Subgroups — #17992671

Order 4736.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557354	C₂	1	1	yes	maximal, characteristic
2	C₄×#10596925	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#364	C₂	1	1	yes	maximal, characteristic
4	#11924476	—	2	1	no	—
5	C₂×#10596925	C₄	1	1	yes	characteristic
6	C₂×#10596925	C₄	1	1	yes	characteristic
7	M₃₂×C₃₇	—	2	1	no	—
8	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
11	C₄²×C₃₇	Q₈	1	1	yes	characteristic
12	C₁₆×C₃₇	—	4	1	no	—
13	#10596925	—	2	1	no	—
14	#10596925	—	4	1	no	—
15	#10596925	C₈	1	2	yes	—
16	C₂×C₄×C₃₇	—	2	1	no	—
17	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
19	C₈×C₃₇	M₁₆	1	1	yes	characteristic
20	C₈×C₃₇	D₈	1	1	yes	characteristic
21	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
22	C₂²×C₃₇	#108	1	1	yes	characteristic
23	C₄×C₃₇	—	2	2	no	—
24	C₄×C₃₇	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₃₇	#107	1	1	yes	characteristic
26	#1373	—	37	1	no	maximal, Sylow
27	C₂×C₃₇	—	2	1	no	—
28	C₂×C₃₇	#335	1	1	yes	characteristic
29	#364	—	37	1	no	—
30	#364	D₃₇	1	1	yes	characteristic
31	C₄×C₁₆	—	37	1	no	—
32	C₃₇	#1373	1	1	yes	characteristic, complemented, Sylow
33	M₃₂	—	2	1	no	—
34	M₃₂	—	74	1	no	—
35	C₂×C₁₆	—	37	1	no	—
36	C₂×C₁₆	—	37	1	no	—
37	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
38	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
40	C₄²	Dic₇₄	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	37	2	no	—
43	C₁₆	—	74	1	no	—
44	C₁₆	—	148	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	#10596936	1	1	yes	characteristic
47	C₈	C₈×D₃₇	1	1	yes	characteristic
48	C₈	#10596929	1	1	yes	characteristic
49	C₈	#10596939	1	1	yes	characteristic
50	C₈	#10596942	1	1	yes	characteristic
51	C₂²	#11924471	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	#11924465	1	1	yes	characteristic
54	C₄	#11924469	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#14557285	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#10596939
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#364	C₂
socle	C₂×C₃₇	#335
prime radical	C₂²×C₃₇	#108
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#364	D₃₇
hypocenter	C₃₇	#1373
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
32. C₃₇	#1373	semidirect

Maximal subgroups

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

subgroup	index
#14557354	2
C₄×#10596925	2
C₃₇×#364	2
#1373	37