Finite Group Databasebeta

← #30611301

Subgroups — #30611301

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#21461260C211yesmaximal, characteristic, complemented
4#21461248C211yesmaximal, characteristic, complemented
5#21461245C211yesmaximal, characteristic, complemented
6#21461239C211yesmaximal, characteristic, complemented
7#21461231C211yesmaximal, characteristic, complemented
8#21461224C211yesmaximal, characteristic, complemented
9#21461220C211yesmaximal, characteristic, complemented
10#21461208C211yesmaximal, characteristic, complemented
11#21461205C211yesmaximal, characteristic, complemented
12#21461199C211yesmaximal, characteristic, complemented
13#21461191C211yesmaximal, characteristic, complemented
14C2×#16840613C211yesmaximal, characteristic, complemented
15#21459551C211yesmaximal, 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#16840613C2211yescharacteristic
41#16840613C2211yescharacteristic
42#16840613C2211yescharacteristic
43#16840613C2211yescharacteristic
44#16840613C2211yescharacteristic
45#16840613C2211yescharacteristic
46#16840613C2211yescharacteristic
47#16840613C2211yescharacteristic
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52#16840476—21no—
53#16840464—21no—
54#16840459—21no—
55#16840443—21no—
56#16840443—21no—
57#16840412—21no—
58#16840399—21no—
59#16840399—21no—
60#16840390C411yescharacteristic, complemented
61#16840381C411yescharacteristic, complemented
62#16840381C411yescharacteristic, complemented
63#16840366C411yescharacteristic, complemented
64#16840366C411yescharacteristic, complemented
65#16840310C2211yescharacteristic
66#16840310C2211yescharacteristic
67#16840291C2211yescharacteristic
68#16840291C2211yescharacteristic
69#16840269C2211yescharacteristic
70C2×#14519748C2211yescharacteristic
71#16840245C411yescharacteristic, complemented
72#16840237C411yescharacteristic, complemented
73#117×D61C2211yescharacteristic
74C61×#535C411yescharacteristic, 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×#11758224—21no—
108C2×#11758224—21no—
109C22×C22⋊D61—21no—
110C22×C4×D61C2311yescharacteristic
111#14519777C2×C411yescharacteristic, complemented
112#14519777C2×C411yescharacteristic, complemented
113#14519776—21no—
114#14519770—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519769C2×C411yescharacteristic, complemented
119#14519769C2×C411yescharacteristic, complemented
120#14519768—21no—
121#14519764—21no—
122#14519764—21no—
123#14519763—21no—
124#14519763—21no—
125#14519761—21no—
126#14519761—21no—
127#14519759—21no—
128#14519759—21no—
129#14519758—21no—
130#14519758—21no—
131#14519758—21no—
132#14519758—21no—
133#14519758—21no—
134#14519754—21no—
135#14519754—21no—
136#14519754—21no—
137#14519754—21no—
138#14519753C2×C411yescharacteristic
139#14519753C2311yescharacteristic
140#14519749—21no—
141#14519749—21no—
142#14519749—21no—
143#14519749—21no—
144#14519748—21no—
145#14519748—21no—
146#14519748—21no—
147#14519748—21no—
148#14519748C2×C411yescharacteristic
149#14519748C2×C411yescharacteristic
150#14519748C2×C411yescharacteristic
151#14519748C2311yescharacteristic
152#14519748C2311yescharacteristic
153#14519748C2311yescharacteristic
154#14519745—21no—
155Q8×Dic61C2×C411yescharacteristic, complemented
156Q8×Dic61C2×C411yescharacteristic, complemented
157D4×Dic61—21no—
158D4×Dic61—21no—
159D4×Dic61—21no—
160D4×Dic61—21no—
161D4×Dic61—21no—
162D4×Dic61—21no—
163D4×Dic61C2×C411yescharacteristic, complemented
164D4×Dic61C2×C411yescharacteristic, complemented
165D4×Dic61C2×C411yescharacteristic, complemented
166D4×Dic61C2×C411yescharacteristic, complemented
167D4×Dic61C2×C411yescharacteristic, complemented
168D4×Dic61C2×C411yescharacteristic, complemented
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171#14519737—21no—
172#14519737—21no—
173#14519736—21no—
174#14519736C2×C411yescharacteristic
175#14519736C2×C411yescharacteristic
176#14519735D411yescharacteristic
177#14519735D411yescharacteristic
178#14519734C2×C411yescharacteristic
179#14519734C2×C411yescharacteristic
180#14519733—21no—
181#14519733—21no—
182#14519733D411yescharacteristic
183#14519733D411yescharacteristic
184C2×C4⋊Dic61—21no—
185C2×C4⋊Dic61C2×C411yescharacteristic
186C4⋊C4×D61D411yescharacteristic
187C4⋊C4×D61D411yescharacteristic
188C2×C22⋊Dic61—21no—
189C2×C22⋊Dic61—21no—
190C2×C22⋊Dic61—21no—
191C22⋊C4×D61D411yescharacteristic
192C22⋊C4×D61D411yescharacteristic
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C22×D4×C61C2×C411yescharacteristic
197#127×C61C2×C411yescharacteristic, complemented
198#127×C61C2×C411yescharacteristic, complemented
199#124×C61C2×C411yescharacteristic, complemented
200#124×C61C2×C411yescharacteristic, complemented
201#121×C61—21no—
202#121×C61—21no—
203#120×C61—21no—
204#120×C61—21no—
205#117×C61C2×C411yescharacteristic
206C24×C61—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×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—42no—
224C2×D4×C61C22×C411yescharacteristic
225C2×D4×C61C22×C411yescharacteristic
226C2×D4×C61C22×C411yescharacteristic
227C22×C4×C61—21no—
228C22×C4×C61C22×C411yescharacteristic
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—81no—
236C2×C22⋊D61—81no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61C2×D411yescharacteristic
245#11758224—81no—
246#11758224—81no—
247#11758224—81no—
248#11758224—81no—
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×C61C22⋊C411yescharacteristic
272C4⋊C4×C61C22⋊C411yescharacteristic
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61C22⋊C411yescharacteristic
278C22⋊C4×C61C22⋊C411yescharacteristic
279C42×C61C22×C411yescharacteristic
280C42×C61C22×C411yescharacteristic
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61C22⋊C411yescharacteristic
295C22⋊Dic61C22⋊C411yescharacteristic
296#11758198—21no—
297#11758198—21no—
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61C22⋊C411yescharacteristic
308C4⋊Dic61C22⋊C411yescharacteristic
309C4⋊Dic61C22×C411yescharacteristic
310C4⋊Dic61C22×C411yescharacteristic
311C4⋊Dic61C22×C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321#11758196C22⋊C411yescharacteristic
322#11758196C22⋊C411yescharacteristic
323C4×Dic61—21no—
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×C61—21no—
334C23×C61—21no—
335C23×C61—42no—
336C23×C61—81no—
337C23×C61—81no—
338C23×C61C2×C22⋊C411yescharacteristic
339C22×D61—22no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—41no—
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—41no—
361D4×C61—41no—
362D4×C61—42no—
363D4×C61—42no—
364D4×C61—81no—
365D4×C61—81no—
366D4×C61—81no—
367D4×C61—81no—
368C2×C4×C61—22no—
369C2×C4×C61—21no—
370C2×C4×C61—42no—
371C2×C4×C61C2×C22⋊C411yescharacteristic
372C2×C4×C61C2×C22⋊C411yescharacteristic
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C23×C411yescharacteristic
377C22⋊D61—41no—
378C22⋊D61—41no—
379C22⋊D61—41no—
380C22⋊D61—41no—
381C22⋊D61—41no—
382C22⋊D61—41no—
383C22⋊D61—81no—
384C22⋊D61—81no—
385C22⋊D61—81no—
386C2×Dic61—22no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—81no—
392C2×Dic61—81no—
393C2×Dic61—81no—
394C2×Dic61—81no—
395C2×Dic61—81no—
396C2×Dic61—81no—
397C2×Dic61—81no—
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C22×D411yescharacteristic
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—21no—
407C4×D61—21no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—41no—
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—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—162no—
433C22×C61#41012yes—
434C22×C61C22×C22⋊C411yescharacteristic
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—42no—
441C2×D61—42no—
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—
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—41no—
462Dic61—41no—
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×C61—81no—
483C2×C61—81no—
484C2×C61C2×#41011yescharacteristic
485C2×C61#289711yescharacteristic
486C2×C61#290111yescharacteristic
487D61—21no—
488D61—21no—
489D61—41no—
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#692311yescharacteristic, complemented
504#532—611no—
505#532—611no—
506#529—611no—
507#529—611no—
508#525—611no—
509C2×#121—611no—
510#520—611no—
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—1221no—
554C22×D4C2×#692311yescharacteristic
555C23×C4—611no—
556C23×C4—1221no—
557C2×M16—1221no—
558C22×C8—1221no—
559C4⋊Q8—611no—
560C4⋊Q8—611no—
561C4⋊Q8—1221no—
562#127C2×#692311yescharacteristic, complemented
563#127C2×#692311yescharacteristic, complemented
564#126—1221no—
565#126—1221no—
566#126—1221no—
567#126—1221no—
568#125—611no—
569#125—611no—
570#125—1221no—
571#124—1221no—
572#124—1221no—
573#124—1221no—
574#124—1221no—
575#124C2×#692311yescharacteristic, complemented
576#124C2×#692311yescharacteristic, complemented
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—21no—
593#121—21no—
594#121—611no—
595#121—611no—
596#121—611no—
597#121—611no—
598#121—611no—
599#121—611no—
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—21no—
609#120—21no—
610#120—1221no—
611C4×Q8—611no—
612C4×Q8—611no—
613C4×D4—611no—
614C4×D4—611no—
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×D4—1221no—
628C4×D4—1221no—
629#117—611no—
630#117—611no—
631#117—611no—
632#117—611no—
633#117—611no—
634#117—611no—
635#117—611no—
636#117—611no—
637#117—1221no—
638#117—1221no—
639#117—1221no—
640#117C2×#692311yescharacteristic
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—1221no—
645C2×C4⋊C4—1221no—
646C2×C4⋊C4—1221no—
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—21no—
682C24—611no—
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—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—42no—
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×D4C22×#692311yescharacteristic
707C2×D4C22×#692311yescharacteristic
708C2×D4C22×#692311yescharacteristic
709C22×C4—21no—
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—611no—
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—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—611no—
742C4⋊C4—611no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—1221no—
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—1221no—
761C4⋊C4—1221no—
762C4⋊C4—4881no—
763C4⋊C4—2442no—
764C4⋊C4C22⋊#692311yescharacteristic
765C4⋊C4C22⋊#692311yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—611no—
771C22⋊C4—611no—
772C22⋊C4—611no—
773C22⋊C4—611no—
774C22⋊C4—611no—
775C22⋊C4—611no—
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—611no—
795C42—611no—
796C42—611no—
797C42—611no—
798C42—611no—
799C42—611no—
800C42—1221no—
801C42—1221no—
802C42—1221no—
803C42—4881no—
804C42—2442no—
805C42C22×#692311yescharacteristic
806C42C22×#692311yescharacteristic
807C23—21no—
808C23—21no—
809C23—21no—
810C23—42no—
811C23—81no—
812C23—81no—
813C23—611no—
814C23—611no—
815C23—1221no—
816C23—1221no—
817C23—1222no—
818C23—2441no—
819C23C2×C22⋊#692311yescharacteristic
820Q8—41no—
821Q8—4881no—
822Q8—4881no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—42no—
827D4—42no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—4881no—
833D4—4881no—
834D4—4881no—
835D4—2441no—
836D4—2441no—
837D4—2441no—
838D4—2441no—
839D4—2441no—
840D4—2441no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—42no—
844C2×C4—611no—
845C2×C4—611no—
846C2×C4—611no—
847C2×C4—611no—
848C2×C4—611no—
849C2×C4—611no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—4881no—
861C2×C4—4881no—
862C2×C4—4881no—
863C2×C4—4881no—
864C2×C4—4881no—
865C2×C4—4881no—
866C2×C4—4884no—
867C2×C4—4881no—
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—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—162no—
907C22—611no—
908C22—611no—
909C22—1221no—
910C22—1221no—
911C22—1221no—
912C22—1221no—
913C22—1221no—
914C22—2442no—
915C22—2442no—
916C22#1684074212yes—
917C22C22×C22⋊#692311yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—41no—
925C4—1221no—
926C4—1221no—
927C4—1221no—
928C4—1221no—
929C4—1221no—
930C4—1221no—
931C4—4881no—
932C4—4881no—
933C4—4881no—
934C4—2442no—
935C4—2441no—
936C4—2441no—
937C4—2441no—
938C4—2441no—
939C2—22no—
940C2—81no—
941C2—81no—
942C2—81no—
943C2—1221no—
944C2—1221no—
945C2—2441no—
946C2C2×#1684074211yescharacteristic
947C2#2146244011yescharacteristic
948C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#535C4
socleC22×C61C22×C22⋊C4
prime radical#21459551C2
cosocleC2×C4×D61C24
hypercenter#535#6923
hypocenterC61#17604
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #21462511C2semidirect
2. #21462326C2semidirect
3. #21461260C2semidirect
4. #21461248C2semidirect
5. #21461245C2semidirect
6. #21461239C2semidirect
7. #21461231C2semidirect
8. #21461224C2semidirect
9. #21461220C2semidirect
10. #21461208C2semidirect
11. #21461205C2semidirect
12. #21461199C2semidirect
13. #21461191C2semidirect
14. C2×#16840613C2semidirect
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. #16840390C4semidirect
61. #16840381C4semidirect
62. #16840381C4semidirect
63. #16840366C4semidirect
64. #16840366C4semidirect
71. #16840245C4semidirect
72. #16840237C4semidirect
74. C61×#535C4semidirect
111. #14519777C2×C4semidirect
112. #14519777C2×C4semidirect
118. #14519769C2×C4semidirect
119. #14519769C2×C4semidirect
155. Q8×Dic61C2×C4semidirect
156. Q8×Dic61C2×C4semidirect
163. D4×Dic61C2×C4semidirect
164. D4×Dic61C2×C4semidirect
165. D4×Dic61C2×C4semidirect
166. D4×Dic61C2×C4semidirect
167. D4×Dic61C2×C4semidirect
168. D4×Dic61C2×C4semidirect
197. #127×C61C2×C4semidirect
198. #127×C61C2×C4semidirect
199. #124×C61C2×C4semidirect
200. #124×C61C2×C4semidirect
503. #535#6923semidirect
549. C61#17604semidirect
562. #127C2×#6923semidirect
563. #127C2×#6923semidirect
575. #124C2×#6923semidirect
576. #124C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625112
#214623262
#214612602
#214612482
#214612452
#214612392
#214612312
#214612242
#214612202
#214612082
#214612052
#214611992
#214611912
C2×#168406132
#214595512
#1760461