Finite Group Databasebeta

← #30680325

Subgroups — #30680325

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#22554052C212yesmaximal, complemented
2#22554051C212yesmaximal, complemented
3#22554033C211yesmaximal, characteristic, complemented
4#22554012C211yesmaximal, characteristic, complemented
5#22554008C211yesmaximal, characteristic, complemented
6#22553981C211yesmaximal, characteristic, complemented
7#22553980C212yesmaximal, complemented
8#22553962C211yesmaximal, characteristic, complemented
9#22553955C211yesmaximal, characteristic, complemented
10#22553952C212yesmaximal, complemented
11D4×C22⋊D131C211yesmaximal, characteristic, complemented
12#22553930C212yesmaximal, complemented
13#22553900C212yesmaximal, complemented
14#22553894C212yesmaximal, complemented
15#22553892C211yesmaximal, characteristic, complemented
16#22553890C211yesmaximal, characteristic, complemented
17#22553879C211yesmaximal, characteristic, complemented
18#22553878C211yesmaximal, characteristic, complemented
19#22553877C212yesmaximal, complemented
20#22553859C211yesmaximal, characteristic, complemented
21#22553859C211yesmaximal, characteristic, complemented
22#22553841C211yesmaximal, characteristic, complemented
23#546×C131C211yesmaximal, characteristic, complemented
24C2×#14523514C2211yescharacteristic, complemented
25C2×#14523513C2211yescharacteristic, complemented
26C2×#14523513C2211yescharacteristic, complemented
27C2×#14523513C2212yescomplemented
28C2×#14523512C2212yescomplemented
29C22×C22⋊D131C2212yes—
30C2×D4×D131C2211yescharacteristic
31#16862245C2211yescharacteristic, complemented
32#16862245C2211yescharacteristic, complemented
33#16862242C2211yescharacteristic
34#16862242C2211yescharacteristic
35#16862242C2212yescomplemented
36#16862242C2212yescomplemented
37#16862242C2212yescomplemented
38#16862241C2212yescomplemented
39#16862241C2212yescomplemented
40#16862239C2212yescomplemented
41#16862239C2212yescomplemented
42#16862239C2212yescomplemented
43#16862238C2211yescharacteristic, complemented
44#16862233C2212yescomplemented
45#16862232C2212yes—
46#16862232C2212yescomplemented
47#16862232C2211yescharacteristic, complemented
48#16862232C2211yescharacteristic, complemented
49#16862232C2212yescomplemented
50#16862229C2212yescomplemented
51#16862228C2212yescomplemented
52#16862228C2212yescomplemented
53#16862228C2212yescomplemented
54#16862228C2212yescomplemented
55#16862227C2212yescomplemented
56#16862225C2212yescomplemented
57#16862224C2212yescomplemented
58#16862223C2212yescomplemented
59#16862222C2211yescharacteristic, complemented
60#16862222C2211yescharacteristic, complemented
61#16862221C2211yescharacteristic, complemented
62#16862221C2211yescharacteristic, complemented
63#16862221C2212yescomplemented
64#16862220C2211yescharacteristic
65#16862220C2211yescharacteristic, complemented
66#16862220C2212yescomplemented
67#16862220C2212yescomplemented
68#16862219C2211yescharacteristic
69#16862219C2211yescharacteristic, complemented
70#16862219C2212yescomplemented
71#16862219C2212yescomplemented
72#16862219C2212yescomplemented
73#16862219C2212yescomplemented
74#16862219C2212yescomplemented
75#16862218C2212yes—
76#16862218C2212yescomplemented
77#16862218C2212yescomplemented
78#16862218C2212yescomplemented
79#16862217C2211yescharacteristic
80#16862217C2211yescharacteristic
81#16862217C2211yescharacteristic
82#16862217C2211yescharacteristic, complemented
83#16862217C2211yescharacteristic, complemented
84#16862217C2211yescharacteristic, complemented
85#16862217C2212yescomplemented
86#16862216C2212yescomplemented
87#16862216C2212yescomplemented
88#16862215C2212yes—
89#16862215C2212yescomplemented
90#16862215C2212yescomplemented
91#16862214C2212yes—
92#16862214C2212yescomplemented
93Q8×Dic131C2211yescharacteristic, complemented
94#16862211C2212yescomplemented
95C4×D524C2211yescharacteristic, complemented
96C4×D524C2211yescharacteristic, complemented
97D4×Dic131C2211yescharacteristic
98C4×C22⋊D131C2211yescharacteristic
99C4×C22⋊D131C2212yescomplemented
100C4×C22⋊D131C2211yescharacteristic, complemented
101C4×C22⋊D131C2212yescomplemented
102C4×C22⋊D131C2212yescomplemented
103(C22⋊D131)⋊C4C2212yescomplemented
104(C22⋊D131)⋊C4C2212yescomplemented
105#16862205C2211yescharacteristic, complemented
106#16862204C2211yescharacteristic, complemented
107#16862202C2212yescomplemented
108C2×C4⋊Dic131C2211yescharacteristic, complemented
109C4⋊C4×D131C2211yescharacteristic, complemented
110C22⋊C4×D131C2212yescomplemented
111C42×D131C2211yescharacteristic, complemented
112C2×#41×C131C2211yescharacteristic, complemented
113C22×D4×C131C2211yescharacteristic
114#124×C131C2211yescharacteristic
115#123×C131C2212yescomplemented
116C22⋊Q8×C131C2211yescharacteristic, complemented
117#121×C131C2211yescharacteristic
118#121×C131C2212yescomplemented
119#120×C131C2212yescomplemented
120C4×D4×C131C2211yescharacteristic, complemented
121C4×D4×C131C2211yescharacteristic, complemented
122C2×C22⋊C4×C131C2212yescomplemented
123C23×D131C2312yes—
124#14523514—42no—
125#14523513—42no—
126#14523513—42no—
127#14523513—44no—
128#14523512—44no—
129C2×Dic262C2312yes—
130C2×Dic262C2311yescharacteristic
131C2×Dic262C2311yescharacteristic
132C2×D524C2311yescharacteristic
133C2×D524C2311yescharacteristic
134C2×D524C2311yescharacteristic
135C2×D524C2312yes—
136C2×D524C2312yes—
137C2×D524C2311yescharacteristic
138C2×C22⋊D131—44no—
139C2×C22⋊D131C2312yes—
140C2×C22⋊D131C2311yescharacteristic
141C2×C22⋊D131C2311yescharacteristic
142C2×C22⋊D131C2312yes—
143C2×C22⋊D131C2312yes—
144C2×C22⋊D131C2311yescharacteristic
145C2×C22⋊D131C2312yes—
146C2×C22⋊D131C2312yes—
147C2×C22⋊D131C2312yes—
148C2×C22⋊D131C2311yescharacteristic
149C2×C22⋊D131C2311yescharacteristic
150C2×C22⋊D131C2312yes—
151C2×C22⋊D131C2312yes—
152C2×C22⋊D131C2312yes—
153C2×C22⋊D131C2312yes—
154C2×C22⋊D131C2311yescharacteristic
155D4×D131—42no—
156C22×Dic131C2312yes—
157C22×Dic131C2312yes—
158C2×C4×D131C2311yescharacteristic
159C2×C4×D131C2311yescharacteristic
160C2×C4×D131C2311yescharacteristic
161C2×C4×D131C2311yescharacteristic
162C2×C4×D131C2312yes—
163C2×C4×D131C2311yescharacteristic
164C2×C4×D131C2312yes—
165C2×C4×D131C2312yes—
166C4⋊Dic131C2311yescharacteristic
167C4⋊Dic131C2311yescharacteristic
168C4⋊Dic131C2311yescharacteristic
169C4⋊Dic131C2311yescharacteristic
170C4⋊Dic131C2312yes—
171C4⋊Dic131C2312yes—
172Dic131⋊C4C2311yescharacteristic
173Dic131⋊C4C2312yes—
174Dic131⋊C4C2312yes—
175Dic131⋊C4C2312yes—
176Dic131⋊C4C2311yescharacteristic
177Dic131⋊C4C2312yes—
178Dic131⋊C4C2312yes—
179Dic131⋊C4C2312yes—
180C22⋊Dic131C2312yes—
181C22⋊Dic131C2312yes—
182C22⋊Dic131C2311yescharacteristic
183C22⋊Dic131C2312yes—
184C22⋊Dic131C2312yes—
185C22⋊Dic131C2312yes—
186C22⋊Dic131C2312yes—
187C22⋊Dic131C2312yes—
188C22⋊Dic131C2311yescharacteristic
189(C2×D131)⋊C4C2312yes—
190(C2×D131)⋊C4C2311yescharacteristic
191(C2×D131)⋊C4C2311yescharacteristic
192(C2×D131)⋊C4C2311yescharacteristic
193(C2×D131)⋊C4C2312yes—
194(C2×D131)⋊C4C2312yes—
195(C2×D131)⋊C4C2312yes—
196(C2×D131)⋊C4C2312yes—
197(C2×D131)⋊C4C2312yes—
198(C2×D131)⋊C4C2312yes—
199(C2×D131)⋊C4C2311yescharacteristic
200C4×Dic131C2311yescharacteristic
201C4×Dic131C2312yes—
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×C131C2311yescharacteristic
215C2×D4×C131C2312yes—
216C22×C4×C131C2311yescharacteristic
217C22×C4×C131C2311yescharacteristic
218C22×C4×C131C2312yes—
219C22×C4×C131C2312yes—
220C4⋊C4×C131C2312yes—
221C4⋊C4×C131C2311yescharacteristic
222C4⋊C4×C131C2311yescharacteristic
223C22⋊C4×C131C2312yes—
224C22⋊C4×C131C2312yes—
225C22⋊C4×C131C2311yescharacteristic
226C22⋊C4×C131C2312yes—
227C22⋊C4×C131C2312yes—
228C22⋊C4×C131C2311yescharacteristic
229C22⋊C4×C131C2312yes—
230C42×C131C2311yescharacteristic
231C22×D131—42no—
232C22×D131—42no—
233C22×D131—42no—
234C22×D131C2411yescharacteristic
235C22×D131C2412yes—
236C22×D131C2411yescharacteristic
237C22×D131C2411yescharacteristic
238Dic262—24no—
239Dic262—41no—
240Dic262—41no—
241D524—22no—
242D524—41no—
243D524—41no—
244D524—41no—
245D524—42no—
246D524—42no—
247C22⋊D131—22no—
248C22⋊D131—24no—
249C22⋊D131—22no—
250C22⋊D131—42no—
251C22⋊D131—42no—
252C22⋊D131—42no—
253C22⋊D131—42no—
254C22⋊D131—42no—
255C22⋊D131—42no—
256C22⋊D131—42no—
257C22⋊D131—42no—
258C22⋊D131—41no—
259C22⋊D131—41no—
260C22⋊D131—41no—
261C22⋊D131—41no—
262C22⋊D131—42no—
263C2×Dic131—24no—
264C2×Dic131—42no—
265C2×Dic131C2412yes—
266C2×Dic131C2411yescharacteristic
267C2×Dic131C2411yescharacteristic
268C2×Dic131C2411yescharacteristic
269C2×Dic131C2412yes—
270C2×Dic131C2412yes—
271C2×Dic131C2411yescharacteristic
272C2×Dic131C2411yescharacteristic
273C4×D131—22no—
274C4×D131—22no—
275C4×D131—22no—
276C4×D131—22no—
277C4×D131—41no—
278C4×D131—42no—
279C4×D131—42no—
280C4×D131—42no—
281C23×C131—42no—
282C23×C131—42no—
283C23×C131—42no—
284C23×C131C2411yescharacteristic
285C23×C131C2412yes—
286C23×C131C2412yes—
287C23×C131C2411yescharacteristic
288Q8×C131—22no—
289D4×C131—22no—
290D4×C131—22no—
291D4×C131—42no—
292D4×C131—41no—
293D4×C131—42no—
294D4×C131—42no—
295C2×C4×C131—22no—
296C2×C4×C131—22no—
297C2×C4×C131—42no—
298C2×C4×C131—42no—
299C2×C4×C131C2411yescharacteristic
300C2×C4×C131C2411yescharacteristic
301C2×C4×C131C2412yes—
302C2×C4×C131C2411yescharacteristic
303C2×C4×C131C2412yes—
304C2×C4×C131C2411yescharacteristic
305C2×C4×C131C2411yescharacteristic
306C22×C131—21no—
307C22×C131—21no—
308C22×C131—22no—
309C22×C131—22no—
310C22×C131—22no—
311C22×C131—21no—
312C22×C131—22no—
313C22×C131—21no—
314C22×C131—21no—
315C22×C131—21no—
316C22×C131—22no—
317C22×C131—22no—
318C22×C131—84no—
319C22×C131C2511yescharacteristic
320C2×D131—21no—
321C2×D131—21no—
322C2×D131—21no—
323C2×D131—21no—
324C2×D131—21no—
325C2×D131—22no—
326C2×D131—22no—
327C2×D131—21no—
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×C131—21no—
339C4×C131H(5,𝔽2)12yes—
340Dic131—21no—
341Dic131—21no—
342Dic131—21no—
343Dic131—22no—
344Dic131—22no—
345Dic131—21no—
346Dic131—22no—
347Dic131H(5,𝔽2)12yes—
348C2×C131—42no—
349C2×C131—41no—
350C2×C131—42no—
351C2×C131—41no—
352C2×C131C2×H(5,𝔽2)11yescharacteristic
353C2×C131C2×H(5,𝔽2)11yescharacteristic
354C2×C131#58511yescharacteristic
355D131—41no—
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—1311no—
367#550—1312no—
368#547—1311no—
369#546—1311no—
370#546—1312no—
371#546D13111yescharacteristic, complemented
372D42—1311no—
373#542—1312no—
374#538—1312no—
375#538—1312no—
376#537—1311no—
377#537—1311no—
378#535—1311no—
379#535—1311no—
380#535—1312no—
381#532—1311no—
382#532—1311no—
383#529—1311no—
384C2×#41—1311no—
385C2×#41—1312no—
386C2×#41—1311no—
387C2×#41—1311no—
388C2×#41—1312no—
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#127—1312no—
400#126—1312no—
401#126—1312no—
402#126—1312no—
403#126—1312no—
404#126—1312no—
405#125—1311no—
406#124—1312no—
407#124—1312no—
408#124—1311no—
409#124—1311no—
410#124—1312no—
411#124—1312no—
412#124C2×D13111yescharacteristic
413#123—1312no—
414#123—1312no—
415#123—1312no—
416#123—1312no—
417#123—1312no—
418#123—1312no—
419#123C2×D13112yescomplemented
420C22⋊Q8—1311no—
421C22⋊Q8—1311no—
422C22⋊Q8—1312no—
423C22⋊Q8—1312no—
424C22⋊Q8—1312no—
425C22⋊Q8C2×D13111yescharacteristic, complemented
426#121—1311no—
427#121—1311no—
428#121—1311no—
429#121—1311no—
430#121—1311no—
431#121—1311no—
432#121—1312no—
433#121—1312no—
434#121—1312no—
435#121—1312no—
436#121—1312no—
437#121—1311no—
438#121—1311no—
439#121—1312no—
440#121—1312no—
441#121—1311no—
442#121—1311no—
443#121—1312no—
444#121—1311no—
445#121—1311no—
446#121—1312no—
447#121—1312no—
448#121—1312no—
449#121—1312no—
450#121—1312no—
451#121C2×D13111yescharacteristic
452#121C2×D13112yescomplemented
453#120—1312no—
454#120—1312no—
455#120—1312no—
456#120—1312no—
457#120—1312no—
458#120—1312no—
459#120—1312no—
460#120C2×D13112yescomplemented
461C4×Q8—1311no—
462C4×Q8—1312no—
463C4×D4—1311no—
464C4×D4—1312no—
465C4×D4—1311no—
466C4×D4—1311no—
467C4×D4—1312no—
468C4×D4—1312no—
469C4×D4—1312no—
470C4×D4—1312no—
471C4×D4—1311no—
472C4×D4—1311no—
473C4×D4C2×D13111yescharacteristic, complemented
474C4×D4C2×D13111yescharacteristic, complemented
475#117—1311no—
476#117—1311no—
477#117—1312no—
478C2×C4⋊C4—1311no—
479C2×C4⋊C4—1311no—
480C2×C22⋊C4—1312no—
481C2×C22⋊C4C2×D13112yescomplemented
482C2×C42—1311no—
483C24—1312no—
484C24C22×D13112yes—
485#41—42no—
486#41—5242no—
487#41—5242no—
488#41—5244no—
489#41—5244no—
490#41—5242no—
491C2×Q8—1312no—
492C2×Q8—1311no—
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—1312no—
502C2×D4—1312no—
503C2×D4—1312no—
504C2×D4—1312no—
505C2×D4—1311no—
506C2×D4—1312no—
507C2×D4—1311no—
508C2×D4—1311no—
509C2×D4—1312no—
510C2×D4—1312no—
511C2×D4—1312no—
512C2×D4—1312no—
513C2×D4—1311no—
514C2×D4—1311no—
515C2×D4—1311no—
516C2×D4—1311no—
517C2×D4—1312no—
518C2×D4—1312no—
519C2×D4—1311no—
520C2×D4C22×D13111yescharacteristic
521C2×D4C22×D13111yescharacteristic
522C2×D4C22×D13111yescharacteristic
523C2×D4C22×D13112yes—
524C2×D4C22×D13112yes—
525C2×D4C22×D13112yes—
526C22×C4—1312no—
527C22×C4—1311no—
528C22×C4—1311no—
529C22×C4—1311no—
530C22×C4—1311no—
531C22×C4—1312no—
532C22×C4—1311no—
533C22×C4—1312no—
534C22×C4—1312no—
535C22×C4—1312no—
536C22×C4C22×D13111yescharacteristic
537C22×C4C22×D13111yescharacteristic
538C22×C4C22×D13112yes—
539C22×C4C22×D13112yes—
540C4⋊C4—1312no—
541C4⋊C4—1312no—
542C4⋊C4—1312no—
543C4⋊C4—1311no—
544C4⋊C4—1312no—
545C4⋊C4—1311no—
546C4⋊C4—1312no—
547C4⋊C4—1312no—
548C4⋊C4—1311no—
549C4⋊C4—1311no—
550C4⋊C4—1312no—
551C4⋊C4—1311no—
552C4⋊C4—1311no—
553C4⋊C4—1312no—
554C4⋊C4C22×D13111yescharacteristic
555C4⋊C4C22×D13111yescharacteristic
556C4⋊C4C22×D13112yes—
557C22⋊C4—1312no—
558C22⋊C4—1312no—
559C22⋊C4—1312no—
560C22⋊C4—1311no—
561C22⋊C4—1312no—
562C22⋊C4—1312no—
563C22⋊C4—1312no—
564C22⋊C4—1312no—
565C22⋊C4—1311no—
566C22⋊C4—1311no—
567C22⋊C4—1312no—
568C22⋊C4—1312no—
569C22⋊C4—1311no—
570C22⋊C4—1311no—
571C22⋊C4—1312no—
572C22⋊C4—1312no—
573C22⋊C4—1312no—
574C22⋊C4—1312no—
575C22⋊C4—1312no—
576C22⋊C4—1311no—
577C22⋊C4C22×D13112yes—
578C22⋊C4C22×D13111yescharacteristic
579C22⋊C4C22×D13112yes—
580C22⋊C4C22×D13112yes—
581C22⋊C4C22×D13112yes—
582C22⋊C4C22×D13111yescharacteristic
583C22⋊C4C22×D13112yes—
584C42—1311no—
585C42—1311no—
586C42—1311no—
587C42—1312no—
588C42—1312no—
589C42—1312no—
590C42C22×D13111yescharacteristic
591C23—42no—
592C23—42no—
593C23—42no—
594C23—5242no—
595C23—5242no—
596C23—5242no—
597C23—1311no—
598C23—1312no—
599C23—1311no—
600C23—1311no—
601C23C23×D13112yes—
602C23C23×D13111yescharacteristic
603C23C23×D13112yes—
604C23C23×D13111yescharacteristic
605Q8—22no—
606Q8—2624no—
607Q8—5241no—
608Q8—5241no—
609D4—22no—
610D4—22no—
611D4—42no—
612D4—42no—
613D4—42no—
614D4—41no—
615D4—2622no—
616D4—2624no—
617D4—2622no—
618D4—2622no—
619D4—5242no—
620D4—5241no—
621D4—5241no—
622D4—5242no—
623D4—5241no—
624D4—5242no—
625D4—5242no—
626D4—5242no—
627D4—5242no—
628D4—5242no—
629D4—5241no—
630D4—5241no—
631D4—5241no—
632D4—5241no—
633D4—5242no—
634D4—5242no—
635D4—5242no—
636D4—5242no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—2622no—
642C2×C4—2624no—
643C2×C4—2622no—
644C2×C4—2622no—
645C2×C4—2622no—
646C2×C4—5242no—
647C2×C4—5242no—
648C2×C4—5242no—
649C2×C4—5241no—
650C2×C4—5242no—
651C2×C4—1312no—
652C2×C4—1311no—
653C2×C4—1311no—
654C2×C4—1311no—
655C2×C4—1312no—
656C2×C4—1311no—
657C2×C4—1312no—
658C2×C4—1311no—
659C2×C4C23×D13111yescharacteristic
660C2×C4C23×D13111yescharacteristic
661C2×C4C23×D13111yescharacteristic
662C2×C4C23×D13112yes—
663C2×C4C23×D13112yes—
664C2×C4C23×D13111yescharacteristic
665C2×C4C23×D13111yescharacteristic
666C22—22no—
667C22—22no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—22no—
673C22—22no—
674C22—21no—
675C22—21no—
676C22—22no—
677C22—22no—
678C22—2621no—
679C22—2621no—
680C22—2622no—
681C22—2621no—
682C22—2621no—
683C22—2621no—
684C22—2621no—
685C22—2622no—
686C22—2621no—
687C22—2621no—
688C22—2622no—
689C22—2621no—
690C22—84no—
691C22—10484no—
692C22C24×D13111yescharacteristic
693C4—21no—
694C4—22no—
695C4—21no—
696C4—21no—
697C4—22no—
698C4—21no—
699C4—2622no—
700C4—2622no—
701C4—2621no—
702C4—2621no—
703C4—2621no—
704C4—2621no—
705C4—2622no—
706C4—1312no—
707C4#1686229112yes—
708C2—41no—
709C2—42no—
710C2—42no—
711C2—41no—
712C2—5241no—
713C2—5242no—
714C2—5241no—
715C2—5241no—
716C2H(5,𝔽2)×D13111yescharacteristic
717C2C2×#1686229111yescharacteristic
718C2#2255414811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D131
commutator, socle, cosocleC22×C131C25
Fitting#546×C131C2
hypercenter#546D131
hypocenterC131#3546
LCSG ▷ C22×C131 ▷ C131
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #22554052C2semidirect
2. #22554051C2semidirect
3. #22554033C2semidirect
4. #22554012C2semidirect
5. #22554008C2semidirect
6. #22553981C2semidirect
7. #22553980C2semidirect
8. #22553962C2semidirect
9. #22553955C2semidirect
10. #22553952C2semidirect
11. D4×C22⋊D131C2semidirect
12. #22553930C2semidirect
13. #22553900C2semidirect
14. #22553894C2semidirect
15. #22553892C2semidirect
16. #22553890C2semidirect
17. #22553879C2semidirect
18. #22553878C2semidirect
19. #22553877C2semidirect
20. #22553859C2semidirect
21. #22553859C2semidirect
22. #22553841C2semidirect
23. #546×C131C2semidirect
24. C2×#14523514C22semidirect
25. C2×#14523513C22semidirect
26. C2×#14523513C22semidirect
27. C2×#14523513C22semidirect
28. C2×#14523512C22semidirect
31. #16862245C22semidirect
32. #16862245C22semidirect
35. #16862242C22semidirect
36. #16862242C22semidirect
37. #16862242C22semidirect
38. #16862241C22semidirect
39. #16862241C22semidirect
40. #16862239C22semidirect
41. #16862239C22semidirect
42. #16862239C22semidirect
43. #16862238C22semidirect
44. #16862233C22semidirect
46. #16862232C22semidirect
47. #16862232C22semidirect
48. #16862232C22semidirect
49. #16862232C22semidirect
50. #16862229C22semidirect
51. #16862228C22semidirect
52. #16862228C22semidirect
53. #16862228C22semidirect
54. #16862228C22semidirect
55. #16862227C22semidirect
56. #16862225C22semidirect
57. #16862224C22semidirect
58. #16862223C22semidirect
59. #16862222C22semidirect
60. #16862222C22semidirect
61. #16862221C22semidirect
62. #16862221C22semidirect
63. #16862221C22semidirect
65. #16862220C22semidirect
66. #16862220C22semidirect
67. #16862220C22semidirect
69. #16862219C22semidirect
70. #16862219C22semidirect
71. #16862219C22semidirect
72. #16862219C22semidirect
73. #16862219C22semidirect
74. #16862219C22semidirect
76. #16862218C22semidirect
77. #16862218C22semidirect
78. #16862218C22semidirect
82. #16862217C22semidirect
83. #16862217C22semidirect
84. #16862217C22semidirect
85. #16862217C22semidirect
86. #16862216C22semidirect
87. #16862216C22semidirect
89. #16862215C22semidirect
90. #16862215C22semidirect
92. #16862214C22semidirect
93. Q8×Dic131C22semidirect
94. #16862211C22semidirect
95. C4×D524C22semidirect
96. C4×D524C22semidirect
99. C4×C22⋊D131C22semidirect
100. C4×C22⋊D131C22semidirect
101. C4×C22⋊D131C22semidirect
102. C4×C22⋊D131C22semidirect
103. (C22⋊D131)⋊C4C22semidirect
104. (C22⋊D131)⋊C4C22semidirect
105. #16862205C22semidirect
106. #16862204C22semidirect
107. #16862202C22semidirect
108. C2×C4⋊Dic131C22semidirect
109. C4⋊C4×D131C22semidirect
110. C22⋊C4×D131C22semidirect
111. C42×D131C22semidirect
112. C2×#41×C131C22semidirect
115. #123×C131C22semidirect
116. C22⋊Q8×C131C22semidirect
118. #121×C131C22semidirect
119. #120×C131C22semidirect
120. C4×D4×C131C22semidirect
121. C4×D4×C131C22semidirect
122. C2×C22⋊C4×C131C22semidirect
359. C131#3546semidirect
371. #546D131semidirect
389. C2×#41C2×D131semidirect
419. #123C2×D131semidirect
425. C22⋊Q8C2×D131semidirect
452. #121C2×D131semidirect
460. #120C2×D131semidirect
473. C4×D4C2×D131semidirect
474. C4×D4C2×D131semidirect
481. C2×C22⋊C4C2×D131semidirect

Maximal subgroups

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

subgroupindex
#225540522
#225540512
#225540332
#225540122
#225540082
#225539812
#225539802
#225539622
#225539552
#225539522
D4×C22⋊D1312
#225539302
#225539002
#225538942
#225538922
#225538902
#225538792
#225538782
#225538772
#225538592
#225538412
#546×C1312
#3546131