Finite Group Databasebeta

← C151×#18900 #50323825

Subgroups — C151×#18900 #50323825

Order 38656.

930 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3514×C151C211yesmaximal, characteristic
2#3248×C151C211yesmaximal, characteristic, complemented
3#3228×C151C211yesmaximal, characteristic, complemented
4#3107×C151C211yesmaximal, characteristic, complemented
5#1652×C151C211yesmaximal, characteristic, complemented
6#1651×C151C211yesmaximal, characteristic, complemented
7#1650×C151C211yesmaximal, characteristic, complemented
8#1649×C151C211yesmaximal, characteristic, complemented
9#1640×C151C211yesmaximal, characteristic, complemented
10#1640×C151C211yesmaximal, characteristic, complemented
11#1639×C151C211yesmaximal, characteristic, complemented
12#1639×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#533×C151C2211yescharacteristic, complemented
28#532×C151C2211yescharacteristic
29#529×C151—21no—
30#529×C151C2211yescharacteristic
31C2×#124×C151—21no—
32#518×C151—21no—
33C4×#41×C151C2211yescharacteristic
34#500×C151C2211yescharacteristic, complemented
35#498×C151C2211yescharacteristic, complemented
36#486×C151C2211yescharacteristic
37#486×C151C2211yescharacteristic
38#485×C151—21no—
39#482×C151—22no—
40#479×C151—21no—
41#478×C151—22no—
42#475×C151C2211yescharacteristic, complemented
43#475×C151C2211yescharacteristic, complemented
44#474×C151C2211yescharacteristic
45#474×C151C2211yescharacteristic
46#467×C151—21no—
47#465×C151—21no—
48#464×C151—21no—
49#462×C151C2211yescharacteristic, complemented
50#462×C151C2211yescharacteristic, complemented
51#461×C151C2211yescharacteristic
52#461×C151C2211yescharacteristic
53#452×C151—21no—
54C4×Q16×C151—21no—
55C4×SD16×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×C151D411yescharacteristic
73C22×Q8×C151—21no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C2×Q16×C151—21no—
77C2×Q16×C151—21no—
78C2×SD16×C151—21no—
79C2×SD16×C151—21no—
80C22×C8×C151—21no—
81C4⋊Q8×C151—21no—
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84C4⋊Q8×C151C2311yescharacteristic
85#127×C151C2311yescharacteristic
86#126×C151—22no—
87#126×C151—22no—
88#126×C151—21no—
89#125×C151—21no—
90#125×C151D411yescharacteristic
91#124×C151—22no—
92#124×C151—22no—
93#124×C151—22no—
94#124×C151—21no—
95#124×C151—21no—
96#124×C151—21no—
97#124×C151—21no—
98#124×C151D411yescharacteristic
99#123×C151—22no—
100#123×C151—22no—
101#123×C151—22no—
102#123×C151—21no—
103C22⋊Q8×C151—22no—
104C22⋊Q8×C151—21no—
105C22⋊Q8×C151—22no—
106C22⋊Q8×C151—21no—
107C22⋊Q8×C151—21no—
108C22⋊Q8×C151—21no—
109C22⋊Q8×C151D411yescharacteristic
110#121×C151—22no—
111#121×C151—22no—
112#121×C151—21no—
113#121×C151—21no—
114#121×C151—21no—
115#121×C151D411yescharacteristic
116#121×C151D412yes—
117#120×C151—22no—
118#120×C151—22no—
119C4×Q8×C151—21no—
120C4×Q8×C151—21no—
121C4×Q8×C151—21no—
122C4×Q8×C151D411yescharacteristic
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×C151—21no—
133C4×D4×C151—21no—
134C4×D4×C151D411yescharacteristic
135C4×D4×C151D412yes—
136C4×D4×C151C2311yescharacteristic
137C4×D4×C151C2311yescharacteristic
138#117×C151—22no—
139#117×C151—21no—
140#117×C151—21no—
141#117×C151—21no—
142#117×C151—21no—
143#117×C151D411yescharacteristic
144C2×C22⋊C4×C151—22no—
145C2×C22⋊C4×C151—22no—
146C2×C22⋊C4×C151—22no—
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#102×C151—21no—
168#102×C151—21no—
169#102×C151—22no—
170#102×C151—22no—
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—
181C2×Q8×C151—22no—
182C2×Q8×C151—21no—
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—42no—
197C2×D4×C151—42no—
198C2×D4×C151—81no—
199C2×D4×C151—81no—
200C2×D4×C151C2×D411yescharacteristic
201C2×D4×C151C2×D411yescharacteristic
202C2×D4×C151C2×D412yes—
203C22×C4×C151—22no—
204C22×C4×C151—22no—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—22no—
210C22×C4×C151C2×D411yescharacteristic
211C22×C4×C151C2×D411yescharacteristic
212C22×C4×C151C2×D411yescharacteristic
213Q16×C151—42no—
214Q16×C151—81no—
215SD16×C151—42no—
216SD16×C151—81no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—21no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—81no—
224C4⋊C4×C151—22no—
225C4⋊C4×C151—22no—
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—21no—
236C4⋊C4×C151—21no—
237C4⋊C4×C151—41no—
238C4⋊C4×C151—41no—
239C4⋊C4×C151C2×D411yescharacteristic
240C4⋊C4×C151C2×D411yescharacteristic
241C4⋊C4×C151C2×D411yescharacteristic
242C4⋊C4×C151C2×D411yescharacteristic
243C4⋊C4×C151C2×D412yes—
244C22⋊C4×C151—22no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151—22no—
248C22⋊C4×C151—22no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—22no—
251C22⋊C4×C151—21no—
252C22⋊C4×C151—21no—
253C22⋊C4×C151—21no—
254C22⋊C4×C151—21no—
255C22⋊C4×C151—21no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—22no—
258C22⋊C4×C151—22no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—21no—
261C22⋊C4×C151—41no—
262C42×C151—22no—
263C42×C151—21no—
264C42×C151—21no—
265C42×C151—21no—
266C42×C151—21no—
267C42×C151—41no—
268C42×C151C2×D411yescharacteristic
269C42×C151C2×D411yescharacteristic
270C42×C151C2×D411yescharacteristic
271C42×C151C2411yescharacteristic
272C23×C151—21no—
273C23×C151—21no—
274C23×C151—22no—
275C23×C151—44no—
276C23×C151—82no—
277C23×C151—82no—
278C23×C151#12011yescharacteristic
279Q8×C151—21no—
280Q8×C151—21no—
281Q8×C151—21no—
282Q8×C151—21no—
283Q8×C151—41no—
284Q8×C151—41no—
285Q8×C151—41no—
286Q8×C151—41no—
287Q8×C151—41no—
288Q8×C151—41no—
289Q8×C151—82no—
290D4×C151—21no—
291D4×C151—21no—
292D4×C151—21no—
293D4×C151—42no—
294D4×C151—42no—
295D4×C151—44no—
296D4×C151—41no—
297D4×C151—41no—
298D4×C151—41no—
299D4×C151—41no—
300D4×C151—82no—
301D4×C151—81no—
302D4×C151—82no—
303D4×C151#13512yes—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—22no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—41no—
316C2×C4×C151—42no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—82no—
324C2×C4×C151—81no—
325C2×C4×C151—82no—
326C2×C4×C151—82no—
327C2×C4×C151#12011yescharacteristic
328C2×C4×C151#12011yescharacteristic
329C2×C4×C151#12011yescharacteristic
330C2×C4×C151C22×D411yescharacteristic
331C2×C4×C151C22×D411yescharacteristic
332C2×C4×C151C22×D411yescharacteristic
333C8×C151—41no—
334C8×C151—41no—
335C8×C151—41no—
336C8×C151—41no—
337C8×C151—41no—
338C8×C151—41no—
339C22×C151—21no—
340C22×C151—22no—
341C22×C151—21no—
342C22×C151—21no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—41no—
346C22×C151—42no—
347C22×C151—42no—
348C22×C151—41no—
349C22×C151—42no—
350C22×C151—41no—
351C22×C151—164no—
352C22×C151C2×#12011yescharacteristic
353C4×C151—21no—
354C4×C151—21no—
355C4×C151—21no—
356C4×C151—21no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—41no—
360C4×C151—42no—
361C4×C151—41no—
362C4×C151—41no—
363C4×C151—41no—
364C4×C151—81no—
365C4×C151—81no—
366C4×C151C2×#13511yescharacteristic
367C4×C151#57511yescharacteristic
368C4×C151#57611yescharacteristic
369C4×C151#57711yescharacteristic
370C2×C151—41no—
371C2×C151—42no—
372C2×C151—82no—
373C2×C151—81no—
374C2×C151#300211yescharacteristic
375C2×C151#301211yescharacteristic
376C2×C151#302211yescharacteristic
377#18900C15111yesmaximal, characteristic, direct product factor, Sylow
378C151#1890011yescharacteristic, direct product factor, Sylow
379#3514C2×C15111yescharacteristic
380#3248C2×C15111yescharacteristic, complemented
381#3228C2×C15111yescharacteristic, complemented
382#3107C2×C15111yescharacteristic, complemented
383#1652C2×C15111yescharacteristic, complemented
384#1651C2×C15111yescharacteristic, complemented
385#1650C2×C15111yescharacteristic, complemented
386#1649C2×C15111yescharacteristic, complemented
387#1640C2×C15111yescharacteristic, complemented
388#1640C2×C15111yescharacteristic, complemented
389#1639C2×C15111yescharacteristic, complemented
390#1639C2×C15111yescharacteristic, complemented
391#1540C2×C15111yescharacteristic, complemented
392#1482C2×C15111yescharacteristic, complemented
393#1477C2×C15111yescharacteristic, complemented
394#559C22×C15111yescharacteristic
395#556C22×C15111yescharacteristic
396#555—21no—
397#551—22no—
398D4×Q8C22×C15111yescharacteristic
399#548—21no—
400#546—21no—
401#546—21no—
402D42C22×C15111yescharacteristic
403#542—21no—
404#538—22no—
405#533C22×C15111yescharacteristic, complemented
406#532C22×C15111yescharacteristic
407#529—21no—
408#529C22×C15111yescharacteristic
409C2×#124—21no—
410#518—21no—
411C4×#41C22×C15111yescharacteristic
412#500C22×C15111yescharacteristic, complemented
413#498C22×C15111yescharacteristic, complemented
414#486C22×C15111yescharacteristic
415#486C22×C15111yescharacteristic
416#485—21no—
417#482—22no—
418#479—21no—
419#478—22no—
420#475C22×C15111yescharacteristic, complemented
421#475C22×C15111yescharacteristic, complemented
422#474C22×C15111yescharacteristic
423#474C22×C15111yescharacteristic
424#467—21no—
425#465—21no—
426#464—21no—
427#462C22×C15111yescharacteristic, complemented
428#462C22×C15111yescharacteristic, complemented
429#461C22×C15111yescharacteristic
430#461C22×C15111yescharacteristic
431#452—21no—
432C4×Q16—21no—
433C4×SD16—21no—
434#431C22×C15111yescharacteristic, complemented
435#431C22×C15111yescharacteristic, complemented
436C2×C4⋊C8C22×C15111yescharacteristic, complemented
437#332C22×C15111yescharacteristic, complemented
438#332C22×C15111yescharacteristic, complemented
439#331C22×C15111yescharacteristic
440#331C22×C15111yescharacteristic
441Q8⋊C8C22×C15111yescharacteristic, complemented
442Q8⋊C8C22×C15111yescharacteristic, complemented
443Q8⋊C8C22×C15111yescharacteristic, complemented
444Q8⋊C8C22×C15111yescharacteristic, complemented
445D4⋊C8C22×C15111yescharacteristic
446D4⋊C8C22×C15111yescharacteristic
447D4⋊C8C22×C15111yescharacteristic
448D4⋊C8C22×C15111yescharacteristic
449C2×#41—21no—
450C2×#41D4×C15111yescharacteristic
451C22×Q8—21no—
452C22×D4—21no—
453C22×D4—21no—
454C2×Q16—21no—
455C2×Q16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C22×C8—21no—
459C4⋊Q8—21no—
460C4⋊Q8C23×C15111yescharacteristic
461C4⋊Q8C23×C15111yescharacteristic
462C4⋊Q8C23×C15111yescharacteristic
463#127C23×C15111yescharacteristic
464#126—22no—
465#126—22no—
466#126—21no—
467#125—21no—
468#125D4×C15111yescharacteristic
469#124—22no—
470#124—22no—
471#124—22no—
472#124—21no—
473#124—21no—
474#124—21no—
475#124—21no—
476#124D4×C15111yescharacteristic
477#123—22no—
478#123—22no—
479#123—22no—
480#123—21no—
481C22⋊Q8—22no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—22no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8D4×C15111yescharacteristic
488#121—22no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—21no—
493#121D4×C15111yescharacteristic
494#121D4×C15112yes—
495#120—22no—
496#120—22no—
497C4×Q8—21no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8D4×C15111yescharacteristic
501C4×Q8C23×C15111yescharacteristic
502C4×Q8C23×C15111yescharacteristic
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4D4×C15111yescharacteristic
513C4×D4D4×C15112yes—
514C4×D4C23×C15111yescharacteristic
515C4×D4C23×C15111yescharacteristic
516#117—22no—
517#117—21no—
518#117—21no—
519#117—21no—
520#117—21no—
521#117D4×C15111yescharacteristic
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C42—21no—
526C2×C42C23×C15111yescharacteristic
527#107—21no—
528#107—21no—
529#107—22no—
530#106—21no—
531#106—21no—
532#106—22no—
533C4⋊C8—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C15111yescharacteristic
536C4⋊C8C23×C15111yescharacteristic
537C4⋊C8C23×C15111yescharacteristic
538C4⋊C8C23×C15111yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#103—21no—
543#103—21no—
544#103—21no—
545#102—21no—
546#102—21no—
547#102—22no—
548#102—22no—
549C22⋊C8—21no—
550C22⋊C8—21no—
551C4×C8—21no—
552C4×C8C23×C15111yescharacteristic
553C4×C8C23×C15111yescharacteristic
554C24—22no—
555#41—22no—
556#41—41no—
557#41—81no—
558#41—81no—
559C2×Q8—22no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—81no—
564C2×Q8—81no—
565C2×Q8C2×D4×C15111yescharacteristic
566C2×Q8C2×D4×C15111yescharacteristic
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4C2×D4×C15111yescharacteristic
579C2×D4C2×D4×C15111yescharacteristic
580C2×D4C2×D4×C15112yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4C2×D4×C15111yescharacteristic
589C22×C4C2×D4×C15111yescharacteristic
590C22×C4C2×D4×C15111yescharacteristic
591Q16—42no—
592Q16—81no—
593SD16—42no—
594SD16—81no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—81no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C4⋊C4C2×D4×C15111yescharacteristic
618C4⋊C4C2×D4×C15111yescharacteristic
619C4⋊C4C2×D4×C15111yescharacteristic
620C4⋊C4C2×D4×C15111yescharacteristic
621C4⋊C4C2×D4×C15112yes—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—41no—
640C42—22no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—41no—
646C42C2×D4×C15111yescharacteristic
647C42C2×D4×C15111yescharacteristic
648C42C2×D4×C15111yescharacteristic
649C42C24×C15111yescharacteristic
650C23—21no—
651C23—21no—
652C23—22no—
653C23—44no—
654C23—82no—
655C23—82no—
656C23#120×C15111yescharacteristic
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—21no—
671D4—42no—
672D4—42no—
673D4—44no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—82no—
679D4—81no—
680D4—82no—
681D4#135×C15112yes—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—81no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C15111yescharacteristic
706C2×C4#120×C15111yescharacteristic
707C2×C4#120×C15111yescharacteristic
708C2×C4C22×D4×C15111yescharacteristic
709C2×C4C22×D4×C15111yescharacteristic
710C2×C4C22×D4×C15111yescharacteristic
711C8—41no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C22—21no—
718C22—22no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—164no—
730C22C2×#120×C15111yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—81no—
743C4—81no—
744C4C2×#135×C15111yescharacteristic
745C4#575×C15111yescharacteristic
746C4#576×C15111yescharacteristic
747C4#577×C15111yescharacteristic
748C2—41no—
749C2—42no—
750C2—81no—
751C2—82no—
752C2#3002×C15111yescharacteristic
753C2#3012×C15111yescharacteristic
754C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3514×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. #3228×C151C2semidirect
4. #3107×C151C2semidirect
5. #1652×C151C2semidirect
6. #1651×C151C2semidirect
7. #1650×C151C2semidirect
8. #1649×C151C2semidirect
9. #1640×C151C2semidirect
10. #1640×C151C2semidirect
11. #1639×C151C2semidirect
12. #1639×C151C2semidirect
13. #1540×C151C2semidirect
14. #1482×C151C2semidirect
15. #1477×C151C2semidirect
27. #533×C151C22semidirect
34. #500×C151C22semidirect
35. #498×C151C22semidirect
42. #475×C151C22semidirect
43. #475×C151C22semidirect
49. #462×C151C22semidirect
50. #462×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
377. #18900C151direct (N × H)
378. C151#18900direct (N × H)
380. #3248C2×C151semidirect
381. #3228C2×C151semidirect
382. #3107C2×C151semidirect
383. #1652C2×C151semidirect
384. #1651C2×C151semidirect
385. #1650C2×C151semidirect
386. #1649C2×C151semidirect
387. #1640C2×C151semidirect
388. #1640C2×C151semidirect
389. #1639C2×C151semidirect
390. #1639C2×C151semidirect
391. #1540C2×C151semidirect
392. #1482C2×C151semidirect
393. #1477C2×C151semidirect
405. #533C22×C151semidirect
412. #500C22×C151semidirect
413. #498C22×C151semidirect
420. #475C22×C151semidirect
421. #475C22×C151semidirect
427. #462C22×C151semidirect
428. #462C22×C151semidirect
434. #431C22×C151semidirect
435. #431C22×C151semidirect
436. C2×C4⋊C8C22×C151semidirect
437. #332C22×C151semidirect
438. #332C22×C151semidirect
441. Q8⋊C8C22×C151semidirect
442. Q8⋊C8C22×C151semidirect
443. Q8⋊C8C22×C151semidirect
444. 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
#3248×C1512
#3228×C1512
#3107×C1512
#1652×C1512
#1651×C1512
#1650×C1512
#1649×C1512
#1640×C1512
#1639×C1512
#1540×C1512
#1482×C1512
#1477×C1512
#18900151