Subgroups — #17992559

Order 4736.

98 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	C₄×#10596925	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₄₈	C₄	1	1	yes	characteristic
5	C₄×Dic₇₄	—	2	1	no	—
6	C₂×#10596925	—	2	1	no	—
7	#11924470	C₄	1	1	yes	characteristic
8	#11924461	—	2	1	no	—
9	C₄⋊C₈×C₃₇	—	2	1	no	—
10	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₄	—	2	1	no	—
12	C₂×C₈×C₃₇	—	4	1	no	—
13	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₄²×C₃₇	D₄	1	1	yes	characteristic
16	C₄⋊Dic₃₇	—	2	1	no	—
17	#10596936	—	4	1	no	—
18	C₄×Dic₃₇	—	4	1	no	—
19	Dic₁₄₈	—	2	1	no	—
20	Dic₁₄₈	C₈	1	2	yes	complemented
21	#10596925	—	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	—	8	1	no	—
31	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
32	C₈×C₃₇	M₁₆	1	1	yes	characteristic
33	C₂²×C₃₇	#102	1	1	yes	characteristic
34	C₄×C₃₇	—	2	1	no	—
35	C₄×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₃₇	#104	1	1	yes	characteristic
37	C₄×C₃₇	SD₃₂	1	1	yes	characteristic
38	C₄×C₃₇	Q₃₂	1	1	yes	characteristic
39	Dic₃₇	—	4	2	no	—
40	Dic₃₇	—	8	1	no	—
41	#1332	—	37	1	no	maximal, Sylow
42	C₂×C₃₇	D₄⋊C₈	1	1	yes	characteristic
43	C₂×C₃₇	#358	1	1	yes	characteristic
44	C₂×C₃₇	#359	1	1	yes	characteristic
45	C₄×Q₁₆	—	37	1	no	—
46	C₄×C₁₆	—	37	1	no	—
47	#335	D₃₇	1	1	yes	characteristic
48	C₃₇	#1332	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₁₆	—	37	1	no	—
50	C₄×Q₈	—	74	1	no	—
51	C₂×C₁₆	—	74	1	no	—
52	#107	—	37	1	no	—
53	C₄⋊C₈	—	2	1	no	—
54	#103	—	74	1	no	—
55	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
56	C₂×Q₈	—	74	1	no	—
57	Q₁₆	—	37	2	no	—
58	Q₁₆	—	74	1	no	—
59	C₂×C₈	—	4	1	no	—
60	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
61	C₂×C₈	D₁₄₈	1	1	yes	characteristic
62	C₄⋊C₄	—	74	1	no	—
63	C₄⋊C₄	—	148	1	no	—
64	C₄²	—	148	1	no	—
65	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
66	C₁₆	—	74	2	no	—
67	Q₈	—	74	2	no	—
68	Q₈	—	148	1	no	—
69	C₂×C₄	—	148	1	no	—
70	C₂×C₄	—	148	1	no	—
71	C₂×C₄	#10596938	1	1	yes	characteristic
72	C₂×C₄	#10596939	1	1	yes	characteristic
73	C₂×C₄	#10596941	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	8	1	no	—
76	C₈	C₈×D₃₇	1	1	yes	characteristic
77	C₈	#10596929	1	1	yes	characteristic
78	C₂²	#11924456	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	296	1	no	—
81	C₄	—	148	2	no	—
82	C₄	#11924448	1	1	yes	characteristic
83	C₄	#11924462	1	1	yes	characteristic
84	C₄	#11924480	1	1	yes	characteristic
85	C₄	#11924482	1	1	yes	characteristic
86	C₂	#14557260	1	1	yes	characteristic
87	C₂	#14557336	1	1	yes	characteristic
88	C₂	#14557339	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10596939
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#335	C₂
socle, prime radical	C₂²×C₃₇	#102
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#335	D₃₇
hypocenter	C₃₇	#1332
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
20. Dic₁₄₈	C₈	semidirect
48. C₃₇	#1332	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
C₄×#10596925	2
C₃₇×#335	2
#1332	37