Subgroups — #18009563

Order 4736.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10596927	C₂	1	1	yes	maximal, characteristic
2	C₄×#10596927	C₂	1	1	yes	maximal, characteristic
3	#14557657	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596927	—	2	1	no	—
5	C₂×#10596927	—	2	1	no	—
6	C₄×Dic₇₄	C₄	1	1	yes	characteristic
7	#11924465	—	2	1	no	—
8	C₄×#64436	C₂²	1	1	yes	characteristic
9	C₈×Dic₃₇	—	2	1	no	—
10	C₄⋊C₈×C₃₇	C₄	1	1	yes	characteristic
11	C₂×Dic₇₄	C₈	1	1	yes	characteristic
12	C₂×C₈×C₃₇	—	2	1	no	—
13	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₃₇	C₈	1	1	yes	characteristic
15	#10596936	—	2	1	no	—
16	C₄×Dic₃₇	—	2	1	no	—
17	C₂×#64436	D₄	1	1	yes	characteristic
18	C₂×#64436	D₄	1	1	yes	characteristic
19	#10596927	—	2	2	no	—
20	#10596927	—	4	1	no	—
21	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
24	C₂×Dic₃₇	—	2	1	no	—
25	C₂×Dic₃₇	—	2	1	no	—
26	Dic₇₄	—	2	1	no	—
27	Dic₇₄	C₁₆	1	2	yes	complemented
28	C₈×C₃₇	—	4	1	no	—
29	#64436	—	2	1	no	—
30	#64436	SD₁₆	1	1	yes	characteristic
31	#64436	Q₁₆	1	1	yes	characteristic
32	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₃₇	—	2	1	no	—
34	C₄×C₃₇	#103	1	1	yes	characteristic
35	C₄×C₃₇	#104	1	1	yes	characteristic
36	C₄×C₃₇	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₃₇	M₃₂	1	1	yes	characteristic
38	Dic₃₇	—	2	2	no	—
39	Dic₃₇	—	4	1	no	—
40	Q₈⋊C₁₆	—	37	1	no	maximal, Sylow
41	C₂×C₃₇	Q₈⋊C₈	1	1	yes	characteristic
42	C₂×C₃₇	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₂×C₃₇	#350	1	1	yes	characteristic
44	C₈×Q₈	—	37	1	no	—
45	C₄⋊C₁₆	—	37	1	no	—
46	C₄×C₁₆	—	37	1	no	—
47	C₃₇	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
48	C₄×Q₈	—	37	1	no	—
49	C₂×C₁₆	—	74	1	no	—
50	C₂×C₁₆	—	74	1	no	—
51	C₄⋊C₈	—	74	1	no	—
52	C₄⋊C₈	#3866	1	1	yes	characteristic
53	C₄×C₈	—	37	1	no	—
54	C₄×C₈	—	74	1	no	—
55	C₂×Q₈	—	37	1	no	—
56	C₂×C₈	—	2	1	no	—
57	C₂×C₈	—	37	1	no	—
58	C₂×C₈	—	37	1	no	—
59	C₄⋊C₄	—	37	1	no	—
60	C₄⋊C₄	—	74	1	no	—
61	C₄²	—	74	1	no	—
62	C₄²	C₂×#3866	1	1	yes	characteristic
63	C₁₆	—	74	2	no	—
64	C₁₆	—	148	1	no	—
65	Q₈	—	37	2	no	—
66	Q₈	—	74	1	no	—
67	C₂×C₄	—	74	1	no	—
68	C₂×C₄	—	74	1	no	—
69	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
70	C₂×C₄	#10596953	1	1	yes	characteristic
71	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
72	C₈	—	4	1	no	—
73	C₈	—	37	1	no	—
74	C₈	—	37	1	no	—
75	C₈	—	74	1	no	—
76	C₂²	#11924593	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	74	2	no	—
79	C₄	—	148	1	no	—
80	C₄	#11924599	1	1	yes	characteristic
81	C₄	#11924600	1	1	yes	characteristic
82	C₄	D₃₇⋊C₁₆	1	1	yes	characteristic
83	C₄	#11924611	1	1	yes	characteristic
84	C₂	#14558383	1	1	yes	characteristic
85	C₂	#14558428	1	1	yes	characteristic
86	C₂	#14558432	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#3866
commutator	C₄×C₃₇	C₂×C₁₆
Frattini	C₄²	C₂×#3866
Fitting	C₄⋊C₈×C₃₇	C₄
socle, prime radical	C₂²×C₃₇	C₂²⋊C₈
cosocle	C₄×#64436	C₂²
hypercenter	C₄⋊C₈	#3866
hypocenter	C₃₇	Q₈⋊C₁₆
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
27. Dic₇₄	C₁₆	semidirect
47. C₃₇	Q₈⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#10596927	2
C₄×#10596927	2
#14557657	2
Q₈⋊C₁₆	37