Subgroups — C₂×#14557931 #18005095

Order 4736.

424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924536	C₂	1	2	yes	maximal
2	#14557931	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11924468	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₇₄	—	2	2	no	—
6	#11924536	—	2	4	no	—
7	#11924536	C₂²	1	8	yes	—
8	C₂×C₄⋊Dic₃₇	—	2	2	no	—
9	C₂×C₄⋊Dic₃₇	C₂²	1	4	yes	—
10	#11924468	C₂²	1	16	yes	—
11	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
12	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₃₇	C₂²	1	4	yes	—
14	C₂²×C₄×C₃₇	D₄	1	2	yes	—
15	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₃₇	—	2	4	no	—
17	C₂×Dic₇₄	—	2	8	no	—
18	C₂×Dic₇₄	—	4	8	no	—
19	C₂×C₈×C₃₇	Q₈	1	8	yes	complemented
20	C₂×C₈×C₃₇	C₂³	1	4	yes	—
21	C₄²×C₃₇	D₄	1	2	yes	—
22	C₄²×C₃₇	C₂³	1	2	yes	—
23	C₄⋊Dic₃₇	—	2	8	no	—
24	C₄⋊Dic₃₇	—	2	4	no	—
25	C₄⋊Dic₃₇	C₂³	1	8	yes	—
26	C₂³×C₃₇	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇	SD₁₆	1	8	yes	—
28	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₃₇	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₃₇	C₂×Q₈	1	4	yes	—
31	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
32	C₂×Dic₃₇	—	2	8	no	—
33	C₂×Dic₃₇	—	4	8	no	—
34	Dic₇₄	—	4	16	no	—
35	C₈×C₃₇	C₂×Q₈	1	8	yes	complemented
36	C₂²×C₃₇	C₄⋊Q₈	1	2	yes	—
37	C₂²×C₃₇	C₂×SD₁₆	1	4	yes	—
38	C₂²×C₃₇	C₂²×D₄	1	1	yes	characteristic
39	C₄×C₃₇	C₄⋊Q₈	1	2	yes	—
40	C₄×C₃₇	C₂×SD₁₆	1	8	yes	—
41	C₄×C₃₇	C₂²×Q₈	1	2	yes	—
42	Dic₃₇	—	4	8	no	—
43	C₂×#498	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	#498	1	4	yes	complemented
45	C₂×C₃₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
46	C₂×C₃₇	C₂²×SD₁₆	1	2	yes	—
47	C₂×C₄⋊Q₈	—	37	2	no	—
48	#498	—	37	8	no	—
49	C₂×#106	—	37	4	no	—
50	C₂×C₄×C₈	D₃₇	1	1	yes	characteristic
51	C₃₇	C₂×#498	1	1	yes	characteristic, complemented, Sylow
52	C₂²×Q₈	—	74	2	no	—
53	C₂²×C₈	C₂×D₃₇	1	2	yes	—
54	C₄⋊Q₈	—	37	8	no	—
55	C₄⋊Q₈	—	74	4	no	—
56	C₂×C₄⋊C₄	—	37	4	no	—
57	C₂×C₄⋊C₄	—	74	2	no	—
58	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
59	#106	—	37	16	no	—
60	C₄×C₈	C₂×D₃₇	1	4	yes	—
61	C₂×Q₈	—	74	8	no	—
62	C₂×Q₈	—	148	8	no	—
63	C₂²×C₄	—	74	4	no	—
64	C₂²×C₄	D₁₄₈	1	2	yes	—
65	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
66	C₂×C₈	Dic₇₄	1	8	yes	complemented
67	C₂×C₈	C₂²×D₃₇	1	4	yes	—
68	C₄⋊C₄	—	37	8	no	—
69	C₄⋊C₄	—	74	4	no	—
70	C₄⋊C₄	—	74	8	no	—
71	C₄²	D₁₄₈	1	2	yes	—
72	C₄²	C₂²×D₃₇	1	2	yes	—
73	C₂³	C₂×D₁₄₈	1	1	yes	characteristic
74	Q₈	—	148	16	no	—
75	C₂×C₄	—	74	8	no	—
76	C₂×C₄	—	148	8	no	—
77	C₂×C₄	#10596930	1	8	yes	—
78	C₂×C₄	C₂×Dic₇₄	1	4	yes	—
79	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
80	C₂×C₄	C₂×D₁₄₈	1	4	yes	—
81	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
82	C₈	C₂×Dic₇₄	1	8	yes	complemented
83	C₂²	#11924536	1	2	yes	—
84	C₂²	C₂×#10596930	1	4	yes	—
85	C₂²	C₂²×D₁₄₈	1	1	yes	characteristic
86	C₄	—	148	8	no	—
87	C₄	#11924536	1	2	yes	—
88	C₄	C₂×#10596930	1	8	yes	—
89	C₄	C₂²×Dic₇₄	1	2	yes	—
90	C₂	#14557931	1	4	yes	direct product factor
91	C₂	C₂×#11924536	1	1	yes	characteristic
92	C₂	C₂²×#10596930	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₄₈
commutator, cosocle	C₂×C₄×C₃₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₃₇
Fitting	C₂×C₄×C₈×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	C₂×D₄
hypercenter	C₂×C₄×C₈	D₃₇
hypocenter	C₃₇	C₂×#498
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #14557931	C₂	direct (N × H)
19. C₂×C₈×C₃₇	Q₈	semidirect
35. C₈×C₃₇	C₂×Q₈	semidirect
44. C₂×C₃₇	#498	semidirect
51. C₃₇	C₂×#498	semidirect
66. C₂×C₈	Dic₇₄	semidirect
82. C₈	C₂×Dic₇₄	semidirect
90. C₂	#14557931	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11924536	2
#14557931	2
C₂×#11924468	2
C₂×C₄×C₈×C₃₇	2
C₂×#498	37

Subgroups — C2×#14557931 #18005095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14557931 #18005095