Subgroups — C₂×#14558478 #18011042

Order 4736.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558478	C₂	1	8	yes	maximal, direct product factor
2	C₂×(C₂×#3866)⋊C₄	C₂	1	6	yes	maximal
3	C₂×C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×#3866	C₂²	1	4	yes	—
5	(C₂×#3866)⋊C₄	C₂²	1	24	yes	—
6	C₂²×C₄×D₃₇	C₂²	1	3	yes	—
7	C₂×C₄×Dic₃₇	C₄	1	3	yes	complemented
8	C₄²×D₃₇	C₄	1	4	yes	complemented
9	C₄²×D₃₇	C₂²	1	4	yes	—
10	C₂×C₄²×C₃₇	C₄	1	1	yes	characteristic, complemented
11	C₂³×D₃₇	C₂³	1	1	yes	characteristic
12	C₂²×#3866	—	2	24	no	—
13	C₂²×#3866	C₂³	1	8	yes	—
14	C₂²×C₄×C₃₇	C₂×C₄	1	3	yes	—
15	C₂²×Dic₃₇	C₂×C₄	1	3	yes	—
16	C₂×C₄×D₃₇	—	2	12	no	—
17	C₂×C₄×D₃₇	C₂×C₄	1	6	yes	—
18	C₂×C₄×D₃₇	C₂³	1	6	yes	—
19	C₄²×C₃₇	C₂×C₄	1	4	yes	complemented
20	C₄×Dic₃₇	C₂×C₄	1	12	yes	complemented
21	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
22	C₂²×D₃₇	C₂²×C₄	1	1	yes	characteristic
23	C₂²×D₃₇	#41	1	12	yes	—
24	C₂²×D₃₇	C₂⁴	1	1	yes	characteristic
25	C₂×#3866	—	2	24	no	—
26	C₂×#3866	—	4	16	no	—
27	C₂×C₄×C₃₇	—	2	6	no	—
28	C₂×C₄×C₃₇	C₂²×C₄	1	6	yes	—
29	C₂×Dic₃₇	—	2	6	no	—
30	C₂×Dic₃₇	C₂²×C₄	1	6	yes	—
31	C₄×D₃₇	—	2	12	no	—
32	C₄×D₃₇	—	2	12	no	—
33	C₂²×C₃₇	#117	1	6	yes	—
34	C₂²×C₃₇	C₂³×C₄	1	1	yes	characteristic
35	C₂×D₃₇	#117	1	6	yes	—
36	C₂×D₃₇	#126	1	16	yes	—
37	C₂×D₃₇	C₂×#41	1	6	yes	—
38	#3866	—	4	8	no	—
39	C₄×C₃₇	—	2	6	no	—
40	Dic₃₇	—	2	6	no	—
41	C₂×#383	—	37	1	no	maximal, Sylow
42	C₂×C₃₇	#383	1	4	yes	complemented
43	C₂×C₃₇	C₂×#117	1	3	yes	—
44	D₃₇	#383	1	4	yes	complemented
45	D₃₇	C₂×#126	1	4	yes	—
46	C₂²×C₄²	—	37	1	no	—
47	#383	—	37	8	no	—
48	C₂×#95	—	37	6	no	—
49	C₃₇	C₂×#383	1	1	yes	characteristic, complemented, Sylow
50	C₂³×C₄	—	37	3	no	—
51	C₂³×C₄	—	37	4	no	—
52	C₂×C₄²	—	37	3	no	—
53	C₂×C₄²	—	37	4	no	—
54	C₂×C₄²	—	37	4	no	—
55	C₂×C₄²	#3866	1	1	yes	characteristic, complemented
56	#95	—	37	24	no	—
57	C₂⁴	—	37	1	no	—
58	C₂²×C₄	—	37	3	no	—
59	C₂²×C₄	—	37	6	no	—
60	C₂²×C₄	—	37	6	no	—
61	C₂²×C₄	—	37	8	no	—
62	C₂²×C₄	—	74	12	no	—
63	C₂²×C₄	—	74	24	no	—
64	C₂²×C₄	C₂×#3866	1	3	yes	—
65	C₄²	—	37	12	no	—
66	C₄²	C₂×#3866	1	4	yes	complemented
67	C₂³	—	37	12	no	—
68	C₂³	—	37	1	no	—
69	C₂³	—	37	1	no	—
70	C₂³	C₂²×#3866	1	1	yes	characteristic
71	C₂×C₄	—	2	6	no	—
72	C₂×C₄	—	37	6	no	—
73	C₂×C₄	—	74	12	no	—
74	C₂×C₄	—	74	12	no	—
75	C₂×C₄	—	74	6	no	—
76	C₂×C₄	—	74	24	no	—
77	C₂×C₄	—	148	16	no	—
78	C₂×C₄	C₂²×#3866	1	6	yes	—
79	C₂²	—	37	16	no	—
80	C₂²	—	37	6	no	—
81	C₂²	—	37	6	no	—
82	C₂²	#11924615	1	6	yes	—
83	C₂²	C₂³×#3866	1	1	yes	characteristic
84	C₄	—	2	6	no	—
85	C₄	—	74	6	no	—
86	C₄	—	148	8	no	—
87	C₂	—	37	4	no	—
88	C₂	—	37	4	no	—
89	C₂	#14558478	1	4	yes	direct product factor
90	C₂	C₂×#11924615	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×#3866
commutator	C₂²×C₃₇	C₂³×C₄
Frattini	C₂²	C₂³×#3866
Fitting	C₂×C₄²×C₃₇	C₄
socle	C₂³×C₃₇	C₂²×C₄
prime radical	C₂³×D₃₇	C₂³
cosocle	C₂²×D₃₇	C₂⁴
hypercenter	C₂×C₄²	#3866
hypocenter	C₃₇	C₂×#383
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #14558478	C₂	direct (N × H)
7. C₂×C₄×Dic₃₇	C₄	semidirect
8. C₄²×D₃₇	C₄	semidirect
10. C₂×C₄²×C₃₇	C₄	semidirect
19. C₄²×C₃₇	C₂×C₄	semidirect
20. C₄×Dic₃₇	C₂×C₄	semidirect
42. C₂×C₃₇	#383	semidirect
44. D₃₇	#383	semidirect
49. C₃₇	C₂×#383	semidirect
55. C₂×C₄²	#3866	semidirect
66. C₄²	C₂×#3866	semidirect
89. C₂	#14558478	direct (N × H)

Maximal subgroups

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

subgroup	index
#14558478	2
C₂×(C₂×#3866)⋊C₄	2
C₂×C₄²×D₃₇	2
C₂×#383	37

Subgroups — C2×#14558478 #18011042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14558478 #18011042