Finite Group Databasebeta

← #29714003

Subgroups — #29714003

Order 15616.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840059C211yesmaximal, characteristic, complemented
2C2×C4×#11758201C211yesmaximal, characteristic, complemented
3#21450720C211yesmaximal, characteristic
4#21447019C211yesmaximal, characteristic, complemented
5#21447012C211yesmaximal, characteristic, complemented
6#21446820C211yesmaximal, characteristic, complemented
7#21446820C211yesmaximal, characteristic, complemented
8#21446785C211yesmaximal, characteristic, complemented
9#21446614C211yesmaximal, characteristic, complemented
10#21446141C211yesmaximal, characteristic, complemented
11#21446136C211yesmaximal, characteristic, complemented
12#21446018C211yesmaximal, characteristic, complemented
13#21446012C211yesmaximal, characteristic, complemented
14#21445834C211yesmaximal, characteristic, complemented
15C2×C61×#552C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20#16840059—24no—
21C4×#11758201—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37#16839688—21no—
38#16839670—21no—
39#16839638—21no—
40#16839638—21no—
41#16839628C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C61×#552—24no—
51C61×#552—24no—
52C2×#126×C61—21no—
53C2×#125×C61—21no—
54C2×#125×C61C2211yescharacteristic
55C2×#123×C61—21no—
56C2×C22⋊Q8×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×C4×D4×C61C2211yescharacteristic
60C2×#117×C61—21no—
61C2×#117×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67C2×#11758201—22no—
68C2×#11758201—22no—
69C2×#11758201—22no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519751—22no—
75#14519751—22no—
76#14519751—41no—
77#14519751—41no—
78C4×D244—22no—
79C4×D244—22no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88#14519710—22no—
89#14519708—22no—
90#14519708—22no—
91C4⋊#92418—22no—
92#14519701—22no—
93#14519701—41no—
94#14519701—41no—
95#14519697—22no—
96#14519697—22no—
97#14519697—22no—
98C22⋊#92418—22no—
99C22⋊#92418—22no—
100C22⋊#92418—41no—
101C22⋊#92418—41no—
102C4×#92418—22no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C22×Q8×C61C2311yescharacteristic
108C22×D4×C61D411yescharacteristic
109C23×C4×C61—21no—
110C23×C4×C61C2311yescharacteristic
111C23×C4×C61C2311yescharacteristic
112#126×C61—28no—
113#125×C61—28no—
114#125×C61—22no—
115#125×C61D414yescomplemented
116#123×C61—28no—
117C22⋊Q8×C61—22no—
118C22⋊Q8×C61—22no—
119C22⋊Q8×C61—22no—
120C22⋊Q8×C61—22no—
121C4×Q8×C61—22no—
122C4×Q8×C61D414yescomplemented
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125#117×C61—28no—
126#117×C61—22no—
127#117×C61—22no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—22no—
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61D411yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C42×C61—21no—
146C2×C42×C61—21no—
147C2×C42×C61C2311yescharacteristic
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C23×D61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61C2×D412yes—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—41no—
160C22×C4×C61—24no—
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—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—42no—
178C22×C4×C61—42no—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2411yescharacteristic
184C2×C22⋊D61—42no—
185C2×C22⋊D61—42no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—81no—
189C2×C22⋊D61—81no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C2×D244—21no—
194C2×D244—21no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244#4112yes—
199C2×C4×D61—42no—
200C2×C4×D61—81no—
201C2×C4×D61—81no—
202C4⋊C4×C61—24no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—24no—
205C4⋊C4×C61—24no—
206C4⋊C4×C61—24no—
207C4⋊C4×C61—24no—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61C2×D412yes—
213C4⋊C4×C61C2×D412yes—
214C4⋊C4×C61C2×D412yes—
215C22⋊C4×C61—24no—
216C22⋊C4×C61—24no—
217C22⋊C4×C61—24no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C42×C61—24no—
221C42×C61—24no—
222C42×C61C2×D412yes—
223C42×C61C2×D412yes—
224C22⋊Dic61—81no—
225C22⋊Dic61—81no—
226#11758201—28no—
227#11758198—42no—
228#11758198—42no—
229#11758198—42no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418#4112yes—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61#13512yes—
262C23×C61C22×D411yescharacteristic
263C22×D61—22no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270Q8×C61—22no—
271Q8×C61—22no—
272Q8×C61—41no—
273Q8×C61—41no—
274D4×C61—44no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—22no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—48no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61#12012yes—
307C2×C4×C61#12012yes—
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C2×C4×C612−1+411yescharacteristic
314C22⋊D61—84no—
315C22⋊D61—84no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325D244—22no—
326D244—22no—
327D244—41no—
328D244—41no—
329C4×D61—84no—
330#92418—22no—
331#92418—41no—
332#92418—41no—
333#92418—41no—
334#24125—611nomaximal, Sylow
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61C2×#12011yescharacteristic
350C22×C61#54611yescharacteristic
351C22×C61#54711yescharacteristic
352C22×C61C2×#13511yescharacteristic
353C22×C61#57511yescharacteristic
354C22×C61#57711yescharacteristic
355C22×C61#57711yescharacteristic
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C2×D61—81no—
363C4×C61—22no—
364C4×C61—22no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61—42no—
370C4×C61—42no—
371C4×C61#52511yescharacteristic
372C4×C61#53711yescharacteristic
373C4×C61#54811yescharacteristic
374C4×C61#55011yescharacteristic
375Dic61—81no—
376Dic61—81no—
377Dic61—81no—
378C2×#552D6111yescharacteristic, complemented
379C2×#478—611no—
380C2×C4×SD16—611no—
381#2535—611no—
382#2036—611no—
383#2035—611no—
384#2000—611no—
385#2000—611no—
386#1991—611no—
387#1954—611no—
388#1875—611no—
389#1874—611no—
390#1854—611no—
391#1853—611no—
392#1805—611no—
393C2×C61—42no—
394C2×C61—81no—
395C2×C61#240711yescharacteristic
396C2×C61#300211yescharacteristic
397C2×C61#301011yescharacteristic
398C2×C61#329611yescharacteristic
399C2×C61#332311yescharacteristic
400C2×C61#333711yescharacteristic
401C2×C61#335111yescharacteristic
402D61—82no—
403C22×SD16—611no—
404#552—24no—
405#552—24no—
406C2×#126—21no—
407C2×#125—21no—
408C2×#125C2×D6111yescharacteristic
409C2×#123—21no—
410C2×C22⋊Q8C2×D6111yescharacteristic
411C2×C22⋊Q8C2×D6111yescharacteristic
412C2×#121—611no—
413C2×#121—611no—
414C2×C4×Q8C2×D6111yescharacteristic
415C2×C4×D4—611no—
416C2×C4×D4C2×D6111yescharacteristic
417C2×#117—21no—
418C2×#117C2×D6111yescharacteristic
419C22×C4⋊C4C2×D6111yescharacteristic
420#478—1224no—
421C4×SD16—1224no—
422C2×#107—611no—
423C2×#106—611no—
424C2×#106—611no—
425C2×C4⋊C8—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×C22⋊C8—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C4×C8—611no—
437#397—1221no—
438#392—1221no—
439#386—1221no—
440#386—1221no—
441#382—611no—
442#380—611no—
443#380—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450C61#2412511yescharacteristic, complemented, Sylow
451C22×Q8C22×D6111yescharacteristic
452C22×D4—611no—
453C22×D4—1221no—
454C22×D4—1221no—
455C22×D4C22⋊D6111yescharacteristic
456C23×C4—21no—
457C23×C4—1221no—
458C23×C4C22×D6111yescharacteristic
459C23×C4C22×D6111yescharacteristic
460C2×SD16—1222no—
461C2×SD16—1222no—
462C2×SD16—1222no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467#126—28no—
468#125—28no—
469#125—22no—
470#125C22⋊D6114yescomplemented
471#123—28no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476#121—1222no—
477#121—1222no—
478#121—2441no—
479#121—2441no—
480C4×Q8—22no—
481C4×Q8C22⋊D6114yescomplemented
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—1222no—
485C4×D4—1222no—
486#117—28no—
487#117—22no—
488#117—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4C22⋊D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C4⋊C4C22×D6111yescharacteristic
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4C22⋊D6111yescharacteristic
513C2×C22⋊C4C22⋊D6111yescharacteristic
514C2×C42—21no—
515C2×C42—21no—
516C2×C42C22×D6111yescharacteristic
517#107—1222no—
518#106—1222no—
519#106—1222no—
520C4⋊C8—1222no—
521#103—1222no—
522#103—2441no—
523#103—2441no—
524#102—1222no—
525#102—1222no—
526#102—1222no—
527C22⋊C8—1222no—
528C22⋊C8—1222no—
529C22⋊C8—2441no—
530C22⋊C8—2441no—
531C4×C8—1222no—
532#95—1221no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536C24—1221no—
537C24C2×C22⋊D6111yescharacteristic
538C24C2×C22⋊D6111yescharacteristic
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8C2×C22⋊D6112yes—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—41no—
548C2×D4—612no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—4881no—
555C2×D4—4881no—
556C2×D4—2442no—
557C2×D4—2442no—
558C2×D4—2442no—
559C2×D4—2442no—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—4881no—
583C22×C4—4881no—
584C22×C4—2442no—
585C22×C4C2×C22⋊D6111yescharacteristic
586C22×C4C2×C22⋊D6111yescharacteristic
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C2×C22⋊D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590SD16—1228no—
591C2×C8—612no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—22no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4C2×C22⋊D6112yes—
620C4⋊C4C2×C22⋊D6112yes—
621C4⋊C4C2×C22⋊D6112yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—4881no—
628C22⋊C4—4881no—
629C22⋊C4—2442no—
630C22⋊C4—2442no—
631C22⋊C4—2442no—
632C42—24no—
633C42—24no—
634C42C2×C22⋊D6112yes—
635C42C2×C22⋊D6112yes—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—1222no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23#1451979712yes—
657C23C22×C22⋊D6111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662D4—44no—
663D4—1222no—
664D4—1222no—
665D4—4884no—
666D4—4884no—
667D4—2441no—
668D4—2441no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—48no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—4884no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4#1451974612yes—
711C2×C4#1451974612yes—
712C2×C4C22×C22⋊D6111yescharacteristic
713C2×C4C22×C22⋊D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4#41×D6111yescharacteristic
716C2×C4#1451982311yescharacteristic
717C2×C4#1451982411yescharacteristic
718C8—1222no—
719C8—2441no—
720C8—2441no—
721C8—2441no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—4881no—
737C22—4881no—
738C22—4881no—
739C22—4881no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22C2×#1451974611yescharacteristic
744C22#1684040011yescharacteristic
745C22#1684041111yescharacteristic
746C22C2×#1451979711yescharacteristic
747C22#1684056011yescharacteristic
748C22#1684057011yescharacteristic
749C22#1684057011yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—41no—
756C4—41no—
757C4—42no—
758C4—4881no—
759C4—4881no—
760C4—4881no—
761C4#1684026911yescharacteristic
762C4#1684034011yescharacteristic
763C4#1684041911yescharacteristic
764C4#1684043111yescharacteristic
765C2—42no—
766C2—81no—
767C2—4882no—
768C2#2144915811yescharacteristic
769C2#2145503711yescharacteristic
770C2#2145510511yescharacteristic
771C2#2145764811yescharacteristic
772C2#2145802911yescharacteristic
773C2#2145819811yescharacteristic
774C2#2145837911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#552C2
socleC23×C61C22×D4
prime radical#21450720C2
hypercenterC2×#552D61
hypocenterC61#24125
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#16840059C2semidirect
2. C2×C4×#11758201C2semidirect
4. #21447019C2semidirect
5. #21447012C2semidirect
6. #21446820C2semidirect
7. #21446820C2semidirect
8. #21446785C2semidirect
9. #21446614C2semidirect
10. #21446141C2semidirect
11. #21446136C2semidirect
12. #21446018C2semidirect
13. #21446012C2semidirect
14. #21445834C2semidirect
15. C2×C61×#552C2semidirect
115. #125×C61D4semidirect
122. C4×Q8×C61D4semidirect
378. C2×#552D61semidirect
450. C61#24125semidirect
470. #125C22⋊D61semidirect
481. C4×Q8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400592
C2×C4×#117582012
#214507202
#214470192
#214470122
#214468202
#214467852
#214466142
#214461412
#214461362
#214460182
#214460122
#214458342
C2×C61×#5522
#2412561