Subgroups — C₂×#11924624 #14558610

Order 2368.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924624	C₂	1	8	yes	maximal, direct product factor
2	C₂×#10596953	C₂	1	3	yes	maximal, complemented
3	C₂×D₃₇⋊C₈	C₂	1	3	yes	maximal, complemented
4	C₂×#10596966	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₃₇	C₄	1	1	yes	characteristic
6	#10596966	C₄	1	4	yes	—
7	#10596966	C₂²	1	4	yes	—
8	C₂×D₁₄₈	C₄	1	3	yes	—
9	C₂×C₄×D₃₇	C₂²	1	3	yes	—
10	C₂×#64438	C₂²	1	1	yes	characteristic
11	C₂×#64438	C₂²	1	3	yes	—
12	#10596953	C₂²	1	12	yes	complemented
13	D₃₇⋊C₈	C₂²	1	12	yes	complemented
14	C₂²×D₃₇	C₂×C₄	1	3	yes	—
15	Q₈×C₃₇	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
17	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
18	D₁₄₈	C₂×C₄	1	12	yes	—
19	C₄×D₃₇	C₂×C₄	1	6	yes	—
20	C₄×D₃₇	C₂³	1	6	yes	—
21	#64438	C₂³	1	2	yes	—
22	#64438	C₂³	1	6	yes	—
23	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₃₇	—	2	6	no	—
25	C₂×D₃₇	C₂²×C₄	1	6	yes	—
26	C₄×C₃₇	C₂²×C₄	1	6	yes	—
27	Dic₃₇	C₂²×C₄	1	1	yes	characteristic
28	Dic₃₇	C₂⁴	1	1	yes	characteristic
29	C₂×C₃₇	#131	1	2	yes	complemented
30	C₂×C₃₇	C₂³×C₄	1	1	yes	characteristic
31	D₃₇	—	2	6	no	—
32	C₂×#131	—	37	1	no	maximal, Sylow
33	C₃₇	C₂×#131	1	1	yes	characteristic, complemented, Sylow
34	C₂×#41	—	37	1	no	—
35	#131	—	37	8	no	—
36	C₂×M₁₆	—	37	3	no	—
37	C₂²×C₈	—	37	3	no	—
38	#41	—	37	4	no	—
39	#41	—	37	4	no	—
40	C₂×Q₈	#3866	1	1	yes	characteristic
41	C₂×D₄	—	37	3	no	—
42	C₂²×C₄	—	37	3	no	—
43	M₁₆	—	37	12	no	—
44	C₂×C₈	—	37	12	no	—
45	C₂×C₈	—	37	1	no	—
46	C₂×C₈	—	37	3	no	—
47	C₂³	—	37	3	no	—
48	Q₈	C₂×#3866	1	4	yes	—
49	D₄	—	37	12	no	—
50	C₂×C₄	—	37	1	no	—
51	C₂×C₄	—	37	6	no	—
52	C₂×C₄	—	37	6	no	—
53	C₂×C₄	C₂×#3866	1	3	yes	—
54	C₈	—	37	2	no	—
55	C₈	—	37	6	no	—
56	C₂²	—	37	6	no	—
57	C₂²	—	74	6	no	—
58	C₂²	C₂²×#3866	1	1	yes	characteristic
59	C₄	—	37	1	no	—
60	C₄	—	37	1	no	—
61	C₄	C₂²×#3866	1	6	yes	—
62	C₂	—	74	6	no	—
63	C₂	#11924624	1	2	yes	direct product factor
64	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	C₂×#10596966	C₂
cosocle	Dic₃₇	C₂⁴
hypercenter	C₂×Q₈	#3866
hypocenter	C₃₇	C₂×#131
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. #11924624	C₂	direct (N × H)
2. C₂×#10596953	C₂	semidirect
3. C₂×D₃₇⋊C₈	C₂	semidirect
12. #10596953	C₂²	semidirect
13. D₃₇⋊C₈	C₂²	semidirect
29. C₂×C₃₇	#131	semidirect
33. C₃₇	C₂×#131	semidirect
63. C₂	#11924624	direct (N × H)

Maximal subgroups

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

subgroup	index
#11924624	2
C₂×#10596953	2
C₂×D₃₇⋊C₈	2
C₂×#10596966	2
C₂×#131	37

Subgroups — C2×#11924624 #14558610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924624 #14558610