Finite Group Databasebeta

← #30610844

Subgroups — #30610844

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462744C211yesmaximal, characteristic, complemented
2C4×#14519864C211yesmaximal, characteristic, complemented
3#21461171C211yesmaximal, characteristic, complemented
4#21461170C211yesmaximal, characteristic, complemented
5#21461167C211yesmaximal, characteristic, complemented
6#21461162C211yesmaximal, characteristic, complemented
7#21461161C211yesmaximal, characteristic, complemented
8#21461154C211yesmaximal, characteristic, complemented
9#21461141C211yesmaximal, characteristic, complemented
10#21461135C211yesmaximal, characteristic, complemented
11#21461134C211yesmaximal, characteristic, complemented
12#21461110C211yesmaximal, characteristic, complemented
13D61⋊(Q8⋊C8)C211yesmaximal, characteristic, complemented
14C2×Q8⋊#92420C211yesmaximal, characteristic, complemented
15#21459435C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840794—21no—
19#16840793—21no—
20#16840789—21no—
21#16840784C2211yescharacteristic
22#16840783C2211yescharacteristic
23#16840778C2211yescharacteristic
24#16840765C2211yescharacteristic
25D61⋊(C4⋊C8)C2211yescharacteristic
26C2×C4⋊#92420C2211yescharacteristic
27#16840727—21no—
28#16840726—21no—
29#16840726—21no—
30C4×#11758213C2211yescharacteristic
31C4×#11758217C2211yescharacteristic
32C4×#11758217C2211yescharacteristic
33C4×D61⋊C8C2211yescharacteristic
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40Q8⋊#92420C2211yescharacteristic
41Q8⋊#92420C2211yescharacteristic
42Q8⋊#92420C2211yescharacteristic
43Q8⋊#92420C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46Q8⋊#92420C2211yescharacteristic
47Q8⋊#92420C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840488C411yescharacteristic
53#16840481—21no—
54#16840481C411yescharacteristic
55#16840452—21no—
56#16840452C411yescharacteristic
57#16840446—21no—
58#16840446C411yescharacteristic
59Q8×C22⋊D61C411yescharacteristic
60#16840419C411yescharacteristic
61#16840412—21no—
62#16840412C411yescharacteristic
63#16840314—21no—
64#16840314C2211yescharacteristic
65#16840293—21no—
66#16840293C2211yescharacteristic
67#16840291—21no—
68#16840291C2211yescharacteristic
69#41×Dic61C2211yescharacteristic
70C4×#11758224—21no—
71C4×#11758224C2211yescharacteristic
72C2×Q8×Dic61C2211yescharacteristic
73C4×Q8×D61C2211yescharacteristic
74C61×#548C411yescharacteristic
75#14519864—28no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×D61⋊C8—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88C4⋊#92420C2311yescharacteristic
89C4⋊#92420C2311yescharacteristic
90C4⋊#92420C2311yescharacteristic
91C4⋊#92420C2311yescharacteristic
92#14519834—21no—
93C22⋊#92420—21no—
94C22⋊#92420—21no—
95#14519832—21no—
96#14519832—21no—
97#14519832—21no—
98#14519832—21no—
99#14519832—21no—
100C4×#92420—21no—
101C4×#92420—21no—
102C4×#92420—21no—
103C4×#92420—21no—
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C4×#92420C2311yescharacteristic
108C2×#11758224—21no—
109C2×#11758224D411yescharacteristic
110C2×Q8×D61C2×C411yescharacteristic
111#14519776—21no—
112#14519776C2×C411yescharacteristic
113#14519775—21no—
114#14519775C2×C411yescharacteristic
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519770—21no—
121#14519769—21no—
122#14519769C2×C411yescharacteristic
123#14519768—21no—
124#14519768C2×C411yescharacteristic
125#14519767—21no—
126#14519767—21no—
127#14519767—21no—
128#14519764—21no—
129#14519764C2×C411yescharacteristic
130#14519759—21no—
131#14519759—21no—
132#14519759—21no—
133#14519758—21no—
134#14519758—21no—
135#14519758—21no—
136#14519756—21no—
137#14519756—21no—
138#14519756C2×C411yescharacteristic
139#14519756C2×C411yescharacteristic
140#14519754—21no—
141#14519754—21no—
142#14519754—21no—
143#14519753—21no—
144#14519753C2×C411yescharacteristic
145#14519748—21no—
146#14519748C2×C411yescharacteristic
147Q8×Dic61—21no—
148Q8×Dic61—21no—
149Q8×Dic61C2×C411yescharacteristic
150Q8×Dic61C2×C411yescharacteristic
151Q8×Dic61C2×C411yescharacteristic
152Q8×Dic61C2311yescharacteristic
153Q8×Dic61C2311yescharacteristic
154C4×Dic122—21no—
155C4×Dic122—21no—
156C4×Dic122C2×C411yescharacteristic
157C4×Dic122C2×C411yescharacteristic
158#14519742—21no—
159#14519742—21no—
160#14519742D411yescharacteristic
161#14519742C2311yescharacteristic
162D4×Dic61—21no—
163D4×Dic61—21no—
164D4×Dic61—21no—
165D4×Dic61C2×C411yescharacteristic
166D4×Dic61D411yescharacteristic
167D4×Dic61C2311yescharacteristic
168C4×C22⋊D61—21no—
169C4×C22⋊D61—21no—
170C4×C22⋊D61C2×C411yescharacteristic
171C4×C22⋊D61C2×C411yescharacteristic
172#14519737—21no—
173#14519737D411yescharacteristic
174#14519737D411yescharacteristic
175#14519736—21no—
176#14519736C2×C411yescharacteristic
177#14519735—21no—
178#14519735D411yescharacteristic
179#14519733—21no—
180#14519733—21no—
181#14519733—21no—
182#14519733—21no—
183#14519733—21no—
184#14519733D411yescharacteristic
185#14519733D411yescharacteristic
186C2×C4⋊Dic61—21no—
187C2×C4⋊Dic61C2×C411yescharacteristic
188C4⋊C4×D61—21no—
189C4⋊C4×D61C2×C411yescharacteristic
190C2×C4×Dic61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61—21no—
195C42×D61C2311yescharacteristic
196C2×#41×C61C2×C411yescharacteristic
197C22×Q8×C61C2×C411yescharacteristic
198#124×C61—21no—
199#124×C61C2×C411yescharacteristic
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202#121×C61—21no—
203#121×C61C2×C411yescharacteristic
204C4×Q8×C61C2×C411yescharacteristic
205C4×D4×C61—21no—
206C4×D4×C61C2×C411yescharacteristic
207#41×C61—22no—
208#41×C61—41no—
209C2×Q8×C61—21no—
210C2×Q8×C61—22no—
211C2×Q8×C61—41no—
212C2×Q8×C61C22×C411yescharacteristic
213C2×Q8×C61C22×C411yescharacteristic
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61C22⋊C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61C22⋊C411yescharacteristic
224C2×C22⋊D61C22⋊C411yescharacteristic
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232Q8×D61—22no—
233Q8×D61—41no—
234#11758224—24no—
235#11758224—44no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61C22×C411yescharacteristic
239C2×C4×D61C2×D411yescharacteristic
240C2×C4×D61C2×D411yescharacteristic
241C2×Dic122—21no—
242C2×Dic122—21no—
243C2×Dic122C22⋊C411yescharacteristic
244C2×Dic122C22×C411yescharacteristic
245#11758217—24no—
246#11758217—24no—
247#11758217—81no—
248C2×#92420—24no—
249C2×#92420—24no—
250C2×#92420—21no—
251C2×#92420—21no—
252C2×#92420—21no—
253C2×#92420—21no—
254C2×#92420—21no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—81no—
259#11758213—24no—
260D61⋊C8—24no—
261D61⋊C8—81no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C22⋊C411yescharacteristic
265C4⋊C4×C61C22×C411yescharacteristic
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61C22⋊C411yescharacteristic
271C22⋊C4×C61C22⋊C411yescharacteristic
272C42×C61—21no—
273C42×C61C22×C411yescharacteristic
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61C22⋊C411yescharacteristic
283C22⋊Dic61C22⋊C411yescharacteristic
284#11758198—21no—
285#11758198C22⋊C411yescharacteristic
286#11758198C22⋊C411yescharacteristic
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61C22⋊C411yescharacteristic
295C4⋊Dic61C22×C411yescharacteristic
296C4⋊Dic61C22×C411yescharacteristic
297C4⋊Dic61C22×C411yescharacteristic
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61C22×C411yescharacteristic
323C4×Dic61C22×C411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2411yescharacteristic
331C23×C61—21no—
332C23×C61C2×C22⋊C411yescharacteristic
333C23×C61C2×C22⋊C411yescharacteristic
334C22×D61C2×C22⋊C411yescharacteristic
335Q8×C61—21no—
336Q8×C61—21no—
337Q8×C61—21no—
338Q8×C61—42no—
339Q8×C61#13112yescomplemented
340D4×C61—22no—
341D4×C61—21no—
342D4×C61—21no—
343D4×C61—42no—
344D4×C61—42no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C2×C22⋊C411yescharacteristic
357C2×C4×C61C2×C22⋊C411yescharacteristic
358C2×C4×C61C23×C411yescharacteristic
359C22⋊D61—22no—
360C22⋊D61—42no—
361C22⋊D61#10414yes—
362C2×Dic61—22no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—22no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—42no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—42no—
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C22×D411yescharacteristic
382C2×Dic61C22×D411yescharacteristic
383C4×D61—22no—
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—42no—
389C4×D61—42no—
390Dic122—22no—
391Dic122—21no—
392Dic122—21no—
393Dic122—42no—
394Dic122—42no—
395#92420—22no—
396#92420—22no—
397#92420—22no—
398#92420—22no—
399#92420—41no—
400#92420—41no—
401#92420—41no—
402#92420—41no—
403#17519—611nomaximal, Sylow
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61C2×#10412yes—
413C22×C61C22×C22⋊C411yescharacteristic
414C2×D61—21no—
415C2×D61—21no—
416C2×D61C2×#10412yes—
417C4×C61—22no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—21no—
421C4×C61—21no—
422C4×C61—41no—
423C4×C61—41no—
424C4×C61C2×#13111yescharacteristic
425C4×C61#56811yescharacteristic
426Dic61—21no—
427Dic61—21no—
428Dic61—21no—
429Dic61—21no—
430Dic61—21no—
431Dic61—41no—
432Dic61—41no—
433Dic61—41no—
434Dic61—41no—
435Dic61C2×#10412yes—
436Dic61#57711yescharacteristic
437Dic61#57811yescharacteristic
438#3482—611no—
439#2990—611no—
440C4×#131—611no—
441#1494—611no—
442#1494—611no—
443#1493—611no—
444#1491—611no—
445#1491—611no—
446#1489—611no—
447#1485—611no—
448#1483—611no—
449#1483—611no—
450#1476—611no—
451C2×Q8⋊C8—611no—
452C2×Q8⋊C8—611no—
453C2×C61—22no—
454C2×C61—41no—
455C2×C61—81no—
456C2×C61#288011yescharacteristic
457C2×C61#289811yescharacteristic
458C2×C61C22×#10411yescharacteristic
459D61—22no—
460C2×#131—1221no—
461#557—611no—
462#556—611no—
463#556—1221no—
464#552—611no—
465#552—611no—
466#552—1221no—
467#552—1221no—
468D4×Q8—611no—
469#548—611no—
470#548#692311yescharacteristic
471#547—611no—
472#547—1221no—
473#533—611no—
474#533—1221no—
475#529—611no—
476#529—611no—
477#529—1221no—
478#529—1221no—
479C4×#41—611no—
480C4×#41—611no—
481C4×#41—1221no—
482C2×C4×Q8—611no—
483C2×C4×Q8—611no—
484#446—1221no—
485#435—1221no—
486#435—1221no—
487C8×D4—1221no—
488#432—611no—
489#432—611no—
490#431—611no—
491#423—611no—
492C2×C4⋊C8—611no—
493C2×C4⋊C8—611no—
494#405—1221no—
495#405—1221no—
496#405—1221no—
497C4×M16—611no—
498C4×M16—611no—
499C4×M16—611no—
500C2×C4×C8—611no—
501C2×C4×C8—611no—
502C2×C4×C8—611no—
503Q8⋊C8—611no—
504Q8⋊C8—611no—
505Q8⋊C8—611no—
506Q8⋊C8—611no—
507Q8⋊C8—611no—
508Q8⋊C8—611no—
509Q8⋊C8—611no—
510Q8⋊C8—611no—
511Q8⋊C8—611no—
512Q8⋊C8—611no—
513Q8⋊C8—611no—
514Q8⋊C8—611no—
515D4⋊C8—611no—
516D4⋊C8—611no—
517D4⋊C8—611no—
518D4⋊C8—611no—
519C61#1751911yescharacteristic, complemented, Sylow
520C2×#41—611no—
521C2×#41—1221no—
522C2×#41C2×#692311yescharacteristic
523C22×Q8—611no—
524C22×Q8C2×#692311yescharacteristic
525#131—1228no—
526C2×M16—1221no—
527C2×M16—1221no—
528C2×M16—1221no—
529C2×M16—1221no—
530C22×C8—1221no—
531C22×C8—1221no—
532C22×C8—1221no—
533C22×C8—1221no—
534C22×C8—1221no—
535C4⋊Q8—611no—
536C4⋊Q8—611no—
537C4⋊Q8—1221no—
538C4⋊Q8—1221no—
539#126—1221no—
540#126—1221no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#126—1221no—
545#125—611no—
546#125—611no—
547#125—1221no—
548#125—1221no—
549#125—1221no—
550#125—1221no—
551#125—1221no—
552#124—21no—
553#124—611no—
554#124—1221no—
555#124C2×#692311yescharacteristic
556#123—1221no—
557#123—1221no—
558#123—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562C22⋊Q8—21no—
563C22⋊Q8—611no—
564C22⋊Q8—611no—
565C22⋊Q8—611no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8C2×#692311yescharacteristic
573#121—21no—
574#121—611no—
575#121—1221no—
576#121C2×#692311yescharacteristic
577C4×Q8—611no—
578C4×Q8—611no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—611no—
585C4×Q8—611no—
586C4×Q8—1221no—
587C4×Q8—1221no—
588C4×Q8—1221no—
589C4×Q8—1221no—
590C4×Q8—1221no—
591C4×Q8—1221no—
592C4×Q8C2×#692311yescharacteristic
593C4×D4—21no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4C2×#692311yescharacteristic
608#117—611no—
609#117—611no—
610#117—611no—
611#117—611no—
612#117—1221no—
613#117—1221no—
614#117—1221no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618#117—1221no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1221no—
623C2×C42—611no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—1221no—
627C2×C42—1221no—
628C2×C42—1221no—
629C4⋊C8—611no—
630C4⋊C8—611no—
631C4⋊C8—611no—
632C4⋊C8—611no—
633C4⋊C8—1221no—
634C4⋊C8—1221no—
635C4⋊C8—1221no—
636C22⋊C8—1221no—
637C22⋊C8—1221no—
638C22⋊C8—1221no—
639#97—1221no—
640#97—1221no—
641#97—1221no—
642#97—1221no—
643#97—1221no—
644C4×C8—611no—
645C4×C8—611no—
646C4×C8—611no—
647C4×C8—611no—
648C4×C8—1221no—
649C4×C8—1221no—
650C4×C8—1221no—
651C4×C8—1221no—
652#41—22no—
653#41—41no—
654#41—1224no—
655#41—2444no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—41no—
659C2×Q8—611no—
660C2×Q8—611no—
661C2×Q8—1221no—
662C2×Q8—1221no—
663C2×Q8—1222no—
664C2×Q8—2441no—
665C2×Q8C22×#692311yescharacteristic
666C2×Q8C22×#692311yescharacteristic
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—611no—
670C2×D4—611no—
671C2×D4—1221no—
672C2×D4C22⋊#692311yescharacteristic
673C2×D4C22×#692311yescharacteristic
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4C22×#692311yescharacteristic
689C22×C4C22×#692311yescharacteristic
690M16—1224no—
691M16—1224no—
692M16—1224no—
693M16—4881no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1224no—
699C2×C8—1224no—
700C2×C8—1224no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—4881no—
706C2×C8—4881no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—611no—
710C4⋊C4—611no—
711C4⋊C4—611no—
712C4⋊C4—611no—
713C4⋊C4—611no—
714C4⋊C4—611no—
715C4⋊C4—611no—
716C4⋊C4—611no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4C22⋊#692311yescharacteristic
737C4⋊C4C22×#692311yescharacteristic
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—611no—
743C22⋊C4—611no—
744C22⋊C4—611no—
745C22⋊C4—611no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4C22⋊#692311yescharacteristic
756C22⋊C4C22⋊#692311yescharacteristic
757C42—21no—
758C42—611no—
759C42—611no—
760C42—611no—
761C42—611no—
762C42—611no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—1221no—
768C42—1221no—
769C42—1221no—
770C42—1221no—
771C42—1221no—
772C42—1221no—
773C42—1221no—
774C42—1221no—
775C42C22×#692311yescharacteristic
776C23—21no—
777C23—611no—
778C23C2×C22⋊#692311yescharacteristic
779C23C2×C22⋊#692311yescharacteristic
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—42no—
784Q8—1222no—
785Q8—1221no—
786Q8—1221no—
787Q8—2442no—
788Q8—2442no—
789Q8#1451986412yescomplemented
790D4—22no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—614no—
796D4—1222no—
797D4—2442no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—611no—
812C2×C4—611no—
813C2×C4—611no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1222no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—2442no—
830C2×C4—2442no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2442no—
834C2×C4—2442no—
835C2×C4C2×C22⋊#692311yescharacteristic
836C2×C4C2×C22⋊#692311yescharacteristic
837C2×C4C2×C22⋊#692311yescharacteristic
838C2×C4C2×C22⋊#692311yescharacteristic
839C2×C4C23×#692311yescharacteristic
840C8—1222no—
841C8—1222no—
842C8—1222no—
843C8—1222no—
844C8—2441no—
845C8—2441no—
846C8—2441no—
847C8—2441no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—612no—
857C22—1221no—
858C22—1221no—
859C22D61⋊#10412yes—
860C22C22×C22⋊#692311yescharacteristic
861C4—21no—
862C4—21no—
863C4—22no—
864C4—21no—
865C4—21no—
866C4—41no—
867C4—41no—
868C4—611no—
869C4—611no—
870C4—612no—
871C4—1221no—
872C4—1221no—
873C4—1221no—
874C4—1221no—
875C4—1221no—
876C4—2441no—
877C4—2441no—
878C4—2441no—
879C4—2441no—
880C4C2×#1451986411yescharacteristic
881C4#1684084011yescharacteristic
882C2—22no—
883C2—41no—
884C2—81no—
885C2—1222no—
886C2#2146240711yescharacteristic
887C2#2146244111yescharacteristic
888C2C2×D61⋊#10411yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#548C4
socleC22×C61C22×C22⋊C4
prime radical#21459435C2
cosocleC4×Dic61C24
hypercenter#548#6923
hypocenterC61#17519
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #21462744C2semidirect
2. C4×#14519864C2semidirect
3. #21461171C2semidirect
4. #21461170C2semidirect
5. #21461167C2semidirect
6. #21461162C2semidirect
7. #21461161C2semidirect
8. #21461154C2semidirect
9. #21461141C2semidirect
10. #21461135C2semidirect
11. #21461134C2semidirect
12. #21461110C2semidirect
13. D61⋊(Q8⋊C8)C2semidirect
14. C2×Q8⋊#92420C2semidirect
339. Q8×C61#131semidirect
519. C61#17519semidirect
789. Q8#14519864semidirect

Maximal subgroups

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

subgroupindex
#214627442
C4×#145198642
#214611712
#214611702
#214611672
#214611622
#214611612
#214611542
#214611412
#214611352
#214611342
#214611102
D61⋊(Q8⋊C8)2
C2×Q8⋊#924202
#214594352
#1751961