Finite Group Databasebeta

← C151×#19780 #50324705

Subgroups — C151×#19780 #50324705

Order 38656.

622 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D8×C151C211yesmaximal, characteristic, complemented
2#3329×C151C211yesmaximal, characteristic, complemented
3#3303×C151C211yesmaximal, characteristic
4#3298×C151C211yesmaximal, characteristic, complemented
5#1718×C151C211yesmaximal, characteristic, complemented
6#1699×C151C211yesmaximal, characteristic, complemented
7#1684×C151C211yesmaximal, characteristic, complemented
8#1683×C151C211yesmaximal, characteristic, complemented
9#1673×C151C211yesmaximal, characteristic, complemented
10#1654×C151C211yesmaximal, characteristic, complemented
11#1651×C151C211yesmaximal, characteristic, complemented
12#1646×C151C211yesmaximal, characteristic, complemented
13#1637×C151C211yesmaximal, characteristic, complemented
14#1581×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic, complemented
16#555×C151C2211yescharacteristic
17D4×Q8×C151C2211yescharacteristic
18D4×Q8×C151C2211yescharacteristic
19#547×C151C2211yescharacteristic
20#500×C151—21no—
21#500×C151C2211yescharacteristic
22#498×C151C2211yescharacteristic
23#487×C151C2211yescharacteristic
24#487×C151C2211yescharacteristic
25#487×C151C2211yescharacteristic
26#487×C151C2211yescharacteristic
27#485×C151—21no—
28#485×C151—21no—
29#483×C151—21no—
30#477×C151C2211yescharacteristic
31#476×C151C2211yescharacteristic
32#475×C151C2211yescharacteristic
33#474×C151—21no—
34#474×C151—21no—
35#474×C151C2211yescharacteristic
36#474×C151C2211yescharacteristic
37#468×C151—21no—
38#465×C151—21no—
39#465×C151—21no—
40#461×C151C2211yescharacteristic
41#461×C151C2211yescharacteristic
42#461×C151C2211yescharacteristic
43#449×C151—21no—
44#448×C151—21no—
45#448×C151—21no—
46C8×Q8×C151C2211yescharacteristic
47C4×SD16×C151C2211yescharacteristic
48C4×D8×C151—21no—
49C4×D8×C151C2211yescharacteristic
50#436×C151C2211yescharacteristic
51C8×D4×C151C2211yescharacteristic
52C8×D4×C151C2211yescharacteristic
53#419×C151—21no—
54#416×C151—21no—
55C2×#103×C151—21no—
56#335×C151C2211yescharacteristic
57#335×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63D4⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C22×Q8×C151—21no—
69C22×Q8×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151D411yescharacteristic
74C2×D8×C151D411yescharacteristic
75C2×M16×C151—21no—
76C22×C8×C151—21no—
77C22×C8×C151—21no—
78C4⋊Q8×C151—21no—
79C4⋊Q8×C151—21no—
80C4⋊Q8×C151C2311yescharacteristic
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84#124×C151—41no—
85#123×C151—41no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—41no—
90C22⋊Q8×C151—41no—
91#121×C151—21no—
92#121×C151—21no—
93#121×C151—21no—
94C4×Q8×C151C2311yescharacteristic
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97C4×D4×C151C2311yescharacteristic
98C4×D4×C151C2311yescharacteristic
99C4×D4×C151C2311yescharacteristic
100#117×C151—21no—
101#117×C151—21no—
102C2×C4⋊C4×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#107×C151—21no—
106#107×C151—21no—
107#107×C151—21no—
108#107×C151D411yescharacteristic
109#106×C151—21no—
110#106×C151—21no—
111#106×C151—41no—
112#106×C151D411yescharacteristic
113C4⋊C8×C151—21no—
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118#103×C151—21no—
119#103×C151—21no—
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—21no—
128#103×C151—21no—
129#103×C151—41no—
130#103×C151D411yescharacteristic
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151D411yescharacteristic
135#102×C151D411yescharacteristic
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138C22⋊C8×C151—21no—
139C22⋊C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151C2311yescharacteristic
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—42no—
145#41×C151—81no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—41no—
151C2×Q8×C151—41no—
152C2×Q8×C151—42no—
153C2×Q8×C151—42no—
154C2×Q8×C151—81no—
155C2×Q8×C151—81no—
156C2×Q8×C151C2×D411yescharacteristic
157C2×D4×C151—41no—
158C2×D4×C151—41no—
159C2×D4×C151C2×D411yescharacteristic
160C2×D4×C151C2×D411yescharacteristic
161C2×D4×C151C2×D411yescharacteristic
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—41no—
166C22×C4×C151—41no—
167C22×C4×C151—41no—
168SD16×C151—22no—
169SD16×C151—81no—
170SD16×C151—81no—
171SD16×C151—81no—
172D8×C151—22no—
173M16×C151—81no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—81no—
180C2×C8×C151—81no—
181C2×C8×C151C2×D411yescharacteristic
182C2×C8×C151C2×D411yescharacteristic
183C2×C8×C151C2×D411yescharacteristic
184C2×C8×C151C2×D411yescharacteristic
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—41no—
195C4⋊C4×C151—41no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151C2×D411yescharacteristic
198C4⋊C4×C151C2×D411yescharacteristic
199C4⋊C4×C151C2×D411yescharacteristic
200C4⋊C4×C151C2×D411yescharacteristic
201C22⋊C4×C151—21no—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C22⋊C4×C151—41no—
207C22⋊C4×C151—41no—
208C22⋊C4×C151—41no—
209C42×C151—21no—
210C42×C151—41no—
211C42×C151C2411yescharacteristic
212C23×C151—21no—
213C23×C151—21no—
214C23×C151—21no—
215Q8×C151—21no—
216Q8×C151—41no—
217Q8×C151—41no—
218Q8×C151—41no—
219Q8×C151—41no—
220Q8×C151—41no—
221Q8×C151—41no—
222Q8×C151—82no—
223Q8×C151—82no—
224Q8×C151—81no—
225Q8×C151#13512yes—
226D4×C151—21no—
227D4×C151—21no—
228D4×C151—21no—
229D4×C151—21no—
230D4×C151—21no—
231D4×C151—82no—
232D4×C151—161no—
233D4×C151#13712yes—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—82no—
250C2×C4×C151—82no—
251C2×C4×C151—82no—
252C2×C4×C151C22×D411yescharacteristic
253C2×C4×C151C22×D411yescharacteristic
254C2×C4×C151H(5,𝔽2)11yescharacteristic
255C8×C151—21no—
256C8×C151—21no—
257C8×C151—21no—
258C8×C151—21no—
259C8×C151—41no—
260C8×C151—41no—
261C8×C151—41no—
262C8×C151—41no—
263C8×C151—41no—
264C22×C151—22no—
265C22×C151—41no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—41no—
269C22×C151—41no—
270C22×C151—41no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151D4211yescharacteristic
274C4×C151—22no—
275C4×C151—21no—
276C4×C151—41no—
277C4×C151—41no—
278C4×C151—41no—
279C4×C151—41no—
280C4×C151—81no—
281C4×C151—81no—
282C4×C151—81no—
283C4×C151—81no—
284C4×C151C2×#13511yescharacteristic
285C4×C151C2×#13711yescharacteristic
286C4×C151#57611yescharacteristic
287C4×C151#57711yescharacteristic
288C2×C151—42no—
289C2×C151—81no—
290C2×C151—81no—
291C2×C151#326611yescharacteristic
292C2×C151#328011yescharacteristic
293C2×C151#328911yescharacteristic
294#19780C15111yesmaximal, characteristic, direct product factor, Sylow
295C151#1978011yescharacteristic, direct product factor, Sylow
296Q8×D8C2×C15111yescharacteristic, complemented
297#3329C2×C15111yescharacteristic, complemented
298#3303C2×C15111yescharacteristic
299#3298C2×C15111yescharacteristic, complemented
300#1718C2×C15111yescharacteristic, complemented
301#1699C2×C15111yescharacteristic, complemented
302#1684C2×C15111yescharacteristic, complemented
303#1683C2×C15111yescharacteristic, complemented
304#1673C2×C15111yescharacteristic, complemented
305#1654C2×C15111yescharacteristic, complemented
306#1651C2×C15111yescharacteristic, complemented
307#1646C2×C15111yescharacteristic, complemented
308#1637C2×C15111yescharacteristic, complemented
309#1581C2×C15111yescharacteristic, complemented
310SD16⋊C8C2×C15111yescharacteristic, complemented
311#555C22×C15111yescharacteristic
312D4×Q8C22×C15111yescharacteristic
313D4×Q8C22×C15111yescharacteristic
314#547C22×C15111yescharacteristic
315#500—21no—
316#500C22×C15111yescharacteristic
317#498C22×C15111yescharacteristic
318#487C22×C15111yescharacteristic
319#487C22×C15111yescharacteristic
320#487C22×C15111yescharacteristic
321#487C22×C15111yescharacteristic
322#485—21no—
323#485—21no—
324#483—21no—
325#477C22×C15111yescharacteristic
326#476C22×C15111yescharacteristic
327#475C22×C15111yescharacteristic
328#474—21no—
329#474—21no—
330#474C22×C15111yescharacteristic
331#474C22×C15111yescharacteristic
332#468—21no—
333#465—21no—
334#465—21no—
335#461C22×C15111yescharacteristic
336#461C22×C15111yescharacteristic
337#461C22×C15111yescharacteristic
338#449—21no—
339#448—21no—
340#448—21no—
341C8×Q8C22×C15111yescharacteristic
342C4×SD16C22×C15111yescharacteristic
343C4×D8—21no—
344C4×D8C22×C15111yescharacteristic
345#436C22×C15111yescharacteristic
346C8×D4C22×C15111yescharacteristic
347C8×D4C22×C15111yescharacteristic
348#419—21no—
349#416—21no—
350C2×#103—21no—
351#335C22×C15111yescharacteristic
352#335C22×C15111yescharacteristic
353#333C22×C15111yescharacteristic
354#332C22×C15111yescharacteristic
355#332C22×C15111yescharacteristic
356#332C22×C15111yescharacteristic
357Q8⋊C8C22×C15111yescharacteristic
358D4⋊C8C22×C15111yescharacteristic
359D4⋊C8C22×C15111yescharacteristic
360D4⋊C8C22×C15111yescharacteristic
361#322C22×C15111yescharacteristic
362C2×#41—21no—
363C22×Q8—21no—
364C22×Q8—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16D4×C15111yescharacteristic
369C2×D8D4×C15111yescharacteristic
370C2×M16—21no—
371C22×C8—21no—
372C22×C8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8C23×C15111yescharacteristic
376C4⋊Q8C23×C15111yescharacteristic
377C4⋊Q8C23×C15111yescharacteristic
378C4⋊Q8C23×C15111yescharacteristic
379#124—41no—
380#123—41no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—41no—
385C22⋊Q8—41no—
386#121—21no—
387#121—21no—
388#121—21no—
389C4×Q8C23×C15111yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4C23×C15111yescharacteristic
393C4×D4C23×C15111yescharacteristic
394C4×D4C23×C15111yescharacteristic
395#117—21no—
396#117—21no—
397C2×C4⋊C4—21no—
398#107—21no—
399#107—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107D4×C15111yescharacteristic
404#106—21no—
405#106—21no—
406#106—41no—
407#106D4×C15111yescharacteristic
408C4⋊C8—21no—
409C4⋊C8C23×C15111yescharacteristic
410C4⋊C8C23×C15111yescharacteristic
411C4⋊C8C23×C15111yescharacteristic
412C4⋊C8C23×C15111yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—41no—
425#103D4×C15111yescharacteristic
426#102—21no—
427#102—21no—
428#102—21no—
429#102D4×C15111yescharacteristic
430#102D4×C15111yescharacteristic
431#102D4×C15111yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C4×C8—21no—
436C4×C8C23×C15111yescharacteristic
437C4×C8C23×C15111yescharacteristic
438C4×C8C23×C15111yescharacteristic
439#41—42no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—42no—
448C2×Q8—42no—
449C2×Q8—81no—
450C2×Q8—81no—
451C2×Q8C2×D4×C15111yescharacteristic
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×D4×C15111yescharacteristic
455C2×D4C2×D4×C15111yescharacteristic
456C2×D4C2×D4×C15111yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463SD16—22no—
464SD16—81no—
465SD16—81no—
466SD16—81no—
467D8—22no—
468M16—81no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—81no—
476C2×C8C2×D4×C15111yescharacteristic
477C2×C8C2×D4×C15111yescharacteristic
478C2×C8C2×D4×C15111yescharacteristic
479C2×C8C2×D4×C15111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C15111yescharacteristic
493C4⋊C4C2×D4×C15111yescharacteristic
494C4⋊C4C2×D4×C15111yescharacteristic
495C4⋊C4C2×D4×C15111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—41no—
506C42C24×C15111yescharacteristic
507C23—21no—
508C23—21no—
509C23—21no—
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8—82no—
519Q8—81no—
520Q8#135×C15112yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—82no—
527D4—161no—
528D4#137×C15112yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4C22×D4×C15111yescharacteristic
548C2×C4C22×D4×C15111yescharacteristic
549C2×C4H(5,𝔽2)×C15111yescharacteristic
550C8—21no—
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22D42×C15111yescharacteristic
569C4—22no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×#135×C15111yescharacteristic
580C4C2×#137×C15111yescharacteristic
581C4#576×C15111yescharacteristic
582C4#577×C15111yescharacteristic
583C2—42no—
584C2—81no—
585C2—81no—
586C2#3266×C15111yescharacteristic
587C2#3280×C15111yescharacteristic
588C2#3289×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radical#3303×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. Q8×D8×C151C2semidirect
2. #3329×C151C2semidirect
4. #3298×C151C2semidirect
5. #1718×C151C2semidirect
6. #1699×C151C2semidirect
7. #1684×C151C2semidirect
8. #1683×C151C2semidirect
9. #1673×C151C2semidirect
10. #1654×C151C2semidirect
11. #1651×C151C2semidirect
12. #1646×C151C2semidirect
13. #1637×C151C2semidirect
14. #1581×C151C2semidirect
15. SD16⋊C8×C151C2semidirect
294. #19780C151direct (N × H)
295. C151#19780direct (N × H)
296. Q8×D8C2×C151semidirect
297. #3329C2×C151semidirect
299. #3298C2×C151semidirect
300. #1718C2×C151semidirect
301. #1699C2×C151semidirect
302. #1684C2×C151semidirect
303. #1683C2×C151semidirect
304. #1673C2×C151semidirect
305. #1654C2×C151semidirect
306. #1651C2×C151semidirect
307. #1646C2×C151semidirect
308. #1637C2×C151semidirect
309. #1581C2×C151semidirect
310. SD16⋊C8C2×C151semidirect

Maximal subgroups

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

subgroupindex
Q8×D8×C1512
#3329×C1512
#3303×C1512
#3298×C1512
#1718×C1512
#1699×C1512
#1684×C1512
#1683×C1512
#1673×C1512
#1654×C1512
#1651×C1512
#1646×C1512
#1637×C1512
#1581×C1512
SD16⋊C8×C1512
#19780151