Subgroups — #18011019

Order 4736.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558465	C₂	1	3	yes	maximal, complemented
2	C₂×#11924586	C₂	1	3	yes	maximal, complemented
3	#14557950	C₂	1	1	yes	maximal, characteristic
4	#11924586	C₂²	1	3	yes	—
5	#11924586	C₂²	1	1	yes	characteristic
6	#11924476	C₄	1	3	yes	—
7	C₂×#10596925	C₂²	1	3	yes	—
8	#131×C₃₇	C₄	1	1	yes	characteristic
9	#41×C₃₇	C₈	1	1	yes	characteristic
10	M₁₆×C₃₇	C₈	1	3	yes	—
11	C₂×C₈×C₃₇	C₂×C₄	1	3	yes	—
12	#10596925	C₂×C₄	1	3	yes	—
13	#10596925	C₂³	1	1	yes	characteristic
14	Q₈×C₃₇	C₁₆	1	1	yes	characteristic
15	D₄×C₃₇	C₁₆	1	3	yes	—
16	C₂×C₄×C₃₇	C₂×C₈	1	3	yes	—
17	C₈×C₃₇	C₂×C₈	1	3	yes	—
18	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₃₇	C₂×C₁₆	1	3	yes	—
20	C₄×C₃₇	C₂×C₁₆	1	3	yes	—
21	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
22	#2258	—	37	1	no	maximal, Sylow
23	C₂×C₃₇	—	2	3	no	—
24	C₂×C₃₇	C₂²×C₁₆	1	1	yes	characteristic
25	#504	—	37	1	no	—
26	M₆₄	—	37	3	no	—
27	C₂×C₃₂	—	37	3	no	—
28	C₃₇	#2258	1	1	yes	characteristic, complemented, Sylow
29	#131	#3866	1	1	yes	characteristic
30	M₃₂	—	37	3	no	—
31	C₂×C₁₆	—	37	3	no	—
32	C₃₂	—	37	1	no	—
33	C₃₂	—	37	3	no	—
34	#41	#64438	1	1	yes	characteristic
35	M₁₆	#64438	1	3	yes	—
36	C₂×C₈	C₂×#3866	1	3	yes	—
37	C₁₆	—	37	3	no	—
38	C₁₆	—	37	1	no	—
39	Q₈	#10596927	1	1	yes	characteristic
40	D₄	#10596927	1	3	yes	—
41	C₂×C₄	C₂×#64438	1	3	yes	—
42	C₈	C₂×#64438	1	3	yes	—
43	C₈	C₂²×#3866	1	1	yes	characteristic
44	C₂²	C₂×#10596927	1	3	yes	—
45	C₄	C₂×#10596927	1	3	yes	—
46	C₄	C₂²×#64438	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#10596927	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#3866
commutator, socle	C₂×C₃₇	C₂²×C₁₆
Fitting	#131×C₃₇	C₄
prime radical	#41×C₃₇	C₈
cosocle	#10596925	C₂³
hypercenter	#131	#3866
hypocenter	C₃₇	#2258
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ 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
28. C₃₇	#2258	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
#2258	37