Subgroups — Q₈×#90770 #16835905

Order 3712.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#90770	C₂	1	3	yes	maximal
2	C₄×#90770	C₂	1	3	yes	maximal
3	Q₈×#6597	C₂	1	1	yes	maximal, characteristic
4	C₄×Q₈×C₂₉	C₄	1	1	yes	characteristic
5	C₂×#90770	C₂²	1	3	yes	—
6	C₂×#90770	C₂²	1	1	yes	characteristic
7	C₄⋊#6597	C₄	1	3	yes	—
8	C₄×#6597	C₂²	1	3	yes	—
9	C₂×Q₈×C₂₉	C₈	1	1	yes	characteristic
10	C₄⋊C₄×C₂₉	C₈	1	3	yes	—
11	C₄²×C₂₉	C₂×C₄	1	3	yes	—
12	C₂×#6597	C₂×C₄	1	3	yes	—
13	C₂×#6597	C₂³	1	1	yes	characteristic
14	#90770	—	2	3	no	—
15	#90770	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	#6597	—	2	3	no	—
21	#6597	C₂×Q₈	1	1	yes	characteristic
22	#6597	#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	—	29	1	no	—
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	#1181	1	1	yes	characteristic
36	C₂×C₁₆	—	29	1	no	—
37	C₂×C₁₆	—	29	3	no	—
38	C₄⋊C₈	—	29	3	no	—
39	C₄×C₈	—	29	3	no	—
40	C₂₉	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₈	#6599	1	1	yes	characteristic
42	C₂×C₈	—	29	1	no	—
43	C₂×C₈	—	29	3	no	—
44	C₄⋊C₄	#6599	1	3	yes	—
45	C₄²	C₂×#1181	1	3	yes	—
46	C₁₆	—	29	2	no	—
47	C₁₆	—	58	3	no	—
48	Q₈	#90770	1	4	yes	direct product factor
49	C₂×C₄	C₂×#6599	1	3	yes	—
50	C₂×C₄	C₂×#6599	1	3	yes	—
51	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
52	C₈	—	29	1	no	—
53	C₈	—	29	1	no	—
54	C₈	—	58	3	no	—
55	C₂²	C₂²×#6599	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×#90770	1	6	yes	—
58	C₄	#11745348	1	1	yes	characteristic
59	C₄	Q₈×#1181	1	1	yes	characteristic
60	C₂	Q₈×#6599	1	1	yes	characteristic
61	C₂	C₂²×#90770	1	1	yes	characteristic
62	C₂	#14272221	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator	C₂×C₂₉	C₂²×C₁₆
Fitting	C₄×Q₈×C₂₉	C₄
socle, prime radical	C₂²×C₂₉	C₂²×C₈
cosocle	C₂×#6597	C₂³
hypercenter	C₄×Q₈	#1181
hypocenter	C₂₉	Q₈×C₁₆
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
15. #90770	Q₈	direct (N × H)
16. Q₈×C₂₉	C₁₆	semidirect
40. C₂₉	Q₈×C₁₆	semidirect
48. Q₈	#90770	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⋊#90770	2
C₄×#90770	2
Q₈×#6597	2
Q₈×C₁₆	29

Subgroups — Q8×#90770 #16835905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#90770 #16835905