Subgroups — C₂×#14557361 #17996376

Order 4736.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924470	C₂	1	2	yes	maximal
2	#14557361	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₃₇	—	2	2	no	—
5	#11924470	—	2	2	no	—
6	#11924470	C₂²	1	4	yes	—
7	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₃₇	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₃₇	C₂²	1	2	yes	—
10	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
11	C₂²×Dic₃₇	—	4	2	no	—
12	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₃₇	Q₈	1	2	yes	—
15	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
16	C₄⋊Dic₃₇	—	2	4	no	—
17	C₄⋊Dic₃₇	—	4	2	no	—
18	C₁₆×C₃₇	C₂×C₄	1	4	yes	complemented
19	C₂³×C₃₇	D₈	1	1	yes	characteristic
20	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
22	C₂×C₄×C₃₇	Q₁₆	1	2	yes	—
23	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₃₇	—	4	4	no	—
25	C₂×Dic₃₇	—	8	4	no	—
26	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
27	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₃₇	#107	1	2	yes	—
30	C₂²×C₃₇	SD₃₂	1	4	yes	—
31	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
32	C₄×C₃₇	#107	1	2	yes	—
33	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
35	Dic₃₇	—	8	4	no	—
36	C₂×#367	—	37	1	no	maximal, Sylow
37	C₂×C₃₇	#367	1	4	yes	complemented
38	C₂×C₃₇	C₂×#107	1	1	yes	characteristic
39	C₂×C₃₇	C₂×SD₃₂	1	2	yes	—
40	C₂²×C₁₆	D₃₇	1	1	yes	characteristic
41	C₂×#107	—	37	2	no	—
42	#367	—	37	4	no	—
43	C₃₇	C₂×#367	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
45	C₂×C₄⋊C₄	—	74	2	no	—
46	C₂×C₁₆	Dic₃₇	1	4	yes	complemented
47	C₂×C₁₆	C₂×D₃₇	1	2	yes	—
48	#107	—	37	4	no	—
49	#107	—	74	2	no	—
50	C₂²×C₄	—	148	2	no	—
51	C₂²×C₄	D₁₄₈	1	1	yes	characteristic
52	C₂×C₈	Dic₇₄	1	2	yes	—
53	C₂×C₈	D₁₄₈	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
55	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
56	C₄⋊C₄	—	74	4	no	—
57	C₄⋊C₄	—	148	2	no	—
58	C₁₆	C₂×Dic₃₇	1	4	yes	complemented
59	C₂³	D₂₉₆	1	1	yes	characteristic
60	C₂×C₄	—	296	4	no	—
61	C₂×C₄	—	148	4	no	—
62	C₂×C₄	D₂₉₆	1	1	yes	characteristic
63	C₂×C₄	Dic₁₄₈	1	2	yes	—
64	C₂×C₄	C₄⋊Dic₃₇	1	2	yes	—
65	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
66	C₈	C₄⋊Dic₃₇	1	2	yes	—
67	C₈	C₂×Dic₇₄	1	1	yes	characteristic
68	C₈	C₂²×Dic₃₇	1	1	yes	characteristic
69	C₂²	#11924470	1	2	yes	—
70	C₂²	#11924481	1	4	yes	—
71	C₂²	C₂×D₂₉₆	1	1	yes	characteristic
72	C₄	—	296	4	no	—
73	C₄	#11924470	1	2	yes	—
74	C₄	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
75	C₄	C₂×Dic₁₄₈	1	1	yes	characteristic
76	C₂	#14557361	1	4	yes	direct product factor
77	C₂	C₂×#11924470	1	1	yes	characteristic
78	C₂	C₂×#11924481	1	2	yes	—

	subgroup	G/H
center	C₂³	D₂₉₆
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₂²×C₁₆×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	D₈
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	C₂²×C₁₆	D₃₇
hypocenter	C₃₇	C₂×#367
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14557361	C₂	direct (N × H)
8. C₂×C₁₆×C₃₇	C₄	semidirect
18. C₁₆×C₃₇	C₂×C₄	semidirect
37. C₂×C₃₇	#367	semidirect
43. C₃₇	C₂×#367	semidirect
46. C₂×C₁₆	Dic₃₇	semidirect
58. C₁₆	C₂×Dic₃₇	semidirect
76. C₂	#14557361	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×#11924470	2
#14557361	2
C₂²×C₁₆×C₃₇	2
C₂×#367	37

Subgroups — C2×#14557361 #17996376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14557361 #17996376