Subgroups — C₂×#11924535 #14558076

Order 2368.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₄	C₂	1	2	yes	maximal
2	#11924535	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596936	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₃₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×C₃₇	C₂²	1	2	yes	—
8	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₇	C₂²	1	2	yes	—
10	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
12	C₂×Dic₇₄	—	2	8	no	—
13	C₂×Dic₇₄	C₂²	1	8	yes	—
14	C₄⋊C₄×C₃₇	C₂²	1	4	yes	—
15	C₄⋊Dic₃₇	C₂²	1	4	yes	—
16	#10596936	C₂²	1	8	yes	—
17	C₄×Dic₃₇	C₂²	1	4	yes	—
18	C₂³×C₃₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₃₇	—	2	4	no	—
20	C₂×C₄×C₃₇	Q₈	1	4	yes	complemented
21	C₂×C₄×C₃₇	C₂³	1	4	yes	—
22	C₂×C₄×C₃₇	C₂³	1	2	yes	—
23	C₂×Dic₃₇	—	2	4	no	—
24	C₂×Dic₃₇	D₄	1	4	yes	—
25	C₂×Dic₃₇	Q₈	1	4	yes	complemented
26	C₂×Dic₃₇	C₂³	1	4	yes	—
27	C₂×Dic₃₇	C₂³	1	2	yes	—
28	C₂×Dic₃₇	C₂³	1	2	yes	—
29	Dic₇₄	—	2	16	no	—
30	C₂²×C₃₇	C₂×D₄	1	2	yes	—
31	C₂²×C₃₇	C₂×Q₈	1	2	yes	—
32	C₂²×C₃₇	C₂×Q₈	1	2	yes	—
33	C₂²×C₃₇	C₂⁴	1	1	yes	characteristic
34	C₄×C₃₇	—	2	4	no	—
35	C₄×C₃₇	C₂×Q₈	1	4	yes	complemented
36	Dic₃₇	—	2	4	no	—
37	Dic₃₇	C₂×D₄	1	4	yes	—
38	Dic₃₇	C₂×Q₈	1	4	yes	complemented
39	C₂×C₃₇	C₄⋊Q₈	1	4	yes	complemented
40	C₂×C₃₇	C₂²×D₄	1	1	yes	characteristic
41	C₂×C₃₇	C₂²×Q₈	1	1	yes	characteristic
42	C₂×C₃₇	C₂²×Q₈	1	1	yes	characteristic
43	C₂×C₄⋊Q₈	—	37	1	no	maximal, Sylow
44	C₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
45	C₂²×Q₈	—	37	2	no	—
46	C₄⋊Q₈	—	37	8	no	—
47	C₂×C₄⋊C₄	—	37	2	no	—
48	C₂×C₄⋊C₄	—	37	1	no	—
49	C₂×C₄⋊C₄	D₃₇	1	1	yes	characteristic
50	C₂×C₄²	—	37	1	no	—
51	C₂×Q₈	—	37	8	no	—
52	C₂×Q₈	—	74	8	no	—
53	C₂²×C₄	—	37	1	no	—
54	C₂²×C₄	—	37	1	no	—
55	C₂²×C₄	—	37	2	no	—
56	C₂²×C₄	C₂×D₃₇	1	2	yes	—
57	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
58	C₄⋊C₄	—	37	8	no	—
59	C₄⋊C₄	—	37	4	no	—
60	C₄⋊C₄	C₂×D₃₇	1	4	yes	—
61	C₄²	—	37	4	no	—
62	C₂³	C₂²×D₃₇	1	1	yes	characteristic
63	Q₈	—	74	16	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	37	4	no	—
66	C₂×C₄	—	37	4	no	—
67	C₂×C₄	—	37	2	no	—
68	C₂×C₄	—	37	2	no	—
69	C₂×C₄	—	37	4	no	—
70	C₂×C₄	—	74	4	no	—
71	C₂×C₄	Dic₇₄	1	4	yes	complemented
72	C₂×C₄	C₂²×D₃₇	1	4	yes	—
73	C₂×C₄	C₂²×D₃₇	1	2	yes	—
74	C₂²	C₂×Dic₇₄	1	2	yes	—
75	C₂²	D₄×D₃₇	1	2	yes	—
76	C₂²	Q₈×D₃₇	1	2	yes	—
77	C₂²	C₂³×D₃₇	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	37	4	no	—
80	C₄	—	37	4	no	—
81	C₄	—	74	4	no	—
82	C₄	C₂×Dic₇₄	1	4	yes	complemented
83	C₂	#11924535	1	4	yes	direct product factor
84	C₂	C₂×D₄×D₃₇	1	1	yes	characteristic
85	C₂	C₂×Q₈×D₃₇	1	1	yes	characteristic
86	C₂	C₂²×Dic₇₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #11924535	C₂	direct (N × H)
20. C₂×C₄×C₃₇	Q₈	semidirect
25. C₂×Dic₃₇	Q₈	semidirect
35. C₄×C₃₇	C₂×Q₈	semidirect
38. Dic₃₇	C₂×Q₈	semidirect
39. C₂×C₃₇	C₄⋊Q₈	semidirect
44. C₃₇	C₂×C₄⋊Q₈	semidirect
71. C₂×C₄	Dic₇₄	semidirect
82. C₄	C₂×Dic₇₄	semidirect
83. C₂	#11924535	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₇₄	2
#11924535	2
C₂×C₄⋊Dic₃₇	2
C₂×#10596936	2
C₂×C₄×Dic₃₇	2
C₂×C₄⋊C₄×C₃₇	2
C₂×C₄⋊Q₈	37

Subgroups — C2×#11924535 #14558076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924535 #14558076