Subgroups — #17996362

Order 4736.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924476	C₂	1	2	yes	maximal
2	#14557354	C₂	1	4	yes	maximal, complemented
3	C₃₇×#405	C₂	1	1	yes	maximal, characteristic
4	#11924476	—	2	2	no	—
5	#11924476	C₂²	1	4	yes	—
6	C₂×#10596925	—	2	2	no	—
7	C₂×M₁₆×C₃₇	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	#117×C₃₇	C₄	1	1	yes	characteristic
10	#97×C₃₇	C₄	1	2	yes	—
11	C₄×C₈×C₃₇	C₂²	1	2	yes	—
12	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
13	M₁₆×C₃₇	C₈	1	4	yes	—
14	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₃₇	D₄	1	2	yes	—
17	C₂×C₈×C₃₇	Q₈	1	2	yes	—
18	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₃₇	—	2	1	no	—
20	C₂²⋊C₄×C₃₇	—	2	1	no	—
21	C₄²×C₃₇	C₂×C₄	1	2	yes	—
22	#10596925	—	2	4	no	—
23	C₂³×C₃₇	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₃₇	—	2	2	no	—
25	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₃₇	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
30	C₈×C₃₇	C₂×C₈	1	4	yes	—
31	C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
32	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₃₇	—	4	1	no	—
34	C₂²×C₃₇	C₄⋊C₈	1	2	yes	—
35	C₂²×C₃₇	C₂×M₁₆	1	1	yes	characteristic
36	C₄×C₃₇	—	4	2	no	—
37	C₄×C₃₇	C₄⋊C₈	1	2	yes	—
38	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
40	#2153	—	37	1	no	maximal, Sylow
41	C₂×C₃₇	—	2	1	no	—
42	C₂×C₃₇	—	2	2	no	—
43	C₂×C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic
44	C₂×M₃₂	—	37	2	no	—
45	#405	D₃₇	1	1	yes	characteristic
46	#364	—	37	4	no	—
47	C₃₇	#2153	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₁₆	Dic₃₇	1	1	yes	characteristic
49	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
50	#117	Dic₃₇	1	1	yes	characteristic
51	M₃₂	—	37	4	no	—
52	M₃₂	—	74	2	no	—
53	C₂×C₁₆	—	74	2	no	—
54	#97	Dic₃₇	1	2	yes	—
55	C₄×C₈	C₂×D₃₇	1	2	yes	—
56	C₂²×C₄	C₂×Dic₃₇	1	1	yes	characteristic
57	M₁₆	#64436	1	4	yes	—
58	C₂×C₈	Dic₇₄	1	2	yes	—
59	C₂×C₈	D₁₄₈	1	2	yes	—
60	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
61	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
62	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×Dic₃₇	1	2	yes	—
66	C₁₆	—	74	4	no	—
67	C₂³	#10596934	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	C₂×#64436	1	2	yes	—
70	C₂×C₄	#10596934	1	1	yes	characteristic
71	C₂×C₄	C₄⋊Dic₃₇	1	2	yes	—
72	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
73	C₈	C₂×#64436	1	4	yes	—
74	C₈	C₄⋊Dic₃₇	1	2	yes	—
75	C₈	C₂×Dic₇₄	1	1	yes	characteristic
76	C₈	C₂×D₁₄₈	1	1	yes	characteristic
77	C₂²	—	4	1	no	—
78	C₂²	C₄⋊#64436	1	2	yes	—
79	C₂²	C₂×#10596934	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	C₄⋊#64436	1	2	yes	—
82	C₄	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
83	C₄	C₂²×#64436	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×C₄⋊#64436	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₁₄₈
commutator	C₄×C₃₇	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#405	C₂
socle	C₂×C₃₇	C₂×C₄⋊C₈
prime radical	C₂³×C₃₇	M₁₆
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	#405	D₃₇
hypocenter	C₃₇	#2153
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #14557354	C₂	semidirect
47. C₃₇	#2153	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924476	2
#14557354	2
C₃₇×#405	2
#2153	37