Finite Group Databasebeta

← #30680331

Subgroups — #30680331

Order 16768.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22554051C212yesmaximal, complemented
2#22554049C212yesmaximal, complemented
3#22554030C211yesmaximal, characteristic, complemented
4#22554014C211yesmaximal, characteristic, complemented
5#22554006C211yesmaximal, characteristic, complemented
6#22553982C212yesmaximal, complemented
7#22553980C211yesmaximal, characteristic, complemented
8#22553962C211yesmaximal, characteristic, complemented
9#22553959C211yesmaximal, characteristic, complemented
10#22553956C211yesmaximal, characteristic, complemented
11#22553949C212yesmaximal, complemented
12D4×C22⋊D131C211yesmaximal, characteristic, complemented
13#22553926C212yesmaximal, complemented
14#22553897C212yesmaximal, complemented
15#22553896C212yesmaximal, complemented
16#22553891C211yesmaximal, characteristic, complemented
17#22553890C211yesmaximal, characteristic, complemented
18#22553878C211yesmaximal, characteristic, complemented
19#22553877C212yesmaximal, complemented
20#22553858C211yesmaximal, characteristic, complemented
21#22553857C211yesmaximal, characteristic, complemented
22#22553843C211yesmaximal, characteristic, complemented
23#535×C131C211yesmaximal, characteristic, complemented
24C2×#14523513C2211yescharacteristic, complemented
25C2×#14523513C2211yescharacteristic, complemented
26C2×#14523512C2212yescomplemented
27C2×#14523512C2212yescomplemented
28C2×#14523512C2211yescharacteristic, complemented
29C22×C22⋊D131C2212yes—
30C2×D4×D131C2211yescharacteristic
31#16862245C2211yescharacteristic, complemented
32#16862244C2211yescharacteristic, complemented
33#16862242C2211yescharacteristic
34#16862242C2211yescharacteristic
35#16862242C2212yescomplemented
36#16862242C2212yescomplemented
37#16862240C2212yescomplemented
38#16862240C2212yescomplemented
39#16862239C2212yescomplemented
40#16862239C2212yescomplemented
41#16862239C2212yescomplemented
42#16862237C2211yescharacteristic, complemented
43#16862235C2211yescharacteristic, complemented
44#16862233C2211yescharacteristic
45#16862233C2211yescharacteristic, complemented
46#16862232C2212yes—
47#16862232C2212yescomplemented
48#16862232C2212yescomplemented
49#16862230C2212yescomplemented
50#16862228C2212yescomplemented
51#16862228C2212yescomplemented
52#16862228C2212yescomplemented
53#16862227C2212yescomplemented
54#16862227C2212yescomplemented
55#16862227C2212yescomplemented
56#16862226C2211yescharacteristic, complemented
57#16862225C2211yescharacteristic, complemented
58#16862225C2211yescharacteristic, complemented
59#16862223C2212yescomplemented
60#16862223C2212yescomplemented
61#16862222C2212yescomplemented
62#16862221C2211yescharacteristic, complemented
63#16862220C2211yescharacteristic
64#16862220C2211yescharacteristic, complemented
65#16862219C2212yescomplemented
66#16862219C2212yescomplemented
67#16862219C2212yescomplemented
68#16862218C2211yescharacteristic
69#16862218C2212yes—
70#16862218C2212yescomplemented
71#16862218C2211yescharacteristic, complemented
72#16862218C2211yescharacteristic, complemented
73#16862218C2211yescharacteristic, complemented
74#16862218C2212yescomplemented
75#16862218C2212yescomplemented
76#16862218C2212yescomplemented
77#16862218C2212yescomplemented
78#16862218C2212yescomplemented
79#16862218C2212yescomplemented
80#16862217C2211yescharacteristic
81#16862217C2211yescharacteristic
82#16862217C2212yescomplemented
83#16862217C2212yescomplemented
84#16862217C2212yescomplemented
85#16862216C2212yescomplemented
86#16862215C2212yes—
87#16862215C2212yescomplemented
88#16862214C2212yes—
89#16862214C2212yescomplemented
90#16862214C2212yescomplemented
91C4×Dic262C2212yescomplemented
92#16862211C2211yescharacteristic, complemented
93C4×D524C2212yescomplemented
94D4×Dic131C2211yescharacteristic
95D4×Dic131C2211yescharacteristic, complemented
96D4×Dic131C2212yescomplemented
97D4×Dic131C2212yescomplemented
98#16862208C2211yescharacteristic, complemented
99C4×C22⋊D131C2211yescharacteristic
100C4×C22⋊D131C2211yescharacteristic, complemented
101C4×C22⋊D131C2211yescharacteristic, complemented
102C4×C22⋊D131C2211yescharacteristic, complemented
103(C22⋊D131)⋊C4C2212yescomplemented
104(C22⋊D131)⋊C4C2212yescomplemented
105#16862204C2211yescharacteristic, complemented
106#16862202C2212yescomplemented
107C2×C4⋊Dic131C2211yescharacteristic, complemented
108C4⋊C4×D131C2211yescharacteristic, complemented
109C2×C22⋊Dic131C2212yescomplemented
110C22⋊C4×D131C2212yescomplemented
111C2×C4×Dic131C2211yescharacteristic, complemented
112C2×#41×C131C2211yescharacteristic, complemented
113C22×D4×C131C2211yescharacteristic
114#127×C131C2212yescomplemented
115#124×C131C2212yescomplemented
116#121×C131C2211yescharacteristic
117#121×C131C2211yescharacteristic
118#121×C131C2211yescharacteristic, complemented
119#121×C131C2211yescharacteristic, complemented
120#120×C131C2212yescomplemented
121#120×C131C2212yescomplemented
122#117×C131C2211yescharacteristic, complemented
123C23×D131C2312yes—
124#14523513—42no—
125#14523513—42no—
126#14523512—42no—
127#14523512—44no—
128#14523512—44no—
129C2×Dic262C2311yescharacteristic
130C2×Dic262C2312yes—
131C2×Dic262C2311yescharacteristic
132C2×D524C2311yescharacteristic
133C2×D524C2312yes—
134C2×D524C2311yescharacteristic
135C2×C22⋊D131—44no—
136C2×C22⋊D131C2311yescharacteristic
137C2×C22⋊D131C2312yes—
138C2×C22⋊D131C2311yescharacteristic
139C2×C22⋊D131C2312yes—
140C2×C22⋊D131C2312yes—
141C2×C22⋊D131C2311yescharacteristic
142C2×C22⋊D131C2311yescharacteristic
143C2×C22⋊D131C2312yes—
144C2×C22⋊D131C2312yes—
145C2×C22⋊D131C2312yes—
146C2×C22⋊D131C2312yes—
147C2×C22⋊D131C2311yescharacteristic
148C2×C22⋊D131C2312yes—
149C2×C22⋊D131C2312yes—
150C2×C22⋊D131C2311yescharacteristic
151D4×D131—42no—
152C22×Dic131C2312yes—
153C22×Dic131C2311yescharacteristic
154C22×Dic131C2312yes—
155C22×Dic131C2312yes—
156C22×Dic131C2311yescharacteristic
157C22×Dic131C2312yes—
158C2×C4×D131C2311yescharacteristic
159C2×C4×D131C2311yescharacteristic
160C2×C4×D131C2312yes—
161C2×C4×D131C2312yes—
162C2×C4×D131C2312yes—
163C4⋊Dic131C2311yescharacteristic
164C4⋊Dic131C2312yes—
165C4⋊Dic131C2311yescharacteristic
166C4⋊Dic131C2312yes—
167C4⋊Dic131C2312yes—
168Dic131⋊C4C2312yes—
169Dic131⋊C4C2311yescharacteristic
170Dic131⋊C4C2312yes—
171Dic131⋊C4C2311yescharacteristic
172Dic131⋊C4C2312yes—
173Dic131⋊C4C2312yes—
174Dic131⋊C4C2312yes—
175Dic131⋊C4C2311yescharacteristic
176Dic131⋊C4C2312yes—
177Dic131⋊C4C2311yescharacteristic
178C22⋊Dic131C2312yes—
179C22⋊Dic131C2311yescharacteristic
180C22⋊Dic131C2312yes—
181C22⋊Dic131C2312yes—
182C22⋊Dic131C2312yes—
183C22⋊Dic131C2312yes—
184C22⋊Dic131C2312yes—
185C22⋊Dic131C2312yes—
186C22⋊Dic131C2311yescharacteristic
187C22⋊Dic131C2312yes—
188C22⋊Dic131C2311yescharacteristic
189C22⋊Dic131C2311yescharacteristic
190(C2×D131)⋊C4C2312yes—
191(C2×D131)⋊C4C2311yescharacteristic
192(C2×D131)⋊C4C2312yes—
193(C2×D131)⋊C4C2311yescharacteristic
194(C2×D131)⋊C4C2312yes—
195(C2×D131)⋊C4C2312yes—
196(C2×D131)⋊C4C2312yes—
197(C2×D131)⋊C4C2312yes—
198(C2×D131)⋊C4C2311yescharacteristic
199(C2×D131)⋊C4C2311yescharacteristic
200C4×Dic131C2311yescharacteristic
201C4×Dic131C2311yescharacteristic
202C4×Dic131C2312yes—
203C4×Dic131C2312yes—
204C4×Dic131C2311yescharacteristic
205C4×Dic131C2311yescharacteristic
206C24×C131C2312yes—
207#41×C131—42no—
208C2×Q8×C131C2311yescharacteristic
209C2×D4×C131—42no—
210C2×D4×C131C2311yescharacteristic
211C2×D4×C131C2311yescharacteristic
212C2×D4×C131C2312yes—
213C2×D4×C131C2312yes—
214C2×D4×C131C2312yes—
215C2×D4×C131C2312yes—
216C2×D4×C131C2311yescharacteristic
217C2×D4×C131C2312yes—
218C2×D4×C131C2311yescharacteristic
219C2×D4×C131C2311yescharacteristic
220C22×C4×C131C2311yescharacteristic
221C22×C4×C131C2311yescharacteristic
222C22×C4×C131C2311yescharacteristic
223C4⋊C4×C131C2311yescharacteristic
224C4⋊C4×C131C2311yescharacteristic
225C22⋊C4×C131C2312yes—
226C22⋊C4×C131C2312yes—
227C22⋊C4×C131C2312yes—
228C22⋊C4×C131C2312yes—
229C22⋊C4×C131C2312yes—
230C42×C131C2312yes—
231C22×D131—42no—
232C22×D131—42no—
233C22×D131—42no—
234C22×D131C2411yescharacteristic
235C22×D131C2412yes—
236C22×D131C2411yescharacteristic
237Dic262—22no—
238Dic262—24no—
239Dic262—41no—
240D524—22no—
241D524—42no—
242D524—41no—
243C22⋊D131—22no—
244C22⋊D131—24no—
245C22⋊D131—22no—
246C22⋊D131—42no—
247C22⋊D131—42no—
248C22⋊D131—42no—
249C22⋊D131—41no—
250C22⋊D131—42no—
251C22⋊D131—41no—
252C22⋊D131—42no—
253C22⋊D131—42no—
254C22⋊D131—42no—
255C22⋊D131—41no—
256C22⋊D131—41no—
257C22⋊D131—42no—
258C2×Dic131—24no—
259C2×Dic131—22no—
260C2×Dic131—41no—
261C2×Dic131—42no—
262C2×Dic131—42no—
263C2×Dic131—42no—
264C2×Dic131C2411yescharacteristic
265C2×Dic131C2411yescharacteristic
266C2×Dic131C2411yescharacteristic
267C2×Dic131C2411yescharacteristic
268C2×Dic131C2412yes—
269C2×Dic131C2412yes—
270C2×Dic131C2411yescharacteristic
271C2×Dic131C2412yes—
272C2×Dic131C2411yescharacteristic
273C4×D131—22no—
274C4×D131—22no—
275C4×D131—42no—
276C4×D131—42no—
277C4×D131—42no—
278C23×C131—42no—
279C23×C131—42no—
280C23×C131—42no—
281C23×C131C2411yescharacteristic
282C23×C131C2412yes—
283C23×C131C2412yes—
284C23×C131C2411yescharacteristic
285C23×C131C2411yescharacteristic
286Q8×C131—41no—
287D4×C131—22no—
288D4×C131—22no—
289D4×C131—42no—
290D4×C131—42no—
291D4×C131—42no—
292D4×C131—41no—
293D4×C131—41no—
294D4×C131—41no—
295D4×C131—42no—
296D4×C131—42no—
297C2×C4×C131—22no—
298C2×C4×C131—22no—
299C2×C4×C131—22no—
300C2×C4×C131C2411yescharacteristic
301C2×C4×C131C2412yes—
302C2×C4×C131C2412yes—
303C2×C4×C131C2411yescharacteristic
304C2×C4×C131C2411yescharacteristic
305C2×C4×C131C2411yescharacteristic
306C22×C131—21no—
307C22×C131—21no—
308C22×C131—21no—
309C22×C131—22no—
310C22×C131—22no—
311C22×C131—21no—
312C22×C131—21no—
313C22×C131—22no—
314C22×C131—22no—
315C22×C131—21no—
316C22×C131—21no—
317C22×C131—21no—
318C22×C131—22no—
319C22×C131—22no—
320C22×C131—21no—
321C22×C131—84no—
322C22×C131C2511yescharacteristic
323C2×D131—21no—
324C2×D131—21no—
325C2×D131—21no—
326C2×D131—22no—
327C2×D131—22no—
328C2×D131—21no—
329C2×D131—21no—
330C2×D131—22no—
331C2×D131—21no—
332C2×D131—84no—
333C4×C131—21no—
334C4×C131—21no—
335C4×C131—21no—
336C4×C131—22no—
337C4×C131—22no—
338C4×C131H(5,𝔽2)12yes—
339Dic131—21no—
340Dic131—21no—
341Dic131—21no—
342Dic131—22no—
343Dic131—22no—
344Dic131—22no—
345Dic131—21no—
346Dic131—21no—
347Dic131H(5,𝔽2)12yes—
348C2×C131—42no—
349C2×C131—41no—
350C2×C131—41no—
351C2×C131—42no—
352C2×C131—41no—
353C2×C131C2×H(5,𝔽2)11yescharacteristic
354C2×C131C2×H(5,𝔽2)11yescharacteristic
355C2×C131#58511yescharacteristic
356D131—41no—
357D131—42no—
358D131—41no—
359C131#354611yescharacteristic, complemented, Sylow
360#3546—1311nomaximal, Sylow
361#560—1312no—
362#560—1312no—
363#556—1311no—
364#553—1311no—
365#553—1311no—
366#550—1312no—
367#550—1311no—
368#547—1311no—
369#546—1311no—
370#546—1311no—
371#546—1312no—
372D42—1311no—
373#542—1312no—
374#538—1312no—
375#538—1312no—
376#537—1311no—
377#537—1311no—
378#535—1311no—
379#535—1312no—
380#535D13111yescharacteristic, complemented
381#532—1311no—
382#532—1311no—
383#529—1311no—
384C2×#41—1312no—
385C2×#41—1312no—
386C2×#41—1311no—
387C2×#41—1311no—
388C2×#41—1311no—
389C2×#41C2×D13111yescharacteristic, complemented
390C22×D4—1312no—
391C22×D4—1311no—
392C22×D4C2×D13111yescharacteristic
393C4⋊Q8—1311no—
394C4⋊Q8—1311no—
395#127—1311no—
396#127—1311no—
397#127—1312no—
398#127—1312no—
399#127C2×D13112yescomplemented
400#126—1312no—
401#126—1312no—
402#126—1312no—
403#126—1312no—
404#126—1312no—
405#125—1311no—
406#124—1311no—
407#124—1311no—
408#124—1311no—
409#124—1312no—
410#124—1312no—
411#124—1312no—
412#124C2×D13112yescomplemented
413#123—1312no—
414#123—1312no—
415#123—1312no—
416#123—1312no—
417#123—1312no—
418#123—1312no—
419#123—1312no—
420C22⋊Q8—1312no—
421C22⋊Q8—1311no—
422C22⋊Q8—1311no—
423C22⋊Q8—1311no—
424C22⋊Q8—1312no—
425C22⋊Q8—1312no—
426#121—1311no—
427#121—1311no—
428#121—1312no—
429#121—1312no—
430#121—1312no—
431#121—1311no—
432#121—1312no—
433#121—1311no—
434#121—1311no—
435#121—1312no—
436#121—1311no—
437#121—1312no—
438#121—1312no—
439#121—1312no—
440#121—1312no—
441#121—1312no—
442#121—1312no—
443#121—1311no—
444#121—1311no—
445#121—1311no—
446#121—1312no—
447#121—1312no—
448#121—1312no—
449#121C2×D13111yescharacteristic
450#121C2×D13111yescharacteristic
451#121C2×D13111yescharacteristic, complemented
452#121C2×D13111yescharacteristic, complemented
453#120—1312no—
454#120—1312no—
455#120—1312no—
456#120—1312no—
457#120—1312no—
458#120—1312no—
459#120C2×D13112yescomplemented
460#120C2×D13112yescomplemented
461C4×Q8—1311no—
462C4×Q8—1312no—
463C4×D4—1311no—
464C4×D4—1312no—
465C4×D4—1311no—
466C4×D4—1312no—
467C4×D4—1311no—
468C4×D4—1311no—
469C4×D4—1311no—
470C4×D4—1311no—
471C4×D4—1311no—
472C4×D4—1312no—
473C4×D4—1312no—
474C4×D4—1312no—
475#117—1311no—
476#117—1312no—
477#117C2×D13111yescharacteristic, complemented
478C2×C4⋊C4—1311no—
479C2×C4⋊C4—1311no—
480C2×C22⋊C4—1312no—
481C2×C22⋊C4—1312no—
482C2×C42—1311no—
483C24—1312no—
484C24C22×D13112yes—
485#41—42no—
486#41—5242no—
487#41—5242no—
488#41—5242no—
489#41—5244no—
490#41—5244no—
491C2×Q8—1311no—
492C2×Q8—1312no—
493C2×Q8—1311no—
494C2×Q8C22×D13111yescharacteristic
495C2×D4—42no—
496C2×D4—5242no—
497C2×D4—5244no—
498C2×D4—1311no—
499C2×D4—1312no—
500C2×D4—1311no—
501C2×D4—1311no—
502C2×D4—1312no—
503C2×D4—1311no—
504C2×D4—1311no—
505C2×D4—1312no—
506C2×D4—1312no—
507C2×D4—1312no—
508C2×D4—1312no—
509C2×D4—1312no—
510C2×D4—1312no—
511C2×D4—1312no—
512C2×D4—1311no—
513C2×D4—1311no—
514C2×D4—1312no—
515C2×D4—1311no—
516C2×D4C22×D13111yescharacteristic
517C2×D4C22×D13111yescharacteristic
518C2×D4C22×D13112yes—
519C2×D4C22×D13112yes—
520C2×D4C22×D13112yes—
521C2×D4C22×D13112yes—
522C2×D4C22×D13111yescharacteristic
523C2×D4C22×D13111yescharacteristic
524C2×D4C22×D13112yes—
525C2×D4C22×D13111yescharacteristic
526C22×C4—1311no—
527C22×C4—1312no—
528C22×C4—1311no—
529C22×C4—1311no—
530C22×C4—1311no—
531C22×C4—1312no—
532C22×C4—1312no—
533C22×C4—1312no—
534C22×C4—1312no—
535C22×C4—1312no—
536C22×C4—1312no—
537C22×C4C22×D13111yescharacteristic
538C22×C4C22×D13111yescharacteristic
539C22×C4C22×D13111yescharacteristic
540C4⋊C4—1312no—
541C4⋊C4—1312no—
542C4⋊C4—1312no—
543C4⋊C4—1311no—
544C4⋊C4—1311no—
545C4⋊C4—1311no—
546C4⋊C4—1312no—
547C4⋊C4—1311no—
548C4⋊C4—1312no—
549C4⋊C4—1312no—
550C4⋊C4—1311no—
551C4⋊C4—1311no—
552C4⋊C4—1312no—
553C4⋊C4—1312no—
554C4⋊C4—1312no—
555C4⋊C4C22×D13111yescharacteristic
556C4⋊C4C22×D13111yescharacteristic
557C22⋊C4—1312no—
558C22⋊C4—1311no—
559C22⋊C4—1312no—
560C22⋊C4—1312no—
561C22⋊C4—1312no—
562C22⋊C4—1311no—
563C22⋊C4—1311no—
564C22⋊C4—1312no—
565C22⋊C4—1312no—
566C22⋊C4—1312no—
567C22⋊C4—1312no—
568C22⋊C4—1311no—
569C22⋊C4—1311no—
570C22⋊C4—1312no—
571C22⋊C4—1312no—
572C22⋊C4—1311no—
573C22⋊C4—1311no—
574C22⋊C4—1312no—
575C22⋊C4—1312no—
576C22⋊C4—1312no—
577C22⋊C4—1312no—
578C22⋊C4—1311no—
579C22⋊C4C22×D13112yes—
580C22⋊C4C22×D13112yes—
581C22⋊C4C22×D13112yes—
582C22⋊C4C22×D13112yes—
583C22⋊C4C22×D13112yes—
584C42—1311no—
585C42—1311no—
586C42—1311no—
587C42—1311no—
588C42—1312no—
589C42—1312no—
590C42C22×D13112yes—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—5242no—
595C23—5242no—
596C23—5242no—
597C23—1311no—
598C23—1312no—
599C23—1311no—
600C23C23×D13112yes—
601C23C23×D13111yescharacteristic
602C23C23×D13112yes—
603C23C23×D13111yescharacteristic
604C23C23×D13111yescharacteristic
605Q8—41no—
606Q8—2624no—
607Q8—2622no—
608Q8—5241no—
609D4—22no—
610D4—22no—
611D4—42no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—42no—
616D4—42no—
617D4—42no—
618D4—42no—
619D4—2622no—
620D4—2624no—
621D4—2622no—
622D4—2622no—
623D4—5241no—
624D4—5242no—
625D4—5242no—
626D4—5242no—
627D4—5242no—
628D4—5242no—
629D4—5242no—
630D4—5241no—
631D4—5241no—
632D4—5242no—
633D4—5242no—
634D4—5241no—
635D4—5242no—
636D4—5241no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—2624no—
641C2×C4—2622no—
642C2×C4—2622no—
643C2×C4—2622no—
644C2×C4—5242no—
645C2×C4—5242no—
646C2×C4—5242no—
647C2×C4—5242no—
648C2×C4—5242no—
649C2×C4—5242no—
650C2×C4—5241no—
651C2×C4—1311no—
652C2×C4—1311no—
653C2×C4—1311no—
654C2×C4—1311no—
655C2×C4—1312no—
656C2×C4—1312no—
657C2×C4—1311no—
658C2×C4—1312no—
659C2×C4—1311no—
660C2×C4C23×D13112yes—
661C2×C4C23×D13111yescharacteristic
662C2×C4C23×D13111yescharacteristic
663C2×C4C23×D13112yes—
664C2×C4C23×D13111yescharacteristic
665C2×C4C23×D13111yescharacteristic
666C22—21no—
667C22—22no—
668C22—21no—
669C22—22no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—22no—
675C22—22no—
676C22—21no—
677C22—21no—
678C22—22no—
679C22—22no—
680C22—21no—
681C22—2621no—
682C22—2622no—
683C22—2621no—
684C22—2621no—
685C22—2621no—
686C22—2622no—
687C22—2621no—
688C22—2622no—
689C22—2621no—
690C22—84no—
691C22—10484no—
692C22C24×D13111yescharacteristic
693C4—22no—
694C4—21no—
695C4—21no—
696C4—21no—
697C4—22no—
698C4—2621no—
699C4—2622no—
700C4—2622no—
701C4—2621no—
702C4—2621no—
703C4—2622no—
704C4—2621no—
705C4—2621no—
706C4—1312no—
707C4#1686229112yes—
708C2—41no—
709C2—42no—
710C2—42no—
711C2—41no—
712C2—41no—
713C2—5241no—
714C2—5242no—
715C2—5241no—
716C2H(5,𝔽2)×D13111yescharacteristic
717C2C2×#1686229111yescharacteristic
718C2#2255414711yescharacteristic
subgroupG/H
center, FrattiniC22C24×D131
commutator, socle, cosocleC22×C131C25
Fitting#535×C131C2
hypercenter#535D131
hypocenterC131#3546
LCSG ▷ C22×C131 ▷ C131
UCSC1 ◁ C22 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #22554051C2semidirect
2. #22554049C2semidirect
3. #22554030C2semidirect
4. #22554014C2semidirect
5. #22554006C2semidirect
6. #22553982C2semidirect
7. #22553980C2semidirect
8. #22553962C2semidirect
9. #22553959C2semidirect
10. #22553956C2semidirect
11. #22553949C2semidirect
12. D4×C22⋊D131C2semidirect
13. #22553926C2semidirect
14. #22553897C2semidirect
15. #22553896C2semidirect
16. #22553891C2semidirect
17. #22553890C2semidirect
18. #22553878C2semidirect
19. #22553877C2semidirect
20. #22553858C2semidirect
21. #22553857C2semidirect
22. #22553843C2semidirect
23. #535×C131C2semidirect
24. C2×#14523513C22semidirect
25. C2×#14523513C22semidirect
26. C2×#14523512C22semidirect
27. C2×#14523512C22semidirect
28. C2×#14523512C22semidirect
31. #16862245C22semidirect
32. #16862244C22semidirect
35. #16862242C22semidirect
36. #16862242C22semidirect
37. #16862240C22semidirect
38. #16862240C22semidirect
39. #16862239C22semidirect
40. #16862239C22semidirect
41. #16862239C22semidirect
42. #16862237C22semidirect
43. #16862235C22semidirect
45. #16862233C22semidirect
47. #16862232C22semidirect
48. #16862232C22semidirect
49. #16862230C22semidirect
50. #16862228C22semidirect
51. #16862228C22semidirect
52. #16862228C22semidirect
53. #16862227C22semidirect
54. #16862227C22semidirect
55. #16862227C22semidirect
56. #16862226C22semidirect
57. #16862225C22semidirect
58. #16862225C22semidirect
59. #16862223C22semidirect
60. #16862223C22semidirect
61. #16862222C22semidirect
62. #16862221C22semidirect
64. #16862220C22semidirect
65. #16862219C22semidirect
66. #16862219C22semidirect
67. #16862219C22semidirect
70. #16862218C22semidirect
71. #16862218C22semidirect
72. #16862218C22semidirect
73. #16862218C22semidirect
74. #16862218C22semidirect
75. #16862218C22semidirect
76. #16862218C22semidirect
77. #16862218C22semidirect
78. #16862218C22semidirect
79. #16862218C22semidirect
82. #16862217C22semidirect
83. #16862217C22semidirect
84. #16862217C22semidirect
85. #16862216C22semidirect
87. #16862215C22semidirect
89. #16862214C22semidirect
90. #16862214C22semidirect
91. C4×Dic262C22semidirect
92. #16862211C22semidirect
93. C4×D524C22semidirect
95. D4×Dic131C22semidirect
96. D4×Dic131C22semidirect
97. D4×Dic131C22semidirect
98. #16862208C22semidirect
100. C4×C22⋊D131C22semidirect
101. C4×C22⋊D131C22semidirect
102. C4×C22⋊D131C22semidirect
103. (C22⋊D131)⋊C4C22semidirect
104. (C22⋊D131)⋊C4C22semidirect
105. #16862204C22semidirect
106. #16862202C22semidirect
107. C2×C4⋊Dic131C22semidirect
108. C4⋊C4×D131C22semidirect
109. C2×C22⋊Dic131C22semidirect
110. C22⋊C4×D131C22semidirect
111. C2×C4×Dic131C22semidirect
112. C2×#41×C131C22semidirect
114. #127×C131C22semidirect
115. #124×C131C22semidirect
118. #121×C131C22semidirect
119. #121×C131C22semidirect
120. #120×C131C22semidirect
121. #120×C131C22semidirect
122. #117×C131C22semidirect
359. C131#3546semidirect
380. #535D131semidirect
389. C2×#41C2×D131semidirect
399. #127C2×D131semidirect
412. #124C2×D131semidirect
451. #121C2×D131semidirect
452. #121C2×D131semidirect
459. #120C2×D131semidirect
460. #120C2×D131semidirect
477. #117C2×D131semidirect

Maximal subgroups

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

subgroupindex
#225540512
#225540492
#225540302
#225540142
#225540062
#225539822
#225539802
#225539622
#225539592
#225539562
#225539492
D4×C22⋊D1312
#225539262
#225538972
#225538962
#225538912
#225538902
#225538782
#225538772
#225538582
#225538572
#225538432
#535×C1312
#3546131