Finite Group Databasebeta

← C151×#18964 #50323889

Subgroups — C151×#18964 #50323889

Order 38656.

900 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#3554×C151C211yesmaximal, characteristic, complemented
2#3254×C151C211yesmaximal, characteristic, complemented
3#3247×C151C211yesmaximal, characteristic, complemented
4#3207×C151C211yesmaximal, characteristic, complemented
5#1637×C151C211yesmaximal, characteristic, complemented
6#1636×C151C211yesmaximal, characteristic, complemented
7#1631×C151C211yesmaximal, characteristic, complemented
8#1630×C151C211yesmaximal, characteristic, complemented
9#1627×C151C211yesmaximal, characteristic, complemented
10#1626×C151C211yesmaximal, characteristic, complemented
11#1621×C151C211yesmaximal, characteristic, complemented
12#1620×C151C211yesmaximal, characteristic, complemented
13#1547×C151C211yesmaximal, characteristic, complemented
14#1495×C151C211yesmaximal, characteristic, complemented
15#1481×C151C211yesmaximal, characteristic, complemented
16#562×C151—22no—
17#559×C151—21no—
18#559×C151C2211yescharacteristic
19#557×C151C2211yescharacteristic
20#554×C151—21no—
21#550×C151C2211yescharacteristic
22D4×Q8×C151C2211yescharacteristic
23#548×C151—21no—
24#547×C151—21no—
25#542×C151—21no—
26#542×C151—21no—
27#540×C151—21no—
28#539×C151—22no—
29#536×C151—21no—
30#533×C151C2211yescharacteristic
31#532×C151C2211yescharacteristic
32#532×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34#493×C151C2211yescharacteristic
35#492×C151C2211yescharacteristic
36#487×C151C2211yescharacteristic
37#486×C151C2211yescharacteristic
38#478×C151—21no—
39#477×C151C2211yescharacteristic
40#477×C151C2211yescharacteristic
41#477×C151C2211yescharacteristic
42#476×C151C2211yescharacteristic
43#474×C151—21no—
44#468×C151—21no—
45#468×C151—21no—
46#466×C151—21no—
47#465×C151—21no—
48#463×C151—21no—
49#463×C151—22no—
50#461×C151—21no—
51#460×C151C2211yescharacteristic
52#460×C151C2211yescharacteristic
53#460×C151C2211yescharacteristic
54#459×C151C2211yescharacteristic
55#449×C151—22no—
56#431×C151C2211yescharacteristic
57#423×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
67Q8⋊C8×C151C2211yescharacteristic
68Q8⋊C8×C151C2211yescharacteristic
69D4⋊C8×C151C2211yescharacteristic
70D4⋊C8×C151C2211yescharacteristic
71C2×#41×C151—21no—
72C2×#41×C151—21no—
73C2×#41×C151—21no—
74C22×Q8×C151—21no—
75C2×SD16×C151—22no—
76C2×SD16×C151—21no—
77C2×SD16×C151—21no—
78C2×SD16×C151—21no—
79C2×D8×C151—22no—
80C2×D8×C151—21no—
81C2×M16×C151—21no—
82C22×C8×C151—21no—
83C4⋊Q8×C151—21no—
84C4⋊Q8×C151—21no—
85C4⋊Q8×C151D411yescharacteristic
86C4⋊Q8×C151D411yescharacteristic
87C4⋊Q8×C151C2311yescharacteristic
88C4⋊Q8×C151C2311yescharacteristic
89#127×C151—21no—
90#127×C151C2311yescharacteristic
91#127×C151C2311yescharacteristic
92#126×C151—22no—
93#126×C151—21no—
94#125×C151—22no—
95#125×C151—21no—
96#125×C151—21no—
97#125×C151D411yescharacteristic
98#124×C151—22no—
99#124×C151—22no—
100#124×C151—21no—
101#124×C151—21no—
102#124×C151—21no—
103#124×C151—21no—
104#124×C151D411yescharacteristic
105#123×C151—22no—
106#123×C151—22no—
107#123×C151—22no—
108#123×C151—22no—
109#123×C151—22no—
110#123×C151—22no—
111#123×C151—21no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—22no—
116C22⋊Q8×C151—21no—
117C22⋊Q8×C151—22no—
118C22⋊Q8×C151—21no—
119C22⋊Q8×C151D411yescharacteristic
120C22⋊Q8×C151D411yescharacteristic
121C22⋊Q8×C151D411yescharacteristic
122#121×C151—22no—
123#121×C151—22no—
124#121×C151—22no—
125#121×C151—21no—
126#121×C151—21no—
127#121×C151—21no—
128#121×C151—21no—
129#121×C151D412yes—
130#121×C151D411yescharacteristic
131C4×Q8×C151—21no—
132C4×Q8×C151—21no—
133C4×Q8×C151—21no—
134C4×Q8×C151C2311yescharacteristic
135C4×Q8×C151C2311yescharacteristic
136C4×Q8×C151C2311yescharacteristic
137C4×D4×C151—22no—
138C4×D4×C151—21no—
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×C151D412yes—
147C4×D4×C151C2311yescharacteristic
148#117×C151—21no—
149#117×C151—21no—
150C2×C4⋊C4×C151—22no—
151C2×C42×C151C2311yescharacteristic
152#107×C151—21no—
153#107×C151—21no—
154#107×C151—21no—
155#106×C151—21no—
156C4⋊C8×C151—21no—
157C4⋊C8×C151—21no—
158C4⋊C8×C151—21no—
159C4⋊C8×C151C2311yescharacteristic
160C4⋊C8×C151C2311yescharacteristic
161C4⋊C8×C151C2311yescharacteristic
162C4⋊C8×C151C2311yescharacteristic
163#103×C151—22no—
164#103×C151—21no—
165#103×C151—21no—
166#103×C151—21no—
167#102×C151—21no—
168#102×C151—22no—
169#102×C151—21no—
170#102×C151—21no—
171#102×C151—21no—
172#102×C151—21no—
173C22⋊C8×C151—21no—
174C4×C8×C151C2311yescharacteristic
175C4×C8×C151C2311yescharacteristic
176#41×C151—81no—
177#41×C151—81no—
178#41×C151—81no—
179#41×C151—81no—
180#41×C151—82no—
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×Q8×C151C2×D411yescharacteristic
190C2×D4×C151—22no—
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—41no—
200C2×D4×C151C2×D411yescharacteristic
201C2×D4×C151C2×D412yes—
202C22×C4×C151—22no—
203C22×C4×C151—22no—
204C22×C4×C151—22no—
205C22×C4×C151—21no—
206C22×C4×C151—22no—
207C22×C4×C151—41no—
208C22×C4×C151C2×D411yescharacteristic
209C22×C4×C151C2×D411yescharacteristic
210C22×C4×C151C2×D411yescharacteristic
211SD16×C151—81no—
212SD16×C151—81no—
213SD16×C151—81no—
214SD16×C151—82no—
215D8×C151—81no—
216D8×C151—82no—
217M16×C151—81no—
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—81no—
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—21no—
241C4⋊C4×C151—21no—
242C4⋊C4×C151—21no—
243C4⋊C4×C151C2×D412yes—
244C4⋊C4×C151C2×D411yescharacteristic
245C4⋊C4×C151C2×D411yescharacteristic
246C4⋊C4×C151C2×D411yescharacteristic
247C4⋊C4×C151C2×D411yescharacteristic
248C22⋊C4×C151—22no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—22no—
251C22⋊C4×C151—22no—
252C22⋊C4×C151—22no—
253C22⋊C4×C151—21no—
254C22⋊C4×C151—21no—
255C22⋊C4×C151—21no—
256C22⋊C4×C151—21no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—21no—
262C22⋊C4×C151—41no—
263C22⋊C4×C151—41no—
264C42×C151—22no—
265C42×C151—21no—
266C42×C151—21no—
267C42×C151—21no—
268C42×C151C2×D411yescharacteristic
269C42×C151C2×D411yescharacteristic
270C42×C151C2×D411yescharacteristic
271C42×C151C2411yescharacteristic
272C23×C151—21no—
273C23×C151—22no—
274C23×C151—41no—
275C23×C151#12011yescharacteristic
276Q8×C151—21no—
277Q8×C151—21no—
278Q8×C151—21no—
279Q8×C151—21no—
280Q8×C151—21no—
281Q8×C151—21no—
282Q8×C151—42no—
283Q8×C151—41no—
284Q8×C151—41no—
285Q8×C151—81no—
286Q8×C151—82no—
287D4×C151—21no—
288D4×C151—21no—
289D4×C151—42no—
290D4×C151—42no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—41no—
298D4×C151—41no—
299D4×C151—82no—
300D4×C151—81no—
301D4×C151—82no—
302D4×C151—82no—
303D4×C151—82no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—22no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—82no—
321C2×C4×C151—82no—
322C2×C4×C151—82no—
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—41no—
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—42no—
344C22×C151—42no—
345C22×C151—41no—
346C22×C151—81no—
347C22×C151—81no—
348C22×C151—81no—
349C22×C151C2×#12011yescharacteristic
350C4×C151—21no—
351C4×C151—21no—
352C4×C151—21no—
353C4×C151—21no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—42no—
357C4×C151—41no—
358C4×C151—41no—
359C4×C151—41no—
360C4×C151—41no—
361C4×C151—41no—
362C4×C151—81no—
363C4×C151#57611yescharacteristic
364C4×C151#57711yescharacteristic
365C4×C151#57711yescharacteristic
366C4×C151#57811yescharacteristic
367C2×C151—41no—
368C2×C151—81no—
369C2×C151—82no—
370C2×C151—161no—
371C2×C151#301211yescharacteristic
372C2×C151#301311yescharacteristic
373C2×C151#302111yescharacteristic
374#18964C15111yesmaximal, characteristic, direct product factor, Sylow
375C151#1896411yescharacteristic, direct product factor, Sylow
376#3554C2×C15111yescharacteristic, complemented
377#3254C2×C15111yescharacteristic, complemented
378#3247C2×C15111yescharacteristic, complemented
379#3207C2×C15111yescharacteristic, complemented
380#1637C2×C15111yescharacteristic, complemented
381#1636C2×C15111yescharacteristic, complemented
382#1631C2×C15111yescharacteristic, complemented
383#1630C2×C15111yescharacteristic, complemented
384#1627C2×C15111yescharacteristic, complemented
385#1626C2×C15111yescharacteristic, complemented
386#1621C2×C15111yescharacteristic, complemented
387#1620C2×C15111yescharacteristic, complemented
388#1547C2×C15111yescharacteristic, complemented
389#1495C2×C15111yescharacteristic, complemented
390#1481C2×C15111yescharacteristic, complemented
391#562—22no—
392#559—21no—
393#559C22×C15111yescharacteristic
394#557C22×C15111yescharacteristic
395#554—21no—
396#550C22×C15111yescharacteristic
397D4×Q8C22×C15111yescharacteristic
398#548—21no—
399#547—21no—
400#542—21no—
401#542—21no—
402#540—21no—
403#539—22no—
404#536—21no—
405#533C22×C15111yescharacteristic
406#532C22×C15111yescharacteristic
407#532C22×C15111yescharacteristic
408#529C22×C15111yescharacteristic
409#493C22×C15111yescharacteristic
410#492C22×C15111yescharacteristic
411#487C22×C15111yescharacteristic
412#486C22×C15111yescharacteristic
413#478—21no—
414#477C22×C15111yescharacteristic
415#477C22×C15111yescharacteristic
416#477C22×C15111yescharacteristic
417#476C22×C15111yescharacteristic
418#474—21no—
419#468—21no—
420#468—21no—
421#466—21no—
422#465—21no—
423#463—21no—
424#463—22no—
425#461—21no—
426#460C22×C15111yescharacteristic
427#460C22×C15111yescharacteristic
428#460C22×C15111yescharacteristic
429#459C22×C15111yescharacteristic
430#449—22no—
431#431C22×C15111yescharacteristic
432#423C22×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
442Q8⋊C8C22×C15111yescharacteristic
443Q8⋊C8C22×C15111yescharacteristic
444D4⋊C8C22×C15111yescharacteristic
445D4⋊C8C22×C15111yescharacteristic
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C22×Q8—21no—
450C2×SD16—21no—
451C2×SD16—21no—
452C2×SD16—21no—
453C2×SD16—22no—
454C2×D8—22no—
455C2×D8—21no—
456C2×M16—21no—
457C22×C8—21no—
458C4⋊Q8—21no—
459C4⋊Q8—21no—
460C4⋊Q8D4×C15111yescharacteristic
461C4⋊Q8D4×C15111yescharacteristic
462C4⋊Q8C23×C15111yescharacteristic
463C4⋊Q8C23×C15111yescharacteristic
464#127—21no—
465#127C23×C15111yescharacteristic
466#127C23×C15111yescharacteristic
467#126—22no—
468#126—21no—
469#125—22no—
470#125—21no—
471#125—21no—
472#125D4×C15111yescharacteristic
473#124—22no—
474#124—22no—
475#124—21no—
476#124—21no—
477#124—21no—
478#124—21no—
479#124D4×C15111yescharacteristic
480#123—22no—
481#123—22no—
482#123—22no—
483#123—22no—
484#123—22no—
485#123—22no—
486#123—21no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—22no—
491C22⋊Q8—21no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8D4×C15111yescharacteristic
495C22⋊Q8D4×C15111yescharacteristic
496C22⋊Q8D4×C15111yescharacteristic
497#121—22no—
498#121—22no—
499#121—22no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121D4×C15111yescharacteristic
505#121D4×C15112yes—
506C4×Q8—21no—
507C4×Q8—21no—
508C4×Q8—21no—
509C4×Q8C23×C15111yescharacteristic
510C4×Q8C23×C15111yescharacteristic
511C4×Q8C23×C15111yescharacteristic
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4D4×C15112yes—
522C4×D4C23×C15111yescharacteristic
523#117—21no—
524#117—21no—
525C2×C4⋊C4—22no—
526C2×C42C23×C15111yescharacteristic
527#107—21no—
528#107—21no—
529#107—21no—
530#106—21no—
531C4⋊C8—21no—
532C4⋊C8—21no—
533C4⋊C8—21no—
534C4⋊C8C23×C15111yescharacteristic
535C4⋊C8C23×C15111yescharacteristic
536C4⋊C8C23×C15111yescharacteristic
537C4⋊C8C23×C15111yescharacteristic
538#103—21no—
539#103—21no—
540#103—21no—
541#103—22no—
542#102—21no—
543#102—22no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—21no—
548C22⋊C8—21no—
549C4×C8C23×C15111yescharacteristic
550C4×C8C23×C15111yescharacteristic
551#41—81no—
552#41—81no—
553#41—81no—
554#41—81no—
555#41—82no—
556C2×Q8—22no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—81no—
561C2×Q8—81no—
562C2×Q8C2×D4×C15111yescharacteristic
563C2×Q8C2×D4×C15111yescharacteristic
564C2×Q8C2×D4×C15111yescharacteristic
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4C2×D4×C15111yescharacteristic
576C2×D4C2×D4×C15112yes—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—41no—
583C22×C4C2×D4×C15111yescharacteristic
584C22×C4C2×D4×C15111yescharacteristic
585C22×C4C2×D4×C15111yescharacteristic
586SD16—81no—
587SD16—81no—
588SD16—81no—
589SD16—82no—
590D8—81no—
591D8—82no—
592M16—81no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—81no—
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—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4C2×D4×C15112yes—
619C4⋊C4C2×D4×C15111yescharacteristic
620C4⋊C4C2×D4×C15111yescharacteristic
621C4⋊C4C2×D4×C15111yescharacteristic
622C4⋊C4C2×D4×C15111yescharacteristic
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—21no—
637C22⋊C4—41no—
638C22⋊C4—41no—
639C42—22no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42C2×D4×C15111yescharacteristic
644C42C2×D4×C15111yescharacteristic
645C42C2×D4×C15111yescharacteristic
646C42C24×C15111yescharacteristic
647C23—21no—
648C23—22no—
649C23—41no—
650C23#120×C15111yescharacteristic
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8—21no—
656Q8—21no—
657Q8—42no—
658Q8—41no—
659Q8—41no—
660Q8—81no—
661Q8—82no—
662D4—21no—
663D4—21no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—82no—
675D4—81no—
676D4—82no—
677D4—82no—
678D4—82no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—82no—
696C2×C4—82no—
697C2×C4—82no—
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—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C8—41no—
711C8—41no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—41no—
716C22—42no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—41no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22C2×#120×C15111yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—81no—
738C4#576×C15111yescharacteristic
739C4#577×C15111yescharacteristic
740C4#577×C15111yescharacteristic
741C4#578×C15111yescharacteristic
742C2—41no—
743C2—81no—
744C2—82no—
745C2—161no—
746C2#3012×C15111yescharacteristic
747C2#3013×C15111yescharacteristic
748C2#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. #3554×C151C2semidirect
2. #3254×C151C2semidirect
3. #3247×C151C2semidirect
4. #3207×C151C2semidirect
5. #1637×C151C2semidirect
6. #1636×C151C2semidirect
7. #1631×C151C2semidirect
8. #1630×C151C2semidirect
9. #1627×C151C2semidirect
10. #1626×C151C2semidirect
11. #1621×C151C2semidirect
12. #1620×C151C2semidirect
13. #1547×C151C2semidirect
14. #1495×C151C2semidirect
15. #1481×C151C2semidirect
374. #18964C151direct (N × H)
375. C151#18964direct (N × H)
376. #3554C2×C151semidirect
377. #3254C2×C151semidirect
378. #3247C2×C151semidirect
379. #3207C2×C151semidirect
380. #1637C2×C151semidirect
381. #1636C2×C151semidirect
382. #1631C2×C151semidirect
383. #1630C2×C151semidirect
384. #1627C2×C151semidirect
385. #1626C2×C151semidirect
386. #1621C2×C151semidirect
387. #1620C2×C151semidirect
388. #1547C2×C151semidirect
389. #1495C2×C151semidirect
390. #1481C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3554×C1512
#3254×C1512
#3247×C1512
#3207×C1512
#1637×C1512
#1636×C1512
#1631×C1512
#1630×C1512
#1627×C1512
#1626×C1512
#1621×C1512
#1620×C1512
#1547×C1512
#1495×C1512
#1481×C1512
#18964151