Finite Group Databasebeta

← #29696346

Subgroups — #29696346

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839834C211yesmaximal, characteristic
2#21448748C211yesmaximal, characteristic
3#21446793C211yesmaximal, characteristic, complemented
4#21446768C211yesmaximal, characteristic, complemented
5#21446253C211yesmaximal, characteristic, complemented
6#21446243C211yesmaximal, characteristic, complemented
7#21446132C211yesmaximal, characteristic, complemented
8#21446127C211yesmaximal, characteristic, complemented
9#21445914C211yesmaximal, characteristic, complemented
10#21445914C211yesmaximal, characteristic, complemented
11#21445834C211yesmaximal, characteristic, complemented
12#21445649C211yesmaximal, characteristic, complemented
13#21445540C211yesmaximal, characteristic, complemented
14#21445535C211yesmaximal, characteristic, complemented
15C2×C61×#556C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20#16839834—24no—
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29#16839655—21no—
30#16839648—21no—
31#16839642—21no—
32#16839628C2211yescharacteristic
33#16839622C2211yescharacteristic
34#16839622C2211yescharacteristic
35C4×C4⋊Dic61C2211yescharacteristic
36C22⋊C4×Dic61—21no—
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C61×#556—24no—
50C61×#556C418yescomplemented
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×#126×C61—21no—
53C2×#126×C61—21no—
54C2×#124×C61—21no—
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×C4×Q8×C61—21no—
58C2×C4×Q8×C61C2211yescharacteristic
59C2×C4×D4×C61C2211yescharacteristic
60C2×#117×C61C2211yescharacteristic
61C2×#117×C61C2211yescharacteristic
62C23×Dic61—21no—
63C2×#11758194—22no—
64C2×#11758194—22no—
65C2×#11758194—41no—
66C22×#92418—22no—
67C22×#92418—22no—
68C22×#92418—41no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519736—22no—
74#14519736—41no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C4⋊#92418—22no—
88#14519701—22no—
89#14519701—22no—
90#14519701—41no—
91#14519701—41no—
92C22⋊#92418—22no—
93C22⋊#92418—22no—
94#14519688—22no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100C22×Q8×C61—21no—
101C22×Q8×C61C2311yescharacteristic
102C22×D4×C61D411yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C4⋊Q8×C61—22no—
106C4⋊Q8×C61C2×C414yescomplemented
107#126×C61—28no—
108#126×C61—28no—
109#124×C61—28no—
110C22⋊Q8×C61—22no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61C2×C414yes—
113C22⋊Q8×C61C2×C414yescomplemented
114C4×Q8×C61—28no—
115C4×Q8×C61—22no—
116C4×Q8×C61C2×C414yescomplemented
117C4×D4×C61C2×C414yes—
118C4×D4×C61D414yes—
119#117×C61—22no—
120#117×C61—22no—
121#117×C61C2×C414yes—
122#117×C61C2×C414yescomplemented
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61—21no—
138C2×C42×C61—21no—
139C2×C42×C61—21no—
140C2×C42×C61C2311yescharacteristic
141C24×C61C2×D411yescharacteristic
142C24×C61C2×D411yescharacteristic
143C2×Q8×C61—24no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—42no—
150C2×Q8×C61—42no—
151C2×Q8×C61C22×C412yes—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61C22⋊C414yes—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61C22×C412yes—
168C22×C4×C61C22×C412yes—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2×D412yes—
175C22×C4×C61C2411yescharacteristic
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—42no—
181C22×Dic61—42no—
182C22×Dic61—81no—
183C4⋊C4×C61—24no—
184C4⋊C4×C61—24no—
185C4⋊C4×C61—24no—
186C4⋊C4×C61—24no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61C22⋊C414yes—
191C4⋊C4×C61C22×C412yes—
192C4⋊C4×C61C22×C412yes—
193C4⋊C4×C61C22×C412yes—
194C22⋊C4×C61—24no—
195C22⋊C4×C61—24no—
196C22⋊C4×C61—24no—
197C22⋊C4×C61—24no—
198C22⋊C4×C61C22⋊C414yes—
199C22⋊C4×C61C22⋊C414yes—
200C42×C61—24no—
201C42×C61—24no—
202C42×C61—24no—
203C42×C61C22×C412yes—
204C42×C61C2×D412yes—
205C22⋊Dic61—42no—
206C22⋊Dic61—42no—
207C22⋊Dic61—81no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—42no—
216C4⋊Dic61#4112yes—
217C4×Dic61—42no—
218C4×Dic61—81no—
219#11758194—44no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—44no—
232C2×#92418#4112yes—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61C2×C22⋊C412yes—
246C23×C61C2×C22⋊C412yes—
247C23×C61C22×D411yescharacteristic
248Q8×C61—22no—
249Q8×C61—22no—
250Q8×C61—48no—
251Q8×C61—41no—
252Q8×C61—41no—
253D4×C61—44no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61C2×C22⋊C412yes—
283C2×C4×C61C2×C22⋊C412yes—
284C2×C4×C61C2×C22⋊C412yes—
285C2×C4×C61C2×C22⋊C412yes—
286C2×C4×C61C23×C411yescharacteristic
287C2×C4×C61C22×D411yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C612−1+411yescharacteristic
292C2×Dic61—22no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—84no—
305#92418—22no—
306#92418—41no—
307#92418—41no—
308#92418—41no—
309#22494—611nomaximal, Sylow
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61C22×C22⋊C411yescharacteristic
325C22×C61#54611yescharacteristic
326C22×C61#54711yescharacteristic
327C22×C61#57511yescharacteristic
328C22×C61#57511yescharacteristic
329C22×C61#57711yescharacteristic
330C22×C61#57811yescharacteristic
331C4×C61—22no—
332C4×C61—22no—
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—42no—
336C4×C61—42no—
337C4×C61—42no—
338C4×C61—42no—
339C4×C61C4×#4111yescharacteristic
340C4×C61#52011yescharacteristic
341C4×C61#54611yescharacteristic
342C4×C61#54711yescharacteristic
343Dic61—42no—
344Dic61—81no—
345Dic61—81no—
346Dic61—81no—
347C2×#556D6111yescharacteristic
348C2×#435—611no—
349#2352—611no—
350#1993—611no—
351#1987—611no—
352#1894—611no—
353#1892—611no—
354#1873—611no—
355#1872—611no—
356#1825—611no—
357#1825—611no—
358#1805—611no—
359#1763—611no—
360#1736—611no—
361#1735—611no—
362C2×C61—42no—
363C2×C61—42no—
364C2×C61#233911yescharacteristic
365C2×C61#289611yescharacteristic
366C2×C61#289811yescharacteristic
367C2×C61#331111yescharacteristic
368C2×C61#331311yescharacteristic
369C2×C61#334911yescharacteristic
370C2×C61#335011yescharacteristic
371C22×M16—611no—
372C23×C8—611no—
373#556—24no—
374#556Dic6118yescomplemented
375C2×C4⋊Q8C2×D6111yescharacteristic
376C2×#126—21no—
377C2×#126—21no—
378C2×#124—21no—
379C2×C22⋊Q8C2×D6111yescharacteristic
380C2×C22⋊Q8C2×D6111yescharacteristic
381C2×C4×Q8—21no—
382C2×C4×Q8C2×D6111yescharacteristic
383C2×C4×D4C2×D6111yescharacteristic
384C2×#117—611no—
385C2×#117C2×D6111yescharacteristic
386C2×#117C2×D6111yescharacteristic
387C22×C4⋊C4—611no—
388#435—1224no—
389C2×C4⋊C8—611no—
390C2×#103—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×C22⋊C8—611no—
395C2×C22⋊C8—611no—
396C2×#97—611no—
397#388—1221no—
398#387—1221no—
399#386—1221no—
400#382—611no—
401#380—611no—
402#380—611no—
403C4×C4⋊C4—611no—
404C4×C22⋊C4—1221no—
405#340—611no—
406#340—611no—
407#340—611no—
408#340—611no—
409#340—611no—
410#340—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417C61#2249411yescharacteristic, complemented, Sylow
418C22×Q8—21no—
419C22×Q8C22×D6111yescharacteristic
420C22×D4C22⋊D6111yescharacteristic
421C23×C4—1221no—
422C23×C4C22×D6111yescharacteristic
423C23×C4C22×D6111yescharacteristic
424C2×M16—1222no—
425C2×M16—1222no—
426C2×M16—2441no—
427C22×C8—611no—
428C22×C8—611no—
429C22×C8—611no—
430C22×C8—611no—
431C22×C8—1222no—
432C22×C8—1222no—
433C22×C8—2441no—
434C4⋊Q8—22no—
435C4⋊Q8C2×Dic6114yescomplemented
436#126—28no—
437#126—28no—
438#124—28no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8C2×Dic6114yes—
442C22⋊Q8C2×Dic6114yescomplemented
443C4×Q8—28no—
444C4×Q8—22no—
445C4×Q8C2×Dic6114yescomplemented
446C4×D4C2×Dic6114yes—
447C4×D4C22⋊D6114yes—
448#117—22no—
449#117—22no—
450#117—1222no—
451#117—2441no—
452#117C2×Dic6114yes—
453#117C2×Dic6114yescomplemented
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—1222no—
463C2×C4⋊C4—1221no—
464C2×C4⋊C4—2441no—
465C2×C4⋊C4C22⋊D6111yescharacteristic
466C2×C4⋊C4C22×D6111yescharacteristic
467C2×C4⋊C4C22×D6111yescharacteristic
468C2×C4⋊C4C22×D6111yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—1221no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4C22⋊D6111yescharacteristic
477C2×C22⋊C4C22⋊D6111yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—1221no—
482C2×C42—1221no—
483C2×C42C22×D6111yescharacteristic
484C4⋊C8—1222no—
485#103—1222no—
486#103—1222no—
487#103—2441no—
488#103—2441no—
489C22⋊C8—1222no—
490C22⋊C8—1222no—
491#97—1222no—
492#95—1221no—
493#95—1221no—
494#95—1221no—
495#95—1221no—
496#95—1221no—
497C24C2×C22⋊D6111yescharacteristic
498C24C2×C22⋊D6111yescharacteristic
499C2×Q8—21no—
500C2×Q8—24no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8C22×Dic6112yes—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4C22⋊Dic6114yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—4881no—
528C22×C4—2442no—
529C22×C4—2442no—
530C22×C4C22×Dic6112yes—
531C22×C4C22×Dic6112yes—
532C22×C4C2×C22⋊D6112yes—
533C22×C4C2×C22⋊D6112yes—
534C22×C4C2×C22⋊D6111yescharacteristic
535C22×C4C2×C22⋊D6111yescharacteristic
536C22×C4C2×C22⋊D6111yescharacteristic
537C22×C4C2×C22⋊D6111yescharacteristic
538C22×C4C23×D6111yescharacteristic
539M16—2444no—
540C2×C8—612no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—2444no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—612no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—2442no—
569C4⋊C4C22⋊Dic6114yes—
570C4⋊C4C22×Dic6112yes—
571C4⋊C4C22×Dic6112yes—
572C4⋊C4C22×Dic6112yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—4881no—
578C22⋊C4—2442no—
579C22⋊C4—2442no—
580C22⋊C4C22⋊Dic6114yes—
581C22⋊C4C22⋊Dic6114yes—
582C42—24no—
583C42—24no—
584C42—24no—
585C42—4881no—
586C42—2442no—
587C42C22×Dic6112yes—
588C42C2×C22⋊D6112yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×C22⋊Dic6112yes—
602C23C2×C22⋊Dic6112yes—
603C23C22×C22⋊D6111yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—48no—
607Q8—41no—
608Q8—41no—
609D4—44no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—1222no—
639C2×C4—4884no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4—2441no—
645C2×C4—2441no—
646C2×C4—2441no—
647C2×C4—2441no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4C2×C22⋊Dic6112yes—
652C2×C4C2×C22⋊Dic6112yes—
653C2×C4C2×C22⋊Dic6112yes—
654C2×C4C2×C22⋊Dic6112yes—
655C2×C4C23×Dic6111yescharacteristic
656C2×C4C22×C22⋊D6111yescharacteristic
657C2×C4#41×D6111yescharacteristic
658C2×C4#41×D6111yescharacteristic
659C2×C4#1451982311yescharacteristic
660C2×C4#1451982411yescharacteristic
661C8—1222no—
662C8—2441no—
663C8—2441no—
664C8—2441no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×C22⋊Dic6111yescharacteristic
680C22#1684040011yescharacteristic
681C22#1684041111yescharacteristic
682C22#1684056011yescharacteristic
683C22#1684056011yescharacteristic
684C22#1684057011yescharacteristic
685C22#1684057711yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—4881no—
695C4—4881no—
696C4—4881no—
697C4—2442no—
698C4#41×Dic6111yescharacteristic
699C4#1684024511yescharacteristic
700C4#1684040011yescharacteristic
701C4#1684041111yescharacteristic
702C2—42no—
703C2—42no—
704C2#2144864911yescharacteristic
705C2#2145433811yescharacteristic
706C2#2145435211yescharacteristic
707C2#2145784911yescharacteristic
708C2#2145787911yescharacteristic
709C2#2145834311yescharacteristic
710C2#2145836411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#556C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
cosocleC22×C4×C61C24
hypercenterC2×#556D61
hypocenterC61#22494
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
3. #21446793C2semidirect
4. #21446768C2semidirect
5. #21446253C2semidirect
6. #21446243C2semidirect
7. #21446132C2semidirect
8. #21446127C2semidirect
9. #21445914C2semidirect
10. #21445914C2semidirect
11. #21445834C2semidirect
12. #21445649C2semidirect
13. #21445540C2semidirect
14. #21445535C2semidirect
50. C61×#556C4semidirect
106. C4⋊Q8×C61C2×C4semidirect
113. C22⋊Q8×C61C2×C4semidirect
116. C4×Q8×C61C2×C4semidirect
122. #117×C61C2×C4semidirect
374. #556Dic61semidirect
417. C61#22494semidirect
435. C4⋊Q8C2×Dic61semidirect
442. C22⋊Q8C2×Dic61semidirect
445. C4×Q8C2×Dic61semidirect
453. #117C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
#214487482
#214467932
#214467682
#214462532
#214462432
#214461322
#214461272
#214459142
#214458342
#214456492
#214455402
#214455352
C2×C61×#5562
#2249461