Finite Group Databasebeta

← C151×#18930 #50323855

Subgroups — C151×#18930 #50323855

Order 38656.

1020 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3543×C151C211yesmaximal, characteristic, complemented
2#3251×C151C211yesmaximal, characteristic, complemented
3#3212×C151C211yesmaximal, characteristic, complemented
4#3205×C151C211yesmaximal, characteristic, complemented
5#1642×C151C211yesmaximal, characteristic, complemented
6#1641×C151C211yesmaximal, characteristic, complemented
7#1640×C151C211yesmaximal, characteristic, complemented
8#1639×C151C211yesmaximal, characteristic, complemented
9#1621×C151C211yesmaximal, characteristic, complemented
10#1621×C151C211yesmaximal, characteristic, complemented
11#1620×C151C211yesmaximal, characteristic, complemented
12#1619×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#532×C151C2211yescharacteristic, complemented
31C2×#127×C151C2211yescharacteristic
32#529×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#495×C151—21no—
35#493×C151C2211yescharacteristic
36#493×C151C2211yescharacteristic, complemented
37#488×C151—21no—
38#486×C151C2211yescharacteristic
39#486×C151C2211yescharacteristic, complemented
40#478×C151—21no—
41#475×C151C2211yescharacteristic, complemented
42#474×C151C2211yescharacteristic, complemented
43#469×C151—21no—
44#468×C151—21no—
45#463×C151—21no—
46#462×C151C2211yescharacteristic, complemented
47#461×C151C2211yescharacteristic, complemented
48#460×C151C2211yescharacteristic, complemented
49#460×C151C2211yescharacteristic, complemented
50#459×C151—22no—
51#459×C151C2211yescharacteristic, complemented
52#459×C151C2211yescharacteristic, complemented
53#452×C151—21no—
54#449×C151—21no—
55#447×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—
73C2×#41×C151—21no—
74C22×D4×C151—22no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151D412yes—
80C2×Q16×C151—21no—
81C2×SD16×C151—21no—
82C2×SD16×C151—21no—
83C2×SD16×C151—21no—
84C2×D8×C151—22no—
85C2×D8×C151—22no—
86C2×D8×C151—21no—
87C2×D8×C151—21no—
88C2×M16×C151—21no—
89C4⋊Q8×C151C2311yescharacteristic
90#127×C151—21no—
91#127×C151—21no—
92#127×C151—21no—
93#127×C151—21no—
94#127×C151D412yes—
95#127×C151C2311yescharacteristic
96#127×C151C2311yescharacteristic
97#127×C151C2311yescharacteristic
98#126×C151—21no—
99#126×C151—21no—
100#125×C151D411yescharacteristic
101#125×C151D411yescharacteristic
102#124×C151—21no—
103#124×C151—21no—
104#124×C151—21no—
105#124×C151D411yescharacteristic
106#124×C151D411yescharacteristic
107#123×C151—22no—
108#123×C151—22no—
109#123×C151—22no—
110#123×C151—22no—
111#123×C151—21no—
112#123×C151—21no—
113C22⋊Q8×C151D411yescharacteristic
114C22⋊Q8×C151D411yescharacteristic
115#121×C151—22no—
116#121×C151—22no—
117#121×C151—22no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—22no—
123#121×C151—21no—
124#121×C151—21no—
125#121×C151—21no—
126#121×C151—21no—
127#121×C151—21no—
128#121×C151—21no—
129#121×C151D411yescharacteristic
130#121×C151D411yescharacteristic
131#120×C151—22no—
132#120×C151—22no—
133#120×C151—22no—
134#120×C151—22no—
135#120×C151—22no—
136#120×C151—22no—
137C4×Q8×C151C2311yescharacteristic
138C4×Q8×C151C2311yescharacteristic
139C4×D4×C151—21no—
140C4×D4×C151—21no—
141C4×D4×C151—21no—
142C4×D4×C151—21no—
143C4×D4×C151—21no—
144C4×D4×C151—21no—
145C4×D4×C151—21no—
146C4×D4×C151—21no—
147C4×D4×C151C2311yescharacteristic
148C4×D4×C151C2311yescharacteristic
149#117×C151—21no—
150#117×C151—21no—
151C2×C22⋊C4×C151—22no—
152C2×C42×C151C2311yescharacteristic
153#107×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#102×C151—22no—
165#102×C151—22no—
166#102×C151—21no—
167#102×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
176C24×C151—22no—
177C24×C151—22no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—81no—
181#41×C151—81no—
182#41×C151—81no—
183#41×C151—81no—
184C2×Q8×C151—21no—
185C2×Q8×C151C2×D411yescharacteristic
186C2×Q8×C151C2×D411yescharacteristic
187C2×D4×C151—21no—
188C2×D4×C151—21no—
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—22no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—41no—
206C2×D4×C151—81no—
207C2×D4×C151—81no—
208C2×D4×C151—81no—
209C2×D4×C151—81no—
210C2×D4×C151—81no—
211C2×D4×C151—81no—
212C2×D4×C151—81no—
213C2×D4×C151—81no—
214C2×D4×C151—82no—
215C2×D4×C151—84no—
216C2×D4×C151C2×D411yescharacteristic
217C2×D4×C151C2×D411yescharacteristic
218C2×D4×C151C2×D412yes—
219C2×D4×C151C2×D412yes—
220C22×C4×C151—22no—
221C22×C4×C151—22no—
222C22×C4×C151—22no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—41no—
226C22×C4×C151C2×D411yescharacteristic
227C22×C4×C151C2×D411yescharacteristic
228C22×C4×C151C2×D411yescharacteristic
229Q16×C151—81no—
230SD16×C151—81no—
231SD16×C151—81no—
232SD16×C151—81no—
233D8×C151—81no—
234D8×C151—81no—
235D8×C151—82no—
236D8×C151—82no—
237M16×C151—81no—
238C2×C8×C151—21no—
239C2×C8×C151—21no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C4⋊C4×C151—21no—
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—21no—
254C4⋊C4×C151C2×D411yescharacteristic
255C4⋊C4×C151C2×D411yescharacteristic
256C4⋊C4×C151C2×D411yescharacteristic
257C4⋊C4×C151C2×D411yescharacteristic
258C22⋊C4×C151—22no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—22no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—22no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—21no—
266C22⋊C4×C151—21no—
267C22⋊C4×C151—21no—
268C22⋊C4×C151—21no—
269C22⋊C4×C151—21no—
270C22⋊C4×C151—21no—
271C22⋊C4×C151—21no—
272C22⋊C4×C151—21no—
273C22⋊C4×C151—21no—
274C22⋊C4×C151—41no—
275C22⋊C4×C151—41no—
276C42×C151—21no—
277C42×C151—21no—
278C42×C151C2×D411yescharacteristic
279C42×C151C2×D411yescharacteristic
280C42×C151C2×D411yescharacteristic
281C42×C151C2411yescharacteristic
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—22no—
285C23×C151—22no—
286C23×C151—44no—
287C23×C151—41no—
288C23×C151—82no—
289C23×C151—82no—
290C23×C151—82no—
291C23×C151—82no—
292C23×C151—82no—
293C23×C151#12011yescharacteristic
294Q8×C151—21no—
295Q8×C151—21no—
296Q8×C151—21no—
297Q8×C151—21no—
298Q8×C151—41no—
299Q8×C151—41no—
300D4×C151—21no—
301D4×C151—21no—
302D4×C151—21no—
303D4×C151—21no—
304D4×C151—42no—
305D4×C151—42no—
306D4×C151—42no—
307D4×C151—42no—
308D4×C151—42no—
309D4×C151—41no—
310D4×C151—41no—
311D4×C151—41no—
312D4×C151—41no—
313D4×C151—41no—
314D4×C151—41no—
315D4×C151—41no—
316D4×C151—41no—
317D4×C151—41no—
318D4×C151—41no—
319D4×C151—41no—
320D4×C151—41no—
321D4×C151—82no—
322D4×C151—82no—
323D4×C151—82no—
324D4×C151—82no—
325D4×C151—82no—
326D4×C151—82no—
327D4×C151—82no—
328D4×C151—82no—
329D4×C151—82no—
330D4×C151—82no—
331C2×C4×C151—21no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—21no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—41no—
342C2×C4×C151—41no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—82no—
348C2×C4×C151—82no—
349C2×C4×C151—82no—
350C2×C4×C151—82no—
351C2×C4×C151#12011yescharacteristic
352C2×C4×C151#12011yescharacteristic
353C2×C4×C151#12011yescharacteristic
354C2×C4×C151C22×D411yescharacteristic
355C2×C4×C151C22×D411yescharacteristic
356C2×C4×C151C22×D411yescharacteristic
357C8×C151—41no—
358C8×C151—41no—
359C8×C151—41no—
360C8×C151—41no—
361C8×C151—41no—
362C8×C151—41no—
363C22×C151—21no—
364C22×C151—21no—
365C22×C151—21no—
366C22×C151—41no—
367C22×C151—42no—
368C22×C151—41no—
369C22×C151—42no—
370C22×C151—41no—
371C22×C151—42no—
372C22×C151—41no—
373C22×C151—42no—
374C22×C151—42no—
375C22×C151—41no—
376C22×C151—41no—
377C22×C151—42no—
378C22×C151—81no—
379C22×C151—81no—
380C22×C151—81no—
381C22×C151—164no—
382C22×C151—164no—
383C22×C151C2×#12011yescharacteristic
384C4×C151—21no—
385C4×C151—21no—
386C4×C151—21no—
387C4×C151—21no—
388C4×C151—41no—
389C4×C151—41no—
390C4×C151—41no—
391C4×C151—41no—
392C4×C151—41no—
393C4×C151—41no—
394C4×C151—81no—
395C4×C151#57611yescharacteristic
396C4×C151#57611yescharacteristic
397C4×C151#57611yescharacteristic
398C4×C151#57711yescharacteristic
399C2×C151—41no—
400C2×C151—82no—
401C2×C151—81no—
402C2×C151—81no—
403C2×C151—82no—
404C2×C151—161no—
405C2×C151#300811yescharacteristic
406C2×C151#301211yescharacteristic
407C2×C151#301911yescharacteristic
408#18930C15111yesmaximal, characteristic, direct product factor, Sylow
409C151#1893011yescharacteristic, direct product factor, Sylow
410#3543C2×C15111yescharacteristic, complemented
411#3251C2×C15111yescharacteristic, complemented
412#3212C2×C15111yescharacteristic, complemented
413#3205C2×C15111yescharacteristic, complemented
414#1642C2×C15111yescharacteristic, complemented
415#1641C2×C15111yescharacteristic, complemented
416#1640C2×C15111yescharacteristic, complemented
417#1639C2×C15111yescharacteristic, complemented
418#1621C2×C15111yescharacteristic, complemented
419#1621C2×C15111yescharacteristic, complemented
420#1620C2×C15111yescharacteristic, complemented
421#1619C2×C15111yescharacteristic, complemented
422#1545C2×C15111yescharacteristic, complemented
423#1495C2×C15111yescharacteristic, complemented
424#1482C2×C15111yescharacteristic, complemented
425#560—22no—
426#559C22×C15111yescharacteristic
427#550C22×C15111yescharacteristic
428#550C22×C15111yescharacteristic
429#546—21no—
430#546—21no—
431D42—21no—
432D42—21no—
433D42C22×C15111yescharacteristic
434#540—21no—
435#540—21no—
436#535—21no—
437#535—21no—
438#534—22no—
439#532C22×C15111yescharacteristic, complemented
440C2×#127C22×C15111yescharacteristic
441#529C22×C15111yescharacteristic
442#529C22×C15111yescharacteristic
443#495—21no—
444#493C22×C15111yescharacteristic
445#493C22×C15111yescharacteristic, complemented
446#488—21no—
447#486C22×C15111yescharacteristic
448#486C22×C15111yescharacteristic, complemented
449#478—21no—
450#475C22×C15111yescharacteristic, complemented
451#474C22×C15111yescharacteristic, complemented
452#469—21no—
453#468—21no—
454#463—21no—
455#462C22×C15111yescharacteristic, complemented
456#461C22×C15111yescharacteristic, complemented
457#460C22×C15111yescharacteristic, complemented
458#460C22×C15111yescharacteristic, complemented
459#459—22no—
460#459C22×C15111yescharacteristic, complemented
461#459C22×C15111yescharacteristic, complemented
462#452—21no—
463#449—21no—
464#447—22no—
465#431C22×C15111yescharacteristic, complemented
466#431C22×C15111yescharacteristic, complemented
467#423C22×C15111yescharacteristic, complemented
468#331C22×C15111yescharacteristic
469#331C22×C15111yescharacteristic
470#331C22×C15111yescharacteristic, complemented
471#331C22×C15111yescharacteristic, complemented
472Q8⋊C8C22×C15111yescharacteristic, complemented
473Q8⋊C8C22×C15111yescharacteristic, complemented
474Q8⋊C8C22×C15111yescharacteristic, complemented
475Q8⋊C8C22×C15111yescharacteristic, complemented
476D4⋊C8C22×C15111yescharacteristic, complemented
477D4⋊C8C22×C15111yescharacteristic, complemented
478D4⋊C8C22×C15111yescharacteristic, complemented
479D4⋊C8C22×C15111yescharacteristic, complemented
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C22×D4—22no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C15112yes—
489C2×Q16—21no—
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×D8—22no—
494C2×D8—22no—
495C2×D8—21no—
496C2×D8—21no—
497C2×M16—21no—
498C4⋊Q8C23×C15111yescharacteristic
499#127—21no—
500#127—21no—
501#127—21no—
502#127—21no—
503#127D4×C15112yes—
504#127C23×C15111yescharacteristic
505#127C23×C15111yescharacteristic
506#127C23×C15111yescharacteristic
507#126—21no—
508#126—21no—
509#125D4×C15111yescharacteristic
510#125D4×C15111yescharacteristic
511#124—21no—
512#124—21no—
513#124—21no—
514#124D4×C15111yescharacteristic
515#124D4×C15111yescharacteristic
516#123—22no—
517#123—22no—
518#123—22no—
519#123—22no—
520#123—21no—
521#123—21no—
522C22⋊Q8D4×C15111yescharacteristic
523C22⋊Q8D4×C15111yescharacteristic
524#121—22no—
525#121—22no—
526#121—22no—
527#121—22no—
528#121—22no—
529#121—22no—
530#121—22no—
531#121—22no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121—21no—
536#121—21no—
537#121—21no—
538#121D4×C15111yescharacteristic
539#121D4×C15111yescharacteristic
540#120—22no—
541#120—22no—
542#120—22no—
543#120—22no—
544#120—22no—
545#120—22no—
546C4×Q8C23×C15111yescharacteristic
547C4×Q8C23×C15111yescharacteristic
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4C23×C15111yescharacteristic
557C4×D4C23×C15111yescharacteristic
558#117—21no—
559#117—21no—
560C2×C22⋊C4—22no—
561C2×C42C23×C15111yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8C23×C15111yescharacteristic
567C4⋊C8C23×C15111yescharacteristic
568C4⋊C8C23×C15111yescharacteristic
569C4⋊C8C23×C15111yescharacteristic
570#103—21no—
571#103—21no—
572#103—21no—
573#102—22no—
574#102—22no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C4×C8—21no—
583C4×C8C23×C15111yescharacteristic
584C4×C8C23×C15111yescharacteristic
585C24—22no—
586C24—22no—
587#41—81no—
588#41—81no—
589#41—81no—
590#41—81no—
591#41—81no—
592#41—81no—
593C2×Q8—21no—
594C2×Q8C2×D4×C15111yescharacteristic
595C2×Q8C2×D4×C15111yescharacteristic
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—41no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—82no—
624C2×D4—84no—
625C2×D4C2×D4×C15111yescharacteristic
626C2×D4C2×D4×C15111yescharacteristic
627C2×D4C2×D4×C15112yes—
628C2×D4C2×D4×C15112yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—41no—
635C22×C4C2×D4×C15111yescharacteristic
636C22×C4C2×D4×C15111yescharacteristic
637C22×C4C2×D4×C15111yescharacteristic
638Q16—81no—
639SD16—81no—
640SD16—81no—
641SD16—81no—
642D8—81no—
643D8—81no—
644D8—82no—
645D8—82no—
646M16—81no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4C2×D4×C15111yescharacteristic
664C4⋊C4C2×D4×C15111yescharacteristic
665C4⋊C4C2×D4×C15111yescharacteristic
666C4⋊C4C2×D4×C15111yescharacteristic
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C42—21no—
686C42—21no—
687C42C2×D4×C15111yescharacteristic
688C42C2×D4×C15111yescharacteristic
689C42C2×D4×C15111yescharacteristic
690C42C24×C15111yescharacteristic
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—44no—
696C23—41no—
697C23—82no—
698C23—82no—
699C23—82no—
700C23—82no—
701C23—82no—
702C23#120×C15111yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—41no—
708Q8—41no—
709D4—21no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—82no—
731D4—82no—
732D4—82no—
733D4—82no—
734D4—82no—
735D4—82no—
736D4—82no—
737D4—82no—
738D4—82no—
739D4—82no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4#120×C15111yescharacteristic
761C2×C4#120×C15111yescharacteristic
762C2×C4#120×C15111yescharacteristic
763C2×C4C22×D4×C15111yescharacteristic
764C2×C4C22×D4×C15111yescharacteristic
765C2×C4C22×D4×C15111yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—164no—
791C22—164no—
792C22C2×#120×C15111yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4#576×C15111yescharacteristic
805C4#576×C15111yescharacteristic
806C4#576×C15111yescharacteristic
807C4#577×C15111yescharacteristic
808C2—41no—
809C2—81no—
810C2—81no—
811C2—82no—
812C2—82no—
813C2—161no—
814C2#3008×C15111yescharacteristic
815C2#3012×C15111yescharacteristic
816C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
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
1. #3543×C151C2semidirect
2. #3251×C151C2semidirect
3. #3212×C151C2semidirect
4. #3205×C151C2semidirect
5. #1642×C151C2semidirect
6. #1641×C151C2semidirect
7. #1640×C151C2semidirect
8. #1639×C151C2semidirect
9. #1621×C151C2semidirect
10. #1621×C151C2semidirect
11. #1620×C151C2semidirect
12. #1619×C151C2semidirect
13. #1545×C151C2semidirect
14. #1495×C151C2semidirect
15. #1482×C151C2semidirect
30. #532×C151C22semidirect
36. #493×C151C22semidirect
39. #486×C151C22semidirect
41. #475×C151C22semidirect
42. #474×C151C22semidirect
46. #462×C151C22semidirect
47. #461×C151C22semidirect
48. #460×C151C22semidirect
49. #460×C151C22semidirect
51. #459×C151C22semidirect
52. #459×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
408. #18930C151direct (N × H)
409. C151#18930direct (N × H)
410. #3543C2×C151semidirect
411. #3251C2×C151semidirect
412. #3212C2×C151semidirect
413. #3205C2×C151semidirect
414. #1642C2×C151semidirect
415. #1641C2×C151semidirect
416. #1640C2×C151semidirect
417. #1639C2×C151semidirect
418. #1621C2×C151semidirect
419. #1621C2×C151semidirect
420. #1620C2×C151semidirect
421. #1619C2×C151semidirect
422. #1545C2×C151semidirect
423. #1495C2×C151semidirect
424. #1482C2×C151semidirect
439. #532C22×C151semidirect
445. #493C22×C151semidirect
448. #486C22×C151semidirect
450. #475C22×C151semidirect
451. #474C22×C151semidirect
455. #462C22×C151semidirect
456. #461C22×C151semidirect
457. #460C22×C151semidirect
458. #460C22×C151semidirect
460. #459C22×C151semidirect
461. #459C22×C151semidirect
465. #431C22×C151semidirect
466. #431C22×C151semidirect
467. #423C22×C151semidirect
470. #331C22×C151semidirect
471. #331C22×C151semidirect
472. Q8⋊C8C22×C151semidirect
473. Q8⋊C8C22×C151semidirect
474. Q8⋊C8C22×C151semidirect
475. Q8⋊C8C22×C151semidirect
476. D4⋊C8C22×C151semidirect
477. D4⋊C8C22×C151semidirect
478. D4⋊C8C22×C151semidirect
479. 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
#3251×C1512
#3212×C1512
#3205×C1512
#1642×C1512
#1641×C1512
#1640×C1512
#1639×C1512
#1621×C1512
#1620×C1512
#1619×C1512
#1545×C1512
#1495×C1512
#1482×C1512
#18930151