Finite Group Databasebeta

← #30680476

Subgroups — #30680476

Order 16768.

1160 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22554058C212yesmaximal, complemented
2#22554054C212yesmaximal, complemented
3#22554047C211yesmaximal, characteristic, complemented
4#22554045C211yesmaximal, characteristic, complemented
5#22553974C211yesmaximal, characteristic, complemented
6#22553972C211yesmaximal, characteristic, complemented
7#22553959C211yesmaximal, characteristic, complemented
8#22553955C212yesmaximal, complemented
9#22553953C211yesmaximal, characteristic, complemented
10#22553953C212yesmaximal, complemented
11D4×D524C211yesmaximal, characteristic, complemented
12#22553946C211yesmaximal, characteristic, complemented
13#22553936C211yesmaximal, characteristic, complemented
14#22553901C212yesmaximal, complemented
15#22553901C212yesmaximal, complemented
16#22553898C212yesmaximal, complemented
17#22553881C211yesmaximal, characteristic, complemented
18#22553880C211yesmaximal, characteristic, complemented
19#22553873C212yesmaximal, complemented
20#22553863C211yesmaximal, characteristic, complemented
21#22553840C211yesmaximal, characteristic, complemented
22#124×D131C211yesmaximal, characteristic, complemented
23#542×C131C211yesmaximal, characteristic, complemented
24C2×#14523514C2212yescomplemented
25C2×#14523514C2211yescharacteristic, complemented
26C2×#14523513C2211yescharacteristic, complemented
27C2×Q8×D131C2211yescharacteristic, complemented
28C22×D524C2212yescomplemented
29C22×D524C2211yescharacteristic, complemented
30C2×D4×D131C2211yescharacteristic
31C2×D4×D131C2212yescomplemented
32C2×D4×D131C2211yescharacteristic, complemented
33#16862243C2211yescharacteristic
34#16862243C2211yescharacteristic, complemented
35#16862242C2211yescharacteristic
36#16862241C2212yescomplemented
37#16862241C2211yescharacteristic, complemented
38#16862239C2211yescharacteristic, complemented
39#16862236C2211yescharacteristic, complemented
40#16862235C2212yescomplemented
41#16862235C2211yescharacteristic, complemented
42#16862235C2212yescomplemented
43#16862235C2211yescharacteristic, complemented
44#16862234C2211yescharacteristic, complemented
45#16862234C2211yescharacteristic, complemented
46#16862234C2212yescomplemented
47#16862234C2212yescomplemented
48#16862233C2211yescharacteristic, complemented
49#16862232C2212yescomplemented
50#16862232C2212yescomplemented
51#16862232C2212yescomplemented
52#16862232C2211yescharacteristic, complemented
53#16862232C2212yescomplemented
54#16862231C2212yescomplemented
55#16862231C2212yescomplemented
56#16862231C2212yescomplemented
57#16862231C2212yescomplemented
58#16862231C2211yescharacteristic, complemented
59#16862229C2212yescomplemented
60#16862228C2212yescomplemented
61#16862228C2212yescomplemented
62#16862228C2211yescharacteristic, complemented
63#16862226C2212yescomplemented
64#16862226C2211yescharacteristic, complemented
65#16862224C2211yescharacteristic, complemented
66#16862224C2212yescomplemented
67#16862222C2212yescomplemented
68#16862221C2211yescharacteristic
69#16862221C2212yescomplemented
70#16862221C2211yescharacteristic, complemented
71#16862221C2211yescharacteristic, complemented
72#16862221C2212yescomplemented
73#16862221C2212yescomplemented
74#16862221C2212yescomplemented
75#16862221C2212yescomplemented
76#16862220C2212yescomplemented
77#16862219C2211yescharacteristic
78#16862219C2212yescomplemented
79#16862219C2212yescomplemented
80#16862219C2212yescomplemented
81#16862219C2212yescomplemented
82#16862217C2212yescomplemented
83#16862216C2212yescomplemented
84#16862216C2212yescomplemented
85#16862216C2212yescomplemented
86#16862216C2212yescomplemented
87#16862216C2212yescomplemented
88#16862216C2212yescomplemented
89#16862216C2212yescomplemented
90#16862216C2212yescomplemented
91#16862214C2212yescomplemented
92#16862214C2212yescomplemented
93C4×Dic262C2211yescharacteristic, complemented
94#16862211C2211yescharacteristic, complemented
95C4×D524C2212yescomplemented
96C4×D524C2212yescomplemented
97C4×D524C2211yescharacteristic, complemented
98#16862208C2212yescomplemented
99#16862208C2211yescharacteristic, complemented
100#16862208C2211yescharacteristic, complemented
101#16862208C2212yescomplemented
102#16862208C2211yescharacteristic, complemented
103C4×C22⋊D131C2212yescomplemented
104C4×C22⋊D131C2211yescharacteristic, complemented
105C4×C22⋊D131C2211yescharacteristic, complemented
106#16862203C2211yescharacteristic, complemented
107C22⋊C4×D131C2212yescomplemented
108C22⋊C4×D131C2212yescomplemented
109C22⋊C4×D131C2212yescomplemented
110C22⋊C4×D131C2212yescomplemented
111C42×D131C2211yescharacteristic, complemented
112C4⋊Q8×C131C2211yescharacteristic, complemented
113#126×C131C2212yescomplemented
114#124×C131C2211yescharacteristic, complemented
115#124×C131C2212yescomplemented
116#123×C131C2212yescomplemented
117C22⋊Q8×C131C2211yescharacteristic, complemented
118C22⋊Q8×C131C2212yescomplemented
119#121×C131C2211yescharacteristic
120C4×Q8×C131C2211yescharacteristic, complemented
121C4×D4×C131C2211yescharacteristic, complemented
122#117×C131C2211yescharacteristic, complemented
123C23×D131C2312yes—
124C23×D131C2312yes—
125C23×D131C2312yes—
126#14523514—42no—
127#14523514—44no—
128#14523513—42no—
129C2×Dic262C2311yescharacteristic
130C2×Dic262C2311yescharacteristic
131C2×Dic262C2312yes—
132Q8×D131—42no—
133C2×D524—42no—
134C2×D524—44no—
135C2×D524C2312yes—
136C2×D524C2311yescharacteristic
137C2×D524C2311yescharacteristic
138C2×D524C2311yescharacteristic
139C2×D524C2312yes—
140C2×D524C2311yescharacteristic
141C2×D524C2312yes—
142C2×D524C2312yes—
143C2×D524C2312yes—
144C2×D524C2312yes—
145C2×D524C2312yes—
146C2×D524C2312yes—
147C2×D524C2312yes—
148C2×C22⋊D131C2311yescharacteristic
149C2×C22⋊D131C2311yescharacteristic
150C2×C22⋊D131C2312yes—
151C2×C22⋊D131C2312yes—
152C2×C22⋊D131C2312yes—
153C2×C22⋊D131C2312yes—
154C2×C22⋊D131C2312yes—
155D4×D131—42no—
156D4×D131—42no—
157D4×D131—44no—
158C2×C4×D131C2311yescharacteristic
159C2×C4×D131C2311yescharacteristic
160C2×C4×D131C2311yescharacteristic
161C2×C4×D131C2312yes—
162C2×C4×D131C2312yes—
163C2×C4×D131C2312yes—
164C2×C4×D131C2312yes—
165C2×C4×D131C2312yes—
166C2×C4×D131C2312yes—
167C2×C4×D131C2311yescharacteristic
168C4⋊Dic131C2311yescharacteristic
169C4⋊Dic131C2312yes—
170C4⋊Dic131C2311yescharacteristic
171Dic131⋊C4C2312yes—
172Dic131⋊C4C2311yescharacteristic
173Dic131⋊C4C2311yescharacteristic
174Dic131⋊C4C2311yescharacteristic
175Dic131⋊C4C2311yescharacteristic
176Dic131⋊C4C2311yescharacteristic
177Dic131⋊C4C2311yescharacteristic
178C22⋊Dic131C2311yescharacteristic
179C22⋊Dic131C2312yes—
180C22⋊Dic131C2311yescharacteristic
181C22⋊Dic131C2312yes—
182(C2×D131)⋊C4C2311yescharacteristic
183(C2×D131)⋊C4C2312yes—
184(C2×D131)⋊C4C2312yes—
185(C2×D131)⋊C4C2312yes—
186(C2×D131)⋊C4C2312yes—
187(C2×D131)⋊C4C2312yes—
188(C2×D131)⋊C4C2312yes—
189(C2×D131)⋊C4C2311yescharacteristic
190(C2×D131)⋊C4C2311yescharacteristic
191(C2×D131)⋊C4C2312yes—
192(C2×D131)⋊C4C2312yes—
193(C2×D131)⋊C4C2312yes—
194(C2×D131)⋊C4C2312yes—
195(C2×D131)⋊C4C2311yescharacteristic
196(C2×D131)⋊C4C2311yescharacteristic
197(C2×D131)⋊C4C2312yes—
198(C2×D131)⋊C4C2312yes—
199(C2×D131)⋊C4C2312yes—
200(C2×D131)⋊C4C2312yes—
201(C2×D131)⋊C4C2312yes—
202(C2×D131)⋊C4C2311yescharacteristic
203C4×Dic131C2311yescharacteristic
204C4×Dic131C2311yescharacteristic
205C4×Dic131C2311yescharacteristic
206C4×Dic131C2312yes—
207C4×Dic131C2311yescharacteristic
208C2×Q8×C131C2311yescharacteristic
209C2×Q8×C131C2312yes—
210C2×D4×C131C2311yescharacteristic
211C2×D4×C131C2312yes—
212C22×C4×C131C2311yescharacteristic
213C22×C4×C131C2312yes—
214C4⋊C4×C131C2311yescharacteristic
215C4⋊C4×C131C2311yescharacteristic
216C4⋊C4×C131C2312yes—
217C4⋊C4×C131C2312yes—
218C4⋊C4×C131C2311yescharacteristic
219C4⋊C4×C131C2311yescharacteristic
220C4⋊C4×C131C2312yes—
221C22⋊C4×C131C2311yescharacteristic
222C22⋊C4×C131C2311yescharacteristic
223C22⋊C4×C131C2312yes—
224C22⋊C4×C131C2312yes—
225C22⋊C4×C131C2312yes—
226C22⋊C4×C131C2312yes—
227C22⋊C4×C131C2312yes—
228C42×C131C2312yes—
229C42×C131C2311yescharacteristic
230C42×C131C2311yescharacteristic
231C22×D131—24no—
232C22×D131—42no—
233C22×D131—42no—
234C22×D131—42no—
235C22×D131—42no—
236C22×D131—42no—
237C22×D131—42no—
238C22×D131—42no—
239C22×D131—42no—
240C22×D131C2411yescharacteristic
241C22×D131C2412yes—
242C22×D131C2412yes—
243C22×D131C2412yes—
244C22×D131C2411yescharacteristic
245Dic262—22no—
246Dic262—42no—
247Dic262—41no—
248D524—24no—
249D524—22no—
250D524—24no—
251D524—22no—
252D524—22no—
253D524—22no—
254D524—42no—
255D524—42no—
256D524—42no—
257D524—42no—
258D524—42no—
259D524—42no—
260D524—42no—
261C22⋊D131—22no—
262C22⋊D131—42no—
263C22⋊D131—42no—
264C22⋊D131—42no—
265C22⋊D131—41no—
266C22⋊D131—42no—
267C22⋊D131—42no—
268C2×Dic131C2411yescharacteristic
269C2×Dic131C2411yescharacteristic
270C2×Dic131C2411yescharacteristic
271C2×Dic131C2411yescharacteristic
272C2×Dic131C2412yes—
273C2×Dic131C2411yescharacteristic
274C2×Dic131C2411yescharacteristic
275C4×D131—22no—
276C4×D131—22no—
277C4×D131—22no—
278C4×D131—41no—
279C4×D131—42no—
280C4×D131—42no—
281C4×D131—42no—
282C4×D131—42no—
283C4×D131—42no—
284C4×D131—42no—
285C23×C131C2411yescharacteristic
286C23×C131C2412yes—
287Q8×C131—22no—
288Q8×C131—42no—
289D4×C131—22no—
290D4×C131—42no—
291C2×C4×C131—22no—
292C2×C4×C131—42no—
293C2×C4×C131C2411yescharacteristic
294C2×C4×C131C2411yescharacteristic
295C2×C4×C131C2412yes—
296C2×C4×C131C2411yescharacteristic
297C2×C4×C131C2411yescharacteristic
298C2×C4×C131C2412yes—
299C2×C4×C131C2411yescharacteristic
300C2×C4×C131C2412yes—
301C2×C4×C131C2411yescharacteristic
302C22×C131—21no—
303C22×C131—22no—
304C22×C131—22no—
305C22×C131—21no—
306C22×C131—22no—
307C22×C131—21no—
308C22×C131C2511yescharacteristic
309C2×D131—21no—
310C2×D131—21no—
311C2×D131—21no—
312C2×D131—22no—
313C2×D131—22no—
314C2×D131—22no—
315C2×D131—22no—
316C2×D131—22no—
317C2×D131—22no—
318C2×D131—21no—
319C2×D131—22no—
320C2×D131—21no—
321C2×D131—22no—
322C2×D131—22no—
323C2×D131—84no—
324C2×D131—84no—
325C2×D131—84no—
326C2×D131H(5,𝔽2)12yes—
327C4×C131—21no—
328C4×C131—21no—
329C4×C131—22no—
330C4×C131—22no—
331C4×C131—22no—
332C4×C131—21no—
333C4×C131—21no—
334C4×C131—21no—
335C4×C131H(5,𝔽2)12yes—
336Dic131—21no—
337Dic131—21no—
338Dic131—21no—
339Dic131—21no—
340Dic131—22no—
341Dic131—21no—
342Dic131—21no—
343C2×C131—42no—
344C2×C131—41no—
345C2×C131C2×H(5,𝔽2)11yescharacteristic
346C2×C131C2×H(5,𝔽2)11yescharacteristic
347C2×C131#58511yescharacteristic
348D131—22no—
349D131—42no—
350D131—42no—
351D131—41no—
352D131—42no—
353C131#355811yescharacteristic, complemented, Sylow
354#3558—1311nomaximal, Sylow
355#562—1312no—
356H(3,𝔽4)—1312no—
357#559—1311no—
358#559—1311no—
359#548—1311no—
360#548—1311no—
361#546—1312no—
362#546—1312no—
363#546—1311no—
364#546—1311no—
365D42—1311no—
366D42—1311no—
367#542—1311no—
368#542D13111yescharacteristic, complemented
369#538—1312no—
370#538—1312no—
371#538—1312no—
372#535—1311no—
373#535—1311no—
374#534—1312no—
375#532—1311no—
376#529—1311no—
377C2×#124—1311no—
378C2×#41—1312no—
379C2×#41—1311no—
380C2×#41—1311no—
381C22×Q8—1311no—
382C22×D4—1311no—
383C22×D4—1312no—
384C22×D4—1311no—
385C22×D4—1312no—
386C22×D4—1311no—
387C4⋊Q8C2×D13111yescharacteristic, complemented
388#127—1311no—
389#127—1311no—
390#127—1311no—
391#126—1311no—
392#126—1312no—
393#126—1311no—
394#126C2×D13112yescomplemented
395#125—1311no—
396#124—1311no—
397#124—1312no—
398#124—1311no—
399#124—1312no—
400#124—1311no—
401#124—1312no—
402#124—1312no—
403#124—1311no—
404#124—1312no—
405#124—1312no—
406#124—1311no—
407#124—1311no—
408#124—1312no—
409#124—1312no—
410#124C2×D13111yescharacteristic, complemented
411#124C2×D13112yescomplemented
412#123—1312no—
413#123—1311no—
414#123—1312no—
415#123—1312no—
416#123—1312no—
417#123—1312no—
418#123—1311no—
419#123—1312no—
420#123—1312no—
421#123C2×D13112yescomplemented
422C22⋊Q8—1312no—
423C22⋊Q8—1311no—
424C22⋊Q8—1312no—
425C22⋊Q8—1312no—
426C22⋊Q8—1311no—
427C22⋊Q8C2×D13111yescharacteristic, complemented
428C22⋊Q8C2×D13112yescomplemented
429#121—1312no—
430#121—1312no—
431#121—1311no—
432#121—1312no—
433#121—1311no—
434#121—1311no—
435#121—1312no—
436#121—1312no—
437#121—1312no—
438#121—1312no—
439#121—1311no—
440#121—1312no—
441#121—1312no—
442#121—1312no—
443#121—1312no—
444#121C2×D13111yescharacteristic
445#120—1312no—
446#120—1312no—
447#120—1312no—
448#120—1312no—
449#120—1312no—
450#120—1312no—
451#120—1312no—
452#120—1312no—
453#120—1312no—
454#120—1312no—
455C4×Q8—1311no—
456C4×Q8—1311no—
457C4×Q8C2×D13111yescharacteristic, complemented
458C4×D4—1311no—
459C4×D4—1311no—
460C4×D4—1312no—
461C4×D4—1312no—
462C4×D4—1311no—
463C4×D4—1311no—
464C4×D4—1312no—
465C4×D4—1311no—
466C4×D4—1311no—
467C4×D4—1312no—
468C4×D4—1312no—
469C4×D4C2×D13111yescharacteristic, complemented
470#117—1311no—
471#117C2×D13111yescharacteristic, complemented
472C2×C22⋊C4—1312no—
473C2×C22⋊C4—1312no—
474C2×C22⋊C4—1312no—
475C2×C22⋊C4—1312no—
476C2×C42—1311no—
477C24—1312no—
478C24—1312no—
479C24—1312no—
480#41—5242no—
481#41—5244no—
482#41—5242no—
483C2×Q8—5242no—
484C2×Q8—1311no—
485C2×Q8—1311no—
486C2×Q8—1312no—
487C2×Q8C22×D13111yescharacteristic
488C2×Q8C22×D13112yes—
489C2×D4—5242no—
490C2×D4—5244no—
491C2×D4—5242no—
492C2×D4—5242no—
493C2×D4—5244no—
494C2×D4—1311no—
495C2×D4—1311no—
496C2×D4—1312no—
497C2×D4—1312no—
498C2×D4—1312no—
499C2×D4—1312no—
500C2×D4—1312no—
501C2×D4—1312no—
502C2×D4—1312no—
503C2×D4—1311no—
504C2×D4—1311no—
505C2×D4—1311no—
506C2×D4—1311no—
507C2×D4—1312no—
508C2×D4—1312no—
509C2×D4—1312no—
510C2×D4—1312no—
511C2×D4—1312no—
512C2×D4—1312no—
513C2×D4—1312no—
514C2×D4C22×D13111yescharacteristic
515C2×D4C22×D13112yes—
516C22×C4—1311no—
517C22×C4—1311no—
518C22×C4—1311no—
519C22×C4—1311no—
520C22×C4—1312no—
521C22×C4—1312no—
522C22×C4—1312no—
523C22×C4—1312no—
524C22×C4—1312no—
525C22×C4—1312no—
526C22×C4C22×D13111yescharacteristic
527C22×C4C22×D13112yes—
528C4⋊C4—1311no—
529C4⋊C4—1311no—
530C4⋊C4—1311no—
531C4⋊C4—1311no—
532C4⋊C4—1311no—
533C4⋊C4—1312no—
534C4⋊C4—1311no—
535C4⋊C4—1311no—
536C4⋊C4—1311no—
537C4⋊C4—1312no—
538C4⋊C4C22×D13111yescharacteristic
539C4⋊C4C22×D13111yescharacteristic
540C4⋊C4C22×D13111yescharacteristic
541C4⋊C4C22×D13111yescharacteristic
542C4⋊C4C22×D13112yes—
543C4⋊C4C22×D13112yes—
544C4⋊C4C22×D13112yes—
545C22⋊C4—1311no—
546C22⋊C4—1312no—
547C22⋊C4—1312no—
548C22⋊C4—1311no—
549C22⋊C4—1311no—
550C22⋊C4—1312no—
551C22⋊C4—1312no—
552C22⋊C4—1312no—
553C22⋊C4—1312no—
554C22⋊C4—1312no—
555C22⋊C4—1312no—
556C22⋊C4—1311no—
557C22⋊C4—1311no—
558C22⋊C4—1311no—
559C22⋊C4—1311no—
560C22⋊C4—1312no—
561C22⋊C4—1311no—
562C22⋊C4—1312no—
563C22⋊C4—1312no—
564C22⋊C4—1312no—
565C22⋊C4—1312no—
566C22⋊C4—1312no—
567C22⋊C4—1312no—
568C22⋊C4—1312no—
569C22⋊C4—1312no—
570C22⋊C4C22×D13112yes—
571C22⋊C4C22×D13112yes—
572C22⋊C4C22×D13112yes—
573C22⋊C4C22×D13112yes—
574C22⋊C4C22×D13111yescharacteristic
575C22⋊C4C22×D13111yescharacteristic
576C22⋊C4C22×D13112yes—
577C42—1311no—
578C42—1311no—
579C42—1311no—
580C42—1311no—
581C42—1312no—
582C42C22×D13111yescharacteristic
583C42C22×D13111yescharacteristic
584C42C22×D13112yes—
585C23—2624no—
586C23—5242no—
587C23—5242no—
588C23—5242no—
589C23—5242no—
590C23—5242no—
591C23—5242no—
592C23—5242no—
593C23—5242no—
594C23—1312no—
595C23—1311no—
596C23—1312no—
597C23—1312no—
598C23—1311no—
599C23C23×D13112yes—
600C23C23×D13111yescharacteristic
601Q8—22no—
602Q8—42no—
603Q8—2622no—
604Q8—5242no—
605Q8—5241no—
606D4—22no—
607D4—42no—
608D4—2622no—
609D4—2624no—
610D4—2624no—
611D4—2622no—
612D4—2622no—
613D4—2622no—
614D4—2622no—
615D4—5242no—
616D4—5242no—
617D4—5242no—
618D4—5242no—
619D4—5242no—
620D4—5242no—
621D4—5242no—
622D4—5242no—
623D4—5242no—
624D4—5242no—
625D4—5242no—
626D4—5241no—
627D4—5242no—
628C2×C4—22no—
629C2×C4—42no—
630C2×C4—2622no—
631C2×C4—2622no—
632C2×C4—2622no—
633C2×C4—5242no—
634C2×C4—5242no—
635C2×C4—5242no—
636C2×C4—5242no—
637C2×C4—5242no—
638C2×C4—5242no—
639C2×C4—5241no—
640C2×C4—1311no—
641C2×C4—1311no—
642C2×C4—1311no—
643C2×C4—1311no—
644C2×C4—1312no—
645C2×C4—1311no—
646C2×C4—1311no—
647C2×C4C23×D13111yescharacteristic
648C2×C4C23×D13111yescharacteristic
649C2×C4C23×D13112yes—
650C2×C4C23×D13111yescharacteristic
651C2×C4C23×D13112yes—
652C2×C4C23×D13112yes—
653C2×C4C23×D13111yescharacteristic
654C2×C4C23×D13111yescharacteristic
655C2×C4C23×D13111yescharacteristic
656C22—22no—
657C22—21no—
658C22—21no—
659C22—22no—
660C22—22no—
661C22—21no—
662C22—2621no—
663C22—2621no—
664C22—2622no—
665C22—2622no—
666C22—2622no—
667C22—2621no—
668C22—2621no—
669C22—2622no—
670C22—2622no—
671C22—2622no—
672C22—2622no—
673C22—2622no—
674C22—2622no—
675C22—2621no—
676C22—10484no—
677C22—10484no—
678C22—10484no—
679C22—1312no—
680C22C24×D13111yescharacteristic
681C4—21no—
682C4—22no—
683C4—21no—
684C4—22no—
685C4—21no—
686C4—22no—
687C4—21no—
688C4—21no—
689C4—2621no—
690C4—2621no—
691C4—2621no—
692C4—2621no—
693C4—2622no—
694C4—2621no—
695C4—2621no—
696C4#1686229212yes—
697C2—42no—
698C2—41no—
699C2—2622no—
700C2—5242no—
701C2—5241no—
702C2—5242no—
703C2—5242no—
704C2H(5,𝔽2)×D13111yescharacteristic
705C2C2×#1686229211yescharacteristic
706C2#2255414911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D131
commutator, socle, cosocleC22×C131C25
Fitting#542×C131C2
hypercenter#542D131
hypocenterC131#3558
LCSG ▷ C22×C131 ▷ C131
UCSC1 ◁ C22 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #22554058C2semidirect
2. #22554054C2semidirect
3. #22554047C2semidirect
4. #22554045C2semidirect
5. #22553974C2semidirect
6. #22553972C2semidirect
7. #22553959C2semidirect
8. #22553955C2semidirect
9. #22553953C2semidirect
10. #22553953C2semidirect
11. D4×D524C2semidirect
12. #22553946C2semidirect
13. #22553936C2semidirect
14. #22553901C2semidirect
15. #22553901C2semidirect
16. #22553898C2semidirect
17. #22553881C2semidirect
18. #22553880C2semidirect
19. #22553873C2semidirect
20. #22553863C2semidirect
21. #22553840C2semidirect
22. #124×D131C2semidirect
23. #542×C131C2semidirect
24. C2×#14523514C22semidirect
25. C2×#14523514C22semidirect
26. C2×#14523513C22semidirect
27. C2×Q8×D131C22semidirect
28. C22×D524C22semidirect
29. C22×D524C22semidirect
31. C2×D4×D131C22semidirect
32. C2×D4×D131C22semidirect
34. #16862243C22semidirect
36. #16862241C22semidirect
37. #16862241C22semidirect
38. #16862239C22semidirect
39. #16862236C22semidirect
40. #16862235C22semidirect
41. #16862235C22semidirect
42. #16862235C22semidirect
43. #16862235C22semidirect
44. #16862234C22semidirect
45. #16862234C22semidirect
46. #16862234C22semidirect
47. #16862234C22semidirect
48. #16862233C22semidirect
49. #16862232C22semidirect
50. #16862232C22semidirect
51. #16862232C22semidirect
52. #16862232C22semidirect
53. #16862232C22semidirect
54. #16862231C22semidirect
55. #16862231C22semidirect
56. #16862231C22semidirect
57. #16862231C22semidirect
58. #16862231C22semidirect
59. #16862229C22semidirect
60. #16862228C22semidirect
61. #16862228C22semidirect
62. #16862228C22semidirect
63. #16862226C22semidirect
64. #16862226C22semidirect
65. #16862224C22semidirect
66. #16862224C22semidirect
67. #16862222C22semidirect
69. #16862221C22semidirect
70. #16862221C22semidirect
71. #16862221C22semidirect
72. #16862221C22semidirect
73. #16862221C22semidirect
74. #16862221C22semidirect
75. #16862221C22semidirect
76. #16862220C22semidirect
78. #16862219C22semidirect
79. #16862219C22semidirect
80. #16862219C22semidirect
81. #16862219C22semidirect
82. #16862217C22semidirect
83. #16862216C22semidirect
84. #16862216C22semidirect
85. #16862216C22semidirect
86. #16862216C22semidirect
87. #16862216C22semidirect
88. #16862216C22semidirect
89. #16862216C22semidirect
90. #16862216C22semidirect
91. #16862214C22semidirect
92. #16862214C22semidirect
93. C4×Dic262C22semidirect
94. #16862211C22semidirect
95. C4×D524C22semidirect
96. C4×D524C22semidirect
97. C4×D524C22semidirect
98. #16862208C22semidirect
99. #16862208C22semidirect
100. #16862208C22semidirect
101. #16862208C22semidirect
102. #16862208C22semidirect
103. C4×C22⋊D131C22semidirect
104. C4×C22⋊D131C22semidirect
105. C4×C22⋊D131C22semidirect
106. #16862203C22semidirect
107. C22⋊C4×D131C22semidirect
108. C22⋊C4×D131C22semidirect
109. C22⋊C4×D131C22semidirect
110. C22⋊C4×D131C22semidirect
111. C42×D131C22semidirect
112. C4⋊Q8×C131C22semidirect
113. #126×C131C22semidirect
114. #124×C131C22semidirect
115. #124×C131C22semidirect
116. #123×C131C22semidirect
117. C22⋊Q8×C131C22semidirect
118. C22⋊Q8×C131C22semidirect
120. C4×Q8×C131C22semidirect
121. C4×D4×C131C22semidirect
122. #117×C131C22semidirect
353. C131#3558semidirect
368. #542D131semidirect
387. C4⋊Q8C2×D131semidirect
394. #126C2×D131semidirect
410. #124C2×D131semidirect
411. #124C2×D131semidirect
421. #123C2×D131semidirect
427. C22⋊Q8C2×D131semidirect
428. C22⋊Q8C2×D131semidirect
457. C4×Q8C2×D131semidirect
469. C4×D4C2×D131semidirect
471. #117C2×D131semidirect

Maximal subgroups

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

subgroupindex
#225540582
#225540542
#225540472
#225540452
#225539742
#225539722
#225539592
#225539552
#225539532
D4×D5242
#225539462
#225539362
#225539012
#225538982
#225538812
#225538802
#225538732
#225538632
#225538402
#124×D1312
#542×C1312
#3558131