Finite Group Databasebeta

← #30610799

Subgroups — #30610799

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462629C211yesmaximal, characteristic, complemented
2#21462464C211yesmaximal, characteristic, complemented
3#21461175C211yesmaximal, characteristic, complemented
4#21461174C211yesmaximal, characteristic, complemented
5#21461167C211yesmaximal, characteristic, complemented
6#21461155C211yesmaximal, characteristic, complemented
7#21461154C211yesmaximal, characteristic, complemented
8#21461144C211yesmaximal, characteristic, complemented
9#21461135C211yesmaximal, characteristic, complemented
10#21461134C211yesmaximal, characteristic, complemented
11#21461127C211yesmaximal, characteristic, complemented
12#21461115C211yesmaximal, characteristic, complemented
13#21461114C211yesmaximal, characteristic, complemented
14C2×D4⋊#92420C211yesmaximal, characteristic, complemented
15#21459370C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840795—21no—
19#16840793—21no—
20#16840791—21no—
21#16840780C2211yescharacteristic, complemented
22#16840779C2211yescharacteristic
23#16840778C2211yescharacteristic, complemented
24#16840769—21no—
25#16840768—21no—
26#16840768—21no—
27#16840766C2211yescharacteristic, complemented
28#16840765C2211yescharacteristic
29#16840765C2211yescharacteristic, complemented
30D61⋊(C4⋊C8)C2211yescharacteristic, complemented
31C2×C4⋊#92420C2211yescharacteristic
32C2×C4⋊#92420C2211yescharacteristic, complemented
33C4×#11758213C2211yescharacteristic, complemented
34C4×#11758217C2211yescharacteristic, complemented
35C2×C4×#92420C2211yescharacteristic
36#16840612C2211yescharacteristic, complemented
37#16840612C2211yescharacteristic, complemented
38#16840612C2211yescharacteristic, complemented
39#16840612C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42Q8⋊#92420C2211yescharacteristic, complemented
43Q8⋊#92420C2211yescharacteristic, complemented
44D4⋊#92420C2211yescharacteristic
45D4⋊#92420C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840481C411yescharacteristic
53#16840476C411yescharacteristic
54#16840471C411yescharacteristic
55#16840455—21no—
56#16840454C411yescharacteristic
57#16840452C411yescharacteristic
58#16840449—21no—
59#16840443—21no—
60#16840438—21no—
61#16840411C411yescharacteristic
62#16840406C411yescharacteristic
63#16840314C2211yescharacteristic
64#16840293—21no—
65#16840293C2211yescharacteristic
66#16840291C2211yescharacteristic
67#16840289—21no—
68#16840268—21no—
69#41×Dic61C2211yescharacteristic
70C4×#11758224C2211yescharacteristic
71C4×#11758224C2211yescharacteristic
72C2×D4×Dic61C2211yescharacteristic
73C2×#14519733—21no—
74C61×#546C411yescharacteristic
75#14519864—44no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×#11758217—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87#14519844—21no—
88#14519844—21no—
89#14519844—21no—
90C4⋊#92420—21no—
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93C4⋊#92420—21no—
94C4⋊#92420C2311yescharacteristic
95C4⋊#92420C2311yescharacteristic
96C4⋊#92420C2311yescharacteristic
97C4⋊#92420C2311yescharacteristic
98#14519834—21no—
99C22⋊#92420—21no—
100C22⋊#92420—21no—
101#14519832—21no—
102#14519832—21no—
103C4×#92420—21no—
104C4×#92420C2311yescharacteristic
105C4×#92420C2311yescharacteristic
106C4×#92420C2311yescharacteristic
107C4×#92420C2311yescharacteristic
108C2×#11758224C2×C411yescharacteristic
109C2×#11758224D411yescharacteristic
110C23×Dic61—21no—
111#14519776C2×C411yescharacteristic
112#14519775C2×C411yescharacteristic
113#14519772—21no—
114#14519770—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519769C2×C411yescharacteristic
120#14519768—21no—
121#14519768C2×C411yescharacteristic
122#14519767—21no—
123#14519767—21no—
124#14519764—21no—
125#14519764C2×C411yescharacteristic
126#14519763—21no—
127#14519761—21no—
128#14519760—21no—
129#14519759—21no—
130#14519758—21no—
131#14519758—21no—
132#14519758—21no—
133#14519758—21no—
134#14519756—21no—
135#14519756C2×C411yescharacteristic
136#14519756C2×C411yescharacteristic
137#14519754—21no—
138#14519754—21no—
139#14519754—21no—
140#14519754—21no—
141#14519753C2×C411yescharacteristic
142#14519749—21no—
143#14519749—21no—
144#14519749—21no—
145#14519748C2×C411yescharacteristic
146#14519746—21no—
147Q8×Dic61C2×C411yescharacteristic
148Q8×Dic61C2311yescharacteristic
149C4×Dic122C2×C411yescharacteristic
150C4×Dic122C2×C411yescharacteristic
151#14519742—21no—
152#14519742D411yescharacteristic
153#14519742C2311yescharacteristic
154D4×Dic61—21no—
155D4×Dic61—21no—
156D4×Dic61—21no—
157D4×Dic61—21no—
158D4×Dic61—21no—
159D4×Dic61C2×C411yescharacteristic
160D4×Dic61C2×C411yescharacteristic
161D4×Dic61C2×C411yescharacteristic
162D4×Dic61D411yescharacteristic
163D4×Dic61C2311yescharacteristic
164D4×Dic61C2311yescharacteristic
165C4×C22⋊D61—21no—
166C4×C22⋊D61C2×C411yescharacteristic
167C4×C22⋊D61C2×C411yescharacteristic
168#14519737—21no—
169#14519737—21no—
170#14519737D411yescharacteristic
171#14519737D411yescharacteristic
172#14519736—21no—
173#14519736C2×C411yescharacteristic
174#14519735C2×C411yescharacteristic
175#14519735D411yescharacteristic
176#14519733—21no—
177#14519733—21no—
178#14519733—21no—
179#14519733—21no—
180#14519733—21no—
181#14519733—21no—
182#14519733—21no—
183#14519733—21no—
184#14519733D411yescharacteristic
185#14519733D411yescharacteristic
186C2×C4⋊Dic61C2×C411yescharacteristic
187C2×#11758196—21no—
188C2×#11758196—21no—
189C2×C22⋊Dic61—21no—
190C2×C22⋊Dic61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61—21no—
193C2×C4×Dic61C2311yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C42×D61C2311yescharacteristic
196C2×#41×C61C2×C411yescharacteristic
197C22×D4×C61C2×C411yescharacteristic
198#124×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic
203#120×C61—21no—
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic
206C2×C22⋊C4×C61—21no—
207C24×C61—21no—
208#41×C61—22no—
209#41×C61—41no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—22no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—41no—
216C2×D4×C61C22⋊C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C2×D4×C61C22×C411yescharacteristic
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61C22⋊C411yescharacteristic
226C2×C22⋊D61C22⋊C411yescharacteristic
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—42no—
235C22×Dic61—42no—
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240#11758224—22no—
241#11758224—22no—
242#11758224—22no—
243#11758224—41no—
244C2×C4×D61C22×C411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×Dic122—21no—
248C2×Dic122C22⋊C411yescharacteristic
249C2×Dic122C22×C411yescharacteristic
250#11758217—42no—
251#11758217—42no—
252#11758217—42no—
253C2×#92420—21no—
254C2×#92420—21no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—42no—
262C2×#92420—42no—
263C2×#92420—42no—
264#11758213—42no—
265#11758213—42no—
266D61⋊C8—42no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61C22⋊C411yescharacteristic
269C4⋊C4×C61C22×C411yescharacteristic
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61C22⋊C411yescharacteristic
276C22⋊C4×C61C22⋊C411yescharacteristic
277C42×C61C22×C411yescharacteristic
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
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⋊Dic61C22⋊C411yescharacteristic
290C22⋊Dic61C22⋊C411yescharacteristic
291#11758198—21no—
292#11758198—21no—
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61C22⋊C411yescharacteristic
300C4⋊Dic61C22×C411yescharacteristic
301C4⋊Dic61C22×C411yescharacteristic
302C4⋊Dic61C22×C411yescharacteristic
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61C22×C411yescharacteristic
325C4×Dic61C22×C411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332C4×Dic61C2411yescharacteristic
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—42no—
336C23×C61—42no—
337C23×C61—81no—
338C23×C61C2×C22⋊C411yescharacteristic
339C23×C61C2×C22⋊C411yescharacteristic
340C22×D61C2×C22⋊C411yescharacteristic
341Q8×C61—21no—
342Q8×C61—21no—
343D4×C61—22no—
344D4×C61—21no—
345D4×C61—21no—
346D4×C61—21no—
347D4×C61—42no—
348D4×C61—42no—
349D4×C61—81no—
350D4×C61#13112yescomplemented
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—42no—
358C2×C4×C61—81no—
359C2×C4×C61C2×C22⋊C411yescharacteristic
360C2×C4×C61C2×C22⋊C411yescharacteristic
361C2×C4×C61C2×C22⋊C411yescharacteristic
362C2×C4×C61C2×C22⋊C411yescharacteristic
363C2×C4×C61C23×C411yescharacteristic
364C22⋊D61—22no—
365C22⋊D61—22no—
366C22⋊D61—42no—
367C22⋊D61—81no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—42no—
377C2×Dic61—42no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—42no—
383C2×Dic61—42no—
384C2×Dic61—81no—
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61C2×C22⋊C411yescharacteristic
387C2×Dic61C2×C22⋊C411yescharacteristic
388C2×Dic61C2×C22⋊C411yescharacteristic
389C2×Dic61C2×C22⋊C411yescharacteristic
390C2×Dic61AGL(1,ℤ/8)12yes—
391C2×Dic61#13712yes—
392C2×Dic61C22×D411yescharacteristic
393C2×Dic61C22×D411yescharacteristic
394C4×D61—21no—
395C4×D61—21no—
396C4×D61—21no—
397C4×D61—21no—
398C4×D61—41no—
399Dic122—22no—
400Dic122—21no—
401Dic122—21no—
402Dic122—81no—
403#92420—22no—
404#92420—41no—
405#92420—41no—
406#92420—41no—
407#92420—41no—
408#92420—41no—
409#92420—41no—
410#92420—41no—
411#17512—611nomaximal, Sylow
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—22no—
415C22×C61—21no—
416C22×C61—21no—
417C22×C61—21no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—84no—
424C22×C61#41712yes—
425C22×C61C22×C22⋊C411yescharacteristic
426C2×D61—21no—
427C2×D61—21no—
428C2×D61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61C2×#13111yescharacteristic
436C4×C61#56811yescharacteristic
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—21no—
441Dic61—21no—
442Dic61—41no—
443Dic61—41no—
444Dic61—41no—
445Dic61—41no—
446Dic61#41712yes—
447Dic61C2×AGL(1,ℤ/8)11yescharacteristic
448Dic61C2×#13711yescharacteristic
449#3475—611no—
450#2965—611no—
451#2906—611no—
452#1495—611no—
453#1495—611no—
454#1493—611no—
455#1489—611no—
456#1489—611no—
457#1486—611no—
458#1483—611no—
459#1483—611no—
460#1481—611no—
461#1477—611no—
462#1477—611no—
463C2×D4⋊C8—611no—
464C2×C61—22no—
465C2×C61—41no—
466C2×C61—42no—
467C2×C61—81no—
468C2×C61#288011yescharacteristic
469C2×C61C2×#41711yescharacteristic
470C2×C61#290111yescharacteristic
471D61—41no—
472C2×#131—1221no—
473#556—611no—
474#555—611no—
475#554—611no—
476#553—1221no—
477#552—611no—
478#552—611no—
479#552—1221no—
480#551—1221no—
481#551—1221no—
482#547—611no—
483#546—611no—
484#546#692311yescharacteristic
485#533—611no—
486#529—611no—
487#529—611no—
488#529—1221no—
489#529—1221no—
490#525—1221no—
491C4×#41—611no—
492C4×#41—611no—
493C4×#41—611no—
494C2×C4×D4—611no—
495C2×#117—1221no—
496#446—1221no—
497#436—1221no—
498#435—1221no—
499#435—1221no—
500#431—611no—
501#431—611no—
502#431—611no—
503#424—1221no—
504#424—1221no—
505#424—1221no—
506#423—611no—
507#423—611no—
508#423—611no—
509C2×C4⋊C8—611no—
510C2×C4⋊C8—611no—
511C2×C4⋊C8—611no—
512C4×M16—611no—
513C4×M16—611no—
514C2×C4×C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8—611no—
517Q8⋊C8—611no—
518Q8⋊C8—611no—
519Q8⋊C8—611no—
520Q8⋊C8—611no—
521Q8⋊C8—611no—
522Q8⋊C8—611no—
523D4⋊C8—611no—
524D4⋊C8—611no—
525D4⋊C8—611no—
526D4⋊C8—611no—
527D4⋊C8—611no—
528D4⋊C8—611no—
529D4⋊C8—611no—
530D4⋊C8—611no—
531C61#1751211yescharacteristic, complemented, Sylow
532C2×#41—611no—
533C2×#41—611no—
534C2×#41C2×#692311yescharacteristic
535C22×D4C2×#692311yescharacteristic
536C23×C4—1221no—
537#131—2444no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1221no—
543C22×C8—1221no—
544C22×C8—1221no—
545C22×C8—1221no—
546C22×C8—1221no—
547C4⋊Q8—611no—
548C4⋊Q8—611no—
549#126—1221no—
550#126—1221no—
551#126—1221no—
552#126—1221no—
553#126—1221no—
554#126—1221no—
555#125—611no—
556#125—611no—
557#125—1221no—
558#125—1221no—
559#125—1221no—
560#124—611no—
561#124—1221no—
562#124—1221no—
563#124C2×#692311yescharacteristic
564#123—21no—
565#123—1221no—
566#123—1221no—
567#123—1221no—
568#123—1221no—
569#123—1221no—
570#123—1221no—
571#123—1221no—
572C22⋊Q8—611no—
573C22⋊Q8—611no—
574C22⋊Q8—611no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8C2×#692311yescharacteristic
581#121—21no—
582#121—611no—
583#121—1221no—
584#121—1221no—
585#121—1221no—
586#121C2×#692311yescharacteristic
587#120—21no—
588#120—1221no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—611no—
595C4×Q8—1221no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4C2×#692311yescharacteristic
615C4×D4C2×#692311yescharacteristic
616#117—611no—
617#117—611no—
618#117—611no—
619#117—611no—
620#117—611no—
621#117—1221no—
622#117—1221no—
623#117—1221no—
624#117—1221no—
625#117—1221no—
626#117—1221no—
627#117—1221no—
628#117—1221no—
629#117—1221no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4—1221no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C42—611no—
637C2×C42—611no—
638C2×C42—611no—
639C2×C42—1221no—
640C2×C42—1221no—
641C4⋊C8—611no—
642C4⋊C8—611no—
643C4⋊C8—611no—
644C4⋊C8—611no—
645C4⋊C8—1221no—
646C4⋊C8—1221no—
647C4⋊C8—1221no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652C4⋊C8—1221no—
653C4⋊C8—1221no—
654C22⋊C8—1221no—
655C22⋊C8—1221no—
656C22⋊C8—1221no—
657#97—1221no—
658#97—1221no—
659C4×C8—611no—
660C4×C8—611no—
661C4×C8—611no—
662C4×C8—611no—
663C4×C8—1221no—
664C24—21no—
665#41—22no—
666#41—41no—
667#41—1222no—
668#41—1222no—
669#41—1222no—
670#41—2441no—
671C2×Q8—611no—
672C2×Q8—611no—
673C2×Q8—1221no—
674C2×Q8C22×#692311yescharacteristic
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4—611no—
681C2×D4—611no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4C22⋊#692311yescharacteristic
685C2×D4C22×#692311yescharacteristic
686C2×D4C22×#692311yescharacteristic
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—2442no—
704C22×C4—2442no—
705C22×C4C22×#692311yescharacteristic
706C22×C4C22×#692311yescharacteristic
707M16—2442no—
708M16—2442no—
709M16—2442no—
710M16—2442no—
711M16—2442no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—2442no—
721C2×C8—2442no—
722C2×C8—2442no—
723C2×C8—2442no—
724C4⋊C4—21no—
725C4⋊C4—611no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4C22⋊#692311yescharacteristic
749C4⋊C4C22×#692311yescharacteristic
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—611no—
756C22⋊C4—611no—
757C22⋊C4—611no—
758C22⋊C4—611no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4C22⋊#692311yescharacteristic
773C22⋊C4C22⋊#692311yescharacteristic
774C42—611no—
775C42—611no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—1221no—
784C42—1221no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42—1221no—
789C42C22×#692311yescharacteristic
790C23—21no—
791C23—21no—
792C23—42no—
793C23—42no—
794C23—81no—
795C23—611no—
796C23C2×C22⋊#692311yescharacteristic
797C23C2×C22⋊#692311yescharacteristic
798Q8—21no—
799Q8—21no—
800Q8—1222no—
801Q8—1221no—
802Q8—1221no—
803Q8—4881no—
804D4—22no—
805D4—21no—
806D4—21no—
807D4—21no—
808D4—42no—
809D4—42no—
810D4—81no—
811D4—1222no—
812D4—1222no—
813D4—4881no—
814D4—2442no—
815D4#1451986412yescomplemented
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—612no—
825C2×C4—612no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—611no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—4881no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2442no—
850C2×C4—2442no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2442no—
854C2×C4—2442no—
855C2×C4C2×C22⋊#692311yescharacteristic
856C2×C4C2×C22⋊#692311yescharacteristic
857C2×C4C2×C22⋊#692311yescharacteristic
858C2×C4C2×C22⋊#692311yescharacteristic
859C2×C4C23×#692311yescharacteristic
860C8—1222no—
861C8—2441no—
862C8—2441no—
863C8—2441no—
864C8—2441no—
865C8—2441no—
866C8—2441no—
867C8—2441no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—22no—
872C22—21no—
873C22—21no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—84no—
880C22—1221no—
881C22—1221no—
882C22—1221no—
883C22#1684075312yes—
884C22C22×C22⋊#692311yescharacteristic
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—41no—
890C4—41no—
891C4—611no—
892C4—611no—
893C4—612no—
894C4—1221no—
895C4—1221no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—2441no—
900C4—2441no—
901C4—2441no—
902C4—2441no—
903C4C2×#1451986411yescharacteristic
904C4#1684084011yescharacteristic
905C2—22no—
906C2—41no—
907C2—42no—
908C2—81no—
909C2—2441no—
910C2#2146240711yescharacteristic
911C2C2×#1684075311yescharacteristic
912C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459370C2
cosocleC4×Dic61C24
hypercenter#546#6923
hypocenterC61#17512
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462629C2semidirect
2. #21462464C2semidirect
3. #21461175C2semidirect
4. #21461174C2semidirect
5. #21461167C2semidirect
6. #21461155C2semidirect
7. #21461154C2semidirect
8. #21461144C2semidirect
9. #21461135C2semidirect
10. #21461134C2semidirect
11. #21461127C2semidirect
12. #21461115C2semidirect
13. #21461114C2semidirect
14. C2×D4⋊#92420C2semidirect
21. #16840780C22semidirect
23. #16840778C22semidirect
27. #16840766C22semidirect
29. #16840765C22semidirect
30. D61⋊(C4⋊C8)C22semidirect
32. C2×C4⋊#92420C22semidirect
33. C4×#11758213C22semidirect
34. C4×#11758217C22semidirect
36. #16840612C22semidirect
37. #16840612C22semidirect
38. #16840612C22semidirect
39. #16840612C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
42. Q8⋊#92420C22semidirect
43. Q8⋊#92420C22semidirect
350. D4×C61#131semidirect
531. C61#17512semidirect
815. D4#14519864semidirect

Maximal subgroups

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

subgroupindex
#214626292
#214624642
#214611752
#214611742
#214611672
#214611552
#214611542
#214611442
#214611352
#214611342
#214611272
#214611152
#214611142
C2×D4⋊#924202
#214593702
#1751261