Finite Group Databasebeta

← C151×#18774 #50323699

Subgroups — C151×#18774 #50323699

Order 38656.

1022 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3483×C151C211yesmaximal, characteristic, complemented
2#3207×C151C211yesmaximal, characteristic, complemented
3#3115×C151C211yesmaximal, characteristic, complemented
4#3035×C151C211yesmaximal, characteristic, complemented
5#1646×C151C211yesmaximal, characteristic, complemented
6#1645×C151C211yesmaximal, characteristic, complemented
7#1642×C151C211yesmaximal, characteristic, complemented
8#1641×C151C211yesmaximal, characteristic, complemented
9#1624×C151C211yesmaximal, characteristic, complemented
10#1623×C151C211yesmaximal, characteristic, complemented
11#1621×C151C211yesmaximal, characteristic, complemented
12#1621×C151C211yesmaximal, characteristic, complemented
13#1551×C151C211yesmaximal, characteristic, complemented
14#1488×C151C211yesmaximal, characteristic, complemented
15#1477×C151C211yesmaximal, characteristic, complemented
16C2×#135×C151—21no—
17Q82×C151C2211yescharacteristic
18#555×C151—22no—
19#555×C151—21no—
20#555×C151—21no—
21#555×C151C2211yescharacteristic
22#550×C151—21no—
23#550×C151—21no—
24#550×C151C2211yescharacteristic
25#550×C151C2211yescharacteristic
26#532×C151—22no—
27#532×C151—21no—
28#532×C151—21no—
29#532×C151C2211yescharacteristic
30#532×C151C2211yescharacteristic
31C4×#41×C151—21no—
32C4×#41×C151—21no—
33C4×#41×C151C2211yescharacteristic
34C4×#41×C151C2211yescharacteristic
35#493×C151C2211yescharacteristic
36#492×C151C2211yescharacteristic
37#487×C151C2211yescharacteristic
38#486×C151C2211yescharacteristic
39#482×C151—21no—
40#475×C151C2211yescharacteristic
41#474×C151C2211yescharacteristic
42#464×C151—21no—
43#463×C151—22no—
44#463×C151—21no—
45#462×C151C2211yescharacteristic
46#461×C151C2211yescharacteristic
47#460×C151C2211yescharacteristic
48#460×C151C2211yescharacteristic
49#459×C151C2211yescharacteristic
50#459×C151C2211yescharacteristic
51#449×C151—21no—
52#449×C151—22no—
53#442×C151—21no—
54#440×C151—21no—
55#432×C151C2211yescharacteristic
56#431×C151C2211yescharacteristic
57C2×C4⋊C8×C151C2211yescharacteristic
58#416×C151—21no—
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic
62#331×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×C151—22no—
73C2×#41×C151—21no—
74C2×#41×C151—21no—
75C2×#41×C151D411yescharacteristic
76C2×#41×C151D411yescharacteristic
77C2×#41×C151D412yes—
78#135×C151—44no—
79C2×Q16×C151—21no—
80C2×SD16×C151—21no—
81C2×SD16×C151—21no—
82C2×SD16×C151—21no—
83C2×SD16×C151—22no—
84C2×D8×C151—21no—
85C2×D8×C151—21no—
86C2×D8×C151—22no—
87C22×C8×C151—21no—
88C4⋊Q8×C151—21no—
89C4⋊Q8×C151—21no—
90C4⋊Q8×C151—22no—
91C4⋊Q8×C151C2311yescharacteristic
92C4⋊Q8×C151C2311yescharacteristic
93#127×C151—22no—
94#127×C151—21no—
95#127×C151—21no—
96#127×C151C2311yescharacteristic
97#127×C151C2311yescharacteristic
98#124×C151—22no—
99#124×C151—22no—
100#124×C151—22no—
101#124×C151—21no—
102#124×C151—22no—
103#124×C151D412yes—
104#121×C151—22no—
105#121×C151—22no—
106#121×C151—22no—
107#121×C151—22no—
108#121×C151—21no—
109#121×C151—21no—
110#121×C151—22no—
111#121×C151—22no—
112#121×C151—21no—
113#121×C151—21no—
114#121×C151—21no—
115#121×C151—21no—
116#121×C151—21no—
117#121×C151—21no—
118C4×Q8×C151—21no—
119C4×Q8×C151—21no—
120C4×Q8×C151D411yescharacteristic
121C4×Q8×C151D411yescharacteristic
122C4×Q8×C151C2311yescharacteristic
123C4×Q8×C151C2311yescharacteristic
124C4×D4×C151—22no—
125C4×D4×C151—22no—
126C4×D4×C151—22no—
127C4×D4×C151—22no—
128C4×D4×C151—21no—
129C4×D4×C151—21no—
130C4×D4×C151—21no—
131C4×D4×C151—21no—
132C4×D4×C151—21no—
133C4×D4×C151—21no—
134C4×D4×C151—21no—
135C4×D4×C151—21no—
136C4×D4×C151—21no—
137C4×D4×C151—21no—
138C4×D4×C151D411yescharacteristic
139C4×D4×C151D411yescharacteristic
140C4×D4×C151C2311yescharacteristic
141C4×D4×C151C2311yescharacteristic
142#117×C151—22no—
143#117×C151—22no—
144#117×C151—21no—
145#117×C151—21no—
146#117×C151—21no—
147#117×C151—21no—
148#117×C151D411yescharacteristic
149#117×C151D411yescharacteristic
150C2×C42×C151—22no—
151C2×C42×C151—21no—
152C2×C42×C151—21no—
153C2×C42×C151C2311yescharacteristic
154#107×C151—21no—
155#106×C151—21no—
156C4⋊C8×C151—21no—
157C4⋊C8×C151—21no—
158C4⋊C8×C151C2311yescharacteristic
159C4⋊C8×C151C2311yescharacteristic
160C4⋊C8×C151C2311yescharacteristic
161C4⋊C8×C151C2311yescharacteristic
162#103×C151—21no—
163#103×C151—21no—
164#103×C151—21no—
165#103×C151—22no—
166#102×C151—21no—
167#102×C151—22no—
168#102×C151—21no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—21no—
172C22⋊C8×C151—21no—
173C22⋊C8×C151—21no—
174#97×C151—21no—
175C4×C8×C151C2311yescharacteristic
176C4×C8×C151C2311yescharacteristic
177#41×C151—22no—
178#41×C151—22no—
179#41×C151—41no—
180#41×C151—41no—
181#41×C151—42no—
182#41×C151—42no—
183#41×C151—42no—
184#41×C151—42no—
185#41×C151—42no—
186#41×C151—42no—
187#41×C151—82no—
188#41×C151—84no—
189C2×Q8×C151—22no—
190C2×Q8×C151—21no—
191C2×Q8×C151C2×D411yescharacteristic
192C2×Q8×C151C2×D411yescharacteristic
193C2×Q8×C151C2×D412yes—
194C2×D4×C151—22no—
195C2×D4×C151—22no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—22no—
199C2×D4×C151—22no—
200C2×D4×C151—22no—
201C2×D4×C151—22no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—41no—
208C2×D4×C151C2×D411yescharacteristic
209C2×D4×C151C2×D411yescharacteristic
210C2×D4×C151C2×D412yes—
211C22×C4×C151—22no—
212C22×C4×C151—22no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—22no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—41no—
221C22×C4×C151C2×D411yescharacteristic
222C22×C4×C151C2×D411yescharacteristic
223C22×C4×C151C2×D411yescharacteristic
224Q16×C151—42no—
225SD16×C151—42no—
226SD16×C151—42no—
227SD16×C151—42no—
228SD16×C151—82no—
229D8×C151—42no—
230D8×C151—42no—
231D8×C151—82no—
232C2×C8×C151—21no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—21no—
238C2×C8×C151—42no—
239C4⋊C4×C151—22no—
240C4⋊C4×C151—22no—
241C4⋊C4×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151—21no—
244C4⋊C4×C151—21no—
245C4⋊C4×C151—21no—
246C4⋊C4×C151—21no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151C2×D411yescharacteristic
250C4⋊C4×C151C2×D411yescharacteristic
251C4⋊C4×C151C2×D411yescharacteristic
252C4⋊C4×C151C2×D411yescharacteristic
253C22⋊C4×C151—22no—
254C22⋊C4×C151—22no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—22no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—21no—
262C22⋊C4×C151—21no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—21no—
265C22⋊C4×C151—41no—
266C22⋊C4×C151—41no—
267C42×C151—22no—
268C42×C151—22no—
269C42×C151—21no—
270C42×C151—21no—
271C42×C151—21no—
272C42×C151—21no—
273C42×C151—21no—
274C42×C151—21no—
275C42×C151C2×D411yescharacteristic
276C42×C151C2×D411yescharacteristic
277C42×C151C2×D411yescharacteristic
278C42×C151C2411yescharacteristic
279C23×C151—21no—
280C23×C151—21no—
281C23×C151—22no—
282C23×C151—41no—
283C23×C151#12011yescharacteristic
284Q8×C151—21no—
285Q8×C151—21no—
286Q8×C151—42no—
287Q8×C151—41no—
288Q8×C151—41no—
289Q8×C151—82no—
290Q8×C151#13512yescomplemented
291Q8×C151AGL(1,ℤ/8)12yes—
292D4×C151—21no—
293D4×C151—21no—
294D4×C151—21no—
295D4×C151—21no—
296D4×C151—42no—
297D4×C151—42no—
298D4×C151—42no—
299D4×C151—44no—
300D4×C151—44no—
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—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—22no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—41no—
327C2×C4×C151—42no—
328C2×C4×C151—42no—
329C2×C4×C151—44no—
330C2×C4×C151—44no—
331C2×C4×C151—44no—
332C2×C4×C151—42no—
333C2×C4×C151—42no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—41no—
337C2×C4×C151—41no—
338C2×C4×C151—41no—
339C2×C4×C151—82no—
340C2×C4×C151#12011yescharacteristic
341C2×C4×C151#12011yescharacteristic
342C2×C4×C151#12011yescharacteristic
343C2×C4×C151C22×D411yescharacteristic
344C2×C4×C151C22×D411yescharacteristic
345C2×C4×C151C22×D411yescharacteristic
346C8×C151—41no—
347C8×C151—41no—
348C8×C151—41no—
349C8×C151—41no—
350C8×C151—41no—
351C8×C151—41no—
352C22×C151—21no—
353C22×C151—21no—
354C22×C151—21no—
355C22×C151—41no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—42no—
360C22×C151—41no—
361C22×C151—42no—
362C22×C151—41no—
363C22×C151—41no—
364C22×C151—81no—
365C22×C151—81no—
366C22×C151—81no—
367C22×C151C2×#12011yescharacteristic
368C4×C151—21no—
369C4×C151—22no—
370C4×C151—21no—
371C4×C151—22no—
372C4×C151—21no—
373C4×C151—21no—
374C4×C151—41no—
375C4×C151—41no—
376C4×C151—42no—
377C4×C151—41no—
378C4×C151—41no—
379C4×C151—81no—
380C4×C151C2×#13511yescharacteristic
381C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
382C4×C151#57511yescharacteristic
383C4×C151#57511yescharacteristic
384C2×C151—41no—
385C2×C151—81no—
386C2×C151—81no—
387C2×C151—82no—
388C2×C151—161no—
389C2×C151#300211yescharacteristic
390C2×C151#300611yescharacteristic
391C2×C151#301911yescharacteristic
392#18774C15111yesmaximal, characteristic, direct product factor, Sylow
393C151#1877411yescharacteristic, direct product factor, Sylow
394#3483C2×C15111yescharacteristic, complemented
395#3207C2×C15111yescharacteristic, complemented
396#3115C2×C15111yescharacteristic, complemented
397#3035C2×C15111yescharacteristic, complemented
398#1646C2×C15111yescharacteristic, complemented
399#1645C2×C15111yescharacteristic, complemented
400#1642C2×C15111yescharacteristic, complemented
401#1641C2×C15111yescharacteristic, complemented
402#1624C2×C15111yescharacteristic, complemented
403#1623C2×C15111yescharacteristic, complemented
404#1621C2×C15111yescharacteristic, complemented
405#1621C2×C15111yescharacteristic, complemented
406#1551C2×C15111yescharacteristic, complemented
407#1488C2×C15111yescharacteristic, complemented
408#1477C2×C15111yescharacteristic, complemented
409C2×#135—21no—
410Q82C22×C15111yescharacteristic
411#555—22no—
412#555—21no—
413#555—21no—
414#555C22×C15111yescharacteristic
415#550—21no—
416#550—21no—
417#550C22×C15111yescharacteristic
418#550C22×C15111yescharacteristic
419#532—22no—
420#532—21no—
421#532—21no—
422#532C22×C15111yescharacteristic
423#532C22×C15111yescharacteristic
424C4×#41—21no—
425C4×#41—21no—
426C4×#41C22×C15111yescharacteristic
427C4×#41C22×C15111yescharacteristic
428#493C22×C15111yescharacteristic
429#492C22×C15111yescharacteristic
430#487C22×C15111yescharacteristic
431#486C22×C15111yescharacteristic
432#482—21no—
433#475C22×C15111yescharacteristic
434#474C22×C15111yescharacteristic
435#464—21no—
436#463—22no—
437#463—21no—
438#462C22×C15111yescharacteristic
439#461C22×C15111yescharacteristic
440#460C22×C15111yescharacteristic
441#460C22×C15111yescharacteristic
442#459C22×C15111yescharacteristic
443#459C22×C15111yescharacteristic
444#449—21no—
445#449—22no—
446#442—21no—
447#440—21no—
448#432C22×C15111yescharacteristic
449#431C22×C15111yescharacteristic
450C2×C4⋊C8C22×C15111yescharacteristic
451#416—21no—
452#333C22×C15111yescharacteristic
453#333C22×C15111yescharacteristic
454#331C22×C15111yescharacteristic
455#331C22×C15111yescharacteristic
456Q8⋊C8C22×C15111yescharacteristic
457Q8⋊C8C22×C15111yescharacteristic
458Q8⋊C8C22×C15111yescharacteristic
459Q8⋊C8C22×C15111yescharacteristic
460D4⋊C8C22×C15111yescharacteristic
461D4⋊C8C22×C15111yescharacteristic
462D4⋊C8C22×C15111yescharacteristic
463D4⋊C8C22×C15111yescharacteristic
464C2×#41—22no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41D4×C15111yescharacteristic
469C2×#41D4×C15111yescharacteristic
470C2×#41D4×C15112yes—
471#135—44no—
472C2×Q16—21no—
473C2×SD16—21no—
474C2×SD16—21no—
475C2×SD16—21no—
476C2×SD16—22no—
477C2×D8—21no—
478C2×D8—21no—
479C2×D8—22no—
480C22×C8—21no—
481C4⋊Q8—22no—
482C4⋊Q8—21no—
483C4⋊Q8—21no—
484C4⋊Q8C23×C15111yescharacteristic
485C4⋊Q8C23×C15111yescharacteristic
486#127—22no—
487#127—21no—
488#127—21no—
489#127C23×C15111yescharacteristic
490#127C23×C15111yescharacteristic
491#124—22no—
492#124—22no—
493#124—22no—
494#124—22no—
495#124—21no—
496#124D4×C15112yes—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—21no—
502#121—21no—
503#121—22no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8D4×C15111yescharacteristic
514C4×Q8D4×C15111yescharacteristic
515C4×Q8C23×C15111yescharacteristic
516C4×Q8C23×C15111yescharacteristic
517C4×D4—22no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4D4×C15111yescharacteristic
532C4×D4D4×C15111yescharacteristic
533C4×D4C23×C15111yescharacteristic
534C4×D4C23×C15111yescharacteristic
535#117—22no—
536#117—22no—
537#117—21no—
538#117—21no—
539#117—21no—
540#117—21no—
541#117D4×C15111yescharacteristic
542#117D4×C15111yescharacteristic
543C2×C42—22no—
544C2×C42—21no—
545C2×C42—21no—
546C2×C42C23×C15111yescharacteristic
547#107—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—22no—
557#103—21no—
558#103—21no—
559#102—21no—
560#102—22no—
561#102—21no—
562#102—21no—
563#102—21no—
564#102—21no—
565C22⋊C8—21no—
566C22⋊C8—21no—
567#97—21no—
568C4×C8C23×C15111yescharacteristic
569C4×C8C23×C15111yescharacteristic
570#41—22no—
571#41—22no—
572#41—41no—
573#41—41no—
574#41—42no—
575#41—42no—
576#41—42no—
577#41—42no—
578#41—42no—
579#41—42no—
580#41—82no—
581#41—84no—
582C2×Q8—22no—
583C2×Q8—21no—
584C2×Q8C2×D4×C15111yescharacteristic
585C2×Q8C2×D4×C15111yescharacteristic
586C2×Q8C2×D4×C15112yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4C2×D4×C15111yescharacteristic
602C2×D4C2×D4×C15111yescharacteristic
603C2×D4C2×D4×C15112yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—41no—
614C22×C4C2×D4×C15111yescharacteristic
615C22×C4C2×D4×C15111yescharacteristic
616C22×C4C2×D4×C15111yescharacteristic
617Q16—42no—
618SD16—42no—
619SD16—42no—
620SD16—42no—
621SD16—82no—
622D8—42no—
623D8—42no—
624D8—82no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—42no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
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—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C42—22no—
661C42—22no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42C2×D4×C15111yescharacteristic
669C42C2×D4×C15111yescharacteristic
670C42C2×D4×C15111yescharacteristic
671C42C24×C15111yescharacteristic
672C23—21no—
673C23—21no—
674C23—22no—
675C23—41no—
676C23#120×C15111yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—42no—
680Q8—41no—
681Q8—41no—
682Q8—82no—
683Q8#135×C15112yescomplemented
684Q8AGL(1,ℤ/8)×C15112yes—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—44no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
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—41no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22C2×#120×C15111yescharacteristic
761C4—21no—
762C4—22no—
763C4—21no—
764C4—22no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—81no—
773C4C2×#135×C15111yescharacteristic
774C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
775C4#575×C15111yescharacteristic
776C4#575×C15111yescharacteristic
777C2—41no—
778C2—81no—
779C2—81no—
780C2—82no—
781C2—161no—
782C2#3002×C15111yescharacteristic
783C2#3006×C15111yescharacteristic
784C2#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. #3483×C151C2semidirect
2. #3207×C151C2semidirect
3. #3115×C151C2semidirect
4. #3035×C151C2semidirect
5. #1646×C151C2semidirect
6. #1645×C151C2semidirect
7. #1642×C151C2semidirect
8. #1641×C151C2semidirect
9. #1624×C151C2semidirect
10. #1623×C151C2semidirect
11. #1621×C151C2semidirect
12. #1621×C151C2semidirect
13. #1551×C151C2semidirect
14. #1488×C151C2semidirect
15. #1477×C151C2semidirect
290. Q8×C151#135semidirect
392. #18774C151direct (N × H)
393. C151#18774direct (N × H)
394. #3483C2×C151semidirect
395. #3207C2×C151semidirect
396. #3115C2×C151semidirect
397. #3035C2×C151semidirect
398. #1646C2×C151semidirect
399. #1645C2×C151semidirect
400. #1642C2×C151semidirect
401. #1641C2×C151semidirect
402. #1624C2×C151semidirect
403. #1623C2×C151semidirect
404. #1621C2×C151semidirect
405. #1621C2×C151semidirect
406. #1551C2×C151semidirect
407. #1488C2×C151semidirect
408. #1477C2×C151semidirect
683. Q8#135×C151semidirect

Maximal subgroups

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

subgroupindex
#3483×C1512
#3207×C1512
#3115×C1512
#3035×C1512
#1646×C1512
#1645×C1512
#1642×C1512
#1641×C1512
#1624×C1512
#1623×C1512
#1621×C1512
#1551×C1512
#1488×C1512
#1477×C1512
#18774151