Finite Group Databasebeta

← C151×#18596 #50323521

Subgroups — C151×#18596 #50323521

Order 38656.

930 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3515×C151C211yesmaximal, characteristic, complemented
2#3251×C151C211yesmaximal, characteristic, complemented
3#3182×C151C211yesmaximal, characteristic, complemented
4#3035×C151C211yesmaximal, characteristic, complemented
5#1648×C151C211yesmaximal, characteristic, complemented
6#1647×C151C211yesmaximal, characteristic, complemented
7#1644×C151C211yesmaximal, characteristic, complemented
8#1643×C151C211yesmaximal, characteristic, complemented
9#1626×C151C211yesmaximal, characteristic, complemented
10#1625×C151C211yesmaximal, characteristic, complemented
11#1622×C151C211yesmaximal, characteristic, complemented
12#1622×C151C211yesmaximal, characteristic, complemented
13#1550×C151C211yesmaximal, characteristic, complemented
14#1489×C151C211yesmaximal, characteristic, complemented
15#1483×C151C211yesmaximal, characteristic, complemented
16C2×#135×C151—21no—
17#557×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19#554×C151C2211yescharacteristic
20#553×C151—21no—
21#552×C151—21no—
22#552×C151—22no—
23#552×C151—21no—
24#547×C151—21no—
25#547×C151C2211yescharacteristic
26#541×C151—21no—
27#539×C151—22no—
28#533×C151C2211yescharacteristic
29#532×C151C2211yescharacteristic
30#529×C151—21no—
31#529×C151C2211yescharacteristic
32C2×#125×C151—21no—
33#520×C151—21no—
34C4×#41×C151C2211yescharacteristic
35#500×C151C2211yescharacteristic
36#492×C151C2211yescharacteristic
37#487×C151C2211yescharacteristic
38#486×C151C2211yescharacteristic
39#478×C151—21no—
40#475×C151C2211yescharacteristic
41#474×C151C2211yescharacteristic
42#469×C151—21no—
43#468×C151—22no—
44#468×C151—21no—
45#464×C151—21no—
46#463×C151—21no—
47#463×C151—21no—
48#462×C151C2211yescharacteristic
49#461×C151C2211yescharacteristic
50#460×C151C2211yescharacteristic
51#460×C151C2211yescharacteristic
52#459×C151C2211yescharacteristic
53#459×C151C2211yescharacteristic
54#440×C151—22no—
55#423×C151C2211yescharacteristic
56C2×C4⋊C8×C151C2211yescharacteristic
57#416×C151—21no—
58C4×M16×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×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—21no—
72C2×#41×C151—21no—
73C2×#41×C151D411yescharacteristic
74#135×C151—44no—
75C2×Q16×C151—21no—
76C2×SD16×C151—21no—
77C2×SD16×C151—22no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C2×D8×C151—21no—
81C2×D8×C151—21no—
82C2×M16×C151—21no—
83C2×M16×C151—21no—
84C22×C8×C151—21no—
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151C2311yescharacteristic
87C4⋊Q8×C151C2311yescharacteristic
88C4⋊Q8×C151C2311yescharacteristic
89#127×C151C2311yescharacteristic
90#126×C151—22no—
91#126×C151—22no—
92#126×C151—22no—
93#126×C151—21no—
94#125×C151—22no—
95#125×C151—22no—
96#125×C151—22no—
97#125×C151—21no—
98#125×C151—21no—
99#125×C151—22no—
100#125×C151—21no—
101#125×C151—21no—
102#125×C151D411yescharacteristic
103#124×C151—21no—
104#124×C151D411yescharacteristic
105#123×C151—22no—
106#123×C151—22no—
107#123×C151—22no—
108#123×C151—21no—
109#123×C151—22no—
110C22⋊Q8×C151—21no—
111C22⋊Q8×C151—21no—
112C22⋊Q8×C151—21no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—21no—
116C22⋊Q8×C151D411yescharacteristic
117C22⋊Q8×C151D412yes—
118#121×C151—22no—
119#121×C151—21no—
120#121×C151—21no—
121#121×C151—21no—
122#121×C151D411yescharacteristic
123C4×Q8×C151—21no—
124C4×Q8×C151—21no—
125C4×Q8×C151—21no—
126C4×Q8×C151D412yes—
127C4×Q8×C151D411yescharacteristic
128C4×Q8×C151C2311yescharacteristic
129C4×Q8×C151C2311yescharacteristic
130C4×D4×C151—22no—
131C4×D4×C151—22no—
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×C151—21no—
139C4×D4×C151D411yescharacteristic
140C4×D4×C151C2311yescharacteristic
141C4×D4×C151C2311yescharacteristic
142#117×C151—22no—
143#117×C151—22no—
144#117×C151—21no—
145#117×C151—21no—
146#117×C151—21no—
147#117×C151D411yescharacteristic
148C2×C4⋊C4×C151—22no—
149C2×C4⋊C4×C151—22no—
150C2×C4⋊C4×C151—21no—
151C2×C4⋊C4×C151—21no—
152C2×C4⋊C4×C151—21no—
153C2×C42×C151—21no—
154C2×C42×C151C2311yescharacteristic
155#107×C151—22no—
156#107×C151—21no—
157#106×C151—21no—
158C4⋊C8×C151—21no—
159C4⋊C8×C151—21no—
160C4⋊C8×C151C2311yescharacteristic
161C4⋊C8×C151C2311yescharacteristic
162C4⋊C8×C151C2311yescharacteristic
163C4⋊C8×C151C2311yescharacteristic
164#103×C151—21no—
165#103×C151—21no—
166#103×C151—22no—
167#103×C151—21no—
168#102×C151—21no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—22no—
172#102×C151—21no—
173#102×C151—21no—
174#97×C151—21no—
175C4×C8×C151C2311yescharacteristic
176C4×C8×C151C2311yescharacteristic
177#41×C151—22no—
178#41×C151—41no—
179#41×C151—42no—
180#41×C151—42no—
181#41×C151—42no—
182#41×C151—42no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151C2×D411yescharacteristic
186C2×Q8×C151C2×D411yescharacteristic
187C2×Q8×C151C2×D412yes—
188C2×D4×C151—22no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—41no—
195C2×D4×C151C2×D411yescharacteristic
196C2×D4×C151C2×D411yescharacteristic
197C22×C4×C151—22no—
198C22×C4×C151—22no—
199C22×C4×C151—22no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—41no—
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208Q16×C151—42no—
209SD16×C151—44no—
210SD16×C151—42no—
211SD16×C151—42no—
212SD16×C151—81no—
213D8×C151—42no—
214D8×C151—81no—
215M16×C151—42no—
216M16×C151—81no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—21no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—42no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—22no—
226C4⋊C4×C151—22no—
227C4⋊C4×C151—22no—
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—22no—
235C4⋊C4×C151—22no—
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—21no—
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—21no—
262C22⋊C4×C151—41no—
263C22⋊C4×C151—41no—
264C42×C151—22no—
265C42×C151—21no—
266C42×C151—21no—
267C42×C151—22no—
268C42×C151—21no—
269C42×C151—21no—
270C42×C151C2×D411yescharacteristic
271C42×C151C2×D411yescharacteristic
272C42×C151C2×D411yescharacteristic
273C42×C151C2411yescharacteristic
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—41no—
277C23×C151#12011yescharacteristic
278Q8×C151—21no—
279Q8×C151—21no—
280Q8×C151—21no—
281Q8×C151—21no—
282Q8×C151—42no—
283Q8×C151—41no—
284Q8×C151—41no—
285Q8×C151—41no—
286Q8×C151—41no—
287D4×C151—21no—
288D4×C151—21no—
289D4×C151—21no—
290D4×C151—42no—
291D4×C151—42no—
292D4×C151—44no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—81no—
298D4×C151—82no—
299D4×C151AGL(1,ℤ/8)12yes—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—22no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—22no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—41no—
313C2×C4×C151—42no—
314C2×C4×C151—44no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—81no—
321C2×C4×C151—82no—
322C2×C4×C151—82no—
323C2×C4×C151—82no—
324C2×C4×C151#12011yescharacteristic
325C2×C4×C151#12011yescharacteristic
326C2×C4×C151#12011yescharacteristic
327C2×C4×C151C22×D411yescharacteristic
328C2×C4×C151C22×D411yescharacteristic
329C2×C4×C151C22×D411yescharacteristic
330C8×C151—22no—
331C8×C151—41no—
332C8×C151—41no—
333C8×C151—41no—
334C8×C151—41no—
335C8×C151—41no—
336C22×C151—21no—
337C22×C151—22no—
338C22×C151—21no—
339C22×C151—21no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—81no—
346C22×C151—81no—
347C22×C151—81no—
348C22×C151C2×#12011yescharacteristic
349C4×C151—21no—
350C4×C151—21no—
351C4×C151—21no—
352C4×C151—21no—
353C4×C151—41no—
354C4×C151—41no—
355C4×C151—42no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—41no—
360C4×C151—42no—
361C4×C151—81no—
362C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
363C4×C151#57511yescharacteristic
364C4×C151#57711yescharacteristic
365C4×C151#57811yescharacteristic
366C2×C151—41no—
367C2×C151—42no—
368C2×C151—81no—
369C2×C151—161no—
370C2×C151#300611yescharacteristic
371C2×C151#301311yescharacteristic
372C2×C151#301811yescharacteristic
373#18596C15111yesmaximal, characteristic, direct product factor, Sylow
374C151#1859611yescharacteristic, direct product factor, Sylow
375#3515C2×C15111yescharacteristic, complemented
376#3251C2×C15111yescharacteristic, complemented
377#3182C2×C15111yescharacteristic, complemented
378#3035C2×C15111yescharacteristic, complemented
379#1648C2×C15111yescharacteristic, complemented
380#1647C2×C15111yescharacteristic, complemented
381#1644C2×C15111yescharacteristic, complemented
382#1643C2×C15111yescharacteristic, complemented
383#1626C2×C15111yescharacteristic, complemented
384#1625C2×C15111yescharacteristic, complemented
385#1622C2×C15111yescharacteristic, complemented
386#1622C2×C15111yescharacteristic, complemented
387#1550C2×C15111yescharacteristic, complemented
388#1489C2×C15111yescharacteristic, complemented
389#1483C2×C15111yescharacteristic, complemented
390C2×#135—21no—
391#557C22×C15111yescharacteristic
392#554C22×C15111yescharacteristic
393#554C22×C15111yescharacteristic
394#553—21no—
395#552—21no—
396#552—22no—
397#552—21no—
398#547—21no—
399#547C22×C15111yescharacteristic
400#541—21no—
401#539—22no—
402#533C22×C15111yescharacteristic
403#532C22×C15111yescharacteristic
404#529—21no—
405#529C22×C15111yescharacteristic
406C2×#125—21no—
407#520—21no—
408C4×#41C22×C15111yescharacteristic
409#500C22×C15111yescharacteristic
410#492C22×C15111yescharacteristic
411#487C22×C15111yescharacteristic
412#486C22×C15111yescharacteristic
413#478—21no—
414#475C22×C15111yescharacteristic
415#474C22×C15111yescharacteristic
416#469—21no—
417#468—22no—
418#468—21no—
419#464—21no—
420#463—21no—
421#463—21no—
422#462C22×C15111yescharacteristic
423#461C22×C15111yescharacteristic
424#460C22×C15111yescharacteristic
425#460C22×C15111yescharacteristic
426#459C22×C15111yescharacteristic
427#459C22×C15111yescharacteristic
428#440—22no—
429#423C22×C15111yescharacteristic
430C2×C4⋊C8C22×C15111yescharacteristic
431#416—21no—
432C4×M16C22×C15111yescharacteristic
433#333C22×C15111yescharacteristic
434#333C22×C15111yescharacteristic
435#332C22×C15111yescharacteristic
436#332C22×C15111yescharacteristic
437Q8⋊C8C22×C15111yescharacteristic
438Q8⋊C8C22×C15111yescharacteristic
439Q8⋊C8C22×C15111yescharacteristic
440Q8⋊C8C22×C15111yescharacteristic
441D4⋊C8C22×C15111yescharacteristic
442D4⋊C8C22×C15111yescharacteristic
443D4⋊C8C22×C15111yescharacteristic
444D4⋊C8C22×C15111yescharacteristic
445C2×#41—21no—
446C2×#41—21no—
447C2×#41D4×C15111yescharacteristic
448#135—44no—
449C2×Q16—21no—
450C2×SD16—21no—
451C2×SD16—22no—
452C2×SD16—21no—
453C2×SD16—21no—
454C2×D8—21no—
455C2×D8—21no—
456C2×M16—21no—
457C2×M16—21no—
458C22×C8—21no—
459C4⋊Q8—21no—
460C4⋊Q8C23×C15111yescharacteristic
461C4⋊Q8C23×C15111yescharacteristic
462C4⋊Q8C23×C15111yescharacteristic
463#127C23×C15111yescharacteristic
464#126—22no—
465#126—22no—
466#126—22no—
467#126—21no—
468#125—22no—
469#125—22no—
470#125—22no—
471#125—21no—
472#125—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C15111yescharacteristic
477#124—21no—
478#124D4×C15111yescharacteristic
479#123—22no—
480#123—22no—
481#123—22no—
482#123—21no—
483#123—22no—
484C22⋊Q8—21no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8D4×C15111yescharacteristic
491C22⋊Q8D4×C15112yes—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121D4×C15111yescharacteristic
497C4×Q8—21no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8D4×C15111yescharacteristic
501C4×Q8D4×C15112yes—
502C4×Q8C23×C15111yescharacteristic
503C4×Q8C23×C15111yescharacteristic
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4D4×C15111yescharacteristic
514C4×D4C23×C15111yescharacteristic
515C4×D4C23×C15111yescharacteristic
516#117—22no—
517#117—22no—
518#117—21no—
519#117—21no—
520#117—21no—
521#117D4×C15111yescharacteristic
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C42—21no—
528C2×C42C23×C15111yescharacteristic
529#107—22no—
530#107—21no—
531#106—21no—
532C4⋊C8—21no—
533C4⋊C8—21no—
534C4⋊C8C23×C15111yescharacteristic
535C4⋊C8C23×C15111yescharacteristic
536C4⋊C8C23×C15111yescharacteristic
537C4⋊C8C23×C15111yescharacteristic
538#103—22no—
539#103—21no—
540#103—21no—
541#103—21no—
542#102—21no—
543#102—21no—
544#102—21no—
545#102—22no—
546#102—21no—
547#102—21no—
548#97—21no—
549C4×C8C23×C15111yescharacteristic
550C4×C8C23×C15111yescharacteristic
551#41—22no—
552#41—41no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—42no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8C2×D4×C15111yescharacteristic
560C2×Q8C2×D4×C15111yescharacteristic
561C2×Q8C2×D4×C15112yes—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—41no—
569C2×D4C2×D4×C15111yescharacteristic
570C2×D4C2×D4×C15111yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—41no—
579C22×C4C2×D4×C15111yescharacteristic
580C22×C4C2×D4×C15111yescharacteristic
581C22×C4C2×D4×C15111yescharacteristic
582Q16—42no—
583SD16—44no—
584SD16—42no—
585SD16—42no—
586SD16—81no—
587D8—42no—
588D8—81no—
589M16—42no—
590M16—81no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—42no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
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⋊C4C2×D4×C15111yescharacteristic
620C4⋊C4C2×D4×C15111yescharacteristic
621C4⋊C4C2×D4×C15111yescharacteristic
622C4⋊C4C2×D4×C15111yescharacteristic
623C4⋊C4C2×D4×C15112yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—41no—
637C22⋊C4—41no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42C2×D4×C15111yescharacteristic
645C42C2×D4×C15111yescharacteristic
646C42C2×D4×C15111yescharacteristic
647C42C24×C15111yescharacteristic
648C23—21no—
649C23—21no—
650C23—41no—
651C23#120×C15111yescharacteristic
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8—21no—
656Q8—42no—
657Q8—41no—
658Q8—41no—
659Q8—41no—
660Q8—41no—
661D4—21no—
662D4—21no—
663D4—21no—
664D4—42no—
665D4—42no—
666D4—44no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—81no—
672D4—82no—
673D4AGL(1,ℤ/8)×C15112yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—81no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—82no—
698C2×C4#120×C15111yescharacteristic
699C2×C4#120×C15111yescharacteristic
700C2×C4#120×C15111yescharacteristic
701C2×C4C22×D4×C15111yescharacteristic
702C2×C4C22×D4×C15111yescharacteristic
703C2×C4C22×D4×C15111yescharacteristic
704C8—22no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—21no—
711C22—22no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22C2×#120×C15111yescharacteristic
723C4—21no—
724C4—21no—
725C4—21no—
726C4—21no—
727C4—41no—
728C4—41no—
729C4—42no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—81no—
736C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
737C4#575×C15111yescharacteristic
738C4#577×C15111yescharacteristic
739C4#578×C15111yescharacteristic
740C2—41no—
741C2—42no—
742C2—81no—
743C2—161no—
744C2#3006×C15111yescharacteristic
745C2#3013×C15111yescharacteristic
746C2#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. #3515×C151C2semidirect
2. #3251×C151C2semidirect
3. #3182×C151C2semidirect
4. #3035×C151C2semidirect
5. #1648×C151C2semidirect
6. #1647×C151C2semidirect
7. #1644×C151C2semidirect
8. #1643×C151C2semidirect
9. #1626×C151C2semidirect
10. #1625×C151C2semidirect
11. #1622×C151C2semidirect
12. #1622×C151C2semidirect
13. #1550×C151C2semidirect
14. #1489×C151C2semidirect
15. #1483×C151C2semidirect
373. #18596C151direct (N × H)
374. C151#18596direct (N × H)
375. #3515C2×C151semidirect
376. #3251C2×C151semidirect
377. #3182C2×C151semidirect
378. #3035C2×C151semidirect
379. #1648C2×C151semidirect
380. #1647C2×C151semidirect
381. #1644C2×C151semidirect
382. #1643C2×C151semidirect
383. #1626C2×C151semidirect
384. #1625C2×C151semidirect
385. #1622C2×C151semidirect
386. #1622C2×C151semidirect
387. #1550C2×C151semidirect
388. #1489C2×C151semidirect
389. #1483C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3515×C1512
#3251×C1512
#3182×C1512
#3035×C1512
#1648×C1512
#1647×C1512
#1644×C1512
#1643×C1512
#1626×C1512
#1625×C1512
#1622×C1512
#1550×C1512
#1489×C1512
#1483×C1512
#18596151