Finite Group Databasebeta

← #30610796

Subgroups — #30610796

Order 15616.

1216 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462629C211yesmaximal, characteristic, complemented
2#21462514C211yesmaximal, characteristic, complemented
3#21461180C211yesmaximal, characteristic, complemented
4#21461178C211yesmaximal, characteristic, complemented
5#21461164C211yesmaximal, characteristic, complemented
6#21461160C211yesmaximal, characteristic, complemented
7#21461159C211yesmaximal, characteristic, complemented
8#21461146C211yesmaximal, characteristic, complemented
9#21461140C211yesmaximal, characteristic, complemented
10#21461138C211yesmaximal, characteristic, complemented
11#21461124C211yesmaximal, characteristic, complemented
12#21461120C211yesmaximal, characteristic, complemented
13#21461119C211yesmaximal, characteristic, complemented
14C2×#16840610C211yesmaximal, characteristic, complemented
15#21459306C211yesmaximal, characteristic
16#16840814—21no—
17#16840795—21no—
18#16840793—21no—
19#16840791—21no—
20#16840787—21no—
21#16840786—21no—
22#16840784C2211yescharacteristic, complemented
23#16840783C2211yescharacteristic, complemented
24#16840781C2211yescharacteristic, complemented
25#16840780C2211yescharacteristic, complemented
26#16840779C2211yescharacteristic, complemented
27#16840778C2211yescharacteristic, complemented
28#16840778C2211yescharacteristic, complemented
29#16840765C2211yescharacteristic, complemented
30C2×C4⋊#92420C2211yescharacteristic, complemented
31#16840735—21no—
32#16840726—21no—
33C4×#11758213C2211yescharacteristic, complemented
34C4×#11758217C2211yescharacteristic, complemented
35C2×C4×#92420C2211yescharacteristic, complemented
36#16840610C2211yescharacteristic
37#16840610C2211yescharacteristic
38#16840610C2211yescharacteristic
39#16840610C2211yescharacteristic
40#16840610C2211yescharacteristic, complemented
41#16840610C2211yescharacteristic, complemented
42#16840610C2211yescharacteristic, complemented
43#16840610C2211yescharacteristic, complemented
44#16840610C2211yescharacteristic, complemented
45#16840610C2211yescharacteristic, complemented
46#16840610C2211yescharacteristic, complemented
47#16840610C2211yescharacteristic, complemented
48D4⋊#92420C2211yescharacteristic, complemented
49D4⋊#92420C2211yescharacteristic, complemented
50D4⋊#92420C2211yescharacteristic, complemented
51D4⋊#92420C2211yescharacteristic, complemented
52C2×#41×D61—21no—
53#16840433C411yescharacteristic
54#16840427C411yescharacteristic
55#16840422—21no—
56#16840413C411yescharacteristic
57#16840413C411yescharacteristic
58#16840404—21no—
59#16840404—21no—
60#16840400—21no—
61D4×D244C411yescharacteristic
62#16840396C411yescharacteristic
63#16840396C411yescharacteristic
64#16840313C2211yescharacteristic
65#16840307C2211yescharacteristic
66#16840307C2211yescharacteristic
67#16840275—21no—
68#16840270—21no—
69#16840270—21no—
70C4×#11758224C2211yescharacteristic
71C2×#14519739C2211yescharacteristic
72C2×#14519739C2211yescharacteristic
73C4×D4×D61C2211yescharacteristic
74C61×#547C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83C4⋊#92420—21no—
84C4⋊#92420—21no—
85C4⋊#92420C2311yescharacteristic
86C4⋊#92420C2311yescharacteristic
87C4⋊#92420C2311yescharacteristic
88C4⋊#92420C2311yescharacteristic
89#14519834—21no—
90#14519834—21no—
91#14519834—21no—
92C22⋊#92420—21no—
93C22⋊#92420—21no—
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420C2311yescharacteristic
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C2×#11758226—21no—
108C2×#11758222—21no—
109C2×#11758222—21no—
110C2×#11758222—21no—
111C2×#11758224—21no—
112C2×#11758224—21no—
113C2×#11758224D411yescharacteristic
114#41×D61—44no—
115#41×D61—44no—
116C2×Q8×D61—21no—
117C22×D244C2×C411yescharacteristic
118C22×D244C2×C411yescharacteristic
119C2×D4×D61—21no—
120C2×D4×D61—21no—
121C2×D4×D61—21no—
122C2×D4×D61C2×C411yescharacteristic
123C22×C4×D61—21no—
124C22×C4×D61—21no—
125C22×C4×D61—21no—
126#14519776C2×C411yescharacteristic
127#14519776C2×C411yescharacteristic
128#14519774C2×C411yescharacteristic
129#14519773C2×C411yescharacteristic
130#14519773C2×C411yescharacteristic
131#14519766—21no—
132#14519763—21no—
133#14519763—21no—
134#14519762—21no—
135#14519762—21no—
136#14519760—21no—
137#14519760—21no—
138#14519755—21no—
139#14519755—21no—
140#14519755—21no—
141#14519755—21no—
142#14519753—21no—
143#14519752—21no—
144#14519752—21no—
145#14519752C2×C411yescharacteristic
146#14519752C2×C411yescharacteristic
147#14519751—21no—
148#14519751C2×C411yescharacteristic
149#14519751C2×C411yescharacteristic
150#14519750—21no—
151#14519750—21no—
152#14519750—21no—
153#14519750—21no—
154#14519749—21no—
155#14519749—21no—
156#14519747—21no—
157#14519747—21no—
158#14519747—21no—
159#14519747—21no—
160#14519745—21no—
161#14519745—21no—
162C4×Dic122C2×C411yescharacteristic
163#14519742D411yescharacteristic
164C4×D244C2×C411yescharacteristic
165D4×Dic61D411yescharacteristic
166D4×Dic61C2311yescharacteristic
167#14519739—21no—
168#14519739—21no—
169#14519739—21no—
170#14519739—21no—
171#14519739—21no—
172#14519739C2×C411yescharacteristic
173#14519739C2×C411yescharacteristic
174#14519739C2×C411yescharacteristic
175#14519739C2×C411yescharacteristic
176#14519739C2311yescharacteristic
177#14519739C2311yescharacteristic
178#14519739C2311yescharacteristic
179C4×C22⋊D61—21no—
180C4×C22⋊D61C2×C411yescharacteristic
181C4×C22⋊D61C2×C411yescharacteristic
182#14519737—21no—
183#14519737—21no—
184#14519737—21no—
185#14519737D411yescharacteristic
186#14519737D411yescharacteristic
187#14519735D411yescharacteristic
188#14519733D411yescharacteristic
189#14519733D411yescharacteristic
190C4⋊C4×D61C2×C411yescharacteristic
191C2×#11758198—21no—
192C2×#11758198—21no—
193C22⋊C4×D61—21no—
194C2×C4×Dic61C2311yescharacteristic
195C2×C4×Dic61C2311yescharacteristic
196C42×D61C2311yescharacteristic
197C2×#41×C61—21no—
198C4⋊Q8×C61C2×C411yescharacteristic
199#123×C61—21no—
200#123×C61—21no—
201C22⋊Q8×C61—21no—
202#121×C61C2×C411yescharacteristic
203#121×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic
206C2×C4⋊C4×C61C2×C411yescharacteristic
207C2×C4⋊C4×C61C2×C411yescharacteristic
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211#41×C61—44no—
212C2×Q8×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61C22⋊C411yescharacteristic
216C2×D4×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61C22⋊C411yescharacteristic
230C2×C22⋊D61C22⋊C411yescharacteristic
231C22×Dic61—21no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236#11758226—42no—
237#11758226—42no—
238Q8×D61—44no—
239#11758224—22no—
240#11758224—22no—
241#11758224—42no—
242#11758224—42no—
243#11758224—42no—
244#11758224—42no—
245D4×D61—22no—
246D4×D61—41no—
247D4×D61—44no—
248D4×D61—44no—
249D4×D61—44no—
250#11758222—44no—
251#11758222—44no—
252#11758222—44no—
253C2×D244—22no—
254C2×D244—22no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—41no—
262C2×D244—41no—
263C2×D244C22×C411yescharacteristic
264C2×D244C22×C411yescharacteristic
265C2×D244C22×C411yescharacteristic
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—42no—
276C2×C4×D61—42no—
277C2×C4×D61—42no—
278C2×C4×D61—42no—
279C2×C4×D61—42no—
280C2×C4×D61—42no—
281C2×C4×D61C22×C411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61C2×D411yescharacteristic
284C2×Dic122—21no—
285C2×Dic122—21no—
286C2×Dic122C22⋊C411yescharacteristic
287#11758217—42no—
288#11758217—42no—
289C2×#92420—21no—
290C2×#92420—21no—
291C2×#92420—21no—
292C2×#92420—21no—
293C2×#92420—21no—
294C2×#92420—21no—
295C2×#92420—21no—
296C2×#92420—21no—
297C2×#92420—42no—
298C2×#92420—42no—
299#11758213—42no—
300C4⋊C4×C61—21no—
301C4⋊C4×C61—21no—
302C4⋊C4×C61—21no—
303C4⋊C4×C61C22⋊C411yescharacteristic
304C4⋊C4×C61C22×C411yescharacteristic
305C4⋊C4×C61C22×C411yescharacteristic
306C4⋊C4×C61C22×C411yescharacteristic
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61C22⋊C411yescharacteristic
311C22⋊C4×C61C22⋊C411yescharacteristic
312C42×C61C22×C411yescharacteristic
313C22⋊Dic61—21no—
314C22⋊Dic61C22⋊C411yescharacteristic
315C22⋊Dic61C22⋊C411yescharacteristic
316#11758198—21no—
317#11758198—21no—
318#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198C22⋊C411yescharacteristic
329#11758198C22⋊C411yescharacteristic
330C4⋊Dic61C22⋊C411yescharacteristic
331C4⋊Dic61C22×C411yescharacteristic
332#11758196—21no—
333#11758196—21no—
334#11758196—21no—
335#11758196C22⋊C411yescharacteristic
336#11758196C22⋊C411yescharacteristic
337#11758196C22⋊C411yescharacteristic
338#11758196C22⋊C411yescharacteristic
339C4×Dic61C22×C411yescharacteristic
340C4×Dic61C22×C411yescharacteristic
341C4×Dic61C2×D411yescharacteristic
342C4×Dic61C2×D411yescharacteristic
343C4×Dic61C2×D411yescharacteristic
344C4×Dic61C2×D411yescharacteristic
345C4×Dic61C2×D411yescharacteristic
346C4×Dic61C2×D411yescharacteristic
347C4×Dic61C2411yescharacteristic
348C23×C61—21no—
349C23×C61C2×C22⋊C411yescharacteristic
350C23×C61C2×C22⋊C411yescharacteristic
351C22×D61—21no—
352C22×D61—21no—
353C22×D61—21no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—42no—
359C22×D61—42no—
360C22×D61—81no—
361C22×D61—81no—
362C22×D61—81no—
363C22×D61C2×C22⋊C411yescharacteristic
364Q8×C61—42no—
365D4×C61—22no—
366D4×C61—21no—
367D4×C61—21no—
368D4×C61—42no—
369D4×C61—42no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—42no—
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C2×C22⋊C411yescharacteristic
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C23×C411yescharacteristic
385C22⋊D61—22no—
386C22⋊D61—22no—
387C22⋊D61—42no—
388C22⋊D61—42no—
389C22⋊D61—42no—
390C22⋊D61—42no—
391C22⋊D61—42no—
392C22⋊D61—81no—
393C22⋊D61—81no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61AGL(1,ℤ/8)12yes—
407C2×Dic61AGL(1,ℤ/8)12yes—
408C2×Dic61C22×D411yescharacteristic
409C2×Dic61C22×D411yescharacteristic
410D244—21no—
411D244—21no—
412D244—21no—
413D244—21no—
414D244—21no—
415D244—42no—
416D244—42no—
417D244—42no—
418D244—42no—
419D244—42no—
420D244—81no—
421D244#13112yes—
422C4×D61—21no—
423C4×D61—21no—
424C4×D61—21no—
425C4×D61—21no—
426C4×D61—41no—
427C4×D61—42no—
428C4×D61—42no—
429C4×D61—42no—
430C4×D61—42no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—41no—
435C4×D61—41no—
436C4×D61—41no—
437C4×D61—42no—
438C4×D61—42no—
439Dic122—22no—
440Dic122—42no—
441Dic122—42no—
442#92420—22no—
443#92420—41no—
444#92420—41no—
445#92420—41no—
446#92420—41no—
447#92420—41no—
448#92420—41no—
449#92420—41no—
450#17511—611nomaximal, Sylow
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61#41812yes—
460C22×C61C22×C22⋊C411yescharacteristic
461C2×D61—21no—
462C2×D61—22no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—41no—
472C2×D61—41no—
473C2×D61—84no—
474C2×D61—84no—
475C2×D61—84no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—41no—
481C4×C61—41no—
482C4×C61—41no—
483C4×C61C2×#13111yescharacteristic
484C4×C61#56811yescharacteristic
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—41no—
491Dic61#41812yes—
492Dic61C2×AGL(1,ℤ/8)11yescharacteristic
493Dic61C2×AGL(1,ℤ/8)11yescharacteristic
494D4×#41—611no—
495#2965—611no—
496#2925—611no—
497#1496—611no—
498#1496—611no—
499#1492—611no—
500#1490—611no—
501#1490—611no—
502#1486—611no—
503#1484—611no—
504#1484—611no—
505#1480—611no—
506#1478—611no—
507#1478—611no—
508C2×D4⋊C8—611no—
509C2×C61—22no—
510C2×C61—41no—
511C2×C61—81no—
512C2×C61#288011yescharacteristic
513C2×C61C2×#41811yescharacteristic
514C2×C61#290111yescharacteristic
515D61—41no—
516D61—42no—
517D61—81no—
518D61—81no—
519C22×#41—1221no—
520#550—611no—
521D4×Q8—611no—
522#548—1221no—
523#547—611no—
524#547—611no—
525#547#692311yescharacteristic
526#546—1221no—
527#546—1221no—
528#546—1221no—
529D42—611no—
530D42—611no—
531D42—611no—
532#532—611no—
533#532—611no—
534#532—611no—
535#525—1221no—
536#525—1221no—
537#525—1221no—
538C4×#41—611no—
539C2×C4×D4—611no—
540C2×C4×D4—611no—
541C2×C4×D4—611no—
542#446—1221no—
543#436—1221no—
544#435—1221no—
545#435—1221no—
546#433—1221no—
547#433—1221no—
548#432—611no—
549#432—611no—
550#431—611no—
551#431—611no—
552#431—611no—
553#431—611no—
554#431—611no—
555#423—611no—
556C2×C4⋊C8—611no—
557#408—1221no—
558#405—1221no—
559C4×M16—611no—
560C4×M16—611no—
561C2×C4×C8—611no—
562D4⋊C8—611no—
563D4⋊C8—611no—
564D4⋊C8—611no—
565D4⋊C8—611no—
566D4⋊C8—611no—
567D4⋊C8—611no—
568D4⋊C8—611no—
569D4⋊C8—611no—
570D4⋊C8—611no—
571D4⋊C8—611no—
572D4⋊C8—611no—
573D4⋊C8—611no—
574D4⋊C8—611no—
575D4⋊C8—611no—
576D4⋊C8—611no—
577D4⋊C8—611no—
578C61#1751111yescharacteristic, complemented, Sylow
579C2×#41—21no—
580C2×#41—611no—
581C2×#41—1221no—
582C2×#41—1221no—
583C2×#41—1221no—
584C2×#41—1221no—
585C2×#41—1221no—
586C2×#41—1221no—
587C2×#41—2444no—
588C2×#41—2444no—
589C22×Q8—1221no—
590C22×D4—611no—
591C22×D4—611no—
592C22×D4—611no—
593C22×D4—1221no—
594C22×D4—1221no—
595C22×D4—1221no—
596C23×C4—1221no—
597C23×C4—1221no—
598C23×C4—1221no—
599C2×M16—1221no—
600C2×M16—1221no—
601C2×M16—1221no—
602C22×C8—1221no—
603C22×C8—1221no—
604C4⋊Q8—611no—
605C4⋊Q8—611no—
606C4⋊Q8C2×#692311yescharacteristic
607#127—611no—
608#127—611no—
609#127—611no—
610#124—1221no—
611#124—1221no—
612#124—1221no—
613#123—21no—
614#123—21no—
615#123—1221no—
616#123—1221no—
617#123—1221no—
618#123—1221no—
619C22⋊Q8—21no—
620C22⋊Q8—1221no—
621C22⋊Q8—1221no—
622C22⋊Q8—1221no—
623C22⋊Q8—1221no—
624C22⋊Q8—1221no—
625#121—611no—
626#121—611no—
627#121—611no—
628#121—611no—
629#121—1221no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121—1221no—
638#121C2×#692311yescharacteristic
639#121C2×#692311yescharacteristic
640#120—1221no—
641#120—1221no—
642#120—1221no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646C4×Q8—611no—
647C4×Q8—611no—
648C4×D4—611no—
649C4×D4—611no—
650C4×D4—611no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—611no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671C4×D4C2×#692311yescharacteristic
672C4×D4C2×#692311yescharacteristic
673#117—611no—
674#117—611no—
675#117—611no—
676C2×C4⋊C4—611no—
677C2×C4⋊C4C2×#692311yescharacteristic
678C2×C4⋊C4C2×#692311yescharacteristic
679C2×C22⋊C4—1221no—
680C2×C22⋊C4—1221no—
681C2×C22⋊C4—1221no—
682C2×C42—611no—
683C2×C42—611no—
684C2×C42—611no—
685C4⋊C8—611no—
686C4⋊C8—611no—
687C4⋊C8—611no—
688C4⋊C8—611no—
689C4⋊C8—1221no—
690C4⋊C8—1221no—
691C4⋊C8—1221no—
692C4⋊C8—1221no—
693C4⋊C8—1221no—
694C22⋊C8—1221no—
695C22⋊C8—1221no—
696C22⋊C8—1221no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701#97—1221no—
702#97—1221no—
703#97—1221no—
704#97—1221no—
705C4×C8—611no—
706C4×C8—611no—
707C4×C8—611no—
708C4×C8—611no—
709C4×C8—1221no—
710C4×C8—1221no—
711C4×C8—1221no—
712C24—1221no—
713C24—1221no—
714C24—1221no—
715#41—44no—
716#41—1222no—
717#41—1222no—
718#41—2444no—
719#41—2444no—
720#41—2444no—
721#41—2442no—
722#41—2442no—
723#41—2442no—
724#41—2442no—
725#41—2442no—
726#41—2442no—
727C2×Q8—21no—
728C2×Q8—611no—
729C2×Q8—1221no—
730C2×Q8—1221no—
731C2×Q8—2444no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—611no—
735C2×D4—611no—
736C2×D4—611no—
737C2×D4—611no—
738C2×D4—611no—
739C2×D4—1222no—
740C2×D4—1222no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—1221no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1222no—
749C2×D4—1221no—
750C2×D4—1221no—
751C2×D4—1221no—
752C2×D4—1221no—
753C2×D4—1221no—
754C2×D4—1221no—
755C2×D4—2441no—
756C2×D4—2441no—
757C2×D4—2441no—
758C2×D4—2444no—
759C2×D4—2444no—
760C2×D4—2444no—
761C2×D4C22⋊#692311yescharacteristic
762C2×D4C22×#692311yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—611no—
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—2442no—
784C22×C4—2442no—
785C22×C4—2442no—
786C22×C4—2442no—
787C22×C4—2442no—
788C22×C4—2442no—
789C22×C4C22×#692311yescharacteristic
790C22×C4C22×#692311yescharacteristic
791M16—2442no—
792M16—2442no—
793M16—2442no—
794C2×C8—1221no—
795C2×C8—1221no—
796C2×C8—1221no—
797C2×C8—1221no—
798C2×C8—1221no—
799C2×C8—1221no—
800C2×C8—1221no—
801C2×C8—1221no—
802C2×C8—2442no—
803C2×C8—2442no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—611no—
808C4⋊C4—611no—
809C4⋊C4—611no—
810C4⋊C4—611no—
811C4⋊C4—611no—
812C4⋊C4—611no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4C22⋊#692311yescharacteristic
817C4⋊C4C22×#692311yescharacteristic
818C4⋊C4C22×#692311yescharacteristic
819C4⋊C4C22×#692311yescharacteristic
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—611no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—611no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4C22⋊#692311yescharacteristic
841C22⋊C4C22⋊#692311yescharacteristic
842C42—611no—
843C42—611no—
844C42—611no—
845C42—611no—
846C42—611no—
847C42—611no—
848C42—611no—
849C42—611no—
850C42—611no—
851C42C22×#692311yescharacteristic
852C23—21no—
853C23—611no—
854C23—1221no—
855C23—1221no—
856C23—1221no—
857C23—4881no—
858C23—4881no—
859C23—4881no—
860C23—2442no—
861C23—2442no—
862C23—2442no—
863C23—2442no—
864C23—2442no—
865C23—2442no—
866C23C2×C22⋊#692311yescharacteristic
867C23C2×C22⋊#692311yescharacteristic
868Q8—42no—
869Q8—1222no—
870Q8—2442no—
871Q8—2442no—
872D4—22no—
873D4—21no—
874D4—21no—
875D4—42no—
876D4—42no—
877D4—612no—
878D4—1222no—
879D4—1222no—
880D4—1221no—
881D4—1221no—
882D4—1221no—
883D4—1221no—
884D4—1221no—
885D4—4881no—
886D4—4881no—
887D4—4881no—
888D4—2442no—
889D4—2442no—
890D4—2442no—
891D4—2442no—
892D4—2442no—
893D4—2442no—
894D4—2442no—
895D4—2442no—
896D4—2442no—
897D4—2442no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—612no—
909C2×C4—612no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—1221no—
923C2×C4—1221no—
924C2×C4—2441no—
925C2×C4—2442no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2442no—
929C2×C4—2442no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2442no—
935C2×C4—2442no—
936C2×C4—2442no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4C2×C22⋊#692311yescharacteristic
942C2×C4C2×C22⋊#692311yescharacteristic
943C2×C4C2×C22⋊#692311yescharacteristic
944C2×C4C2×C22⋊#692311yescharacteristic
945C2×C4C23×#692311yescharacteristic
946C8—1222no—
947C8—2441no—
948C8—2441no—
949C8—2441no—
950C8—2441no—
951C8—2441no—
952C8—2441no—
953C8—2441no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—1221no—
963C22—1222no—
964C22—1221no—
965C22—1221no—
966C22—4884no—
967C22—4884no—
968C22—4884no—
969C22—2441no—
970C22—2441no—
971C22—2441no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22#1684075412yes—
978C22C22×C22⋊#692311yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—611no—
987C4—611no—
988C4—612no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—1221no—
993C4—1221no—
994C4—2441no—
995C4D61⋊#13111yescharacteristic
996C4#1684084111yescharacteristic
997C2—22no—
998C2—41no—
999C2—81no—
1000C2—4881no—
1001C2—4881no—
1002C2—2441no—
1003C2—2442no—
1004C2#2146240911yescharacteristic
1005C2C2×#1684075411yescharacteristic
1006C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#21459306C2
cosocleC4×Dic61C24
hypercenter#547#6923
hypocenterC61#17511
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #21462629C2semidirect
2. #21462514C2semidirect
3. #21461180C2semidirect
4. #21461178C2semidirect
5. #21461164C2semidirect
6. #21461160C2semidirect
7. #21461159C2semidirect
8. #21461146C2semidirect
9. #21461140C2semidirect
10. #21461138C2semidirect
11. #21461124C2semidirect
12. #21461120C2semidirect
13. #21461119C2semidirect
14. C2×#16840610C2semidirect
22. #16840784C22semidirect
23. #16840783C22semidirect
24. #16840781C22semidirect
25. #16840780C22semidirect
26. #16840779C22semidirect
27. #16840778C22semidirect
28. #16840778C22semidirect
29. #16840765C22semidirect
30. C2×C4⋊#92420C22semidirect
33. C4×#11758213C22semidirect
34. C4×#11758217C22semidirect
35. C2×C4×#92420C22semidirect
40. #16840610C22semidirect
41. #16840610C22semidirect
42. #16840610C22semidirect
43. #16840610C22semidirect
44. #16840610C22semidirect
45. #16840610C22semidirect
46. #16840610C22semidirect
47. #16840610C22semidirect
48. D4⋊#92420C22semidirect
49. D4⋊#92420C22semidirect
50. D4⋊#92420C22semidirect
51. D4⋊#92420C22semidirect
578. C61#17511semidirect

Maximal subgroups

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

subgroupindex
#214626292
#214625142
#214611802
#214611782
#214611642
#214611602
#214611592
#214611462
#214611402
#214611382
#214611242
#214611202
#214611192
C2×#168406102
#214593062
#1751161