Finite Group Databasebeta

← #30611305

Subgroups — #30611305

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#21461262C211yesmaximal, characteristic, complemented
4#21461250C211yesmaximal, characteristic, complemented
5#21461247C211yesmaximal, characteristic, complemented
6#21461240C211yesmaximal, characteristic, complemented
7#21461233C211yesmaximal, characteristic, complemented
8#21461226C211yesmaximal, characteristic, complemented
9#21461222C211yesmaximal, characteristic, complemented
10#21461210C211yesmaximal, characteristic, complemented
11#21461207C211yesmaximal, characteristic, complemented
12#21461200C211yesmaximal, characteristic, complemented
13#21461193C211yesmaximal, characteristic, complemented
14C2×#16840614C211yesmaximal, characteristic, complemented
15#21459557C211yesmaximal, 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#16840615C2211yescharacteristic, complemented
37#16840615C2211yescharacteristic, complemented
38#16840615C2211yescharacteristic, complemented
39#16840615C2211yescharacteristic, complemented
40#16840614C2211yescharacteristic
41#16840614C2211yescharacteristic
42#16840614C2211yescharacteristic
43#16840614C2211yescharacteristic
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840614C2211yescharacteristic, complemented
49#16840614C2211yescharacteristic, complemented
50#16840614C2211yescharacteristic, complemented
51#16840614C2211yescharacteristic, complemented
52#16840478—21no—
53#16840465—21no—
54#16840465—21no—
55#16840439—21no—
56#16840439—21no—
57#16840415—21no—
58#16840403—21no—
59#16840403—21no—
60#16840386C411yescharacteristic, complemented
61#16840386C411yescharacteristic, complemented
62#16840368C411yescharacteristic, complemented
63#16840368C411yescharacteristic, complemented
64#16840331C411yescharacteristic, complemented
65#16840313C2211yescharacteristic
66#16840313C2211yescharacteristic
67#16840297C2211yescharacteristic
68#16840297C2211yescharacteristic
69#16840274C2211yescharacteristic
70C2×#14519752C2211yescharacteristic
71#16840243C411yescharacteristic, complemented
72#16840236C411yescharacteristic, complemented
73#117×D61C2211yescharacteristic
74C61×#544C411yescharacteristic, 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×#11758226—21no—
108C2×#11758226—21no—
109C2×#11758222C2×C411yescharacteristic
110C22×D244—21no—
111C22×D244C2×C411yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519774C2×C411yescharacteristic, complemented
114#14519774C2×C411yescharacteristic, complemented
115#14519772—21no—
116#14519772—21no—
117#14519772—21no—
118#14519772—21no—
119#14519766—21no—
120#14519766—21no—
121#14519766—21no—
122#14519766—21no—
123#14519765C2×C411yescharacteristic, complemented
124#14519765C2×C411yescharacteristic, complemented
125#14519762—21no—
126#14519762—21no—
127#14519762—21no—
128#14519762—21no—
129#14519762—21no—
130#14519762—21no—
131#14519762—21no—
132#14519762—21no—
133#14519761—21no—
134#14519757C2×C411yescharacteristic
135#14519757C2311yescharacteristic
136#14519753—21no—
137#14519753—21no—
138#14519752—21no—
139#14519752—21no—
140#14519752—21no—
141#14519752—21no—
142#14519752—21no—
143#14519752—21no—
144#14519752—21no—
145#14519752—21no—
146#14519752—21no—
147#14519752—21no—
148#14519752C2×C411yescharacteristic
149#14519752C2×C411yescharacteristic
150#14519752C2×C411yescharacteristic
151#14519752C2311yescharacteristic
152#14519752C2311yescharacteristic
153#14519752C2311yescharacteristic
154#14519747—21no—
155#14519747—21no—
156#14519747—21no—
157#14519742C2×C411yescharacteristic, complemented
158#14519742C2×C411yescharacteristic, complemented
159C4×D244—21no—
160C4×D244—21no—
161C4×D244—21no—
162C4×D244—21no—
163#14519739—21no—
164#14519739—21no—
165#14519739—21no—
166#14519739—21no—
167#14519739C2×C411yescharacteristic, complemented
168#14519739C2×C411yescharacteristic, complemented
169#14519739C2×C411yescharacteristic, complemented
170#14519739C2×C411yescharacteristic, complemented
171#14519739C2×C411yescharacteristic, complemented
172#14519739C2×C411yescharacteristic, complemented
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175#14519736C2×C411yescharacteristic
176#14519735—21no—
177#14519735—21no—
178#14519735—21no—
179#14519735D411yescharacteristic
180#14519735D411yescharacteristic
181#14519734C2×C411yescharacteristic
182#14519734C2×C411yescharacteristic
183#14519733D411yescharacteristic
184#14519733D411yescharacteristic
185C4⋊C4×D61—21no—
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×C61—21no—
196C4⋊Q8×C61C2×C411yescharacteristic, complemented
197C4⋊Q8×C61C2×C411yescharacteristic, complemented
198#125×C61—21no—
199#125×C61C2×C411yescharacteristic, complemented
200#125×C61C2×C411yescharacteristic, complemented
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61—21no—
203#117×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
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—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61C22×C411yescharacteristic
219C2×C22⋊D61—21no—
220C22×Dic61C2×D411yescharacteristic
221#11758226—81no—
222#11758226—81no—
223#11758226—81no—
224#11758226—81no—
225#11758222—42no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—42no—
238C2×D244—81no—
239C2×D244—81no—
240C2×D244C22×C411yescharacteristic
241C2×D244C22×C411yescharacteristic
242C2×D244C22×C411yescharacteristic
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—42no—
251C2×C4×D61C22×C411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2411yescharacteristic
259C2×Dic122C22×C411yescharacteristic
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×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61C22⋊C411yescharacteristic
279C4⋊C4×C61C22⋊C411yescharacteristic
280C4⋊C4×C61C22×C411yescharacteristic
281C4⋊C4×C61C22×C411yescharacteristic
282C4⋊C4×C61C22×C411yescharacteristic
283C4⋊C4×C61C22×C411yescharacteristic
284C22⋊C4×C61—21no—
285C22⋊C4×C61C22⋊C411yescharacteristic
286C22⋊C4×C61C22⋊C411yescharacteristic
287C42×C61—21no—
288C42×C61C22×C411yescharacteristic
289C42×C61C22×C411yescharacteristic
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#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61C22⋊C411yescharacteristic
317C4⋊Dic61C22⋊C411yescharacteristic
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×C61C2×C22⋊C411yescharacteristic
333C22×D61—22no—
334C22×D61—21no—
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—81no—
359Q8×C61—81no—
360C2×C4×C61—22no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
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—42no—
373C2×Dic61—22no—
374C2×Dic61—21no—
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C22×D411yescharacteristic
381D244—41no—
382D244—41no—
383D244—41no—
384D244—42no—
385D244—41no—
386D244—41no—
387D244—41no—
388D244—41no—
389D244—41no—
390D244—41no—
391D244—81no—
392D244—81no—
393D244—81no—
394D244—81no—
395D244—81no—
396D244—81no—
397D244—81no—
398C4×D61—21no—
399C4×D61—21no—
400C4×D61—21no—
401C4×D61—21no—
402C4×D61—41no—
403C4×D61—41no—
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—
414C4×D61—81no—
415Dic122—41no—
416#92420—41no—
417#92420—41no—
418#92420—41no—
419#92420—41no—
420#17604—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61#41012yes—
424C22×C61C22×C22⋊C411yescharacteristic
425C2×D61—21no—
426C2×D61—21no—
427C2×D61—21no—
428C2×D61—21no—
429C2×D61—21no—
430C2×D61—42no—
431C2×D61—42no—
432C2×D61—41no—
433C2×D61—41no—
434C2×D61—41no—
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—
457C4×C61—41no—
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
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×C61C2×#41011yescharacteristic
482C2×C61#289711yescharacteristic
483C2×C61#290111yescharacteristic
484D61—21no—
485D61—21no—
486D61—41no—
487D61—81no—
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#692311yescharacteristic, complemented
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—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—611no—
551C2×#41—1221no—
552C2×#41—1221no—
553C22×D4—611no—
554C22×D4—1221no—
555C23×C4—611no—
556C23×C4—1221no—
557C2×M16—1221no—
558C22×C8—1221no—
559C4⋊Q8—21no—
560C4⋊Q8C2×#692311yescharacteristic, complemented
561C4⋊Q8C2×#692311yescharacteristic, complemented
562#127—611no—
563#127—611no—
564#126—1221no—
565#126—1221no—
566#126—1221no—
567#126—1221no—
568#125—21no—
569#125C2×#692311yescharacteristic, complemented
570#125C2×#692311yescharacteristic, complemented
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—21no—
587C22⋊Q8—21no—
588C22⋊Q8—611no—
589C22⋊Q8—611no—
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×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—1221no—
637#117—1221no—
638#117—1221no—
639#117C2×#692311yescharacteristic
640#117C2×#692311yescharacteristic
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—1221no—
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—4881no—
684#41—4881no—
685#41—4881no—
686#41—4881no—
687#41—2442no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—611no—
691C2×D4—611no—
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—1221no—
706C2×D4—4881no—
707C2×D4—4881no—
708C2×D4—2442no—
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—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4—611no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—4881no—
759C4⋊C4—2442no—
760C4⋊C4C22⋊#692311yescharacteristic
761C4⋊C4C22⋊#692311yescharacteristic
762C4⋊C4C22×#692311yescharacteristic
763C4⋊C4C22×#692311yescharacteristic
764C4⋊C4C22×#692311yescharacteristic
765C4⋊C4C22×#692311yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—611no—
768C22⋊C4—611no—
769C22⋊C4—611no—
770C22⋊C4—611no—
771C22⋊C4—611no—
772C22⋊C4—611no—
773C22⋊C4—1221no—
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—611no—
796C42—611no—
797C42—611no—
798C42—611no—
799C42—611no—
800C42—611no—
801C42—1221no—
802C42—1221no—
803C42—4881no—
804C42—2442no—
805C42C22×#692311yescharacteristic
806C42C22×#692311yescharacteristic
807C23—611no—
808C23—611no—
809C23—1221no—
810C23—1221no—
811C23—1222no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—4881no—
816C23—4881no—
817C23—2441no—
818C23—2442no—
819C23C2×C22⋊#692311yescharacteristic
820Q8—81no—
821Q8—81no—
822Q8—2441no—
823D4—4881no—
824D4—4881no—
825D4—4881no—
826D4—4881no—
827D4—4881no—
828D4—4881no—
829D4—4881no—
830D4—2441no—
831D4—2441no—
832D4—2441no—
833D4—2442no—
834D4—2441no—
835D4—2441no—
836D4—2441no—
837D4—2441no—
838D4—2441no—
839D4—2441no—
840D4—2442no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—81no—
847C2×C4—611no—
848C2×C4—611no—
849C2×C4—611no—
850C2×C4—611no—
851C2×C4—611no—
852C2×C4—611no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1222no—
858C2×C4—1222no—
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—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2442no—
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—611no—
898C22—611no—
899C22—1221no—
900C22—1221no—
901C22—1221no—
902C22—1221no—
903C22—1221no—
904C22—9762no—
905C22—2442no—
906C22—2442no—
907C22—2441no—
908C22—2441no—
909C22—2441no—
910C22—2441no—
911C22—2441no—
912C22—2441no—
913C22—2441no—
914C22—2441no—
915C22—2441no—
916C22#1684074312yes—
917C22C22×C22⋊#692311yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—41no—
928C4—1221no—
929C4—1221no—
930C4—1221no—
931C4—1221no—
932C4—1221no—
933C4—1221no—
934C4—4881no—
935C4—4881no—
936C4—4881no—
937C4—2442no—
938C4—2441no—
939C2—22no—
940C2—1221no—
941C2—1221no—
942C2—4881no—
943C2—4881no—
944C2—4881no—
945C2—2441no—
946C2C2×#1684074311yescharacteristic
947C2#2146244011yescharacteristic
948C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radical#21459557C2
cosocleC2×C4×D61C24
hypercenter#544#6923
hypocenterC61#17604
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. #21462511C2semidirect
2. #21462326C2semidirect
3. #21461262C2semidirect
4. #21461250C2semidirect
5. #21461247C2semidirect
6. #21461240C2semidirect
7. #21461233C2semidirect
8. #21461226C2semidirect
9. #21461222C2semidirect
10. #21461210C2semidirect
11. #21461207C2semidirect
12. #21461200C2semidirect
13. #21461193C2semidirect
14. C2×#16840614C2semidirect
18. #16840785C22semidirect
19. #16840784C22semidirect
20. #16840781C22semidirect
21. #16840780C22semidirect
29. #16840707C22semidirect
30. #16840706C22semidirect
32. C4×C4⋊#6923C22semidirect
34. #16840698C22semidirect
36. #16840615C22semidirect
37. #16840615C22semidirect
38. #16840615C22semidirect
39. #16840615C22semidirect
48. #16840614C22semidirect
49. #16840614C22semidirect
50. #16840614C22semidirect
51. #16840614C22semidirect
60. #16840386C4semidirect
61. #16840386C4semidirect
62. #16840368C4semidirect
63. #16840368C4semidirect
64. #16840331C4semidirect
71. #16840243C4semidirect
72. #16840236C4semidirect
74. C61×#544C4semidirect
113. #14519774C2×C4semidirect
114. #14519774C2×C4semidirect
123. #14519765C2×C4semidirect
124. #14519765C2×C4semidirect
157. #14519742C2×C4semidirect
158. #14519742C2×C4semidirect
167. #14519739C2×C4semidirect
168. #14519739C2×C4semidirect
169. #14519739C2×C4semidirect
170. #14519739C2×C4semidirect
171. #14519739C2×C4semidirect
172. #14519739C2×C4semidirect
196. C4⋊Q8×C61C2×C4semidirect
197. C4⋊Q8×C61C2×C4semidirect
199. #125×C61C2×C4semidirect
200. #125×C61C2×C4semidirect
498. #544#6923semidirect
549. C61#17604semidirect
560. C4⋊Q8C2×#6923semidirect
561. C4⋊Q8C2×#6923semidirect
569. #125C2×#6923semidirect
570. #125C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625112
#214623262
#214612622
#214612502
#214612472
#214612402
#214612332
#214612262
#214612222
#214612102
#214612072
#214612002
#214611932
C2×#168406142
#214595572
#1760461