Finite Group Databasebeta

← C151×#18708 #50323633

Subgroups — C151×#18708 #50323633

Order 38656.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3554×C151C211yesmaximal, characteristic, complemented
2#3251×C151C211yesmaximal, characteristic, complemented
3#3216×C151C211yesmaximal, characteristic, complemented
4#3169×C151C211yesmaximal, characteristic, complemented
5#1649×C151C211yesmaximal, characteristic, complemented
6#1648×C151C211yesmaximal, characteristic, complemented
7#1641×C151C211yesmaximal, characteristic, complemented
8#1640×C151C211yesmaximal, characteristic, complemented
9#1627×C151C211yesmaximal, characteristic, complemented
10#1626×C151C211yesmaximal, characteristic, complemented
11#1621×C151C211yesmaximal, characteristic, complemented
12#1620×C151C211yesmaximal, characteristic, complemented
13#1557×C151C211yesmaximal, characteristic, complemented
14#1494×C151C211yesmaximal, characteristic, complemented
15#1493×C151C211yesmaximal, characteristic, complemented
16#562×C151—22no—
17#559×C151—21no—
18#559×C151C2211yescharacteristic
19#557×C151C2211yescharacteristic
20#554×C151—21no—
21#550×C151C2211yescharacteristic
22D4×Q8×C151C2211yescharacteristic
23#548×C151—21no—
24#547×C151—21no—
25#542×C151—21no—
26#542×C151—21no—
27#540×C151—21no—
28#539×C151—22no—
29#536×C151—21no—
30#533×C151C2211yescharacteristic
31#532×C151C2211yescharacteristic
32#532×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#500×C151C2211yescharacteristic
35#497×C151—21no—
36#493×C151C2211yescharacteristic
37#489×C151—21no—
38#486×C151C2211yescharacteristic
39#486×C151C2211yescharacteristic
40#478×C151—21no—
41#475×C151C2211yescharacteristic
42#474×C151C2211yescharacteristic
43#469×C151—21no—
44#468×C151—21no—
45#466×C151—22no—
46#463×C151—21no—
47#462×C151C2211yescharacteristic
48#462×C151C2211yescharacteristic
49#460×C151C2211yescharacteristic
50#460×C151C2211yescharacteristic
51#460×C151C2211yescharacteristic
52#459×C151C2211yescharacteristic
53#452×C151—21no—
54#452×C151—21no—
55C4×D8×C151—22no—
56#432×C151C2211yescharacteristic
57#423×C151C2211yescharacteristic
58C2×C4×C8×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic
62#331×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64Q8⋊C8×C151C2211yescharacteristic
65Q8⋊C8×C151C2211yescharacteristic
66Q8⋊C8×C151C2211yescharacteristic
67Q8⋊C8×C151C2211yescharacteristic
68Q8⋊C8×C151C2211yescharacteristic
69D4⋊C8×C151C2211yescharacteristic
70D4⋊C8×C151C2211yescharacteristic
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C2×#41×C151—21no—
74C22×Q8×C151—21no—
75C2×Q16×C151—21no—
76C2×Q16×C151—21no—
77C2×SD16×C151—21no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C2×D8×C151—22no—
81C2×D8×C151—21no—
82C2×M16×C151—21no—
83C22×C8×C151—21no—
84C4⋊Q8×C151—21no—
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151D411yescharacteristic
87C4⋊Q8×C151D411yescharacteristic
88C4⋊Q8×C151C2311yescharacteristic
89C4⋊Q8×C151C2311yescharacteristic
90#127×C151—21no—
91#127×C151C2311yescharacteristic
92#127×C151C2311yescharacteristic
93#126×C151—22no—
94#126×C151—21no—
95#125×C151—22no—
96#125×C151—21no—
97#125×C151—21no—
98#125×C151D411yescharacteristic
99#124×C151—22no—
100#124×C151—22no—
101#124×C151—21no—
102#124×C151—21no—
103#124×C151—21no—
104#124×C151—21no—
105#124×C151D411yescharacteristic
106#123×C151—22no—
107#123×C151—22no—
108#123×C151—22no—
109#123×C151—22no—
110#123×C151—22no—
111#123×C151—22no—
112#123×C151—21no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—22no—
116C22⋊Q8×C151—22no—
117C22⋊Q8×C151—21no—
118C22⋊Q8×C151—22no—
119C22⋊Q8×C151—21no—
120C22⋊Q8×C151D411yescharacteristic
121C22⋊Q8×C151D411yescharacteristic
122C22⋊Q8×C151D411yescharacteristic
123#121×C151—22no—
124#121×C151—22no—
125#121×C151—22no—
126#121×C151—21no—
127#121×C151—21no—
128#121×C151—21no—
129#121×C151—21no—
130#121×C151D412yes—
131#121×C151D411yescharacteristic
132C4×Q8×C151—21no—
133C4×Q8×C151—21no—
134C4×Q8×C151—21no—
135C4×Q8×C151C2311yescharacteristic
136C4×Q8×C151C2311yescharacteristic
137C4×Q8×C151C2311yescharacteristic
138C4×D4×C151—22no—
139C4×D4×C151—21no—
140C4×D4×C151—21no—
141C4×D4×C151—21no—
142C4×D4×C151—21no—
143C4×D4×C151—21no—
144C4×D4×C151—21no—
145C4×D4×C151—21no—
146C4×D4×C151—21no—
147C4×D4×C151D412yes—
148C4×D4×C151C2311yescharacteristic
149#117×C151—21no—
150#117×C151—21no—
151C2×C4⋊C4×C151—22no—
152C2×C42×C151C2311yescharacteristic
153#107×C151—22no—
154#107×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—21no—
162#103×C151—21no—
163#103×C151—21no—
164#102×C151—22no—
165#102×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
176#41×C151—81no—
177#41×C151—81no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—81no—
181#41×C151—81no—
182C2×Q8×C151—22no—
183C2×Q8×C151—21no—
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×Q8×C151C2×D411yescharacteristic
191C2×D4×C151—22no—
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—41no—
201C2×D4×C151C2×D411yescharacteristic
202C2×D4×C151C2×D412yes—
203C22×C4×C151—22no—
204C22×C4×C151—22no—
205C22×C4×C151—22no—
206C22×C4×C151—21no—
207C22×C4×C151—22no—
208C22×C4×C151—41no—
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151C2×D411yescharacteristic
212Q16×C151—81no—
213Q16×C151—81no—
214SD16×C151—81no—
215SD16×C151—81no—
216SD16×C151—81no—
217D8×C151—44no—
218D8×C151—81no—
219M16×C151—81no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—42no—
227C4⋊C4×C151—22no—
228C4⋊C4×C151—22no—
229C4⋊C4×C151—22no—
230C4⋊C4×C151—22no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—21no—
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—21no—
244C4⋊C4×C151—21no—
245C4⋊C4×C151C2×D411yescharacteristic
246C4⋊C4×C151C2×D411yescharacteristic
247C4⋊C4×C151C2×D411yescharacteristic
248C4⋊C4×C151C2×D411yescharacteristic
249C4⋊C4×C151C2×D412yes—
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—41no—
265C22⋊C4×C151—41no—
266C42×C151—22no—
267C42×C151—21no—
268C42×C151—21no—
269C42×C151—21no—
270C42×C151C2×D411yescharacteristic
271C42×C151C2×D411yescharacteristic
272C42×C151C2×D411yescharacteristic
273C42×C151C2411yescharacteristic
274C23×C151—21no—
275C23×C151—22no—
276C23×C151—41no—
277C23×C151#12011yescharacteristic
278Q8×C151—21no—
279Q8×C151—21no—
280Q8×C151—21no—
281Q8×C151—21no—
282Q8×C151—21no—
283Q8×C151—21no—
284Q8×C151—41no—
285Q8×C151—41no—
286Q8×C151—41no—
287Q8×C151—41no—
288Q8×C151—81no—
289Q8×C151—82no—
290D4×C151—21no—
291D4×C151—21no—
292D4×C151—42no—
293D4×C151—42no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—41no—
298D4×C151—41no—
299D4×C151—41no—
300D4×C151—41no—
301D4×C151—41no—
302D4×C151—82no—
303D4×C151—81no—
304D4×C151—82no—
305D4×C151—82no—
306D4×C151—82no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—22no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—82no—
324C2×C4×C151—82no—
325C2×C4×C151—82no—
326C2×C4×C151—82no—
327C2×C4×C151—82no—
328C2×C4×C151#12011yescharacteristic
329C2×C4×C151#12011yescharacteristic
330C2×C4×C151#12011yescharacteristic
331C2×C4×C151C22×D411yescharacteristic
332C2×C4×C151C22×D411yescharacteristic
333C2×C4×C151C22×D411yescharacteristic
334C8×C151—22no—
335C8×C151—41no—
336C8×C151—41no—
337C8×C151—41no—
338C8×C151—41no—
339C8×C151—41no—
340C22×C151—21no—
341C22×C151—21no—
342C22×C151—21no—
343C22×C151—41no—
344C22×C151—42no—
345C22×C151—41no—
346C22×C151—42no—
347C22×C151—42no—
348C22×C151—41no—
349C22×C151—81no—
350C22×C151—81no—
351C22×C151—81no—
352C22×C151C2×#12011yescharacteristic
353C4×C151—21no—
354C4×C151—21no—
355C4×C151—21no—
356C4×C151—21no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—42no—
360C4×C151—41no—
361C4×C151—41no—
362C4×C151—41no—
363C4×C151—41no—
364C4×C151—41no—
365C4×C151—81no—
366C4×C151#57611yescharacteristic
367C4×C151#57611yescharacteristic
368C4×C151#57711yescharacteristic
369C4×C151#57811yescharacteristic
370C2×C151—41no—
371C2×C151—81no—
372C2×C151—82no—
373C2×C151—161no—
374C2×C151#300811yescharacteristic
375C2×C151#301311yescharacteristic
376C2×C151#301811yescharacteristic
377#18708C15111yesmaximal, characteristic, direct product factor, Sylow
378C151#1870811yescharacteristic, direct product factor, Sylow
379#3554C2×C15111yescharacteristic, complemented
380#3251C2×C15111yescharacteristic, complemented
381#3216C2×C15111yescharacteristic, complemented
382#3169C2×C15111yescharacteristic, complemented
383#1649C2×C15111yescharacteristic, complemented
384#1648C2×C15111yescharacteristic, complemented
385#1641C2×C15111yescharacteristic, complemented
386#1640C2×C15111yescharacteristic, complemented
387#1627C2×C15111yescharacteristic, complemented
388#1626C2×C15111yescharacteristic, complemented
389#1621C2×C15111yescharacteristic, complemented
390#1620C2×C15111yescharacteristic, complemented
391#1557C2×C15111yescharacteristic, complemented
392#1494C2×C15111yescharacteristic, complemented
393#1493C2×C15111yescharacteristic, complemented
394#562—22no—
395#559—21no—
396#559C22×C15111yescharacteristic
397#557C22×C15111yescharacteristic
398#554—21no—
399#550C22×C15111yescharacteristic
400D4×Q8C22×C15111yescharacteristic
401#548—21no—
402#547—21no—
403#542—21no—
404#542—21no—
405#540—21no—
406#539—22no—
407#536—21no—
408#533C22×C15111yescharacteristic
409#532C22×C15111yescharacteristic
410#532C22×C15111yescharacteristic
411#529C22×C15111yescharacteristic
412#500C22×C15111yescharacteristic
413#497—21no—
414#493C22×C15111yescharacteristic
415#489—21no—
416#486C22×C15111yescharacteristic
417#486C22×C15111yescharacteristic
418#478—21no—
419#475C22×C15111yescharacteristic
420#474C22×C15111yescharacteristic
421#469—21no—
422#468—21no—
423#466—22no—
424#463—21no—
425#462C22×C15111yescharacteristic
426#462C22×C15111yescharacteristic
427#460C22×C15111yescharacteristic
428#460C22×C15111yescharacteristic
429#460C22×C15111yescharacteristic
430#459C22×C15111yescharacteristic
431#452—21no—
432#452—21no—
433C4×D8—22no—
434#432C22×C15111yescharacteristic
435#423C22×C15111yescharacteristic
436C2×C4×C8C22×C15111yescharacteristic
437#332C22×C15111yescharacteristic
438#332C22×C15111yescharacteristic
439#331C22×C15111yescharacteristic
440#331C22×C15111yescharacteristic
441Q8⋊C8C22×C15111yescharacteristic
442Q8⋊C8C22×C15111yescharacteristic
443Q8⋊C8C22×C15111yescharacteristic
444Q8⋊C8C22×C15111yescharacteristic
445Q8⋊C8C22×C15111yescharacteristic
446Q8⋊C8C22×C15111yescharacteristic
447D4⋊C8C22×C15111yescharacteristic
448D4⋊C8C22×C15111yescharacteristic
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×Q16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C15111yescharacteristic
465C4⋊Q8D4×C15111yescharacteristic
466C4⋊Q8C23×C15111yescharacteristic
467C4⋊Q8C23×C15111yescharacteristic
468#127—21no—
469#127C23×C15111yescharacteristic
470#127C23×C15111yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C15111yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C15111yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C15111yescharacteristic
499C22⋊Q8D4×C15111yescharacteristic
500C22⋊Q8D4×C15111yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C15111yescharacteristic
509#121D4×C15112yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C15111yescharacteristic
514C4×Q8C23×C15111yescharacteristic
515C4×Q8C23×C15111yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C15112yes—
526C4×D4C23×C15111yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C15111yescharacteristic
531#107—22no—
532#107—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C15111yescharacteristic
536C4⋊C8C23×C15111yescharacteristic
537C4⋊C8C23×C15111yescharacteristic
538C4⋊C8C23×C15111yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#102—22no—
543#102—21no—
544#102—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C15111yescharacteristic
553C4×C8C23×C15111yescharacteristic
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C15111yescharacteristic
567C2×Q8C2×D4×C15111yescharacteristic
568C2×Q8C2×D4×C15111yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C15111yescharacteristic
580C2×D4C2×D4×C15112yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C15111yescharacteristic
588C22×C4C2×D4×C15111yescharacteristic
589C22×C4C2×D4×C15111yescharacteristic
590Q16—81no—
591Q16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—81no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C15111yescharacteristic
624C4⋊C4C2×D4×C15111yescharacteristic
625C4⋊C4C2×D4×C15111yescharacteristic
626C4⋊C4C2×D4×C15111yescharacteristic
627C4⋊C4C2×D4×C15112yes—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C15111yescharacteristic
649C42C2×D4×C15111yescharacteristic
650C42C2×D4×C15111yescharacteristic
651C42C24×C15111yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C15111yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—81no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C15111yescharacteristic
707C2×C4#120×C15111yescharacteristic
708C2×C4#120×C15111yescharacteristic
709C2×C4C22×D4×C15111yescharacteristic
710C2×C4C22×D4×C15111yescharacteristic
711C2×C4C22×D4×C15111yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C15111yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4#576×C15111yescharacteristic
745C4#576×C15111yescharacteristic
746C4#577×C15111yescharacteristic
747C4#578×C15111yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2#3008×C15111yescharacteristic
753C2#3013×C15111yescharacteristic
754C2#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. #3554×C151C2semidirect
2. #3251×C151C2semidirect
3. #3216×C151C2semidirect
4. #3169×C151C2semidirect
5. #1649×C151C2semidirect
6. #1648×C151C2semidirect
7. #1641×C151C2semidirect
8. #1640×C151C2semidirect
9. #1627×C151C2semidirect
10. #1626×C151C2semidirect
11. #1621×C151C2semidirect
12. #1620×C151C2semidirect
13. #1557×C151C2semidirect
14. #1494×C151C2semidirect
15. #1493×C151C2semidirect
377. #18708C151direct (N × H)
378. C151#18708direct (N × H)
379. #3554C2×C151semidirect
380. #3251C2×C151semidirect
381. #3216C2×C151semidirect
382. #3169C2×C151semidirect
383. #1649C2×C151semidirect
384. #1648C2×C151semidirect
385. #1641C2×C151semidirect
386. #1640C2×C151semidirect
387. #1627C2×C151semidirect
388. #1626C2×C151semidirect
389. #1621C2×C151semidirect
390. #1620C2×C151semidirect
391. #1557C2×C151semidirect
392. #1494C2×C151semidirect
393. #1493C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3554×C1512
#3251×C1512
#3216×C1512
#3169×C1512
#1649×C1512
#1648×C1512
#1641×C1512
#1640×C1512
#1627×C1512
#1626×C1512
#1621×C1512
#1620×C1512
#1557×C1512
#1494×C1512
#1493×C1512
#18708151