Finite Group Databasebeta

← C151×#18976 #50323901

Subgroups — C151×#18976 #50323901

Order 38656.

866 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3554×C151C211yesmaximal, characteristic
2#3255×C151C211yesmaximal, characteristic, complemented
3#3248×C151C211yesmaximal, characteristic, complemented
4#3228×C151C211yesmaximal, characteristic, complemented
5#1653×C151C211yesmaximal, characteristic, complemented
6#1651×C151C211yesmaximal, characteristic, complemented
7#1649×C151C211yesmaximal, characteristic, complemented
8#1648×C151C211yesmaximal, characteristic, complemented
9#1642×C151C211yesmaximal, characteristic, complemented
10#1641×C151C211yesmaximal, characteristic, complemented
11#1640×C151C211yesmaximal, characteristic, complemented
12#1640×C151C211yesmaximal, characteristic, complemented
13#1547×C151C211yesmaximal, characteristic, complemented
14#1495×C151C211yesmaximal, characteristic, complemented
15#1481×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#533×C151C2211yescharacteristic
32#532×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#500×C151C2211yescharacteristic
35#498×C151C2211yescharacteristic
36#486×C151C2211yescharacteristic
37#486×C151C2211yescharacteristic
38#482×C151—22no—
39#479×C151—21no—
40#478×C151—22no—
41#475×C151—21no—
42#475×C151C2211yescharacteristic
43#475×C151C2211yescharacteristic
44#475×C151C2211yescharacteristic
45#474×C151C2211yescharacteristic
46#470×C151—21no—
47#470×C151—21no—
48#467×C151—21no—
49#465×C151—21no—
50#464×C151—21no—
51#462×C151—21no—
52#462×C151C2211yescharacteristic
53#462×C151C2211yescharacteristic
54#462×C151C2211yescharacteristic
55#461×C151C2211yescharacteristic
56#431×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—
73C22×Q8×C151—21no—
74C2×Q16×C151—21no—
75C2×Q16×C151—21no—
76C2×Q16×C151—21no—
77C2×SD16×C151—21no—
78C2×M16×C151—21no—
79C22×C8×C151—21no—
80C4⋊Q8×C151—21no—
81C4⋊Q8×C151—21no—
82C4⋊Q8×C151D411yescharacteristic
83C4⋊Q8×C151D411yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86C4⋊Q8×C151C2311yescharacteristic
87#127×C151—21no—
88#127×C151C2311yescharacteristic
89#126×C151—22no—
90#126×C151—21no—
91#125×C151—22no—
92#125×C151—21no—
93#125×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×C151D411yescharacteristic
102#123×C151—22no—
103#123×C151—22no—
104#123×C151—22no—
105#123×C151—22no—
106#123×C151—22no—
107#123×C151—22no—
108#123×C151—21no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—21no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—21no—
116C22⋊Q8×C151—21no—
117C22⋊Q8×C151—21no—
118C22⋊Q8×C151D411yescharacteristic
119C22⋊Q8×C151D411yescharacteristic
120C22⋊Q8×C151D411yescharacteristic
121#121×C151—22no—
122#121×C151—22no—
123#121×C151—22no—
124#121×C151—21no—
125#121×C151—21no—
126#121×C151D411yescharacteristic
127#121×C151D412yes—
128C4×Q8×C151—21no—
129C4×Q8×C151—21no—
130C4×Q8×C151—21no—
131C4×Q8×C151—21no—
132C4×Q8×C151—21no—
133C4×Q8×C151C2311yescharacteristic
134C4×Q8×C151C2311yescharacteristic
135C4×Q8×C151C2311yescharacteristic
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×C151—21no—
143C4×D4×C151D412yes—
144C4×D4×C151C2311yescharacteristic
145#117×C151—21no—
146#117×C151—21no—
147#117×C151—21no—
148C2×C4⋊C4×C151—22no—
149C2×C42×C151C2311yescharacteristic
150#107×C151—21no—
151#107×C151—22no—
152#106×C151—21no—
153#106×C151—21no—
154#106×C151—21no—
155#106×C151—22no—
156C4⋊C8×C151—21no—
157C4⋊C8×C151—21no—
158C4⋊C8×C151—21no—
159C4⋊C8×C151C2311yescharacteristic
160C4⋊C8×C151C2311yescharacteristic
161C4⋊C8×C151C2311yescharacteristic
162C4⋊C8×C151C2311yescharacteristic
163#103×C151—21no—
164#103×C151—21no—
165#103×C151—21no—
166#103×C151—21no—
167#103×C151—21no—
168#103×C151—21no—
169#103×C151—21no—
170#102×C151—21no—
171#102×C151—22no—
172#102×C151—22no—
173C22⋊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—
180C2×Q8×C151—22no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—81no—
186C2×Q8×C151—81no—
187C2×Q8×C151C2×D411yescharacteristic
188C2×Q8×C151C2×D411yescharacteristic
189C2×Q8×C151C2×D411yescharacteristic
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—21no—
193C2×D4×C151—22no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151C2×D411yescharacteristic
197C2×D4×C151C2×D412yes—
198C22×C4×C151—22no—
199C22×C4×C151—22no—
200C22×C4×C151—22no—
201C22×C4×C151—21no—
202C22×C4×C151—22no—
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D411yescharacteristic
205C22×C4×C151C2×D411yescharacteristic
206Q16×C151—81no—
207Q16×C151—81no—
208Q16×C151—81no—
209SD16×C151—81no—
210M16×C151—81no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—81no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—22no—
220C4⋊C4×C151—22no—
221C4⋊C4×C151—22no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
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—41no—
239C4⋊C4×C151—41no—
240C4⋊C4×C151C2×D411yescharacteristic
241C4⋊C4×C151C2×D411yescharacteristic
242C4⋊C4×C151C2×D411yescharacteristic
243C4⋊C4×C151C2×D411yescharacteristic
244C4⋊C4×C151C2×D412yes—
245C22⋊C4×C151—22no—
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—22no—
257C22⋊C4×C151—22no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—41no—
260C42×C151—22no—
261C42×C151—21no—
262C42×C151—21no—
263C42×C151—21no—
264C42×C151—41no—
265C42×C151C2×D411yescharacteristic
266C42×C151C2×D411yescharacteristic
267C42×C151C2×D411yescharacteristic
268C42×C151C2411yescharacteristic
269C23×C151—21no—
270C23×C151—22no—
271C23×C151#12011yescharacteristic
272Q8×C151—21no—
273Q8×C151—21no—
274Q8×C151—21no—
275Q8×C151—21no—
276Q8×C151—21no—
277Q8×C151—21no—
278Q8×C151—41no—
279Q8×C151—41no—
280Q8×C151—41no—
281Q8×C151—41no—
282Q8×C151—41no—
283Q8×C151—41no—
284Q8×C151—81no—
285Q8×C151—82no—
286D4×C151—21no—
287D4×C151—21no—
288D4×C151—42no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—82no—
294D4×C151—81no—
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—21no—
302C2×C4×C151—22no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—82no—
315C2×C4×C151—82no—
316C2×C4×C151—82no—
317C2×C4×C151—82no—
318C2×C4×C151#12011yescharacteristic
319C2×C4×C151#12011yescharacteristic
320C2×C4×C151#12011yescharacteristic
321C2×C4×C151C22×D411yescharacteristic
322C2×C4×C151C22×D411yescharacteristic
323C2×C4×C151C22×D411yescharacteristic
324C8×C151—41no—
325C8×C151—41no—
326C8×C151—41no—
327C8×C151—41no—
328C8×C151—41no—
329C8×C151—41no—
330C22×C151—21no—
331C22×C151—21no—
332C22×C151—21no—
333C22×C151—41no—
334C22×C151—42no—
335C22×C151—41no—
336C22×C151—42no—
337C22×C151—42no—
338C22×C151—41no—
339C22×C151C2×#12011yescharacteristic
340C4×C151—21no—
341C4×C151—21no—
342C4×C151—21no—
343C4×C151—21no—
344C4×C151—41no—
345C4×C151—41no—
346C4×C151—42no—
347C4×C151—41no—
348C4×C151—41no—
349C4×C151—41no—
350C4×C151—41no—
351C4×C151—41no—
352C4×C151—81no—
353C4×C151—81no—
354C4×C151#57611yescharacteristic
355C4×C151#57711yescharacteristic
356C4×C151#57711yescharacteristic
357C4×C151#57811yescharacteristic
358C2×C151—41no—
359C2×C151—81no—
360C2×C151—82no—
361C2×C151#301211yescharacteristic
362C2×C151#301311yescharacteristic
363C2×C151#302211yescharacteristic
364#18976C15111yesmaximal, characteristic, direct product factor, Sylow
365C151#1897611yescharacteristic, direct product factor, Sylow
366#3554C2×C15111yescharacteristic
367#3255C2×C15111yescharacteristic, complemented
368#3248C2×C15111yescharacteristic, complemented
369#3228C2×C15111yescharacteristic, complemented
370#1653C2×C15111yescharacteristic, complemented
371#1651C2×C15111yescharacteristic, complemented
372#1649C2×C15111yescharacteristic, complemented
373#1648C2×C15111yescharacteristic, complemented
374#1642C2×C15111yescharacteristic, complemented
375#1641C2×C15111yescharacteristic, complemented
376#1640C2×C15111yescharacteristic, complemented
377#1640C2×C15111yescharacteristic, complemented
378#1547C2×C15111yescharacteristic, complemented
379#1495C2×C15111yescharacteristic, complemented
380#1481C2×C15111yescharacteristic, complemented
381#562—22no—
382#559—21no—
383#559C22×C15111yescharacteristic
384#557C22×C15111yescharacteristic
385#554—21no—
386#550C22×C15111yescharacteristic
387D4×Q8C22×C15111yescharacteristic
388#548—21no—
389#547—21no—
390#542—21no—
391#542—21no—
392#540—21no—
393#539—22no—
394#536—21no—
395#533C22×C15111yescharacteristic
396#533C22×C15111yescharacteristic
397#532C22×C15111yescharacteristic
398#529C22×C15111yescharacteristic
399#500C22×C15111yescharacteristic
400#498C22×C15111yescharacteristic
401#486C22×C15111yescharacteristic
402#486C22×C15111yescharacteristic
403#482—22no—
404#479—21no—
405#478—22no—
406#475—21no—
407#475C22×C15111yescharacteristic
408#475C22×C15111yescharacteristic
409#475C22×C15111yescharacteristic
410#474C22×C15111yescharacteristic
411#470—21no—
412#470—21no—
413#467—21no—
414#465—21no—
415#464—21no—
416#462—21no—
417#462C22×C15111yescharacteristic
418#462C22×C15111yescharacteristic
419#462C22×C15111yescharacteristic
420#461C22×C15111yescharacteristic
421#431C22×C15111yescharacteristic
422#423C22×C15111yescharacteristic
423C2×C4⋊C8C22×C15111yescharacteristic
424#332C22×C15111yescharacteristic
425#332C22×C15111yescharacteristic
426#331C22×C15111yescharacteristic
427#331C22×C15111yescharacteristic
428Q8⋊C8C22×C15111yescharacteristic
429Q8⋊C8C22×C15111yescharacteristic
430Q8⋊C8C22×C15111yescharacteristic
431Q8⋊C8C22×C15111yescharacteristic
432Q8⋊C8C22×C15111yescharacteristic
433Q8⋊C8C22×C15111yescharacteristic
434D4⋊C8C22×C15111yescharacteristic
435D4⋊C8C22×C15111yescharacteristic
436C2×#41—21no—
437C2×#41—21no—
438C22×Q8—21no—
439C2×Q16—21no—
440C2×Q16—21no—
441C2×Q16—21no—
442C2×SD16—21no—
443C2×M16—21no—
444C22×C8—21no—
445C4⋊Q8—21no—
446C4⋊Q8—21no—
447C4⋊Q8D4×C15111yescharacteristic
448C4⋊Q8D4×C15111yescharacteristic
449C4⋊Q8C23×C15111yescharacteristic
450C4⋊Q8C23×C15111yescharacteristic
451C4⋊Q8C23×C15111yescharacteristic
452#127—21no—
453#127C23×C15111yescharacteristic
454#126—22no—
455#126—21no—
456#125—22no—
457#125—21no—
458#125—21no—
459#125—21no—
460#125D4×C15111yescharacteristic
461#124—22no—
462#124—22no—
463#124—21no—
464#124—21no—
465#124—21no—
466#124D4×C15111yescharacteristic
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—21no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—21no—
479C22⋊Q8—22no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8D4×C15111yescharacteristic
484C22⋊Q8D4×C15111yescharacteristic
485C22⋊Q8D4×C15111yescharacteristic
486#121—22no—
487#121—22no—
488#121—22no—
489#121—21no—
490#121—21no—
491#121D4×C15111yescharacteristic
492#121D4×C15112yes—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8C23×C15111yescharacteristic
499C4×Q8C23×C15111yescharacteristic
500C4×Q8C23×C15111yescharacteristic
501C4×D4—22no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4D4×C15112yes—
509C4×D4C23×C15111yescharacteristic
510#117—21no—
511#117—21no—
512#117—21no—
513C2×C4⋊C4—22no—
514C2×C42C23×C15111yescharacteristic
515#107—21no—
516#107—22no—
517#106—21no—
518#106—21no—
519#106—21no—
520#106—22no—
521C4⋊C8—21no—
522C4⋊C8—21no—
523C4⋊C8—21no—
524C4⋊C8C23×C15111yescharacteristic
525C4⋊C8C23×C15111yescharacteristic
526C4⋊C8C23×C15111yescharacteristic
527C4⋊C8C23×C15111yescharacteristic
528#103—21no—
529#103—21no—
530#103—21no—
531#103—21no—
532#103—21no—
533#103—21no—
534#103—21no—
535#102—21no—
536#102—22no—
537#102—22no—
538C22⋊C8—21no—
539C4×C8C23×C15111yescharacteristic
540C4×C8C23×C15111yescharacteristic
541#41—81no—
542#41—81no—
543#41—81no—
544#41—81no—
545C2×Q8—22no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—81no—
551C2×Q8—81no—
552C2×Q8C2×D4×C15111yescharacteristic
553C2×Q8C2×D4×C15111yescharacteristic
554C2×Q8C2×D4×C15111yescharacteristic
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4C2×D4×C15111yescharacteristic
562C2×D4C2×D4×C15112yes—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4C2×D4×C15111yescharacteristic
569C22×C4C2×D4×C15111yescharacteristic
570C22×C4C2×D4×C15111yescharacteristic
571Q16—81no—
572Q16—81no—
573Q16—81no—
574SD16—81no—
575M16—81no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—81no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4C2×D4×C15111yescharacteristic
606C4⋊C4C2×D4×C15111yescharacteristic
607C4⋊C4C2×D4×C15111yescharacteristic
608C4⋊C4C2×D4×C15111yescharacteristic
609C4⋊C4C2×D4×C15112yes—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—21no—
624C22⋊C4—41no—
625C42—22no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—41no—
630C42C2×D4×C15111yescharacteristic
631C42C2×D4×C15111yescharacteristic
632C42C2×D4×C15111yescharacteristic
633C42C24×C15111yescharacteristic
634C23—21no—
635C23—22no—
636C23#120×C15111yescharacteristic
637Q8—21no—
638Q8—21no—
639Q8—21no—
640Q8—21no—
641Q8—21no—
642Q8—21no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—81no—
650Q8—82no—
651D4—21no—
652D4—21no—
653D4—42no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—82no—
659D4—81no—
660D4—82no—
661D4—82no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—82no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4#120×C15111yescharacteristic
684C2×C4#120×C15111yescharacteristic
685C2×C4#120×C15111yescharacteristic
686C2×C4C22×D4×C15111yescharacteristic
687C2×C4C22×D4×C15111yescharacteristic
688C2×C4C22×D4×C15111yescharacteristic
689C8—41no—
690C8—41no—
691C8—41no—
692C8—41no—
693C8—41no—
694C8—41no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—41no—
699C22—42no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22C2×#120×C15111yescharacteristic
705C4—21no—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—41no—
710C4—41no—
711C4—42no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—41no—
716C4—41no—
717C4—81no—
718C4—81no—
719C4#576×C15111yescharacteristic
720C4#577×C15111yescharacteristic
721C4#577×C15111yescharacteristic
722C4#578×C15111yescharacteristic
723C2—41no—
724C2—81no—
725C2—82no—
726C2#3012×C15111yescharacteristic
727C2#3013×C15111yescharacteristic
728C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3554×C151C2
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
2. #3255×C151C2semidirect
3. #3248×C151C2semidirect
4. #3228×C151C2semidirect
5. #1653×C151C2semidirect
6. #1651×C151C2semidirect
7. #1649×C151C2semidirect
8. #1648×C151C2semidirect
9. #1642×C151C2semidirect
10. #1641×C151C2semidirect
11. #1640×C151C2semidirect
12. #1640×C151C2semidirect
13. #1547×C151C2semidirect
14. #1495×C151C2semidirect
15. #1481×C151C2semidirect
364. #18976C151direct (N × H)
365. C151#18976direct (N × H)
367. #3255C2×C151semidirect
368. #3248C2×C151semidirect
369. #3228C2×C151semidirect
370. #1653C2×C151semidirect
371. #1651C2×C151semidirect
372. #1649C2×C151semidirect
373. #1648C2×C151semidirect
374. #1642C2×C151semidirect
375. #1641C2×C151semidirect
376. #1640C2×C151semidirect
377. #1640C2×C151semidirect
378. #1547C2×C151semidirect
379. #1495C2×C151semidirect
380. #1481C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3554×C1512
#3255×C1512
#3248×C1512
#3228×C1512
#1653×C1512
#1651×C1512
#1649×C1512
#1648×C1512
#1642×C1512
#1641×C1512
#1640×C1512
#1547×C1512
#1495×C1512
#1481×C1512
#18976151