Subgroups — #17996355

Order 4736.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924476	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10596925	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10596925	C₂	1	4	yes	maximal, complemented
4	C₃₇×#405	C₂	1	1	yes	maximal, characteristic
5	#11924476	—	2	2	no	—
6	C₂×#10596925	—	2	2	no	—
7	C₂×#10596925	C₂²	1	2	yes	—
8	C₂×#10596925	C₂²	1	2	yes	—
9	C₂×M₁₆×C₃₇	C₄	1	1	yes	characteristic
10	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	#117×C₃₇	C₄	1	1	yes	characteristic
12	#97×C₃₇	C₄	1	2	yes	—
13	C₄×C₈×C₃₇	C₂²	1	2	yes	—
14	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	M₁₆×C₃₇	—	2	2	no	—
16	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₃₇	D₄	1	2	yes	—
19	C₂×C₈×C₃₇	Q₈	1	2	yes	—
20	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₃₇	C₈	1	2	yes	—
22	C₂²⋊C₄×C₃₇	C₈	1	2	yes	—
23	C₄²×C₃₇	C₂×C₄	1	2	yes	—
24	#10596925	—	2	2	no	—
25	#10596925	—	2	2	no	—
26	C₂³×C₃₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₃₇	C₂×C₈	1	4	yes	—
29	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₃₇	M₁₆	1	2	yes	—
31	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₃₇	—	2	2	no	—
33	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
34	C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
35	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₃₇	—	2	2	no	—
37	C₂²×C₃₇	C₄⋊C₈	1	2	yes	—
38	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₃₇	—	2	4	no	—
40	C₄×C₃₇	C₄⋊C₈	1	2	yes	—
41	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
43	#2151	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	2	2	no	—
45	C₂×C₃₇	C₂×C₄⋊C₈	1	1	yes	characteristic
46	C₂×C₃₇	#504	1	2	yes	—
47	C₂×M₃₂	—	37	1	no	—
48	C₂²×C₁₆	—	37	1	no	—
49	#405	D₃₇	1	1	yes	characteristic
50	C₄⋊C₁₆	—	37	4	no	—
51	C₃₇	#2151	1	1	yes	characteristic, complemented, Sylow
52	C₂×M₁₆	Dic₃₇	1	1	yes	characteristic
53	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
54	#117	Dic₃₇	1	1	yes	characteristic
55	M₃₂	—	74	2	no	—
56	C₂×C₁₆	—	37	2	no	—
57	C₂×C₁₆	—	37	2	no	—
58	C₂×C₁₆	—	74	2	no	—
59	#97	Dic₃₇	1	2	yes	—
60	C₄×C₈	C₂×D₃₇	1	2	yes	—
61	C₂²×C₄	C₂×Dic₃₇	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	C₂×C₈	Dic₇₄	1	2	yes	—
64	C₂×C₈	D₁₄₈	1	2	yes	—
65	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
66	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
68	C₄⋊C₄	#64436	1	2	yes	—
69	C₂²⋊C₄	#64436	1	2	yes	—
70	C₄²	C₂×Dic₃₇	1	2	yes	—
71	C₁₆	—	74	2	no	—
72	C₁₆	—	74	2	no	—
73	C₂³	C₂×#64436	1	1	yes	characteristic
74	C₂×C₄	C₂×#64436	1	4	yes	—
75	C₂×C₄	C₂×#64436	1	1	yes	characteristic
76	C₂×C₄	#10596934	1	2	yes	—
77	C₂×C₄	C₄⋊Dic₃₇	1	2	yes	—
78	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	C₄⋊Dic₃₇	1	2	yes	—
81	C₈	C₂×Dic₇₄	1	1	yes	characteristic
82	C₈	C₂×D₁₄₈	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	C₄⋊#64436	1	2	yes	—
85	C₂²	C₂²×#64436	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄⋊#64436	1	2	yes	—
88	C₄	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
89	C₄	C₂×#10596934	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#64436	1	1	yes	characteristic
92	C₂	#14557950	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₃₇
commutator, socle	C₂²×C₃₇	C₂²×C₈
Fitting	C₃₇×#405	C₂
prime radical	C₂³×C₃₇	C₂×C₈
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	#405	D₃₇
hypocenter	C₃₇	#2151
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
3. C₄⋊#10596925	C₂	semidirect
51. C₃₇	#2151	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
C₂²×#10596925	2
C₄⋊#10596925	2
C₃₇×#405	2
#2151	37