Finite Group Databasebeta

← #30611303

Subgroups — #30611303

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462511C211yesmaximal, characteristic, complemented
2#21462326C211yesmaximal, characteristic, complemented
3#21461263C211yesmaximal, characteristic, complemented
4#21461249C211yesmaximal, characteristic, complemented
5#21461245C211yesmaximal, characteristic, complemented
6#21461238C211yesmaximal, characteristic, complemented
7#21461232C211yesmaximal, characteristic, complemented
8#21461226C211yesmaximal, characteristic, complemented
9#21461223C211yesmaximal, characteristic, complemented
10#21461209C211yesmaximal, characteristic, complemented
11#21461205C211yesmaximal, characteristic, complemented
12#21461198C211yesmaximal, characteristic, complemented
13#21461192C211yesmaximal, characteristic, complemented
14C2×#16840614C211yesmaximal, characteristic, complemented
15#21459555C211yesmaximal, characteristic
16#16840787—21no—
17#16840787—21no—
18#16840785C2211yescharacteristic, complemented
19#16840784C2211yescharacteristic, complemented
20#16840781C2211yescharacteristic, complemented
21#16840780C2211yescharacteristic, complemented
22#16840768—21no—
23#16840734C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25#16840726—21no—
26#16840711—21no—
27#16840711—21no—
28#16840709—21no—
29#16840707C2211yescharacteristic, complemented
30#16840706C2211yescharacteristic, complemented
31#16840705C2211yescharacteristic
32C4×C4⋊#6923C2211yescharacteristic, complemented
33C22⋊C4×#6923—21no—
34#16840698C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic
41#16840614C2211yescharacteristic
42#16840614C2211yescharacteristic
43#16840614C2211yescharacteristic
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52#16840475—21no—
53#16840460—21no—
54#16840456—21no—
55#16840441—21no—
56#16840441—21no—
57#16840413—21no—
58#16840408—21no—
59#16840408—21no—
60#16840393C411yescharacteristic, complemented
61#16840384C411yescharacteristic, complemented
62#16840384C411yescharacteristic, complemented
63#16840363C411yescharacteristic, complemented
64#16840363C411yescharacteristic, complemented
65#16840326C411yescharacteristic, complemented
66#16840309C2211yescharacteristic
67#16840309C2211yescharacteristic
68#16840299C2211yescharacteristic
69#16840299C2211yescharacteristic
70#16840269C2211yescharacteristic
71C2×#14519752C2211yescharacteristic
72#16840236C411yescharacteristic, complemented
73#117×D61C2211yescharacteristic
74C61×#520C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758217—21no—
77C22×#92420—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—21no—
80C2×C22⋊#6923—21no—
81C2×C4×#6923—21no—
82C2×C4×#6923—21no—
83#14519844—21no—
84#14519844—21no—
85C4⋊#92420—21no—
86C4⋊#92420—21no—
87#14519834—21no—
88#14519834—21no—
89#14519834C2311yescharacteristic
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519832—21no—
94#14519832—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97(C2×#6923)⋊C4—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4C2311yescharacteristic
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107C2×#11758222—21no—
108C2×#11758222—21no—
109C22×D244—21no—
110C22×D244C2×C411yescharacteristic
111C22×C4×D61C2311yescharacteristic
112#14519776—21no—
113#14519776C2×C411yescharacteristic, complemented
114#14519776C2×C411yescharacteristic, complemented
115#14519773C2×C411yescharacteristic, complemented
116#14519773C2×C411yescharacteristic, complemented
117#14519772—21no—
118#14519772—21no—
119#14519771—21no—
120#14519771—21no—
121#14519768—21no—
122#14519768C2×C411yescharacteristic, complemented
123#14519768C2×C411yescharacteristic, complemented
124#14519766C2×C411yescharacteristic, complemented
125#14519766C2×C411yescharacteristic, complemented
126#14519765—21no—
127#14519765—21no—
128#14519763—21no—
129#14519763—21no—
130#14519762—21no—
131#14519762—21no—
132#14519762—21no—
133#14519762—21no—
134#14519760—21no—
135#14519760—21no—
136#14519759—21no—
137#14519759—21no—
138#14519758—21no—
139#14519756—21no—
140#14519756—21no—
141#14519755—21no—
142#14519755—21no—
143#14519753C2×C411yescharacteristic
144#14519753C2311yescharacteristic
145#14519752—21no—
146#14519752—21no—
147#14519752C2×C411yescharacteristic
148#14519752C2×C411yescharacteristic
149#14519752C2311yescharacteristic
150#14519752C2311yescharacteristic
151#14519751—21no—
152#14519751—21no—
153#14519751—21no—
154#14519751—21no—
155#14519750—21no—
156#14519750—21no—
157#14519750—21no—
158#14519750—21no—
159#14519748C2×C411yescharacteristic
160#14519748C2311yescharacteristic
161#14519745—21no—
162#14519745—21no—
163#14519745—21no—
164C4×D244—21no—
165C4×D244—21no—
166C4×D244C2×C411yescharacteristic, complemented
167C4×D244C2×C411yescharacteristic, complemented
168C4×D244C2×C411yescharacteristic, complemented
169C4×D244C2×C411yescharacteristic, complemented
170#14519739—21no—
171#14519739—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176#14519736C2×C411yescharacteristic
177#14519736C2×C411yescharacteristic
178#14519735D411yescharacteristic
179#14519735D411yescharacteristic
180#14519734—21no—
181#14519734—21no—
182#14519734C2×C411yescharacteristic
183#14519734C2×C411yescharacteristic
184#14519733D411yescharacteristic
185#14519733D411yescharacteristic
186C4⋊C4×D61D411yescharacteristic
187C4⋊C4×D61D411yescharacteristic
188C2×#11758198—21no—
189C22⋊C4×D61—21no—
190C22⋊C4×D61—21no—
191C22⋊C4×D61D411yescharacteristic
192C22⋊C4×D61D411yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C4×Q8×C61C2×C411yescharacteristic, complemented
197C4×Q8×C61C2×C411yescharacteristic, complemented
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200C4×D4×C61C2×C411yescharacteristic, complemented
201C4×D4×C61C2×C411yescharacteristic, complemented
202#117×C61—21no—
203#117×C61C2×C411yescharacteristic
204C2×C4⋊C4×C61—21no—
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—42no—
213C22×#6923—42no—
214C22×#6923—81no—
215#41×C61—42no—
216C2×Q8×C61C22×C411yescharacteristic
217C2×D4×C61—21no—
218C2×D4×C61C22×C411yescharacteristic
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61C22×C411yescharacteristic
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C22×Dic61C2×D411yescharacteristic
231#11758222—81no—
232#11758222—81no—
233#11758222—81no—
234#11758222—81no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—42no—
241C2×D244—81no—
242C2×D244—81no—
243C2×D244C22×C411yescharacteristic
244C2×D244C22×C411yescharacteristic
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—42no—
250C2×C4×D61C22×C411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2411yescharacteristic
258C2×Dic122—21no—
259C2×Dic122—21no—
260C22⋊#6923—42no—
261#11758217—42no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—42no—
267C4⋊#6923—42no—
268C4⋊#6923—81no—
269C4×#6923—42no—
270C4×#6923—81no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61C22⋊C411yescharacteristic
275C4⋊C4×C61C22⋊C411yescharacteristic
276C4⋊C4×C61C22×C411yescharacteristic
277C4⋊C4×C61C22×C411yescharacteristic
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61C22⋊C411yescharacteristic
281C22⋊C4×C61C22⋊C411yescharacteristic
282C42×C61—21no—
283C42×C61—21no—
284C42×C61C22×C411yescharacteristic
285C42×C61C22×C411yescharacteristic
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61C22⋊C411yescharacteristic
290C22⋊Dic61C22⋊C411yescharacteristic
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61C22⋊C411yescharacteristic
312C4⋊Dic61C22⋊C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314C4⋊Dic61C22×C411yescharacteristic
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196C22⋊C411yescharacteristic
322#11758196C22⋊C411yescharacteristic
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325C4×Dic61—21no—
326C4×Dic61C22×C411yescharacteristic
327C4×Dic61C22×C411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332C23×C61—21no—
333C23×C61C2×C22⋊C411yescharacteristic
334C22×D61—22no—
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—41no—
340C22×D61—42no—
341C22×D61—81no—
342C22×D61—81no—
343C22×D61C2×C22⋊C411yescharacteristic
344C22×D61C22×D411yescharacteristic
345C2×#6923—22no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—84no—
358Q8×C61—41no—
359D4×C61—41no—
360D4×C61—42no—
361C2×C4×C61—22no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—42no—
366C2×C4×C61—81no—
367C2×C4×C61—81no—
368C2×C4×C61—81no—
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C2×C22⋊C411yescharacteristic
372C2×C4×C61C2×C22⋊C411yescharacteristic
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C23×C411yescharacteristic
375C22⋊D61—41no—
376C22⋊D61—41no—
377C22⋊D61—81no—
378C22⋊D61—81no—
379C22⋊D61—81no—
380C22⋊D61—81no—
381C22⋊D61—81no—
382C2×Dic61—22no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C2×C22⋊C411yescharacteristic
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61C22×D411yescharacteristic
391D244—41no—
392D244—41no—
393D244—42no—
394D244—41no—
395D244—41no—
396D244—41no—
397D244—41no—
398D244—81no—
399D244—81no—
400C4×D61—21no—
401C4×D61—21no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—81no—
411C4×D61—81no—
412C4×D61—81no—
413C4×D61—81no—
414Dic122—81no—
415Dic122—81no—
416#92420—41no—
417#92420—41no—
418#92420—41no—
419#92420—41no—
420#17604—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61#41012yes—
427C22×C61C22×C22⋊C411yescharacteristic
428C2×D61—21no—
429C2×D61—21no—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—42no—
434C2×D61—42no—
435C2×D61—41no—
436C2×D61—41no—
437C2×D61—41no—
438C2×D61—41no—
439C2×D61—41no—
440C2×D61—41no—
441C2×D61—162no—
442C2×D61#57611yescharacteristic
443C2×D61#57711yescharacteristic
444#6923—42no—
445#6923—81no—
446#6923—81no—
447#6923—81no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—41no—
455C4×C61—41no—
456C4×C61—41no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—41no—
464Dic61—41no—
465#3494—611no—
466#2924—611no—
467#2343—611no—
468#1521—611no—
469#1517—611no—
470#1516—611no—
471#1514—611no—
472#1512—611no—
473#1510—611no—
474#1509—611no—
475#1505—611no—
476#1504—611no—
477#1502—611no—
478#1500—611no—
479C2×#327—611no—
480C2×C61—22no—
481C2×C61—81no—
482C2×C61C2×#41011yescharacteristic
483C2×C61#289711yescharacteristic
484C2×C61#290111yescharacteristic
485D61—21no—
486D61—21no—
487D61—41no—
488D61—81no—
489D61—81no—
490#555—1221no—
491#553—1221no—
492#553—1221no—
493#551—1221no—
494#551—1221no—
495#547—1221no—
496#546—1221no—
497#546—1221no—
498#544—611no—
499#542—611no—
500#542—611no—
501#540—611no—
502#540—611no—
503#535—611no—
504#532—611no—
505#532—611no—
506#529—611no—
507#529—611no—
508#525—611no—
509C2×#121—611no—
510#520#692311yescharacteristic, complemented
511#518—611no—
512C2×#117—611no—
513#433—1221no—
514#433—1221no—
515#432—611no—
516#432—611no—
517#431—611no—
518#431—611no—
519#424—1221no—
520#407—611no—
521C2×C22⋊C8—611no—
522#405—1221no—
523#387—1221no—
524#387—1221no—
525#385—1221no—
526#383—611no—
527#382—611no—
528#381—611no—
529C4×C4⋊C4—611no—
530C4×C22⋊C4—1221no—
531#376—611no—
532C2×#95—611no—
533#328—611no—
534#328—611no—
535#328—611no—
536#328—611no—
537#327—611no—
538#327—611no—
539#327—611no—
540#327—611no—
541#327—611no—
542#327—611no—
543#327—611no—
544#327—611no—
545#327—611no—
546#327—611no—
547#327—611no—
548#327—611no—
549C61#1760411yescharacteristic, complemented, Sylow
550C2×#41—1221no—
551C2×#41—1221no—
552C2×#41C2×#692311yescharacteristic
553C22×D4—611no—
554C22×D4—1221no—
555C23×C4—611no—
556C23×C4—1221no—
557C2×M16—1221no—
558C22×C8—1221no—
559C4⋊Q8—611no—
560C4⋊Q8—611no—
561C4⋊Q8—1221no—
562#127—611no—
563#127—611no—
564#126—1221no—
565#126—1221no—
566#126—1221no—
567#126—1221no—
568#125—611no—
569#125—611no—
570#125—1221no—
571#124—611no—
572#124—611no—
573#124—1221no—
574#124—1221no—
575#124—1221no—
576#124—1221no—
577#123—1221no—
578#123—1221no—
579#123—1221no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586C22⋊Q8—611no—
587C22⋊Q8—611no—
588C22⋊Q8—1221no—
589C22⋊Q8—1221no—
590C22⋊Q8—1221no—
591C22⋊Q8—1221no—
592#121—611no—
593#121—611no—
594#121—611no—
595#121—611no—
596#121—611no—
597#121—611no—
598#121—1221no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602#121—1221no—
603#121—1221no—
604#121—1221no—
605#121—1221no—
606#121—1221no—
607#121—1221no—
608#120—1221no—
609#120—1221no—
610#120—1221no—
611C4×Q8C2×#692311yescharacteristic, complemented
612C4×Q8C2×#692311yescharacteristic, complemented
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4C2×#692311yescharacteristic, complemented
628C4×D4C2×#692311yescharacteristic, complemented
629#117—21no—
630#117—611no—
631#117—611no—
632#117—611no—
633#117—611no—
634#117—611no—
635#117—611no—
636#117—611no—
637#117—611no—
638#117—1221no—
639#117—1221no—
640#117C2×#692311yescharacteristic
641C2×C4⋊C4—21no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—1221no—
645C2×C4⋊C4—1221no—
646C2×C4⋊C4C2×#692311yescharacteristic
647C2×C22⋊C4—611no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C42—611no—
654C2×C42—611no—
655C2×C42—1221no—
656C2×C42—1221no—
657C4⋊C8—1221no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
660C4⋊C8—1221no—
661C22⋊C8—611no—
662C22⋊C8—611no—
663C22⋊C8—611no—
664C22⋊C8—611no—
665C22⋊C8—1221no—
666C22⋊C8—1221no—
667#97—1221no—
668#97—1221no—
669C4×C8—1221no—
670C4×C8—1221no—
671#95—611no—
672#95—611no—
673#95—611no—
674#95—611no—
675#95—1221no—
676#95—1221no—
677#95—1221no—
678#95—1221no—
679#95—1221no—
680#95—1221no—
681C24—611no—
682C24—1221no—
683#41—42no—
684#41—4881no—
685#41—4881no—
686#41—4881no—
687#41—4881no—
688C2×Q8—1221no—
689C2×Q8—1221no—
690C2×Q8C22×#692311yescharacteristic
691C2×D4—21no—
692C2×D4—611no—
693C2×D4—611no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—4881no—
706C2×D4—4881no—
707C2×D4—2442no—
708C2×D4C22×#692311yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—4881no—
731C22×C4—2442no—
732C22×C4—2442no—
733C22×C4—2442no—
734C22×C4C22×#692311yescharacteristic
735M16—2442no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—2442no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—4881no—
761C4⋊C4—2442no—
762C4⋊C4C22⋊#692311yescharacteristic
763C4⋊C4C22⋊#692311yescharacteristic
764C4⋊C4C22×#692311yescharacteristic
765C4⋊C4C22×#692311yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—611no—
769C22⋊C4—611no—
770C22⋊C4—611no—
771C22⋊C4—611no—
772C22⋊C4—611no—
773C22⋊C4—611no—
774C22⋊C4—1221no—
775C22⋊C4—1221no—
776C22⋊C4—1221no—
777C22⋊C4—1221no—
778C22⋊C4—1221no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—2442no—
792C22⋊C4C22⋊#692311yescharacteristic
793C22⋊C4C22⋊#692311yescharacteristic
794C42—21no—
795C42—21no—
796C42—611no—
797C42—611no—
798C42—611no—
799C42—611no—
800C42—611no—
801C42—611no—
802C42—1221no—
803C42—4881no—
804C42—2442no—
805C42C22×#692311yescharacteristic
806C42C22×#692311yescharacteristic
807C23—21no—
808C23—611no—
809C23—611no—
810C23—1221no—
811C23—1221no—
812C23—1222no—
813C23—1221no—
814C23—1221no—
815C23—4881no—
816C23—4881no—
817C23—2441no—
818C23—2442no—
819C23C2×C22⋊#692311yescharacteristic
820Q8—41no—
821Q8—4881no—
822Q8—4881no—
823D4—41no—
824D4—42no—
825D4—4881no—
826D4—4881no—
827D4—4881no—
828D4—4881no—
829D4—4881no—
830D4—4881no—
831D4—4881no—
832D4—2441no—
833D4—2441no—
834D4—2442no—
835D4—2441no—
836D4—2441no—
837D4—2441no—
838D4—2441no—
839D4—2441no—
840D4—2441no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—42no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—611no—
850C2×C4—611no—
851C2×C4—611no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—611no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—4881no—
864C2×C4—4881no—
865C2×C4—4881no—
866C2×C4—4881no—
867C2×C4—4884no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4C2×C22⋊#692311yescharacteristic
886C2×C4C2×C22⋊#692311yescharacteristic
887C2×C4C2×C22⋊#692311yescharacteristic
888C2×C4C2×C22⋊#692311yescharacteristic
889C2×C4C2×C22⋊#692311yescharacteristic
890C2×C4C23×#692311yescharacteristic
891C8—2441no—
892C8—2441no—
893C8—2441no—
894C8—2441no—
895C22—21no—
896C22—21no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—611no—
901C22—611no—
902C22—1221no—
903C22—1221no—
904C22—1221no—
905C22—1221no—
906C22—1221no—
907C22—9762no—
908C22—2442no—
909C22—2442no—
910C22—2441no—
911C22—2441no—
912C22—2441no—
913C22—2441no—
914C22—2441no—
915C22—2441no—
916C22#1684074112yes—
917C22C22×C22⋊#692311yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—1221no—
928C4—1221no—
929C4—1221no—
930C4—1221no—
931C4—1221no—
932C4—1221no—
933C4—4881no—
934C4—4881no—
935C4—4881no—
936C4—2442no—
937C4—2441no—
938C4—2441no—
939C2—22no—
940C2—81no—
941C2—1221no—
942C2—1221no—
943C2—4881no—
944C2—4881no—
945C2—2441no—
946C2C2×#1684074111yescharacteristic
947C2#2146244011yescharacteristic
948C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#520C4
socleC22×C61C22×C22⋊C4
prime radical#21459555C2
cosocleC2×C4×D61C24
hypercenter#520#6923
hypocenterC61#17604
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #21462511C2semidirect
2. #21462326C2semidirect
3. #21461263C2semidirect
4. #21461249C2semidirect
5. #21461245C2semidirect
6. #21461238C2semidirect
7. #21461232C2semidirect
8. #21461226C2semidirect
9. #21461223C2semidirect
10. #21461209C2semidirect
11. #21461205C2semidirect
12. #21461198C2semidirect
13. #21461192C2semidirect
14. C2×#16840614C2semidirect
18. #16840785C22semidirect
19. #16840784C22semidirect
20. #16840781C22semidirect
21. #16840780C22semidirect
29. #16840707C22semidirect
30. #16840706C22semidirect
32. C4×C4⋊#6923C22semidirect
34. #16840698C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
60. #16840393C4semidirect
61. #16840384C4semidirect
62. #16840384C4semidirect
63. #16840363C4semidirect
64. #16840363C4semidirect
65. #16840326C4semidirect
72. #16840236C4semidirect
74. C61×#520C4semidirect
113. #14519776C2×C4semidirect
114. #14519776C2×C4semidirect
115. #14519773C2×C4semidirect
116. #14519773C2×C4semidirect
122. #14519768C2×C4semidirect
123. #14519768C2×C4semidirect
124. #14519766C2×C4semidirect
125. #14519766C2×C4semidirect
166. C4×D244C2×C4semidirect
167. C4×D244C2×C4semidirect
168. C4×D244C2×C4semidirect
169. C4×D244C2×C4semidirect
196. C4×Q8×C61C2×C4semidirect
197. C4×Q8×C61C2×C4semidirect
200. C4×D4×C61C2×C4semidirect
201. C4×D4×C61C2×C4semidirect
510. #520#6923semidirect
549. C61#17604semidirect
611. C4×Q8C2×#6923semidirect
612. C4×Q8C2×#6923semidirect
627. C4×D4C2×#6923semidirect
628. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625112
#214623262
#214612632
#214612492
#214612452
#214612382
#214612322
#214612262
#214612232
#214612092
#214612052
#214611982
#214611922
C2×#168406142
#214595552
#1760461