Subgroups — #18010965

Order 4736.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558456	C₂	1	2	yes	maximal, complemented
2	#14558429	C₂	1	2	yes	maximal
3	#14558425	C₂	1	2	yes	maximal, complemented
4	C₄×#10596934	C₂	1	1	yes	maximal, characteristic
5	#11924610	C₂²	1	4	yes	—
6	C₂×#10596934	C₄	1	1	yes	characteristic
7	C₂×#10596934	C₂²	1	1	yes	characteristic
8	#11924447	C₄	1	1	yes	characteristic
9	#11924447	C₂²	1	1	yes	characteristic
10	C₄×#64436	C₄	1	1	yes	characteristic
11	C₄×#64436	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₃₇	C₄	1	1	yes	characteristic
13	C₂²×C₄×C₃₇	—	2	1	no	—
14	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₄²×C₃₇	—	2	1	no	—
16	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
18	#10596934	—	2	2	no	—
19	#10596934	—	2	2	no	—
20	C₂×#64436	C₂×C₄	1	1	yes	characteristic
21	C₂×#64436	C₂×C₄	1	1	yes	characteristic
22	C₂×#64436	C₂×C₄	1	1	yes	characteristic
23	C₂×#64436	C₂³	1	1	yes	characteristic
24	#10596927	—	2	4	no	—
25	C₂³×C₃₇	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₃₇	—	2	1	no	—
27	C₂×C₄×C₃₇	—	2	1	no	—
28	C₂×C₄×C₃₇	—	2	1	no	—
29	C₂×C₄×C₃₇	—	2	1	no	—
30	C₂×C₄×C₃₇	—	4	2	no	—
31	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	#64436	—	2	1	no	—
34	#64436	—	2	1	no	—
35	#64436	M₁₆	1	2	yes	—
36	#64436	#41	1	2	yes	—
37	C₂²×C₃₇	—	2	1	no	—
38	C₂²×C₃₇	—	4	1	no	—
39	C₂²×C₃₇	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₃₇	—	2	2	no	—
41	C₄×C₃₇	—	2	1	no	—
42	C₄×C₃₇	—	4	1	no	—
43	C₄×C₃₇	#117	1	1	yes	characteristic
44	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
45	#2165	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	—	2	1	no	—
47	C₂×C₃₇	—	4	1	no	—
48	C₂×C₃₇	#432	1	1	yes	characteristic
49	C₄×M₁₆	—	37	1	no	—
50	#364	—	37	2	no	—
51	#349	—	37	2	no	—
52	#347	—	37	2	no	—
53	C₃₇	#2165	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	37	1	no	—
55	C₂×M₁₆	—	37	1	no	—
56	C₂×C₄²	#3866	1	1	yes	characteristic
57	M₃₂	—	37	4	no	—
58	#97	—	37	1	no	—
59	#97	—	37	1	no	—
60	C₄×C₈	—	37	1	no	—
61	C₄×C₈	—	37	1	no	—
62	C₂²×C₄	—	2	1	no	—
63	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
64	M₁₆	—	74	2	no	—
65	M₁₆	—	74	2	no	—
66	C₂×C₈	—	37	1	no	—
67	C₂×C₈	—	37	1	no	—
68	C₂×C₈	—	37	1	no	—
69	C₂×C₈	—	37	1	no	—
70	C₄²	—	2	1	no	—
71	C₄²	C₂×#3866	1	1	yes	characteristic
72	C₄²	C₂×#3866	1	1	yes	characteristic
73	C₁₆	—	74	4	no	—
74	C₂³	#10596957	1	1	yes	characteristic
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	#10596957	1	1	yes	characteristic
81	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
82	C₈	—	37	2	no	—
83	C₈	—	37	2	no	—
84	C₈	—	74	1	no	—
85	C₈	—	74	1	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	4	1	no	—
88	C₂²	C₂×#10596957	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	—	2	1	no	—
91	C₄	—	4	1	no	—
92	C₄	#11924615	1	1	yes	characteristic
93	C₄	D₃₇⋊M₁₆	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#14558553	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924615
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#3866
Fitting	C₂×C₄²×C₃₇	C₄
socle	C₂×C₃₇	#432
prime radical	C₂³×C₃₇	M₁₆
cosocle	C₂×#64436	C₂³
hypercenter	C₂×C₄²	#3866
hypocenter	C₃₇	#2165
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #14558456	C₂	semidirect
3. #14558425	C₂	semidirect
53. C₃₇	#2165	semidirect

Maximal subgroups

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

subgroup	index
#14558456	2
#14558429	2
#14558425	2
C₄×#10596934	2
#2165	37