Subgroups — Q₈×#90768 #16821396

Order 3712.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#90768	C₂	1	3	yes	maximal
2	C₄×#90768	C₂	1	3	yes	maximal
3	C₈×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×C₂₉	C₄	1	1	yes	characteristic
5	C₂₉×C₄⋊C₈	C₄	1	3	yes	—
6	C₄×C₈×C₂₉	C₂²	1	3	yes	—
7	C₂×#90768	C₂²	1	3	yes	—
8	C₂×#90768	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₂₉	C₈	1	1	yes	characteristic
10	C₂×C₈×C₂₉	C₂×C₄	1	3	yes	—
11	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
12	C₄⋊C₄×C₂₉	C₈	1	3	yes	—
13	C₄²×C₂₉	C₂×C₄	1	3	yes	—
14	#90768	—	2	3	no	—
15	#90768	Q₈	1	2	yes	direct product factor
16	Q₈×C₂₉	C₁₆	1	4	yes	complemented
17	C₂×C₄×C₂₉	C₂×C₈	1	3	yes	—
18	C₂×C₄×C₂₉	C₂×C₈	1	3	yes	—
19	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
20	C₈×C₂₉	—	2	3	no	—
21	C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
22	C₈×C₂₉	#41	1	1	yes	characteristic
23	Q₈×C₁₆	—	29	1	no	maximal, Sylow
24	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
25	C₄×C₂₉	—	2	3	no	—
26	C₄×C₂₉	C₂×C₁₆	1	6	yes	—
27	C₄×C₂₉	C₄×Q₈	1	1	yes	characteristic
28	C₄×C₂₉	#131	1	1	yes	characteristic
29	C₈×Q₈	D₂₉	1	1	yes	characteristic
30	C₄⋊C₁₆	—	29	3	no	—
31	C₄×C₁₆	—	29	3	no	—
32	C₂×C₂₉	C₈×Q₈	1	1	yes	characteristic
33	C₂×C₂₉	C₂²×C₁₆	1	1	yes	characteristic
34	C₂×C₂₉	#504	1	1	yes	characteristic
35	C₄×Q₈	Dic₂₉	1	1	yes	characteristic
36	C₂×C₁₆	—	29	1	no	—
37	C₂×C₁₆	—	29	3	no	—
38	C₄⋊C₈	Dic₂₉	1	3	yes	—
39	C₄×C₈	C₂×D₂₉	1	3	yes	—
40	C₂₉	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₈	#6597	1	1	yes	characteristic
42	C₂×C₈	C₂×Dic₂₉	1	3	yes	—
43	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
44	C₄⋊C₄	#6597	1	3	yes	—
45	C₄²	C₂×Dic₂₉	1	3	yes	—
46	C₁₆	—	29	2	no	—
47	C₁₆	—	58	3	no	—
48	Q₈	#90768	1	4	yes	direct product factor
49	C₂×C₄	C₂×#6597	1	3	yes	—
50	C₂×C₄	C₂×#6597	1	3	yes	—
51	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
52	C₈	—	2	3	no	—
53	C₈	Q₈×D₂₉	1	1	yes	characteristic
54	C₈	#90809	1	1	yes	characteristic
55	C₂²	C₂²×#6597	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×#90768	1	6	yes	—
58	C₄	Q₈×Dic₂₉	1	1	yes	characteristic
59	C₄	#11745310	1	1	yes	characteristic
60	C₂	Q₈×#6597	1	1	yes	characteristic
61	C₂	C₂²×#90768	1	1	yes	characteristic
62	C₂	#14271580	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₉
commutator	C₂×C₂₉	C₂²×C₁₆
Fitting	C₈×Q₈×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂²×C₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	C₈×Q₈	D₂₉
hypocenter	C₂₉	Q₈×C₁₆
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
15. #90768	Q₈	direct (N × H)
16. Q₈×C₂₉	C₁₆	semidirect
40. C₂₉	Q₈×C₁₆	semidirect
48. Q₈	#90768	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊#90768	2
C₄×#90768	2
C₈×Q₈×C₂₉	2
Q₈×C₁₆	29

Subgroups — Q8×#90768 #16821396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#90768 #16821396