Finite Group Databasebeta

← C151×#18658 #50323583

Subgroups — C151×#18658 #50323583

Order 38656.

972 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3514×C151C211yesmaximal, characteristic, complemented
2#3212×C151C211yesmaximal, characteristic, complemented
3#3169×C151C211yesmaximal, characteristic, complemented
4#3115×C151C211yesmaximal, characteristic, complemented
5#1650×C151C211yesmaximal, characteristic, complemented
6#1649×C151C211yesmaximal, characteristic, complemented
7#1640×C151C211yesmaximal, characteristic, complemented
8#1639×C151C211yesmaximal, characteristic, complemented
9#1628×C151C211yesmaximal, characteristic, complemented
10#1627×C151C211yesmaximal, characteristic, complemented
11#1620×C151C211yesmaximal, characteristic, complemented
12#1619×C151C211yesmaximal, characteristic, complemented
13#1553×C151C211yesmaximal, characteristic, complemented
14#1494×C151C211yesmaximal, characteristic, complemented
15#1476×C151C211yesmaximal, characteristic, complemented
16#559×C151C2211yescharacteristic
17#556×C151C2211yescharacteristic
18#555×C151—21no—
19#551×C151—22no—
20D4×Q8×C151C2211yescharacteristic
21#548×C151—21no—
22#546×C151—21no—
23#546×C151—21no—
24D42×C151C2211yescharacteristic
25#542×C151—21no—
26#538×C151—22no—
27#532×C151C2211yescharacteristic
28#532×C151C2211yescharacteristic, complemented
29#529×C151—21no—
30#529×C151C2211yescharacteristic
31C2×#124×C151—21no—
32#518×C151—21no—
33C4×#41×C151C2211yescharacteristic
34#500×C151C2211yescharacteristic, complemented
35#495×C151—21no—
36#493×C151C2211yescharacteristic
37#488×C151—21no—
38#486×C151C2211yescharacteristic
39#486×C151C2211yescharacteristic, complemented
40#482×C151—21no—
41#475×C151C2211yescharacteristic, complemented
42#474×C151C2211yescharacteristic
43#466×C151—22no—
44#462×C151C2211yescharacteristic, complemented
45#461×C151C2211yescharacteristic
46#460×C151C2211yescharacteristic, complemented
47#460×C151C2211yescharacteristic, complemented
48#459×C151C2211yescharacteristic
49#459×C151C2211yescharacteristic
50#452×C151—21no—
51#449×C151—21no—
52#449×C151—21no—
53#442×C151—21no—
54#440×C151—21no—
55C4×D8×C151—22no—
56#432×C151C2211yescharacteristic, complemented
57#431×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
65Q8⋊C8×C151C2211yescharacteristic, complemented
66Q8⋊C8×C151C2211yescharacteristic, complemented
67D4⋊C8×C151C2211yescharacteristic
68D4⋊C8×C151C2211yescharacteristic
69D4⋊C8×C151C2211yescharacteristic
70D4⋊C8×C151C2211yescharacteristic
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C2×#41×C151D411yescharacteristic
74C22×Q8×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C2×Q16×C151—21no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C2×SD16×C151—21no—
81C2×D8×C151—22no—
82C2×D8×C151—21no—
83C2×D8×C151—21no—
84C22×C8×C151—21no—
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151C2311yescharacteristic
87C4⋊Q8×C151C2311yescharacteristic
88#127×C151C2311yescharacteristic
89#127×C151C2311yescharacteristic
90#126×C151—22no—
91#126×C151—22no—
92#126×C151—21no—
93#125×C151D411yescharacteristic
94#124×C151—22no—
95#124×C151—22no—
96#124×C151—22no—
97#124×C151—21no—
98#124×C151—21no—
99#124×C151—21no—
100#124×C151—21no—
101#124×C151—21no—
102#124×C151D411yescharacteristic
103#123×C151—22no—
104#123×C151—22no—
105#123×C151—22no—
106#123×C151—21no—
107C22⋊Q8×C151—22no—
108C22⋊Q8×C151—21no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—21no—
111C22⋊Q8×C151D411yescharacteristic
112#121×C151—22no—
113#121×C151—22no—
114#121×C151—21no—
115#121×C151—21no—
116#121×C151—21no—
117#121×C151—21no—
118#121×C151—21no—
119#121×C151D411yescharacteristic
120#121×C151D412yes—
121#120×C151—22no—
122#120×C151—22no—
123C4×Q8×C151—21no—
124C4×Q8×C151D411yescharacteristic
125C4×Q8×C151C2311yescharacteristic
126C4×Q8×C151C2311yescharacteristic
127C4×D4×C151—22no—
128C4×D4×C151—22no—
129C4×D4×C151—21no—
130C4×D4×C151—21no—
131C4×D4×C151—21no—
132C4×D4×C151—21no—
133C4×D4×C151—21no—
134C4×D4×C151—21no—
135C4×D4×C151—21no—
136C4×D4×C151—21no—
137C4×D4×C151—21no—
138C4×D4×C151D412yes—
139C4×D4×C151D411yescharacteristic
140C4×D4×C151C2311yescharacteristic
141C4×D4×C151C2311yescharacteristic
142#117×C151—22no—
143#117×C151—21no—
144#117×C151—21no—
145#117×C151—21no—
146#117×C151D411yescharacteristic
147C2×C22⋊C4×C151—22no—
148C2×C22⋊C4×C151—22no—
149C2×C22⋊C4×C151—22no—
150C2×C42×C151—21no—
151C2×C42×C151C2311yescharacteristic
152#107×C151—22no—
153#107×C151—21no—
154#106×C151—21no—
155C4⋊C8×C151C2311yescharacteristic
156C4⋊C8×C151C2311yescharacteristic
157C4⋊C8×C151C2311yescharacteristic
158C4⋊C8×C151C2311yescharacteristic
159#103×C151—21no—
160#103×C151—21no—
161#103×C151—21no—
162#102×C151—22no—
163#102×C151—21no—
164#102×C151—22no—
165#102×C151—21no—
166#102×C151—21no—
167#102×C151—21no—
168#102×C151—21no—
169C22⋊C8×C151—21no—
170C22⋊C8×C151—21no—
171#97×C151—21no—
172C4×C8×C151—21no—
173C4×C8×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176C24×C151—22no—
177#41×C151—22no—
178#41×C151—41no—
179#41×C151—81no—
180#41×C151—81no—
181#41×C151—81no—
182#41×C151—81no—
183C2×Q8×C151—22no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—81no—
187C2×Q8×C151—81no—
188C2×Q8×C151C2×D411yescharacteristic
189C2×Q8×C151C2×D411yescharacteristic
190C2×D4×C151—22no—
191C2×D4×C151—21no—
192C2×D4×C151—22no—
193C2×D4×C151—21no—
194C2×D4×C151—22no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—42no—
201C2×D4×C151—42no—
202C2×D4×C151—41no—
203C2×D4×C151—81no—
204C2×D4×C151—81no—
205C2×D4×C151C2×D411yescharacteristic
206C2×D4×C151C2×D411yescharacteristic
207C2×D4×C151C2×D412yes—
208C22×C4×C151—22no—
209C22×C4×C151—22no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—22no—
215C22×C4×C151—41no—
216C22×C4×C151C2×D411yescharacteristic
217C22×C4×C151C2×D411yescharacteristic
218C22×C4×C151C2×D411yescharacteristic
219Q16×C151—81no—
220SD16×C151—42no—
221SD16×C151—81no—
222SD16×C151—81no—
223D8×C151—44no—
224D8×C151—42no—
225D8×C151—81no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—42no—
233C4⋊C4×C151—22no—
234C4⋊C4×C151—22no—
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—21no—
244C4⋊C4×C151C2×D411yescharacteristic
245C4⋊C4×C151C2×D411yescharacteristic
246C4⋊C4×C151C2×D411yescharacteristic
247C4⋊C4×C151C2×D411yescharacteristic
248C4⋊C4×C151C2×D412yes—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—22no—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—22no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—21no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—22no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—41no—
267C22⋊C4×C151—41no—
268C42×C151—22no—
269C42×C151—21no—
270C42×C151—21no—
271C42×C151—21no—
272C42×C151—21no—
273C42×C151C2×D411yescharacteristic
274C42×C151C2×D411yescharacteristic
275C42×C151C2×D411yescharacteristic
276C42×C151C2411yescharacteristic
277C23×C151—21no—
278C23×C151—21no—
279C23×C151—22no—
280C23×C151—44no—
281C23×C151—41no—
282C23×C151—82no—
283C23×C151—82no—
284C23×C151#12011yescharacteristic
285Q8×C151—21no—
286Q8×C151—21no—
287Q8×C151—21no—
288Q8×C151—21no—
289Q8×C151—41no—
290Q8×C151—41no—
291Q8×C151—41no—
292Q8×C151—41no—
293Q8×C151—82no—
294D4×C151—21no—
295D4×C151—21no—
296D4×C151—21no—
297D4×C151—42no—
298D4×C151—42no—
299D4×C151—42no—
300D4×C151—44no—
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—82no—
310D4×C151—81no—
311D4×C151—82no—
312D4×C151—82no—
313D4×C151#13512yes—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—21no—
320C2×C4×C151—22no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—41no—
326C2×C4×C151—42no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—82no—
333C2×C4×C151—81no—
334C2×C4×C151—82no—
335C2×C4×C151—82no—
336C2×C4×C151—82no—
337C2×C4×C151#12011yescharacteristic
338C2×C4×C151#12011yescharacteristic
339C2×C4×C151#12011yescharacteristic
340C2×C4×C151C22×D411yescharacteristic
341C2×C4×C151C22×D411yescharacteristic
342C2×C4×C151C22×D411yescharacteristic
343C8×C151—22no—
344C8×C151—41no—
345C8×C151—41no—
346C8×C151—41no—
347C8×C151—41no—
348C8×C151—41no—
349C22×C151—21no—
350C22×C151—22no—
351C22×C151—21no—
352C22×C151—21no—
353C22×C151—41no—
354C22×C151—41no—
355C22×C151—41no—
356C22×C151—42no—
357C22×C151—42no—
358C22×C151—41no—
359C22×C151—42no—
360C22×C151—41no—
361C22×C151—81no—
362C22×C151—81no—
363C22×C151—81no—
364C22×C151—164no—
365C22×C151C2×#12011yescharacteristic
366C4×C151—21no—
367C4×C151—21no—
368C4×C151—21no—
369C4×C151—21no—
370C4×C151—41no—
371C4×C151—41no—
372C4×C151—41no—
373C4×C151—42no—
374C4×C151—41no—
375C4×C151—41no—
376C4×C151—41no—
377C4×C151—81no—
378C4×C151C2×#13511yescharacteristic
379C4×C151#57511yescharacteristic
380C4×C151#57611yescharacteristic
381C4×C151#57611yescharacteristic
382C2×C151—41no—
383C2×C151—42no—
384C2×C151—82no—
385C2×C151—81no—
386C2×C151—161no—
387C2×C151#300211yescharacteristic
388C2×C151#300811yescharacteristic
389C2×C151#301811yescharacteristic
390#18658C15111yesmaximal, characteristic, direct product factor, Sylow
391C151#1865811yescharacteristic, direct product factor, Sylow
392#3514C2×C15111yescharacteristic, complemented
393#3212C2×C15111yescharacteristic, complemented
394#3169C2×C15111yescharacteristic, complemented
395#3115C2×C15111yescharacteristic, complemented
396#1650C2×C15111yescharacteristic, complemented
397#1649C2×C15111yescharacteristic, complemented
398#1640C2×C15111yescharacteristic, complemented
399#1639C2×C15111yescharacteristic, complemented
400#1628C2×C15111yescharacteristic, complemented
401#1627C2×C15111yescharacteristic, complemented
402#1620C2×C15111yescharacteristic, complemented
403#1619C2×C15111yescharacteristic, complemented
404#1553C2×C15111yescharacteristic, complemented
405#1494C2×C15111yescharacteristic, complemented
406#1476C2×C15111yescharacteristic, complemented
407#559C22×C15111yescharacteristic
408#556C22×C15111yescharacteristic
409#555—21no—
410#551—22no—
411D4×Q8C22×C15111yescharacteristic
412#548—21no—
413#546—21no—
414#546—21no—
415D42C22×C15111yescharacteristic
416#542—21no—
417#538—22no—
418#532C22×C15111yescharacteristic
419#532C22×C15111yescharacteristic, complemented
420#529—21no—
421#529C22×C15111yescharacteristic
422C2×#124—21no—
423#518—21no—
424C4×#41C22×C15111yescharacteristic
425#500C22×C15111yescharacteristic, complemented
426#495—21no—
427#493C22×C15111yescharacteristic
428#488—21no—
429#486C22×C15111yescharacteristic
430#486C22×C15111yescharacteristic, complemented
431#482—21no—
432#475C22×C15111yescharacteristic, complemented
433#474C22×C15111yescharacteristic
434#466—22no—
435#462C22×C15111yescharacteristic, complemented
436#461C22×C15111yescharacteristic
437#460C22×C15111yescharacteristic, complemented
438#460C22×C15111yescharacteristic, complemented
439#459C22×C15111yescharacteristic
440#459C22×C15111yescharacteristic
441#452—21no—
442#449—21no—
443#449—21no—
444#442—21no—
445#440—21no—
446C4×D8—22no—
447#432C22×C15111yescharacteristic, complemented
448#431C22×C15111yescharacteristic, complemented
449C2×C4×C8C22×C15111yescharacteristic, complemented
450#332C22×C15111yescharacteristic, complemented
451#332C22×C15111yescharacteristic, complemented
452#331C22×C15111yescharacteristic
453#331C22×C15111yescharacteristic
454Q8⋊C8C22×C15111yescharacteristic, complemented
455Q8⋊C8C22×C15111yescharacteristic, complemented
456Q8⋊C8C22×C15111yescharacteristic, complemented
457Q8⋊C8C22×C15111yescharacteristic, complemented
458D4⋊C8C22×C15111yescharacteristic
459D4⋊C8C22×C15111yescharacteristic
460D4⋊C8C22×C15111yescharacteristic
461D4⋊C8C22×C15111yescharacteristic
462C2×#41—21no—
463C2×#41—21no—
464C2×#41D4×C15111yescharacteristic
465C22×Q8—21no—
466C22×D4—21no—
467C22×D4—21no—
468C2×Q16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×SD16—21no—
472C2×D8—22no—
473C2×D8—21no—
474C2×D8—21no—
475C22×C8—21no—
476C4⋊Q8—21no—
477C4⋊Q8C23×C15111yescharacteristic
478C4⋊Q8C23×C15111yescharacteristic
479#127C23×C15111yescharacteristic
480#127C23×C15111yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125D4×C15111yescharacteristic
485#124—22no—
486#124—22no—
487#124—22no—
488#124—21no—
489#124—21no—
490#124—21no—
491#124—21no—
492#124—21no—
493#124D4×C15111yescharacteristic
494#123—22no—
495#123—22no—
496#123—22no—
497#123—21no—
498C22⋊Q8—22no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—22no—
502C22⋊Q8D4×C15111yescharacteristic
503#121—22no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C15111yescharacteristic
511#121D4×C15112yes—
512#120—22no—
513#120—22no—
514C4×Q8—21no—
515C4×Q8D4×C15111yescharacteristic
516C4×Q8C23×C15111yescharacteristic
517C4×Q8C23×C15111yescharacteristic
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4D4×C15111yescharacteristic
530C4×D4D4×C15112yes—
531C4×D4C23×C15111yescharacteristic
532C4×D4C23×C15111yescharacteristic
533#117—22no—
534#117—21no—
535#117—21no—
536#117—21no—
537#117D4×C15111yescharacteristic
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C42—21no—
542C2×C42C23×C15111yescharacteristic
543#107—22no—
544#107—21no—
545#106—21no—
546C4⋊C8C23×C15111yescharacteristic
547C4⋊C8C23×C15111yescharacteristic
548C4⋊C8C23×C15111yescharacteristic
549C4⋊C8C23×C15111yescharacteristic
550#103—21no—
551#103—21no—
552#103—21no—
553#102—22no—
554#102—21no—
555#102—22no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102—21no—
560C22⋊C8—21no—
561C22⋊C8—21no—
562#97—21no—
563C4×C8—21no—
564C4×C8—21no—
565C4×C8C23×C15111yescharacteristic
566C4×C8C23×C15111yescharacteristic
567C24—22no—
568#41—22no—
569#41—41no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574C2×Q8—22no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—81no—
578C2×Q8—81no—
579C2×Q8C2×D4×C15111yescharacteristic
580C2×Q8C2×D4×C15111yescharacteristic
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—41no—
594C2×D4—81no—
595C2×D4—81no—
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—21no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4C2×D4×C15111yescharacteristic
608C22×C4C2×D4×C15111yescharacteristic
609C22×C4C2×D4×C15111yescharacteristic
610Q16—81no—
611SD16—42no—
612SD16—81no—
613SD16—81no—
614D8—44no—
615D8—42no—
616D8—81no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—42no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4C2×D4×C15111yescharacteristic
636C4⋊C4C2×D4×C15111yescharacteristic
637C4⋊C4C2×D4×C15111yescharacteristic
638C4⋊C4C2×D4×C15111yescharacteristic
639C4⋊C4C2×D4×C15112yes—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C42—22no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42C2×D4×C15111yescharacteristic
665C42C2×D4×C15111yescharacteristic
666C42C2×D4×C15111yescharacteristic
667C42C24×C15111yescharacteristic
668C23—21no—
669C23—21no—
670C23—22no—
671C23—44no—
672C23—41no—
673C23—82no—
674C23—82no—
675C23#120×C15111yescharacteristic
676Q8—21no—
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—82no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—44no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—82no—
701D4—81no—
702D4—82no—
703D4—82no—
704D4#135×C15112yes—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—81no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4#120×C15111yescharacteristic
729C2×C4#120×C15111yescharacteristic
730C2×C4#120×C15111yescharacteristic
731C2×C4C22×D4×C15111yescharacteristic
732C2×C4C22×D4×C15111yescharacteristic
733C2×C4C22×D4×C15111yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—41no—
739C8—41no—
740C22—21no—
741C22—22no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—41no—
750C22—42no—
751C22—41no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—164no—
756C22C2×#120×C15111yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—81no—
769C4C2×#135×C15111yescharacteristic
770C4#575×C15111yescharacteristic
771C4#576×C15111yescharacteristic
772C4#576×C15111yescharacteristic
773C2—41no—
774C2—42no—
775C2—81no—
776C2—82no—
777C2—161no—
778C2#3002×C15111yescharacteristic
779C2#3008×C15111yescharacteristic
780C2#3018×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. #3514×C151C2semidirect
2. #3212×C151C2semidirect
3. #3169×C151C2semidirect
4. #3115×C151C2semidirect
5. #1650×C151C2semidirect
6. #1649×C151C2semidirect
7. #1640×C151C2semidirect
8. #1639×C151C2semidirect
9. #1628×C151C2semidirect
10. #1627×C151C2semidirect
11. #1620×C151C2semidirect
12. #1619×C151C2semidirect
13. #1553×C151C2semidirect
14. #1494×C151C2semidirect
15. #1476×C151C2semidirect
28. #532×C151C22semidirect
34. #500×C151C22semidirect
39. #486×C151C22semidirect
41. #475×C151C22semidirect
44. #462×C151C22semidirect
46. #460×C151C22semidirect
47. #460×C151C22semidirect
56. #432×C151C22semidirect
57. #431×C151C22semidirect
58. C2×C4×C8×C151C22semidirect
59. #332×C151C22semidirect
60. #332×C151C22semidirect
63. Q8⋊C8×C151C22semidirect
64. Q8⋊C8×C151C22semidirect
65. Q8⋊C8×C151C22semidirect
66. Q8⋊C8×C151C22semidirect
390. #18658C151direct (N × H)
391. C151#18658direct (N × H)
392. #3514C2×C151semidirect
393. #3212C2×C151semidirect
394. #3169C2×C151semidirect
395. #3115C2×C151semidirect
396. #1650C2×C151semidirect
397. #1649C2×C151semidirect
398. #1640C2×C151semidirect
399. #1639C2×C151semidirect
400. #1628C2×C151semidirect
401. #1627C2×C151semidirect
402. #1620C2×C151semidirect
403. #1619C2×C151semidirect
404. #1553C2×C151semidirect
405. #1494C2×C151semidirect
406. #1476C2×C151semidirect
419. #532C22×C151semidirect
425. #500C22×C151semidirect
430. #486C22×C151semidirect
432. #475C22×C151semidirect
435. #462C22×C151semidirect
437. #460C22×C151semidirect
438. #460C22×C151semidirect
447. #432C22×C151semidirect
448. #431C22×C151semidirect
449. C2×C4×C8C22×C151semidirect
450. #332C22×C151semidirect
451. #332C22×C151semidirect
454. Q8⋊C8C22×C151semidirect
455. Q8⋊C8C22×C151semidirect
456. Q8⋊C8C22×C151semidirect
457. Q8⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3514×C1512
#3212×C1512
#3169×C1512
#3115×C1512
#1650×C1512
#1649×C1512
#1640×C1512
#1639×C1512
#1628×C1512
#1627×C1512
#1620×C1512
#1619×C1512
#1553×C1512
#1494×C1512
#1476×C1512
#18658151