Finite Group Databasebeta

← #29648725

Subgroups — #29648725

Order 15616.

1104 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459602C211yesmaximal, characteristic
2#21454933C211yesmaximal, characteristic, complemented
3#21454480C211yesmaximal, characteristic, complemented
4#21444540C211yesmaximal, characteristic, complemented
5#21444539C211yesmaximal, characteristic, complemented
6#21444536C211yesmaximal, characteristic, complemented
7#21444534C211yesmaximal, characteristic, complemented
8#21444523C211yesmaximal, characteristic, complemented
9#21444522C211yesmaximal, characteristic, complemented
10#21444502C211yesmaximal, characteristic, complemented
11#21444495C211yesmaximal, characteristic, complemented
12#21444489C211yesmaximal, characteristic, complemented
13#21444467C211yesmaximal, characteristic, complemented
14#332×D61C211yesmaximal, characteristic, complemented
15C61×#1549C211yesmaximal, characteristic, complemented
16C2×#14519825—21no—
17#16840427—21no—
18#16840427C412yes—
19#16840415—21no—
20#16840415C412yes—
21#16840413—21no—
22#16840413—21no—
23#16840413C412yes—
24#16840413C412yes—
25#16840337—21no—
26#16840337—21no—
27#16840336—21no—
28#16840313C2211yescharacteristic
29#16840313C2211yescharacteristic
30#16840312C2211yescharacteristic
31C4⋊Q8×D61C2211yescharacteristic
32C4⋊Q8×D61C2211yescharacteristic
33C4×#11758222C2211yescharacteristic
34#16839891—21no—
35#16839838—21no—
36#16839832—21no—
37#16839831—21no—
38#16839821—21no—
39#16839820—21no—
40#16839819C2211yescharacteristic
41#16839819C2211yescharacteristic
42#16839818C2211yescharacteristic
43#16839818C2211yescharacteristic
44#16839814C2211yescharacteristic
45#16839814C2211yescharacteristic
46#16839784C2211yescharacteristic
47#16839784C2211yescharacteristic
48C4⋊C8×D61C2211yescharacteristic
49C4⋊C8×D61C2211yescharacteristic
50#16839727—21no—
51#16839716—21no—
52#16839509C2211yescharacteristic
53#16839509C2211yescharacteristic
54#16839508C2211yescharacteristic
55#16839508C2211yescharacteristic
56#16839508C2211yescharacteristic
57#16839508C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60#16839505C2211yescharacteristic
61#16839505C2211yescharacteristic
62#16839505C2211yescharacteristic
63#16839505C2211yescharacteristic
64C2×C4⋊Q8×C61C2211yescharacteristic
65C61×#431C2211yescharacteristic
66C61×#423C2211yescharacteristic
67C61×#332C2211yescharacteristic
68C61×#332C2211yescharacteristic
69C61×#332C2211yescharacteristic
70C61×#332C2211yescharacteristic
71#14519825—44no—
72#14519825—44no—
73C2×#11758226—22no—
74C2×#11758226—21no—
75C2×#11758226—21no—
76C2×#11758222—21no—
77C2×#11758222—22no—
78C2×#11758222—22no—
79C2×#11758222D411yescharacteristic
80C2×Q8×D61—21no—
81C2×Q8×D61—21no—
82C2×Q8×D61—22no—
83C2×#11758189—21no—
84C2×#11758189—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519777C2311yescharacteristic
88#14519776—21no—
89#14519776—21no—
90#14519776C2×C412yes—
91#14519776C2×C412yes—
92#14519775—21no—
93#14519775—21no—
94#14519774C2311yescharacteristic
95#14519766—21no—
96#14519766—21no—
97#14519765—21no—
98#14519762—22no—
99#14519762—22no—
100#14519762—22no—
101#14519762—22no—
102#14519760—22no—
103#14519760—22no—
104#14519755—22no—
105#14519755—22no—
106#14519755—22no—
107#14519755—22no—
108#14519753—22no—
109#14519753—22no—
110#14519752—21no—
111#14519752—21no—
112#14519752C2×C412yes—
113#14519752C2×C412yes—
114#14519751—21no—
115#14519751C2×C412yes—
116C4×Dic122C2×C411yescharacteristic
117C4×Dic122D411yescharacteristic
118C4×D244—21no—
119C4×D244C2×C411yescharacteristic
120C4×D244C2×C412yes—
121C4×D244D411yescharacteristic
122#14519739—21no—
123#14519739—21no—
124#14519739C2×C412yes—
125#14519739C2×C412yes—
126C4×C22⋊D61C2×C411yescharacteristic
127C4×C22⋊D61C2×C411yescharacteristic
128C4×C22⋊D61D411yescharacteristic
129C4×C22⋊D61D411yescharacteristic
130#14519736D411yescharacteristic
131#14519734D411yescharacteristic
132#14519734D411yescharacteristic
133C4⋊C4×D61—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61C2×C412yes—
136C4⋊C4×D61C2×C412yes—
137C42×D61C2311yescharacteristic
138C42×D61C2311yescharacteristic
139C4⋊#92418C2311yescharacteristic
140C4⋊#92418C2311yescharacteristic
141C4⋊#92418C2311yescharacteristic
142C4⋊#92418C2311yescharacteristic
143#14519706—21no—
144#14519706—21no—
145#14519706—21no—
146#14519706—21no—
147C22⋊#92418—21no—
148C22⋊#92418—21no—
149#14519689—21no—
150#14519689—21no—
151#14519689—21no—
152#14519689—21no—
153#14519688—21no—
154#14519688—21no—
155#14519687—21no—
156#14519687—21no—
157C8×Dic61—21no—
158C8×Dic61—21no—
159C22×Q8×C61—21no—
160C2×M16×C61—21no—
161C4⋊Q8×C61—21no—
162C4⋊Q8×C61—21no—
163C4⋊Q8×C61C2×C412yes—
164C4⋊Q8×C61C2311yescharacteristic
165C4⋊Q8×C61C2311yescharacteristic
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61C2×C412yes—
168C2×C42×C61C2311yescharacteristic
169C4⋊C8×C61—21no—
170C4⋊C8×C61C2311yescharacteristic
171C4⋊C8×C61C2311yescharacteristic
172C4⋊C8×C61C2311yescharacteristic
173C4⋊C8×C61C2311yescharacteristic
174C22⋊C8×C61—21no—
175C4×C8×C61—21no—
176C2×Q8×C61—22no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—42no—
180C2×Q8×C61—42no—
181C22×C4×C61—22no—
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C2×C22⋊D61—22no—
186C2×C22⋊D61C22⋊C411yescharacteristic
187C2×C22⋊D61C22⋊C411yescharacteristic
188#11758226—42no—
189#11758226—42no—
190#11758226—48no—
191#11758226—42no—
192#11758226—42no—
193Q8×D61—48no—
194Q8×D61—42no—
195Q8×D61—42no—
196Q8×D61—42no—
197Q8×D61—42no—
198#11758222—22no—
199#11758222—22no—
200#11758222—48no—
201#11758222—48no—
202#11758222—42no—
203#11758222—42no—
204C2×D244—22no—
205C2×D244—22no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244C22⋊C411yescharacteristic
209C2×D244C22×C412yes—
210C2×C4×D61—22no—
211C2×C4×D61—22no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61C22×C411yescharacteristic
216C2×C4×D61C22×C411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×Dic122—21no—
222C2×Dic122—22no—
223C2×Dic122—22no—
224C2×Dic122C22⋊C411yescharacteristic
225M16×C61—81no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—22no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C22×C412yes—
235C4⋊C4×C61C22×C412yes—
236C42×C61C22×C411yescharacteristic
237C42×C61C2×D411yescharacteristic
238C42×C61C2×D411yescharacteristic
239C42×C61C2411yescharacteristic
240C22⋊Dic61C22⋊C411yescharacteristic
241C22⋊Dic61C22⋊C411yescharacteristic
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—22no—
246#11758198—22no—
247#11758198—22no—
248#11758198C22⋊C411yescharacteristic
249#11758198C22⋊C411yescharacteristic
250#11758198C22⋊C411yescharacteristic
251#11758198C22⋊C411yescharacteristic
252C4⋊Dic61—21no—
253C4⋊Dic61C22⋊C411yescharacteristic
254C4⋊Dic61C22⋊C411yescharacteristic
255C4⋊Dic61C22×C412yes—
256#11758196—22no—
257#11758196—22no—
258#11758196—22no—
259#11758196—22no—
260#11758196C22⋊C411yescharacteristic
261#11758196C22⋊C411yescharacteristic
262#11758196C22⋊C411yescharacteristic
263#11758196C22⋊C411yescharacteristic
264C4×Dic61C22×C411yescharacteristic
265C4×Dic61C22×C411yescharacteristic
266C4×Dic61C2×D411yescharacteristic
267C4×Dic61C2×D411yescharacteristic
268C4×Dic61C2×D411yescharacteristic
269C4×Dic61C2×D411yescharacteristic
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274#11758189—42no—
275#11758189—81no—
276C8×D61—42no—
277C8×D61—81no—
278C23×C61C2×C22⋊C411yescharacteristic
279C22×D61—22no—
280C22×D61C2×C22⋊C411yescharacteristic
281C22×D61C2×C22⋊C411yescharacteristic
282Q8×C61—44no—
283Q8×C61—41no—
284Q8×C61—41no—
285Q8×C61—41no—
286Q8×C61—41no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—41no—
294C2×C4×C61—44no—
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C23×C411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C22⋊D61—22no—
302C22⋊D61—22no—
303C22⋊D61—44no—
304C2×Dic61—22no—
305C2×Dic61C2×C22⋊C411yescharacteristic
306C2×Dic61C2×C22⋊C411yescharacteristic
307C2×Dic61C2×C22⋊C411yescharacteristic
308C2×Dic61C2×C22⋊C411yescharacteristic
309C2×Dic61C2×C22⋊C411yescharacteristic
310C2×Dic61C2×C22⋊C411yescharacteristic
311D244—22no—
312D244—42no—
313D244—44no—
314D244—44no—
315D244—41no—
316D244—41no—
317D244—41no—
318D244—41no—
319C4×D61—21no—
320C4×D61—21no—
321C4×D61—21no—
322C4×D61—21no—
323C4×D61—21no—
324C4×D61—21no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—44no—
328C4×D61—44no—
329C4×D61—44no—
330C4×D61—44no—
331C4×D61—44no—
332C4×D61AGL(1,ℤ/8)12yes—
333C4×D61AGL(1,ℤ/8)12yes—
334Dic122—22no—
335Dic122—44no—
336Dic122—41no—
337Dic122—41no—
338Dic122—44no—
339C8×C61—41no—
340C8×C61—41no—
341C8×C61—41no—
342C8×C61—41no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#92418—41no—
347#17759—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61C22×C22⋊C411yescharacteristic
352C2×D61—21no—
353C2×D61—21no—
354C2×D61—21no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61#41812yes—
361C4×C61—21no—
362C4×C61—21no—
363C4×C61—21no—
364C4×C61—21no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
368C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
369C4×C61#57711yescharacteristic
370C4×C61#57811yescharacteristic
371Dic61—21no—
372Dic61—21no—
373Dic61—21no—
374Dic61—21no—
375Dic61—21no—
376Dic61—42no—
377Dic61#41812yes—
378#3499—611no—
379#2989—611no—
380#2925—611no—
381#1557—611no—
382#1557—611no—
383#1556—611no—
384#1556—611no—
385#1553—611no—
386#1553—611no—
387#1549—611no—
388#1549D6111yescharacteristic, complemented
389#1547—611no—
390#1546—611no—
391#1540—611no—
392C2×#332—611no—
393C2×C61—41no—
394C2×C61#288911yescharacteristic
395C2×C61C2×#41811yescharacteristic
396C2×C61#289811yescharacteristic
397D61—22no—
398D61—41no—
399D61—82no—
400C2×2−1+4—1221no—
401D4×Q8—612no—
402D4×Q8—1221no—
403#547—612no—
404#547—612no—
405#547—612no—
406#547—1221no—
407#547—1221no—
408#547—1221no—
409#536—1221no—
410#536—1221no—
411#536—1221no—
412#532—611no—
413#532—611no—
414#532—611no—
415C2×C4⋊Q8—611no—
416C2×C4⋊Q8—611no—
417C2×C4⋊Q8C2×D6111yescharacteristic
418C4×#41—611no—
419#446—1221no—
420#436—1221no—
421#435—1221no—
422#435—1221no—
423#433—1221no—
424#433—1221no—
425#432—611no—
426#432—611no—
427#432—611no—
428#432—611no—
429#431—611no—
430#431—611no—
431#431C2×D6111yescharacteristic
432#423—611no—
433#423—611no—
434#423C2×D6111yescharacteristic
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437#408—1221no—
438#405—1221no—
439#332—611no—
440#332—611no—
441#332—611no—
442#332—611no—
443#332—611no—
444#332—611no—
445#332—611no—
446#332—611no—
447#332C2×D6111yescharacteristic
448#332C2×D6111yescharacteristic
449#332C2×D6111yescharacteristic
450#332C2×D6111yescharacteristic
451#331—611no—
452#331—611no—
453#331—611no—
454#331—611no—
455C61#1775911yescharacteristic, complemented, Sylow
4562−1+4—2444no—
4572−1+4—2444no—
458C2×#41—611no—
459C2×#41—1222no—
460C2×#41—1222no—
461C2×#41—1221no—
462C2×#41—1221no—
463C2×#41—1222no—
464C2×#41—1221no—
465C22×Q8—21no—
466C22×Q8—1221no—
467C22×Q8—1221no—
468C22×Q8—1222no—
469C2×M16—21no—
470C2×M16—1221no—
471C2×M16—1221no—
472C22×C8—1221no—
473C22×C8—1221no—
474C4⋊Q8—21no—
475C4⋊Q8—21no—
476C4⋊Q8—612no—
477C4⋊Q8—612no—
478C4⋊Q8—611no—
479C4⋊Q8—1221no—
480C4⋊Q8—1221no—
481C4⋊Q8—1221no—
482C4⋊Q8—1221no—
483C4⋊Q8C4×D6112yes—
484C4⋊Q8C22×D6111yescharacteristic
485C4⋊Q8C22×D6111yescharacteristic
486#127—611no—
487#124—1221no—
488#124—1221no—
489#124—1221no—
490#123—1222no—
491#123—1222no—
492#123—1222no—
493#123—1222no—
494#123—1222no—
495#123—1222no—
496C22⋊Q8—1222no—
497C22⋊Q8—1222no—
498C22⋊Q8—1222no—
499C22⋊Q8—1222no—
500C22⋊Q8—1222no—
501C22⋊Q8—1222no—
502#121—612no—
503#121—612no—
504#121—612no—
505#121—1221no—
506#121—1221no—
507#121—1221no—
508C4×Q8—611no—
509C4×Q8—611no—
510C4×D4—611no—
511C4×D4—611no—
512C4×D4—611no—
513C4×D4—611no—
514C4×D4—612no—
515C4×D4—612no—
516C4×D4—611no—
517C4×D4—612no—
518C4×D4—611no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522#117—611no—
523#117—611no—
524#117—611no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—612no—
527C2×C4⋊C4—612no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4C4×D6112yes—
531C2×C42—611no—
532C2×C42—611no—
533C2×C42C22×D6111yescharacteristic
534C4⋊C8—21no—
535C4⋊C8—611no—
536C4⋊C8—611no—
537C4⋊C8—611no—
538C4⋊C8—611no—
539C4⋊C8—1221no—
540C4⋊C8—1221no—
541C4⋊C8—1221no—
542C4⋊C8—1221no—
543C4⋊C8C22×D6111yescharacteristic
544C4⋊C8C22×D6111yescharacteristic
545C4⋊C8C22×D6111yescharacteristic
546C4⋊C8C22×D6111yescharacteristic
547C22⋊C8—21no—
548C22⋊C8—1221no—
549C22⋊C8—1221no—
550C22⋊C8—1221no—
551C22⋊C8—1221no—
552C22⋊C8—1221no—
553C22⋊C8—1221no—
554#97—1221no—
555#97—1221no—
556#97—1221no—
557#97—1221no—
558C4×C8—21no—
559C4×C8—1221no—
560C4×C8—1221no—
561#41—1222no—
562#41—1222no—
563#41—2442no—
564#41—2442no—
565#41—2448no—
566#41—2448no—
567#41—2442no—
568#41—2442no—
569#41—2442no—
570#41—2442no—
571#41—2448no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—42no—
576C2×Q8—42no—
577C2×Q8—611no—
578C2×Q8—1222no—
579C2×Q8—1222no—
580C2×Q8—1221no—
581C2×Q8—2442no—
582C2×Q8—2442no—
583C2×Q8—2442no—
584C2×Q8—2442no—
585C2×Q8—2448no—
586C2×D4—611no—
587C2×D4—611no—
588C2×D4—612no—
589C2×D4—611no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1221no—
594C2×D4—1221no—
595C22×C4—22no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4D4×D6111yescharacteristic
610M16—81no—
611M16—4881no—
612M16—2442no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—4881no—
622C2×C8—2442no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—611no—
628C4⋊C4—611no—
629C4⋊C4—611no—
630C4⋊C4—611no—
631C4⋊C4—611no—
632C4⋊C4—611no—
633C4⋊C4—612no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1221no—
639C4⋊C4C2×C4×D6112yes—
640C4⋊C4C2×C4×D6112yes—
641C22⋊C4—611no—
642C22⋊C4—611no—
643C22⋊C4—611no—
644C22⋊C4—611no—
645C22⋊C4—611no—
646C22⋊C4—611no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C42—611no—
654C42—611no—
655C42—611no—
656C42—611no—
657C42—611no—
658C42—611no—
659C42C2×C4×D6111yescharacteristic
660C42D4×D6111yescharacteristic
661C42D4×D6111yescharacteristic
662C42C23×D6111yescharacteristic
663C23—611no—
664C23—611no—
665C23—1222no—
666C23C22⋊C4×D6111yescharacteristic
667Q8—44no—
668Q8—41no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—1222no—
673Q8—2444no—
674Q8—2444no—
675Q8—2441no—
676Q8—2441no—
677D4—1222no—
678D4—1222no—
679D4—1222no—
680D4—2442no—
681D4—2444no—
682D4—2444no—
683D4—2444no—
684D4—2441no—
685D4—2441no—
686D4—2441no—
687D4—2441no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—44no—
696C2×C4—611no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—611no—
700C2×C4—611no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1222no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2444no—
714C2×C4—2444no—
715C2×C4—2444no—
716C2×C4—2444no—
717C2×C4—2444no—
718C2×C4C22⋊C4×D6111yescharacteristic
719C2×C4C22⋊C4×D6111yescharacteristic
720C2×C4C22⋊C4×D6111yescharacteristic
721C2×C4C22×C4×D6111yescharacteristic
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×D4×D6111yescharacteristic
724C8—41no—
725C8—41no—
726C8—41no—
727C8—41no—
728C8—2441no—
729C8—2441no—
730C8—2441no—
731C8—2441no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—612no—
736C22—1221no—
737C22—1221no—
738C22—1221no—
739C22—1221no—
740C22—1221no—
741C22—2442no—
742C22—2442no—
743C22—2442no—
744C22C2×C22⋊C4×D6111yescharacteristic
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—42no—
750C4—42no—
751C4—612no—
752C4—1221no—
753C4—1221no—
754C4—1221no—
755C4—1221no—
756C4—1221no—
757C4—2442no—
758C4AGL(1,ℤ/8)×D6111yescharacteristic
759C4AGL(1,ℤ/8)×D6111yescharacteristic
760C4#1684056811yescharacteristic
761C4#1684057511yescharacteristic
762C2—41no—
763C2—1222no—
764C2—4882no—
765C2—2441no—
766C2#2145429911yescharacteristic
767C2#418×D6111yescharacteristic
768C2#2145434711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1549C2
socleC22×C61C22×C22⋊C4
prime radical#21459602C2
cosocleC42×C61C24
hypercenter#1549D61
hypocenterC61#17759
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
2. #21454933C2semidirect
3. #21454480C2semidirect
4. #21444540C2semidirect
5. #21444539C2semidirect
6. #21444536C2semidirect
7. #21444534C2semidirect
8. #21444523C2semidirect
9. #21444522C2semidirect
10. #21444502C2semidirect
11. #21444495C2semidirect
12. #21444489C2semidirect
13. #21444467C2semidirect
14. #332×D61C2semidirect
15. C61×#1549C2semidirect
388. #1549D61semidirect
455. C61#17759semidirect

Maximal subgroups

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

subgroupindex
#214596022
#214549332
#214544802
#214445402
#214445392
#214445362
#214445342
#214445232
#214445222
#214445022
#214444952
#214444892
#214444672
#332×D612
C61×#15492
#1775961