Subgroups — #18009742

Order 4736.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558442	C₂	1	1	yes	maximal, characteristic
2	#14558440	C₂	1	1	yes	maximal, characteristic
3	#14557890	C₂	1	1	yes	maximal, characteristic
4	#11924597	—	2	1	no	—
5	#11924595	—	2	1	no	—
6	#11924524	C₂²	1	1	yes	characteristic
7	#11924459	—	2	1	no	—
8	#11924456	—	2	1	no	—
9	C₄×#64436	C₄	1	1	yes	characteristic, complemented
10	#125×C₃₇	C₄	1	1	yes	characteristic, complemented
11	C₂×D₁₄₈	D₄	1	1	yes	characteristic
12	C₂×Dic₇₄	D₄	1	1	yes	characteristic
13	C₂²⋊#3866	—	4	1	no	—
14	#10596957	—	4	1	no	—
15	C₄⋊C₄×C₃₇	—	2	1	no	—
16	C₄⋊C₄×C₃₇	—	4	1	no	—
17	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
18	#10596938	—	4	1	no	—
19	C₂×#64436	—	2	1	no	—
20	C₂²×D₃₇	—	2	1	no	—
21	C₂×#3866	—	8	1	no	—
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	—	4	1	no	—
24	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×Dic₃₇	—	2	1	no	—
26	D₁₄₈	—	4	1	no	—
27	Dic₇₄	—	4	1	no	—
28	#64438	—	8	1	no	—
29	#64436	—	4	1	no	—
30	C₂²×C₃₇	#99	1	1	yes	characteristic
31	C₂×D₃₇	—	4	1	no	—
32	C₂×D₃₇	—	8	1	no	—
33	#3866	—	16	1	no	—
34	C₄×C₃₇	—	2	1	no	—
35	C₄×C₃₇	—	4	1	no	—
36	C₄×C₃₇	—	8	1	no	—
37	Dic₃₇	—	4	1	no	—
38	#1414	—	37	1	no	maximal, Sylow
39	C₂×C₃₇	—	2	1	no	—
40	C₂×C₃₇	#354	1	1	yes	characteristic
41	D₃₇	—	8	1	no	—
42	#488	—	37	1	no	—
43	#355	—	37	1	no	—
44	#354	—	37	1	no	—
45	C₃₇	#1414	1	1	yes	characteristic, complemented, Sylow
46	#125	#3866	1	1	yes	characteristic, complemented
47	#124	—	37	1	no	—
48	#103	—	74	1	no	—
49	#102	—	74	1	no	—
50	#101	—	74	1	no	—
51	#99	—	74	1	no	—
52	C₄×C₈	—	37	1	no	—
53	C₂×Q₈	—	37	1	no	—
54	C₂×D₄	—	37	1	no	—
55	M₁₆	—	148	1	no	—
56	C₂×C₈	—	74	1	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	—	4	1	no	—
59	C₂²⋊C₄	—	148	1	no	—
60	C₂²⋊C₄	—	148	1	no	—
61	C₄²	C₂×#3866	1	1	yes	characteristic
62	C₂³	—	74	1	no	—
63	Q₈	—	148	1	no	—
64	D₄	—	148	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	4	1	no	—
67	C₂×C₄	—	296	1	no	—
68	C₂×C₄	—	74	1	no	—
69	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
70	C₈	—	296	1	no	—
71	C₈	—	148	1	no	—
72	C₂²	—	296	1	no	—
73	C₂²	—	148	1	no	—
74	C₂²	#11924594	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	8	1	no	—
78	C₄	—	592	1	no	—
79	C₄	—	148	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	296	1	no	—
82	C₂	#14558439	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14558439
commutator	C₄²×C₃₇	C₂×C₄
Frattini	C₄²	C₂×#3866
Fitting	#125×C₃₇	C₄
socle	C₂×C₃₇	#354
prime radical	C₂×D₁₄₈	D₄
cosocle	#11924524	C₂²
hypercenter	#125	#3866
hypocenter	C₃₇	#1414
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
9. C₄×#64436	C₄	semidirect
10. #125×C₃₇	C₄	semidirect
45. C₃₇	#1414	semidirect
46. #125	#3866	semidirect

Maximal subgroups

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

subgroup	index
#14558442	2
#14558440	2
#14557890	2
#1414	37