Subgroups — C₂×#11924590 #14558490

Order 2368.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#3866	C₂	1	1	yes	maximal, characteristic
3	#11924590	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#3866	C₄	1	2	yes	—
6	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
7	C₂×#64438	C₄	1	2	yes	complemented
8	C₄×#3866	C₄	1	2	yes	—
9	C₄×#3866	C₂²	1	2	yes	—
10	D₃₇⋊C₈	C₄	1	2	yes	complemented
11	D₃₇⋊C₈	C₂²	1	2	yes	—
12	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic, complemented
13	C₂×#64436	C₄	1	1	yes	characteristic, complemented
14	C₈×D₃₇	C₄	1	2	yes	complemented
15	C₈×D₃₇	C₂²	1	2	yes	—
16	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×#3866	—	2	4	no	—
18	C₂×#3866	C₂×C₄	1	4	yes	—
19	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
21	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
22	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
23	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
24	C₄×D₃₇	C₂³	1	1	yes	characteristic
25	#64438	C₂×C₄	1	4	yes	complemented
26	C₈×C₃₇	C₂×C₄	1	2	yes	complemented
27	#64436	C₂×C₄	1	2	yes	complemented
28	C₂²×C₃₇	C₄²	1	1	yes	characteristic
29	C₂×D₃₇	C₄²	1	1	yes	characteristic
30	C₂×D₃₇	M₁₆	1	4	yes	—
31	C₂×D₃₇	C₂²×C₄	1	1	yes	characteristic
32	#3866	—	2	4	no	—
33	C₄×C₃₇	C₄²	1	1	yes	characteristic
34	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
35	Dic₃₇	C₄²	1	1	yes	characteristic
36	Dic₃₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₃₇	#97	1	2	yes	complemented
38	C₂×C₃₇	C₂×C₄²	1	1	yes	characteristic
39	D₃₇	#97	1	2	yes	complemented
40	D₃₇	C₂×M₁₆	1	2	yes	—
41	C₂×#97	—	37	1	no	maximal, Sylow
42	C₃₇	C₂×#97	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₈	—	37	1	no	—
44	C₂²×C₈	—	37	1	no	—
45	C₂×C₄²	—	37	1	no	—
46	#97	—	37	4	no	—
47	C₂²×C₄	—	37	1	no	—
48	C₂²×C₄	—	37	2	no	—
49	C₂×C₈	—	37	2	no	—
50	C₂×C₈	—	37	2	no	—
51	C₂×C₈	—	37	2	no	—
52	C₂×C₈	—	37	1	no	—
53	C₂×C₈	—	37	2	no	—
54	C₂×C₈	—	37	2	no	—
55	C₂×C₈	#3866	1	1	yes	characteristic, complemented
56	C₄²	—	37	2	no	—
57	C₄²	—	37	2	no	—
58	C₂³	—	37	1	no	—
59	C₂×C₄	—	37	1	no	—
60	C₂×C₄	—	37	1	no	—
61	C₂×C₄	—	37	1	no	—
62	C₂×C₄	—	37	1	no	—
63	C₂×C₄	—	37	1	no	—
64	C₂×C₄	—	37	4	no	—
65	C₂×C₄	—	74	4	no	—
66	C₂×C₄	C₂×#3866	1	1	yes	characteristic
67	C₈	—	37	4	no	—
68	C₈	—	37	2	no	—
69	C₈	C₂×#3866	1	2	yes	complemented
70	C₂²	—	37	4	no	—
71	C₂²	—	37	1	no	—
72	C₂²	—	37	1	no	—
73	C₂²	C₄×#3866	1	1	yes	characteristic
74	C₄	—	37	1	no	—
75	C₄	—	37	1	no	—
76	C₄	—	74	4	no	—
77	C₄	C₄×#3866	1	1	yes	characteristic
78	C₄	C₂²×#3866	1	1	yes	characteristic
79	C₂	—	37	2	no	—
80	C₂	—	37	2	no	—
81	C₂	#11924590	1	2	yes	direct product factor
82	C₂	C₂×C₄×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#3866
commutator	C₂×C₃₇	C₂×C₄²
Frattini	C₄	C₂²×#3866
Fitting	C₂×C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₄²
prime radical	C₂²×D₃₇	C₂×C₄
cosocle	C₄×D₃₇	C₂³
hypercenter	C₂×C₈	#3866
hypocenter	C₃₇	C₂×#97
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #11924590	C₂	direct (N × H)
7. C₂×#64438	C₄	semidirect
10. D₃₇⋊C₈	C₄	semidirect
12. C₂×C₈×C₃₇	C₄	semidirect
13. C₂×#64436	C₄	semidirect
14. C₈×D₃₇	C₄	semidirect
25. #64438	C₂×C₄	semidirect
26. C₈×C₃₇	C₂×C₄	semidirect
27. #64436	C₂×C₄	semidirect
37. C₂×C₃₇	#97	semidirect
39. D₃₇	#97	semidirect
42. C₃₇	C₂×#97	semidirect
55. C₂×C₈	#3866	semidirect
69. C₈	C₂×#3866	semidirect
81. C₂	#11924590	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₃₇⋊C₈	2
C₂×C₄×#3866	2
#11924590	2
C₂×C₈×D₃₇	2
C₂×#97	37

Subgroups — C2×#11924590 #14558490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924590 #14558490