113yes—
894C2×C4⋊C4C23×C6116yes—
895C2×C4⋊C4C23×C61112yes—
896C2×C4⋊C4C23×C6116yes—
897C2×C4⋊C4C23×C6116yes—
898C2×C4⋊C4C23×C6116yes—
899C2×C4⋊C4C23×C61112yes—
900C2×C42C23×C6113yes—
901C2×C42C23×C6113yes—
902C2×C42C23×C6113yes—
903C2×C42C23×C6116yes—
904C2×C42C23×C6116yes—
905#41—28no—
906#41—412no—
907#41—412no—
908C2×Q8—24no—
909C2×Q8—28no—
910C2×Q8—46no—
911C2×Q8C24×C6113yes—
912C2×Q8C24×C6116yes—
913C2×Q8C24×C6116yes—
914C2×Q8C24×C6113yes—
915C2×Q8C24×C6111yescharacteristic
916C2×Q8C24×C6116yes—
917C2×Q8C24×C6116yes—
918C2×Q8C24×C6116yes—
919C2×Q8C24×C6116yes—
920C2×Q8C24×C6111yescharacteristic
921C2×D4C24×C6116yes—
922C2×D4C24×C6112yes—
923C2×D4C24×C6116yes—
924C2×D4C24×C6116yes—
925C2×D4C24×C6111yescharacteristic
926C2×D4C24×C6113yes—
927C2×D4C24×C6116yes—
928C2×D4C24×C6116yes—
929C22×C4C24×C6113yes—
930C22×C4C24×C6111yescharacteristic
931C22×C4C24×C6113yes—
932C22×C4C24×C6113yes—
933C22×C4C24×C6116yes—
934C22×C4C24×C6116yes—
935C22×C4C24×C6111yescharacteristic
936C22×C4C24×C6111yescharacteristic
937C22×C4C24×C6112yes—
938C22×C4C24×C6113yes—
939C22×C4C24×C6116yes—
940C22×C4C24×C6116yes—
941C22×C4C24×C6116yes—
942C22×C4C24×C61112yes—
943C22×C4C24×C61112yes—
944C4⋊C4C24×C6116yes—
945C4⋊C4C24×C6113yes—
946C4⋊C4C24×C6116yes—
947C4⋊C4C24×C6116yes—
948C4⋊C4C24×C6116yes—
949C4⋊C4C24×C6116yes—
950C4⋊C4C24×C6116yes—
951C4⋊C4C24×C6116yes—
952C4⋊C4C24×C6116yes—
953C4⋊C4C24×C61112yes—
954C4⋊C4C24×C6116yes—
955C4⋊C4C24×C6116yes—
956C4⋊C4C24×C6116yes—
957C4⋊C4C24×C6113yes—
958C4⋊C4C24×C61112yes—
959C4⋊C4C24×C61112yes—
960C4⋊C4C24×C6116yes—
961C4⋊C4C24×C61112yes—
962C4⋊C4C24×C6112yes—
963C4⋊C4C24×C6112yes—
964C4⋊C4C24×C6116yes—
965C4⋊C4C24×C6116yes—
966C4⋊C4C24×C6116yes—
967C4⋊C4C24×C6116yes—
968C4⋊C4C24×C6116yes—
969C4⋊C4C24×C61112yes—
970C4⋊C4C24×C6112yes—
971C4⋊C4C24×C6116yes—
972C4⋊C4C24×C6112yes—
973C4⋊C4C24×C6112yes—
974C4⋊C4C24×C6116yes—
975C4⋊C4C24×C6116yes—
976C4⋊C4C24×C61112yes—
977C4⋊C4C24×C6116yes—
978C4⋊C4C24×C6116yes—
979C4⋊C4C24×C6116yes—
980C4⋊C4C24×C6116yes—
981C4⋊C4C24×C6116yes—
982C4⋊C4C24×C6116yes—
983C4⋊C4C24×C6116yes—
984C4⋊C4C24×C6116yes—
985C4⋊C4C24×C6111yescharacteristic
986C4⋊C4C24×C6113yes—
987C4⋊C4C24×C6113yes—
988C4⋊C4C24×C6111yescharacteristic
989C4⋊C4C24×C6112yes—
990C4⋊C4C24×C6116yes—
991C22⋊C4C24×C6116yes—
992C22⋊C4C24×C6112yes—
993C22⋊C4C24×C6112yes—
994C22⋊C4C24×C6116yes—
995C22⋊C4C24×C6112yes—
996C22⋊C4C24×C6116yes—
997C22⋊C4C24×C6116yes—
998C22⋊C4C24×C6112yes—
999C22⋊C4C24×C6116yes—
1000C22⋊C4C24×C61112yes—
1001C22⋊C4C24×C61112yes—
1002C22⋊C4C24×C6116yes—
1003C22⋊C4C24×C6116yes—
1004C22⋊C4C24×C6116yes—
1005C22⋊C4C24×C61112yes—
1006C22⋊C4C24×C61112yes—
1007C22⋊C4C24×C6116yes—
1008C22⋊C4C24×C6116yes—
1009C22⋊C4C24×C6116yes—
1010C22⋊C4C24×C6116yes—
1011C22⋊C4C24×C6116yes—
1012C22⋊C4C24×C6112yes—
1013C42C24×C6116yes—
1014C42C24×C6112yes—
1015C42C24×C6116yes—
1016C42C24×C6116yes—
1017C42C24×C6116yes—
1018C42C24×C6113yes—
1019C42C24×C6116yes—
1020C42C24×C6116yes—
1021C42C24×C6116yes—
1022C42C24×C6113yes—
1023C42C24×C6116yes—
1024C42C24×C6116yes—
1025C42C24×C6113yes—
1026C42C24×C6113yes—
1027C42C24×C61112yes—
1028C42C24×C61112yes—
1029C23C25×C6112yes—
1030C23C25×C6116yes—
1031C23C25×C6111yescharacteristic
1032Q8—26no—
1033Q8—212no—
1034Q8—46no—
1035Q8—46no—
1036Q8—46no—
1037Q8—43no—
1038Q8—41no—
1039Q8—46no—
1040Q8—46no—
1041Q82−1+4×C6114yes—
1042D4—24no—
1043D4—212no—
1044D4—212no—
1045D4—46no—
1046D4—43no—
1047D4—41no—
1048D4—46no—
1049D4—46no—
1050C2×C4—22no—
1051C2×C4—26no—
1052C2×C4—26no—
1053C2×C4—26no—
1054C2×C4—212no—
1055C2×C4—212no—
1056C2×C4—41no—
1057C2×C4—46no—
1058C2×C4—42no—
1059C2×C4—43no—
1060C2×C4—412no—
1061C2×C4—41no—
1062C2×C4—412no—
1063C2×C4—46no—
1064C2×C4—46no—
1065C2×C4C25×C6112yes—
1066C2×C4C25×C6113yes—
1067C2×C4C25×C6116yes—
1068C2×C4C25×C6112yes—
1069C2×C4C25×C6112yes—
1070C2×C4C25×C6111yescharacteristic
1071C2×C4C25×C6113yes—
1072C2×C4C25×C6111yescharacteristic
1073C2×C4C25×C6112yes—
1074C2×C4C25×C6116yes—
1075C2×C4C25×C6116yes—
1076C2×C4C25×C6116yes—
1077C2×C4C25×C6112yes—
1078C2×C4C25×C6116yes—
1079C2×C4C25×C6113yes—
1080C2×C4C25×C6113yes—
1081C22—21no—
1082C22—21no—
1083C22—22no—
1084C22—26no—
1085C22—22no—
1086C22—26no—
1087C22—26no—
1088C22—22no—
1089C22C61×#58512yes—
1090C22C26×C6111yescharacteristic
1091C4—22no—
1092C4—23no—
1093C4—26no—
1094C4—23no—
1095C4—26no—
1096C4—23no—
1097C4—22no—
1098C4—26no—
1099C4—22no—
1100C4—22no—
1101C4—26no—
1102C4—26no—
1103C4—21no—
1104C4—21no—
1105C4—22no—
1106C4C2×2−1+4×C6116yes—
1107C2—22no—
1108C2—42no—
1109C2—46no—
1110C2C22×2−1+4×C6111yescharacteristic
1111C2C2×C61×#58511yescharacteristic
1112C2C61×2−1+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×#3563C2semidirect
3. C61×#3563C2semidirect
4. C61×#3559C2semidirect
5. C61×#3557C2semidirect
6. C61×#3555C2semidirect
7. C61×#3544C2semidirect
8. C61×#3524C2semidirect
9. C61×#3523C2semidirect
10. C61×#3522C2semidirect
11. C61×#3516C2semidirect
12. C61×#3516C2semidirect
13. C61×#3515C2semidirect
14. C61×#3507C2semidirect
15. C61×#3504C2semidirect
16. C61×#3502C2semidirect
17. C61×#3482C2semidirect
18. C2×C61×#557C2semidirect
19. C61×#3461C2semidirect
524. #62949C61direct (N × H)
551. #3565C2×C61semidirect
552. #3563C2×C61semidirect
553. #3563C2×C61semidirect
554. #3559C2×C61semidirect
555. #3557C2×C61semidirect
556. #3555C2×C61semidirect
557. #3544C2×C61semidirect
558. #3524C2×C61semidirect
559. #3523C2×C61semidirect
560. #3522C2×C61semidirect
561. #3516C2×C61semidirect
562. #3516C2×C61semidirect
563. #3515C2×C61semidirect
564. #3507C2×C61semidirect
565. #3504C2×C61semidirect
566. #3502C2×C61semidirect
567. #3482C2×C61semidirect
568. C2×#557C2×C61semidirect
569. #3461C2×C61semidirect
694. C61#62949direct (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×#35572
C61×#35552
C61×#35442
C61×#35242
C61×#35232
C61×#35222
C61×#35162
C61×#35152
C61×#35072
C61×#35042
C61×#35022
C61×#34822
C2×C61×#5572
C61×#34612
#6294961