Finite Group Databasebeta

← #30610822

Subgroups — #30610822

Order 15616.

994 conjugacy classes of subgroups.

The subgroup lattice has 912 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#21461177C211yesmaximal, characteristic, complemented
4#21461174C211yesmaximal, characteristic, complemented
5#21461164C211yesmaximal, characteristic, complemented
6#21461156C211yesmaximal, characteristic, complemented
7#21461155C211yesmaximal, characteristic, complemented
8#21461149C211yesmaximal, characteristic, complemented
9#21461137C211yesmaximal, characteristic, complemented
10#21461134C211yesmaximal, characteristic, complemented
11#21461124C211yesmaximal, characteristic, complemented
12#21461116C211yesmaximal, characteristic, complemented
13#21461115C211yesmaximal, characteristic, complemented
14C2×#16840612C211yesmaximal, characteristic, complemented
15#21459413C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840795—21no—
19#16840793—21no—
20#16840791—21no—
21#16840780C2211yescharacteristic
22#16840779C2211yescharacteristic
23#16840778C2211yescharacteristic
24#16840769—21no—
25#16840768—21no—
26#16840768—21no—
27#16840766C2211yescharacteristic
28#16840765C2211yescharacteristic
29#16840765C2211yescharacteristic
30D61⋊(C4⋊C8)C2211yescharacteristic
31C2×C4⋊#92420C2211yescharacteristic
32C2×C4⋊#92420C2211yescharacteristic
33C4×#11758213C2211yescharacteristic
34C4×#11758217C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840612C2211yescharacteristic
37#16840612C2211yescharacteristic
38#16840612C2211yescharacteristic
39#16840612C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48D4⋊#92420C2211yescharacteristic
49D4⋊#92420C2211yescharacteristic
50D4⋊#92420C2211yescharacteristic
51D4⋊#92420C2211yescharacteristic
52#16840496—21no—
53#16840495C411yescharacteristic
54#16840489C411yescharacteristic
55#16840480C411yescharacteristic
56#16840479—21no—
57#16840461—21no—
58#16840460C411yescharacteristic
59#16840455—21no—
60#16840430C411yescharacteristic
61#16840421C411yescharacteristic
62#16840418C411yescharacteristic
63#16840307—21no—
64#16840307C2211yescharacteristic
65#16840297C2211yescharacteristic
66#16840295—21no—
67#16840293C2211yescharacteristic
68#16840289—21no—
69#16840230C2211yescharacteristic
70C4×#11758224—21no—
71C4×#11758224C2211yescharacteristic
72C4×#11758224C2211yescharacteristic
73C2×#14519742C2211yescharacteristic
74C61×#553C411yescharacteristic
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×#11758222C2×C411yescharacteristic
109C2×#11758224—21no—
110C2×#11758224C2×C411yescharacteristic
111C2×#11758224D411yescharacteristic
112C22×Dic122C2×C411yescharacteristic
113#14519776—21no—
114#14519776C2×C411yescharacteristic
115#14519773—21no—
116#14519773C2×C411yescharacteristic
117#14519772—21no—
118#14519772—21no—
119#14519771—21no—
120#14519770—21no—
121#14519770—21no—
122#14519768C2×C411yescharacteristic
123#14519767—21no—
124#14519767—21no—
125#14519765C2×C411yescharacteristic
126#14519764C2×C411yescharacteristic
127#14519763—21no—
128#14519763—21no—
129#14519763—21no—
130#14519763—21no—
131#14519763—21no—
132#14519762—21no—
133#14519762—21no—
134#14519760—21no—
135#14519759—21no—
136#14519758—21no—
137#14519757C2×C411yescharacteristic
138#14519756C2×C411yescharacteristic
139#14519755—21no—
140#14519754—21no—
141#14519752C2×C411yescharacteristic
142#14519751—21no—
143#14519751C2×C411yescharacteristic
144#14519750—21no—
145#14519749—21no—
146#14519749—21no—
147#14519749—21no—
148#14519749—21no—
149C4×Dic122—21no—
150C4×Dic122C2×C411yescharacteristic
151C4×Dic122C2×C411yescharacteristic
152#14519742—21no—
153#14519742—21no—
154#14519742—21no—
155#14519742C2×C411yescharacteristic
156#14519742C2×C411yescharacteristic
157#14519742C2×C411yescharacteristic
158#14519742D411yescharacteristic
159#14519742C2311yescharacteristic
160#14519742C2311yescharacteristic
161D4×Dic61—21no—
162D4×Dic61—21no—
163D4×Dic61D411yescharacteristic
164D4×Dic61C2311yescharacteristic
165#14519739—21no—
166#14519739C2×C411yescharacteristic
167#14519739C2311yescharacteristic
168C4×C22⋊D61—21no—
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61C2×C411yescharacteristic
172C4×C22⋊D61C2×C411yescharacteristic
173#14519737—21no—
174#14519737—21no—
175#14519737—21no—
176#14519737—21no—
177#14519737—21no—
178#14519737—21no—
179#14519737D411yescharacteristic
180#14519737D411yescharacteristic
181#14519735—21no—
182#14519735C2×C411yescharacteristic
183#14519735D411yescharacteristic
184#14519734—21no—
185#14519733—21no—
186#14519733—21no—
187#14519733D411yescharacteristic
188#14519733D411yescharacteristic
189C2×#11758196—21no—
190C2×C4×Dic61—21no—
191C2×C4×Dic61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61—21no—
195C42×D61C2311yescharacteristic
196#126×C61—21no—
197#125×C61C2×C411yescharacteristic
198#123×C61—21no—
199#121×C61—21no—
200#121×C61C2×C411yescharacteristic
201#121×C61C2×C411yescharacteristic
202C4×D4×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205#117×C61C2×C411yescharacteristic
206C2×C4⋊C4×C61C2×C411yescharacteristic
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61C22⋊C411yescharacteristic
210C2×D4×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61C22⋊C411yescharacteristic
221C2×C22⋊D61C22⋊C411yescharacteristic
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758224—22no—
230#11758224—22no—
231#11758224—22no—
232#11758224—41no—
233#11758224—42no—
234#11758224—42no—
235#11758222—22no—
236#11758222—41no—
237C2×D244—21no—
238C2×D244C22×C411yescharacteristic
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×Dic122—22no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—41no—
249C2×Dic122C22⋊C411yescharacteristic
250C2×Dic122C22×C411yescharacteristic
251C2×Dic122C22×C411yescharacteristic
252#11758217—42no—
253#11758217—42no—
254#11758217—42no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—42no—
264C2×#92420—42no—
265C2×#92420—42no—
266#11758213—42no—
267#11758213—42no—
268D61⋊C8—42no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61C22⋊C411yescharacteristic
273C4⋊C4×C61C22×C411yescharacteristic
274C4⋊C4×C61C22×C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61C22⋊C411yescharacteristic
281C22⋊C4×C61C22⋊C411yescharacteristic
282C42×C61—21no—
283C42×C61C22×C411yescharacteristic
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61C22⋊C411yescharacteristic
289C22⋊Dic61C22⋊C411yescharacteristic
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61C22⋊C411yescharacteristic
303C4⋊Dic61C22×C411yescharacteristic
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#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317C4×Dic61—21no—
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×C61C2×C22⋊C411yescharacteristic
335C23×C61C2×C22⋊C411yescharacteristic
336C22×D61—21no—
337C22×D61C2×C22⋊C411yescharacteristic
338D4×C61—22no—
339D4×C61—21no—
340D4×C61—21no—
341D4×C61—42no—
342D4×C61—81no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—81no—
351C2×C4×C61—81no—
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C23×C411yescharacteristic
357C22⋊D61—22no—
358C22⋊D61—22no—
359C22⋊D61—42no—
360C22⋊D61—42no—
361C22⋊D61—42no—
362C22⋊D61—42no—
363C22⋊D61—81no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61AGL(1,ℤ/8)12yes—
381C2×Dic61#13712yes—
382C2×Dic61C22×D411yescharacteristic
383C2×Dic61C22×D411yescharacteristic
384D244—21no—
385D244—21no—
386D244—81no—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—41no—
392C4×D61—42no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—81no—
396Dic122—21no—
397Dic122—22no—
398Dic122—21no—
399Dic122—21no—
400Dic122—42no—
401Dic122—42no—
402Dic122#13112yescomplemented
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#17515—611nomaximal, Sylow
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—21no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61#41712yes—
421C22×C61C22×C22⋊C411yescharacteristic
422C2×D61—21no—
423C2×D61—21no—
424C2×D61—21no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—41no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61C2×#13111yescharacteristic
436C4×C61#56811yescharacteristic
437Dic61—22no—
438Dic61—21no—
439Dic61—21no—
440Dic61—21no—
441Dic61—21no—
442Dic61—21no—
443Dic61—41no—
444Dic61—41no—
445Dic61#41712yes—
446Dic61C2×AGL(1,ℤ/8)11yescharacteristic
447Dic61C2×#13711yescharacteristic
448#3480—611no—
449#2965—611no—
450#2906—611no—
451#1495—611no—
452#1495—611no—
453#1492—611no—
454#1489—611no—
455#1489—611no—
456#1487—611no—
457#1483—611no—
458#1483—611no—
459#1480—611no—
460#1477—611no—
461#1477—611no—
462C2×Q8⋊C8—611no—
463C2×C61—22no—
464C2×C61—41no—
465C2×C61—81no—
466C2×C61#288011yescharacteristic
467C2×C61C2×#41711yescharacteristic
468C2×C61#290111yescharacteristic
469D61—41no—
470D61—81no—
471C2×#131—1221no—
472#559—611no—
473#559—1221no—
474#557—611no—
475#556—611no—
476#556—1221no—
477#553—611no—
478#553—1221no—
479#553—1221no—
480#553#692311yescharacteristic
481#550—611no—
482#548—611no—
483#548—611no—
484#532—611no—
485#532—1221no—
486#529—611no—
487#529—611no—
488#529—1221no—
489#529—1221no—
490C4×#41—611no—
491C4×#41—611no—
492C4×#41—611no—
493C4×#41—1221no—
494C2×C4×Q8—611no—
495#446—1221no—
496#436—1221no—
497#435—1221no—
498#435—1221no—
499#431—611no—
500#431—611no—
501#431—611no—
502#424—1221no—
503#424—1221no—
504#424—1221no—
505#423—611no—
506#423—611no—
507#423—611no—
508C2×C4⋊C8—611no—
509C2×C4⋊C8—611no—
510C2×C4⋊C8—611no—
511C4×M16—611no—
512C4×M16—611no—
513C2×C4×C8—611no—
514Q8⋊C8—611no—
515Q8⋊C8—611no—
516Q8⋊C8—611no—
517Q8⋊C8—611no—
518Q8⋊C8—611no—
519Q8⋊C8—611no—
520Q8⋊C8—611no—
521Q8⋊C8—611no—
522D4⋊C8—611no—
523D4⋊C8—611no—
524D4⋊C8—611no—
525D4⋊C8—611no—
526D4⋊C8—611no—
527D4⋊C8—611no—
528D4⋊C8—611no—
529D4⋊C8—611no—
530C61#1751511yescharacteristic, complemented, Sylow
531C2×#41—611no—
532C2×#41—611no—
533C2×#41—611no—
534C2×#41—1221no—
535C22×Q8—611no—
536#131—2444no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C22×C8—1221no—
543C22×C8—1221no—
544C22×C8—1221no—
545C22×C8—1221no—
546C4⋊Q8—611no—
547C4⋊Q8—1221no—
548#127—611no—
549#127—1221no—
550#126—21no—
551#126—1221no—
552#126—1221no—
553#126—1221no—
554#126—1221no—
555#126—1221no—
556#125—611no—
557#125—1221no—
558#125—1221no—
559#125C2×#692311yescharacteristic
560#124—611no—
561#124—611no—
562#124—1221no—
563#124—1221no—
564#124—1221no—
565#124—1221no—
566#124—1221no—
567#123—21no—
568#123—1221no—
569#123—1221no—
570#123—1221no—
571#123—1221no—
572#123—1221no—
573C22⋊Q8—611no—
574C22⋊Q8—611no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577#121—21no—
578#121—611no—
579#121—611no—
580#121—1221no—
581#121—1221no—
582#121—1221no—
583#121—1221no—
584#121—1221no—
585#121—1221no—
586#121C2×#692311yescharacteristic
587#121C2×#692311yescharacteristic
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—611no—
595C4×Q8—611no—
596C4×Q8—1221no—
597C4×Q8—1221no—
598C4×Q8—1221no—
599C4×Q8—1221no—
600C4×D4—21no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—611no—
606C4×D4—611no—
607C4×D4—611no—
608C4×D4—611no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4C2×#692311yescharacteristic
622C4×D4C2×#692311yescharacteristic
623#117—611no—
624#117—611no—
625#117—611no—
626#117—611no—
627#117—1221no—
628#117—1221no—
629#117—1221no—
630#117—1221no—
631#117C2×#692311yescharacteristic
632C2×C4⋊C4—1221no—
633C2×C4⋊C4C2×#692311yescharacteristic
634C2×C42—611no—
635C2×C42—611no—
636C2×C42—611no—
637C2×C42—1221no—
638C2×C42—1221no—
639C2×C42—1221no—
640C4⋊C8—611no—
641C4⋊C8—611no—
642C4⋊C8—611no—
643C4⋊C8—611no—
644C4⋊C8—1221no—
645C4⋊C8—1221no—
646C4⋊C8—1221no—
647C4⋊C8—1221no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652C4⋊C8—1221no—
653C22⋊C8—1221no—
654C22⋊C8—1221no—
655C22⋊C8—1221no—
656#97—1221no—
657#97—1221no—
658C4×C8—611no—
659C4×C8—611no—
660C4×C8—611no—
661C4×C8—611no—
662C4×C8—1221no—
663#41—1222no—
664#41—1222no—
665#41—1222no—
666#41—1222no—
667#41—2441no—
668#41—2442no—
669#41—2442no—
670#41—2441no—
671C2×Q8—611no—
672C2×Q8—611no—
673C2×Q8—611no—
674C2×Q8—1221no—
675C2×Q8—1222no—
676C2×Q8—1221no—
677C2×Q8—2441no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—611no—
681C2×D4—611no—
682C2×D4—611no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4C22⋊#692311yescharacteristic
690C2×D4C22×#692311yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4C22×#692311yescharacteristic
707C22×C4C22×#692311yescharacteristic
708M16—2442no—
709M16—2442no—
710M16—2442no—
711M16—2442no—
712M16—2442no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—2442no—
722C2×C8—2442no—
723C2×C8—2442no—
724C2×C8—2442no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
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⋊C4C22⋊#692311yescharacteristic
746C4⋊C4C22×#692311yescharacteristic
747C4⋊C4C22×#692311yescharacteristic
748C4⋊C4C22×#692311yescharacteristic
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—611no—
754C22⋊C4—611no—
755C22⋊C4—611no—
756C22⋊C4—611no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
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⋊C4C22⋊#692311yescharacteristic
770C22⋊C4C22⋊#692311yescharacteristic
771C42—21no—
772C42—611no—
773C42—611no—
774C42—611no—
775C42—611no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—1221no—
782C42—1221no—
783C42—1221no—
784C42—1221no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42C22×#692311yescharacteristic
789C23—21no—
790C23—611no—
791C23—1221no—
792C23C2×C22⋊#692311yescharacteristic
793C23C2×C22⋊#692311yescharacteristic
794Q8—612no—
795Q8—1222no—
796Q8—1221no—
797Q8—1221no—
798Q8—1221no—
799Q8—2442no—
800Q8—2442no—
801D4—22no—
802D4—21no—
803D4—21no—
804D4—42no—
805D4—81no—
806D4—1222no—
807D4—1222no—
808D4—1221no—
809D4—1221no—
810D4—4881no—
811D4—4881no—
812D4—2442no—
813D4—2442no—
814D4—2442no—
815D4—2442no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—612no—
826C2×C4—612no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—611no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—611no—
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—2442no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2442no—
853C2×C4—2442no—
854C2×C4C2×C22⋊#692311yescharacteristic
855C2×C4C2×C22⋊#692311yescharacteristic
856C2×C4C2×C22⋊#692311yescharacteristic
857C2×C4C2×C22⋊#692311yescharacteristic
858C2×C4C23×#692311yescharacteristic
859C8—1222no—
860C8—2441no—
861C8—2441no—
862C8—2441no—
863C8—2441no—
864C8—2441no—
865C8—2441no—
866C8—2441no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—1221no—
876C22—1221no—
877C22—1221no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22#1684075312yes—
882C22C22×C22⋊#692311yescharacteristic
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—41no—
888C4—41no—
889C4—41no—
890C4—611no—
891C4—611no—
892C4—612no—
893C4—1221no—
894C4—1222no—
895C4—1221no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—2441no—
900C4—2441no—
901C4D61⋊#13111yescharacteristic
902C4#1684084111yescharacteristic
903C2—22no—
904C2—41no—
905C2—81no—
906C2—4881no—
907C2—2441no—
908C2#2146240911yescharacteristic
909C2C2×#1684075311yescharacteristic
910C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#21459413C2
cosocleC4×Dic61C24
hypercenter#553#6923
hypocenterC61#17515
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #21462629C2semidirect
2. #21462464C2semidirect
3. #21461177C2semidirect
4. #21461174C2semidirect
5. #21461164C2semidirect
6. #21461156C2semidirect
7. #21461155C2semidirect
8. #21461149C2semidirect
9. #21461137C2semidirect
10. #21461134C2semidirect
11. #21461124C2semidirect
12. #21461116C2semidirect
13. #21461115C2semidirect
14. C2×#16840612C2semidirect
402. Dic122#131semidirect
530. C61#17515semidirect

Maximal subgroups

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

subgroupindex
#214626292
#214624642
#214611772
#214611742
#214611642
#214611562
#214611552
#214611492
#214611372
#214611342
#214611242
#214611162
#214611152
C2×#168406122
#214594132
#1751561