Subgroups — Q₈×#10596925 #17996500

Order 4736.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10596925	C₂	1	3	yes	maximal
2	C₄×#10596925	C₂	1	3	yes	maximal
3	C₈×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596925	C₂²	1	3	yes	—
5	C₂×#10596925	C₂²	1	1	yes	characteristic
6	C₄×Q₈×C₃₇	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₃₇	C₄	1	3	yes	—
8	C₄×C₈×C₃₇	C₂²	1	3	yes	—
9	C₂×Q₈×C₃₇	C₈	1	1	yes	characteristic
10	C₂×C₈×C₃₇	C₂×C₄	1	3	yes	—
11	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
12	C₄⋊C₄×C₃₇	C₈	1	3	yes	—
13	C₄²×C₃₇	C₂×C₄	1	3	yes	—
14	#10596925	—	2	3	no	—
15	#10596925	Q₈	1	2	yes	direct product factor
16	Q₈×C₃₇	C₁₆	1	4	yes	complemented
17	C₂×C₄×C₃₇	C₂×C₈	1	3	yes	—
18	C₂×C₄×C₃₇	C₂×C₈	1	3	yes	—
19	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
20	C₈×C₃₇	—	2	3	no	—
21	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
22	C₈×C₃₇	#41	1	1	yes	characteristic
23	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
24	C₄×C₃₇	—	2	3	no	—
25	C₄×C₃₇	C₂×C₁₆	1	6	yes	—
26	C₄×C₃₇	C₄×Q₈	1	1	yes	characteristic
27	C₄×C₃₇	#131	1	1	yes	characteristic
28	Q₈×C₁₆	—	37	1	no	maximal, Sylow
29	C₂×C₃₇	C₈×Q₈	1	1	yes	characteristic
30	C₂×C₃₇	C₂²×C₁₆	1	1	yes	characteristic
31	C₂×C₃₇	#504	1	1	yes	characteristic
32	C₈×Q₈	D₃₇	1	1	yes	characteristic
33	C₄⋊C₁₆	—	37	3	no	—
34	C₄×C₁₆	—	37	3	no	—
35	C₃₇	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₄×Q₈	Dic₃₇	1	1	yes	characteristic
37	C₂×C₁₆	—	37	1	no	—
38	C₂×C₁₆	—	37	3	no	—
39	C₄⋊C₈	Dic₃₇	1	3	yes	—
40	C₄×C₈	C₂×D₃₇	1	3	yes	—
41	C₂×Q₈	#64436	1	1	yes	characteristic
42	C₂×C₈	C₂×Dic₃₇	1	3	yes	—
43	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
44	C₄⋊C₄	#64436	1	3	yes	—
45	C₄²	C₂×Dic₃₇	1	3	yes	—
46	C₁₆	—	37	2	no	—
47	C₁₆	—	74	3	no	—
48	Q₈	#10596925	1	4	yes	direct product factor
49	C₂×C₄	C₂×#64436	1	3	yes	—
50	C₂×C₄	C₂×#64436	1	3	yes	—
51	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
52	C₈	—	2	3	no	—
53	C₈	Q₈×D₃₇	1	1	yes	characteristic
54	C₈	#10596966	1	1	yes	characteristic
55	C₂²	C₂²×#64436	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×#10596925	1	6	yes	—
58	C₄	Q₈×Dic₃₇	1	1	yes	characteristic
59	C₄	#11924543	1	1	yes	characteristic
60	C₂	Q₈×#64436	1	1	yes	characteristic
61	C₂	C₂²×#10596925	1	1	yes	characteristic
62	C₂	#14557950	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₃₇
commutator	C₂×C₃₇	C₂²×C₁₆
Fitting	C₈×Q₈×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂²×C₈
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	C₈×Q₈	D₃₇
hypocenter	C₃₇	Q₈×C₁₆
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
15. #10596925	Q₈	direct (N × H)
16. Q₈×C₃₇	C₁₆	semidirect
35. C₃₇	Q₈×C₁₆	semidirect
48. Q₈	#10596925	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⋊#10596925	2
C₄×#10596925	2
C₈×Q₈×C₃₇	2
Q₈×C₁₆	37

Subgroups — Q8×#10596925 #17996500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#10596925 #17996500