Finite Group Databasebeta

← #30611321

Subgroups — #30611321

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462511C211yesmaximal, characteristic, complemented
2#21462330C211yesmaximal, characteristic, complemented
3#21461263C211yesmaximal, characteristic, complemented
4#21461260C211yesmaximal, characteristic, complemented
5#21461254C211yesmaximal, characteristic, complemented
6#21461240C211yesmaximal, characteristic, complemented
7#21461238C211yesmaximal, characteristic, complemented
8#21461237C211yesmaximal, characteristic, complemented
9#21461223C211yesmaximal, characteristic, complemented
10#21461220C211yesmaximal, characteristic, complemented
11#21461214C211yesmaximal, characteristic, complemented
12#21461200C211yesmaximal, characteristic, complemented
13#21461198C211yesmaximal, characteristic, complemented
14#21461197C211yesmaximal, characteristic, complemented
15#21459552C211yesmaximal, 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#16840713—21no—
27#16840712—21no—
28#16840712—21no—
29#16840707C2211yescharacteristic, complemented
30#16840707C2211yescharacteristic, complemented
31#16840704C2211yescharacteristic
32C4⋊C4×#6923—21no—
33C4×C4⋊#6923C2211yescharacteristic, complemented
34C4×C4⋊#6923C2211yescharacteristic, complemented
35C4×C22⋊#6923C2211yescharacteristic
36#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic
41#16840614C2211yescharacteristic
42#16840614C2211yescharacteristic
43#16840614C2211yescharacteristic
44#16840614C2211yescharacteristic, complemented
45#16840614C2211yescharacteristic, complemented
46#16840614C2211yescharacteristic, complemented
47#16840614C2211yescharacteristic, complemented
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840474—21no—
53#16840463—21no—
54#16840457—21no—
55#16840439—21no—
56#16840437—21no—
57#16840414—21no—
58#16840405—21no—
59#16840404—21no—
60#16840389C411yescharacteristic, complemented
61#16840385C411yescharacteristic, complemented
62#16840367C411yescharacteristic, complemented
63#16840365C411yescharacteristic, complemented
64#16840330C411yescharacteristic, complemented
65#16840313C2211yescharacteristic
66#16840309C2211yescharacteristic
67#16840299C2211yescharacteristic
68#16840291C2211yescharacteristic
69#16840275C2211yescharacteristic
70#121×D61C2211yescharacteristic
71#16840244C411yescharacteristic, complemented
72#16840234C411yescharacteristic, complemented
73#117×D61C2211yescharacteristic
74C61×#542C411yescharacteristic, complemented
75C2×#11758217—21no—
76C22×#92420—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923—21no—
79C2×C4⋊#6923—21no—
80C2×C22⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85#14519844—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88C4⋊#92420—21no—
89#14519834—21no—
90#14519834—21no—
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519832—21no—
96#14519832—21no—
97C4×#92420—21no—
98C4×#92420—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×#11758226—21no—
108C2×#11758226C2×C411yescharacteristic
109C2×#11758222—21no—
110C2×D4×D61—21no—
111C2×D4×D61C2×C411yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519776C2×C411yescharacteristic
114#14519775—21no—
115#14519774C2×C411yescharacteristic
116#14519773C2×C411yescharacteristic
117#14519772—21no—
118#14519772—21no—
119#14519770—21no—
120#14519769C2×C411yescharacteristic
121#14519768C2×C411yescharacteristic
122#14519767—21no—
123#14519766—21no—
124#14519766C2×C411yescharacteristic
125#14519763—21no—
126#14519763—21no—
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519762—21no—
131#14519761—21no—
132#14519759—21no—
133#14519759—21no—
134#14519759—21no—
135#14519757—21no—
136#14519755—21no—
137#14519753—21no—
138#14519753C2311yescharacteristic
139#14519752—21no—
140#14519752C2311yescharacteristic
141#14519752C2311yescharacteristic
142#14519751C2×C411yescharacteristic
143#14519751C2×C411yescharacteristic
144#14519750—21no—
145#14519750—21no—
146#14519750—21no—
147#14519750—21no—
148#14519750—21no—
149#14519750—21no—
150#14519749—21no—
151#14519749—21no—
152#14519748—21no—
153#14519748C2311yescharacteristic
154#14519747—21no—
155#14519747—21no—
156#14519747—21no—
157Q8×Dic61C2×C411yescharacteristic
158C4×D244—21no—
159C4×D244—21no—
160C4×D244C2×C411yescharacteristic
161C4×D244C2×C411yescharacteristic
162D4×Dic61C2×C411yescharacteristic
163#14519739—21no—
164#14519739—21no—
165#14519739—21no—
166#14519739C2×C411yescharacteristic
167#14519739C2×C411yescharacteristic
168C4×C22⋊D61—21no—
169C4×C22⋊D61—21no—
170#14519737—21no—
171#14519737—21no—
172#14519737—21no—
173#14519736C2×C411yescharacteristic
174#14519735C2×C411yescharacteristic
175#14519735D411yescharacteristic
176#14519735D411yescharacteristic
177#14519734—21no—
178#14519734—21no—
179#14519734C2×C411yescharacteristic
180#14519734C2×C411yescharacteristic
181#14519733—21no—
182#14519733D411yescharacteristic
183#14519733D411yescharacteristic
184C4⋊C4×D61—21no—
185C4⋊C4×D61C2×C411yescharacteristic
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
195C4⋊Q8×C61C2×C411yescharacteristic
196#126×C61—21no—
197#124×C61—21no—
198#124×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202#121×C61C2×C411yescharacteristic
203C4×Q8×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C23×D61—21no—
207C23×D61C2×D411yescharacteristic
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C2×Q8×C61—21no—
213C2×Q8×C61C22×C411yescharacteristic
214C2×D4×C61—21no—
215C2×D4×C61C22×C411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61C22×C411yescharacteristic
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C22×Dic61—21no—
225C22×Dic61C2×D411yescharacteristic
226#11758226—42no—
227#11758226—81no—
228#11758226—81no—
229D4×D61—42no—
230D4×D61—81no—
231D4×D61—81no—
232#11758222—81no—
233#11758222—81no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244C22×C411yescharacteristic
240C2×D244C22×C411yescharacteristic
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—42no—
248C2×C4×D61C22×C411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2411yescharacteristic
256C2×Dic122—21no—
257C22⋊#6923—42no—
258C22⋊#6923—81no—
259#11758217—42no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—42no—
265C4⋊#6923—42no—
266C4⋊#6923—42no—
267C4⋊#6923—42no—
268C4×#6923—42no—
269C4×#6923—81no—
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×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61C22⋊C411yescharacteristic
284C22⋊C4×C61C22⋊C411yescharacteristic
285C42×C61—21no—
286C42×C61C22×C411yescharacteristic
287C42×C61C22×C411yescharacteristic
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61C22⋊C411yescharacteristic
291C22⋊Dic61C22⋊C411yescharacteristic
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#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61C22⋊C411yescharacteristic
311C4⋊Dic61C22⋊C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196C22⋊C411yescharacteristic
321#11758196C22⋊C411yescharacteristic
322#11758196C22⋊C411yescharacteristic
323#11758196C22⋊C411yescharacteristic
324C4×Dic61—21no—
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—21no—
335C22×D61—21no—
336C22×D61—21no—
337C22×D61—21no—
338C22×D61—41no—
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—
357Q8×C61—41no—
358Q8×C61—81no—
359D4×C61—41no—
360D4×C61—81no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—41no—
365C2×C4×C61—81no—
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C23×C411yescharacteristic
372C22⋊D61—41no—
373C22⋊D61—41no—
374C22⋊D61—42no—
375C22⋊D61—81no—
376C22⋊D61—81no—
377C22⋊D61—81no—
378C22⋊D61—81no—
379C2×Dic61—22no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—81no—
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C2×C22⋊C411yescharacteristic
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C22×D411yescharacteristic
389D244—41no—
390D244—41no—
391D244—42no—
392D244—41no—
393D244—41no—
394D244—41no—
395D244—41no—
396D244—81no—
397D244—81no—
398C4×D61—21no—
399C4×D61—21no—
400C4×D61—21no—
401C4×D61—21no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—42no—
409C4×D61—81no—
410C4×D61—81no—
411C4×D61—81no—
412C4×D61—81no—
413C4×D61—81no—
414Dic122—81no—
415#92420—41no—
416#92420—41no—
417#92420—41no—
418#92420—41no—
419#17607—611nomaximal, Sylow
420C22×C61—21no—
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61C22×C22⋊C411yescharacteristic
427C2×D61—21no—
428C2×D61—21no—
429C2×D61—21no—
430C2×D61—21no—
431C2×D61—21no—
432C2×D61—41no—
433C2×D61—41no—
434C2×D61—41no—
435C2×D61—41no—
436C2×D61—41no—
437C2×D61—41no—
438C2×D61—81no—
439C2×D61—81no—
440C2×D61—162no—
441C2×D61#57611yescharacteristic
442C2×D61#57711yescharacteristic
443#6923—42no—
444#6923—81no—
445#6923—81no—
446#6923—81no—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—41no—
454C4×C61—41no—
455C4×C61—41no—
456Dic61—21no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—41no—
462Dic61—41no—
463Dic61#41012yes—
464#3494—611no—
465#2924—611no—
466#2347—611no—
467#1521—611no—
468#1521—611no—
469#1519—611no—
470#1514—611no—
471#1514—611no—
472#1513—611no—
473#1509—611no—
474#1509—611no—
475#1507—611no—
476#1502—611no—
477#1502—611no—
478#1501—611no—
479C2×C61—41no—
480C2×C61—81no—
481C2×C61C2×#41011yescharacteristic
482C2×C61#289711yescharacteristic
483C2×C61#290111yescharacteristic
484D61—21no—
485D61—21no—
486D61—41no—
487D61—81no—
488D61—81no—
489#555—1221no—
490#553—1221no—
491#553—1221no—
492#551—1221no—
493#551—1221no—
494#547—1221no—
495#546—1221no—
496#546—1221no—
497#544—611no—
498#542—611no—
499#542#692311yescharacteristic, complemented
500#540—611no—
501#540—611no—
502#535—611no—
503#532—611no—
504#532—611no—
505#529—611no—
506#529—611no—
507#525—611no—
508C2×#121—611no—
509#520—611no—
510#518—611no—
511C2×#117—611no—
512#433—1221no—
513#433—1221no—
514#432—611no—
515#432—611no—
516#431—611no—
517#431—611no—
518#424—1221no—
519#407—611no—
520C2×C22⋊C8—611no—
521#405—1221no—
522#389—1221no—
523#388—1221no—
524#388—1221no—
525#383—611no—
526#383—611no—
527#380—611no—
528C4×C4⋊C4—611no—
529C4×C4⋊C4—611no—
530C4×C4⋊C4—1221no—
531C4×C22⋊C4—611no—
532#328—611no—
533#328—611no—
534#328—611no—
535#328—611no—
536#327—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—
548C61#1760711yescharacteristic, complemented, Sylow
549C2×#41—611no—
550C2×#41—1221no—
551C2×#41—1221no—
552C22×D4—611no—
553C22×D4—1221no—
554C23×C4—611no—
555C2×M16—1221no—
556C22×C8—1221no—
557C4⋊Q8—611no—
558C4⋊Q8—1221no—
559C4⋊Q8C2×#692311yescharacteristic
560#127—611no—
561#127—611no—
562#126—21no—
563#126—1221no—
564#126—1221no—
565#126—1221no—
566#125—611no—
567#125—611no—
568#125—1221no—
569#124—21no—
570#124—611no—
571#124—1221no—
572#124—1221no—
573#124—1221no—
574#124C2×#692311yescharacteristic
575#123—21no—
576#123—1221no—
577#123—1221no—
578#123—1221no—
579#123—1221no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584C22⋊Q8—21no—
585C22⋊Q8—611no—
586C22⋊Q8—1221no—
587C22⋊Q8—1221no—
588C22⋊Q8—1221no—
589C22⋊Q8C2×#692311yescharacteristic
590#121—611no—
591#121—611no—
592#121—611no—
593#121—611no—
594#121—611no—
595#121—1221no—
596#121—1221no—
597#121—1221no—
598#121—1221no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602#121—1221no—
603#121—1221no—
604#121—1221no—
605#121C2×#692311yescharacteristic
606#120—1221no—
607#120—1221no—
608#120—1221no—
609C4×Q8—611no—
610C4×Q8C2×#692311yescharacteristic
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—611no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4C2×#692311yescharacteristic
627#117—611no—
628#117—611no—
629#117—611no—
630#117—611no—
631#117—611no—
632#117—611no—
633#117—611no—
634#117—611no—
635#117—1221no—
636#117—1221no—
637#117—1221no—
638#117C2×#692311yescharacteristic
639C2×C4⋊C4—611no—
640C2×C4⋊C4—611no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—1221no—
643C2×C4⋊C4—1221no—
644C2×C4⋊C4—1221no—
645C2×C4⋊C4—1221no—
646C2×C22⋊C4—611no—
647C2×C22⋊C4—611no—
648C2×C22⋊C4—1221no—
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—
657C2×C42—1221no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
660C4⋊C8—1221no—
661C4⋊C8—1221no—
662C22⋊C8—611no—
663C22⋊C8—611no—
664C22⋊C8—611no—
665C22⋊C8—611no—
666C22⋊C8—1221no—
667C22⋊C8—1221no—
668#97—1221no—
669#97—1221no—
670C4×C8—1221no—
671C4×C8—1221no—
672#95—611no—
673#95—611no—
674#95—611no—
675#95—611no—
676#95—1221no—
677#95—1221no—
678#95—1221no—
679#95—1221no—
680C24—611no—
681C24—1221no—
682#41—4881no—
683#41—4881no—
684#41—4881no—
685#41—4881no—
686#41—2442no—
687C2×Q8—21no—
688C2×Q8—1221no—
689C2×Q8C22×#692311yescharacteristic
690C2×D4—21no—
691C2×D4—611no—
692C2×D4—611no—
693C2×D4—1221no—
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—4881no—
705C2×D4—4881no—
706C2×D4—2442no—
707C2×D4C22×#692311yescharacteristic
708C22×C4—21no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—2442no—
730C22×C4C22×#692311yescharacteristic
731M16—2442no—
732C2×C8—1221no—
733C2×C8—1221no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—2442no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—611no—
741C4⋊C4—611no—
742C4⋊C4—611no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—2442no—
757C4⋊C4—2442no—
758C4⋊C4—2442no—
759C4⋊C4C22⋊#692311yescharacteristic
760C4⋊C4C22⋊#692311yescharacteristic
761C4⋊C4C22×#692311yescharacteristic
762C4⋊C4C22×#692311yescharacteristic
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
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—4881no—
789C22⋊C4—2442no—
790C22⋊C4C22⋊#692311yescharacteristic
791C22⋊C4C22⋊#692311yescharacteristic
792C42—21no—
793C42—611no—
794C42—611no—
795C42—611no—
796C42—611no—
797C42—611no—
798C42—611no—
799C42—1221no—
800C42—1221no—
801C42—4881no—
802C42—4881no—
803C42—2442no—
804C42C22×#692311yescharacteristic
805C42C22×#692311yescharacteristic
806C23—21no—
807C23—611no—
808C23—611no—
809C23—1221no—
810C23—1221no—
811C23—1221no—
812C23—1221no—
813C23—4881no—
814C23—4881no—
815C23—2441no—
816C23—2441no—
817C23—2442no—
818C23C2×C22⋊#692311yescharacteristic
819Q8—41no—
820Q8—81no—
821Q8—4881no—
822D4—41no—
823D4—81no—
824D4—4881no—
825D4—4881no—
826D4—4881no—
827D4—4881no—
828D4—4881no—
829D4—4881no—
830D4—2441no—
831D4—2441no—
832D4—2441no—
833D4—2441no—
834D4—2441no—
835D4—2441no—
836D4—2442no—
837D4—2442no—
838D4—2441no—
839D4—2441no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—81no—
845C2×C4—611no—
846C2×C4—611no—
847C2×C4—611no—
848C2×C4—611no—
849C2×C4—611no—
850C2×C4—611no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1222no—
858C2×C4—1222no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—4881no—
862C2×C4—4881no—
863C2×C4—4881no—
864C2×C4—4881no—
865C2×C4—4881no—
866C2×C4—4881no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2442no—
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×C4C2×C22⋊#692311yescharacteristic
884C2×C4C2×C22⋊#692311yescharacteristic
885C2×C4C2×C22⋊#692311yescharacteristic
886C2×C4C2×C22⋊#692311yescharacteristic
887C2×C4C2×C22⋊#692311yescharacteristic
888C2×C4C23×#692311yescharacteristic
889C8—2441no—
890C8—2441no—
891C8—2441no—
892C8—2441no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—611no—
900C22—611no—
901C22—1221no—
902C22—1221no—
903C22—1221no—
904C22—1221no—
905C22—1221no—
906C22—9762no—
907C22—4881no—
908C22—4881no—
909C22—2441no—
910C22—2441no—
911C22—2441no—
912C22—2441no—
913C22—2441no—
914C22—2441no—
915C22C22×C22⋊#692311yescharacteristic
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—612no—
926C4—1221no—
927C4—1221no—
928C4—1221no—
929C4—1221no—
930C4—1221no—
931C4—4881no—
932C4—4881no—
933C4—4881no—
934C4—2442no—
935C4—2441no—
936C4—2441no—
937C2—41no—
938C2—81no—
939C2—1221no—
940C2—1221no—
941C2—4881no—
942C2—4881no—
943C2—2441no—
944C2D61⋊#41011yescharacteristic
945C2#2146244011yescharacteristic
946C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#542C4
socleC22×C61C22×C22⋊C4
prime radical#21459552C2
cosocleC2×C4×D61C24
hypercenter#542#6923
hypocenterC61#17607
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #21462511C2semidirect
2. #21462330C2semidirect
3. #21461263C2semidirect
4. #21461260C2semidirect
5. #21461254C2semidirect
6. #21461240C2semidirect
7. #21461238C2semidirect
8. #21461237C2semidirect
9. #21461223C2semidirect
10. #21461220C2semidirect
11. #21461214C2semidirect
12. #21461200C2semidirect
13. #21461198C2semidirect
14. #21461197C2semidirect
18. #16840785C22semidirect
19. #16840784C22semidirect
20. #16840781C22semidirect
21. #16840780C22semidirect
29. #16840707C22semidirect
30. #16840707C22semidirect
33. C4×C4⋊#6923C22semidirect
34. C4×C4⋊#6923C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
44. #16840614C22semidirect
45. #16840614C22semidirect
46. #16840614C22semidirect
47. #16840614C22semidirect
60. #16840389C4semidirect
61. #16840385C4semidirect
62. #16840367C4semidirect
63. #16840365C4semidirect
64. #16840330C4semidirect
71. #16840244C4semidirect
72. #16840234C4semidirect
74. C61×#542C4semidirect
499. #542#6923semidirect
548. C61#17607semidirect

Maximal subgroups

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

subgroupindex
#214625112
#214623302
#214612632
#214612602
#214612542
#214612402
#214612382
#214612372
#214612232
#214612202
#214612142
#214612002
#214611982
#214611972
#214595522
#1760761