Finite Group Databasebeta

← C151×#18726 #50323651

Subgroups — C151×#18726 #50323651

Order 38656.

892 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3552×C151C211yesmaximal, characteristic, complemented
2#3247×C151C211yesmaximal, characteristic, complemented
3#3247×C151C211yesmaximal, characteristic, complemented
4#3141×C151C211yesmaximal, characteristic, complemented
5#1638×C151C211yesmaximal, characteristic, complemented
6#1637×C151C211yesmaximal, characteristic, complemented
7#1636×C151C211yesmaximal, characteristic, complemented
8#1635×C151C211yesmaximal, characteristic, complemented
9#1628×C151C211yesmaximal, characteristic, complemented
10#1627×C151C211yesmaximal, characteristic, complemented
11#1626×C151C211yesmaximal, characteristic, complemented
12#1625×C151C211yesmaximal, characteristic, complemented
13C2×#332×C151C211yesmaximal, characteristic, complemented
14#1483×C151C211yesmaximal, characteristic, complemented
15#1483×C151C211yesmaximal, characteristic, complemented
16#563×C151—22no—
17#557×C151C2211yescharacteristic
18#556×C151C2211yescharacteristic
19#554×C151—21no—
20#553×C151—21no—
21D4×Q8×C151—21no—
22D4×Q8×C151C2211yescharacteristic
23#548×C151—21no—
24#547×C151C2211yescharacteristic
25#544×C151—21no—
26#542×C151—21no—
27#541×C151—21no—
28#539×C151—22no—
29#536×C151—21no—
30#532×C151C2211yescharacteristic
31C2×C4⋊Q8×C151C2211yescharacteristic
32#529×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#489×C151—22no—
35#487×C151C2211yescharacteristic
36#487×C151C2211yescharacteristic
37#486×C151C2211yescharacteristic
38#486×C151C2211yescharacteristic
39#478×C151—21no—
40#478×C151—21no—
41#477×C151C2211yescharacteristic
42#477×C151C2211yescharacteristic
43#476×C151C2211yescharacteristic
44#476×C151C2211yescharacteristic
45#466×C151—21no—
46#466×C151—21no—
47#465×C151—21no—
48#465×C151—21no—
49#463×C151—21no—
50#463×C151—21no—
51#460×C151C2211yescharacteristic
52#460×C151C2211yescharacteristic
53#459×C151C2211yescharacteristic
54#459×C151C2211yescharacteristic
55C2×C4⋊C8×C151C2211yescharacteristic
56C2×C4⋊C8×C151C2211yescharacteristic
57#417×C151—22no—
58C4×M16×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×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—
73C22×Q8×C151—21no—
74C22×Q8×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151—21no—
77C2×D8×C151—21no—
78C2×D8×C151—21no—
79C2×M16×C151—21no—
80C22×C8×C151—21no—
81C22×C8×C151—21no—
82C4⋊Q8×C151—22no—
83C4⋊Q8×C151—21no—
84C4⋊Q8×C151—21no—
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151—21no—
87C4⋊Q8×C151D412yes—
88C4⋊Q8×C151C2311yescharacteristic
89C4⋊Q8×C151C2311yescharacteristic
90C4⋊Q8×C151C2311yescharacteristic
91#127×C151C2311yescharacteristic
92#126×C151—22no—
93#126×C151—22no—
94#126×C151—22no—
95#126×C151—21no—
96#126×C151—21no—
97#125×C151—22no—
98#125×C151—22no—
99#125×C151—22no—
100#125×C151—21no—
101#125×C151D411yescharacteristic
102#125×C151D411yescharacteristic
103#124×C151—22no—
104#124×C151—21no—
105#124×C151—21no—
106#124×C151D411yescharacteristic
107#124×C151D411yescharacteristic
108#123×C151—22no—
109#123×C151—22no—
110#123×C151—21no—
111#123×C151—21no—
112#123×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—22no—
116C22⋊Q8×C151—22no—
117C22⋊Q8×C151—22no—
118C22⋊Q8×C151—22no—
119C22⋊Q8×C151—21no—
120C22⋊Q8×C151—21no—
121C22⋊Q8×C151—21no—
122C22⋊Q8×C151D411yescharacteristic
123C22⋊Q8×C151D411yescharacteristic
124#121×C151—22no—
125#121×C151—21no—
126#121×C151—21no—
127#121×C151—21no—
128#121×C151D411yescharacteristic
129#121×C151D411yescharacteristic
130C4×Q8×C151—21no—
131C4×Q8×C151—21no—
132C4×Q8×C151—21no—
133C4×Q8×C151C2311yescharacteristic
134C4×Q8×C151C2311yescharacteristic
135C4×D4×C151—22no—
136C4×D4×C151—22no—
137C4×D4×C151—21no—
138C4×D4×C151—21no—
139C4×D4×C151—21no—
140C4×D4×C151—21no—
141C4×D4×C151—21no—
142C4×D4×C151C2311yescharacteristic
143C4×D4×C151C2311yescharacteristic
144#117×C151—21no—
145#117×C151—21no—
146#117×C151—21no—
147C2×C4⋊C4×C151—21no—
148C2×C4⋊C4×C151—21no—
149C2×C4⋊C4×C151D412yes—
150C2×C42×C151C2311yescharacteristic
151#107×C151—21no—
152#107×C151—21no—
153#106×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—22no—
162#103×C151—22no—
163#103×C151—21no—
164#103×C151—21no—
165#102×C151—21no—
166#102×C151—21no—
167#102×C151—22no—
168#102×C151—22no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—21no—
172#102×C151—21no—
173#97×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176#41×C151—44no—
177#41×C151—81no—
178#41×C151—81no—
179C2×Q8×C151—22no—
180C2×Q8×C151—22no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—81no—
185C2×Q8×C151—81no—
186C2×Q8×C151—81no—
187C2×Q8×C151—81no—
188C2×Q8×C151C2×D411yescharacteristic
189C2×Q8×C151C2×D411yescharacteristic
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—22no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—41no—
197C2×D4×C151C2×D411yescharacteristic
198C2×D4×C151C2×D411yescharacteristic
199C22×C4×C151—22no—
200C22×C4×C151—22no—
201C22×C4×C151—22no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—41no—
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151C2×D411yescharacteristic
208SD16×C151—81no—
209SD16×C151—81no—
210D8×C151—81no—
211D8×C151—81no—
212M16×C151—42no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—81no—
220C2×C8×C151—81no—
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—22no—
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×C151C2×D412yes—
242C4⋊C4×C151C2×D412yes—
243C4⋊C4×C151C2×D411yescharacteristic
244C4⋊C4×C151C2×D411yescharacteristic
245C4⋊C4×C151C2×D411yescharacteristic
246C4⋊C4×C151C2×D411yescharacteristic
247C22⋊C4×C151—22no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—22no—
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—21no—
261C22⋊C4×C151—41no—
262C22⋊C4×C151—41no—
263C42×C151—22no—
264C42×C151—22no—
265C42×C151—21no—
266C42×C151—21no—
267C42×C151C2×D411yescharacteristic
268C42×C151C2×D411yescharacteristic
269C42×C151C2×D411yescharacteristic
270C42×C151C2411yescharacteristic
271C23×C151—21no—
272C23×C151—21no—
273C23×C151—41no—
274C23×C151#12011yescharacteristic
275Q8×C151—21no—
276Q8×C151—21no—
277Q8×C151—21no—
278Q8×C151—21no—
279Q8×C151—42no—
280Q8×C151—41no—
281Q8×C151—41no—
282Q8×C151—41no—
283Q8×C151—41no—
284Q8×C151—82no—
285Q8×C151—82no—
286D4×C151—21no—
287D4×C151—21no—
288D4×C151—21no—
289D4×C151—21no—
290D4×C151—42no—
291D4×C151—42no—
292D4×C151—42no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—82no—
298D4×C151—82no—
299C2×C4×C151—22no—
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—22no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—82no—
318C2×C4×C151—82no—
319C2×C4×C151—82no—
320C2×C4×C151—82no—
321C2×C4×C151#12011yescharacteristic
322C2×C4×C151#12011yescharacteristic
323C2×C4×C151#12011yescharacteristic
324C2×C4×C151C22×D411yescharacteristic
325C2×C4×C151C22×D411yescharacteristic
326C2×C4×C151C22×D411yescharacteristic
327C8×C151—41no—
328C8×C151—41no—
329C8×C151—41no—
330C8×C151—41no—
331C8×C151—41no—
332C8×C151—41no—
333C22×C151—21no—
334C22×C151—21no—
335C22×C151—41no—
336C22×C151—41no—
337C22×C151—41no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—81no—
342C22×C151—81no—
343C22×C151—81no—
344C22×C151#45412yes—
345C22×C151C2×#12011yescharacteristic
346C4×C151—21no—
347C4×C151—21no—
348C4×C151—21no—
349C4×C151—21no—
350C4×C151—41no—
351C4×C151—42no—
352C4×C151—41no—
353C4×C151—42no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151—81no—
359C4×C151#57611yescharacteristic
360C4×C151#57711yescharacteristic
361C4×C151#57711yescharacteristic
362C4×C151#57811yescharacteristic
363C2×C151—22no—
364C2×C151—81no—
365C2×C151—81no—
366C2×C151—161no—
367C2×C151#301211yescharacteristic
368C2×C151#301311yescharacteristic
369C2×C151C2×#45411yescharacteristic
370#18726C15111yesmaximal, characteristic, direct product factor, Sylow
371C151#1872611yescharacteristic, direct product factor, Sylow
372#3552C2×C15111yescharacteristic, complemented
373#3247C2×C15111yescharacteristic, complemented
374#3247C2×C15111yescharacteristic, complemented
375#3141C2×C15111yescharacteristic, complemented
376#1638C2×C15111yescharacteristic, complemented
377#1637C2×C15111yescharacteristic, complemented
378#1636C2×C15111yescharacteristic, complemented
379#1635C2×C15111yescharacteristic, complemented
380#1628C2×C15111yescharacteristic, complemented
381#1627C2×C15111yescharacteristic, complemented
382#1626C2×C15111yescharacteristic, complemented
383#1625C2×C15111yescharacteristic, complemented
384C2×#332C2×C15111yescharacteristic, complemented
385#1483C2×C15111yescharacteristic, complemented
386#1483C2×C15111yescharacteristic, complemented
387#563—22no—
388#557C22×C15111yescharacteristic
389#556C22×C15111yescharacteristic
390#554—21no—
391#553—21no—
392D4×Q8—21no—
393D4×Q8C22×C15111yescharacteristic
394#548—21no—
395#547C22×C15111yescharacteristic
396#544—21no—
397#542—21no—
398#541—21no—
399#539—22no—
400#536—21no—
401#532C22×C15111yescharacteristic
402C2×C4⋊Q8C22×C15111yescharacteristic
403#529C22×C15111yescharacteristic
404#529C22×C15111yescharacteristic
405#489—22no—
406#487C22×C15111yescharacteristic
407#487C22×C15111yescharacteristic
408#486C22×C15111yescharacteristic
409#486C22×C15111yescharacteristic
410#478—21no—
411#478—21no—
412#477C22×C15111yescharacteristic
413#477C22×C15111yescharacteristic
414#476C22×C15111yescharacteristic
415#476C22×C15111yescharacteristic
416#466—21no—
417#466—21no—
418#465—21no—
419#465—21no—
420#463—21no—
421#463—21no—
422#460C22×C15111yescharacteristic
423#460C22×C15111yescharacteristic
424#459C22×C15111yescharacteristic
425#459C22×C15111yescharacteristic
426C2×C4⋊C8C22×C15111yescharacteristic
427C2×C4⋊C8C22×C15111yescharacteristic
428#417—22no—
429C4×M16C22×C15111yescharacteristic
430#332C22×C15111yescharacteristic
431#332C22×C15111yescharacteristic
432#332C22×C15111yescharacteristic
433#332C22×C15111yescharacteristic
434Q8⋊C8C22×C15111yescharacteristic
435Q8⋊C8C22×C15111yescharacteristic
436Q8⋊C8C22×C15111yescharacteristic
437Q8⋊C8C22×C15111yescharacteristic
438D4⋊C8C22×C15111yescharacteristic
439D4⋊C8C22×C15111yescharacteristic
440D4⋊C8C22×C15111yescharacteristic
441D4⋊C8C22×C15111yescharacteristic
442C2×#41—21no—
443C2×#41—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C2×SD16—21no—
447C2×SD16—21no—
448C2×D8—21no—
449C2×D8—21no—
450C2×M16—21no—
451C22×C8—21no—
452C22×C8—21no—
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—22no—
466#126—21no—
467#126—21no—
468#125—22no—
469#125—22no—
470#125—22no—
471#125—21no—
472#125D4×C15111yescharacteristic
473#125D4×C15111yescharacteristic
474#124—22no—
475#124—21no—
476#124—21no—
477#124D4×C15111yescharacteristic
478#124D4×C15111yescharacteristic
479#123—22no—
480#123—22no—
481#123—21no—
482#123—21no—
483#123—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—21no—
490C22⋊Q8—22no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8D4×C15111yescharacteristic
494C22⋊Q8D4×C15111yescharacteristic
495#121—22no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121D4×C15111yescharacteristic
500#121D4×C15111yescharacteristic
501C4×Q8—21no—
502C4×Q8—21no—
503C4×Q8—21no—
504C4×Q8C23×C15111yescharacteristic
505C4×Q8C23×C15111yescharacteristic
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4C23×C15111yescharacteristic
514C4×D4C23×C15111yescharacteristic
515#117—21no—
516#117—21no—
517#117—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C15112yes—
521C2×C42C23×C15111yescharacteristic
522#107—21no—
523#107—21no—
524#106—21no—
525#106—21no—
526C4⋊C8—21no—
527C4⋊C8—21no—
528C4⋊C8C23×C15111yescharacteristic
529C4⋊C8C23×C15111yescharacteristic
530C4⋊C8C23×C15111yescharacteristic
531C4⋊C8C23×C15111yescharacteristic
532#103—21no—
533#103—21no—
534#103—22no—
535#103—22no—
536#102—21no—
537#102—21no—
538#102—22no—
539#102—22no—
540#102—21no—
541#102—21no—
542#102—21no—
543#102—21no—
544#97—21no—
545C4×C8C23×C15111yescharacteristic
546C4×C8C23×C15111yescharacteristic
547#41—44no—
548#41—81no—
549#41—81no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—81no—
556C2×Q8—81no—
557C2×Q8—81no—
558C2×Q8—81no—
559C2×Q8C2×D4×C15111yescharacteristic
560C2×Q8C2×D4×C15111yescharacteristic
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—41no—
568C2×D4C2×D4×C15111yescharacteristic
569C2×D4C2×D4×C15111yescharacteristic
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—41no—
576C22×C4C2×D4×C15111yescharacteristic
577C22×C4C2×D4×C15111yescharacteristic
578C22×C4C2×D4×C15111yescharacteristic
579SD16—81no—
580SD16—81no—
581D8—81no—
582D8—81no—
583M16—42no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—81no—
591C2×C8—81no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
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⋊C4—21no—
612C4⋊C4C2×D4×C15112yes—
613C4⋊C4C2×D4×C15112yes—
614C4⋊C4C2×D4×C15111yescharacteristic
615C4⋊C4C2×D4×C15111yescharacteristic
616C4⋊C4C2×D4×C15111yescharacteristic
617C4⋊C4C2×D4×C15111yescharacteristic
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C42—22no—
635C42—22no—
636C42—21no—
637C42—21no—
638C42C2×D4×C15111yescharacteristic
639C42C2×D4×C15111yescharacteristic
640C42C2×D4×C15111yescharacteristic
641C42C24×C15111yescharacteristic
642C23—21no—
643C23—21no—
644C23—41no—
645C23#120×C15111yescharacteristic
646Q8—21no—
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—42no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—82no—
656Q8—82no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—82no—
669D4—82no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—82no—
689C2×C4—82no—
690C2×C4—82no—
691C2×C4—82no—
692C2×C4#120×C15111yescharacteristic
693C2×C4#120×C15111yescharacteristic
694C2×C4#120×C15111yescharacteristic
695C2×C4C22×D4×C15111yescharacteristic
696C2×C4C22×D4×C15111yescharacteristic
697C2×C4C22×D4×C15111yescharacteristic
698C8—41no—
699C8—41no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C22—21no—
705C22—21no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22#454×C15112yes—
716C22C2×#120×C15111yescharacteristic
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—41no—
722C4—42no—
723C4—41no—
724C4—42no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4#576×C15111yescharacteristic
731C4#577×C15111yescharacteristic
732C4#577×C15111yescharacteristic
733C4#578×C15111yescharacteristic
734C2—22no—
735C2—81no—
736C2—81no—
737C2—161no—
738C2#3012×C15111yescharacteristic
739C2#3013×C15111yescharacteristic
740C2C2×#454×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. #3552×C151C2semidirect
2. #3247×C151C2semidirect
3. #3247×C151C2semidirect
4. #3141×C151C2semidirect
5. #1638×C151C2semidirect
6. #1637×C151C2semidirect
7. #1636×C151C2semidirect
8. #1635×C151C2semidirect
9. #1628×C151C2semidirect
10. #1627×C151C2semidirect
11. #1626×C151C2semidirect
12. #1625×C151C2semidirect
13. C2×#332×C151C2semidirect
14. #1483×C151C2semidirect
15. #1483×C151C2semidirect
370. #18726C151direct (N × H)
371. C151#18726direct (N × H)
372. #3552C2×C151semidirect
373. #3247C2×C151semidirect
374. #3247C2×C151semidirect
375. #3141C2×C151semidirect
376. #1638C2×C151semidirect
377. #1637C2×C151semidirect
378. #1636C2×C151semidirect
379. #1635C2×C151semidirect
380. #1628C2×C151semidirect
381. #1627C2×C151semidirect
382. #1626C2×C151semidirect
383. #1625C2×C151semidirect
384. C2×#332C2×C151semidirect
385. #1483C2×C151semidirect
386. #1483C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3552×C1512
#3247×C1512
#3141×C1512
#1638×C1512
#1637×C1512
#1636×C1512
#1635×C1512
#1628×C1512
#1627×C1512
#1626×C1512
#1625×C1512
C2×#332×C1512
#1483×C1512
#18726151