Finite Group Databasebeta

← C151×#18743 #50323668

Subgroups — C151×#18743 #50323668

Order 38656.

874 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3554×C151C211yesmaximal, characteristic
2#3249×C151C211yesmaximal, characteristic, complemented
3#3233×C151C211yesmaximal, characteristic, complemented
4#3182×C151C211yesmaximal, characteristic, complemented
5#1649×C151C211yesmaximal, characteristic, complemented
6#1648×C151C211yesmaximal, characteristic, complemented
7#1641×C151C211yesmaximal, characteristic, complemented
8#1640×C151C211yesmaximal, characteristic, complemented
9#1637×C151C211yesmaximal, characteristic, complemented
10#1636×C151C211yesmaximal, characteristic, complemented
11#1631×C151C211yesmaximal, characteristic, complemented
12#1630×C151C211yesmaximal, characteristic, complemented
13#1540×C151C211yesmaximal, characteristic, complemented
14#1485×C151C211yesmaximal, characteristic, complemented
15#1483×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#499×C151—21no—
36#492×C151C2211yescharacteristic
37#488×C151—21no—
38#487×C151C2211yescharacteristic
39#486×C151C2211yescharacteristic
40#485×C151—21no—
41#482×C151—21no—
42#477×C151—21no—
43#477×C151C2211yescharacteristic
44#477×C151C2211yescharacteristic
45#477×C151C2211yescharacteristic
46#476×C151C2211yescharacteristic
47#475×C151C2211yescharacteristic
48#474×C151C2211yescharacteristic
49#468×C151—22no—
50#467×C151—21no—
51#467×C151—21no—
52#462×C151—21no—
53#462×C151C2211yescharacteristic
54#462×C151C2211yescharacteristic
55#440×C151—22no—
56#431×C151C2211yescharacteristic
57C2×C4⋊C8×C151C2211yescharacteristic
58C4×M16×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×SD16×C151—22no—
77C2×M16×C151—21no—
78C22×C8×C151—21no—
79C4⋊Q8×C151—21no—
80C4⋊Q8×C151—21no—
81C4⋊Q8×C151D411yescharacteristic
82C4⋊Q8×C151D411yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86#127×C151—21no—
87#127×C151C2311yescharacteristic
88#126×C151—22no—
89#126×C151—21no—
90#125×C151—22no—
91#125×C151—21no—
92#125×C151—21no—
93#125×C151—21no—
94#125×C151D411yescharacteristic
95#124×C151—22no—
96#124×C151—22no—
97#124×C151—21no—
98#124×C151—21no—
99#124×C151—21no—
100#124×C151D411yescharacteristic
101#123×C151—22no—
102#123×C151—22no—
103#123×C151—22no—
104#123×C151—22no—
105#123×C151—22no—
106#123×C151—22no—
107#123×C151—21no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—21no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—21no—
115C22⋊Q8×C151—21no—
116C22⋊Q8×C151—21no—
117C22⋊Q8×C151D411yescharacteristic
118C22⋊Q8×C151D411yescharacteristic
119C22⋊Q8×C151D411yescharacteristic
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—22no—
123#121×C151—21no—
124#121×C151—21no—
125#121×C151D412yes—
126#121×C151D411yescharacteristic
127C4×Q8×C151—21no—
128C4×Q8×C151—21no—
129C4×Q8×C151—21no—
130C4×Q8×C151—21no—
131C4×Q8×C151—21no—
132C4×Q8×C151C2311yescharacteristic
133C4×Q8×C151C2311yescharacteristic
134C4×Q8×C151C2311yescharacteristic
135C4×D4×C151—22no—
136C4×D4×C151—21no—
137C4×D4×C151—21no—
138C4×D4×C151—21no—
139C4×D4×C151—21no—
140C4×D4×C151—21no—
141C4×D4×C151—21no—
142C4×D4×C151D412yes—
143C4×D4×C151C2311yescharacteristic
144#117×C151—21no—
145#117×C151—21no—
146#117×C151—21no—
147C2×C4⋊C4×C151—22no—
148C2×C42×C151C2311yescharacteristic
149#107×C151—22no—
150#107×C151—21no—
151#107×C151—21no—
152#107×C151—21no—
153#107×C151—21no—
154#106×C151—21no—
155#106×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—21no—
163#103×C151—21no—
164#103×C151—21no—
165#103×C151—21no—
166#103×C151—21no—
167#103×C151—21no—
168#102×C151—22no—
169#102×C151—21no—
170#102×C151—21no—
171C22⋊C8×C151—21no—
172#97×C151—21no—
173C4×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—
208SD16×C151—44no—
209M16×C151—42no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—81no—
217C4⋊C4×C151—22no—
218C4⋊C4×C151—22no—
219C4⋊C4×C151—22no—
220C4⋊C4×C151—22no—
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—21no—
235C4⋊C4×C151—21no—
236C4⋊C4×C151—21no—
237C4⋊C4×C151—41no—
238C4⋊C4×C151—41no—
239C4⋊C4×C151C2×D411yescharacteristic
240C4⋊C4×C151C2×D412yes—
241C4⋊C4×C151C2×D411yescharacteristic
242C4⋊C4×C151C2×D411yescharacteristic
243C4⋊C4×C151C2×D411yescharacteristic
244C22⋊C4×C151—22no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151—22no—
248C22⋊C4×C151—22no—
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—22no—
256C22⋊C4×C151—22no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—41no—
259C42×C151—22no—
260C42×C151—21no—
261C42×C151—21no—
262C42×C151—21no—
263C42×C151—41no—
264C42×C151C2×D411yescharacteristic
265C42×C151C2×D411yescharacteristic
266C42×C151C2×D411yescharacteristic
267C42×C151C2411yescharacteristic
268C23×C151—21no—
269C23×C151—22no—
270C23×C151#12011yescharacteristic
271Q8×C151—21no—
272Q8×C151—21no—
273Q8×C151—21no—
274Q8×C151—21no—
275Q8×C151—21no—
276Q8×C151—21no—
277Q8×C151—42no—
278Q8×C151—41no—
279Q8×C151—41no—
280Q8×C151—41no—
281Q8×C151—41no—
282Q8×C151—81no—
283Q8×C151—82no—
284D4×C151—21no—
285D4×C151—21no—
286D4×C151—42no—
287D4×C151—41no—
288D4×C151—41no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—82no—
292D4×C151—81no—
293D4×C151—82no—
294D4×C151—82no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—22no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—82no—
313C2×C4×C151—82no—
314C2×C4×C151—82no—
315C2×C4×C151—82no—
316C2×C4×C151#12011yescharacteristic
317C2×C4×C151#12011yescharacteristic
318C2×C4×C151#12011yescharacteristic
319C2×C4×C151C22×D411yescharacteristic
320C2×C4×C151C22×D411yescharacteristic
321C2×C4×C151C22×D411yescharacteristic
322C8×C151—22no—
323C8×C151—41no—
324C8×C151—41no—
325C8×C151—41no—
326C8×C151—41no—
327C8×C151—41no—
328C22×C151—21no—
329C22×C151—21no—
330C22×C151—21no—
331C22×C151—41no—
332C22×C151—42no—
333C22×C151—41no—
334C22×C151—42no—
335C22×C151—42no—
336C22×C151—41no—
337C22×C151C2×#12011yescharacteristic
338C4×C151—21no—
339C4×C151—21no—
340C4×C151—21no—
341C4×C151—21no—
342C4×C151—41no—
343C4×C151—41no—
344C4×C151—41no—
345C4×C151—42no—
346C4×C151—41no—
347C4×C151—41no—
348C4×C151—41no—
349C4×C151—41no—
350C4×C151—81no—
351C4×C151—81no—
352C4×C151#57611yescharacteristic
353C4×C151#57711yescharacteristic
354C4×C151#57811yescharacteristic
355C4×C151#57811yescharacteristic
356C2×C151—41no—
357C2×C151—81no—
358C2×C151—82no—
359C2×C151#301111yescharacteristic
360C2×C151#301211yescharacteristic
361C2×C151#301811yescharacteristic
362#18743C15111yesmaximal, characteristic, direct product factor, Sylow
363C151#1874311yescharacteristic, direct product factor, Sylow
364#3554C2×C15111yescharacteristic
365#3249C2×C15111yescharacteristic, complemented
366#3233C2×C15111yescharacteristic, complemented
367#3182C2×C15111yescharacteristic, complemented
368#1649C2×C15111yescharacteristic, complemented
369#1648C2×C15111yescharacteristic, complemented
370#1641C2×C15111yescharacteristic, complemented
371#1640C2×C15111yescharacteristic, complemented
372#1637C2×C15111yescharacteristic, complemented
373#1636C2×C15111yescharacteristic, complemented
374#1631C2×C15111yescharacteristic, complemented
375#1630C2×C15111yescharacteristic, complemented
376#1540C2×C15111yescharacteristic, complemented
377#1485C2×C15111yescharacteristic, complemented
378#1483C2×C15111yescharacteristic, complemented
379#562—22no—
380#559—21no—
381#559C22×C15111yescharacteristic
382#557C22×C15111yescharacteristic
383#554—21no—
384#550C22×C15111yescharacteristic
385D4×Q8C22×C15111yescharacteristic
386#548—21no—
387#547—21no—
388#542—21no—
389#542—21no—
390#540—21no—
391#539—22no—
392#536—21no—
393#533C22×C15111yescharacteristic
394#533C22×C15111yescharacteristic
395#532C22×C15111yescharacteristic
396#529C22×C15111yescharacteristic
397#500C22×C15111yescharacteristic
398#499—21no—
399#492C22×C15111yescharacteristic
400#488—21no—
401#487C22×C15111yescharacteristic
402#486C22×C15111yescharacteristic
403#485—21no—
404#482—21no—
405#477—21no—
406#477C22×C15111yescharacteristic
407#477C22×C15111yescharacteristic
408#477C22×C15111yescharacteristic
409#476C22×C15111yescharacteristic
410#475C22×C15111yescharacteristic
411#474C22×C15111yescharacteristic
412#468—22no—
413#467—21no—
414#467—21no—
415#462—21no—
416#462C22×C15111yescharacteristic
417#462C22×C15111yescharacteristic
418#440—22no—
419#431C22×C15111yescharacteristic
420C2×C4⋊C8C22×C15111yescharacteristic
421C4×M16C22×C15111yescharacteristic
422#332C22×C15111yescharacteristic
423#332C22×C15111yescharacteristic
424#331C22×C15111yescharacteristic
425#331C22×C15111yescharacteristic
426Q8⋊C8C22×C15111yescharacteristic
427Q8⋊C8C22×C15111yescharacteristic
428Q8⋊C8C22×C15111yescharacteristic
429Q8⋊C8C22×C15111yescharacteristic
430Q8⋊C8C22×C15111yescharacteristic
431Q8⋊C8C22×C15111yescharacteristic
432D4⋊C8C22×C15111yescharacteristic
433D4⋊C8C22×C15111yescharacteristic
434C2×#41—21no—
435C2×#41—21no—
436C22×Q8—21no—
437C2×Q16—21no—
438C2×Q16—21no—
439C2×SD16—22no—
440C2×M16—21no—
441C22×C8—21no—
442C4⋊Q8—21no—
443C4⋊Q8—21no—
444C4⋊Q8D4×C15111yescharacteristic
445C4⋊Q8D4×C15111yescharacteristic
446C4⋊Q8C23×C15111yescharacteristic
447C4⋊Q8C23×C15111yescharacteristic
448C4⋊Q8C23×C15111yescharacteristic
449#127—21no—
450#127C23×C15111yescharacteristic
451#126—22no—
452#126—21no—
453#125—22no—
454#125—21no—
455#125—21no—
456#125—21no—
457#125D4×C15111yescharacteristic
458#124—22no—
459#124—22no—
460#124—21no—
461#124—21no—
462#124—21no—
463#124D4×C15111yescharacteristic
464#123—22no—
465#123—22no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—21no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—21no—
476C22⋊Q8—22no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8D4×C15111yescharacteristic
481C22⋊Q8D4×C15111yescharacteristic
482C22⋊Q8D4×C15111yescharacteristic
483#121—22no—
484#121—22no—
485#121—22no—
486#121—21no—
487#121—21no—
488#121D4×C15111yescharacteristic
489#121D4×C15112yes—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8C23×C15111yescharacteristic
496C4×Q8C23×C15111yescharacteristic
497C4×Q8C23×C15111yescharacteristic
498C4×D4—22no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4D4×C15112yes—
506C4×D4C23×C15111yescharacteristic
507#117—21no—
508#117—21no—
509#117—21no—
510C2×C4⋊C4—22no—
511C2×C42C23×C15111yescharacteristic
512#107—22no—
513#107—21no—
514#107—21no—
515#107—21no—
516#107—21no—
517#106—21no—
518#106—21no—
519C4⋊C8—21no—
520C4⋊C8C23×C15111yescharacteristic
521C4⋊C8C23×C15111yescharacteristic
522C4⋊C8C23×C15111yescharacteristic
523C4⋊C8C23×C15111yescharacteristic
524#103—21no—
525#103—21no—
526#103—21no—
527#103—21no—
528#103—22no—
529#103—21no—
530#103—21no—
531#102—22no—
532#102—21no—
533#102—21no—
534C22⋊C8—21no—
535#97—21no—
536C4×C8—21no—
537C4×C8C23×C15111yescharacteristic
538C4×C8C23×C15111yescharacteristic
539#41—81no—
540#41—81no—
541#41—81no—
542#41—81no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—81no—
549C2×Q8—81no—
550C2×Q8C2×D4×C15111yescharacteristic
551C2×Q8C2×D4×C15111yescharacteristic
552C2×Q8C2×D4×C15111yescharacteristic
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4C2×D4×C15111yescharacteristic
560C2×D4C2×D4×C15112yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4C2×D4×C15111yescharacteristic
567C22×C4C2×D4×C15111yescharacteristic
568C22×C4C2×D4×C15111yescharacteristic
569Q16—81no—
570Q16—81no—
571SD16—44no—
572M16—42no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—81no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
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—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4C2×D4×C15111yescharacteristic
603C4⋊C4C2×D4×C15112yes—
604C4⋊C4C2×D4×C15111yescharacteristic
605C4⋊C4C2×D4×C15111yescharacteristic
606C4⋊C4C2×D4×C15111yescharacteristic
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—41no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—41no—
627C42C2×D4×C15111yescharacteristic
628C42C2×D4×C15111yescharacteristic
629C42C2×D4×C15111yescharacteristic
630C42C24×C15111yescharacteristic
631C23—21no—
632C23—22no—
633C23#120×C15111yescharacteristic
634Q8—21no—
635Q8—21no—
636Q8—21no—
637Q8—21no—
638Q8—21no—
639Q8—21no—
640Q8—42no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—81no—
646Q8—82no—
647D4—21no—
648D4—21no—
649D4—42no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—82no—
655D4—81no—
656D4—82no—
657D4—82no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4#120×C15111yescharacteristic
680C2×C4#120×C15111yescharacteristic
681C2×C4#120×C15111yescharacteristic
682C2×C4C22×D4×C15111yescharacteristic
683C2×C4C22×D4×C15111yescharacteristic
684C2×C4C22×D4×C15111yescharacteristic
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—41no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—42no—
698C22—42no—
699C22—41no—
700C22C2×#120×C15111yescharacteristic
701C4—21no—
702C4—21no—
703C4—21no—
704C4—21no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—42no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4#576×C15111yescharacteristic
716C4#577×C15111yescharacteristic
717C4#578×C15111yescharacteristic
718C4#578×C15111yescharacteristic
719C2—41no—
720C2—81no—
721C2—82no—
722C2#3011×C15111yescharacteristic
723C2#3012×C15111yescharacteristic
724C2#3018×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. #3249×C151C2semidirect
3. #3233×C151C2semidirect
4. #3182×C151C2semidirect
5. #1649×C151C2semidirect
6. #1648×C151C2semidirect
7. #1641×C151C2semidirect
8. #1640×C151C2semidirect
9. #1637×C151C2semidirect
10. #1636×C151C2semidirect
11. #1631×C151C2semidirect
12. #1630×C151C2semidirect
13. #1540×C151C2semidirect
14. #1485×C151C2semidirect
15. #1483×C151C2semidirect
362. #18743C151direct (N × H)
363. C151#18743direct (N × H)
365. #3249C2×C151semidirect
366. #3233C2×C151semidirect
367. #3182C2×C151semidirect
368. #1649C2×C151semidirect
369. #1648C2×C151semidirect
370. #1641C2×C151semidirect
371. #1640C2×C151semidirect
372. #1637C2×C151semidirect
373. #1636C2×C151semidirect
374. #1631C2×C151semidirect
375. #1630C2×C151semidirect
376. #1540C2×C151semidirect
377. #1485C2×C151semidirect
378. #1483C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3554×C1512
#3249×C1512
#3233×C1512
#3182×C1512
#1649×C1512
#1648×C1512
#1641×C1512
#1640×C1512
#1637×C1512
#1636×C1512
#1631×C1512
#1630×C1512
#1540×C1512
#1485×C1512
#1483×C1512
#18743151