Finite Group Databasebeta

← #29689784

Subgroups — #29689784

Order 15616.

1086 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839823C211yesmaximal, characteristic, complemented
2#21448442C211yesmaximal, characteristic, complemented
3#21446793C211yesmaximal, characteristic, complemented
4#21446781C211yesmaximal, characteristic, complemented
5#21446636C211yesmaximal, characteristic, complemented
6#21446631C211yesmaximal, characteristic, complemented
7#21446142C211yesmaximal, characteristic
8#21446137C211yesmaximal, characteristic
9#21446132C211yesmaximal, characteristic, complemented
10#21446127C211yesmaximal, characteristic, complemented
11#21445834C211yesmaximal, characteristic, complemented
12#21445829C211yesmaximal, characteristic, complemented
13#21445824C211yesmaximal, characteristic, complemented
14#21445819C211yesmaximal, characteristic, complemented
15C2×C61×#542C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18#16839823—24no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519701C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519698C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839661—21no—
34#16839661—21no—
35#16839637—21no—
36#16839637—21no—
37#16839632C2211yescharacteristic
38#16839632C2211yescharacteristic
39#16839628C2211yescharacteristic
40#16839628C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C61×#542—24no—
50C61×#542C418yescomplemented
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×#126×C61—21no—
53C2×#124×C61—21no—
54C2×#124×C61C2211yescharacteristic
55C2×#123×C61—21no—
56C2×C22⋊Q8×C61—21no—
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×#121×C61C2211yescharacteristic
59C2×C4×Q8×C61C2211yescharacteristic
60C2×C4×D4×C61C2211yescharacteristic
61C2×#117×C61C2211yescharacteristic
62C23×Dic61—21no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519736—41no—
68#14519736—41no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—41no—
75C2×C4⋊Dic61—41no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C22⋊Dic61—21no—
81C2×C4×Dic61—21no—
82C4⋊#92418—22no—
83C4⋊#92418—22no—
84#14519701—41no—
85#14519701—41no—
86#14519701—41no—
87#14519701—41no—
88#14519698—41no—
89#14519698—41no—
90#14519698—41no—
91#14519698—41no—
92C22⋊#92418—22no—
93C22⋊#92418—22no—
94#14519688—22no—
95C4×#92418—22no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100C22×Q8×C61—21no—
101C22×Q8×C61C2311yescharacteristic
102C22×D4×C61—21no—
103C22×D4×C61C2311yescharacteristic
104C23×C4×C61—21no—
105C23×C4×C61C2311yescharacteristic
106C4⋊Q8×C61—22no—
107C4⋊Q8×C61C2×C414yescomplemented
108#126×C61—28no—
109#124×C61—28no—
110#124×C61—22no—
111#124×C61C2×C414yescomplemented
112#123×C61—28no—
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61—28no—
115C22⋊Q8×C61C2×C414yes—
116#121×C61—22no—
117#121×C61C2×C414yes—
118C4×Q8×C61—22no—
119C4×Q8×C61C2×C414yescomplemented
120C4×D4×C61—22no—
121C4×D4×C61C2×C414yescomplemented
122#117×C61C2×C414yes—
123#117×C61D414yes—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C4⋊C4×C61D411yescharacteristic
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×C61—21no—
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140C2×C42×C61C2311yescharacteristic
141C24×C61—21no—
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—81no—
150C2×Q8×C61—81no—
151C2×Q8×C61C22×C412yes—
152C2×D4×C61—24no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—81no—
159C2×D4×C61—81no—
160C2×D4×C61C22×C412yes—
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×C61—21no—
168C22×C4×C61—24no—
169C22×C4×C61—81no—
170C22×C4×C61—81no—
171C22×C4×C61C22×C412yes—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D412yes—
178C22×C4×C61C2411yescharacteristic
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—42no—
184C22×Dic61—81no—
185C22×Dic61—81no—
186C4⋊C4×C61—24no—
187C4⋊C4×C61—24no—
188C4⋊C4×C61—24no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61C22⋊C414yes—
192C4⋊C4×C61C22⋊C414yes—
193C4⋊C4×C61C22×C412yes—
194C4⋊C4×C61C22×C412yes—
195C22⋊C4×C61—24no—
196C22⋊C4×C61—24no—
197C22⋊C4×C61—24no—
198C22⋊C4×C61—24no—
199C22⋊C4×C61—24no—
200C22⋊C4×C61C22⋊C414yes—
201C22⋊C4×C61C22⋊C414yes—
202C42×C61—24no—
203C42×C61C22×C412yes—
204C42×C61C22×C412yes—
205C42×C61C2×D412yes—
206C42×C61C2×D412yes—
207C22⋊Dic61—42no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—42no—
217C4⋊Dic61—81no—
218C4⋊Dic61—81no—
219C4⋊Dic61—81no—
220C4⋊Dic61—81no—
221C4×Dic61—42no—
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—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—22no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61C2×C22⋊C412yes—
248C23×C61C22×D411yescharacteristic
249Q8×C61—22no—
250Q8×C61—22no—
251Q8×C61—41no—
252Q8×C61—41no—
253Q8×C61—84no—
254D4×C61—22no—
255D4×C61—22no—
256D4×C61—41no—
257D4×C61—41no—
258D4×C61—84no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
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×C61—84no—
283C2×C4×C61C2×C22⋊C412yes—
284C2×C4×C61C2×C22⋊C412yes—
285C2×C4×C61C2×C22⋊C412yes—
286C2×C4×C61C2×C22⋊C412yes—
287C2×C4×C61C2×C22⋊C412yes—
288C2×C4×C61C23×C411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C2×C4×C612−1+411yescharacteristic
293C2×C4×C612−1+411yescharacteristic
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—41no—
305C2×Dic61—41no—
306C2×Dic61—84no—
307#92418—41no—
308#92418—41no—
309#92418—41no—
310#92418—41no—
311#21871—611nomaximal, Sylow
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—81no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61C22×C22⋊C411yescharacteristic
327C22×C61#53511yescharacteristic
328C22×C61#53611yescharacteristic
329C22×C61#57611yescharacteristic
330C22×C61#57711yescharacteristic
331C22×C61#57711yescharacteristic
332C22×C61#57811yescharacteristic
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—22no—
338C4×C61—42no—
339C4×C61—42no—
340C4×C61—42no—
341C4×C61#52011yescharacteristic
342C4×C61#52011yescharacteristic
343C4×C61#53711yescharacteristic
344C4×C61#53711yescharacteristic
345Dic61—81no—
346Dic61—81no—
347Dic61—81no—
348Dic61—81no—
349C2×#542D6111yescharacteristic
350C2×#433—611no—
351#2317—611no—
352#1993—611no—
353#1990—611no—
354#1959—611no—
355#1958—611no—
356#1875—611no—
357#1874—611no—
358#1873—611no—
359#1872—611no—
360#1805—611no—
361#1804—611no—
362#1803—611no—
363#1802—611no—
364C2×C61—42no—
365C2×C61—82no—
366C2×C61#231111yescharacteristic
367C2×C61#289711yescharacteristic
368C2×C61#289811yescharacteristic
369C2×C61#322411yescharacteristic
370C2×C61#322511yescharacteristic
371C2×C61#324311yescharacteristic
372C2×C61#324411yescharacteristic
373#542—24no—
374#542Dic6118yescomplemented
375C2×C4⋊Q8C2×D6111yescharacteristic
376C2×#126—21no—
377C2×#124—21no—
378C2×#124C2×D6111yescharacteristic
379C2×#123—21no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8C2×D6111yescharacteristic
382C2×#121C2×D6111yescharacteristic
383C2×C4×Q8C2×D6111yescharacteristic
384C2×C4×D4C2×D6111yescharacteristic
385C2×#117—611no—
386C2×#117C2×D6111yescharacteristic
387C22×C4⋊C4—611no—
388#433—1224no—
389C2×C4⋊C8—611no—
390C2×C4⋊C8—611no—
391C2×#103—611no—
392C2×#103—611no—
393C2×#103—611no—
394C2×#103—611no—
395C2×#102—611no—
396C2×#102—611no—
397C2×#102—611no—
398C2×#102—611no—
399C2×C22⋊C8—611no—
400C2×C22⋊C8—611no—
401C2×#97—611no—
402C2×C4×C8—611no—
403#389—1221no—
404#389—1221no—
405#385—1221no—
406#385—1221no—
407#384—611no—
408#384—611no—
409#382—611no—
410#382—611no—
411#340—611no—
412#340—611no—
413#340—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419C61#2187111yescharacteristic, complemented, Sylow
420C22×Q8—21no—
421C22×Q8C22×D6111yescharacteristic
422C22×D4—21no—
423C22×D4C22×D6111yescharacteristic
424C23×C4—21no—
425C23×C4—1221no—
426C23×C4C22×D6111yescharacteristic
427C22×C8—611no—
428C22×C8—611no—
429C22×C8—611no—
430C22×C8—611no—
431C4⋊Q8—22no—
432C4⋊Q8C2×Dic6114yescomplemented
433#126—28no—
434#124—28no—
435#124—22no—
436#124C2×Dic6114yescomplemented
437#123—28no—
438C22⋊Q8—22no—
439C22⋊Q8—28no—
440C22⋊Q8C2×Dic6114yes—
441#121—22no—
442#121C2×Dic6114yes—
443C4×Q8—22no—
444C4×Q8C2×Dic6114yescomplemented
445C4×D4—22no—
446C4×D4C2×Dic6114yescomplemented
447#117—2441no—
448#117—2441no—
449#117C2×Dic6114yes—
450#117C22⋊D6114yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4—1221no—
461C2×C4⋊C4—1221no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4—2441no—
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—21no—
474C2×C22⋊C4—1221no—
475C2×C22⋊C4C22⋊D6111yescharacteristic
476C2×C22⋊C4C22⋊D6111yescharacteristic
477C2×C42—21no—
478C2×C42—1221no—
479C2×C42C22×D6111yescharacteristic
480C2×C42C22×D6111yescharacteristic
481C4⋊C8—1222no—
482C4⋊C8—1222no—
483#103—2441no—
484#103—2441no—
485#103—2441no—
486#103—2441no—
487#102—2441no—
488#102—2441no—
489#102—2441no—
490#102—2441no—
491C22⋊C8—1222no—
492C22⋊C8—1222no—
493#97—1222no—
494C4×C8—1222no—
495#95—1221no—
496#95—1221no—
497#95—1221no—
498#95—1221no—
499C24—21no—
500C24C2×C22⋊D6111yescharacteristic
501C2×Q8—21no—
502C2×Q8—24no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8C22×Dic6112yes—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C22×Dic6112yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—4881no—
534C22×C4—4881no—
535C22×C4—2442no—
536C22×C4C22×Dic6112yes—
537C22×C4C2×C22⋊D6112yes—
538C22×C4C2×C22⋊D6111yescharacteristic
539C22×C4C2×C22⋊D6111yescharacteristic
540C22×C4C2×C22⋊D6111yescharacteristic
541C22×C4C2×C22⋊D6111yescharacteristic
542C22×C4C2×C22⋊D6111yescharacteristic
543C22×C4C23×D6111yescharacteristic
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—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1221no—
568C4⋊C4—1221no—
569C4⋊C4—4881no—
570C4⋊C4—4881no—
571C4⋊C4—4881no—
572C4⋊C4—4881no—
573C4⋊C4—2442no—
574C4⋊C4C22⋊Dic6114yes—
575C4⋊C4C22⋊Dic6114yes—
576C4⋊C4C22×Dic6112yes—
577C4⋊C4C22×Dic6112yes—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—2442no—
584C22⋊C4C22⋊Dic6114yes—
585C22⋊C4C22⋊Dic6114yes—
586C42—24no—
587C42—2442no—
588C42C22×Dic6112yes—
589C42C22×Dic6112yes—
590C42C2×C22⋊D6112yes—
591C42C2×C22⋊D6112yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C22⋊Dic6112yes—
606C23C22×C22⋊D6111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—4884no—
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×C4—2441no—
652C2×C4—2441no—
653C2×C4—2441no—
654C2×C4C2×C22⋊Dic6112yes—
655C2×C4C2×C22⋊Dic6112yes—
656C2×C4C2×C22⋊Dic6112yes—
657C2×C4C2×C22⋊Dic6112yes—
658C2×C4C2×C22⋊Dic6112yes—
659C2×C4C23×Dic6111yescharacteristic
660C2×C4C22×C22⋊D6111yescharacteristic
661C2×C4#1451982311yescharacteristic
662C2×C4#1451982311yescharacteristic
663C2×C4#1451982411yescharacteristic
664C2×C4#1451982411yescharacteristic
665C8—2441no—
666C8—2441no—
667C8—2441no—
668C8—2441no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊Dic6111yescharacteristic
684C22#1684032611yescharacteristic
685C22#1684033311yescharacteristic
686C22#1684056511yescharacteristic
687C22#1684057011yescharacteristic
688C22#1684057311yescharacteristic
689C22#1684057711yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—4881no—
699C4—4881no—
700C4—4881no—
701C4—4881no—
702C4#1684024511yescharacteristic
703C4#1684024511yescharacteristic
704C4#1684034011yescharacteristic
705C4#1684034011yescharacteristic
706C2—42no—
707C2—82no—
708C2#2144841111yescharacteristic
709C2#2145434511yescharacteristic
710C2#2145435211yescharacteristic
711C2#2145690711yescharacteristic
712C2#2145692211yescharacteristic
713C2#2145709611yescharacteristic
714C2#2145711111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
prime radicalC2×#121×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#542D61
hypocenterC61#21871
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16839823C2semidirect
2. #21448442C2semidirect
3. #21446793C2semidirect
4. #21446781C2semidirect
5. #21446636C2semidirect
6. #21446631C2semidirect
9. #21446132C2semidirect
10. #21446127C2semidirect
11. #21445834C2semidirect
12. #21445829C2semidirect
13. #21445824C2semidirect
14. #21445819C2semidirect
50. C61×#542C4semidirect
107. C4⋊Q8×C61C2×C4semidirect
111. #124×C61C2×C4semidirect
119. C4×Q8×C61C2×C4semidirect
121. C4×D4×C61C2×C4semidirect
374. #542Dic61semidirect
419. C61#21871semidirect
432. C4⋊Q8C2×Dic61semidirect
436. #124C2×Dic61semidirect
444. C4×Q8C2×Dic61semidirect
446. C4×D4C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398232
#214484422
#214467932
#214467812
#214466362
#214466312
#214461422
#214461372
#214461322
#214461272
#214458342
#214458292
#214458242
#214458192
C2×C61×#5422
#2187161