Finite Group Databasebeta

← #29685775

Subgroups — #29685775

Order 15616.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840244C211yesmaximal, characteristic
2C2×#16839923C211yesmaximal, characteristic
3C2×C4×#11758201C211yesmaximal, characteristic, complemented
4#21448495C211yesmaximal, characteristic, complemented
5#21446162C211yesmaximal, characteristic, complemented
6#21446150C211yesmaximal, characteristic, complemented
7#21446123C211yesmaximal, characteristic, complemented
8#21446085C211yesmaximal, characteristic, complemented
9#21446077C211yesmaximal, characteristic, complemented
10#21446010C211yesmaximal, characteristic, complemented
11#21445758C211yesmaximal, characteristic
12#21445645C211yesmaximal, characteristic, complemented
13C4×#14519701C211yesmaximal, characteristic, complemented
14#21445588C211yesmaximal, characteristic, complemented
15C2×C61×#441C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×#11758201C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19#16840244—24no—
20#16840244—24no—
21C2×Q8×Dic61C2211yescharacteristic
22C2×C4×D244—21no—
23C2×C4×D244C2211yescharacteristic
24C2×#14519739—21no—
25C2×#14519739C2211yescharacteristic
26C2×#14519734—21no—
27C2×#14519734C2211yescharacteristic
28C2×C4⋊C4×D61—21no—
29C2×C4⋊C4×D61C2211yescharacteristic
30#16839923C418yescomplemented
31C4×#11758201—24no—
32C2×#14519708C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839669C2211yescharacteristic
43#16839658C2211yescharacteristic
44#16839657—21no—
45#16839653—21no—
46#16839652—21no—
47#16839646—21no—
48#16839619C2211yescharacteristic
49C4×C4⋊Dic61C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C61×#441—24no—
60C2×#106×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×#97×C61C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226C2×C414yes—
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61C2311yescharacteristic
77C2×#11758201—22no—
78C2×#11758201—22no—
79C2×#11758201C2×C414yescomplemented
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519753—22no—
83#14519753C2×C414yescomplemented
84Q8×Dic61—22no—
85Q8×Dic61—22no—
86C4×D244—28no—
87C4×D244—22no—
88C4×D244D414yes—
89#14519739—28no—
90#14519739—22no—
91#14519739—22no—
92#14519734—28no—
93#14519734—22no—
94#14519734—22no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196D411yescharacteristic
103C2×#11758196D411yescharacteristic
104C4⋊C4×D61—28no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198D411yescharacteristic
112C2×#11758198D411yescharacteristic
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61C2311yescharacteristic
116#14519708—22no—
117#14519701—22no—
118#14519701—22no—
119#14519701C2×C414yescomplemented
120#14519699—22no—
121#14519699C2×C414yescomplemented
122#14519697—22no—
123#14519689—22no—
124#14519689C2×C414yescomplemented
125C4×#92418—22no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C2×Q16×C61—22no—
134C2×Q16×C61—22no—
135C2×Q16×C61C2×C414yescomplemented
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C4×Q8×C61—22no—
139C4×Q8×C61—22no—
140C4×Q8×C61—22no—
141C4×Q8×C61D414yes—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C42×C61—21no—
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#106×C61—22no—
150#103×C61—22no—
151#103×C61—22no—
152#97×C61—22no—
153C23×D61—21no—
154C23×D61C2×D411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61C22×C412yes—
164C2×Q8×C61C22×C412yes—
165C2×Q8×C61C2×D412yes—
166C2×Q8×C61#4112yes—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180#11758226—28no—
181#11758226—28no—
182#11758226—28no—
183#11758226—28no—
184C2×D244—24no—
185C2×D244—24no—
186C2×D244—24no—
187C2×D244—21no—
188C2×D244—21no—
189C2×D244—21no—
190C2×D244C22×C412yes—
191C2×D244C2×D412yes—
192C2×D244#4112yes—
193C2×C4×D61—24no—
194C2×C4×D61—24no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—24no—
200C2×C4×D61—24no—
201C2×C4×D61—24no—
202C2×C4×D61—24no—
203C2×C4×D61—81no—
204C2×C4×D61—81no—
205C2×C4×D61—81no—
206C2×C4×D61—81no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209C2×C4×D61C22×C412yes—
210C2×C4×D61#4112yes—
211Q16×C61—28no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61C22×C412yes—
218C4⋊C4×C61—24no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—42no—
223C4⋊C4×C61C2×D412yes—
224C42×C61—24no—
225C42×C61—42no—
226C42×C61C2×D412yes—
227C42×C61C2×D412yes—
228#11758201—28no—
229#11758198—24no—
230#11758198—24no—
231#11758198—24no—
232#11758198—22no—
233#11758198—22no—
234#11758198—81no—
235C4⋊Dic61—24no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61C22×C412yes—
241C4⋊Dic61C2×D412yes—
242#11758196—24no—
243#11758196—22no—
244#11758196—22no—
245#11758196—24no—
246#11758196—81no—
247C4×Dic61—24no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—81no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418C22×C412yes—
257C23×C61C22×D411yescharacteristic
258C22×D61—22no—
259C22×D61—21no—
260C22×D61—22no—
261C22×D61—21no—
262C22×D61—22no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61C4×D412yes—
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61—22no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—41no—
278Q8×C61—41no—
279Q8×C61C4×D414yes—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—41no—
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#12012yes—
297C2×C4×C61#12012yes—
298C2×C4×C61C23×C411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—22no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61C4×D412yes—
322D244—216no—
323D244—22no—
324D244—22no—
325D244—22no—
326D244C4×D414yes—
327C4×D61—216no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—84no—
333C4×D61—84no—
334C4×D61—84no—
335C8×C61—22no—
336C8×C61—41no—
337#92418—22no—
338#92418—41no—
339#21461—611nomaximal, Sylow
340C22×C61C2×C4×D411yescharacteristic
341C22×C61C2×#12011yescharacteristic
342C22×C61#52511yescharacteristic
343C22×C61#57711yescharacteristic
344C22×C61#57711yescharacteristic
345C22×C61#57711yescharacteristic
346C22×C61#57811yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—24no—
351C2×D61—41no—
352C2×D61—42no—
353C2×D61—41no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—41no—
358C2×D61—42no—
359C2×D61—41no—
360C2×D61—42no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—24no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61—81no—
367C4×C61C2×C4×D411yescharacteristic
368C4×C61C2×C4×D411yescharacteristic
369C4×C61#52511yescharacteristic
370C4×C61#52511yescharacteristic
371Dic61—22no—
372Dic61—42no—
373Dic61—41no—
374Dic61—42no—
375Dic61—41no—
376Dic61—81no—
377C2×#520—611no—
378C2×#452—611no—
379C2×#441D6111yescharacteristic, complemented
380C2×C4×SD16—611no—
381#2323—611no—
382#1878—611no—
383#1877—611no—
384#1872—611no—
385#1865—611no—
386#1864—611no—
387#1853—611no—
388#1788—611no—
389#1762—611no—
390C4×#103—611no—
391#1750—611no—
392C2×C61C4×#12011yescharacteristic
393C2×C61#294711yescharacteristic
394C2×C61#295211yescharacteristic
395C2×C61#300911yescharacteristic
396C2×C61#301311yescharacteristic
397C2×C61#312011yescharacteristic
398C2×C61#312511yescharacteristic
399D61—42no—
400D61—44no—
401C22×#41—611no—
402C22×Q16C2×D6111yescharacteristic
403C22×SD16—611no—
404C2×C22⋊Q8—611no—
405#520—1224no—
406#520—1224no—
407C2×C4×Q8—611no—
408C2×C4×Q8C2×D6111yescharacteristic
409C2×C4×Q8C2×D6111yescharacteristic
410C2×C4×D4—611no—
411C2×C4×D4—611no—
412C2×C4×D4—1221no—
413C2×C4×D4—1221no—
414C2×#117—611no—
415C2×#117—1221no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—1221no—
418#452—618no—
419#441—24no—
420C4×SD16—1224no—
421C2×#106—611no—
422C2×#106C2×D6111yescharacteristic
423C2×#103—611no—
424C2×#103—611no—
425C2×#103—611no—
426C2×#103C2×D6111yescharacteristic
427C2×#103C2×D6111yescharacteristic
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×C22⋊C8—611no—
432C2×C22⋊C8—611no—
433C2×#97C2×D6111yescharacteristic
434C2×C4×C8—611no—
435#391—611no—
436#389—611no—
437#389—1221no—
438#388—1221no—
439#388—1221no—
440#387—1221no—
441#380—611no—
442C4×C4⋊C4—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#336—611no—
448#336—611no—
449C61#2146111yescharacteristic, complemented, Sylow
450C2×#41—614no—
451C2×#41—1222no—
452C2×#41—1222no—
453C2×#41—1222no—
454C2×#41—1222no—
455C2×#41—1222no—
456C22×Q8C22×D6111yescharacteristic
457C22×Q8C22×D6111yescharacteristic
458C22×D4—611no—
459C22×D4—1221no—
460C23×C4—611no—
461C23×C4—1221no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4—1221no—
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16C4×D6114yescomplemented
468C2×SD16—614no—
469C2×SD16—1222no—
470C2×SD16—1222no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8C22×D6111yescharacteristic
474C22×C8C22×D6111yescharacteristic
475C22⋊Q8—614no—
476C22⋊Q8—1222no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—1222no—
481C4×Q8—1222no—
482C4×Q8C22⋊D6114yes—
483C4×D4—614no—
484C4×D4—1228no—
485C4×D4—1222no—
486C4×D4—1228no—
487C4×D4—1222no—
488C4×D4—1222no—
489#117—1228no—
490#117—1222no—
491#117—1222no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1228no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—611no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42C22×D6111yescharacteristic
520#106—22no—
521#106—1222no—
522#103—22no—
523#103—22no—
524#103—614no—
525#103—1222no—
526#103—1222no—
527#102—614no—
528#102—1222no—
529#102—1222no—
530C22⋊C8—614no—
531C22⋊C8—1222no—
532#97—22no—
533C4×C8—1222no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—611no—
540C24—1221no—
541#41—1228no—
542#41—1228no—
543#41—1228no—
544#41—1228no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C2×C4×D6112yes—
554C2×Q8C2×C4×D6112yes—
555C2×Q8#1175822212yes—
556C2×Q8C2×C22⋊D6112yes—
557C2×D4—612no—
558C2×D4—612no—
559C2×D4—612no—
560C2×D4—1224no—
561C2×D4—1224no—
562C2×D4—1224no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—611no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1224no—
578C22×C4—1224no—
579C22×C4—1224no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1224no—
587C22×C4—1221no—
588C22×C4—4881no—
589C22×C4—4881no—
590C22×C4—4881no—
591C22×C4—4881no—
592C22×C4—4881no—
593C22×C4—4881no—
594C22×C4D4×D6111yescharacteristic
595C22×C4D4×D6111yescharacteristic
596C22×C4C23×D6111yescharacteristic
597Q16—28no—
598SD16—1228no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—612no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8C2×C4×D6112yes—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—42no—
616C4⋊C4—612no—
617C4⋊C4—612no—
618C4⋊C4—1224no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1222no—
624C4⋊C4—1222no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—4881no—
628C4⋊C4C2×C22⋊D6112yes—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1222no—
632C22⋊C4—1222no—
633C22⋊C4—1224no—
634C22⋊C4—4881no—
635C42—24no—
636C42—42no—
637C42—1224no—
638C42—1221no—
639C42—1221no—
640C42—4881no—
641C42D4×D6112yes—
642C42C2×C22⋊D6112yes—
643C23—612no—
644C23—1222no—
645C23—1222no—
646C23—1221no—
647C23—1222no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—2441no—
654C23—2441no—
655C23—2441no—
656C23—2441no—
657C23C2×D4×D6111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665Q8C4×C22⋊D6114yes—
666D4—614no—
667D4—12216no—
668D4—1222no—
669D4—1222no—
670D4—1222no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—612no—
688C2×C4—12216no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1221no—
697C2×C4—1222no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—4884no—
704C2×C4—4884no—
705C2×C4—4884no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4#1451974512yes—
714C2×C4#1451974512yes—
715C2×C4C22×C4×D6111yescharacteristic
716C2×C4C2×D4×D6111yescharacteristic
717C2×C4C22×C22⋊D6111yescharacteristic
718C2×C4#41×D6111yescharacteristic
719C2×C4#41×D6111yescharacteristic
720C2×C4C2×#1175822211yescharacteristic
721C8—22no—
722C8—41no—
723C8—1222no—
724C8—2441no—
725C22—1222no—
726C22—1222no—
727C22—1224no—
728C22—1222no—
729C22—2441no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—2441no—
734C22—2442no—
735C22—2441no—
736C22—2442no—
737C22—2441no—
738C22—2442no—
739C22C4×D4×D6111yescharacteristic
740C22C2×#1451974511yescharacteristic
741C22#1684027111yescharacteristic
742C22#1684057111yescharacteristic
743C22#1684057111yescharacteristic
744C22#1684057111yescharacteristic
745C22#1684057811yescharacteristic
746C4—22no—
747C4—24no—
748C4—22no—
749C4—42no—
750C4—42no—
751C4—81no—
752C4—1222no—
753C4—4881no—
754C4—2441no—
755C4—2442no—
756C4—2441no—
757C4—2442no—
758C4C4×D4×D6111yescharacteristic
759C4C2×C4×C22⋊D6111yescharacteristic
760C4#1684026911yescharacteristic
761C4#1684027111yescharacteristic
762C2—2442no—
763C2—2444no—
764C2C4×#1451974511yescharacteristic
765C2#2145466111yescharacteristic
766C2#2145469911yescharacteristic
767C2#2145509511yescharacteristic
768C2#2145513311yescharacteristic
769C2#2145603111yescharacteristic
770C2#2145609411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#441C2
socleC23×C61C22×D4
prime radicalC22×#11758226C22
cosocleC22×C4×C61C24
hypercenterC2×#441D61
hypocenterC61#21461
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758201C2semidirect
4. #21448495C2semidirect
5. #21446162C2semidirect
6. #21446150C2semidirect
7. #21446123C2semidirect
8. #21446085C2semidirect
9. #21446077C2semidirect
10. #21446010C2semidirect
12. #21445645C2semidirect
13. C4×#14519701C2semidirect
14. #21445588C2semidirect
15. C2×C61×#441C2semidirect
30. #16839923C4semidirect
79. C2×#11758201C2×C4semidirect
83. #14519753C2×C4semidirect
119. #14519701C2×C4semidirect
121. #14519699C2×C4semidirect
124. #14519689C2×C4semidirect
135. C2×Q16×C61C2×C4semidirect
379. C2×#441D61semidirect
449. C61#21461semidirect
467. C2×Q16C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402442
C2×#168399232
C2×C4×#117582012
#214484952
#214461622
#214461502
#214461232
#214460852
#214460772
#214460102
#214457582
#214456452
C4×#145197012
#214455882
C2×C61×#4412
#2146161