Subgroups — #18010817

Order 4736.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924610	C₂	1	2	yes	maximal
2	#14558425	C₂	1	4	yes	maximal, complemented
3	#14557489	C₂	1	1	yes	maximal, characteristic
4	#11924610	C₄	1	4	yes	complemented
5	#11924610	C₂²	1	4	yes	—
6	C₂×#10596927	C₄	1	4	yes	complemented
7	C₂×#10596934	C₄	1	1	yes	characteristic
8	C₂²×#64436	C₂²	1	1	yes	characteristic
9	#11924447	C₂²	1	2	yes	—
10	C₄×#64436	C₄	1	2	yes	—
11	#117×C₃₇	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₄⋊C₄×C₃₇	—	2	1	no	—
14	C₂²⋊C₄×C₃₇	—	2	1	no	—
15	C₄²×C₃₇	C₂×C₄	1	2	yes	—
16	#10596934	—	2	2	no	—
17	C₂×#64436	C₂×C₄	1	2	yes	—
18	C₂×#64436	C₂×C₄	1	1	yes	characteristic
19	C₂×#64436	C₂×C₄	1	2	yes	—
20	C₂×#64436	C₂×C₄	1	2	yes	—
21	C₂×#64436	C₂³	1	1	yes	characteristic
22	#10596927	C₂×C₄	1	8	yes	—
23	C₂³×C₃₇	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₃₇	—	2	2	no	—
25	C₂×C₄×C₃₇	C₄²	1	2	yes	—
26	C₂×C₄×C₃₇	M₁₆	1	2	yes	—
27	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
29	#64436	—	2	2	no	—
30	#64436	C₄²	1	1	yes	characteristic
31	#64436	C₄²	1	1	yes	characteristic
32	#64436	C₂²×C₄	1	2	yes	—
33	C₂²×C₃₇	—	4	1	no	—
34	C₂²×C₃₇	#97	1	2	yes	—
35	C₂²×C₃₇	C₂×M₁₆	1	1	yes	characteristic
36	C₄×C₃₇	—	4	2	no	—
37	C₄×C₃₇	#97	1	2	yes	—
38	C₄×C₃₇	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
40	#2110	—	37	1	no	maximal, Sylow
41	C₂×C₃₇	—	2	1	no	—
42	C₂×C₃₇	—	2	2	no	—
43	C₂×C₃₇	C₂×#97	1	1	yes	characteristic
44	C₂×M₃₂	—	37	2	no	—
45	#405	—	37	1	no	—
46	#347	—	37	4	no	—
47	C₃₇	#2110	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₁₆	—	37	1	no	—
49	C₂²×C₈	—	37	1	no	—
50	#117	#3866	1	1	yes	characteristic
51	M₃₂	—	37	4	no	—
52	M₃₂	—	37	4	no	—
53	C₂×C₁₆	—	37	4	no	—
54	#97	—	37	2	no	—
55	C₄×C₈	—	37	2	no	—
56	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
57	M₁₆	—	74	2	no	—
58	C₂×C₈	—	37	2	no	—
59	C₂×C₈	—	37	2	no	—
60	C₂×C₈	—	37	1	no	—
61	C₂×C₈	—	37	1	no	—
62	C₂×C₈	—	37	2	no	—
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×#3866	1	2	yes	—
66	C₁₆	—	37	8	no	—
67	C₂³	#10596957	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	#10596953	1	2	yes	—
70	C₂×C₄	C₄×#3866	1	2	yes	—
71	C₂×C₄	#10596957	1	1	yes	characteristic
72	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
73	C₈	—	37	2	no	—
74	C₈	—	37	1	no	—
75	C₈	—	37	1	no	—
76	C₈	—	74	2	no	—
77	C₂²	—	4	1	no	—
78	C₂²	#11924591	1	2	yes	—
79	C₂²	C₂×#10596957	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	#11924591	1	2	yes	—
82	C₄	C₂×C₄×#3866	1	1	yes	characteristic
83	C₄	C₂×#10596953	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×#11924591	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄×#3866
commutator	C₄×C₃₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×#3866
Fitting	#117×C₃₇	C₄
socle	C₂×C₃₇	C₂×#97
prime radical	C₂³×C₃₇	M₁₆
cosocle	C₂×#64436	C₂³
hypercenter	#117	#3866
hypocenter	C₃₇	#2110
LCS	G ▷ C₄×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #14558425	C₂	semidirect
4. #11924610	C₄	semidirect
6. C₂×#10596927	C₄	semidirect
47. C₃₇	#2110	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924610	2
#14558425	2
#14557489	2
#2110	37