Subgroups — #18009713

Order 4736.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558465	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11924586	C₂	1	1	yes	maximal, characteristic, complemented
3	#14557950	C₂	1	1	yes	maximal, characteristic
4	#11924586	—	2	1	no	—
5	#11924586	—	2	1	no	—
6	#11924476	—	2	1	no	—
7	#11924476	C₄	1	1	yes	characteristic
8	C₂×#10596925	—	2	1	no	—
9	C₂×#10596925	C₂²	1	1	yes	characteristic
10	#131×C₃₇	C₄	1	1	yes	characteristic
11	#41×C₃₇	C₈	1	1	yes	characteristic
12	M₁₆×C₃₇	—	2	1	no	—
13	M₁₆×C₃₇	C₈	1	1	yes	characteristic
14	C₂×C₈×C₃₇	—	2	1	no	—
15	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
16	#10596925	—	2	1	no	—
17	#10596925	D₄	1	1	yes	characteristic
18	#10596925	D₄	1	1	yes	characteristic
19	Q₈×C₃₇	C₁₆	1	1	yes	characteristic
20	D₄×C₃₇	—	2	1	no	—
21	D₄×C₃₇	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
24	C₈×C₃₇	—	2	1	no	—
25	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₃₇	M₁₆	1	1	yes	characteristic
27	C₂²×C₃₇	—	2	1	no	—
28	C₂²×C₃₇	M₃₂	1	1	yes	characteristic
29	C₄×C₃₇	—	2	1	no	—
30	C₄×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₃₇	C₂×C₁₆	1	1	yes	characteristic
32	#1401	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	—	2	1	no	—
34	C₂×C₃₇	—	4	1	no	—
35	C₂×C₃₇	C₂²⋊C₁₆	1	1	yes	characteristic
36	#504	—	37	1	no	—
37	M₆₄	—	37	1	no	—
38	C₂×C₃₂	—	37	1	no	—
39	C₃₇	#1401	1	1	yes	characteristic, complemented, Sylow
40	#131	#3866	1	1	yes	characteristic
41	M₃₂	—	37	1	no	—
42	M₃₂	—	74	1	no	—
43	C₂×C₁₆	—	37	1	no	—
44	C₂×C₁₆	—	74	1	no	—
45	C₃₂	—	74	1	no	—
46	C₃₂	—	74	1	no	—
47	#41	#64438	1	1	yes	characteristic
48	M₁₆	—	2	1	no	—
49	M₁₆	#64438	1	1	yes	characteristic
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	C₂×#3866	1	1	yes	characteristic
52	C₁₆	—	37	1	no	—
53	C₁₆	—	37	1	no	—
54	C₁₆	—	74	1	no	—
55	Q₈	#10596927	1	1	yes	characteristic
56	D₄	—	2	1	no	—
57	D₄	#10596927	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₂×#64438	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	#10596957	1	1	yes	characteristic
62	C₈	C₂²⋊#3866	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₂²	#11924610	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	C₂²⋊#64438	1	1	yes	characteristic
67	C₄	C₂×#10596927	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	C₂²⋊#10596927	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#3866
commutator	C₄×C₃₇	C₂×C₁₆
Frattini	C₂×C₈	C₂×#3866
Fitting	#131×C₃₇	C₄
socle	C₂×C₃₇	C₂²⋊C₁₆
prime radical	#41×C₃₇	C₈
cosocle	C₂×#10596925	C₂²
hypercenter	#131	#3866
hypocenter	C₃₇	#1401
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #14558465	C₂	semidirect
2. C₂×#11924586	C₂	semidirect
39. C₃₇	#1401	semidirect

Maximal subgroups

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

subgroup	index
#14558465	2
C₂×#11924586	2
#14557950	2
#1401	37