Finite Group Databasebeta

← C151×#18945 #50323870

Subgroups — C151×#18945 #50323870

Order 38656.

846 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3552×C151C211yesmaximal, characteristic
2#3252×C151C211yesmaximal, characteristic, complemented
3#3233×C151C211yesmaximal, characteristic, complemented
4#3230×C151C211yesmaximal, characteristic, complemented
5#1650×C151C211yesmaximal, characteristic, complemented
6#1649×C151C211yesmaximal, characteristic, complemented
7#1648×C151C211yesmaximal, characteristic, complemented
8#1647×C151C211yesmaximal, characteristic, complemented
9#1638×C151C211yesmaximal, characteristic, complemented
10#1637×C151C211yesmaximal, characteristic, complemented
11#1636×C151C211yesmaximal, characteristic, complemented
12#1635×C151C211yesmaximal, characteristic, complemented
13#1546×C151C211yesmaximal, characteristic, complemented
14#1495×C151C211yesmaximal, characteristic, complemented
15#1482×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#533×C151C2211yescharacteristic
31C2×C4⋊Q8×C151C2211yescharacteristic
32#529×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#500×C151C2211yescharacteristic
35#500×C151C2211yescharacteristic
36#499×C151—21no—
37#488×C151—21no—
38#487×C151C2211yescharacteristic
39#487×C151C2211yescharacteristic
40#485×C151—21no—
41#484×C151—22no—
42#482×C151—21no—
43#479×C151—21no—
44#477×C151—22no—
45#477×C151C2211yescharacteristic
46#477×C151C2211yescharacteristic
47#476×C151C2211yescharacteristic
48#476×C151C2211yescharacteristic
49#475×C151C2211yescharacteristic
50#474×C151C2211yescharacteristic
51#470×C151—21no—
52#468×C151—21no—
53#464×C151—21no—
54#462×C151C2211yescharacteristic
55#461×C151C2211yescharacteristic
56#431×C151C2211yescharacteristic
57#431×C151C2211yescharacteristic
58#423×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—
72C22×Q8×C151—21no—
73C22×Q8×C151—21no—
74C2×Q16×C151—21no—
75C2×SD16×C151—21no—
76C2×M16×C151—21no—
77C4⋊Q8×C151—22no—
78C4⋊Q8×C151—21no—
79C4⋊Q8×C151—21no—
80C4⋊Q8×C151—21no—
81C4⋊Q8×C151—21no—
82C4⋊Q8×C151D412yes—
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86C4⋊Q8×C151C2311yescharacteristic
87#126×C151—22no—
88#126×C151—22no—
89#126×C151—22no—
90#126×C151—21no—
91#126×C151—21no—
92#125×C151—22no—
93#125×C151—22no—
94#125×C151—22no—
95#125×C151—21no—
96#125×C151—21no—
97#125×C151D411yescharacteristic
98#125×C151D411yescharacteristic
99#124×C151—22no—
100#124×C151—21no—
101#124×C151D411yescharacteristic
102#124×C151D411yescharacteristic
103#123×C151—22no—
104#123×C151—22no—
105#123×C151—21no—
106#123×C151—21no—
107#123×C151—22no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—21no—
115C22⋊Q8×C151—21no—
116C22⋊Q8×C151—21no—
117C22⋊Q8×C151—21no—
118C22⋊Q8×C151—21no—
119C22⋊Q8×C151D411yescharacteristic
120C22⋊Q8×C151D411yescharacteristic
121#121×C151—22no—
122#121×C151—21no—
123#121×C151D411yescharacteristic
124#121×C151D411yescharacteristic
125C4×Q8×C151—21no—
126C4×Q8×C151—21no—
127C4×Q8×C151—21no—
128C4×Q8×C151—21no—
129C4×Q8×C151—21no—
130C4×Q8×C151C2311yescharacteristic
131C4×Q8×C151C2311yescharacteristic
132C4×D4×C151—22no—
133C4×D4×C151—22no—
134C4×D4×C151—21no—
135C4×D4×C151—21no—
136C4×D4×C151—21no—
137C4×D4×C151C2311yescharacteristic
138C4×D4×C151C2311yescharacteristic
139#117×C151—21no—
140#117×C151—21no—
141#117×C151—21no—
142#117×C151—21no—
143C2×C4⋊C4×C151—21no—
144C2×C4⋊C4×C151—21no—
145C2×C4⋊C4×C151D412yes—
146C2×C42×C151C2311yescharacteristic
147#107×C151—21no—
148#107×C151—21no—
149#107×C151—22no—
150#107×C151—22no—
151#107×C151—21no—
152#106×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—21no—
162#103×C151—21no—
163#103×C151—22no—
164#103×C151—22no—
165#103×C151—21no—
166#103×C151—21no—
167#103×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—
178C2×Q8×C151—22no—
179C2×Q8×C151—22no—
180C2×Q8×C151—21no—
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×C151C2×D411yescharacteristic
194C2×D4×C151C2×D411yescharacteristic
195C22×C4×C151—22no—
196C22×C4×C151—22no—
197C22×C4×C151—22no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203Q16×C151—81no—
204SD16×C151—81no—
205M16×C151—81no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C4⋊C4×C151—22no—
213C4⋊C4×C151—22no—
214C4⋊C4×C151—22no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—22no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—22no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
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—41no—
235C4⋊C4×C151—41no—
236C4⋊C4×C151C2×D411yescharacteristic
237C4⋊C4×C151C2×D412yes—
238C4⋊C4×C151C2×D412yes—
239C4⋊C4×C151C2×D411yescharacteristic
240C4⋊C4×C151C2×D411yescharacteristic
241C4⋊C4×C151C2×D411yescharacteristic
242C22⋊C4×C151—22no—
243C22⋊C4×C151—22no—
244C22⋊C4×C151—22no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—21no—
247C22⋊C4×C151—21no—
248C22⋊C4×C151—21no—
249C22⋊C4×C151—21no—
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—41no—
257C42×C151—22no—
258C42×C151—22no—
259C42×C151—21no—
260C42×C151—21no—
261C42×C151—41no—
262C42×C151C2×D411yescharacteristic
263C42×C151C2×D411yescharacteristic
264C42×C151C2×D411yescharacteristic
265C42×C151C2411yescharacteristic
266C23×C151—21no—
267C23×C151—21no—
268C23×C151#12011yescharacteristic
269Q8×C151—21no—
270Q8×C151—21no—
271Q8×C151—21no—
272Q8×C151—21no—
273Q8×C151—42no—
274Q8×C151—41no—
275Q8×C151—41no—
276Q8×C151—41no—
277Q8×C151—41no—
278Q8×C151—41no—
279Q8×C151—41no—
280Q8×C151—82no—
281Q8×C151—82no—
282D4×C151—21no—
283D4×C151—21no—
284D4×C151—21no—
285D4×C151—21no—
286D4×C151—42no—
287D4×C151—42no—
288D4×C151—82no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—22no—
294C2×C4×C151—21no—
295C2×C4×C151—22no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—82no—
309C2×C4×C151—82no—
310C2×C4×C151—82no—
311C2×C4×C151#12011yescharacteristic
312C2×C4×C151#12011yescharacteristic
313C2×C4×C151#12011yescharacteristic
314C2×C4×C151C22×D411yescharacteristic
315C2×C4×C151C22×D411yescharacteristic
316C2×C4×C151C22×D411yescharacteristic
317C8×C151—41no—
318C8×C151—41no—
319C8×C151—41no—
320C8×C151—41no—
321C8×C151—41no—
322C8×C151—41no—
323C22×C151—21no—
324C22×C151—21no—
325C22×C151—21no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151—41no—
329C22×C151—41no—
330C22×C151—41no—
331C22×C151—41no—
332C22×C151C2×#12011yescharacteristic
333C4×C151—21no—
334C4×C151—21no—
335C4×C151—21no—
336C4×C151—21no—
337C4×C151—41no—
338C4×C151—41no—
339C4×C151—41no—
340C4×C151—42no—
341C4×C151—41no—
342C4×C151—42no—
343C4×C151—41no—
344C4×C151—41no—
345C4×C151—81no—
346C4×C151—81no—
347C4×C151#57611yescharacteristic
348C4×C151#57711yescharacteristic
349C4×C151#57811yescharacteristic
350C4×C151#57811yescharacteristic
351C2×C151—41no—
352C2×C151—81no—
353C2×C151—81no—
354C2×C151#301111yescharacteristic
355C2×C151#301211yescharacteristic
356C2×C151#302011yescharacteristic
357#18945C15111yesmaximal, characteristic, direct product factor, Sylow
358C151#1894511yescharacteristic, direct product factor, Sylow
359#3552C2×C15111yescharacteristic
360#3252C2×C15111yescharacteristic, complemented
361#3233C2×C15111yescharacteristic, complemented
362#3230C2×C15111yescharacteristic, complemented
363#1650C2×C15111yescharacteristic, complemented
364#1649C2×C15111yescharacteristic, complemented
365#1648C2×C15111yescharacteristic, complemented
366#1647C2×C15111yescharacteristic, complemented
367#1638C2×C15111yescharacteristic, complemented
368#1637C2×C15111yescharacteristic, complemented
369#1636C2×C15111yescharacteristic, complemented
370#1635C2×C15111yescharacteristic, complemented
371#1546C2×C15111yescharacteristic, complemented
372#1495C2×C15111yescharacteristic, complemented
373#1482C2×C15111yescharacteristic, complemented
374#563—22no—
375#557C22×C15111yescharacteristic
376#556C22×C15111yescharacteristic
377#554—21no—
378#553—21no—
379D4×Q8—21no—
380D4×Q8C22×C15111yescharacteristic
381#548—21no—
382#547C22×C15111yescharacteristic
383#544—21no—
384#542—21no—
385#541—21no—
386#539—22no—
387#536—21no—
388#533C22×C15111yescharacteristic
389C2×C4⋊Q8C22×C15111yescharacteristic
390#529C22×C15111yescharacteristic
391#529C22×C15111yescharacteristic
392#500C22×C15111yescharacteristic
393#500C22×C15111yescharacteristic
394#499—21no—
395#488—21no—
396#487C22×C15111yescharacteristic
397#487C22×C15111yescharacteristic
398#485—21no—
399#484—22no—
400#482—21no—
401#479—21no—
402#477—22no—
403#477C22×C15111yescharacteristic
404#477C22×C15111yescharacteristic
405#476C22×C15111yescharacteristic
406#476C22×C15111yescharacteristic
407#475C22×C15111yescharacteristic
408#474C22×C15111yescharacteristic
409#470—21no—
410#468—21no—
411#464—21no—
412#462C22×C15111yescharacteristic
413#461C22×C15111yescharacteristic
414#431C22×C15111yescharacteristic
415#431C22×C15111yescharacteristic
416#423C22×C15111yescharacteristic
417#332C22×C15111yescharacteristic
418#332C22×C15111yescharacteristic
419#332C22×C15111yescharacteristic
420#332C22×C15111yescharacteristic
421Q8⋊C8C22×C15111yescharacteristic
422Q8⋊C8C22×C15111yescharacteristic
423Q8⋊C8C22×C15111yescharacteristic
424Q8⋊C8C22×C15111yescharacteristic
425D4⋊C8C22×C15111yescharacteristic
426D4⋊C8C22×C15111yescharacteristic
427D4⋊C8C22×C15111yescharacteristic
428D4⋊C8C22×C15111yescharacteristic
429C2×#41—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C2×Q16—21no—
433C2×SD16—21no—
434C2×M16—21no—
435C4⋊Q8—22no—
436C4⋊Q8—21no—
437C4⋊Q8—21no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440C4⋊Q8D4×C15112yes—
441C4⋊Q8C23×C15111yescharacteristic
442C4⋊Q8C23×C15111yescharacteristic
443C4⋊Q8C23×C15111yescharacteristic
444C4⋊Q8C23×C15111yescharacteristic
445#126—22no—
446#126—22no—
447#126—22no—
448#126—21no—
449#126—21no—
450#125—22no—
451#125—22no—
452#125—22no—
453#125—21no—
454#125—21no—
455#125D4×C15111yescharacteristic
456#125D4×C15111yescharacteristic
457#124—22no—
458#124—21no—
459#124D4×C15111yescharacteristic
460#124D4×C15111yescharacteristic
461#123—22no—
462#123—22no—
463#123—21no—
464#123—21no—
465#123—22no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8D4×C15111yescharacteristic
478C22⋊Q8D4×C15111yescharacteristic
479#121—22no—
480#121—21no—
481#121D4×C15111yescharacteristic
482#121D4×C15111yescharacteristic
483C4×Q8—21no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8C23×C15111yescharacteristic
489C4×Q8C23×C15111yescharacteristic
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4C23×C15111yescharacteristic
496C4×D4C23×C15111yescharacteristic
497#117—21no—
498#117—21no—
499#117—21no—
500#117—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4D4×C15112yes—
504C2×C42C23×C15111yescharacteristic
505#107—21no—
506#107—21no—
507#107—22no—
508#107—22no—
509#107—21no—
510#106—21no—
511#106—21no—
512#106—21no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8C23×C15111yescharacteristic
516C4⋊C8C23×C15111yescharacteristic
517C4⋊C8C23×C15111yescharacteristic
518C4⋊C8C23×C15111yescharacteristic
519#103—21no—
520#103—21no—
521#103—21no—
522#103—21no—
523#103—21no—
524#103—22no—
525#103—22no—
526#102—21no—
527#102—21no—
528#102—21no—
529C22⋊C8—21no—
530C22⋊C8—21no—
531C4×C8—21no—
532C4×C8C23×C15111yescharacteristic
533C4×C8C23×C15111yescharacteristic
534#41—81no—
535#41—81no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—81no—
543C2×Q8—81no—
544C2×Q8—81no—
545C2×Q8—81no—
546C2×Q8C2×D4×C15111yescharacteristic
547C2×Q8C2×D4×C15111yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4C2×D4×C15111yescharacteristic
552C2×D4C2×D4×C15111yescharacteristic
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4C2×D4×C15111yescharacteristic
559C22×C4C2×D4×C15111yescharacteristic
560C22×C4C2×D4×C15111yescharacteristic
561Q16—81no—
562SD16—81no—
563M16—81no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4C2×D4×C15111yescharacteristic
595C4⋊C4C2×D4×C15112yes—
596C4⋊C4C2×D4×C15112yes—
597C4⋊C4C2×D4×C15111yescharacteristic
598C4⋊C4C2×D4×C15111yescharacteristic
599C4⋊C4C2×D4×C15111yescharacteristic
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—41no—
615C42—22no—
616C42—22no—
617C42—21no—
618C42—21no—
619C42—41no—
620C42C2×D4×C15111yescharacteristic
621C42C2×D4×C15111yescharacteristic
622C42C2×D4×C15111yescharacteristic
623C42C24×C15111yescharacteristic
624C23—21no—
625C23—21no—
626C23#120×C15111yescharacteristic
627Q8—21no—
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—42no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—82no—
639Q8—82no—
640D4—21no—
641D4—21no—
642D4—21no—
643D4—21no—
644D4—42no—
645D4—42no—
646D4—82no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—82no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4#120×C15111yescharacteristic
670C2×C4#120×C15111yescharacteristic
671C2×C4#120×C15111yescharacteristic
672C2×C4C22×D4×C15111yescharacteristic
673C2×C4C22×D4×C15111yescharacteristic
674C2×C4C22×D4×C15111yescharacteristic
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C8—41no—
680C8—41no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C2×#120×C15111yescharacteristic
691C4—21no—
692C4—21no—
693C4—21no—
694C4—21no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—42no—
699C4—41no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4#576×C15111yescharacteristic
706C4#577×C15111yescharacteristic
707C4#578×C15111yescharacteristic
708C4#578×C15111yescharacteristic
709C2—41no—
710C2—81no—
711C2—81no—
712C2#3011×C15111yescharacteristic
713C2#3012×C15111yescharacteristic
714C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3552×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. #3252×C151C2semidirect
3. #3233×C151C2semidirect
4. #3230×C151C2semidirect
5. #1650×C151C2semidirect
6. #1649×C151C2semidirect
7. #1648×C151C2semidirect
8. #1647×C151C2semidirect
9. #1638×C151C2semidirect
10. #1637×C151C2semidirect
11. #1636×C151C2semidirect
12. #1635×C151C2semidirect
13. #1546×C151C2semidirect
14. #1495×C151C2semidirect
15. #1482×C151C2semidirect
357. #18945C151direct (N × H)
358. C151#18945direct (N × H)
360. #3252C2×C151semidirect
361. #3233C2×C151semidirect
362. #3230C2×C151semidirect
363. #1650C2×C151semidirect
364. #1649C2×C151semidirect
365. #1648C2×C151semidirect
366. #1647C2×C151semidirect
367. #1638C2×C151semidirect
368. #1637C2×C151semidirect
369. #1636C2×C151semidirect
370. #1635C2×C151semidirect
371. #1546C2×C151semidirect
372. #1495C2×C151semidirect
373. #1482C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3552×C1512
#3252×C1512
#3233×C1512
#3230×C1512
#1650×C1512
#1649×C1512
#1648×C1512
#1647×C1512
#1638×C1512
#1637×C1512
#1636×C1512
#1635×C1512
#1546×C1512
#1495×C1512
#1482×C1512
#18945151