Finite Group Databasebeta

← C151×#18932 #50323857

Subgroups — C151×#18932 #50323857

Order 38656.

892 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3544×C151C211yesmaximal, characteristic, complemented
2#3251×C151C211yesmaximal, characteristic, complemented
3#3212×C151C211yesmaximal, characteristic, complemented
4#3206×C151C211yesmaximal, characteristic, complemented
5#1646×C151C211yesmaximal, characteristic, complemented
6#1645×C151C211yesmaximal, characteristic, complemented
7#1644×C151C211yesmaximal, characteristic, complemented
8#1643×C151C211yesmaximal, characteristic, complemented
9#1624×C151C211yesmaximal, characteristic, complemented
10#1623×C151C211yesmaximal, characteristic, complemented
11#1622×C151C211yesmaximal, characteristic, complemented
12#1622×C151C211yesmaximal, characteristic, complemented
13#1548×C151C211yesmaximal, characteristic, complemented
14#1495×C151C211yesmaximal, characteristic, complemented
15#1482×C151C211yesmaximal, characteristic, complemented
16#563×C151—22no—
17Q82×C151C2211yescharacteristic
18#555×C151C2211yescharacteristic
19#554×C151C2211yescharacteristic
20#554×C151C2211yescharacteristic
21#552×C151—21no—
22#552×C151—21no—
23#547×C151—21no—
24#547×C151—21no—
25#544×C151—21no—
26#544×C151—21no—
27#542×C151—21no—
28#542×C151—21no—
29#536×C151—22no—
30#532×C151C2211yescharacteristic
31C2×C4⋊Q8×C151C2211yescharacteristic
32#529×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#495×C151—21no—
35#492×C151C2211yescharacteristic
36#492×C151C2211yescharacteristic
37#488×C151—21no—
38#487×C151C2211yescharacteristic
39#487×C151C2211yescharacteristic
40#478×C151—21no—
41#475×C151C2211yescharacteristic
42#474×C151C2211yescharacteristic
43#469×C151—21no—
44#468×C151—21no—
45#463×C151—21no—
46#462×C151C2211yescharacteristic
47#461×C151—22no—
48#461×C151C2211yescharacteristic
49#460×C151C2211yescharacteristic
50#460×C151C2211yescharacteristic
51#459×C151C2211yescharacteristic
52#459×C151C2211yescharacteristic
53#452×C151—21no—
54#449×C151—21no—
55#448×C151—22no—
56#431×C151C2211yescharacteristic
57#431×C151C2211yescharacteristic
58#423×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#333×C151C2211yescharacteristic
62#333×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64Q8⋊C8×C151C2211yescharacteristic
65Q8⋊C8×C151C2211yescharacteristic
66Q8⋊C8×C151C2211yescharacteristic
67D4⋊C8×C151C2211yescharacteristic
68D4⋊C8×C151C2211yescharacteristic
69D4⋊C8×C151C2211yescharacteristic
70D4⋊C8×C151C2211yescharacteristic
71C2×#41×C151—22no—
72C2×#41×C151—21no—
73C22×Q8×C151D412yes—
74C2×Q16×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151—22no—
77C2×SD16×C151—22no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C2×D8×C151—21no—
81C2×D8×C151—21no—
82C2×M16×C151—21no—
83C4⋊Q8×C151—22no—
84C4⋊Q8×C151—21no—
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151—21no—
87C4⋊Q8×C151—21no—
88C4⋊Q8×C151—22no—
89C4⋊Q8×C151D412yes—
90C4⋊Q8×C151C2311yescharacteristic
91C4⋊Q8×C151C2311yescharacteristic
92C4⋊Q8×C151C2311yescharacteristic
93#127×C151C2311yescharacteristic
94#126×C151—22no—
95#126×C151—22no—
96#126×C151—21no—
97#126×C151—21no—
98#125×C151—22no—
99#125×C151—22no—
100#125×C151—21no—
101#125×C151—21no—
102#125×C151D411yescharacteristic
103#125×C151D411yescharacteristic
104#124×C151—22no—
105#124×C151—21no—
106#124×C151—22no—
107#124×C151D411yescharacteristic
108#124×C151D411yescharacteristic
109#123×C151—22no—
110#123×C151—22no—
111#123×C151—22no—
112#123×C151—22no—
113#123×C151—21no—
114#123×C151—21no—
115C22⋊Q8×C151—22no—
116C22⋊Q8×C151—22no—
117C22⋊Q8×C151—22no—
118C22⋊Q8×C151—22no—
119C22⋊Q8×C151—22no—
120C22⋊Q8×C151—22no—
121C22⋊Q8×C151—21no—
122C22⋊Q8×C151—21no—
123C22⋊Q8×C151D411yescharacteristic
124C22⋊Q8×C151D411yescharacteristic
125#121×C151—21no—
126#121×C151—21no—
127#121×C151—21no—
128#121×C151—21no—
129#121×C151D411yescharacteristic
130#121×C151D411yescharacteristic
131C4×Q8×C151—21no—
132C4×Q8×C151—21no—
133C4×Q8×C151C2311yescharacteristic
134C4×Q8×C151C2311yescharacteristic
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×C151C2311yescharacteristic
142C4×D4×C151C2311yescharacteristic
143#117×C151—22no—
144#117×C151—21no—
145#117×C151—21no—
146#117×C151—21no—
147#117×C151—21no—
148C2×C4⋊C4×C151—21no—
149C2×C4⋊C4×C151—21no—
150C2×C4⋊C4×C151—21no—
151C2×C4⋊C4×C151—21no—
152C2×C42×C151C2311yescharacteristic
153#107×C151—21no—
154#106×C151—21no—
155C4⋊C8×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—22no—
164#103×C151—22no—
165#103×C151—21no—
166#102×C151—21no—
167#102×C151—21no—
168#102×C151—21no—
169#102×C151—21no—
170#102×C151—21no—
171C22⋊C8×C151—21no—
172C22⋊C8×C151—21no—
173C4×C8×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176#41×C151—81no—
177#41×C151—81no—
178#41×C151—84no—
179C2×Q8×C151—22no—
180C2×Q8×C151—22no—
181C2×Q8×C151—21no—
182C2×Q8×C151—82no—
183C2×Q8×C151C2×D411yescharacteristic
184C2×Q8×C151C2×D411yescharacteristic
185C2×Q8×C151C2×D412yes—
186C2×Q8×C151C2×D412yes—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—22no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—41no—
194C2×D4×C151C2×D411yescharacteristic
195C2×D4×C151C2×D411yescharacteristic
196C22×C4×C151—22no—
197C22×C4×C151—22no—
198C22×C4×C151—22no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—41no—
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D411yescharacteristic
205Q16×C151—81no—
206SD16×C151—81no—
207SD16×C151—81no—
208SD16×C151—81no—
209SD16×C151—82no—
210SD16×C151—82no—
211D8×C151—81no—
212D8×C151—81no—
213M16×C151—81no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—21no—
220C4⋊C4×C151—22no—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—22no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—22no—
226C4⋊C4×C151—22no—
227C4⋊C4×C151—22no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
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×C151C2×D411yescharacteristic
243C4⋊C4×C151C2×D411yescharacteristic
244C4⋊C4×C151C2×D411yescharacteristic
245C4⋊C4×C151C2×D411yescharacteristic
246C22⋊C4×C151—22no—
247C22⋊C4×C151—22no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—21no—
251C22⋊C4×C151—21no—
252C22⋊C4×C151—21no—
253C22⋊C4×C151—21no—
254C22⋊C4×C151—21no—
255C22⋊C4×C151—21no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—41no—
261C22⋊C4×C151—41no—
262C42×C151—22no—
263C42×C151—22no—
264C42×C151—21no—
265C42×C151—21no—
266C42×C151C2×D411yescharacteristic
267C42×C151C2×D411yescharacteristic
268C42×C151C2×D411yescharacteristic
269C42×C151C2411yescharacteristic
270C23×C151—21no—
271C23×C151—21no—
272C23×C151—41no—
273C23×C151#12011yescharacteristic
274Q8×C151—21no—
275Q8×C151—21no—
276Q8×C151—21no—
277Q8×C151—21no—
278Q8×C151—42no—
279Q8×C151—42no—
280Q8×C151—41no—
281Q8×C151—41no—
282Q8×C151—82no—
283Q8×C151—82no—
284D4×C151—21no—
285D4×C151—21no—
286D4×C151—21no—
287D4×C151—21no—
288D4×C151—42no—
289D4×C151—42no—
290D4×C151—42no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—82no—
296D4×C151—82no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—22no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—22no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—41no—
310C2×C4×C151—44no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—82no—
317C2×C4×C151—82no—
318C2×C4×C151—82no—
319C2×C4×C151#12011yescharacteristic
320C2×C4×C151#12011yescharacteristic
321C2×C4×C151#12011yescharacteristic
322C2×C4×C151C22×D411yescharacteristic
323C2×C4×C151C22×D411yescharacteristic
324C2×C4×C151C22×D411yescharacteristic
325C8×C151—41no—
326C8×C151—41no—
327C8×C151—41no—
328C8×C151—41no—
329C8×C151—41no—
330C8×C151—41no—
331C22×C151—21no—
332C22×C151—21no—
333C22×C151—21no—
334C22×C151—41no—
335C22×C151—41no—
336C22×C151—41no—
337C22×C151—41no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151—81no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151C2×#12011yescharacteristic
344C4×C151—21no—
345C4×C151—21no—
346C4×C151—21no—
347C4×C151—21no—
348C4×C151—41no—
349C4×C151—41no—
350C4×C151—41no—
351C4×C151—41no—
352C4×C151—42no—
353C4×C151—42no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—81no—
357C4×C151#57711yescharacteristic
358C4×C151#57711yescharacteristic
359C4×C151#57711yescharacteristic
360C4×C151#57811yescharacteristic
361C2×C151—41no—
362C2×C151—81no—
363C2×C151—81no—
364C2×C151—161no—
365C2×C151#301011yescharacteristic
366C2×C151#301311yescharacteristic
367C2×C151#301911yescharacteristic
368#18932C15111yesmaximal, characteristic, direct product factor, Sylow
369C151#1893211yescharacteristic, direct product factor, Sylow
370#3544C2×C15111yescharacteristic, complemented
371#3251C2×C15111yescharacteristic, complemented
372#3212C2×C15111yescharacteristic, complemented
373#3206C2×C15111yescharacteristic, complemented
374#1646C2×C15111yescharacteristic, complemented
375#1645C2×C15111yescharacteristic, complemented
376#1644C2×C15111yescharacteristic, complemented
377#1643C2×C15111yescharacteristic, complemented
378#1624C2×C15111yescharacteristic, complemented
379#1623C2×C15111yescharacteristic, complemented
380#1622C2×C15111yescharacteristic, complemented
381#1622C2×C15111yescharacteristic, complemented
382#1548C2×C15111yescharacteristic, complemented
383#1495C2×C15111yescharacteristic, complemented
384#1482C2×C15111yescharacteristic, complemented
385#563—22no—
386Q82C22×C15111yescharacteristic
387#555C22×C15111yescharacteristic
388#554C22×C15111yescharacteristic
389#554C22×C15111yescharacteristic
390#552—21no—
391#552—21no—
392#547—21no—
393#547—21no—
394#544—21no—
395#544—21no—
396#542—21no—
397#542—21no—
398#536—22no—
399#532C22×C15111yescharacteristic
400C2×C4⋊Q8C22×C15111yescharacteristic
401#529C22×C15111yescharacteristic
402#529C22×C15111yescharacteristic
403#495—21no—
404#492C22×C15111yescharacteristic
405#492C22×C15111yescharacteristic
406#488—21no—
407#487C22×C15111yescharacteristic
408#487C22×C15111yescharacteristic
409#478—21no—
410#475C22×C15111yescharacteristic
411#474C22×C15111yescharacteristic
412#469—21no—
413#468—21no—
414#463—21no—
415#462C22×C15111yescharacteristic
416#461—22no—
417#461C22×C15111yescharacteristic
418#460C22×C15111yescharacteristic
419#460C22×C15111yescharacteristic
420#459C22×C15111yescharacteristic
421#459C22×C15111yescharacteristic
422#452—21no—
423#449—21no—
424#448—22no—
425#431C22×C15111yescharacteristic
426#431C22×C15111yescharacteristic
427#423C22×C15111yescharacteristic
428#333C22×C15111yescharacteristic
429#333C22×C15111yescharacteristic
430#333C22×C15111yescharacteristic
431#333C22×C15111yescharacteristic
432Q8⋊C8C22×C15111yescharacteristic
433Q8⋊C8C22×C15111yescharacteristic
434Q8⋊C8C22×C15111yescharacteristic
435Q8⋊C8C22×C15111yescharacteristic
436D4⋊C8C22×C15111yescharacteristic
437D4⋊C8C22×C15111yescharacteristic
438D4⋊C8C22×C15111yescharacteristic
439D4⋊C8C22×C15111yescharacteristic
440C2×#41—22no—
441C2×#41—21no—
442C22×Q8D4×C15112yes—
443C2×Q16—21no—
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16—21no—
447C2×SD16—21no—
448C2×SD16—21no—
449C2×D8—21no—
450C2×D8—21no—
451C2×M16—21no—
452C4⋊Q8—22no—
453C4⋊Q8—22no—
454C4⋊Q8—21no—
455C4⋊Q8—21no—
456C4⋊Q8—21no—
457C4⋊Q8—21no—
458C4⋊Q8D4×C15112yes—
459C4⋊Q8C23×C15111yescharacteristic
460C4⋊Q8C23×C15111yescharacteristic
461C4⋊Q8C23×C15111yescharacteristic
462#127C23×C15111yescharacteristic
463#126—22no—
464#126—22no—
465#126—21no—
466#126—21no—
467#125—22no—
468#125—22no—
469#125—21no—
470#125—21no—
471#125D4×C15111yescharacteristic
472#125D4×C15111yescharacteristic
473#124—22no—
474#124—22no—
475#124—21no—
476#124D4×C15111yescharacteristic
477#124D4×C15111yescharacteristic
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—21no—
483#123—21no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8D4×C15111yescharacteristic
493C22⋊Q8D4×C15111yescharacteristic
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121D4×C15111yescharacteristic
499#121D4×C15111yescharacteristic
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8C23×C15111yescharacteristic
503C4×Q8C23×C15111yescharacteristic
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4C23×C15111yescharacteristic
511C4×D4C23×C15111yescharacteristic
512#117—22no—
513#117—21no—
514#117—21no—
515#117—21no—
516#117—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C42C23×C15111yescharacteristic
522#107—21no—
523#106—21no—
524C4⋊C8—21no—
525C4⋊C8—21no—
526C4⋊C8C23×C15111yescharacteristic
527C4⋊C8C23×C15111yescharacteristic
528C4⋊C8C23×C15111yescharacteristic
529C4⋊C8C23×C15111yescharacteristic
530#103—22no—
531#103—22no—
532#103—21no—
533#103—21no—
534#103—21no—
535#102—21no—
536#102—21no—
537#102—21no—
538#102—21no—
539#102—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C4×C8—21no—
543C4×C8C23×C15111yescharacteristic
544C4×C8C23×C15111yescharacteristic
545#41—81no—
546#41—81no—
547#41—84no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—21no—
551C2×Q8—82no—
552C2×Q8C2×D4×C15111yescharacteristic
553C2×Q8C2×D4×C15111yescharacteristic
554C2×Q8C2×D4×C15112yes—
555C2×Q8C2×D4×C15112yes—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4C2×D4×C15111yescharacteristic
564C2×D4C2×D4×C15111yescharacteristic
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—41no—
571C22×C4C2×D4×C15111yescharacteristic
572C22×C4C2×D4×C15111yescharacteristic
573C22×C4C2×D4×C15111yescharacteristic
574Q16—81no—
575SD16—81no—
576SD16—81no—
577SD16—81no—
578SD16—82no—
579SD16—82no—
580D8—81no—
581D8—81no—
582M16—81no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4C2×D4×C15111yescharacteristic
612C4⋊C4C2×D4×C15111yescharacteristic
613C4⋊C4C2×D4×C15111yescharacteristic
614C4⋊C4C2×D4×C15111yescharacteristic
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—41no—
630C22⋊C4—41no—
631C42—22no—
632C42—22no—
633C42—21no—
634C42—21no—
635C42C2×D4×C15111yescharacteristic
636C42C2×D4×C15111yescharacteristic
637C42C2×D4×C15111yescharacteristic
638C42C24×C15111yescharacteristic
639C23—21no—
640C23—21no—
641C23—41no—
642C23#120×C15111yescharacteristic
643Q8—21no—
644Q8—21no—
645Q8—21no—
646Q8—21no—
647Q8—42no—
648Q8—42no—
649Q8—41no—
650Q8—41no—
651Q8—82no—
652Q8—82no—
653D4—21no—
654D4—21no—
655D4—21no—
656D4—21no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—82no—
665D4—82no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4—82no—
688C2×C4#120×C15111yescharacteristic
689C2×C4#120×C15111yescharacteristic
690C2×C4#120×C15111yescharacteristic
691C2×C4C22×D4×C15111yescharacteristic
692C2×C4C22×D4×C15111yescharacteristic
693C2×C4C22×D4×C15111yescharacteristic
694C8—41no—
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22C2×#120×C15111yescharacteristic
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—41no—
724C4—41no—
725C4—81no—
726C4#577×C15111yescharacteristic
727C4#577×C15111yescharacteristic
728C4#577×C15111yescharacteristic
729C4#578×C15111yescharacteristic
730C2—41no—
731C2—81no—
732C2—81no—
733C2—161no—
734C2#3010×C15111yescharacteristic
735C2#3013×C15111yescharacteristic
736C2#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. #3544×C151C2semidirect
2. #3251×C151C2semidirect
3. #3212×C151C2semidirect
4. #3206×C151C2semidirect
5. #1646×C151C2semidirect
6. #1645×C151C2semidirect
7. #1644×C151C2semidirect
8. #1643×C151C2semidirect
9. #1624×C151C2semidirect
10. #1623×C151C2semidirect
11. #1622×C151C2semidirect
12. #1622×C151C2semidirect
13. #1548×C151C2semidirect
14. #1495×C151C2semidirect
15. #1482×C151C2semidirect
368. #18932C151direct (N × H)
369. C151#18932direct (N × H)
370. #3544C2×C151semidirect
371. #3251C2×C151semidirect
372. #3212C2×C151semidirect
373. #3206C2×C151semidirect
374. #1646C2×C151semidirect
375. #1645C2×C151semidirect
376. #1644C2×C151semidirect
377. #1643C2×C151semidirect
378. #1624C2×C151semidirect
379. #1623C2×C151semidirect
380. #1622C2×C151semidirect
381. #1622C2×C151semidirect
382. #1548C2×C151semidirect
383. #1495C2×C151semidirect
384. #1482C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3544×C1512
#3251×C1512
#3212×C1512
#3206×C1512
#1646×C1512
#1645×C1512
#1644×C1512
#1643×C1512
#1624×C1512
#1623×C1512
#1622×C1512
#1548×C1512
#1495×C1512
#1482×C1512
#18932151