Finite Group Databasebeta

← C151×#18931 #50323856

Subgroups — C151×#18931 #50323856

Order 38656.

986 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3543×C151C211yesmaximal, characteristic
2#3252×C151C211yesmaximal, characteristic, complemented
3#3233×C151C211yesmaximal, characteristic, complemented
4#3208×C151C211yesmaximal, characteristic, complemented
5#1642×C151C211yesmaximal, characteristic, complemented
6#1641×C151C211yesmaximal, characteristic, complemented
7#1640×C151C211yesmaximal, characteristic, complemented
8#1639×C151C211yesmaximal, characteristic, complemented
9#1631×C151C211yesmaximal, characteristic, complemented
10#1631×C151C211yesmaximal, characteristic, complemented
11#1630×C151C211yesmaximal, characteristic, complemented
12#1629×C151C211yesmaximal, characteristic, complemented
13#1545×C151C211yesmaximal, characteristic, complemented
14#1495×C151C211yesmaximal, characteristic, complemented
15#1482×C151C211yesmaximal, characteristic, complemented
16#560×C151—22no—
17#559×C151C2211yescharacteristic
18#550×C151C2211yescharacteristic
19#550×C151C2211yescharacteristic
20#546×C151—21no—
21#546×C151—21no—
22D42×C151—21no—
23D42×C151—21no—
24D42×C151C2211yescharacteristic
25#540×C151—21no—
26#540×C151—21no—
27#535×C151—21no—
28#535×C151—21no—
29#534×C151—22no—
30#533×C151C2211yescharacteristic, complemented
31C2×#127×C151C2211yescharacteristic
32#529×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#499×C151—21no—
35#492×C151C2211yescharacteristic
36#492×C151C2211yescharacteristic, complemented
37#488×C151—21no—
38#486×C151C2211yescharacteristic
39#486×C151C2211yescharacteristic, complemented
40#485×C151—21no—
41#482×C151—21no—
42#479×C151—21no—
43#477×C151C2211yescharacteristic, complemented
44#477×C151C2211yescharacteristic, complemented
45#476×C151C2211yescharacteristic, complemented
46#476×C151C2211yescharacteristic, complemented
47#475×C151C2211yescharacteristic, complemented
48#474×C151C2211yescharacteristic, complemented
49#470×C151—21no—
50#468×C151—21no—
51#464×C151—21no—
52#462×C151C2211yescharacteristic, complemented
53#461×C151C2211yescharacteristic, complemented
54#460×C151—22no—
55#450×C151—22no—
56#431×C151C2211yescharacteristic, complemented
57#431×C151C2211yescharacteristic, complemented
58#423×C151C2211yescharacteristic, complemented
59#331×C151C2211yescharacteristic
60#331×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic, complemented
62#331×C151C2211yescharacteristic, complemented
63Q8⋊C8×C151C2211yescharacteristic, complemented
64Q8⋊C8×C151C2211yescharacteristic, complemented
65Q8⋊C8×C151C2211yescharacteristic, complemented
66Q8⋊C8×C151C2211yescharacteristic, complemented
67D4⋊C8×C151C2211yescharacteristic, complemented
68D4⋊C8×C151C2211yescharacteristic, complemented
69D4⋊C8×C151C2211yescharacteristic, complemented
70D4⋊C8×C151C2211yescharacteristic, complemented
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C22×D4×C151—22no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151D412yes—
79C2×Q16×C151—21no—
80C2×SD16×C151—22no—
81C2×SD16×C151—22no—
82C2×SD16×C151—21no—
83C2×M16×C151—21no—
84C4⋊Q8×C151C2311yescharacteristic
85C4⋊Q8×C151C2311yescharacteristic
86#127×C151—21no—
87#127×C151—21no—
88#127×C151—21no—
89#127×C151—21no—
90#127×C151D412yes—
91#127×C151C2311yescharacteristic
92#127×C151C2311yescharacteristic
93#126×C151—21no—
94#126×C151—21no—
95#125×C151—21no—
96#125×C151D411yescharacteristic
97#125×C151D411yescharacteristic
98#124×C151—21no—
99#124×C151—21no—
100#124×C151D411yescharacteristic
101#124×C151D411yescharacteristic
102#123×C151—22no—
103#123×C151—22no—
104#123×C151—22no—
105#123×C151—22no—
106#123×C151—21no—
107#123×C151—21no—
108C22⋊Q8×C151—21no—
109C22⋊Q8×C151—21no—
110C22⋊Q8×C151D411yescharacteristic
111C22⋊Q8×C151D411yescharacteristic
112#121×C151—22no—
113#121×C151—22no—
114#121×C151—22no—
115#121×C151—22no—
116#121×C151—22no—
117#121×C151—22no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—21no—
121#121×C151—21no—
122#121×C151—21no—
123#121×C151—21no—
124#121×C151D411yescharacteristic
125#121×C151D411yescharacteristic
126#120×C151—22no—
127#120×C151—22no—
128#120×C151—22no—
129#120×C151—22no—
130#120×C151—22no—
131#120×C151—22no—
132C4×Q8×C151—21no—
133C4×Q8×C151—21no—
134C4×Q8×C151C2311yescharacteristic
135C4×Q8×C151C2311yescharacteristic
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×C151C2311yescharacteristic
143C4×D4×C151C2311yescharacteristic
144#117×C151—21no—
145#117×C151—21no—
146#117×C151—21no—
147C2×C22⋊C4×C151—22no—
148C2×C42×C151C2311yescharacteristic
149#107×C151—21no—
150#107×C151—21no—
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—21no—
164#103×C151—21no—
165#103×C151—21no—
166#102×C151—22no—
167#102×C151—22no—
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
176C24×C151—22no—
177C24×C151—22no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—81no—
181#41×C151—81no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151C2×D411yescharacteristic
185C2×Q8×C151C2×D411yescharacteristic
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—22no—
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—22no—
194C2×D4×C151—22no—
195C2×D4×C151—22no—
196C2×D4×C151—22no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—81no—
202C2×D4×C151—81no—
203C2×D4×C151—81no—
204C2×D4×C151—81no—
205C2×D4×C151—81no—
206C2×D4×C151—81no—
207C2×D4×C151—81no—
208C2×D4×C151—81no—
209C2×D4×C151—82no—
210C2×D4×C151—84no—
211C2×D4×C151C2×D411yescharacteristic
212C2×D4×C151C2×D411yescharacteristic
213C2×D4×C151C2×D412yes—
214C2×D4×C151C2×D412yes—
215C22×C4×C151—22no—
216C22×C4×C151—22no—
217C22×C4×C151—22no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151C2×D411yescharacteristic
221C22×C4×C151C2×D411yescharacteristic
222C22×C4×C151C2×D411yescharacteristic
223Q16×C151—81no—
224SD16×C151—81no—
225SD16×C151—82no—
226SD16×C151—82no—
227M16×C151—81no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—21no—
231C2×C8×C151—21no—
232C2×C8×C151—21no—
233C2×C8×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×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—21no—
244C4⋊C4×C151—21no—
245C4⋊C4×C151—21no—
246C4⋊C4×C151—41no—
247C4⋊C4×C151—41no—
248C4⋊C4×C151C2×D411yescharacteristic
249C4⋊C4×C151C2×D411yescharacteristic
250C4⋊C4×C151C2×D411yescharacteristic
251C4⋊C4×C151C2×D411yescharacteristic
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—22no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—22no—
257C22⋊C4×C151—22no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—21no—
262C22⋊C4×C151—21no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—21no—
267C22⋊C4×C151—21no—
268C22⋊C4×C151—41no—
269C42×C151—21no—
270C42×C151—21no—
271C42×C151—41no—
272C42×C151C2×D411yescharacteristic
273C42×C151C2×D411yescharacteristic
274C42×C151C2×D411yescharacteristic
275C42×C151C2411yescharacteristic
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—22no—
279C23×C151—22no—
280C23×C151—44no—
281C23×C151—82no—
282C23×C151—82no—
283C23×C151—82no—
284C23×C151—82no—
285C23×C151—82no—
286C23×C151#12011yescharacteristic
287Q8×C151—21no—
288Q8×C151—21no—
289Q8×C151—21no—
290Q8×C151—21no—
291Q8×C151—42no—
292Q8×C151—41no—
293Q8×C151—41no—
294D4×C151—21no—
295D4×C151—21no—
296D4×C151—21no—
297D4×C151—21no—
298D4×C151—42no—
299D4×C151—42no—
300D4×C151—42no—
301D4×C151—42no—
302D4×C151—41no—
303D4×C151—41no—
304D4×C151—41no—
305D4×C151—41no—
306D4×C151—41no—
307D4×C151—41no—
308D4×C151—41no—
309D4×C151—41no—
310D4×C151—82no—
311D4×C151—82no—
312D4×C151—82no—
313D4×C151—82no—
314D4×C151—82no—
315D4×C151—82no—
316D4×C151—82no—
317D4×C151—82no—
318D4×C151—82no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—21no—
328C2×C4×C151—21no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—41no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—82no—
337C2×C4×C151—82no—
338C2×C4×C151—82no—
339C2×C4×C151#12011yescharacteristic
340C2×C4×C151#12011yescharacteristic
341C2×C4×C151#12011yescharacteristic
342C2×C4×C151C22×D411yescharacteristic
343C2×C4×C151C22×D411yescharacteristic
344C2×C4×C151C22×D411yescharacteristic
345C8×C151—41no—
346C8×C151—41no—
347C8×C151—41no—
348C8×C151—41no—
349C8×C151—41no—
350C8×C151—41no—
351C22×C151—21no—
352C22×C151—21no—
353C22×C151—21no—
354C22×C151—41no—
355C22×C151—42no—
356C22×C151—41no—
357C22×C151—42no—
358C22×C151—41no—
359C22×C151—42no—
360C22×C151—41no—
361C22×C151—42no—
362C22×C151—42no—
363C22×C151—41no—
364C22×C151—41no—
365C22×C151—42no—
366C22×C151—164no—
367C22×C151—164no—
368C22×C151C2×#12011yescharacteristic
369C4×C151—21no—
370C4×C151—21no—
371C4×C151—21no—
372C4×C151—21no—
373C4×C151—41no—
374C4×C151—41no—
375C4×C151—41no—
376C4×C151—41no—
377C4×C151—41no—
378C4×C151—41no—
379C4×C151—81no—
380C4×C151—81no—
381C4×C151#57611yescharacteristic
382C4×C151#57711yescharacteristic
383C4×C151#57711yescharacteristic
384C4×C151#57711yescharacteristic
385C2×C151—41no—
386C2×C151—82no—
387C2×C151—81no—
388C2×C151—81no—
389C2×C151—82no—
390C2×C151#300911yescharacteristic
391C2×C151#301211yescharacteristic
392C2×C151#301911yescharacteristic
393#18931C15111yesmaximal, characteristic, direct product factor, Sylow
394C151#1893111yescharacteristic, direct product factor, Sylow
395#3543C2×C15111yescharacteristic
396#3252C2×C15111yescharacteristic, complemented
397#3233C2×C15111yescharacteristic, complemented
398#3208C2×C15111yescharacteristic, complemented
399#1642C2×C15111yescharacteristic, complemented
400#1641C2×C15111yescharacteristic, complemented
401#1640C2×C15111yescharacteristic, complemented
402#1639C2×C15111yescharacteristic, complemented
403#1631C2×C15111yescharacteristic, complemented
404#1631C2×C15111yescharacteristic, complemented
405#1630C2×C15111yescharacteristic, complemented
406#1629C2×C15111yescharacteristic, complemented
407#1545C2×C15111yescharacteristic, complemented
408#1495C2×C15111yescharacteristic, complemented
409#1482C2×C15111yescharacteristic, complemented
410#560—22no—
411#559C22×C15111yescharacteristic
412#550C22×C15111yescharacteristic
413#550C22×C15111yescharacteristic
414#546—21no—
415#546—21no—
416D42—21no—
417D42—21no—
418D42C22×C15111yescharacteristic
419#540—21no—
420#540—21no—
421#535—21no—
422#535—21no—
423#534—22no—
424#533C22×C15111yescharacteristic, complemented
425C2×#127C22×C15111yescharacteristic
426#529C22×C15111yescharacteristic
427#529C22×C15111yescharacteristic
428#499—21no—
429#492C22×C15111yescharacteristic
430#492C22×C15111yescharacteristic, complemented
431#488—21no—
432#486C22×C15111yescharacteristic
433#486C22×C15111yescharacteristic, complemented
434#485—21no—
435#482—21no—
436#479—21no—
437#477C22×C15111yescharacteristic, complemented
438#477C22×C15111yescharacteristic, complemented
439#476C22×C15111yescharacteristic, complemented
440#476C22×C15111yescharacteristic, complemented
441#475C22×C15111yescharacteristic, complemented
442#474C22×C15111yescharacteristic, complemented
443#470—21no—
444#468—21no—
445#464—21no—
446#462C22×C15111yescharacteristic, complemented
447#461C22×C15111yescharacteristic, complemented
448#460—22no—
449#450—22no—
450#431C22×C15111yescharacteristic, complemented
451#431C22×C15111yescharacteristic, complemented
452#423C22×C15111yescharacteristic, complemented
453#331C22×C15111yescharacteristic
454#331C22×C15111yescharacteristic
455#331C22×C15111yescharacteristic, complemented
456#331C22×C15111yescharacteristic, complemented
457Q8⋊C8C22×C15111yescharacteristic, complemented
458Q8⋊C8C22×C15111yescharacteristic, complemented
459Q8⋊C8C22×C15111yescharacteristic, complemented
460Q8⋊C8C22×C15111yescharacteristic, complemented
461D4⋊C8C22×C15111yescharacteristic, complemented
462D4⋊C8C22×C15111yescharacteristic, complemented
463D4⋊C8C22×C15111yescharacteristic, complemented
464D4⋊C8C22×C15111yescharacteristic, complemented
465C2×#41—21no—
466C2×#41—21no—
467C22×D4—22no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4D4×C15112yes—
473C2×Q16—21no—
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—21no—
477C2×M16—21no—
478C4⋊Q8C23×C15111yescharacteristic
479C4⋊Q8C23×C15111yescharacteristic
480#127—21no—
481#127—21no—
482#127—21no—
483#127—21no—
484#127D4×C15112yes—
485#127C23×C15111yescharacteristic
486#127C23×C15111yescharacteristic
487#126—21no—
488#126—21no—
489#125—21no—
490#125D4×C15111yescharacteristic
491#125D4×C15111yescharacteristic
492#124—21no—
493#124—21no—
494#124D4×C15111yescharacteristic
495#124D4×C15111yescharacteristic
496#123—22no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—21no—
501#123—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8D4×C15111yescharacteristic
505C22⋊Q8D4×C15111yescharacteristic
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121D4×C15111yescharacteristic
519#121D4×C15111yescharacteristic
520#120—22no—
521#120—22no—
522#120—22no—
523#120—22no—
524#120—22no—
525#120—22no—
526C4×Q8—21no—
527C4×Q8—21no—
528C4×Q8C23×C15111yescharacteristic
529C4×Q8C23×C15111yescharacteristic
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4C23×C15111yescharacteristic
537C4×D4C23×C15111yescharacteristic
538#117—21no—
539#117—21no—
540#117—21no—
541C2×C22⋊C4—22no—
542C2×C42C23×C15111yescharacteristic
543#107—21no—
544#107—21no—
545#107—21no—
546#106—21no—
547#106—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551C4⋊C8C23×C15111yescharacteristic
552C4⋊C8C23×C15111yescharacteristic
553C4⋊C8C23×C15111yescharacteristic
554C4⋊C8C23×C15111yescharacteristic
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#102—22no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565C22⋊C8—21no—
566C22⋊C8—21no—
567C4×C8—21no—
568C4×C8C23×C15111yescharacteristic
569C4×C8C23×C15111yescharacteristic
570C24—22no—
571C24—22no—
572#41—81no—
573#41—81no—
574#41—81no—
575#41—81no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C15111yescharacteristic
579C2×Q8C2×D4×C15111yescharacteristic
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—82no—
604C2×D4—84no—
605C2×D4C2×D4×C15111yescharacteristic
606C2×D4C2×D4×C15111yescharacteristic
607C2×D4C2×D4×C15112yes—
608C2×D4C2×D4×C15112yes—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4C2×D4×C15111yescharacteristic
615C22×C4C2×D4×C15111yescharacteristic
616C22×C4C2×D4×C15111yescharacteristic
617Q16—81no—
618SD16—81no—
619SD16—82no—
620SD16—82no—
621M16—81no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C15111yescharacteristic
643C4⋊C4C2×D4×C15111yescharacteristic
644C4⋊C4C2×D4×C15111yescharacteristic
645C4⋊C4C2×D4×C15111yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—41no—
666C42C2×D4×C15111yescharacteristic
667C42C2×D4×C15111yescharacteristic
668C42C2×D4×C15111yescharacteristic
669C42C24×C15111yescharacteristic
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—44no—
675C23—82no—
676C23—82no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23#120×C15111yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—41no—
687Q8—41no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708D4—82no—
709D4—82no—
710D4—82no—
711D4—82no—
712D4—82no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4#120×C15111yescharacteristic
734C2×C4#120×C15111yescharacteristic
735C2×C4#120×C15111yescharacteristic
736C2×C4C22×D4×C15111yescharacteristic
737C2×C4C22×D4×C15111yescharacteristic
738C2×C4C22×D4×C15111yescharacteristic
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—164no—
761C22—164no—
762C22C2×#120×C15111yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—81no—
775C4#576×C15111yescharacteristic
776C4#577×C15111yescharacteristic
777C4#577×C15111yescharacteristic
778C4#577×C15111yescharacteristic
779C2—41no—
780C2—81no—
781C2—81no—
782C2—82no—
783C2—82no—
784C2#3009×C15111yescharacteristic
785C2#3012×C15111yescharacteristic
786C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3543×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. #3208×C151C2semidirect
5. #1642×C151C2semidirect
6. #1641×C151C2semidirect
7. #1640×C151C2semidirect
8. #1639×C151C2semidirect
9. #1631×C151C2semidirect
10. #1631×C151C2semidirect
11. #1630×C151C2semidirect
12. #1629×C151C2semidirect
13. #1545×C151C2semidirect
14. #1495×C151C2semidirect
15. #1482×C151C2semidirect
30. #533×C151C22semidirect
36. #492×C151C22semidirect
39. #486×C151C22semidirect
43. #477×C151C22semidirect
44. #477×C151C22semidirect
45. #476×C151C22semidirect
46. #476×C151C22semidirect
47. #475×C151C22semidirect
48. #474×C151C22semidirect
52. #462×C151C22semidirect
53. #461×C151C22semidirect
56. #431×C151C22semidirect
57. #431×C151C22semidirect
58. #423×C151C22semidirect
61. #331×C151C22semidirect
62. #331×C151C22semidirect
63. Q8⋊C8×C151C22semidirect
64. Q8⋊C8×C151C22semidirect
65. Q8⋊C8×C151C22semidirect
66. Q8⋊C8×C151C22semidirect
67. D4⋊C8×C151C22semidirect
68. D4⋊C8×C151C22semidirect
69. D4⋊C8×C151C22semidirect
70. D4⋊C8×C151C22semidirect
393. #18931C151direct (N × H)
394. C151#18931direct (N × H)
396. #3252C2×C151semidirect
397. #3233C2×C151semidirect
398. #3208C2×C151semidirect
399. #1642C2×C151semidirect
400. #1641C2×C151semidirect
401. #1640C2×C151semidirect
402. #1639C2×C151semidirect
403. #1631C2×C151semidirect
404. #1631C2×C151semidirect
405. #1630C2×C151semidirect
406. #1629C2×C151semidirect
407. #1545C2×C151semidirect
408. #1495C2×C151semidirect
409. #1482C2×C151semidirect
424. #533C22×C151semidirect
430. #492C22×C151semidirect
433. #486C22×C151semidirect
437. #477C22×C151semidirect
438. #477C22×C151semidirect
439. #476C22×C151semidirect
440. #476C22×C151semidirect
441. #475C22×C151semidirect
442. #474C22×C151semidirect
446. #462C22×C151semidirect
447. #461C22×C151semidirect
450. #431C22×C151semidirect
451. #431C22×C151semidirect
452. #423C22×C151semidirect
455. #331C22×C151semidirect
456. #331C22×C151semidirect
457. Q8⋊C8C22×C151semidirect
458. Q8⋊C8C22×C151semidirect
459. Q8⋊C8C22×C151semidirect
460. Q8⋊C8C22×C151semidirect
461. D4⋊C8C22×C151semidirect
462. D4⋊C8C22×C151semidirect
463. D4⋊C8C22×C151semidirect
464. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3543×C1512
#3252×C1512
#3233×C1512
#3208×C1512
#1642×C1512
#1641×C1512
#1640×C1512
#1639×C1512
#1631×C1512
#1630×C1512
#1629×C1512
#1545×C1512
#1495×C1512
#1482×C1512
#18931151