Subgroups — C₂×#14557403 #17996997

Order 4736.

888 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Dic₃₇	C₂	1	6	yes	maximal
2	#14557403	C₂	1	8	yes	maximal, direct product factor
3	C₂²×C₄²×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₃₇	C₂²	1	4	yes	—
5	C₂×C₄⋊Dic₃₇	—	2	24	no	—
6	C₂×C₄⋊Dic₃₇	C₂²	1	24	yes	—
7	C₂³×C₄×C₃₇	C₂²	1	3	yes	—
8	C₂×C₄²×C₃₇	C₄	1	8	yes	complemented
9	C₂×C₄²×C₃₇	C₂²	1	4	yes	—
10	C₂⁴×C₃₇	C₂³	1	1	yes	characteristic
11	C₂²×C₄×C₃₇	C₂×C₄	1	12	yes	—
12	C₂²×C₄×C₃₇	D₄	1	12	yes	—
13	C₂²×C₄×C₃₇	Q₈	1	12	yes	—
14	C₂²×C₄×C₃₇	C₂³	1	6	yes	—
15	C₂²×Dic₃₇	—	2	24	no	—
16	C₂²×Dic₃₇	C₂³	1	8	yes	—
17	C₄²×C₃₇	C₂×C₄	1	16	yes	complemented
18	C₄⋊Dic₃₇	—	2	48	no	—
19	C₂³×C₃₇	C₂²×C₄	1	2	yes	—
20	C₂³×C₃₇	C₂×D₄	1	6	yes	—
21	C₂³×C₃₇	C₂×Q₈	1	6	yes	—
22	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
23	C₂×C₄×C₃₇	C₄⋊C₄	1	48	yes	complemented
24	C₂×C₄×C₃₇	C₂²×C₄	1	12	yes	—
25	C₂×C₄×C₃₇	C₂×D₄	1	12	yes	—
26	C₂×C₄×C₃₇	C₂×Q₈	1	12	yes	—
27	C₂×Dic₃₇	—	2	24	no	—
28	C₂×Dic₃₇	—	4	16	no	—
29	C₂²×C₃₇	C₂×C₄⋊C₄	1	12	yes	—
30	C₂²×C₃₇	#127	1	4	yes	—
31	C₂²×C₃₇	C₄⋊Q₈	1	12	yes	—
32	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
33	C₂²×C₃₇	C₂²×D₄	1	3	yes	—
34	C₂²×C₃₇	C₂²×Q₈	1	3	yes	—
35	C₄×C₃₇	C₂×C₄⋊C₄	1	24	yes	complemented
36	Dic₃₇	—	4	8	no	—
37	C₂×#384	—	37	1	no	maximal, Sylow
38	C₂×C₃₇	#384	1	8	yes	complemented
39	C₂×C₃₇	C₂²×C₄⋊C₄	1	3	yes	—
40	C₂×C₃₇	C₂×#127	1	1	yes	characteristic
41	C₂×C₃₇	C₂×C₄⋊Q₈	1	3	yes	—
42	C₂²×C₄⋊C₄	—	37	6	no	—
43	C₂²×C₄²	D₃₇	1	1	yes	characteristic
44	#384	—	37	8	no	—
45	C₃₇	C₂×#384	1	1	yes	characteristic, complemented, Sylow
46	C₂³×C₄	—	37	4	no	—
47	C₂³×C₄	C₂×D₃₇	1	3	yes	—
48	C₂×C₄⋊C₄	—	37	24	no	—
49	C₂×C₄⋊C₄	—	74	24	no	—
50	C₂×C₄²	Dic₃₇	1	8	yes	complemented
51	C₂×C₄²	C₂×D₃₇	1	4	yes	—
52	C₂⁴	C₂²×D₃₇	1	1	yes	characteristic
53	C₂²×C₄	—	37	8	no	—
54	C₂²×C₄	—	74	24	no	—
55	C₂²×C₄	Dic₇₄	1	12	yes	—
56	C₂²×C₄	D₁₄₈	1	12	yes	—
57	C₂²×C₄	C₂×Dic₃₇	1	12	yes	—
58	C₂²×C₄	C₂²×D₃₇	1	6	yes	—
59	C₄⋊C₄	—	74	48	no	—
60	C₄²	C₂×Dic₃₇	1	16	yes	complemented
61	C₂³	C₂×Dic₇₄	1	6	yes	—
62	C₂³	C₂×D₁₄₈	1	6	yes	—
63	C₂³	C₂²×Dic₃₇	1	2	yes	—
64	C₂³	C₂³×D₃₇	1	1	yes	characteristic
65	C₂×C₄	—	74	24	no	—
66	C₂×C₄	—	148	16	no	—
67	C₂×C₄	C₄⋊Dic₃₇	1	48	yes	complemented
68	C₂×C₄	C₂×Dic₇₄	1	12	yes	—
69	C₂×C₄	C₂×D₁₄₈	1	12	yes	—
70	C₂×C₄	C₂²×Dic₃₇	1	12	yes	—
71	C₂²	C₂×C₄⋊Dic₃₇	1	12	yes	—
72	C₂²	#11924533	1	4	yes	—
73	C₂²	#11924536	1	12	yes	—
74	C₂²	C₂³×Dic₃₇	1	1	yes	characteristic
75	C₂²	C₂²×D₁₄₈	1	3	yes	—
76	C₂²	C₂²×Dic₇₄	1	3	yes	—
77	C₄	—	148	8	no	—
78	C₄	C₂×C₄⋊Dic₃₇	1	24	yes	complemented
79	C₂	#14557403	1	8	yes	direct product factor
80	C₂	C₂²×C₄⋊Dic₃₇	1	3	yes	—
81	C₂	C₂×#11924533	1	1	yes	characteristic
82	C₂	C₂×#11924536	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₃₇
commutator	C₂²×C₃₇	C₂³×C₄
Frattini	C₂³	C₂³×D₃₇
Fitting	C₂²×C₄²×C₃₇	C₂
socle, prime radical	C₂⁴×C₃₇	C₂³
cosocle	C₂³×C₃₇	C₂⁴
hypercenter	C₂²×C₄²	D₃₇
hypocenter	C₃₇	C₂×#384
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. #14557403	C₂	direct (N × H)
8. C₂×C₄²×C₃₇	C₄	semidirect
17. C₄²×C₃₇	C₂×C₄	semidirect
23. C₂×C₄×C₃₇	C₄⋊C₄	semidirect
35. C₄×C₃₇	C₂×C₄⋊C₄	semidirect
38. C₂×C₃₇	#384	semidirect
45. C₃₇	C₂×#384	semidirect
50. C₂×C₄²	Dic₃₇	semidirect
60. C₄²	C₂×Dic₃₇	semidirect
67. C₂×C₄	C₄⋊Dic₃₇	semidirect
78. C₄	C₂×C₄⋊Dic₃₇	semidirect
79. C₂	#14557403	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×C₄⋊Dic₃₇	2
#14557403	2
C₂²×C₄²×C₃₇	2
C₂×#384	37

Subgroups — C2×#14557403 #17996997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14557403 #17996997