Subgroups — #17992567

Order 4736.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₁₄₈	C₂	1	1	yes	maximal, characteristic
2	#14557284	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#346	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₄₈	C₄	1	1	yes	characteristic
5	C₄×Dic₇₄	—	2	1	no	—
6	#11924470	C₄	1	1	yes	characteristic
7	C₄⋊#64436	—	2	1	no	—
8	#11924461	—	2	1	no	—
9	C₂×C₁₆×C₃₇	—	2	1	no	—
10	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₄	—	2	1	no	—
12	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₄²×C₃₇	D₄	1	1	yes	characteristic
15	C₄⋊Dic₃₇	—	2	1	no	—
16	#10596936	—	4	1	no	—
17	C₄×Dic₃₇	—	4	1	no	—
18	C₂×#64436	—	4	1	no	—
19	Dic₁₄₈	—	2	1	no	—
20	Dic₁₄₈	C₈	1	2	yes	complemented
21	C₁₆×C₃₇	—	2	2	no	—
22	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
24	C₂×C₄×C₃₇	SD₁₆	1	1	yes	characteristic
25	C₂×Dic₃₇	—	4	1	no	—
26	C₂×Dic₃₇	—	4	1	no	—
27	Dic₇₄	—	2	2	no	—
28	Dic₇₄	—	4	1	no	—
29	C₈×C₃₇	—	2	1	no	—
30	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
31	C₈×C₃₇	M₁₆	1	1	yes	characteristic
32	#64436	—	8	1	no	—
33	C₂²×C₃₇	#102	1	1	yes	characteristic
34	C₄×C₃₇	—	2	1	no	—
35	C₄×C₃₇	—	2	1	no	—
36	C₄×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₃₇	#104	1	1	yes	characteristic
38	Dic₃₇	—	4	2	no	—
39	Dic₃₇	—	8	1	no	—
40	#1334	—	37	1	no	maximal, Sylow
41	C₂×C₃₇	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₃₇	#360	1	1	yes	characteristic
43	C₂×C₃₇	#362	1	1	yes	characteristic
44	C₄×Q₁₆	—	37	1	no	—
45	#346	D₃₇	1	1	yes	characteristic
46	#334	—	37	1	no	—
47	C₃₇	#1334	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₁₆	—	37	1	no	—
49	C₄×Q₈	—	74	1	no	—
50	C₂×C₁₆	—	2	1	no	—
51	#107	—	37	1	no	—
52	C₄⋊C₈	—	74	1	no	—
53	#103	—	74	1	no	—
54	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
55	C₂×Q₈	—	74	1	no	—
56	Q₁₆	—	37	2	no	—
57	Q₁₆	—	74	1	no	—
58	C₂×C₈	—	148	1	no	—
59	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
60	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
61	C₄⋊C₄	—	74	1	no	—
62	C₄⋊C₄	—	148	1	no	—
63	C₄²	—	148	1	no	—
64	C₄²	D₁₄₈	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	Q₈	—	74	2	no	—
67	Q₈	—	148	1	no	—
68	C₂×C₄	—	148	1	no	—
69	C₂×C₄	—	148	1	no	—
70	C₂×C₄	#10596930	1	1	yes	characteristic
71	C₂×C₄	D₂₉₆	1	1	yes	characteristic
72	C₂×C₄	#10596938	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	296	1	no	—
75	C₈	C₈×D₃₇	1	1	yes	characteristic
76	C₈	#10596929	1	1	yes	characteristic
77	C₂²	#11924458	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	296	1	no	—
81	C₄	—	148	2	no	—
82	C₄	#11924448	1	1	yes	characteristic
83	C₄	#11924464	1	1	yes	characteristic
84	C₂	#14557262	1	1	yes	characteristic
85	C₂	#14557344	1	1	yes	characteristic
86	C₂	#14557350	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924458
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#346	C₂
socle, prime radical	C₂²×C₃₇	#102
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#346	D₃₇
hypocenter	C₃₇	#1334
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
20. Dic₁₄₈	C₈	semidirect
47. C₃₇	#1334	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₁₄₈	2
#14557284	2
C₃₇×#346	2
#1334	37