Finite Group Databasebeta

← #44564520

Subgroups — #44564520

Order 32128.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30632430C211yesmaximal, characteristic, complemented
2#30632426C212yesmaximal, complemented
3#30632426C211yesmaximal, characteristic, complemented
4#30632368C211yesmaximal, characteristic, complemented
5#30632363C212yesmaximal, complemented
6#30632331C212yesmaximal, complemented
7#30632327C212yesmaximal, complemented
8#30632324C212yesmaximal, complemented
9D4×C22⋊D251C212yesmaximal, complemented
10#30632319C211yesmaximal, characteristic, complemented
11#30632275C212yesmaximal, complemented
12#30632272C212yesmaximal, complemented
13#30632272C212yesmaximal, complemented
14#30632254C211yesmaximal, characteristic, complemented
15#30632252C212yesmaximal, complemented
16#30632247C212yesmaximal, complemented
17#30632246C211yesmaximal, characteristic, complemented
18C2×#22548684C212yesmaximal, complemented
19C2×#120×C251C211yesmaximal, characteristic, complemented
20C2×#16860810C2211yescharacteristic, complemented
21C2×#16860809C2212yescomplemented
22C22×C22⋊D251C2212yescomplemented
23C22×C22⋊D251C2212yescomplemented
24C22×C22⋊D251C2212yescomplemented
25C22×C22⋊D251C2211yescharacteristic, complemented
26C2×D4×D251C2212yescomplemented
27#22548711C2211yescharacteristic, complemented
28#22548711C2212yescomplemented
29#22548711C2211yescharacteristic, complemented
30#22548708C2212yescomplemented
31#22548708C2212yescomplemented
32#22548708C2212yescomplemented
33#22548708C2212yescomplemented
34#22548702C2211yescharacteristic, complemented
35#22548702C2211yescharacteristic, complemented
36#22548702C2212yescomplemented
37#22548701C2212yescomplemented
38#22548701C2212yescomplemented
39#22548701C2212yescomplemented
40#22548701C2212yescomplemented
41#22548699C2212yescomplemented
42#22548698C2212yescomplemented
43#22548697C2212yescomplemented
44#22548697C2212yescomplemented
45#22548697C2212yescomplemented
46#22548697C2212yescomplemented
47#22548696C2211yescharacteristic, complemented
48#22548696C2211yescharacteristic, complemented
49#22548696C2212yescomplemented
50#22548696C2212yescomplemented
51#22548694C2212yescomplemented
52#22548692C2212yescomplemented
53#22548692C2212yescomplemented
54#22548689C2212yescomplemented
55#22548688C2212yescomplemented
56#22548688C2212yescomplemented
57#22548688C2212yescomplemented
58#22548688C2212yescomplemented
59#22548687C2212yescomplemented
60#22548687C2212yescomplemented
61#22548687C2212yescomplemented
62#22548687C2212yescomplemented
63#22548687C2212yescomplemented
64#22548687C2212yescomplemented
65#22548686C2212yescomplemented
66#22548686C2212yescomplemented
67#22548686C2212yescomplemented
68#22548686C2212yescomplemented
69#22548685C2212yescomplemented
70#22548684C2212yes—
71#22548684C2212yescomplemented
72#22548684C2212yescomplemented
73#22548684C2212yescomplemented
74#22548684C2212yescomplemented
75#22548684C2212yescomplemented
76#22548684C2212yescomplemented
77#22548684C2212yescomplemented
78#22548684C2212yescomplemented
79#22548683C2212yescomplemented
80#22548683C2211yescharacteristic, complemented
81#22548683C2211yescharacteristic, complemented
82#22548683C2212yescomplemented
83D4×Dic251C2212yescomplemented
84D4×Dic251C2212yescomplemented
85C4×C22⋊D251C2212yescomplemented
86C4×C22⋊D251C2212yescomplemented
87(C22⋊D251)⋊C4C2212yescomplemented
88(C22⋊D251)⋊C4C2212yescomplemented
89#22548674C2211yescharacteristic, complemented
90#22548671C2212yescomplemented
91C2×C22⋊Dic251C2212yescomplemented
92C2×C22⋊Dic251C2212yescomplemented
93C2×C22⋊Dic251C2212yescomplemented
94C2×C22⋊Dic251C2211yescharacteristic, complemented
95C22⋊C4×D251C2212yescomplemented
96C25×C251C2211yescharacteristic, complemented
97C22×D4×C251C2211yescharacteristic, complemented
98C22×D4×C251C2212yescomplemented
99#120×C251C2211yescharacteristic
100#120×C251C2212yescomplemented
101#120×C251C2212yescomplemented
102#120×C251C2211yescharacteristic, complemented
103#120×C251C2211yescharacteristic, complemented
104#120×C251C2211yescharacteristic, complemented
105C2×C22⋊C4×C251C2211yescharacteristic, complemented
106C2×C22⋊C4×C251C2212yescomplemented
107C23×D251C2312yes—
108C23×D251C2311yescharacteristic, complemented
109#16860810—42no—
110#16860809—44no—
111C2×Dic502C2312yescomplemented
112C2×Dic502C2311yescharacteristic, complemented
113C2×D1004C2312yescomplemented
114C2×D1004C2311yescharacteristic, complemented
115C2×C22⋊D251—44no—
116C2×C22⋊D251—44no—
117C2×C22⋊D251—44no—
118C2×C22⋊D251—42no—
119C2×C22⋊D251C2312yes—
120C2×C22⋊D251C2312yes—
121C2×C22⋊D251C2312yes—
122C2×C22⋊D251C2312yes—
123C2×C22⋊D251C2312yes—
124C2×C22⋊D251C2312yes—
125C2×C22⋊D251C2312yes—
126C2×C22⋊D251C2312yes—
127C2×C22⋊D251C2312yes—
128C2×C22⋊D251C2312yes—
129C2×C22⋊D251C2312yes—
130C2×C22⋊D251C2312yes—
131C2×C22⋊D251C2312yescomplemented
132C2×C22⋊D251C2312yescomplemented
133C2×C22⋊D251C2312yescomplemented
134D4×D251—44no—
135C22×Dic251C2312yes—
136C22×Dic251C2312yes—
137C22×Dic251C2312yes—
138C22×Dic251C2311yescharacteristic, complemented
139C22×Dic251C2312yescomplemented
140C2×C4×D251C2312yescomplemented
141C2×C4×D251C2312yescomplemented
142C2×C4×D251C2312yescomplemented
143C4⋊Dic251C2312yescomplemented
144C4⋊Dic251C2312yescomplemented
145C4⋊Dic251C2312yescomplemented
146Dic251⋊C4C2312yescomplemented
147Dic251⋊C4C2312yescomplemented
148Dic251⋊C4C2312yescomplemented
149Dic251⋊C4C2312yescomplemented
150Dic251⋊C4C2312yescomplemented
151Dic251⋊C4C2312yescomplemented
152C22⋊Dic251C2312yes—
153C22⋊Dic251C2312yes—
154C22⋊Dic251C2312yes—
155C22⋊Dic251C2312yes—
156C22⋊Dic251C2312yes—
157C22⋊Dic251C2312yes—
158C22⋊Dic251C2312yes—
159C22⋊Dic251C2312yes—
160C22⋊Dic251C2312yes—
161C22⋊Dic251C2312yes—
162C22⋊Dic251C2312yes—
163C22⋊Dic251C2312yes—
164C22⋊Dic251C2311yescharacteristic, complemented
165C22⋊Dic251C2311yescharacteristic, complemented
166C22⋊Dic251C2312yescomplemented
167C22⋊Dic251C2312yescomplemented
168(C2×D251)⋊C4C2312yescomplemented
169(C2×D251)⋊C4C2312yescomplemented
170(C2×D251)⋊C4C2312yescomplemented
171(C2×D251)⋊C4C2312yescomplemented
172(C2×D251)⋊C4C2312yescomplemented
173(C2×D251)⋊C4C2312yescomplemented
174C4×Dic251C2311yescharacteristic, complemented
175C4×Dic251C2312yescomplemented
176C4×Dic251C2311yescharacteristic, complemented
177C4×Dic251C2312yescomplemented
178C24×C251—44no—
179C24×C251—42no—
180C24×C251C2311yescharacteristic
181C24×C251C2312yes—
182C24×C251C2312yes—
183C24×C251C2311yescharacteristic
184C24×C251C2311yescharacteristic
185C24×C251C2311yescharacteristic
186C2×D4×C251—42no—
187C2×D4×C251—44no—
188C2×D4×C251C2312yes—
189C2×D4×C251C2312yes—
190C2×D4×C251C2311yescharacteristic
191C2×D4×C251C2311yescharacteristic
192C2×D4×C251C2312yes—
193C2×D4×C251C2311yescharacteristic
194C2×D4×C251C2312yes—
195C2×D4×C251C2311yescharacteristic
196C22×C4×C251C2311yescharacteristic
197C22×C4×C251C2312yes—
198C22⋊C4×C251C2312yes—
199C22⋊C4×C251C2311yescharacteristic
200C22⋊C4×C251C2312yes—
201C22⋊C4×C251C2312yes—
202C22⋊C4×C251C2312yes—
203C22⋊C4×C251C2312yes—
204C22⋊C4×C251C2311yescharacteristic
205C22×D251—24no—
206C22×D251—42no—
207C22×D251—42no—
208C22×D251—42no—
209C22×D251—41no—
210C22×D251C2412yes—
211C22×D251C2412yes—
212Dic502—42no—
213Dic502—41no—
214D1004—42no—
215D1004—41no—
216C22⋊D251—24no—
217C22⋊D251—24no—
218C22⋊D251—24no—
219C22⋊D251—24no—
220C22⋊D251—42no—
221C22⋊D251—42no—
222C22⋊D251—42no—
223C22⋊D251—42no—
224C22⋊D251—42no—
225C22⋊D251—42no—
226C22⋊D251—42no—
227C22⋊D251—42no—
228C22⋊D251—42no—
229C22⋊D251—42no—
230C22⋊D251—42no—
231C2×Dic251—24no—
232C2×Dic251—42no—
233C2×Dic251—42no—
234C2×Dic251—41no—
235C2×Dic251—42no—
236C2×Dic251C2412yes—
237C2×Dic251C2412yes—
238C2×Dic251C2412yes—
239C2×Dic251C2412yes—
240C2×Dic251C2412yes—
241C2×Dic251C2412yes—
242C4×D251—42no—
243C4×D251—42no—
244C4×D251—42no—
245C23×C251—24no—
246C23×C251—22no—
247C23×C251—24no—
248C23×C251—24no—
249C23×C251—24no—
250C23×C251—22no—
251C23×C251—42no—
252C23×C251—42no—
253C23×C251—41no—
254C23×C251—42no—
255C23×C251—42no—
256C23×C251—42no—
257C23×C251—41no—
258C23×C251—42no—
259C23×C251—416no—
260C23×C251C2411yescharacteristic
261C23×C251C2412yes—
262C23×C251C2411yescharacteristic
263C23×C251C2411yescharacteristic
264C23×C251C2411yescharacteristic
265C23×C251C2412yes—
266C23×C251C2411yescharacteristic
267D4×C251—24no—
268D4×C251—24no—
269D4×C251—41no—
270D4×C251—41no—
271D4×C251—41no—
272D4×C251—41no—
273D4×C251—42no—
274D4×C251—42no—
275C2×C4×C251—22no—
276C2×C4×C251—42no—
277C2×C4×C251C2411yescharacteristic
278C2×C4×C251C2412yes—
279C2×C4×C251C2412yes—
280C2×C4×C251C2411yescharacteristic
281C22×C251—22no—
282C22×C251—22no—
283C22×C251—22no—
284C22×C251—22no—
285C22×C251—22no—
286C22×C251—22no—
287C22×C251—21no—
288C22×C251—21no—
289C22×C251—21no—
290C22×C251—21no—
291C22×C251—22no—
292C22×C251—22no—
293C22×C251—22no—
294C22×C251—22no—
295C22×C251—44no—
296C22×C251—48no—
297C22×C251—48no—
298C22×C251—44no—
299C22×C251—44no—
300C22×C251—82no—
301C22×C251H(5,𝔽2)12yes—
302C22×C251H(5,𝔽2)14yes—
303C22×C251C2511yescharacteristic
304C2×D251—22no—
305C2×D251—22no—
306C2×D251—22no—
307C2×D251—22no—
308C2×D251—22no—
309C2×D251—22no—
310C2×D251—84no—
311C2×D251—82no—
312C4×C251—21no—
313C4×C251—21no—
314C4×C251—22no—
315C4×C251—22no—
316Dic251—22no—
317Dic251—22no—
318Dic251—22no—
319Dic251—22no—
320Dic251—22no—
321Dic251—22no—
322C2×C251—24no—
323C2×C251—22no—
324C2×C251—41no—
325C2×C251—41no—
326C2×C251—42no—
327C2×C251—41no—
328C2×C251—41no—
329C2×C251C2×H(5,𝔽2)12yes—
330C2×C251C2×H(5,𝔽2)11yescharacteristic
331D251—42no—
332D251—42no—
333C251#353211yescharacteristic, complemented, Sylow
334#3532—2511nomaximal, Sylow
335H(3,𝔽4)—2511no—
336#560—2511no—
337#560—2512no—
338#551—2511no—
339#551—2512no—
340#546—2512no—
341#546—2512no—
342#546—2512no—
343D42—2512no—
344D42—2511no—
345#538—2512no—
346#538—2512no—
347#538—2512no—
348#535—2511no—
349#535—2512no—
350#534—2511no—
351#534—2512no—
352C2×#120—2512no—
353C2×#120D25111yescharacteristic, complemented
354C25C2×D25111yescharacteristic, complemented
355C2×#41—2512no—
356C2×#41—2511no—
357C22×D4—2512no—
358C22×D4—2512no—
359C22×D4—2512no—
360C22×D4—2511no—
361C22×D4—2512no—
362C22×D4C2×D25111yescharacteristic, complemented
363C22×D4C2×D25112yescomplemented
364#127—2511no—
365#127—2512no—
366#127—2511no—
367#126—2512no—
368#126—2512no—
369#126—2512no—
370#126—2512no—
371#124—2511no—
372#124—2511no—
373#124—2512no—
374#124—2512no—
375#124—2512no—
376#124—2512no—
377#124—2512no—
378#123—2511no—
379#123—2512no—
380#123—2511no—
381#123—2512no—
382#123—2512no—
383#123—2512no—
384#123—2512no—
385#123—2512no—
386#123—2512no—
387#123—2512no—
388C22⋊Q8—2512no—
389C22⋊Q8—2512no—
390C22⋊Q8—2512no—
391#121—2512no—
392#121—2512no—
393#121—2512no—
394#121—2512no—
395#121—2512no—
396#121—2512no—
397#121—2512no—
398#121—2512no—
399#121—2512no—
400#121—2512no—
401#121—2512no—
402#121—2512no—
403#121—2512no—
404#121—2512no—
405#121—2512no—
406#120—2512no—
407#120—2512no—
408#120—2512no—
409#120—2512no—
410#120—2512no—
411#120—2512no—
412#120—2512no—
413#120—2512no—
414#120—2512no—
415#120—2511no—
416#120—2511no—
417#120—2512no—
418#120—2512no—
419#120—2512no—
420#120C2×D25111yescharacteristic
421#120C2×D25112yescomplemented
422#120C2×D25112yescomplemented
423#120C2×D25111yescharacteristic, complemented
424#120C2×D25111yescharacteristic, complemented
425#120C2×D25111yescharacteristic, complemented
426C4×D4—2512no—
427C4×D4—2512no—
428C4×D4—2512no—
429C4×D4—2512no—
430C4×D4—2512no—
431C4×D4—2512no—
432#117—2511no—
433#117—2512no—
434C2×C22⋊C4—2512no—
435C2×C22⋊C4—2512no—
436C2×C22⋊C4—2512no—
437C2×C22⋊C4—2511no—
438C2×C22⋊C4—2512no—
439C2×C22⋊C4C2×D25111yescharacteristic, complemented
440C2×C22⋊C4C2×D25112yescomplemented
441C24—44no—
442C24—42no—
443C24—2511no—
444C24—2512no—
445C24C22×D25111yescharacteristic
446C24C22×D25112yes—
447C24C22×D25112yes—
448C24C22×D25111yescharacteristic
449C24C22×D25111yescharacteristic
450C24C22×D25111yescharacteristic
451#41—10042no—
452#41—10044no—
453C2×Q8—2512no—
454C2×Q8—2511no—
455C2×D4—42no—
456C2×D4—44no—
457C2×D4—10044no—
458C2×D4—10042no—
459C2×D4—10044no—
460C2×D4—10044no—
461C2×D4—10044no—
462C2×D4—2512no—
463C2×D4—2512no—
464C2×D4—2512no—
465C2×D4—2512no—
466C2×D4—2512no—
467C2×D4—2512no—
468C2×D4—2512no—
469C2×D4—2512no—
470C2×D4—2512no—
471C2×D4—2512no—
472C2×D4—2512no—
473C2×D4—2512no—
474C2×D4—2512no—
475C2×D4—2512no—
476C2×D4—2512no—
477C2×D4—2511no—
478C2×D4—2512no—
479C2×D4C22×D25112yes—
480C2×D4C22×D25112yes—
481C2×D4C22×D25111yescharacteristic
482C2×D4C22×D25111yescharacteristic
483C2×D4C22×D25112yes—
484C2×D4C22×D25111yescharacteristic
485C2×D4C22×D25112yes—
486C2×D4C22×D25111yescharacteristic
487C22×C4—2512no—
488C22×C4—2512no—
489C22×C4—2512no—
490C22×C4—2511no—
491C22×C4—2512no—
492C22×C4—2512no—
493C22×C4—2512no—
494C22×C4—2512no—
495C22×C4C22×D25111yescharacteristic
496C22×C4C22×D25112yes—
497C4⋊C4—2512no—
498C4⋊C4—2512no—
499C4⋊C4—2512no—
500C4⋊C4—2512no—
501C4⋊C4—2512no—
502C4⋊C4—2512no—
503C4⋊C4—2512no—
504C4⋊C4—2512no—
505C4⋊C4—2512no—
506C22⋊C4—2512no—
507C22⋊C4—2512no—
508C22⋊C4—2512no—
509C22⋊C4—2512no—
510C22⋊C4—2512no—
511C22⋊C4—2512no—
512C22⋊C4—2512no—
513C22⋊C4—2512no—
514C22⋊C4—2512no—
515C22⋊C4—2512no—
516C22⋊C4—2512no—
517C22⋊C4—2512no—
518C22⋊C4—2511no—
519C22⋊C4—2511no—
520C22⋊C4—2512no—
521C22⋊C4—2512no—
522C22⋊C4—2512no—
523C22⋊C4—2512no—
524C22⋊C4—2512no—
525C22⋊C4—2512no—
526C22⋊C4—2512no—
527C22⋊C4—2512no—
528C22⋊C4C22×D25112yes—
529C22⋊C4C22×D25112yes—
530C22⋊C4C22×D25111yescharacteristic
531C22⋊C4C22×D25112yes—
532C22⋊C4C22×D25112yes—
533C22⋊C4C22×D25112yes—
534C22⋊C4C22×D25111yescharacteristic
535C42—2511no—
536C42—2512no—
537C42—2511no—
538C42—2512no—
539C23—24no—
540C23—22no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—22no—
545C23—42no—
546C23—42no—
547C23—41no—
548C23—42no—
549C23—42no—
550C23—41no—
551C23—42no—
552C23—42no—
553C23—416no—
554C23—10042no—
555C23—10042no—
556C23—10041no—
557C23—10042no—
558C23—5024no—
559C23—2512no—
560C23—2512no—
561C23C23×D25112yes—
562C23C23×D25111yescharacteristic
563C23C23×D25111yescharacteristic
564C23C23×D25111yescharacteristic
565C23C23×D25111yescharacteristic
566C23C23×D25111yescharacteristic
567C23C23×D25112yes—
568Q8—10041no—
569Q8—10042no—
570D4—24no—
571D4—24no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—42no—
577D4—42no—
578D4—10042no—
579D4—10041no—
580D4—10042no—
581D4—10042no—
582D4—10042no—
583D4—10042no—
584D4—10042no—
585D4—10042no—
586D4—10042no—
587D4—10042no—
588D4—10042no—
589D4—10042no—
590D4—10042no—
591D4—5024no—
592D4—5024no—
593D4—5024no—
594D4—5024no—
595C2×C4—22no—
596C2×C4—42no—
597C2×C4—10042no—
598C2×C4—10042no—
599C2×C4—10042no—
600C2×C4—10041no—
601C2×C4—10042no—
602C2×C4—10042no—
603C2×C4—10042no—
604C2×C4—5024no—
605C2×C4—2512no—
606C2×C4—2512no—
607C2×C4—2512no—
608C2×C4—2512no—
609C2×C4—2512no—
610C2×C4—2512no—
611C2×C4C23×D25111yescharacteristic
612C2×C4C23×D25112yes—
613C2×C4C23×D25112yes—
614C2×C4C23×D25111yescharacteristic
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—21no—
620C22—22no—
621C22—21no—
622C22—21no—
623C22—22no—
624C22—21no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—48no—
630C22—44no—
631C22—44no—
632C22—48no—
633C22—44no—
634C22—82no—
635C22—20084no—
636C22—20082no—
637C22—5022no—
638C22—5022no—
639C22—5022no—
640C22—5022no—
641C22—5022no—
642C22—5022no—
643C22#2254876012yes—
644C22#2254876014yes—
645C22C24×D25111yescharacteristic
646C4—21no—
647C4—21no—
648C4—22no—
649C4—22no—
650C4—5022no—
651C4—5022no—
652C4—5022no—
653C4—5022no—
654C4—5022no—
655C4—5022no—
656C2—22no—
657C2—24no—
658C2—42no—
659C2—41no—
660C2—41no—
661C2—41no—
662C2—41no—
663C2—10042no—
664C2—10042no—
665C2C2×#2254876011yescharacteristic
666C2C2×#2254876012yes—
subgroupG/H
center, FrattiniC22C24×D251
commutator, socle, cosocleC22×C251C25
FittingC2×#120×C251C2
hypercenterC2×#120D251
hypocenterC251#3532
LCSG ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #30632430C2semidirect
2. #30632426C2semidirect
3. #30632426C2semidirect
4. #30632368C2semidirect
5. #30632363C2semidirect
6. #30632331C2semidirect
7. #30632327C2semidirect
8. #30632324C2semidirect
9. D4×C22⋊D251C2semidirect
10. #30632319C2semidirect
11. #30632275C2semidirect
12. #30632272C2semidirect
13. #30632272C2semidirect
14. #30632254C2semidirect
15. #30632252C2semidirect
16. #30632247C2semidirect
17. #30632246C2semidirect
18. C2×#22548684C2semidirect
19. C2×#120×C251C2semidirect
20. C2×#16860810C22semidirect
21. C2×#16860809C22semidirect
22. C22×C22⋊D251C22semidirect
23. C22×C22⋊D251C22semidirect
24. C22×C22⋊D251C22semidirect
25. C22×C22⋊D251C22semidirect
26. C2×D4×D251C22semidirect
27. #22548711C22semidirect
28. #22548711C22semidirect
29. #22548711C22semidirect
30. #22548708C22semidirect
31. #22548708C22semidirect
32. #22548708C22semidirect
33. #22548708C22semidirect
34. #22548702C22semidirect
35. #22548702C22semidirect
36. #22548702C22semidirect
37. #22548701C22semidirect
38. #22548701C22semidirect
39. #22548701C22semidirect
40. #22548701C22semidirect
41. #22548699C22semidirect
42. #22548698C22semidirect
43. #22548697C22semidirect
44. #22548697C22semidirect
45. #22548697C22semidirect
46. #22548697C22semidirect
47. #22548696C22semidirect
48. #22548696C22semidirect
49. #22548696C22semidirect
50. #22548696C22semidirect
51. #22548694C22semidirect
52. #22548692C22semidirect
53. #22548692C22semidirect
54. #22548689C22semidirect
55. #22548688C22semidirect
56. #22548688C22semidirect
57. #22548688C22semidirect
58. #22548688C22semidirect
59. #22548687C22semidirect
60. #22548687C22semidirect
61. #22548687C22semidirect
62. #22548687C22semidirect
63. #22548687C22semidirect
64. #22548687C22semidirect
65. #22548686C22semidirect
66. #22548686C22semidirect
67. #22548686C22semidirect
68. #22548686C22semidirect
69. #22548685C22semidirect
71. #22548684C22semidirect
72. #22548684C22semidirect
73. #22548684C22semidirect
74. #22548684C22semidirect
75. #22548684C22semidirect
76. #22548684C22semidirect
77. #22548684C22semidirect
78. #22548684C22semidirect
79. #22548683C22semidirect
80. #22548683C22semidirect
81. #22548683C22semidirect
82. #22548683C22semidirect
83. D4×Dic251C22semidirect
84. D4×Dic251C22semidirect
85. C4×C22⋊D251C22semidirect
86. C4×C22⋊D251C22semidirect
87. (C22⋊D251)⋊C4C22semidirect
88. (C22⋊D251)⋊C4C22semidirect
89. #22548674C22semidirect
90. #22548671C22semidirect
91. C2×C22⋊Dic251C22semidirect
92. C2×C22⋊Dic251C22semidirect
93. C2×C22⋊Dic251C22semidirect
94. C2×C22⋊Dic251C22semidirect
95. C22⋊C4×D251C22semidirect
96. C25×C251C22semidirect
97. C22×D4×C251C22semidirect
98. C22×D4×C251C22semidirect
100. #120×C251C22semidirect
101. #120×C251C22semidirect
102. #120×C251C22semidirect
103. #120×C251C22semidirect
104. #120×C251C22semidirect
105. C2×C22⋊C4×C251C22semidirect
106. C2×C22⋊C4×C251C22semidirect
108. C23×D251C23semidirect
111. C2×Dic502C23semidirect
112. C2×Dic502C23semidirect
113. C2×D1004C23semidirect
114. C2×D1004C23semidirect
131. C2×C22⋊D251C23semidirect
132. C2×C22⋊D251C23semidirect
133. C2×C22⋊D251C23semidirect
138. C22×Dic251C23semidirect
139. C22×Dic251C23semidirect
140. C2×C4×D251C23semidirect
141. C2×C4×D251C23semidirect
142. C2×C4×D251C23semidirect
143. C4⋊Dic251C23semidirect
144. C4⋊Dic251C23semidirect
145. C4⋊Dic251C23semidirect
146. Dic251⋊C4C23semidirect
147. Dic251⋊C4C23semidirect
148. Dic251⋊C4C23semidirect
149. Dic251⋊C4C23semidirect
150. Dic251⋊C4C23semidirect
151. Dic251⋊C4C23semidirect
164. C22⋊Dic251C23semidirect
165. C22⋊Dic251C23semidirect
166. C22⋊Dic251C23semidirect
167. C22⋊Dic251C23semidirect
168. (C2×D251)⋊C4C23semidirect
169. (C2×D251)⋊C4C23semidirect
170. (C2×D251)⋊C4C23semidirect
171. (C2×D251)⋊C4C23semidirect
172. (C2×D251)⋊C4C23semidirect
173. (C2×D251)⋊C4C23semidirect
174. C4×Dic251C23semidirect
175. C4×Dic251C23semidirect
176. C4×Dic251C23semidirect
177. C4×Dic251C23semidirect
333. C251#3532semidirect
353. C2×#120D251semidirect
354. C25C2×D251semidirect
362. C22×D4C2×D251semidirect
363. C22×D4C2×D251semidirect
421. #120C2×D251semidirect
422. #120C2×D251semidirect
423. #120C2×D251semidirect
424. #120C2×D251semidirect
425. #120C2×D251semidirect
439. C2×C22⋊C4C2×D251semidirect
440. C2×C22⋊C4C2×D251semidirect

Maximal subgroups

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

subgroupindex
#306324302
#306324262
#306323682
#306323632
#306323312
#306323272
#306323242
D4×C22⋊D2512
#306323192
#306322752
#306322722
#306322542
#306322522
#306322472
#306322462
C2×#225486842
C2×#120×C2512
#3532251