Subgroups — C₂×C₂²⋊#64438 #14558500

Order 2368.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#64438	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#64438	C₂	1	4	yes	maximal, direct product factor
3	C₂³×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×C₃₇	C₄	1	1	yes	characteristic
5	C₂²×Dic₃₇	—	2	4	no	—
6	C₂²×Dic₃₇	C₄	1	2	yes	—
7	C₂²×Dic₃₇	C₄	1	1	yes	characteristic
8	C₂²×Dic₃₇	C₂²	1	2	yes	—
9	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
10	C₂×#64438	—	2	4	no	—
11	C₂×#64438	C₂²	1	4	yes	complemented
12	C₂³×C₃₇	—	2	2	no	—
13	C₂³×C₃₇	—	2	2	no	—
14	C₂³×C₃₇	C₈	1	4	yes	complemented
15	C₂³×C₃₇	C₂×C₄	1	2	yes	—
16	C₂³×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₃₇	—	2	2	no	—
18	C₂×Dic₃₇	—	2	4	no	—
19	C₂×Dic₃₇	—	2	4	no	—
20	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
21	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₃₇	D₄	1	4	yes	—
23	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
24	#64438	—	2	4	no	—
25	C₂²×C₃₇	—	2	8	no	—
26	C₂²×C₃₇	—	2	2	no	—
27	C₂²×C₃₇	—	2	2	no	—
28	C₂²×C₃₇	C₂²⋊C₄	1	2	yes	—
29	C₂²×C₃₇	C₂×C₈	1	2	yes	—
30	C₂²×C₃₇	C₂×C₈	1	4	yes	complemented
31	C₂²×C₃₇	M₁₆	1	2	yes	—
32	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₃₇	—	2	2	no	—
34	Dic₃₇	C₂²⋊C₄	1	2	yes	—
35	Dic₃₇	C₂×D₄	1	2	yes	—
36	C₂×C₃₇	—	2	4	no	—
37	C₂×C₃₇	C₂²⋊C₈	1	4	yes	complemented
38	C₂×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₃₇	C₂²×C₈	1	1	yes	characteristic
40	C₂×C₃₇	C₂×M₁₆	1	1	yes	characteristic
41	C₂×C₂²⋊C₈	—	37	1	no	maximal, Sylow
42	C₃₇	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
43	C₂³×C₄	—	37	1	no	—
44	C₂²×C₈	—	37	2	no	—
45	C₂²⋊C₈	—	37	4	no	—
46	C₂⁴	#3866	1	1	yes	characteristic
47	C₂²×C₄	—	37	1	no	—
48	C₂²×C₄	—	37	2	no	—
49	C₂²×C₄	—	37	2	no	—
50	C₂²×C₄	—	37	1	no	—
51	C₂²×C₄	—	74	4	no	—
52	C₂×C₈	—	37	4	no	—
53	C₂×C₈	—	74	4	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	2	2	no	—
56	C₂³	#64438	1	4	yes	complemented
57	C₂³	C₂×#3866	1	2	yes	—
58	C₂³	C₂×#3866	1	1	yes	characteristic
59	C₂×C₄	—	37	4	no	—
60	C₂×C₄	—	37	1	no	—
61	C₂×C₄	—	37	1	no	—
62	C₂×C₄	—	37	2	no	—
63	C₂×C₄	—	74	4	no	—
64	C₂×C₄	—	74	4	no	—
65	C₂×C₄	—	74	2	no	—
66	C₈	—	74	4	no	—
67	C₂²	—	2	8	no	—
68	C₂²	—	2	2	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂×#64438	1	2	yes	—
71	C₂²	C₂×#64438	1	4	yes	complemented
72	C₂²	#10596957	1	2	yes	—
73	C₂²	C₂²⋊#3866	1	2	yes	—
74	C₂²	C₂²×#3866	1	1	yes	characteristic
75	C₄	—	37	2	no	—
76	C₄	—	37	2	no	—
77	C₄	—	74	2	no	—
78	C₂	—	2	4	no	—
79	C₂	C₂²⋊#64438	1	4	yes	direct product factor
80	C₂	C₂×C₂²⋊#3866	1	1	yes	characteristic
81	C₂	C₂²×#64438	1	1	yes	characteristic
82	C₂	C₂×#10596957	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#3866
commutator	C₂×C₃₇	C₂²×C₈
Frattini	C₂²	C₂²×#3866
Fitting, prime radical	C₂⁴×C₃₇	C₄
socle	C₂³×C₃₇	C₂×C₄
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₂⁴	#3866
hypocenter	C₃₇	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂²×#64438	C₂	semidirect
2. C₂²⋊#64438	C₂	direct (N × H)
11. C₂×#64438	C₂²	semidirect
14. C₂³×C₃₇	C₈	semidirect
30. C₂²×C₃₇	C₂×C₈	semidirect
37. C₂×C₃₇	C₂²⋊C₈	semidirect
42. C₃₇	C₂×C₂²⋊C₈	semidirect
56. C₂³	#64438	semidirect
71. C₂²	C₂×#64438	semidirect
79. C₂	C₂²⋊#64438	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×#64438	2
C₂²⋊#64438	2
C₂³×Dic₃₇	2
C₂×C₂²⋊C₈	37

Subgroups — C2×C22⋊#64438 #14558500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊#64438 #14558500