Subgroups — #17992672

Order 4736.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557354	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
3	#11924476	—	2	2	no	—
4	C₂×C₁₆×C₃₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₃₇	C₄	1	1	yes	characteristic
6	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
9	C₄²×C₃₇	Q₈	1	1	yes	characteristic
10	C₁₆×C₃₇	—	2	1	no	—
11	C₁₆×C₃₇	C₈	1	2	yes	—
12	#10596925	—	4	2	no	—
13	C₂×C₄×C₃₇	—	2	1	no	—
14	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
16	C₈×C₃₇	M₁₆	1	1	yes	characteristic
17	C₈×C₃₇	D₈	1	1	yes	characteristic
18	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
19	C₂²×C₃₇	#108	1	1	yes	characteristic
20	C₄×C₃₇	—	2	2	no	—
21	C₄×C₃₇	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₃₇	#107	1	1	yes	characteristic
23	#1373	—	37	1	no	maximal, Sylow
24	C₂×C₃₇	—	2	1	no	—
25	C₂×C₃₇	#335	1	1	yes	characteristic
26	#364	—	37	2	no	—
27	C₄×C₁₆	D₃₇	1	1	yes	characteristic
28	C₃₇	#1373	1	1	yes	characteristic, complemented, Sylow
29	M₃₂	—	74	2	no	—
30	C₂×C₁₆	Dic₃₇	1	1	yes	characteristic
31	C₂×C₁₆	Dic₃₇	1	1	yes	characteristic
32	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
33	C₂×C₈	D₁₄₈	1	1	yes	characteristic
34	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
35	C₄²	Dic₇₄	1	1	yes	characteristic
36	C₁₆	—	2	1	no	—
37	C₁₆	—	148	2	no	—
38	C₁₆	#64436	1	2	yes	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
41	C₈	D₂₉₆	1	1	yes	characteristic
42	C₈	Dic₁₄₈	1	1	yes	characteristic
43	C₈	C₂×#64436	1	1	yes	characteristic
44	C₈	#10596934	1	1	yes	characteristic
45	C₂²	#11924472	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊#64436	1	1	yes	characteristic
48	C₄	#11924470	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#14557286	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₂₉₆
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₄×C₁₆×C₃₇	C₂
socle	C₂×C₃₇	#335
prime radical	C₂²×C₃₇	#108
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	C₄×C₁₆	D₃₇
hypocenter	C₃₇	#1373
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
28. 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×C₁₆×C₃₇	2
#1373	37