Subgroups — C₂×Q₈×#3866 #14558598

Order 2368.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#3866	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₄⋊#3866	C₂	1	3	yes	maximal
3	C₂×C₄×#3866	C₂	1	3	yes	maximal
4	C₂×Q₈×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#3866	C₂²	1	3	yes	—
6	C₂²×#3866	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₃₇	C₄	1	1	yes	characteristic, complemented
8	Q₈×D₃₇	C₄	1	4	yes	complemented
9	Q₈×D₃₇	C₂²	1	4	yes	—
10	C₂×C₄×D₃₇	C₂²	1	3	yes	—
11	C₂×Dic₇₄	C₄	1	3	yes	complemented
12	C₄⋊#3866	C₂²	1	12	yes	—
13	C₄×#3866	C₂²	1	12	yes	—
14	C₂²×D₃₇	C₂³	1	1	yes	characteristic
15	C₂×#3866	—	2	6	no	—
16	C₂×#3866	Q₈	1	4	yes	direct product factor
17	C₂×#3866	C₂³	1	6	yes	—
18	C₂×#3866	C₂³	1	2	yes	—
19	Q₈×C₃₇	C₂×C₄	1	4	yes	complemented
20	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
21	C₂×Dic₃₇	C₂×C₄	1	3	yes	—
22	C₄×D₃₇	C₂×C₄	1	6	yes	—
23	C₄×D₃₇	C₂³	1	6	yes	—
24	Dic₇₄	C₂×C₄	1	12	yes	complemented
25	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×D₃₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₃₇	C₂×Q₈	1	2	yes	—
28	C₂×D₃₇	#41	1	2	yes	—
29	C₂×D₃₇	C₂⁴	1	1	yes	characteristic
30	#3866	—	2	6	no	—
31	#3866	C₂×Q₈	1	4	yes	direct product factor
32	C₄×C₃₇	C₂²×C₄	1	6	yes	—
33	Dic₃₇	C₂²×C₄	1	6	yes	—
34	C₂×C₃₇	C₄×Q₈	1	2	yes	complemented
35	C₂×C₃₇	C₂³×C₄	1	1	yes	characteristic
36	D₃₇	C₄×Q₈	1	2	yes	complemented
37	D₃₇	C₂²×Q₈	1	1	yes	characteristic
38	D₃₇	C₂×#41	1	1	yes	characteristic
39	C₂×C₄×Q₈	—	37	1	no	maximal, Sylow
40	C₃₇	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
41	C₂²×Q₈	—	37	1	no	—
42	C₄×Q₈	—	37	8	no	—
43	C₂×C₄⋊C₄	—	37	3	no	—
44	C₂×C₄²	—	37	3	no	—
45	C₂×Q₈	—	37	4	no	—
46	C₂×Q₈	—	37	4	no	—
47	C₂×Q₈	—	37	3	no	—
48	C₂×Q₈	#3866	1	1	yes	characteristic, direct product factor
49	C₂²×C₄	—	37	1	no	—
50	C₂²×C₄	—	37	3	no	—
51	C₂²×C₄	—	37	3	no	—
52	C₄⋊C₄	—	37	12	no	—
53	C₄²	—	37	12	no	—
54	C₂³	—	37	1	no	—
55	Q₈	—	37	12	no	—
56	Q₈	C₂×#3866	1	4	yes	direct product factor
57	C₂×C₄	—	37	2	no	—
58	C₂×C₄	—	37	4	no	—
59	C₂×C₄	—	37	3	no	—
60	C₂×C₄	—	37	6	no	—
61	C₂×C₄	—	37	6	no	—
62	C₂×C₄	—	37	6	no	—
63	C₂×C₄	—	74	6	no	—
64	C₂×C₄	C₂×#3866	1	3	yes	—
65	C₂²	—	37	2	no	—
66	C₂²	—	37	2	no	—
67	C₂²	—	37	1	no	—
68	C₂²	—	37	1	no	—
69	C₂²	C₂²×#3866	1	1	yes	characteristic
70	C₄	—	37	4	no	—
71	C₄	—	37	6	no	—
72	C₄	—	74	6	no	—
73	C₄	C₂²×#3866	1	6	yes	—
74	C₂	—	37	1	no	—
75	C₂	—	37	1	no	—
76	C₂	—	37	2	no	—
77	C₂	Q₈×#3866	1	2	yes	direct product factor
78	C₂	C₂³×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#3866
commutator	C₂×C₃₇	C₂³×C₄
Frattini	C₂	C₂³×#3866
Fitting	C₂×Q₈×C₃₇	C₄
socle	C₂²×C₃₇	C₂²×C₄
prime radical	C₂²×D₃₇	C₂³
cosocle	C₂×D₃₇	C₂⁴
hypercenter	C₂×Q₈	#3866
hypocenter	C₃₇	C₂×C₄×Q₈
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. Q₈×#3866	C₂	direct (N × H)
7. C₂×Q₈×C₃₇	C₄	semidirect
8. Q₈×D₃₇	C₄	semidirect
11. C₂×Dic₇₄	C₄	semidirect
16. C₂×#3866	Q₈	direct (N × H)
19. Q₈×C₃₇	C₂×C₄	semidirect
24. Dic₇₄	C₂×C₄	semidirect
31. #3866	C₂×Q₈	direct (N × H)
34. C₂×C₃₇	C₄×Q₈	semidirect
36. D₃₇	C₄×Q₈	semidirect
40. C₃₇	C₂×C₄×Q₈	semidirect
48. C₂×Q₈	#3866	direct (N × H)
56. Q₈	C₂×#3866	direct (N × H)
77. C₂	Q₈×#3866	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×#3866	2
C₂×C₄⋊#3866	2
C₂×C₄×#3866	2
C₂×Q₈×D₃₇	2
C₂×C₄×Q₈	37

Subgroups — C2×Q8×#3866 #14558598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×#3866 #14558598