Finite Group Databasebeta

← C151×#18901 #50323826

Subgroups — C151×#18901 #50323826

Order 38656.

866 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#3515×C151C211yesmaximal, characteristic
2#3248×C151C211yesmaximal, characteristic, complemented
3#3231×C151C211yesmaximal, characteristic, complemented
4#3107×C151C211yesmaximal, characteristic, complemented
5#1654×C151C211yesmaximal, characteristic, complemented
6#1653×C151C211yesmaximal, characteristic, complemented
7#1648×C151C211yesmaximal, characteristic, complemented
8#1647×C151C211yesmaximal, characteristic, complemented
9#1644×C151C211yesmaximal, characteristic, complemented
10#1644×C151C211yesmaximal, characteristic, complemented
11#1643×C151C211yesmaximal, characteristic, complemented
12#1643×C151C211yesmaximal, characteristic, complemented
13#1542×C151C211yesmaximal, characteristic, complemented
14#1482×C151C211yesmaximal, characteristic, complemented
15#1477×C151C211yesmaximal, characteristic, complemented
16#557×C151C2211yescharacteristic
17#554×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19#553×C151—21no—
20#552×C151—21no—
21#552×C151—22no—
22#552×C151—21no—
23#547×C151—21no—
24#547×C151C2211yescharacteristic
25#541×C151—21no—
26#539×C151—22no—
27#533×C151C2211yescharacteristic
28#533×C151C2211yescharacteristic
29#529×C151—21no—
30#529×C151C2211yescharacteristic
31C2×#125×C151—21no—
32#520×C151—21no—
33C4×#41×C151C2211yescharacteristic
34#500×C151C2211yescharacteristic
35#498×C151C2211yescharacteristic
36#487×C151C2211yescharacteristic
37#487×C151C2211yescharacteristic
38#485×C151—22no—
39#485×C151—21no—
40#479×C151—21no—
41#479×C151—22no—
42#475×C151C2211yescharacteristic
43#475×C151C2211yescharacteristic
44#474×C151C2211yescharacteristic
45#474×C151C2211yescharacteristic
46#467×C151—21no—
47#465×C151—21no—
48#464×C151—21no—
49#462×C151C2211yescharacteristic
50#462×C151C2211yescharacteristic
51#461×C151C2211yescharacteristic
52#461×C151C2211yescharacteristic
53#452×C151—21no—
54C4×Q16×C151—21no—
55C4×SD16×C151—21no—
56#431×C151C2211yescharacteristic
57#431×C151C2211yescharacteristic
58C2×C4⋊C8×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×C151D411yescharacteristic
73C2×Q16×C151—21no—
74C2×Q16×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151—21no—
77C22×C8×C151—21no—
78C4⋊Q8×C151—21no—
79C4⋊Q8×C151C2311yescharacteristic
80C4⋊Q8×C151C2311yescharacteristic
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83#126×C151—22no—
84#126×C151—22no—
85#126×C151—22no—
86#126×C151—21no—
87#125×C151—22no—
88#125×C151—22no—
89#125×C151—22no—
90#125×C151—21no—
91#125×C151—21no—
92#125×C151—22no—
93#125×C151—21no—
94#125×C151—21no—
95#125×C151—21no—
96#125×C151D411yescharacteristic
97#124×C151D411yescharacteristic
98#123×C151—22no—
99#123×C151—22no—
100#123×C151—22no—
101#123×C151—21no—
102#123×C151—22no—
103C22⋊Q8×C151—21no—
104C22⋊Q8×C151—21no—
105C22⋊Q8×C151—21no—
106C22⋊Q8×C151—21no—
107C22⋊Q8×C151—21no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—21no—
111C22⋊Q8×C151D411yescharacteristic
112C22⋊Q8×C151D412yes—
113#121×C151—22no—
114#121×C151—21no—
115#121×C151D411yescharacteristic
116C4×Q8×C151—21no—
117C4×Q8×C151—21no—
118C4×Q8×C151—21no—
119C4×Q8×C151—21no—
120C4×Q8×C151—21no—
121C4×Q8×C151D411yescharacteristic
122C4×Q8×C151D412yes—
123C4×Q8×C151C2311yescharacteristic
124C4×Q8×C151C2311yescharacteristic
125C4×D4×C151—22no—
126C4×D4×C151—22no—
127C4×D4×C151—21no—
128C4×D4×C151—21no—
129C4×D4×C151—21no—
130C4×D4×C151—21no—
131C4×D4×C151—21no—
132C4×D4×C151D411yescharacteristic
133C4×D4×C151C2311yescharacteristic
134C4×D4×C151C2311yescharacteristic
135#117×C151—22no—
136#117×C151—22no—
137#117×C151—21no—
138#117×C151—21no—
139#117×C151—21no—
140#117×C151—21no—
141#117×C151D411yescharacteristic
142C2×C4⋊C4×C151—22no—
143C2×C4⋊C4×C151—22no—
144C2×C4⋊C4×C151—21no—
145C2×C4⋊C4×C151—21no—
146C2×C4⋊C4×C151—21no—
147C2×C42×C151—21no—
148C2×C42×C151C2311yescharacteristic
149#107×C151—21no—
150#107×C151—21no—
151#107×C151—22no—
152#106×C151—21no—
153#106×C151—21no—
154#106×C151—22no—
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—21no—
164#103×C151—21no—
165#103×C151—21no—
166#103×C151—21no—
167#103×C151—22no—
168#103×C151—22no—
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—22no—
177#41×C151—41no—
178#41×C151—42no—
179#41×C151—42no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151C2×D411yescharacteristic
184C2×Q8×C151C2×D411yescharacteristic
185C2×Q8×C151C2×D412yes—
186C2×D4×C151—22no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151C2×D411yescharacteristic
190C2×D4×C151C2×D411yescharacteristic
191C22×C4×C151—22no—
192C22×C4×C151—22no—
193C22×C4×C151—22no—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201Q16×C151—42no—
202Q16×C151—81no—
203SD16×C151—42no—
204SD16×C151—81no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—81no—
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—22no—
223C4⋊C4×C151—22no—
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—41no—
236C4⋊C4×C151—41no—
237C4⋊C4×C151C2×D411yescharacteristic
238C4⋊C4×C151C2×D411yescharacteristic
239C4⋊C4×C151C2×D411yescharacteristic
240C4⋊C4×C151C2×D411yescharacteristic
241C4⋊C4×C151C2×D412yes—
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—41no—
255C42×C151—22no—
256C42×C151—21no—
257C42×C151—21no—
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—
280D4×C151—21no—
281D4×C151—21no—
282D4×C151—21no—
283D4×C151—42no—
284D4×C151—44no—
285D4×C151—81no—
286D4×C151#13512yes—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—22no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—22no—
295C2×C4×C151—21no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—41no—
300C2×C4×C151—42no—
301C2×C4×C151—44no—
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—81no—
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—22no—
325C22×C151—21no—
326C22×C151—21no—
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—42no—
340C4×C151—41no—
341C4×C151—41no—
342C4×C151—41no—
343C4×C151—41no—
344C4×C151—42no—
345C4×C151—81no—
346C4×C151—81no—
347C4×C151C2×#13511yescharacteristic
348C4×C151#57511yescharacteristic
349C4×C151#57711yescharacteristic
350C4×C151#57811yescharacteristic
351C2×C151—41no—
352C2×C151—42no—
353C2×C151—81no—
354C2×C151#300211yescharacteristic
355C2×C151#301311yescharacteristic
356C2×C151#302211yescharacteristic
357#18901C15111yesmaximal, characteristic, direct product factor, Sylow
358C151#1890111yescharacteristic, direct product factor, Sylow
359#3515C2×C15111yescharacteristic
360#3248C2×C15111yescharacteristic, complemented
361#3231C2×C15111yescharacteristic, complemented
362#3107C2×C15111yescharacteristic, complemented
363#1654C2×C15111yescharacteristic, complemented
364#1653C2×C15111yescharacteristic, complemented
365#1648C2×C15111yescharacteristic, complemented
366#1647C2×C15111yescharacteristic, complemented
367#1644C2×C15111yescharacteristic, complemented
368#1644C2×C15111yescharacteristic, complemented
369#1643C2×C15111yescharacteristic, complemented
370#1643C2×C15111yescharacteristic, complemented
371#1542C2×C15111yescharacteristic, complemented
372#1482C2×C15111yescharacteristic, complemented
373#1477C2×C15111yescharacteristic, complemented
374#557C22×C15111yescharacteristic
375#554C22×C15111yescharacteristic
376#554C22×C15111yescharacteristic
377#553—21no—
378#552—21no—
379#552—22no—
380#552—21no—
381#547—21no—
382#547C22×C15111yescharacteristic
383#541—21no—
384#539—22no—
385#533C22×C15111yescharacteristic
386#533C22×C15111yescharacteristic
387#529—21no—
388#529C22×C15111yescharacteristic
389C2×#125—21no—
390#520—21no—
391C4×#41C22×C15111yescharacteristic
392#500C22×C15111yescharacteristic
393#498C22×C15111yescharacteristic
394#487C22×C15111yescharacteristic
395#487C22×C15111yescharacteristic
396#485—22no—
397#485—21no—
398#479—21no—
399#479—22no—
400#475C22×C15111yescharacteristic
401#475C22×C15111yescharacteristic
402#474C22×C15111yescharacteristic
403#474C22×C15111yescharacteristic
404#467—21no—
405#465—21no—
406#464—21no—
407#462C22×C15111yescharacteristic
408#462C22×C15111yescharacteristic
409#461C22×C15111yescharacteristic
410#461C22×C15111yescharacteristic
411#452—21no—
412C4×Q16—21no—
413C4×SD16—21no—
414#431C22×C15111yescharacteristic
415#431C22×C15111yescharacteristic
416C2×C4⋊C8C22×C15111yescharacteristic
417#333C22×C15111yescharacteristic
418#333C22×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—
430C2×#41D4×C15111yescharacteristic
431C2×Q16—21no—
432C2×Q16—21no—
433C2×SD16—21no—
434C2×SD16—21no—
435C22×C8—21no—
436C4⋊Q8—21no—
437C4⋊Q8C23×C15111yescharacteristic
438C4⋊Q8C23×C15111yescharacteristic
439C4⋊Q8C23×C15111yescharacteristic
440C4⋊Q8C23×C15111yescharacteristic
441#126—22no—
442#126—22no—
443#126—22no—
444#126—21no—
445#125—22no—
446#125—22no—
447#125—22no—
448#125—21no—
449#125—21no—
450#125—22no—
451#125—21no—
452#125—21no—
453#125—21no—
454#125D4×C15111yescharacteristic
455#124D4×C15111yescharacteristic
456#123—22no—
457#123—22no—
458#123—22no—
459#123—21no—
460#123—22no—
461C22⋊Q8—21no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8D4×C15111yescharacteristic
470C22⋊Q8D4×C15112yes—
471#121—22no—
472#121—21no—
473#121D4×C15111yescharacteristic
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8D4×C15111yescharacteristic
480C4×Q8D4×C15112yes—
481C4×Q8C23×C15111yescharacteristic
482C4×Q8C23×C15111yescharacteristic
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4D4×C15111yescharacteristic
491C4×D4C23×C15111yescharacteristic
492C4×D4C23×C15111yescharacteristic
493#117—22no—
494#117—22no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117D4×C15111yescharacteristic
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C42—21no—
506C2×C42C23×C15111yescharacteristic
507#107—21no—
508#107—21no—
509#107—22no—
510#106—21no—
511#106—21no—
512#106—22no—
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—22no—
522#103—22no—
523#103—21no—
524#103—21no—
525#103—21no—
526#103—21no—
527#102—21no—
528#102—21no—
529C22⋊C8—21no—
530C22⋊C8—21no—
531C4×C8—21no—
532C4×C8C23×C15111yescharacteristic
533C4×C8C23×C15111yescharacteristic
534#41—22no—
535#41—41no—
536#41—42no—
537#41—42no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C2×D4×C15111yescharacteristic
542C2×Q8C2×D4×C15111yescharacteristic
543C2×Q8C2×D4×C15112yes—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4C2×D4×C15111yescharacteristic
548C2×D4C2×D4×C15111yescharacteristic
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4C2×D4×C15111yescharacteristic
557C22×C4C2×D4×C15111yescharacteristic
558C22×C4C2×D4×C15111yescharacteristic
559Q16—42no—
560Q16—81no—
561SD16—42no—
562SD16—81no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—81no—
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—22no—
581C4⋊C4—22no—
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—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4C2×D4×C15111yescharacteristic
596C4⋊C4C2×D4×C15111yescharacteristic
597C4⋊C4C2×D4×C15111yescharacteristic
598C4⋊C4C2×D4×C15111yescharacteristic
599C4⋊C4C2×D4×C15112yes—
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—41no—
613C42—22no—
614C42—21no—
615C42—21no—
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—
638D4—21no—
639D4—21no—
640D4—21no—
641D4—42no—
642D4—44no—
643D4—81no—
644D4#135×C15112yes—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—44no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—81no—
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—22no—
683C22—21no—
684C22—21no—
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—42no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4C2×#135×C15111yescharacteristic
706C4#575×C15111yescharacteristic
707C4#577×C15111yescharacteristic
708C4#578×C15111yescharacteristic
709C2—41no—
710C2—42no—
711C2—81no—
712C2#3002×C15111yescharacteristic
713C2#3013×C15111yescharacteristic
714C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3515×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. #3248×C151C2semidirect
3. #3231×C151C2semidirect
4. #3107×C151C2semidirect
5. #1654×C151C2semidirect
6. #1653×C151C2semidirect
7. #1648×C151C2semidirect
8. #1647×C151C2semidirect
9. #1644×C151C2semidirect
10. #1644×C151C2semidirect
11. #1643×C151C2semidirect
12. #1643×C151C2semidirect
13. #1542×C151C2semidirect
14. #1482×C151C2semidirect
15. #1477×C151C2semidirect
357. #18901C151direct (N × H)
358. C151#18901direct (N × H)
360. #3248C2×C151semidirect
361. #3231C2×C151semidirect
362. #3107C2×C151semidirect
363. #1654C2×C151semidirect
364. #1653C2×C151semidirect
365. #1648C2×C151semidirect
366. #1647C2×C151semidirect
367. #1644C2×C151semidirect
368. #1644C2×C151semidirect
369. #1643C2×C151semidirect
370. #1643C2×C151semidirect
371. #1542C2×C151semidirect
372. #1482C2×C151semidirect
373. #1477C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3515×C1512
#3248×C1512
#3231×C1512
#3107×C1512
#1654×C1512
#1653×C1512
#1648×C1512
#1647×C1512
#1644×C1512
#1643×C1512
#1542×C1512
#1482×C1512
#1477×C1512
#18901151