Subgroups — #17996380

Order 4736.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557571	C₂	1	2	yes	maximal
2	#14557361	C₂	1	2	yes	maximal, complemented
3	#14557359	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
5	#11924495	—	2	2	no	—
6	#11924470	C₂²	1	4	yes	—
7	#11924468	—	2	2	no	—
8	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₃₇	C₄	1	4	yes	complemented
10	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	Q₈	1	2	yes	—
16	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
17	C₂²⋊Dic₃₇	—	4	2	no	—
18	C₄⋊Dic₃₇	—	2	4	no	—
19	C₄×Dic₃₇	—	4	2	no	—
20	C₁₆×C₃₇	C₂×C₄	1	2	yes	—
21	C₁₆×C₃₇	C₂×C₄	1	2	yes	—
22	C₂³×C₃₇	D₈	1	1	yes	characteristic
23	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
25	C₂×C₄×C₃₇	Q₁₆	1	2	yes	—
26	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₃₇	—	4	4	no	—
28	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
29	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
31	C₂²×C₃₇	—	2	2	no	—
32	C₂²×C₃₇	#107	1	2	yes	—
33	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
34	C₄×C₃₇	#107	1	2	yes	—
35	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
37	Dic₃₇	—	8	4	no	—
38	#2158	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	—	2	2	no	—
40	C₂×C₃₇	C₂×#107	1	1	yes	characteristic
41	C₂×C₃₇	#508	1	2	yes	—
42	C₂²×C₁₆	D₃₇	1	1	yes	characteristic
43	#427	—	37	2	no	—
44	#367	—	37	2	no	—
45	#366	—	37	2	no	—
46	C₃₇	#2158	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
48	#117	—	74	2	no	—
49	C₂×C₁₆	Dic₃₇	1	4	yes	complemented
50	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
51	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
52	#107	—	37	4	no	—
53	#106	—	74	2	no	—
54	C₂²×C₄	D₁₄₈	1	1	yes	characteristic
55	C₂×C₈	Dic₇₄	1	2	yes	—
56	C₂×C₈	D₁₄₈	1	1	yes	characteristic
57	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
58	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
59	C₄⋊C₄	—	74	4	no	—
60	C₂²⋊C₄	—	148	2	no	—
61	C₄²	—	148	2	no	—
62	C₁₆	C₂×Dic₃₇	1	2	yes	—
63	C₁₆	C₂×Dic₃₇	1	2	yes	—
64	C₂³	D₂₉₆	1	1	yes	characteristic
65	C₂×C₄	—	148	4	no	—
66	C₂×C₄	D₂₉₆	1	1	yes	characteristic
67	C₂×C₄	Dic₁₄₈	1	2	yes	—
68	C₂×C₄	C₄⋊Dic₃₇	1	2	yes	—
69	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
70	C₈	C₄⋊Dic₃₇	1	2	yes	—
71	C₈	C₂×Dic₇₄	1	1	yes	characteristic
72	C₈	C₂²×Dic₃₇	1	1	yes	characteristic
73	C₂²	—	2	2	no	—
74	C₂²	#11924470	1	2	yes	—
75	C₂²	C₂×D₂₉₆	1	1	yes	characteristic
76	C₄	—	296	4	no	—
77	C₄	#11924470	1	2	yes	—
78	C₄	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
79	C₄	C₂×Dic₁₄₈	1	1	yes	characteristic
80	C₂	—	2	2	no	—
81	C₂	C₂×#11924470	1	1	yes	characteristic
82	C₂	#14557965	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₂₉₆
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₂²×C₁₆×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₈
prime radical	C₂³×C₃₇	D₈
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	C₂²×C₁₆	D₃₇
hypocenter	C₃₇	#2158
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ 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	semidirect
3. #14557359	C₂	semidirect
9. C₂×C₁₆×C₃₇	C₄	semidirect
46. C₃₇	#2158	semidirect
49. C₂×C₁₆	Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
#14557571	2
#14557361	2
#14557359	2
C₂²×C₁₆×C₃₇	2
#2158	37