Subgroups — #17992576

Order 4736.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₇₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#10596925	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₇₄	C₄	1	1	yes	characteristic
5	C₂×#10596925	—	2	1	no	—
6	C₄⋊#64436	C₄	1	1	yes	characteristic
7	#11924465	—	2	1	no	—
8	C₈×Dic₃₇	—	2	1	no	—
9	C₂×C₁₆×C₃₇	—	2	1	no	—
10	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₄	C₈	1	1	yes	characteristic
12	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₃₇	C₈	1	1	yes	characteristic
16	#10596936	—	2	1	no	—
17	C₄×Dic₃₇	—	2	1	no	—
18	C₂×#64436	—	2	1	no	—
19	C₁₆×C₃₇	—	2	2	no	—
20	#10596925	—	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	—	2	1	no	—
29	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
30	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
31	#64436	—	4	1	no	—
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	D₃₇	1	1	yes	characteristic
47	C₃₇	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
48	C₄×Q₈	—	37	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	74	1	no	—
51	C₄⋊C₈	—	37	1	no	—
52	C₄⋊C₈	—	74	1	no	—
53	C₄×C₈	—	74	1	no	—
54	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
55	C₂×Q₈	—	37	1	no	—
56	C₂×C₈	—	74	1	no	—
57	C₂×C₈	D₁₄₈	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
59	C₄⋊C₄	—	37	1	no	—
60	C₄⋊C₄	—	74	1	no	—
61	C₄²	—	74	1	no	—
62	C₄²	C₄×D₃₇	1	1	yes	characteristic
63	C₁₆	—	2	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	C₈×D₃₇	1	1	yes	characteristic
70	C₂×C₄	#10596929	1	1	yes	characteristic
71	C₂×C₄	#10596938	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	148	1	no	—
74	C₈	#10596930	1	1	yes	characteristic
75	C₈	Dic₁₄₈	1	1	yes	characteristic
76	C₂²	#11924448	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	74	2	no	—
79	C₄	—	148	1	no	—
80	C₄	#11924461	1	1	yes	characteristic
81	C₄	#11924464	1	1	yes	characteristic
82	C₄	C₁₆×D₃₇	1	1	yes	characteristic
83	C₄	#11924475	1	1	yes	characteristic
84	C₂	#14557265	1	1	yes	characteristic
85	C₂	#14557312	1	1	yes	characteristic
86	C₂	#14557316	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₁₄₈
commutator	C₄×C₃₇	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₄×C₁₆×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂²⋊C₈
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	C₄×C₁₆	D₃₇
hypocenter	C₃₇	Q₈⋊C₁₆
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

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
C₈×Dic₇₄	2
C₄⋊#10596925	2
C₄×C₁₆×C₃₇	2
Q₈⋊C₁₆	37