Subgroups — #17992688

Order 4736.

152 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	C₂²×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₃₇	—	2	2	no	—
4	#11924470	—	2	2	no	—
5	#11924470	C₄	1	4	yes	complemented
6	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₃₇	—	2	2	no	—
8	C₂×C₁₆×C₃₇	C₄	1	2	yes	complemented
9	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
10	C₂²×Dic₃₇	—	4	2	no	—
11	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₃₇	D₄	1	2	yes	—
14	C₂×C₈×C₃₇	Q₈	1	1	yes	characteristic
15	C₄⋊Dic₃₇	—	2	4	no	—
16	C₄⋊Dic₃₇	—	4	2	no	—
17	C₁₆×C₃₇	—	2	2	no	—
18	C₂³×C₃₇	D₈	1	1	yes	characteristic
19	C₂×C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₃₇	SD₁₆	1	2	yes	—
22	C₂×C₄×C₃₇	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₃₇	—	4	4	no	—
24	C₂×Dic₃₇	—	8	2	no	—
25	C₂×Dic₃₇	—	8	2	no	—
26	C₈×C₃₇	C₄²	1	1	yes	characteristic
27	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
29	C₂²×C₃₇	#102	1	2	yes	—
30	C₂²×C₃₇	#107	1	1	yes	characteristic
31	C₂²×C₃₇	D₁₆	1	1	yes	characteristic
32	C₂²×C₃₇	SD₃₂	1	2	yes	—
33	C₂²×C₃₇	Q₃₂	1	1	yes	characteristic
34	C₄×C₃₇	#95	1	1	yes	characteristic
35	C₄×C₃₇	#103	1	2	yes	—
36	C₄×C₃₇	#106	1	1	yes	characteristic
37	Dic₃₇	—	8	4	no	—
38	#1380	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	#340	1	1	yes	characteristic
40	C₂×C₃₇	#357	1	2	yes	—
41	C₂×C₃₇	#358	1	2	yes	—
42	C₂×C₃₇	#366	1	1	yes	characteristic
43	C₂×C₃₇	#367	1	1	yes	characteristic
44	C₂²×C₁₆	D₃₇	1	1	yes	characteristic
45	C₂×#107	—	37	2	no	—
46	C₃₇	#1380	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	74	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	Dic₃₇	1	2	yes	complemented
51	#107	—	37	4	no	—
52	#107	—	74	2	no	—
53	C₂²×C₄	—	148	2	no	—
54	C₂²×C₄	D₁₄₈	1	1	yes	characteristic
55	C₂×C₈	Dic₇₄	1	1	yes	characteristic
56	C₂×C₈	C₄×D₃₇	1	2	yes	—
57	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
59	C₄⋊C₄	—	74	4	no	—
60	C₄⋊C₄	—	148	2	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₂₉₆	1	1	yes	characteristic
63	C₂×C₄	—	296	2	no	—
64	C₂×C₄	—	296	2	no	—
65	C₂×C₄	—	148	4	no	—
66	C₂×C₄	#10596930	1	2	yes	—
67	C₂×C₄	Dic₁₄₈	1	1	yes	characteristic
68	C₂×C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
69	C₂×C₄	#10596938	1	2	yes	—
70	C₈	C₄×Dic₃₇	1	1	yes	characteristic
71	C₈	#10596936	1	2	yes	—
72	C₈	C₂²⋊Dic₃₇	1	1	yes	characteristic
73	C₂²	#11924458	1	2	yes	—
74	C₂²	#11924470	1	1	yes	characteristic
75	C₂²	D₅₉₂	1	1	yes	characteristic
76	C₂²	#11924481	1	2	yes	—
77	C₂²	Dic₂₉₆	1	1	yes	characteristic
78	C₄	—	296	4	no	—
79	C₄	#11924443	1	1	yes	characteristic
80	C₄	#11924461	1	2	yes	—
81	C₄	#11924468	1	1	yes	characteristic
82	C₂	#14557296	1	1	yes	characteristic
83	C₂	#14557335	1	2	yes	—
84	C₂	#14557338	1	2	yes	—
85	C₂	#14557359	1	1	yes	characteristic
86	C₂	#14557361	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₉₆
commutator	C₈×C₃₇	C₄²
Frattini	C₂²×C₈	C₂×D₃₇
Fitting	C₂²×C₁₆×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	D₈
cosocle	C₂²×C₈×C₃₇	C₂²
hypercenter	C₂²×C₁₆	D₃₇
hypocenter	C₃₇	#1380
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
5. #11924470	C₄	semidirect
8. C₂×C₁₆×C₃₇	C₄	semidirect
46. C₃₇	#1380	semidirect
50. 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
C₂×#11924470	2
C₂²×C₁₆×C₃₇	2
#1380	37