Finite Group Databasebeta

← C151×#18962 #50323887

Subgroups — C151×#18962 #50323887

Order 38656.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3546×C151C211yesmaximal, characteristic, complemented
2#3253×C151C211yesmaximal, characteristic, complemented
3#3247×C151C211yesmaximal, characteristic, complemented
4#3207×C151C211yesmaximal, characteristic, complemented
5#1638×C151C211yesmaximal, characteristic, complemented
6#1635×C151C211yesmaximal, characteristic, complemented
7#1631×C151C211yesmaximal, characteristic, complemented
8#1629×C151C211yesmaximal, characteristic, complemented
9#1628×C151C211yesmaximal, characteristic, complemented
10#1625×C151C211yesmaximal, characteristic, complemented
11#1621×C151C211yesmaximal, characteristic, complemented
12#1619×C151C211yesmaximal, characteristic, complemented
13#1547×C151C211yesmaximal, characteristic, complemented
14#1495×C151C211yesmaximal, characteristic, complemented
15#1480×C151C211yesmaximal, characteristic, complemented
16#560×C151—22no—
17#556×C151C2211yescharacteristic
18#553×C151—21no—
19#550×C151—21no—
20#550×C151C2211yescharacteristic
21#547×C151C2211yescharacteristic
22#546×C151—21no—
23#546×C151—21no—
24D42×C151C2211yescharacteristic
25#542×C151—21no—
26#538×C151—22no—
27#537×C151—21no—
28#535×C151—21no—
29#535×C151—21no—
30#532×C151C2211yescharacteristic
31#532×C151C2211yescharacteristic
32#532×C151C2211yescharacteristic, complemented
33#529×C151C2211yescharacteristic
34#493×C151C2211yescharacteristic
35#492×C151C2211yescharacteristic
36#487×C151C2211yescharacteristic, complemented
37#486×C151C2211yescharacteristic, complemented
38#478×C151—21no—
39#477×C151C2211yescharacteristic, complemented
40#476×C151—21no—
41#476×C151C2211yescharacteristic
42#476×C151C2211yescharacteristic
43#476×C151C2211yescharacteristic, complemented
44#469×C151—21no—
45#469×C151—21no—
46#466×C151—21no—
47#465×C151—21no—
48#463×C151—21no—
49#463×C151—22no—
50#460×C151C2211yescharacteristic, complemented
51#459×C151—21no—
52#459×C151C2211yescharacteristic
53#459×C151C2211yescharacteristic
54#459×C151C2211yescharacteristic, complemented
55#449×C151—22no—
56#431×C151C2211yescharacteristic, complemented
57#423×C151C2211yescharacteristic, complemented
58C2×C4⋊C8×C151C2211yescharacteristic, complemented
59#332×C151C2211yescharacteristic, complemented
60#332×C151C2211yescharacteristic, complemented
61#331×C151C2211yescharacteristic
62#331×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic, complemented
64Q8⋊C8×C151C2211yescharacteristic, complemented
65D4⋊C8×C151C2211yescharacteristic
66D4⋊C8×C151C2211yescharacteristic
67D4⋊C8×C151C2211yescharacteristic
68D4⋊C8×C151C2211yescharacteristic
69D4⋊C8×C151C2211yescharacteristic, complemented
70D4⋊C8×C151C2211yescharacteristic, complemented
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C2×#41×C151—21no—
74C2×#41×C151—21no—
75C2×#41×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C2×SD16×C151—22no—
79C2×SD16×C151—21no—
80C2×D8×C151—22no—
81C2×D8×C151—21no—
82C2×D8×C151—21no—
83C2×D8×C151—21no—
84C2×M16×C151—21no—
85C22×C8×C151—21no—
86C4⋊Q8×C151D411yescharacteristic
87C4⋊Q8×C151C2311yescharacteristic
88C4⋊Q8×C151C2311yescharacteristic
89#127×C151—22no—
90#127×C151—21no—
91#127×C151D411yescharacteristic
92#127×C151C2311yescharacteristic
93#127×C151C2311yescharacteristic
94#126×C151—22no—
95#126×C151—22no—
96#126×C151—21no—
97#125×C151D411yescharacteristic
98#124×C151—22no—
99#124×C151—21no—
100#124×C151—21no—
101#124×C151—21no—
102#124×C151—21no—
103#124×C151D411yescharacteristic
104#123×C151—22no—
105#123×C151—22no—
106#123×C151—21no—
107#123×C151—22no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151—21no—
110C22⋊Q8×C151—21no—
111C22⋊Q8×C151D411yescharacteristic
112#121×C151—22no—
113#121×C151—22no—
114#121×C151—22no—
115#121×C151—22no—
116#121×C151—22no—
117#121×C151—21no—
118#121×C151—22no—
119#121×C151—21no—
120#121×C151—21no—
121#121×C151—21no—
122#121×C151—21no—
123#121×C151—21no—
124#121×C151—21no—
125#121×C151—21no—
126#121×C151D412yes—
127#121×C151D411yescharacteristic
128#121×C151D411yescharacteristic
129#121×C151D411yescharacteristic
130#120×C151—22no—
131#120×C151—22no—
132#120×C151—22no—
133#120×C151—22no—
134C4×Q8×C151—21no—
135C4×Q8×C151C2311yescharacteristic
136C4×D4×C151—22no—
137C4×D4×C151—21no—
138C4×D4×C151—21no—
139C4×D4×C151—21no—
140C4×D4×C151—21no—
141C4×D4×C151—21no—
142C4×D4×C151—21no—
143C4×D4×C151D412yes—
144C4×D4×C151C2311yescharacteristic
145C4×D4×C151C2311yescharacteristic
146C4×D4×C151C2311yescharacteristic
147#117×C151—21no—
148#117×C151—21no—
149C2×C4⋊C4×C151—21no—
150C2×C22⋊C4×C151—22no—
151C2×C42×C151C2311yescharacteristic
152#107×C151—21no—
153#106×C151—21no—
154#106×C151—21no—
155#106×C151—21no—
156C4⋊C8×C151—21no—
157C4⋊C8×C151—21no—
158C4⋊C8×C151—21no—
159C4⋊C8×C151C2311yescharacteristic
160C4⋊C8×C151C2311yescharacteristic
161C4⋊C8×C151C2311yescharacteristic
162C4⋊C8×C151C2311yescharacteristic
163#103×C151—22no—
164#103×C151—21no—
165#102×C151—21no—
166#102×C151—21no—
167#102×C151—21no—
168#102×C151—22no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—21no—
172#102×C151—21no—
173C22⋊C8×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176C24×C151—22no—
177#41×C151—81no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—81no—
181#41×C151—81no—
182#41×C151—81no—
183#41×C151—81no—
184#41×C151—81no—
185#41×C151—82no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151C2×D411yescharacteristic
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—22no—
194C2×D4×C151—22no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—22no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—41no—
207C2×D4×C151—81no—
208C2×D4×C151—81no—
209C2×D4×C151—81no—
210C2×D4×C151—81no—
211C2×D4×C151C2×D411yescharacteristic
212C2×D4×C151C2×D411yescharacteristic
213C2×D4×C151C2×D411yescharacteristic
214C2×D4×C151C2×D412yes—
215C22×C4×C151—22no—
216C22×C4×C151—22no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—22no—
221C22×C4×C151—41no—
222C22×C4×C151C2×D411yescharacteristic
223C22×C4×C151C2×D411yescharacteristic
224C22×C4×C151C2×D411yescharacteristic
225SD16×C151—81no—
226SD16×C151—82no—
227D8×C151—81no—
228D8×C151—81no—
229D8×C151—81no—
230D8×C151—82no—
231M16×C151—81no—
232C2×C8×C151—21no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—21no—
238C2×C8×C151—81no—
239C4⋊C4×C151—22no—
240C4⋊C4×C151—22no—
241C4⋊C4×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—21no—
244C4⋊C4×C151—21no—
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151C2×D412yes—
250C4⋊C4×C151C2×D411yescharacteristic
251C4⋊C4×C151C2×D411yescharacteristic
252C4⋊C4×C151C2×D411yescharacteristic
253C4⋊C4×C151C2×D411yescharacteristic
254C22⋊C4×C151—22no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—22no—
257C22⋊C4×C151—22no—
258C22⋊C4×C151—22no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—21no—
262C22⋊C4×C151—21no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—22no—
266C22⋊C4×C151—22no—
267C22⋊C4×C151—21no—
268C22⋊C4×C151—21no—
269C22⋊C4×C151—21no—
270C22⋊C4×C151—41no—
271C22⋊C4×C151—41no—
272C42×C151—22no—
273C42×C151—21no—
274C42×C151C2×D411yescharacteristic
275C42×C151C2×D411yescharacteristic
276C42×C151C2×D411yescharacteristic
277C42×C151C2411yescharacteristic
278C23×C151—21no—
279C23×C151—21no—
280C23×C151—22no—
281C23×C151—21no—
282C23×C151—41no—
283C23×C151—82no—
284C23×C151—82no—
285C23×C151—82no—
286C23×C151#12011yescharacteristic
287Q8×C151—21no—
288Q8×C151—21no—
289Q8×C151—42no—
290Q8×C151—41no—
291Q8×C151—41no—
292Q8×C151—81no—
293D4×C151—21no—
294D4×C151—21no—
295D4×C151—21no—
296D4×C151—21no—
297D4×C151—21no—
298D4×C151—21no—
299D4×C151—42no—
300D4×C151—42no—
301D4×C151—41no—
302D4×C151—41no—
303D4×C151—41no—
304D4×C151—41no—
305D4×C151—41no—
306D4×C151—41no—
307D4×C151—41no—
308D4×C151—41no—
309D4×C151—81no—
310D4×C151—81no—
311D4×C151—81no—
312D4×C151—81no—
313D4×C151—82no—
314D4×C151—81no—
315D4×C151—82no—
316D4×C151—82no—
317D4×C151—82no—
318D4×C151—82no—
319D4×C151—82no—
320D4×C151—82no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—22no—
327C2×C4×C151—21no—
328C2×C4×C151—21no—
329C2×C4×C151—21no—
330C2×C4×C151—21no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—41no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—41no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—82no—
340C2×C4×C151—82no—
341C2×C4×C151—82no—
342C2×C4×C151—82no—
343C2×C4×C151#12011yescharacteristic
344C2×C4×C151#12011yescharacteristic
345C2×C4×C151#12011yescharacteristic
346C2×C4×C151C22×D411yescharacteristic
347C2×C4×C151C22×D411yescharacteristic
348C2×C4×C151C22×D411yescharacteristic
349C8×C151—41no—
350C8×C151—41no—
351C8×C151—41no—
352C8×C151—41no—
353C8×C151—41no—
354C8×C151—41no—
355C22×C151—21no—
356C22×C151—21no—
357C22×C151—21no—
358C22×C151—41no—
359C22×C151—41no—
360C22×C151—41no—
361C22×C151—41no—
362C22×C151—42no—
363C22×C151—42no—
364C22×C151—41no—
365C22×C151—41no—
366C22×C151—42no—
367C22×C151—41no—
368C22×C151—41no—
369C22×C151—41no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151—164no—
374C22×C151C2×#12011yescharacteristic
375C4×C151—21no—
376C4×C151—21no—
377C4×C151—21no—
378C4×C151—21no—
379C4×C151—41no—
380C4×C151—41no—
381C4×C151—41no—
382C4×C151—41no—
383C4×C151—42no—
384C4×C151—41no—
385C4×C151—81no—
386C4×C151#57611yescharacteristic
387C4×C151#57611yescharacteristic
388C4×C151#57711yescharacteristic
389C4×C151#57711yescharacteristic
390C2×C151—41no—
391C2×C151—81no—
392C2×C151—82no—
393C2×C151—81no—
394C2×C151—81no—
395C2×C151—161no—
396C2×C151#301211yescharacteristic
397C2×C151#301211yescharacteristic
398C2×C151#302111yescharacteristic
399#18962C15111yesmaximal, characteristic, direct product factor, Sylow
400C151#1896211yescharacteristic, direct product factor, Sylow
401#3546C2×C15111yescharacteristic, complemented
402#3253C2×C15111yescharacteristic, complemented
403#3247C2×C15111yescharacteristic, complemented
404#3207C2×C15111yescharacteristic, complemented
405#1638C2×C15111yescharacteristic, complemented
406#1635C2×C15111yescharacteristic, complemented
407#1631C2×C15111yescharacteristic, complemented
408#1629C2×C15111yescharacteristic, complemented
409#1628C2×C15111yescharacteristic, complemented
410#1625C2×C15111yescharacteristic, complemented
411#1621C2×C15111yescharacteristic, complemented
412#1619C2×C15111yescharacteristic, complemented
413#1547C2×C15111yescharacteristic, complemented
414#1495C2×C15111yescharacteristic, complemented
415#1480C2×C15111yescharacteristic, complemented
416#560—22no—
417#556C22×C15111yescharacteristic
418#553—21no—
419#550—21no—
420#550C22×C15111yescharacteristic
421#547C22×C15111yescharacteristic
422#546—21no—
423#546—21no—
424D42C22×C15111yescharacteristic
425#542—21no—
426#538—22no—
427#537—21no—
428#535—21no—
429#535—21no—
430#532C22×C15111yescharacteristic
431#532C22×C15111yescharacteristic
432#532C22×C15111yescharacteristic, complemented
433#529C22×C15111yescharacteristic
434#493C22×C15111yescharacteristic
435#492C22×C15111yescharacteristic
436#487C22×C15111yescharacteristic, complemented
437#486C22×C15111yescharacteristic, complemented
438#478—21no—
439#477C22×C15111yescharacteristic, complemented
440#476—21no—
441#476C22×C15111yescharacteristic
442#476C22×C15111yescharacteristic
443#476C22×C15111yescharacteristic, complemented
444#469—21no—
445#469—21no—
446#466—21no—
447#465—21no—
448#463—21no—
449#463—22no—
450#460C22×C15111yescharacteristic, complemented
451#459—21no—
452#459C22×C15111yescharacteristic
453#459C22×C15111yescharacteristic
454#459C22×C15111yescharacteristic, complemented
455#449—22no—
456#431C22×C15111yescharacteristic, complemented
457#423C22×C15111yescharacteristic, complemented
458C2×C4⋊C8C22×C15111yescharacteristic, complemented
459#332C22×C15111yescharacteristic, complemented
460#332C22×C15111yescharacteristic, complemented
461#331C22×C15111yescharacteristic
462#331C22×C15111yescharacteristic
463Q8⋊C8C22×C15111yescharacteristic, complemented
464Q8⋊C8C22×C15111yescharacteristic, complemented
465D4⋊C8C22×C15111yescharacteristic
466D4⋊C8C22×C15111yescharacteristic
467D4⋊C8C22×C15111yescharacteristic
468D4⋊C8C22×C15111yescharacteristic
469D4⋊C8C22×C15111yescharacteristic, complemented
470D4⋊C8C22×C15111yescharacteristic, complemented
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C15111yescharacteristic
487C4⋊Q8C23×C15111yescharacteristic
488C4⋊Q8C23×C15111yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C15111yescharacteristic
492#127C23×C15111yescharacteristic
493#127C23×C15111yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C15111yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C15111yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C15111yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C15111yescharacteristic
527#121D4×C15111yescharacteristic
528#121D4×C15111yescharacteristic
529#121D4×C15112yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C15111yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C15112yes—
544C4×D4C23×C15111yescharacteristic
545C4×D4C23×C15111yescharacteristic
546C4×D4C23×C15111yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C15111yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C15111yescharacteristic
560C4⋊C8C23×C15111yescharacteristic
561C4⋊C8C23×C15111yescharacteristic
562C4⋊C8C23×C15111yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C15111yescharacteristic
575C4×C8C23×C15111yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C15111yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C15111yescharacteristic
612C2×D4C2×D4×C15111yescharacteristic
613C2×D4C2×D4×C15111yescharacteristic
614C2×D4C2×D4×C15112yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C15111yescharacteristic
623C22×C4C2×D4×C15111yescharacteristic
624C22×C4C2×D4×C15111yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C15112yes—
650C4⋊C4C2×D4×C15111yescharacteristic
651C4⋊C4C2×D4×C15111yescharacteristic
652C4⋊C4C2×D4×C15111yescharacteristic
653C4⋊C4C2×D4×C15111yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C15111yescharacteristic
675C42C2×D4×C15111yescharacteristic
676C42C2×D4×C15111yescharacteristic
677C42C24×C15111yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C15111yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—82no—
714D4—81no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C15111yescharacteristic
744C2×C4#120×C15111yescharacteristic
745C2×C4#120×C15111yescharacteristic
746C2×C4C22×D4×C15111yescharacteristic
747C2×C4C22×D4×C15111yescharacteristic
748C2×C4C22×D4×C15111yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C15111yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4#576×C15111yescharacteristic
787C4#576×C15111yescharacteristic
788C4#577×C15111yescharacteristic
789C4#577×C15111yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2#3012×C15111yescharacteristic
797C2#3012×C15111yescharacteristic
798C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3546×C151C2semidirect
2. #3253×C151C2semidirect
3. #3247×C151C2semidirect
4. #3207×C151C2semidirect
5. #1638×C151C2semidirect
6. #1635×C151C2semidirect
7. #1631×C151C2semidirect
8. #1629×C151C2semidirect
9. #1628×C151C2semidirect
10. #1625×C151C2semidirect
11. #1621×C151C2semidirect
12. #1619×C151C2semidirect
13. #1547×C151C2semidirect
14. #1495×C151C2semidirect
15. #1480×C151C2semidirect
32. #532×C151C22semidirect
36. #487×C151C22semidirect
37. #486×C151C22semidirect
39. #477×C151C22semidirect
43. #476×C151C22semidirect
50. #460×C151C22semidirect
54. #459×C151C22semidirect
56. #431×C151C22semidirect
57. #423×C151C22semidirect
58. C2×C4⋊C8×C151C22semidirect
59. #332×C151C22semidirect
60. #332×C151C22semidirect
63. Q8⋊C8×C151C22semidirect
64. Q8⋊C8×C151C22semidirect
69. D4⋊C8×C151C22semidirect
70. D4⋊C8×C151C22semidirect
399. #18962C151direct (N × H)
400. C151#18962direct (N × H)
401. #3546C2×C151semidirect
402. #3253C2×C151semidirect
403. #3247C2×C151semidirect
404. #3207C2×C151semidirect
405. #1638C2×C151semidirect
406. #1635C2×C151semidirect
407. #1631C2×C151semidirect
408. #1629C2×C151semidirect
409. #1628C2×C151semidirect
410. #1625C2×C151semidirect
411. #1621C2×C151semidirect
412. #1619C2×C151semidirect
413. #1547C2×C151semidirect
414. #1495C2×C151semidirect
415. #1480C2×C151semidirect
432. #532C22×C151semidirect
436. #487C22×C151semidirect
437. #486C22×C151semidirect
439. #477C22×C151semidirect
443. #476C22×C151semidirect
450. #460C22×C151semidirect
454. #459C22×C151semidirect
456. #431C22×C151semidirect
457. #423C22×C151semidirect
458. C2×C4⋊C8C22×C151semidirect
459. #332C22×C151semidirect
460. #332C22×C151semidirect
463. Q8⋊C8C22×C151semidirect
464. Q8⋊C8C22×C151semidirect
469. D4⋊C8C22×C151semidirect
470. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3546×C1512
#3253×C1512
#3247×C1512
#3207×C1512
#1638×C1512
#1635×C1512
#1631×C1512
#1629×C1512
#1628×C1512
#1625×C1512
#1621×C1512
#1619×C1512
#1547×C1512
#1495×C1512
#1480×C1512
#18962151