Finite Group Databasebeta

← C151×#18739 #50323664

Subgroups — C151×#18739 #50323664

Order 38656.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3546×C151C211yesmaximal, characteristic
2#3246×C151C211yesmaximal, characteristic, complemented
3#3233×C151C211yesmaximal, characteristic, complemented
4#3182×C151C211yesmaximal, characteristic, complemented
5#1650×C151C211yesmaximal, characteristic, complemented
6#1647×C151C211yesmaximal, characteristic, complemented
7#1642×C151C211yesmaximal, characteristic, complemented
8#1639×C151C211yesmaximal, characteristic, complemented
9#1638×C151C211yesmaximal, characteristic, complemented
10#1635×C151C211yesmaximal, characteristic, complemented
11#1631×C151C211yesmaximal, characteristic, complemented
12#1629×C151C211yesmaximal, characteristic, complemented
13#1540×C151C211yesmaximal, characteristic, complemented
14#1484×C151C211yesmaximal, characteristic, complemented
15#1483×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#533×C151C2211yescharacteristic, complemented
31#532×C151C2211yescharacteristic
32#532×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#500×C151C2211yescharacteristic, complemented
35#499×C151—21no—
36#492×C151C2211yescharacteristic
37#488×C151—21no—
38#487×C151C2211yescharacteristic, complemented
39#486×C151C2211yescharacteristic
40#485×C151—21no—
41#482×C151—21no—
42#477×C151C2211yescharacteristic, complemented
43#476×C151C2211yescharacteristic
44#476×C151C2211yescharacteristic
45#476×C151C2211yescharacteristic, complemented
46#475×C151—21no—
47#475×C151C2211yescharacteristic, complemented
48#474×C151C2211yescharacteristic
49#468×C151—22no—
50#465×C151—21no—
51#465×C151—21no—
52#461×C151C2211yescharacteristic
53#461×C151C2211yescharacteristic, complemented
54#460×C151—21no—
55#440×C151—22no—
56#431×C151C2211yescharacteristic, complemented
57C2×C4⋊C8×C151C2211yescharacteristic, complemented
58C4×M16×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—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C2×SD16×C151—22no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C2×M16×C151—21no—
81C22×C8×C151—21no—
82C4⋊Q8×C151D411yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86#127×C151—22no—
87#127×C151—21no—
88#127×C151D411yescharacteristic
89#127×C151C2311yescharacteristic
90#126×C151—22no—
91#126×C151—22no—
92#126×C151—21no—
93#125×C151—21no—
94#125×C151D411yescharacteristic
95#124×C151—22no—
96#124×C151—21no—
97#124×C151—21no—
98#124×C151—21no—
99#124×C151D411yescharacteristic
100#123×C151—22no—
101#123×C151—22no—
102#123×C151—21no—
103#123×C151—22no—
104C22⋊Q8×C151—22no—
105C22⋊Q8×C151—21no—
106C22⋊Q8×C151—21no—
107C22⋊Q8×C151—21no—
108C22⋊Q8×C151—21no—
109C22⋊Q8×C151D411yescharacteristic
110#121×C151—22no—
111#121×C151—22no—
112#121×C151—22no—
113#121×C151—22no—
114#121×C151—22no—
115#121×C151—21no—
116#121×C151—22no—
117#121×C151—21no—
118#121×C151—21no—
119#121×C151—21no—
120#121×C151—21no—
121#121×C151—21no—
122#121×C151D411yescharacteristic
123#121×C151D411yescharacteristic
124#121×C151D412yes—
125#121×C151D411yescharacteristic
126#120×C151—22no—
127#120×C151—22no—
128#120×C151—22no—
129#120×C151—22no—
130C4×Q8×C151—21no—
131C4×Q8×C151—21no—
132C4×Q8×C151—21no—
133C4×Q8×C151C2311yescharacteristic
134C4×D4×C151—22no—
135C4×D4×C151—21no—
136C4×D4×C151—21no—
137C4×D4×C151—21no—
138C4×D4×C151—21no—
139C4×D4×C151D412yes—
140C4×D4×C151C2311yescharacteristic
141C4×D4×C151C2311yescharacteristic
142C4×D4×C151C2311yescharacteristic
143#117×C151—21no—
144#117×C151—21no—
145#117×C151—21no—
146C2×C4⋊C4×C151—21no—
147C2×C22⋊C4×C151—22no—
148C2×C42×C151C2311yescharacteristic
149#107×C151—22no—
150#107×C151—21no—
151#107×C151—21no—
152#106×C151—21no—
153#106×C151—21no—
154#106×C151—21no—
155#106×C151—21no—
156C4⋊C8×C151—21no—
157C4⋊C8×C151C2311yescharacteristic
158C4⋊C8×C151C2311yescharacteristic
159C4⋊C8×C151C2311yescharacteristic
160C4⋊C8×C151C2311yescharacteristic
161#103×C151—22no—
162#103×C151—21no—
163#103×C151—21no—
164#103×C151—21no—
165#103×C151—21no—
166#102×C151—22no—
167#102×C151—21no—
168#102×C151—21no—
169#102×C151—21no—
170#102×C151—21no—
171C22⋊C8×C151—21no—
172#97×C151—21no—
173C4×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—
185C2×Q8×C151—21no—
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—81no—
204C2×D4×C151—81no—
205C2×D4×C151—81no—
206C2×D4×C151—81no—
207C2×D4×C151C2×D411yescharacteristic
208C2×D4×C151C2×D411yescharacteristic
209C2×D4×C151C2×D411yescharacteristic
210C2×D4×C151C2×D412yes—
211C22×C4×C151—22no—
212C22×C4×C151—22no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—22no—
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219C22×C4×C151C2×D411yescharacteristic
220SD16×C151—44no—
221SD16×C151—81no—
222SD16×C151—81no—
223M16×C151—42no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—81no—
231C4⋊C4×C151—22no—
232C4⋊C4×C151—22no—
233C4⋊C4×C151—21no—
234C4⋊C4×C151—21no—
235C4⋊C4×C151—21no—
236C4⋊C4×C151—21no—
237C4⋊C4×C151—21no—
238C4⋊C4×C151—21no—
239C4⋊C4×C151—21no—
240C4⋊C4×C151—21no—
241C4⋊C4×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—41no—
244C4⋊C4×C151—41no—
245C4⋊C4×C151C2×D411yescharacteristic
246C4⋊C4×C151C2×D411yescharacteristic
247C4⋊C4×C151C2×D412yes—
248C4⋊C4×C151C2×D411yescharacteristic
249C4⋊C4×C151C2×D411yescharacteristic
250C22⋊C4×C151—22no—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—22no—
255C22⋊C4×C151—21no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—22no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—41no—
267C42×C151—22no—
268C42×C151—21no—
269C42×C151—41no—
270C42×C151C2×D411yescharacteristic
271C42×C151C2×D411yescharacteristic
272C42×C151C2×D411yescharacteristic
273C42×C151C2411yescharacteristic
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—22no—
277C23×C151—21no—
278C23×C151—82no—
279C23×C151—82no—
280C23×C151—82no—
281C23×C151#12011yescharacteristic
282Q8×C151—21no—
283Q8×C151—21no—
284Q8×C151—42no—
285Q8×C151—41no—
286Q8×C151—41no—
287Q8×C151—41no—
288Q8×C151—41no—
289Q8×C151—81no—
290D4×C151—21no—
291D4×C151—21no—
292D4×C151—21no—
293D4×C151—21no—
294D4×C151—21no—
295D4×C151—21no—
296D4×C151—42no—
297D4×C151—41no—
298D4×C151—41no—
299D4×C151—41no—
300D4×C151—41no—
301D4×C151—81no—
302D4×C151—81no—
303D4×C151—81no—
304D4×C151—81no—
305D4×C151—82no—
306D4×C151—81no—
307D4×C151—82no—
308D4×C151—82no—
309D4×C151—82no—
310D4×C151—82no—
311D4×C151—82no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—22no—
318C2×C4×C151—21no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—82no—
332C2×C4×C151—82no—
333C2×C4×C151—82no—
334C2×C4×C151#12011yescharacteristic
335C2×C4×C151#12011yescharacteristic
336C2×C4×C151#12011yescharacteristic
337C2×C4×C151C22×D411yescharacteristic
338C2×C4×C151C22×D411yescharacteristic
339C2×C4×C151C22×D411yescharacteristic
340C8×C151—22no—
341C8×C151—41no—
342C8×C151—41no—
343C8×C151—41no—
344C8×C151—41no—
345C8×C151—41no—
346C22×C151—21no—
347C22×C151—21no—
348C22×C151—21no—
349C22×C151—41no—
350C22×C151—41no—
351C22×C151—42no—
352C22×C151—41no—
353C22×C151—41no—
354C22×C151—41no—
355C22×C151—42no—
356C22×C151—41no—
357C22×C151—42no—
358C22×C151—41no—
359C22×C151—41no—
360C22×C151—41no—
361C22×C151—164no—
362C22×C151C2×#12011yescharacteristic
363C4×C151—21no—
364C4×C151—21no—
365C4×C151—21no—
366C4×C151—21no—
367C4×C151—41no—
368C4×C151—41no—
369C4×C151—41no—
370C4×C151—41no—
371C4×C151—42no—
372C4×C151—41no—
373C4×C151—81no—
374C4×C151—81no—
375C4×C151#57611yescharacteristic
376C4×C151#57711yescharacteristic
377C4×C151#57711yescharacteristic
378C4×C151#57711yescharacteristic
379C2×C151—41no—
380C2×C151—81no—
381C2×C151—82no—
382C2×C151—81no—
383C2×C151—81no—
384C2×C151#300911yescharacteristic
385C2×C151#301211yescharacteristic
386C2×C151#301811yescharacteristic
387#18739C15111yesmaximal, characteristic, direct product factor, Sylow
388C151#1873911yescharacteristic, direct product factor, Sylow
389#3546C2×C15111yescharacteristic
390#3246C2×C15111yescharacteristic, complemented
391#3233C2×C15111yescharacteristic, complemented
392#3182C2×C15111yescharacteristic, complemented
393#1650C2×C15111yescharacteristic, complemented
394#1647C2×C15111yescharacteristic, complemented
395#1642C2×C15111yescharacteristic, complemented
396#1639C2×C15111yescharacteristic, complemented
397#1638C2×C15111yescharacteristic, complemented
398#1635C2×C15111yescharacteristic, complemented
399#1631C2×C15111yescharacteristic, complemented
400#1629C2×C15111yescharacteristic, complemented
401#1540C2×C15111yescharacteristic, complemented
402#1484C2×C15111yescharacteristic, complemented
403#1483C2×C15111yescharacteristic, complemented
404#560—22no—
405#556C22×C15111yescharacteristic
406#553—21no—
407#550—21no—
408#550C22×C15111yescharacteristic
409#547C22×C15111yescharacteristic
410#546—21no—
411#546—21no—
412D42C22×C15111yescharacteristic
413#542—21no—
414#538—22no—
415#537—21no—
416#535—21no—
417#535—21no—
418#533C22×C15111yescharacteristic, complemented
419#532C22×C15111yescharacteristic
420#532C22×C15111yescharacteristic
421#529C22×C15111yescharacteristic
422#500C22×C15111yescharacteristic, complemented
423#499—21no—
424#492C22×C15111yescharacteristic
425#488—21no—
426#487C22×C15111yescharacteristic, complemented
427#486C22×C15111yescharacteristic
428#485—21no—
429#482—21no—
430#477C22×C15111yescharacteristic, complemented
431#476C22×C15111yescharacteristic
432#476C22×C15111yescharacteristic
433#476C22×C15111yescharacteristic, complemented
434#475—21no—
435#475C22×C15111yescharacteristic, complemented
436#474C22×C15111yescharacteristic
437#468—22no—
438#465—21no—
439#465—21no—
440#461C22×C15111yescharacteristic
441#461C22×C15111yescharacteristic, complemented
442#460—21no—
443#440—22no—
444#431C22×C15111yescharacteristic, complemented
445C2×C4⋊C8C22×C15111yescharacteristic, complemented
446C4×M16C22×C15111yescharacteristic, complemented
447#332C22×C15111yescharacteristic, complemented
448#332C22×C15111yescharacteristic, complemented
449#331C22×C15111yescharacteristic
450#331C22×C15111yescharacteristic
451Q8⋊C8C22×C15111yescharacteristic, complemented
452Q8⋊C8C22×C15111yescharacteristic, complemented
453D4⋊C8C22×C15111yescharacteristic
454D4⋊C8C22×C15111yescharacteristic
455D4⋊C8C22×C15111yescharacteristic
456D4⋊C8C22×C15111yescharacteristic
457D4⋊C8C22×C15111yescharacteristic, complemented
458D4⋊C8C22×C15111yescharacteristic, complemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×SD16—22no—
466C2×SD16—21no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C15111yescharacteristic
471C4⋊Q8C23×C15111yescharacteristic
472C4⋊Q8C23×C15111yescharacteristic
473C4⋊Q8C23×C15111yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C15111yescharacteristic
477#127C23×C15111yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C15111yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C15111yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C15111yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C15111yescharacteristic
511#121D4×C15111yescharacteristic
512#121D4×C15111yescharacteristic
513#121D4×C15112yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C15111yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C15112yes—
528C4×D4C23×C15111yescharacteristic
529C4×D4C23×C15111yescharacteristic
530C4×D4C23×C15111yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C15111yescharacteristic
537#107—22no—
538#107—21no—
539#107—21no—
540#106—21no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C15111yescharacteristic
546C4⋊C8C23×C15111yescharacteristic
547C4⋊C8C23×C15111yescharacteristic
548C4⋊C8C23×C15111yescharacteristic
549#103—21no—
550#103—21no—
551#103—22no—
552#103—21no—
553#103—21no—
554#102—22no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C15111yescharacteristic
563C4×C8C23×C15111yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C15111yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C15111yescharacteristic
596C2×D4C2×D4×C15111yescharacteristic
597C2×D4C2×D4×C15111yescharacteristic
598C2×D4C2×D4×C15112yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C15111yescharacteristic
606C22×C4C2×D4×C15111yescharacteristic
607C22×C4C2×D4×C15111yescharacteristic
608SD16—44no—
609SD16—81no—
610SD16—81no—
611M16—42no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C15111yescharacteristic
634C4⋊C4C2×D4×C15111yescharacteristic
635C4⋊C4C2×D4×C15112yes—
636C4⋊C4C2×D4×C15111yescharacteristic
637C4⋊C4C2×D4×C15111yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C15111yescharacteristic
659C42C2×D4×C15111yescharacteristic
660C42C2×D4×C15111yescharacteristic
661C42C24×C15111yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C15111yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—82no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C15111yescharacteristic
723C2×C4#120×C15111yescharacteristic
724C2×C4#120×C15111yescharacteristic
725C2×C4C22×D4×C15111yescharacteristic
726C2×C4C22×D4×C15111yescharacteristic
727C2×C4C22×D4×C15111yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C15111yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4#576×C15111yescharacteristic
764C4#577×C15111yescharacteristic
765C4#577×C15111yescharacteristic
766C4#577×C15111yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2#3009×C15111yescharacteristic
773C2#3012×C15111yescharacteristic
774C2#3018×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3546×C151C2
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
2. #3246×C151C2semidirect
3. #3233×C151C2semidirect
4. #3182×C151C2semidirect
5. #1650×C151C2semidirect
6. #1647×C151C2semidirect
7. #1642×C151C2semidirect
8. #1639×C151C2semidirect
9. #1638×C151C2semidirect
10. #1635×C151C2semidirect
11. #1631×C151C2semidirect
12. #1629×C151C2semidirect
13. #1540×C151C2semidirect
14. #1484×C151C2semidirect
15. #1483×C151C2semidirect
30. #533×C151C22semidirect
34. #500×C151C22semidirect
38. #487×C151C22semidirect
42. #477×C151C22semidirect
45. #476×C151C22semidirect
47. #475×C151C22semidirect
53. #461×C151C22semidirect
56. #431×C151C22semidirect
57. C2×C4⋊C8×C151C22semidirect
58. C4×M16×C151C22semidirect
59. #332×C151C22semidirect
60. #332×C151C22semidirect
63. Q8⋊C8×C151C22semidirect
64. Q8⋊C8×C151C22semidirect
69. D4⋊C8×C151C22semidirect
70. D4⋊C8×C151C22semidirect
387. #18739C151direct (N × H)
388. C151#18739direct (N × H)
390. #3246C2×C151semidirect
391. #3233C2×C151semidirect
392. #3182C2×C151semidirect
393. #1650C2×C151semidirect
394. #1647C2×C151semidirect
395. #1642C2×C151semidirect
396. #1639C2×C151semidirect
397. #1638C2×C151semidirect
398. #1635C2×C151semidirect
399. #1631C2×C151semidirect
400. #1629C2×C151semidirect
401. #1540C2×C151semidirect
402. #1484C2×C151semidirect
403. #1483C2×C151semidirect
418. #533C22×C151semidirect
422. #500C22×C151semidirect
426. #487C22×C151semidirect
430. #477C22×C151semidirect
433. #476C22×C151semidirect
435. #475C22×C151semidirect
441. #461C22×C151semidirect
444. #431C22×C151semidirect
445. C2×C4⋊C8C22×C151semidirect
446. C4×M16C22×C151semidirect
447. #332C22×C151semidirect
448. #332C22×C151semidirect
451. Q8⋊C8C22×C151semidirect
452. Q8⋊C8C22×C151semidirect
457. D4⋊C8C22×C151semidirect
458. 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
#3246×C1512
#3233×C1512
#3182×C1512
#1650×C1512
#1647×C1512
#1642×C1512
#1639×C1512
#1638×C1512
#1635×C1512
#1631×C1512
#1629×C1512
#1540×C1512
#1484×C1512
#1483×C1512
#18739151