Finite Group Databasebeta

← C151×#18890 #50323815

Subgroups — C151×#18890 #50323815

Order 38656.

964 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3514×C151C211yesmaximal, characteristic, complemented
2#3247×C151C211yesmaximal, characteristic, complemented
3#3207×C151C211yesmaximal, characteristic, complemented
4#3106×C151C211yesmaximal, characteristic, complemented
5#1638×C151C211yesmaximal, characteristic, complemented
6#1637×C151C211yesmaximal, characteristic, complemented
7#1630×C151C211yesmaximal, characteristic, complemented
8#1629×C151C211yesmaximal, characteristic, complemented
9#1628×C151C211yesmaximal, characteristic, complemented
10#1627×C151C211yesmaximal, characteristic, complemented
11#1620×C151C211yesmaximal, characteristic, complemented
12#1619×C151C211yesmaximal, characteristic, complemented
13#1540×C151C211yesmaximal, characteristic, complemented
14#1482×C151C211yesmaximal, characteristic, complemented
15#1477×C151C211yesmaximal, characteristic, complemented
16#559×C151C2211yescharacteristic
17#556×C151C2211yescharacteristic
18#555×C151—21no—
19#551×C151—22no—
20D4×Q8×C151C2211yescharacteristic
21#548×C151—21no—
22#546×C151—21no—
23#546×C151—21no—
24D42×C151C2211yescharacteristic
25#542×C151—21no—
26#538×C151—22no—
27#532×C151C2211yescharacteristic
28#532×C151C2211yescharacteristic, complemented
29#529×C151—21no—
30#529×C151C2211yescharacteristic
31C2×#124×C151—21no—
32#518×C151—21no—
33C4×#41×C151C2211yescharacteristic
34#493×C151C2211yescharacteristic
35#492×C151C2211yescharacteristic
36#487×C151C2211yescharacteristic, complemented
37#486×C151C2211yescharacteristic, complemented
38#482×C151—21no—
39#478×C151—21no—
40#477×C151C2211yescharacteristic, complemented
41#477×C151C2211yescharacteristic, complemented
42#476×C151C2211yescharacteristic
43#476×C151C2211yescharacteristic
44#466×C151—21no—
45#465×C151—21no—
46#463×C151—21no—
47#463×C151—22no—
48#460×C151C2211yescharacteristic, complemented
49#460×C151C2211yescharacteristic, complemented
50#459×C151C2211yescharacteristic
51#459×C151C2211yescharacteristic
52#449×C151—21no—
53#449×C151—22no—
54C4×SD16×C151—21no—
55C4×D8×C151—21no—
56#431×C151C2211yescharacteristic, complemented
57#431×C151C2211yescharacteristic, complemented
58C2×C4⋊C8×C151C2211yescharacteristic, complemented
59#332×C151C2211yescharacteristic, complemented
60#332×C151C2211yescharacteristic, complemented
61#331×C151C2211yescharacteristic
62#331×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic, complemented
64Q8⋊C8×C151C2211yescharacteristic, complemented
65Q8⋊C8×C151C2211yescharacteristic, complemented
66Q8⋊C8×C151C2211yescharacteristic, complemented
67D4⋊C8×C151C2211yescharacteristic
68D4⋊C8×C151C2211yescharacteristic
69D4⋊C8×C151C2211yescharacteristic
70D4⋊C8×C151C2211yescharacteristic
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C2×#41×C151D411yescharacteristic
74C22×Q8×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C2×SD16×C151—22no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C2×D8×C151—21no—
81C2×D8×C151—22no—
82C2×D8×C151—21no—
83C22×C8×C151—21no—
84C4⋊Q8×C151—21no—
85C4⋊Q8×C151C2311yescharacteristic
86C4⋊Q8×C151C2311yescharacteristic
87#127×C151C2311yescharacteristic
88#127×C151C2311yescharacteristic
89#126×C151—22no—
90#126×C151—22no—
91#126×C151—21no—
92#125×C151D411yescharacteristic
93#124×C151—22no—
94#124×C151—22no—
95#124×C151—22no—
96#124×C151—21no—
97#124×C151—21no—
98#124×C151—21no—
99#124×C151—21no—
100#124×C151—21no—
101#124×C151D411yescharacteristic
102#123×C151—22no—
103#123×C151—22no—
104#123×C151—22no—
105#123×C151—21no—
106C22⋊Q8×C151—22no—
107C22⋊Q8×C151—21no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151—21no—
110C22⋊Q8×C151D411yescharacteristic
111#121×C151—22no—
112#121×C151—22no—
113#121×C151—21no—
114#121×C151—21no—
115#121×C151—21no—
116#121×C151—21no—
117#121×C151—21no—
118#121×C151D412yes—
119#121×C151D411yescharacteristic
120#120×C151—22no—
121#120×C151—22no—
122C4×Q8×C151—21no—
123C4×Q8×C151D411yescharacteristic
124C4×Q8×C151C2311yescharacteristic
125C4×Q8×C151C2311yescharacteristic
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×C151D411yescharacteristic
138C4×D4×C151D412yes—
139C4×D4×C151C2311yescharacteristic
140C4×D4×C151C2311yescharacteristic
141#117×C151—22no—
142#117×C151—21no—
143#117×C151—21no—
144#117×C151—21no—
145#117×C151D411yescharacteristic
146C2×C22⋊C4×C151—22no—
147C2×C22⋊C4×C151—22no—
148C2×C22⋊C4×C151—22no—
149C2×C42×C151—21no—
150C2×C42×C151C2311yescharacteristic
151#107×C151—21no—
152#107×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—22no—
162#103×C151—21no—
163#103×C151—21no—
164#102×C151—21no—
165#102×C151—21no—
166#102×C151—21no—
167#102×C151—21no—
168#102×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
176C24×C151—22no—
177#41×C151—22no—
178#41×C151—41no—
179#41×C151—81no—
180#41×C151—81no—
181#41×C151—82no—
182C2×Q8×C151—22no—
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×D4×C151—22no—
190C2×D4×C151—21no—
191C2×D4×C151—22no—
192C2×D4×C151—21no—
193C2×D4×C151—22no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—42no—
200C2×D4×C151—42no—
201C2×D4×C151—41no—
202C2×D4×C151—81no—
203C2×D4×C151—81no—
204C2×D4×C151C2×D411yescharacteristic
205C2×D4×C151C2×D411yescharacteristic
206C2×D4×C151C2×D412yes—
207C22×C4×C151—22no—
208C22×C4×C151—22no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—22no—
214C22×C4×C151—41no—
215C22×C4×C151C2×D411yescharacteristic
216C22×C4×C151C2×D411yescharacteristic
217C22×C4×C151C2×D411yescharacteristic
218SD16×C151—42no—
219SD16×C151—81no—
220SD16×C151—82no—
221D8×C151—42no—
222D8×C151—81no—
223D8×C151—82no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—21no—
229C2×C8×C151—21no—
230C2×C8×C151—81no—
231C4⋊C4×C151—22no—
232C4⋊C4×C151—22no—
233C4⋊C4×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×C151C2×D412yes—
243C4⋊C4×C151C2×D411yescharacteristic
244C4⋊C4×C151C2×D411yescharacteristic
245C4⋊C4×C151C2×D411yescharacteristic
246C4⋊C4×C151C2×D411yescharacteristic
247C22⋊C4×C151—22no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—22no—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—22no—
254C22⋊C4×C151—21no—
255C22⋊C4×C151—21no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—22no—
262C22⋊C4×C151—21no—
263C22⋊C4×C151—21no—
264C22⋊C4×C151—41no—
265C22⋊C4×C151—41no—
266C42×C151—22no—
267C42×C151—21no—
268C42×C151—21no—
269C42×C151—21no—
270C42×C151—21no—
271C42×C151C2×D411yescharacteristic
272C42×C151C2×D411yescharacteristic
273C42×C151C2×D411yescharacteristic
274C42×C151C2411yescharacteristic
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—22no—
278C23×C151—44no—
279C23×C151—41no—
280C23×C151—82no—
281C23×C151—82no—
282C23×C151#12011yescharacteristic
283Q8×C151—21no—
284Q8×C151—21no—
285Q8×C151—21no—
286Q8×C151—21no—
287Q8×C151—42no—
288Q8×C151—41no—
289Q8×C151—41no—
290Q8×C151—82no—
291D4×C151—21no—
292D4×C151—21no—
293D4×C151—21no—
294D4×C151—42no—
295D4×C151—42no—
296D4×C151—42no—
297D4×C151—44no—
298D4×C151—41no—
299D4×C151—41no—
300D4×C151—41no—
301D4×C151—41no—
302D4×C151—41no—
303D4×C151—41no—
304D4×C151—41no—
305D4×C151—41no—
306D4×C151—82no—
307D4×C151—81no—
308D4×C151—82no—
309D4×C151—82no—
310D4×C151#13512yes—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—21no—
317C2×C4×C151—22no—
318C2×C4×C151—21no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—41no—
323C2×C4×C151—42no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—82no—
330C2×C4×C151—81no—
331C2×C4×C151—82no—
332C2×C4×C151—82no—
333C2×C4×C151—82no—
334C2×C4×C151#12011yescharacteristic
335C2×C4×C151#12011yescharacteristic
336C2×C4×C151#12011yescharacteristic
337C2×C4×C151C22×D411yescharacteristic
338C2×C4×C151C22×D411yescharacteristic
339C2×C4×C151C22×D411yescharacteristic
340C8×C151—41no—
341C8×C151—41no—
342C8×C151—41no—
343C8×C151—41no—
344C8×C151—41no—
345C8×C151—41no—
346C22×C151—21no—
347C22×C151—22no—
348C22×C151—21no—
349C22×C151—21no—
350C22×C151—41no—
351C22×C151—41no—
352C22×C151—41no—
353C22×C151—42no—
354C22×C151—42no—
355C22×C151—41no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—81no—
359C22×C151—81no—
360C22×C151—81no—
361C22×C151—164no—
362C22×C151C2×#12011yescharacteristic
363C4×C151—21no—
364C4×C151—21no—
365C4×C151—21no—
366C4×C151—21no—
367C4×C151—41no—
368C4×C151—41no—
369C4×C151—41no—
370C4×C151—42no—
371C4×C151—41no—
372C4×C151—41no—
373C4×C151—41no—
374C4×C151—81no—
375C4×C151C2×#13511yescharacteristic
376C4×C151#57511yescharacteristic
377C4×C151#57611yescharacteristic
378C4×C151#57711yescharacteristic
379C2×C151—41no—
380C2×C151—42no—
381C2×C151—82no—
382C2×C151—81no—
383C2×C151—161no—
384C2×C151#300211yescharacteristic
385C2×C151#301211yescharacteristic
386C2×C151#302111yescharacteristic
387#18890C15111yesmaximal, characteristic, direct product factor, Sylow
388C151#1889011yescharacteristic, direct product factor, Sylow
389#3514C2×C15111yescharacteristic, complemented
390#3247C2×C15111yescharacteristic, complemented
391#3207C2×C15111yescharacteristic, complemented
392#3106C2×C15111yescharacteristic, complemented
393#1638C2×C15111yescharacteristic, complemented
394#1637C2×C15111yescharacteristic, complemented
395#1630C2×C15111yescharacteristic, complemented
396#1629C2×C15111yescharacteristic, complemented
397#1628C2×C15111yescharacteristic, complemented
398#1627C2×C15111yescharacteristic, complemented
399#1620C2×C15111yescharacteristic, complemented
400#1619C2×C15111yescharacteristic, complemented
401#1540C2×C15111yescharacteristic, complemented
402#1482C2×C15111yescharacteristic, complemented
403#1477C2×C15111yescharacteristic, complemented
404#559C22×C15111yescharacteristic
405#556C22×C15111yescharacteristic
406#555—21no—
407#551—22no—
408D4×Q8C22×C15111yescharacteristic
409#548—21no—
410#546—21no—
411#546—21no—
412D42C22×C15111yescharacteristic
413#542—21no—
414#538—22no—
415#532C22×C15111yescharacteristic
416#532C22×C15111yescharacteristic, complemented
417#529—21no—
418#529C22×C15111yescharacteristic
419C2×#124—21no—
420#518—21no—
421C4×#41C22×C15111yescharacteristic
422#493C22×C15111yescharacteristic
423#492C22×C15111yescharacteristic
424#487C22×C15111yescharacteristic, complemented
425#486C22×C15111yescharacteristic, complemented
426#482—21no—
427#478—21no—
428#477C22×C15111yescharacteristic, complemented
429#477C22×C15111yescharacteristic, complemented
430#476C22×C15111yescharacteristic
431#476C22×C15111yescharacteristic
432#466—21no—
433#465—21no—
434#463—21no—
435#463—22no—
436#460C22×C15111yescharacteristic, complemented
437#460C22×C15111yescharacteristic, complemented
438#459C22×C15111yescharacteristic
439#459C22×C15111yescharacteristic
440#449—21no—
441#449—22no—
442C4×SD16—21no—
443C4×D8—21no—
444#431C22×C15111yescharacteristic, complemented
445#431C22×C15111yescharacteristic, complemented
446C2×C4⋊C8C22×C15111yescharacteristic, complemented
447#332C22×C15111yescharacteristic, complemented
448#332C22×C15111yescharacteristic, complemented
449#331C22×C15111yescharacteristic
450#331C22×C15111yescharacteristic
451Q8⋊C8C22×C15111yescharacteristic, complemented
452Q8⋊C8C22×C15111yescharacteristic, complemented
453Q8⋊C8C22×C15111yescharacteristic, complemented
454Q8⋊C8C22×C15111yescharacteristic, complemented
455D4⋊C8C22×C15111yescharacteristic
456D4⋊C8C22×C15111yescharacteristic
457D4⋊C8C22×C15111yescharacteristic
458D4⋊C8C22×C15111yescharacteristic
459C2×#41—21no—
460C2×#41—21no—
461C2×#41D4×C15111yescharacteristic
462C22×Q8—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×SD16—21no—
466C2×SD16—21no—
467C2×SD16—22no—
468C2×D8—21no—
469C2×D8—22no—
470C2×D8—21no—
471C22×C8—21no—
472C4⋊Q8—21no—
473C4⋊Q8C23×C15111yescharacteristic
474C4⋊Q8C23×C15111yescharacteristic
475#127C23×C15111yescharacteristic
476#127C23×C15111yescharacteristic
477#126—22no—
478#126—22no—
479#126—21no—
480#125D4×C15111yescharacteristic
481#124—22no—
482#124—22no—
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124—21no—
488#124—21no—
489#124D4×C15111yescharacteristic
490#123—22no—
491#123—22no—
492#123—22no—
493#123—21no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—22no—
498C22⋊Q8D4×C15111yescharacteristic
499#121—22no—
500#121—22no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121D4×C15111yescharacteristic
507#121D4×C15112yes—
508#120—22no—
509#120—22no—
510C4×Q8—21no—
511C4×Q8D4×C15111yescharacteristic
512C4×Q8C23×C15111yescharacteristic
513C4×Q8C23×C15111yescharacteristic
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C15111yescharacteristic
526C4×D4D4×C15112yes—
527C4×D4C23×C15111yescharacteristic
528C4×D4C23×C15111yescharacteristic
529#117—22no—
530#117—21no—
531#117—21no—
532#117—21no—
533#117D4×C15111yescharacteristic
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C42—21no—
538C2×C42C23×C15111yescharacteristic
539#107—21no—
540#107—21no—
541#106—21no—
542#106—21no—
543C4⋊C8—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C15111yescharacteristic
546C4⋊C8C23×C15111yescharacteristic
547C4⋊C8C23×C15111yescharacteristic
548C4⋊C8C23×C15111yescharacteristic
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—21no—
555#102—21no—
556#102—22no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560C22⋊C8—21no—
561C4×C8—21no—
562C4×C8C23×C15111yescharacteristic
563C4×C8C23×C15111yescharacteristic
564C24—22no—
565#41—22no—
566#41—41no—
567#41—81no—
568#41—81no—
569#41—82no—
570C2×Q8—22no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—81no—
574C2×Q8—81no—
575C2×Q8C2×D4×C15111yescharacteristic
576C2×Q8C2×D4×C15111yescharacteristic
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—41no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C15111yescharacteristic
593C2×D4C2×D4×C15111yescharacteristic
594C2×D4C2×D4×C15112yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—41no—
603C22×C4C2×D4×C15111yescharacteristic
604C22×C4C2×D4×C15111yescharacteristic
605C22×C4C2×D4×C15111yescharacteristic
606SD16—42no—
607SD16—81no—
608SD16—82no—
609D8—42no—
610D8—81no—
611D8—82no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4C2×D4×C15112yes—
631C4⋊C4C2×D4×C15111yescharacteristic
632C4⋊C4C2×D4×C15111yescharacteristic
633C4⋊C4C2×D4×C15111yescharacteristic
634C4⋊C4C2×D4×C15111yescharacteristic
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C42—22no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42C2×D4×C15111yescharacteristic
660C42C2×D4×C15111yescharacteristic
661C42C2×D4×C15111yescharacteristic
662C42C24×C15111yescharacteristic
663C23—21no—
664C23—21no—
665C23—22no—
666C23—44no—
667C23—41no—
668C23—82no—
669C23—82no—
670C23#120×C15111yescharacteristic
671Q8—21no—
672Q8—21no—
673Q8—21no—
674Q8—21no—
675Q8—42no—
676Q8—41no—
677Q8—41no—
678Q8—82no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—82no—
695D4—81no—
696D4—82no—
697D4—82no—
698D4#135×C15112yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—82no—
718C2×C4—81no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C15111yescharacteristic
723C2×C4#120×C15111yescharacteristic
724C2×C4#120×C15111yescharacteristic
725C2×C4C22×D4×C15111yescharacteristic
726C2×C4C22×D4×C15111yescharacteristic
727C2×C4C22×D4×C15111yescharacteristic
728C8—41no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—22no—
736C22—21no—
737C22—21no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—164no—
750C22C2×#120×C15111yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—42no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—81no—
763C4C2×#135×C15111yescharacteristic
764C4#575×C15111yescharacteristic
765C4#576×C15111yescharacteristic
766C4#577×C15111yescharacteristic
767C2—41no—
768C2—42no—
769C2—81no—
770C2—82no—
771C2—161no—
772C2#3002×C15111yescharacteristic
773C2#3012×C15111yescharacteristic
774C2#3021×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. #3514×C151C2semidirect
2. #3247×C151C2semidirect
3. #3207×C151C2semidirect
4. #3106×C151C2semidirect
5. #1638×C151C2semidirect
6. #1637×C151C2semidirect
7. #1630×C151C2semidirect
8. #1629×C151C2semidirect
9. #1628×C151C2semidirect
10. #1627×C151C2semidirect
11. #1620×C151C2semidirect
12. #1619×C151C2semidirect
13. #1540×C151C2semidirect
14. #1482×C151C2semidirect
15. #1477×C151C2semidirect
28. #532×C151C22semidirect
36. #487×C151C22semidirect
37. #486×C151C22semidirect
40. #477×C151C22semidirect
41. #477×C151C22semidirect
48. #460×C151C22semidirect
49. #460×C151C22semidirect
56. #431×C151C22semidirect
57. #431×C151C22semidirect
58. C2×C4⋊C8×C151C22semidirect
59. #332×C151C22semidirect
60. #332×C151C22semidirect
63. Q8⋊C8×C151C22semidirect
64. Q8⋊C8×C151C22semidirect
65. Q8⋊C8×C151C22semidirect
66. Q8⋊C8×C151C22semidirect
387. #18890C151direct (N × H)
388. C151#18890direct (N × H)
389. #3514C2×C151semidirect
390. #3247C2×C151semidirect
391. #3207C2×C151semidirect
392. #3106C2×C151semidirect
393. #1638C2×C151semidirect
394. #1637C2×C151semidirect
395. #1630C2×C151semidirect
396. #1629C2×C151semidirect
397. #1628C2×C151semidirect
398. #1627C2×C151semidirect
399. #1620C2×C151semidirect
400. #1619C2×C151semidirect
401. #1540C2×C151semidirect
402. #1482C2×C151semidirect
403. #1477C2×C151semidirect
416. #532C22×C151semidirect
424. #487C22×C151semidirect
425. #486C22×C151semidirect
428. #477C22×C151semidirect
429. #477C22×C151semidirect
436. #460C22×C151semidirect
437. #460C22×C151semidirect
444. #431C22×C151semidirect
445. #431C22×C151semidirect
446. C2×C4⋊C8C22×C151semidirect
447. #332C22×C151semidirect
448. #332C22×C151semidirect
451. Q8⋊C8C22×C151semidirect
452. Q8⋊C8C22×C151semidirect
453. Q8⋊C8C22×C151semidirect
454. Q8⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3514×C1512
#3247×C1512
#3207×C1512
#3106×C1512
#1638×C1512
#1637×C1512
#1630×C1512
#1629×C1512
#1628×C1512
#1627×C1512
#1620×C1512
#1619×C1512
#1540×C1512
#1482×C1512
#1477×C1512
#18890151