Subgroups — #14557655

Order 2368.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924543	C₂	1	2	yes	maximal, complemented
2	#11924472	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924463	C₂	1	2	yes	maximal, complemented
4	#11924446	C₂	1	1	yes	maximal, characteristic, complemented
5	#135×C₃₇	C₂	1	1	yes	maximal, characteristic
6	#41×C₃₇	C₂²	1	2	yes	—
7	Q₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
8	SD₁₆×C₃₇	C₄	1	2	yes	complemented
9	D₈×C₃₇	C₄	1	1	yes	characteristic, complemented
10	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
12	#10596934	—	2	2	no	—
13	#10596934	C₂²	1	2	yes	—
14	C₂×#64436	—	2	2	no	—
15	C₂×#64436	C₂²	1	1	yes	characteristic
16	Q₈×C₃₇	C₂×C₄	1	2	yes	—
17	D₄×C₃₇	—	2	2	no	—
18	D₄×C₃₇	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₃₇	—	2	2	no	—
20	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
21	C₂×Dic₃₇	—	2	1	no	—
22	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
23	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
24	#64436	—	2	2	no	—
25	#64436	D₄	1	2	yes	—
26	C₂²×C₃₇	—	2	2	no	—
27	C₂²×C₃₇	#41	1	1	yes	characteristic
28	C₄×C₃₇	—	2	2	no	—
29	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
31	Dic₃₇	—	4	1	no	—
32	C₂×C₃₇	—	2	1	no	—
33	C₂×C₃₇	—	4	2	no	—
34	C₂×C₃₇	C₄×D₄	1	1	yes	characteristic
35	#444	—	37	1	no	maximal, Sylow
36	C₃₇	#444	1	1	yes	characteristic, complemented, Sylow
37	#135	D₃₇	1	1	yes	characteristic
38	#131	—	37	2	no	—
39	#108	—	37	1	no	—
40	#104	—	37	2	no	—
41	#97	—	37	1	no	—
42	#41	C₂×D₃₇	1	2	yes	—
43	Q₁₆	Dic₃₇	1	1	yes	characteristic, complemented
44	SD₁₆	Dic₃₇	1	2	yes	complemented
45	D₈	Dic₃₇	1	1	yes	characteristic, complemented
46	M₁₆	—	37	2	no	—
47	M₁₆	—	74	2	no	—
48	C₂×C₈	—	37	1	no	—
49	C₂×C₈	—	74	2	no	—
50	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
51	C₄²	—	37	1	no	—
52	Q₈	C₂×Dic₃₇	1	2	yes	—
53	D₄	—	2	2	no	—
54	D₄	C₂×Dic₃₇	1	2	yes	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	74	1	no	—
57	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
58	C₈	—	37	2	no	—
59	C₈	—	74	2	no	—
60	C₈	C₂×Dic₃₇	1	1	yes	characteristic
61	C₈	C₂×Dic₃₇	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	#10596964	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	148	1	no	—
66	C₄	D₄×D₃₇	1	1	yes	characteristic
67	C₄	C₂²×Dic₃₇	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	2	no	—
70	C₂	D₄×Dic₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₃₇
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting, prime radical	#135×C₃₇	C₂
socle	C₂×C₃₇	C₄×D₄
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	#135	D₃₇
hypocenter	C₃₇	#444
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #11924543	C₂	semidirect
2. #11924472	C₂	semidirect
3. #11924463	C₂	semidirect
4. #11924446	C₂	semidirect
7. Q₁₆×C₃₇	C₄	semidirect
8. SD₁₆×C₃₇	C₄	semidirect
9. D₈×C₃₇	C₄	semidirect
36. C₃₇	#444	semidirect
43. Q₁₆	Dic₃₇	semidirect
44. SD₁₆	Dic₃₇	semidirect
45. D₈	Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924543	2
#11924472	2
#11924463	2
#11924446	2
#135×C₃₇	2
#444	37