Subgroups — #17994214

Order 4736.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557938	C₂	1	4	yes	maximal
2	#14557913	C₂	1	2	yes	maximal
3	C₈²×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₄₈	—	2	4	no	—
5	#11924536	C₂²	1	4	yes	—
6	#11924470	—	2	8	no	—
7	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₃₇	C₂²	1	2	yes	—
9	C₂×Dic₇₄	—	2	4	no	—
10	C₂×C₈×C₃₇	D₄	1	2	yes	—
11	C₂×C₈×C₃₇	D₄	1	4	yes	—
12	C₄²×C₃₇	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₃₇	—	2	8	no	—
14	Dic₁₄₈	—	4	8	no	—
15	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
17	C₂×Dic₃₇	—	4	4	no	—
18	Dic₇₄	—	4	8	no	—
19	C₈×C₃₇	D₈	1	4	yes	—
20	C₈×C₃₇	Q₁₆	1	8	yes	complemented
21	C₂²×C₃₇	#127	1	1	yes	characteristic
22	C₄×C₃₇	C₂×D₈	1	2	yes	—
23	C₄×C₃₇	C₂×Q₁₆	1	4	yes	—
24	Dic₃₇	—	8	4	no	—
25	#1713	—	37	1	no	maximal, Sylow
26	C₂×C₃₇	#493	1	1	yes	characteristic
27	C₂×C₃₇	#494	1	2	yes	—
28	#500	—	37	4	no	—
29	#494	—	37	2	no	—
30	C₈²	D₃₇	1	1	yes	characteristic
31	C₃₇	#1713	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₁₆	—	74	4	no	—
33	C₄⋊Q₈	—	37	4	no	—
34	#107	—	74	8	no	—
35	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
36	C₄×C₈	C₂×D₃₇	1	2	yes	—
37	C₂×Q₈	—	74	4	no	—
38	Q₁₆	—	148	8	no	—
39	C₂×C₈	D₁₄₈	1	2	yes	—
40	C₂×C₈	D₁₄₈	1	4	yes	—
41	C₄⋊C₄	—	74	8	no	—
42	C₄²	C₂²×D₃₇	1	1	yes	characteristic
43	Q₈	—	148	8	no	—
44	C₂×C₄	—	148	4	no	—
45	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
46	C₂×C₄	C₂×D₁₄₈	1	2	yes	—
47	C₈	D₂₉₆	1	4	yes	—
48	C₈	Dic₁₄₈	1	8	yes	complemented
49	C₂²	#11924533	1	1	yes	characteristic
50	C₄	—	296	4	no	—
51	C₄	C₂×D₂₉₆	1	2	yes	—
52	C₄	C₂×Dic₁₄₈	1	4	yes	—
53	C₂	#14557910	1	1	yes	characteristic
54	C₂	#14557913	1	2	yes	—

	subgroup	G/H
center	C₂²	#11924533
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₈²×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	#127
hypercenter	C₈²	D₃₇
hypocenter	C₃₇	#1713
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₃₇	Q₁₆	semidirect
31. C₃₇	#1713	semidirect
48. C₈	Dic₁₄₈	semidirect

Maximal subgroups

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

subgroup	index
#14557938	2
#14557913	2
C₈²×C₃₇	2
#1713	37