Subgroups — #17994212

Order 4736.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557936	C₂	1	4	yes	maximal
2	#14557913	C₂	1	1	yes	maximal, characteristic
3	C₈×#64436	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#494	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₄₈	—	2	2	no	—
6	#11924536	C₂²	1	2	yes	—
7	#11924469	—	2	8	no	—
8	C₄×#64436	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₃₇	—	2	2	no	—
10	C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
11	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₃₇	—	2	2	no	—
13	C₂×Dic₇₄	—	2	2	no	—
14	Q₁₆×C₃₇	—	4	4	no	—
15	C₂×C₈×C₃₇	D₄	1	2	yes	—
16	C₄⋊C₄×C₃₇	—	2	4	no	—
17	C₄²×C₃₇	C₂³	1	1	yes	characteristic
18	C₄⋊Dic₃₇	—	2	4	no	—
19	C₂×#64436	D₄	1	4	yes	—
20	Dic₁₄₈	—	4	4	no	—
21	Q₈×C₃₇	—	4	4	no	—
22	C₂×C₄×C₃₇	—	4	2	no	—
23	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
24	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₃₇	—	4	2	no	—
26	Dic₇₄	—	4	4	no	—
27	C₈×C₃₇	D₈	1	4	yes	—
28	#64436	Q₁₆	1	8	yes	complemented
29	C₂²×C₃₇	#127	1	1	yes	characteristic
30	C₄×C₃₇	—	8	2	no	—
31	C₄×C₃₇	C₂×D₈	1	2	yes	—
32	C₄×C₃₇	C₂×Q₁₆	1	4	yes	—
33	Dic₃₇	—	8	2	no	—
34	#1713	—	37	1	no	maximal, Sylow
35	C₂×C₃₇	#493	1	1	yes	characteristic
36	C₂×C₃₇	#494	1	2	yes	—
37	#500	—	37	4	no	—
38	#494	—	37	1	no	—
39	#494	D₃₇	1	1	yes	characteristic
40	C₈²	—	37	1	no	—
41	C₃₇	#1713	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₁₆	—	2	2	no	—
43	C₂×Q₁₆	—	74	2	no	—
44	C₄⋊Q₈	—	37	2	no	—
45	C₄⋊Q₈	C₂×D₃₇	1	2	yes	—
46	#107	—	74	8	no	—
47	C₄×C₈	—	37	2	no	—
48	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
49	C₂×Q₈	—	2	2	no	—
50	C₂×Q₈	—	74	2	no	—
51	Q₁₆	—	4	4	no	—
52	Q₁₆	—	148	4	no	—
53	C₂×C₈	—	37	4	no	—
54	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
55	C₄⋊C₄	—	2	4	no	—
56	C₄⋊C₄	—	74	4	no	—
57	C₄²	C₂²×D₃₇	1	1	yes	characteristic
58	Q₈	—	4	4	no	—
59	Q₈	—	148	4	no	—
60	C₂×C₄	—	4	2	no	—
61	C₂×C₄	—	148	2	no	—
62	C₂×C₄	D₄×D₃₇	1	2	yes	—
63	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
64	C₈	—	37	8	no	—
65	C₈	#10596939	1	4	yes	—
66	C₂²	#11924532	1	1	yes	characteristic
67	C₄	—	8	2	no	—
68	C₄	—	296	2	no	—
69	C₄	C₂×#10596939	1	2	yes	—
70	C₄	Q₁₆×D₃₇	1	4	yes	—
71	C₂	#14557909	1	1	yes	characteristic
72	C₂	#14557911	1	2	yes	—

	subgroup	G/H
center	C₂²	#11924532
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₃₇×#494	C₂
socle, prime radical	C₂²×C₃₇	#127
hypercenter	#494	D₃₇
hypocenter	C₃₇	#1713
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
28. #64436	Q₁₆	semidirect
41. C₃₇	#1713	semidirect

Maximal subgroups

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

subgroup	index
#14557936	2
#14557913	2
C₈×#64436	2
C₃₇×#494	2
#1713	37