Finite Group Databasebeta

← #30622086

Subgroups — #30622086

Order 15616.

878 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462348C211yesmaximal, characteristic, complemented
2#21462332C211yesmaximal, characteristic
3#21462003C211yesmaximal, characteristic, complemented
4#21461932C211yesmaximal, characteristic, complemented
5#21461925C211yesmaximal, characteristic, complemented
6#21461922C211yesmaximal, characteristic, complemented
7#21461882C211yesmaximal, characteristic, complemented
8#21461881C211yesmaximal, characteristic, complemented
9#21461784C211yesmaximal, characteristic
10#21461782C211yesmaximal, characteristic
11#21461620C211yesmaximal, characteristic, complemented
12#21461590C211yesmaximal, characteristic
13#21461589C211yesmaximal, characteristic
14#102×#6923C211yesmaximal, characteristic
15#476×D61C211yesmaximal, characteristic
16C2×Q8×#6923—21no—
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23#16840721C2211yescharacteristic
24C2×#14519831C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26(C2×#6923)⋊Q8—21no—
27#16840713C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840713C2211yescharacteristic
30#16840713C2211yescharacteristic
31#16840711—21no—
32#16840711—21no—
33#16840709—21no—
34#16840709—21no—
35#16840706C2211yescharacteristic
36#16840704—21no—
37C4⋊C4×#6923C2211yescharacteristic
38C4⋊C4×#6923C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40C4×C4⋊#6923C2211yescharacteristic
41C2×(C2×#6923)⋊C4—21no—
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C4⋊Q8×D61C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840053C411yescharacteristic, complemented
55#16840052C411yescharacteristic, complemented
56#16840051C411yescharacteristic, complemented
57#16840051C411yescharacteristic, complemented
58#16840050C411yescharacteristic, complemented
59#16840050C411yescharacteristic, complemented
60#16840049C411yescharacteristic, complemented
61#106×D61C2211yescharacteristic
62#106×D61C2211yescharacteristic
63C4⋊C8×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#102×D61C2211yescharacteristic
66C61×#476C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71Q8×#6923—44no—
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923—41no—
75D4×#6923—41no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923D411yescharacteristic
81C2×C4⋊#6923D411yescharacteristic
82C2×C4⋊#6923C2311yescharacteristic
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923C2311yescharacteristic
92C2×C4×#6923C2311yescharacteristic
93#14519846—41no—
94#14519845—41no—
95#14519839—22no—
96#14519839Q814yescomplemented
97#14519832—21no—
98#14519832—21no—
99#14519831—41no—
100C8×#6923—41no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4D411yescharacteristic
111(C2×#6923)⋊C4D411yescharacteristic
112C2×Q8×D61—21no—
113C2×D4×D61C2311yescharacteristic
114C22×C4×D61—21no—
115C2×C8×D61C2311yescharacteristic
116C2×C8×D61C2311yescharacteristic
117#14519777C2×C411yescharacteristic, complemented
118#14519776—21no—
119#14519776C2×C411yescharacteristic, complemented
120#14519776C2×C411yescharacteristic, complemented
121#14519775—21no—
122C4×D244C2×C411yescharacteristic
123D4×Dic61C2×C411yescharacteristic
124#14519739C2×C411yescharacteristic
125C4×C22⋊D61—21no—
126#14519737—21no—
127C4⋊C4×D61—21no—
128C4⋊C4×D61C2311yescharacteristic
129C4⋊C4×D61C2311yescharacteristic
130C4⋊C4×D61C2311yescharacteristic
131C22⋊C4×D61—21no—
132C42×D61C2311yescharacteristic
133#14519709C2×C411yescharacteristic, complemented
134#14519709C2×C411yescharacteristic, complemented
135#14519708C2×C411yescharacteristic, complemented
136#14519708C2×C411yescharacteristic, complemented
137#14519708C2×C411yescharacteristic, complemented
138#14519708C2×C411yescharacteristic, complemented
139C4⋊#92418C2×C411yescharacteristic, complemented
140#14519706C2×C411yescharacteristic, complemented
141#14519706C2×C411yescharacteristic, complemented
142#14519699C2×C411yescharacteristic
143#14519699C2×C411yescharacteristic
144#14519698C2×C411yescharacteristic
145#14519698C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147#14519697C2×C411yescharacteristic
148C4⋊Q8×C61C2×C411yescharacteristic, complemented
149C4×D4×C61C2×C411yescharacteristic
150#106×C61C2×C411yescharacteristic, complemented
151#106×C61C2×C411yescharacteristic, complemented
152C4⋊C8×C61C2×C411yescharacteristic, complemented
153#102×C61C2×C411yescharacteristic
154#102×C61C2×C411yescharacteristic
155C23×D61—21no—
156C22×#6923—21no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—42no—
161C22×#6923—42no—
162C22×#6923—42no—
163C22×#6923—42no—
164C22×#6923—81no—
165C22×#6923—81no—
166C22×#6923C2×D411yescharacteristic
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C2×Q8×C61—21no—
171C2×D4×C61C22×C411yescharacteristic
172C22×C4×C61—21no—
173C2×C22⋊D61—21no—
174C22×Dic61—21no—
175Q8×D61—42no—
176Q8×D61—42no—
177D4×D61—21no—
178D4×D61—21no—
179D4×D61C2×Q812yes—
180D4×D61#4112yes—
181C2×D244C22×C411yescharacteristic
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—81no—
188C2×C4×D61—81no—
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2411yescharacteristic
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C22⋊#6923—42no—
196C22⋊#6923—42no—
197C2×#92420—21no—
198C2×#92420—21no—
199C4⋊#6923—22no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—21no—
207C4⋊#6923—41no—
208C4⋊#6923—42no—
209C4⋊#6923—42no—
210C4⋊#6923—81no—
211C4⋊#6923—81no—
212C4⋊#6923C2×Q812yes—
213C4×#6923—21no—
214C4×#6923—21no—
215C4×#6923—21no—
216C4×#6923—21no—
217C4×#6923—42no—
218C4×#6923—42no—
219C4×#6923—42no—
220D61⋊C8—21no—
221D61⋊C8—21no—
222D61⋊C8—21no—
223D61⋊C8C2×Q812yes—
224C2×C8×C61C22×C411yescharacteristic
225C2×C8×C61C22×C411yescharacteristic
226C4⋊C4×C61—21no—
227C4⋊C4×C61C22×C411yescharacteristic
228C4⋊C4×C61C22×C411yescharacteristic
229C4⋊C4×C61C22×C411yescharacteristic
230C22⋊C4×C61—21no—
231C42×C61C22×C411yescharacteristic
232C22⋊Dic61—21no—
233#11758198—21no—
234#11758198—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61C22×C411yescharacteristic
237C4⋊Dic61C22×C411yescharacteristic
238C4⋊Dic61C22×C411yescharacteristic
239#11758196—21no—
240#11758196—21no—
241#11758196—21no—
242#11758196—21no—
243#11758196—21no—
244C4×Dic61C22×C411yescharacteristic
245C4×Dic61#4111yescharacteristic
246C4×Dic61#4111yescharacteristic
247C2×#92418C22×C411yescharacteristic
248C2×#92418C22×C411yescharacteristic
249C8×D61—21no—
250C8×D61—21no—
251C8×D61—21no—
252C8×D61—21no—
253C23×C61—21no—
254C22×D61—21no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61C22×D411yescharacteristic
262C2×#6923—21no—
263C2×#6923—21no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—21no—
267C2×#6923—22no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—21no—
271C2×#6923—21no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—41no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923—41no—
278C2×#6923—41no—
279C2×#6923—41no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923—84no—
286C2×#6923—84no—
287C2×#6923AGL(1,ℤ/8)12yes—
288Q8×C61—42no—
289D4×C61—21no—
290D4×C61C4×Q812yescomplemented
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—81no—
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C23×C411yescharacteristic
298C22⋊D61—22no—
299C22⋊D61—22no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—81no—
304C2×Dic61C4×D411yescharacteristic
305C2×Dic61C4×D411yescharacteristic
306C2×Dic61C2×#4111yescharacteristic
307D244—21no—
308D244C4×Q812yescomplemented
309C4×D61—21no—
310C4×D61—21no—
311C4×D61—21no—
312C4×D61—21no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—81no—
320C4×D61—81no—
321C4×D61C22×Q811yescharacteristic
322C4×D61C2×#4111yescharacteristic
323C4×D61H(5,𝔽2)11yescharacteristic
324C4×D612−1+411yescharacteristic
325Dic122—42no—
326Dic122—42no—
327Dic122—42no—
328#92420—22no—
329#92420—41no—
330C8×C61—21no—
331C8×C61—21no—
332#92418—21no—
333#92418—21no—
334#22975—611nomaximal, Sylow
335C22×C61—22no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61C2×C4×D411yescharacteristic
339C2×D61—22no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61#54611yescharacteristic
347C2×D61D4×Q811yescharacteristic
348C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
349C2×D61#57511yescharacteristic
350C2×D61#57711yescharacteristic
351C2×D61#57711yescharacteristic
352#6923—22no—
353#6923—42no—
354#6923—41no—
355#6923—41no—
356#6923—41no—
357#6923—81no—
358#6923—81no—
359#6923—81no—
360C4×C61—21no—
361C4×C61—21no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61C2×C4×Q811yescharacteristic
366C4×C61#52011yescharacteristic
367Dic61—21no—
368Dic61—21no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61#55211yescharacteristic
373Dic61#55411yescharacteristic
374C2×#476—611no—
375#2365—611no—
376#2349—611no—
377#1993—611no—
378#1949—611no—
379#1944—611no—
380#1941—611no—
381#1920—611no—
382#1919—611no—
383#1864—611no—
384#1862—611no—
385#1771—611no—
386#1762—611no—
387#1762—611no—
388C4×#102—611no—
389C2×C61—42no—
390C2×C61#236011yescharacteristic
391C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
392C2×C61#294911yescharacteristic
393D61—42no—
394D61#330611yescharacteristic
395D61#331111yescharacteristic
396D61#338411yescharacteristic
397D61#338811yescharacteristic
398C2×C4⋊Q8—611no—
399C2×C4×Q8—1221no—
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×C4×D4—611no—
403#476—611no—
404#476—611no—
405#476—611no—
406#476—611no—
407#476—611no—
408#476—611no—
409#476—611no—
410#476#692311yescharacteristic, complemented
411C2×#107—611no—
412C2×#106—611no—
413C2×#106—611no—
414C2×#106—611no—
415C2×C4⋊C8—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#97—611no—
421C2×#97—611no—
422C2×C4×C8—611no—
423#391—1221no—
424#389—611no—
425#389—611no—
426#389—611no—
427#389—611no—
428#387—1221no—
429#387—1221no—
430#385—1221no—
431#385—1221no—
432#382—611no—
433#380—1221no—
434C4×C4⋊C4—611no—
435C4×C4⋊C4—611no—
436C4×C4⋊C4—611no—
437C4×C4⋊C4—611no—
438C2×#95—1221no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#336—611no—
448#336—611no—
449C61#2297511yescharacteristic, complemented, Sylow
450C22×Q8—1221no—
451C22×D4—611no—
452C23×C4—1221no—
453C23×C4—1221no—
454C23×C4—1221no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C4⋊Q8—611no—
460C4⋊Q8—611no—
461C4⋊Q8—611no—
462C4⋊Q8—1221no—
463C4⋊Q8—1221no—
464C4⋊Q8C2×#692311yescharacteristic, complemented
465C4×Q8—2444no—
466C4×D4—611no—
467C4×D4—611no—
468C4×D4—611no—
469C4×D4—1221no—
470C4×D4—1221no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—2441no—
474C4×D4—2441no—
475C4×D4C2×#692311yescharacteristic
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—611no—
496C2×C42—1221no—
497C2×C42—1221no—
498C2×C42—1221no—
499#107—2441no—
500#106—611no—
501#106—611no—
502#106—611no—
503#106—611no—
504#106—611no—
505#106—611no—
506#106—2441no—
507#106C2×#692311yescharacteristic, complemented
508#106C2×#692311yescharacteristic, complemented
509C4⋊C8—611no—
510C4⋊C8—611no—
511C4⋊C8—611no—
512C4⋊C8C2×#692311yescharacteristic, complemented
513#102—614no—
514#102—611no—
515#102—611no—
516#102—611no—
517#102—611no—
518#102—611no—
519#102—611no—
520#102—1222no—
521#102C2×#692311yescharacteristic
522#102C2×#692311yescharacteristic
523#97—1221no—
524#97—1221no—
525#97—2441no—
526C4×C8—2441no—
527#95—611no—
528#95—611no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538C24—1221no—
539C2×Q8—21no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—2442no—
544C2×Q8—2442no—
545C2×D4—612no—
546C2×D4—612no—
547C2×D4—611no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4C22×#692311yescharacteristic
552C22×C4—21no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—4881no—
571C22×C4—4881no—
572C22×C4—4881no—
573C22×C4—4881no—
574C22×C4—2442no—
575C22×C4—2442no—
576C22×C4—2442no—
577C22×C4—2442no—
578C2×C8—612no—
579C2×C8—611no—
580C2×C8—611no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8C22×#692311yescharacteristic
591C2×C8C22×#692311yescharacteristic
592C4⋊C4—21no—
593C4⋊C4—612no—
594C4⋊C4—611no—
595C4⋊C4—611no—
596C4⋊C4—611no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1222no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—4881no—
612C4⋊C4—4881no—
613C4⋊C4—2442no—
614C4⋊C4—2441no—
615C4⋊C4—2442no—
616C4⋊C4C22×#692311yescharacteristic
617C4⋊C4C22×#692311yescharacteristic
618C4⋊C4C22×#692311yescharacteristic
619C22⋊C4—21no—
620C22⋊C4—1221no—
621C22⋊C4—1221no—
622C22⋊C4—1221no—
623C22⋊C4—2442no—
624C22⋊C4—2442no—
625C42—611no—
626C42—611no—
627C42—611no—
628C42—1221no—
629C42—1221no—
630C42—1221no—
631C42—1221no—
632C42—2442no—
633C42—2442no—
634C42—2442no—
635C42C22×#692311yescharacteristic
636C23—21no—
637C23—611no—
638C23—1222no—
639C23—1222no—
640C23—1221no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645Q8—42no—
646Q8—2442no—
647Q8—2442no—
648Q8—2442no—
649D4—21no—
650D4—612no—
651D4—1222no—
652D4—1222no—
653D4—1221no—
654D4Q8×#692312yescomplemented
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—81no—
659C2×C4—611no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—611no—
664C2×C4—612no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1222no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—4881no—
687C2×C4—4881no—
688C2×C4—4884no—
689C2×C4—4881no—
690C2×C4—4884no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4D4×#692311yescharacteristic
709C2×C4D4×#692311yescharacteristic
710C2×C4C23×#692311yescharacteristic
711C8—21no—
712C8—21no—
713C8—1222no—
714C8—1221no—
715C8—1221no—
716C8—2441no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—611no—
721C22—611no—
722C22—611no—
723C22—611no—
724C22—611no—
725C22—611no—
726C22—1222no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22—2441no—
732C22—2441no—
733C22C2×D4×#692311yescharacteristic
734C4—21no—
735C4—21no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—611no—
740C4—611no—
741C4—1222no—
742C4—1221no—
743C4—1221no—
744C4—4881no—
745C4—4881no—
746C4—4881no—
747C4—2441no—
748C4—2441no—
749C4—2441no—
750C4—2442no—
751C4—2441no—
752C4—2441no—
753C4—2441no—
754C4C2×Q8×#692311yescharacteristic
755C4#1684083111yescharacteristic
756C2—42no—
757C2—611no—
758C2—611no—
759C2—611no—
760C2—611no—
761C2—2442no—
762C2#2146234311yescharacteristic
763C2AGL(1,ℤ/8)×#692311yescharacteristic
764C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#476C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#476#6923
hypocenterC61#22975
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #21462348C2semidirect
3. #21462003C2semidirect
4. #21461932C2semidirect
5. #21461925C2semidirect
6. #21461922C2semidirect
7. #21461882C2semidirect
8. #21461881C2semidirect
11. #21461620C2semidirect
54. #16840053C4semidirect
55. #16840052C4semidirect
56. #16840051C4semidirect
57. #16840051C4semidirect
58. #16840050C4semidirect
59. #16840050C4semidirect
60. #16840049C4semidirect
66. C61×#476C4semidirect
96. #14519839Q8semidirect
117. #14519777C2×C4semidirect
119. #14519776C2×C4semidirect
120. #14519776C2×C4semidirect
133. #14519709C2×C4semidirect
134. #14519709C2×C4semidirect
135. #14519708C2×C4semidirect
136. #14519708C2×C4semidirect
137. #14519708C2×C4semidirect
138. #14519708C2×C4semidirect
139. C4⋊#92418C2×C4semidirect
140. #14519706C2×C4semidirect
141. #14519706C2×C4semidirect
148. C4⋊Q8×C61C2×C4semidirect
150. #106×C61C2×C4semidirect
151. #106×C61C2×C4semidirect
152. C4⋊C8×C61C2×C4semidirect
290. D4×C61C4×Q8semidirect
308. D244C4×Q8semidirect
410. #476#6923semidirect
449. C61#22975semidirect
464. C4⋊Q8C2×#6923semidirect
507. #106C2×#6923semidirect
508. #106C2×#6923semidirect
512. C4⋊C8C2×#6923semidirect
654. D4Q8×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623482
#214623322
#214620032
#214619322
#214619252
#214619222
#214618822
#214618812
#214617842
#214617822
#214616202
#214615902
#214615892
#102×#69232
#476×D612
#2297561