Finite Group Databasebeta

← C151×#18868 #50323793

Subgroups — C151×#18868 #50323793

Order 38656.

946 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#3522×C151C211yesmaximal, characteristic, complemented
2#3212×C151C211yesmaximal, characteristic, complemented
3#3207×C151C211yesmaximal, characteristic, complemented
4#3103×C151C211yesmaximal, characteristic, complemented
5#1645×C151C211yesmaximal, characteristic, complemented
6#1643×C151C211yesmaximal, characteristic, complemented
7#1642×C151C211yesmaximal, characteristic, complemented
8#1640×C151C211yesmaximal, characteristic, complemented
9#1623×C151C211yesmaximal, characteristic, complemented
10#1622×C151C211yesmaximal, characteristic, complemented
11#1621×C151C211yesmaximal, characteristic, complemented
12#1620×C151C211yesmaximal, characteristic, complemented
13#1543×C151C211yesmaximal, characteristic, complemented
14#1482×C151C211yesmaximal, characteristic, complemented
15#1479×C151C211yesmaximal, characteristic, complemented
16#559×C151—21no—
17#559×C151C2211yescharacteristic
18Q82×C151C2211yescharacteristic
19#554×C151—21no—
20#554×C151C2211yescharacteristic
21#550×C151C2211yescharacteristic
22#548×C151—21no—
23#547×C151—22no—
24#547×C151—21no—
25#542×C151—22no—
26#542×C151—21no—
27#532×C151—21no—
28#532×C151C2211yescharacteristic
29#532×C151C2211yescharacteristic
30#529×C151—21no—
31#529×C151C2211yescharacteristic
32#520×C151—21no—
33C2×C4×Q8×C151C2211yescharacteristic
34#495×C151—21no—
35#493×C151C2211yescharacteristic
36#492×C151C2211yescharacteristic
37#488×C151—21no—
38#487×C151C2211yescharacteristic
39#486×C151C2211yescharacteristic
40#481×C151—21no—
41#475×C151C2211yescharacteristic
42#475×C151C2211yescharacteristic
43#463×C151—22no—
44#462×C151C2211yescharacteristic
45#461×C151C2211yescharacteristic
46#460×C151C2211yescharacteristic
47#460×C151C2211yescharacteristic
48#460×C151C2211yescharacteristic
49#459×C151C2211yescharacteristic
50#452×C151—21no—
51#449×C151—22no—
52#449×C151—21no—
53#448×C151—21no—
54C4×SD16×C151—21no—
55C4×SD16×C151—21no—
56#431×C151C2211yescharacteristic
57#431×C151C2211yescharacteristic
58#431×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×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—22no—
72C2×#41×C151—21no—
73C2×#41×C151—21no—
74C2×#41×C151D412yes—
75C22×Q8×C151D411yescharacteristic
76C2×Q16×C151—21no—
77C2×SD16×C151—21no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C2×SD16×C151—22no—
81C2×SD16×C151—21no—
82C2×D8×C151—21no—
83C2×D8×C151—22no—
84C4⋊Q8×C151—21no—
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151—22no—
87C4⋊Q8×C151C2311yescharacteristic
88C4⋊Q8×C151C2311yescharacteristic
89#127×C151—21no—
90#127×C151C2311yescharacteristic
91#127×C151C2311yescharacteristic
92#126×C151—22no—
93#126×C151—21no—
94#125×C151—21no—
95#125×C151D411yescharacteristic
96#124×C151—22no—
97#124×C151—22no—
98#124×C151—21no—
99#124×C151—21no—
100#124×C151—21no—
101#124×C151D412yes—
102#124×C151D411yescharacteristic
103#123×C151—22no—
104#123×C151—22no—
105#123×C151—22no—
106#123×C151—22no—
107#123×C151—21no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—21no—
113C22⋊Q8×C151D411yescharacteristic
114#121×C151—22no—
115#121×C151—22no—
116#121×C151—21no—
117#121×C151—21no—
118#121×C151—21no—
119#121×C151—21no—
120#121×C151—21no—
121#121×C151D411yescharacteristic
122C4×Q8×C151—21no—
123C4×Q8×C151—21no—
124C4×Q8×C151—21no—
125C4×Q8×C151—21no—
126C4×Q8×C151D411yescharacteristic
127C4×Q8×C151D411yescharacteristic
128C4×Q8×C151C2311yescharacteristic
129C4×Q8×C151C2311yescharacteristic
130C4×Q8×C151C2311yescharacteristic
131C4×D4×C151—22no—
132C4×D4×C151—22no—
133C4×D4×C151—22no—
134C4×D4×C151—21no—
135C4×D4×C151—21no—
136C4×D4×C151—21no—
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×C151C2311yescharacteristic
144#117×C151—22no—
145#117×C151—21no—
146C2×C4⋊C4×C151—22no—
147C2×C4⋊C4×C151—21no—
148C2×C4⋊C4×C151—21no—
149C2×C4⋊C4×C151D411yescharacteristic
150C2×C42×C151—21no—
151C2×C42×C151C2311yescharacteristic
152#106×C151—21no—
153#106×C151—21no—
154C4⋊C8×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#103×C151—21no—
163#103×C151—22no—
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—
171C22⋊C8×C151—21no—
172C4×C8×C151—21no—
173C4×C8×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176#41×C151—42no—
177#41×C151—42no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—84no—
181#41×C151—82no—
182C2×Q8×C151—22no—
183C2×Q8×C151—21no—
184C2×Q8×C151—22no—
185C2×Q8×C151—21no—
186C2×Q8×C151—41no—
187C2×Q8×C151C2×D411yescharacteristic
188C2×Q8×C151C2×D411yescharacteristic
189C2×Q8×C151C2×D411yescharacteristic
190C2×Q8×C151C2×D412yes—
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—21no—
205C22×C4×C151—21no—
206C22×C4×C151—22no—
207C22×C4×C151—22no—
208C22×C4×C151—21no—
209C22×C4×C151—22no—
210C22×C4×C151—41no—
211C22×C4×C151C2×D411yescharacteristic
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2×D411yescharacteristic
214Q16×C151—81no—
215SD16×C151—42no—
216SD16×C151—42no—
217SD16×C151—81no—
218SD16×C151—81no—
219SD16×C151—82no—
220D8×C151—81no—
221D8×C151—82no—
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C4⋊C4×C151—22no—
229C4⋊C4×C151—22no—
230C4⋊C4×C151—22no—
231C4⋊C4×C151—22no—
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
249C22⋊C4×C151—22no—
250C22⋊C4×C151—22no—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—21no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—22no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—41no—
262C22⋊C4×C151—41no—
263C42×C151—22no—
264C42×C151—21no—
265C42×C151—21no—
266C42×C151—21no—
267C42×C151—21no—
268C42×C151—21no—
269C42×C151C2×D411yescharacteristic
270C42×C151C2×D411yescharacteristic
271C42×C151C2×D411yescharacteristic
272C42×C151C2411yescharacteristic
273C23×C151—21no—
274C23×C151—22no—
275C23×C151—41no—
276C23×C151#12011yescharacteristic
277Q8×C151—21no—
278Q8×C151—21no—
279Q8×C151—21no—
280Q8×C151—21no—
281Q8×C151—21no—
282Q8×C151—42no—
283Q8×C151—42no—
284Q8×C151—41no—
285Q8×C151—41no—
286Q8×C151—82no—
287Q8×C151#13512yes—
288D4×C151—21no—
289D4×C151—21no—
290D4×C151—42no—
291D4×C151—44no—
292D4×C151—42no—
293D4×C151—44no—
294D4×C151—42no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—41no—
298D4×C151—41no—
299D4×C151—41no—
300D4×C151—41no—
301D4×C151—41no—
302D4×C151—41no—
303D4×C151—82no—
304D4×C151—82no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—22no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—41no—
318C2×C4×C151—42no—
319C2×C4×C151—44no—
320C2×C4×C151—42no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
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—41no—
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—42no—
344C22×C151—41no—
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—22no—
355C4×C151—21no—
356C4×C151—21no—
357C4×C151—21no—
358C4×C151—41no—
359C4×C151—41no—
360C4×C151—41no—
361C4×C151—41no—
362C4×C151—41no—
363C4×C151—42no—
364C4×C151—41no—
365C4×C151—81no—
366C4×C151C2×#13511yescharacteristic
367C4×C151#57511yescharacteristic
368C4×C151#57711yescharacteristic
369C4×C151#57711yescharacteristic
370C2×C151—41no—
371C2×C151—81no—
372C2×C151—82no—
373C2×C151—161no—
374C2×C151#300211yescharacteristic
375C2×C151#301011yescharacteristic
376C2×C151#301911yescharacteristic
377#18868C15111yesmaximal, characteristic, direct product factor, Sylow
378C151#1886811yescharacteristic, direct product factor, Sylow
379#3522C2×C15111yescharacteristic, complemented
380#3212C2×C15111yescharacteristic, complemented
381#3207C2×C15111yescharacteristic, complemented
382#3103C2×C15111yescharacteristic, complemented
383#1645C2×C15111yescharacteristic, complemented
384#1643C2×C15111yescharacteristic, complemented
385#1642C2×C15111yescharacteristic, complemented
386#1640C2×C15111yescharacteristic, complemented
387#1623C2×C15111yescharacteristic, complemented
388#1622C2×C15111yescharacteristic, complemented
389#1621C2×C15111yescharacteristic, complemented
390#1620C2×C15111yescharacteristic, complemented
391#1543C2×C15111yescharacteristic, complemented
392#1482C2×C15111yescharacteristic, complemented
393#1479C2×C15111yescharacteristic, complemented
394#559—21no—
395#559C22×C15111yescharacteristic
396Q82C22×C15111yescharacteristic
397#554—21no—
398#554C22×C15111yescharacteristic
399#550C22×C15111yescharacteristic
400#548—21no—
401#547—22no—
402#547—21no—
403#542—22no—
404#542—21no—
405#532—21no—
406#532C22×C15111yescharacteristic
407#532C22×C15111yescharacteristic
408#529—21no—
409#529C22×C15111yescharacteristic
410#520—21no—
411C2×C4×Q8C22×C15111yescharacteristic
412#495—21no—
413#493C22×C15111yescharacteristic
414#492C22×C15111yescharacteristic
415#488—21no—
416#487C22×C15111yescharacteristic
417#486C22×C15111yescharacteristic
418#481—21no—
419#475C22×C15111yescharacteristic
420#475C22×C15111yescharacteristic
421#463—22no—
422#462C22×C15111yescharacteristic
423#461C22×C15111yescharacteristic
424#460C22×C15111yescharacteristic
425#460C22×C15111yescharacteristic
426#460C22×C15111yescharacteristic
427#459C22×C15111yescharacteristic
428#452—21no—
429#449—22no—
430#449—21no—
431#448—21no—
432C4×SD16—21no—
433C4×SD16—21no—
434#431C22×C15111yescharacteristic
435#431C22×C15111yescharacteristic
436#431C22×C15111yescharacteristic
437#333C22×C15111yescharacteristic
438#333C22×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—22no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41D4×C15112yes—
453C22×Q8D4×C15111yescharacteristic
454C2×Q16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—22no—
458C2×SD16—21no—
459C2×SD16—21no—
460C2×D8—21no—
461C2×D8—22no—
462C4⋊Q8—22no—
463C4⋊Q8—21no—
464C4⋊Q8—21no—
465C4⋊Q8C23×C15111yescharacteristic
466C4⋊Q8C23×C15111yescharacteristic
467#127—21no—
468#127C23×C15111yescharacteristic
469#127C23×C15111yescharacteristic
470#126—22no—
471#126—21no—
472#125—21no—
473#125D4×C15111yescharacteristic
474#124—22no—
475#124—22no—
476#124—21no—
477#124—21no—
478#124—21no—
479#124D4×C15111yescharacteristic
480#124D4×C15112yes—
481#123—22no—
482#123—22no—
483#123—22no—
484#123—22no—
485#123—21no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—21no—
491C22⋊Q8D4×C15111yescharacteristic
492#121—22no—
493#121—22no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121D4×C15111yescharacteristic
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8—21no—
503C4×Q8—21no—
504C4×Q8D4×C15111yescharacteristic
505C4×Q8D4×C15111yescharacteristic
506C4×Q8C23×C15111yescharacteristic
507C4×Q8C23×C15111yescharacteristic
508C4×Q8C23×C15111yescharacteristic
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4C23×C15111yescharacteristic
522#117—22no—
523#117—21no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4D4×C15111yescharacteristic
528C2×C42—21no—
529C2×C42C23×C15111yescharacteristic
530#106—21no—
531#106—21no—
532C4⋊C8—21no—
533C4⋊C8C23×C15111yescharacteristic
534C4⋊C8C23×C15111yescharacteristic
535C4⋊C8C23×C15111yescharacteristic
536C4⋊C8C23×C15111yescharacteristic
537#103—21no—
538#103—21no—
539#103—22no—
540#103—21no—
541#103—21no—
542#102—22no—
543#102—21no—
544#102—21no—
545#102—21no—
546#102—21no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550C4×C8—21no—
551C4×C8—21no—
552C4×C8C23×C15111yescharacteristic
553C4×C8C23×C15111yescharacteristic
554#41—42no—
555#41—42no—
556#41—81no—
557#41—81no—
558#41—84no—
559#41—82no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—21no—
564C2×Q8—41no—
565C2×Q8C2×D4×C15111yescharacteristic
566C2×Q8C2×D4×C15111yescharacteristic
567C2×Q8C2×D4×C15111yescharacteristic
568C2×Q8C2×D4×C15112yes—
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—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—41no—
589C22×C4C2×D4×C15111yescharacteristic
590C22×C4C2×D4×C15111yescharacteristic
591C22×C4C2×D4×C15111yescharacteristic
592Q16—81no—
593SD16—42no—
594SD16—42no—
595SD16—81no—
596SD16—81no—
597SD16—82no—
598D8—81no—
599D8—82no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
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
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—21no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—41no—
640C22⋊C4—41no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42C2×D4×C15111yescharacteristic
648C42C2×D4×C15111yescharacteristic
649C42C2×D4×C15111yescharacteristic
650C42C24×C15111yescharacteristic
651C23—21no—
652C23—22no—
653C23—41no—
654C23#120×C15111yescharacteristic
655Q8—21no—
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—42no—
661Q8—42no—
662Q8—41no—
663Q8—41no—
664Q8—82no—
665Q8#135×C15112yes—
666D4—21no—
667D4—21no—
668D4—42no—
669D4—44no—
670D4—42no—
671D4—44no—
672D4—42no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—82no—
682D4—82no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
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—41no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—42no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C15111yescharacteristic
731C4—21no—
732C4—22no—
733C4—21no—
734C4—21no—
735C4—21no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—42no—
742C4—41no—
743C4—81no—
744C4C2×#135×C15111yescharacteristic
745C4#575×C15111yescharacteristic
746C4#577×C15111yescharacteristic
747C4#577×C15111yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2#3002×C15111yescharacteristic
753C2#3010×C15111yescharacteristic
754C2#3019×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. #3522×C151C2semidirect
2. #3212×C151C2semidirect
3. #3207×C151C2semidirect
4. #3103×C151C2semidirect
5. #1645×C151C2semidirect
6. #1643×C151C2semidirect
7. #1642×C151C2semidirect
8. #1640×C151C2semidirect
9. #1623×C151C2semidirect
10. #1622×C151C2semidirect
11. #1621×C151C2semidirect
12. #1620×C151C2semidirect
13. #1543×C151C2semidirect
14. #1482×C151C2semidirect
15. #1479×C151C2semidirect
377. #18868C151direct (N × H)
378. C151#18868direct (N × H)
379. #3522C2×C151semidirect
380. #3212C2×C151semidirect
381. #3207C2×C151semidirect
382. #3103C2×C151semidirect
383. #1645C2×C151semidirect
384. #1643C2×C151semidirect
385. #1642C2×C151semidirect
386. #1640C2×C151semidirect
387. #1623C2×C151semidirect
388. #1622C2×C151semidirect
389. #1621C2×C151semidirect
390. #1620C2×C151semidirect
391. #1543C2×C151semidirect
392. #1482C2×C151semidirect
393. #1479C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3522×C1512
#3212×C1512
#3207×C1512
#3103×C1512
#1645×C1512
#1643×C1512
#1642×C1512
#1640×C1512
#1623×C1512
#1622×C1512
#1621×C1512
#1620×C1512
#1543×C1512
#1482×C1512
#1479×C1512
#18868151