Subgroups — C₂×#11924603 #14558535

Order 2368.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#64438	C₂	1	2	yes	maximal
2	#11924603	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₃₇	C₄	1	1	yes	characteristic
5	C₂²×Dic₃₇	C₄	1	1	yes	characteristic
6	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
7	C₂×#64438	—	2	4	no	—
8	C₂×#64438	C₂²	1	4	yes	—
9	C₄×Dic₃₇	C₄	1	2	yes	—
10	C₄×Dic₃₇	C₂²	1	2	yes	—
11	C₂³×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₃₇	—	2	2	no	—
13	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
14	C₂×Dic₃₇	C₈	1	4	yes	complemented
15	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
17	C₂×Dic₃₇	D₄	1	2	yes	—
18	C₂×Dic₃₇	Q₈	1	2	yes	—
19	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
20	#64438	—	2	4	no	—
21	C₂²×C₃₇	C₄⋊C₄	1	2	yes	—
22	C₂²×C₃₇	C₂×C₈	1	2	yes	—
23	C₂²×C₃₇	M₁₆	1	2	yes	—
24	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₃₇	—	2	2	no	—
26	Dic₃₇	C₄⋊C₄	1	2	yes	—
27	Dic₃₇	C₂×C₈	1	4	yes	complemented
28	Dic₃₇	C₂×D₄	1	1	yes	characteristic
29	Dic₃₇	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₃₇	C₄⋊C₈	1	4	yes	complemented
31	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₃₇	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₃₇	C₂×M₁₆	1	1	yes	characteristic
34	C₂×C₄⋊C₈	—	37	1	no	maximal, Sylow
35	C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	—	37	2	no	—
37	C₂×C₄²	—	37	1	no	—
38	C₄⋊C₈	—	37	4	no	—
39	C₂²×C₄	—	37	1	no	—
40	C₂²×C₄	—	37	1	no	—
41	C₂²×C₄	#3866	1	1	yes	characteristic
42	C₂×C₈	—	37	4	no	—
43	C₂×C₈	—	74	4	no	—
44	C₄²	—	37	2	no	—
45	C₄²	—	37	2	no	—
46	C₂³	C₂×#3866	1	1	yes	characteristic
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	37	4	no	—
49	C₂×C₄	—	37	2	no	—
50	C₂×C₄	—	37	2	no	—
51	C₂×C₄	—	37	1	no	—
52	C₂×C₄	—	37	1	no	—
53	C₂×C₄	—	37	2	no	—
54	C₂×C₄	C₂×#3866	1	2	yes	—
55	C₈	—	74	4	no	—
56	C₂²	D₃₇⋊C₈	1	2	yes	—
57	C₂²	C₄⋊#3866	1	2	yes	—
58	C₂²	#10596957	1	2	yes	—
59	C₂²	C₂²×#3866	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	—	37	1	no	—
62	C₄	—	37	2	no	—
63	C₄	—	37	1	no	—
64	C₄	—	37	4	no	—
65	C₂	#11924603	1	4	yes	direct product factor
66	C₂	C₂×C₄⋊#3866	1	1	yes	characteristic
67	C₂	C₂×D₃₇⋊C₈	1	1	yes	characteristic
68	C₂	C₂×#10596957	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #11924603	C₂	direct (N × H)
14. C₂×Dic₃₇	C₈	semidirect
27. Dic₃₇	C₂×C₈	semidirect
30. C₂×C₃₇	C₄⋊C₈	semidirect
35. C₃₇	C₂×C₄⋊C₈	semidirect
65. C₂	#11924603	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
#11924603	2
C₂×C₄×Dic₃₇	2
C₂×C₄⋊C₈	37

Subgroups — C2×#11924603 #14558535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924603 #14558535