Finite Group Databasebeta

← C151×#18671 #50323596

Subgroups — C151×#18671 #50323596

Order 38656.

928 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3517×C151C211yesmaximal, characteristic
2#3233×C151C211yesmaximal, characteristic, complemented
3#3167×C151C211yesmaximal, characteristic, complemented
4#3116×C151C211yesmaximal, characteristic, complemented
5#1654×C151C211yesmaximal, characteristic, complemented
6#1653×C151C211yesmaximal, characteristic, complemented
7#1642×C151C211yesmaximal, characteristic, complemented
8#1641×C151C211yesmaximal, characteristic, complemented
9#1636×C151C211yesmaximal, characteristic, complemented
10#1635×C151C211yesmaximal, characteristic, complemented
11#1631×C151C211yesmaximal, characteristic, complemented
12#1631×C151C211yesmaximal, characteristic, complemented
13#1553×C151C211yesmaximal, characteristic, complemented
14#1494×C151C211yesmaximal, characteristic, complemented
15#1476×C151C211yesmaximal, characteristic, complemented
16#557×C151C2211yescharacteristic
17#553×C151—22no—
18#553×C151—21no—
19#550×C151—21no—
20#550×C151—21no—
21#550×C151C2211yescharacteristic
22#550×C151C2211yescharacteristic
23#547×C151—21no—
24#547×C151C2211yescharacteristic
25#540×C151—22no—
26#540×C151—21no—
27#533×C151C2211yescharacteristic
28#532×C151—21no—
29#532×C151C2211yescharacteristic
30#529×C151—21no—
31#529×C151C2211yescharacteristic
32#520×C151—21no—
33C4×#41×C151C2211yescharacteristic
34#499×C151—21no—
35#498×C151C2211yescharacteristic
36#492×C151C2211yescharacteristic
37#488×C151—21no—
38#487×C151C2211yescharacteristic
39#486×C151C2211yescharacteristic
40#485×C151—21no—
41#485×C151—21no—
42#482×C151—21no—
43#477×C151C2211yescharacteristic
44#477×C151C2211yescharacteristic
45#476×C151C2211yescharacteristic
46#476×C151C2211yescharacteristic
47#475×C151C2211yescharacteristic
48#474×C151C2211yescharacteristic
49#465×C151—22no—
50#462×C151C2211yescharacteristic
51#461×C151C2211yescharacteristic
52#452×C151—21no—
53#441×C151—21no—
54#440×C151—21no—
55C4×SD16×C151—22no—
56#432×C151C2211yescharacteristic
57#431×C151C2211yescharacteristic
58C2×C4×C8×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×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—21no—
73C2×#41×C151—21no—
74C2×#41×C151—21no—
75C2×#41×C151D411yescharacteristic
76C2×Q16×C151—21no—
77C2×SD16×C151—22no—
78C2×SD16×C151—21no—
79C22×C8×C151—21no—
80C4⋊Q8×C151—21no—
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84#127×C151—22no—
85#127×C151—21no—
86#127×C151—21no—
87#127×C151C2311yescharacteristic
88#126×C151—22no—
89#126×C151—21no—
90#125×C151—22no—
91#125×C151—21no—
92#125×C151—21no—
93#125×C151D411yescharacteristic
94#124×C151—21no—
95#124×C151D411yescharacteristic
96#123×C151—22no—
97#123×C151—22no—
98#123×C151—22no—
99#123×C151—21no—
100#123×C151—22no—
101C22⋊Q8×C151—21no—
102C22⋊Q8×C151—21no—
103C22⋊Q8×C151—21no—
104C22⋊Q8×C151D411yescharacteristic
105#121×C151—22no—
106#121×C151—22no—
107#121×C151—22no—
108#121×C151—22no—
109#121×C151—22no—
110#121×C151—21no—
111#121×C151—22no—
112#121×C151—22no—
113#121×C151—21no—
114#121×C151—21no—
115#121×C151—21no—
116#121×C151D412yes—
117#121×C151D411yescharacteristic
118C4×Q8×C151—21no—
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—22no—
128C4×D4×C151—22no—
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×C151D412yes—
136C4×D4×C151D411yescharacteristic
137C4×D4×C151C2311yescharacteristic
138C4×D4×C151C2311yescharacteristic
139#117×C151—22no—
140#117×C151—21no—
141#117×C151—21no—
142#117×C151—21no—
143#117×C151D411yescharacteristic
144C2×C4⋊C4×C151—22no—
145C2×C4⋊C4×C151—21no—
146C2×C42×C151—21no—
147C2×C42×C151C2311yescharacteristic
148#107×C151—21no—
149#107×C151—21no—
150#107×C151—21no—
151#106×C151—22no—
152#106×C151—21no—
153#106×C151—21no—
154#106×C151—21no—
155C4⋊C8×C151C2311yescharacteristic
156C4⋊C8×C151C2311yescharacteristic
157C4⋊C8×C151C2311yescharacteristic
158C4⋊C8×C151C2311yescharacteristic
159#103×C151—22no—
160#103×C151—21no—
161#103×C151—21no—
162#103×C151—21no—
163#103×C151—21no—
164#103×C151—21no—
165#102×C151—22no—
166#102×C151—21no—
167#102×C151—21no—
168#102×C151—21no—
169C22⋊C8×C151—21no—
170C22⋊C8×C151—21no—
171#97×C151—21no—
172C4×C8×C151—21no—
173C4×C8×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176#41×C151—22no—
177#41×C151—41no—
178#41×C151—42no—
179#41×C151—42no—
180#41×C151—81no—
181#41×C151—81no—
182#41×C151—81no—
183#41×C151—81no—
184#41×C151—81no—
185#41×C151—81no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151C2×D411yescharacteristic
190C2×Q8×C151C2×D411yescharacteristic
191C2×D4×C151—22no—
192C2×D4×C151—21no—
193C2×D4×C151—22no—
194C2×D4×C151—22no—
195C2×D4×C151—22no—
196C2×D4×C151—22no—
197C2×D4×C151—21no—
198C2×D4×C151—22no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151C2×D411yescharacteristic
202C2×D4×C151C2×D411yescharacteristic
203C2×D4×C151C2×D412yes—
204C22×C4×C151—22no—
205C22×C4×C151—22no—
206C22×C4×C151—22no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—22no—
212C22×C4×C151C2×D411yescharacteristic
213C22×C4×C151C2×D411yescharacteristic
214C22×C4×C151C2×D411yescharacteristic
215Q16×C151—42no—
216SD16×C151—44no—
217SD16×C151—42no—
218C2×C8×C151—21no—
219C2×C8×C151—21no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—42no—
225C4⋊C4×C151—22no—
226C4⋊C4×C151—22no—
227C4⋊C4×C151—22no—
228C4⋊C4×C151—22no—
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—21no—
238C4⋊C4×C151—21no—
239C4⋊C4×C151—21no—
240C4⋊C4×C151—41no—
241C4⋊C4×C151—41no—
242C4⋊C4×C151C2×D411yescharacteristic
243C4⋊C4×C151C2×D412yes—
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—21no—
251C22⋊C4×C151—21no—
252C22⋊C4×C151—21no—
253C22⋊C4×C151—21no—
254C22⋊C4×C151—22no—
255C22⋊C4×C151—21no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—22no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—21no—
260C22⋊C4×C151—41no—
261C42×C151—22no—
262C42×C151—21no—
263C42×C151—21no—
264C42×C151—21no—
265C42×C151—21no—
266C42×C151—41no—
267C42×C151C2×D411yescharacteristic
268C42×C151C2×D411yescharacteristic
269C42×C151C2×D411yescharacteristic
270C42×C151C2411yescharacteristic
271C23×C151—21no—
272C23×C151—21no—
273C23×C151—22no—
274C23×C151#12011yescharacteristic
275Q8×C151—21no—
276Q8×C151—21no—
277Q8×C151—21no—
278Q8×C151—42no—
279Q8×C151—41no—
280Q8×C151—41no—
281Q8×C151—41no—
282Q8×C151—41no—
283Q8×C151#13512yes—
284D4×C151—21no—
285D4×C151—21no—
286D4×C151—21no—
287D4×C151—21no—
288D4×C151—42no—
289D4×C151—42no—
290D4×C151—44no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—82no—
296D4×C151—81no—
297D4×C151—82no—
298D4×C151—82no—
299D4×C151—82no—
300D4×C151—82no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—22no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—41no—
313C2×C4×C151—42no—
314C2×C4×C151—44no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—82no—
322C2×C4×C151—81no—
323C2×C4×C151—82no—
324C2×C4×C151—82no—
325C2×C4×C151#12011yescharacteristic
326C2×C4×C151#12011yescharacteristic
327C2×C4×C151#12011yescharacteristic
328C2×C4×C151C22×D411yescharacteristic
329C2×C4×C151C22×D411yescharacteristic
330C2×C4×C151C22×D411yescharacteristic
331C8×C151—22no—
332C8×C151—41no—
333C8×C151—41no—
334C8×C151—41no—
335C8×C151—41no—
336C8×C151—41no—
337C22×C151—21no—
338C22×C151—21no—
339C22×C151—21no—
340C22×C151—41no—
341C22×C151—42no—
342C22×C151—41no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—42no—
346C22×C151—41no—
347C22×C151—42no—
348C22×C151—41no—
349C22×C151C2×#12011yescharacteristic
350C4×C151—21no—
351C4×C151—22no—
352C4×C151—21no—
353C4×C151—21no—
354C4×C151—21no—
355C4×C151—41no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151—42no—
359C4×C151—41no—
360C4×C151—41no—
361C4×C151—81no—
362C4×C151—81no—
363C4×C151C2×#13511yescharacteristic
364C4×C151#57511yescharacteristic
365C4×C151#57711yescharacteristic
366C4×C151#57711yescharacteristic
367C2×C151—41no—
368C2×C151—81no—
369C2×C151—81no—
370C2×C151—82no—
371C2×C151#300211yescharacteristic
372C2×C151#300911yescharacteristic
373C2×C151#301811yescharacteristic
374#18671C15111yesmaximal, characteristic, direct product factor, Sylow
375C151#1867111yescharacteristic, direct product factor, Sylow
376#3517C2×C15111yescharacteristic
377#3233C2×C15111yescharacteristic, complemented
378#3167C2×C15111yescharacteristic, complemented
379#3116C2×C15111yescharacteristic, complemented
380#1654C2×C15111yescharacteristic, complemented
381#1653C2×C15111yescharacteristic, complemented
382#1642C2×C15111yescharacteristic, complemented
383#1641C2×C15111yescharacteristic, complemented
384#1636C2×C15111yescharacteristic, complemented
385#1635C2×C15111yescharacteristic, complemented
386#1631C2×C15111yescharacteristic, complemented
387#1631C2×C15111yescharacteristic, complemented
388#1553C2×C15111yescharacteristic, complemented
389#1494C2×C15111yescharacteristic, complemented
390#1476C2×C15111yescharacteristic, complemented
391#557C22×C15111yescharacteristic
392#553—22no—
393#553—21no—
394#550—21no—
395#550—21no—
396#550C22×C15111yescharacteristic
397#550C22×C15111yescharacteristic
398#547—21no—
399#547C22×C15111yescharacteristic
400#540—22no—
401#540—21no—
402#533C22×C15111yescharacteristic
403#532—21no—
404#532C22×C15111yescharacteristic
405#529—21no—
406#529C22×C15111yescharacteristic
407#520—21no—
408C4×#41C22×C15111yescharacteristic
409#499—21no—
410#498C22×C15111yescharacteristic
411#492C22×C15111yescharacteristic
412#488—21no—
413#487C22×C15111yescharacteristic
414#486C22×C15111yescharacteristic
415#485—21no—
416#485—21no—
417#482—21no—
418#477C22×C15111yescharacteristic
419#477C22×C15111yescharacteristic
420#476C22×C15111yescharacteristic
421#476C22×C15111yescharacteristic
422#475C22×C15111yescharacteristic
423#474C22×C15111yescharacteristic
424#465—22no—
425#462C22×C15111yescharacteristic
426#461C22×C15111yescharacteristic
427#452—21no—
428#441—21no—
429#440—21no—
430C4×SD16—22no—
431#432C22×C15111yescharacteristic
432#431C22×C15111yescharacteristic
433C2×C4×C8C22×C15111yescharacteristic
434#332C22×C15111yescharacteristic
435#332C22×C15111yescharacteristic
436#331C22×C15111yescharacteristic
437#331C22×C15111yescharacteristic
438Q8⋊C8C22×C15111yescharacteristic
439Q8⋊C8C22×C15111yescharacteristic
440Q8⋊C8C22×C15111yescharacteristic
441Q8⋊C8C22×C15111yescharacteristic
442D4⋊C8C22×C15111yescharacteristic
443D4⋊C8C22×C15111yescharacteristic
444D4⋊C8C22×C15111yescharacteristic
445D4⋊C8C22×C15111yescharacteristic
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41D4×C15111yescharacteristic
451C2×Q16—21no—
452C2×SD16—22no—
453C2×SD16—21no—
454C22×C8—21no—
455C4⋊Q8—21no—
456C4⋊Q8C23×C15111yescharacteristic
457C4⋊Q8C23×C15111yescharacteristic
458C4⋊Q8C23×C15111yescharacteristic
459#127—22no—
460#127—21no—
461#127—21no—
462#127C23×C15111yescharacteristic
463#126—22no—
464#126—21no—
465#125—22no—
466#125—21no—
467#125—21no—
468#125D4×C15111yescharacteristic
469#124—21no—
470#124D4×C15111yescharacteristic
471#123—22no—
472#123—22no—
473#123—22no—
474#123—21no—
475#123—22no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8D4×C15111yescharacteristic
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—21no—
490#121—21no—
491#121D4×C15111yescharacteristic
492#121D4×C15112yes—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8D4×C15111yescharacteristic
498C4×Q8C23×C15111yescharacteristic
499C4×Q8C23×C15111yescharacteristic
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4D4×C15111yescharacteristic
511C4×D4D4×C15112yes—
512C4×D4C23×C15111yescharacteristic
513C4×D4C23×C15111yescharacteristic
514#117—22no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117D4×C15111yescharacteristic
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C42—21no—
522C2×C42C23×C15111yescharacteristic
523#107—21no—
524#107—21no—
525#107—21no—
526#106—22no—
527#106—21no—
528#106—21no—
529#106—21no—
530C4⋊C8C23×C15111yescharacteristic
531C4⋊C8C23×C15111yescharacteristic
532C4⋊C8C23×C15111yescharacteristic
533C4⋊C8C23×C15111yescharacteristic
534#103—21no—
535#103—21no—
536#103—21no—
537#103—22no—
538#103—21no—
539#103—21no—
540#102—22no—
541#102—21no—
542#102—21no—
543#102—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546#97—21no—
547C4×C8—21no—
548C4×C8—21no—
549C4×C8C23×C15111yescharacteristic
550C4×C8C23×C15111yescharacteristic
551#41—22no—
552#41—41no—
553#41—42no—
554#41—42no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560#41—81no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8C2×D4×C15111yescharacteristic
565C2×Q8C2×D4×C15111yescharacteristic
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4C2×D4×C15111yescharacteristic
577C2×D4C2×D4×C15111yescharacteristic
578C2×D4C2×D4×C15112yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4C2×D4×C15111yescharacteristic
588C22×C4C2×D4×C15111yescharacteristic
589C22×C4C2×D4×C15111yescharacteristic
590Q16—42no—
591SD16—44no—
592SD16—42no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—42no—
600C4⋊C4—22no—
601C4⋊C4—22no—
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×C15112yes—
619C4⋊C4C2×D4×C15111yescharacteristic
620C4⋊C4C2×D4×C15111yescharacteristic
621C4⋊C4C2×D4×C15111yescharacteristic
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—22no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—41no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—41no—
642C42C2×D4×C15111yescharacteristic
643C42C2×D4×C15111yescharacteristic
644C42C2×D4×C15111yescharacteristic
645C42C24×C15111yescharacteristic
646C23—21no—
647C23—21no—
648C23—22no—
649C23#120×C15111yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—42no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8#135×C15112yes—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—42no—
664D4—42no—
665D4—44no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—82no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—82no—
675D4—82no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—82no—
697C2×C4—81no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4#120×C15111yescharacteristic
701C2×C4#120×C15111yescharacteristic
702C2×C4#120×C15111yescharacteristic
703C2×C4C22×D4×C15111yescharacteristic
704C2×C4C22×D4×C15111yescharacteristic
705C2×C4C22×D4×C15111yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C8—41no—
711C8—41no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22C2×#120×C15111yescharacteristic
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—42no—
734C4—41no—
735C4—41no—
736C4—81no—
737C4—81no—
738C4C2×#135×C15111yescharacteristic
739C4#575×C15111yescharacteristic
740C4#577×C15111yescharacteristic
741C4#577×C15111yescharacteristic
742C2—41no—
743C2—81no—
744C2—81no—
745C2—82no—
746C2#3002×C15111yescharacteristic
747C2#3009×C15111yescharacteristic
748C2#3018×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3517×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. #3233×C151C2semidirect
3. #3167×C151C2semidirect
4. #3116×C151C2semidirect
5. #1654×C151C2semidirect
6. #1653×C151C2semidirect
7. #1642×C151C2semidirect
8. #1641×C151C2semidirect
9. #1636×C151C2semidirect
10. #1635×C151C2semidirect
11. #1631×C151C2semidirect
12. #1631×C151C2semidirect
13. #1553×C151C2semidirect
14. #1494×C151C2semidirect
15. #1476×C151C2semidirect
374. #18671C151direct (N × H)
375. C151#18671direct (N × H)
377. #3233C2×C151semidirect
378. #3167C2×C151semidirect
379. #3116C2×C151semidirect
380. #1654C2×C151semidirect
381. #1653C2×C151semidirect
382. #1642C2×C151semidirect
383. #1641C2×C151semidirect
384. #1636C2×C151semidirect
385. #1635C2×C151semidirect
386. #1631C2×C151semidirect
387. #1631C2×C151semidirect
388. #1553C2×C151semidirect
389. #1494C2×C151semidirect
390. #1476C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3517×C1512
#3233×C1512
#3167×C1512
#3116×C1512
#1654×C1512
#1653×C1512
#1642×C1512
#1641×C1512
#1636×C1512
#1635×C1512
#1631×C1512
#1553×C1512
#1494×C1512
#1476×C1512
#18671151