Subgroups — #16817472

Order 3712.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₅₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#90768	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₅₈	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₂₉	—	2	1	no	—
6	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	#11745162	—	2	1	no	—
8	C₈×Dic₂₉	—	2	1	no	—
9	C₂×#90768	—	2	1	no	—
10	C₄⋊#6597	C₄	1	1	yes	characteristic
11	C₂×Dic₅₈	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₂₉	C₈	1	1	yes	characteristic
16	#90779	—	2	1	no	—
17	C₄×Dic₂₉	—	2	1	no	—
18	C₂×#6597	—	2	1	no	—
19	C₁₆×C₂₉	—	2	2	no	—
20	#90768	—	4	1	no	—
21	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
24	C₂×Dic₂₉	—	2	1	no	—
25	C₂×Dic₂₉	—	2	1	no	—
26	Dic₅₈	—	2	1	no	—
27	Dic₅₈	C₁₆	1	2	yes	complemented
28	C₈×C₂₉	—	2	1	no	—
29	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
30	C₈×C₂₉	Q₁₆	1	1	yes	characteristic
31	#6597	—	4	1	no	—
32	Q₈⋊C₁₆	—	29	1	no	maximal, Sylow
33	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₂₉	—	2	1	no	—
35	C₄×C₂₉	#103	1	1	yes	characteristic
36	C₄×C₂₉	#104	1	1	yes	characteristic
37	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
38	C₄×C₂₉	M₃₂	1	1	yes	characteristic
39	Dic₂₉	—	2	2	no	—
40	Dic₂₉	—	4	1	no	—
41	C₈×Q₈	—	29	1	no	—
42	C₄⋊C₁₆	—	29	1	no	—
43	C₄×C₁₆	D₂₉	1	1	yes	characteristic
44	C₂×C₂₉	Q₈⋊C₈	1	1	yes	characteristic
45	C₂×C₂₉	C₂²⋊C₁₆	1	1	yes	characteristic
46	C₂×C₂₉	#350	1	1	yes	characteristic
47	C₄×Q₈	—	29	1	no	—
48	C₂×C₁₆	—	2	1	no	—
49	C₂×C₁₆	—	58	1	no	—
50	C₄⋊C₈	—	29	1	no	—
51	C₄⋊C₈	—	58	1	no	—
52	C₄×C₈	—	58	1	no	—
53	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
54	C₂₉	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₈	—	29	1	no	—
56	C₂×C₈	—	58	1	no	—
57	C₂×C₈	D₁₁₆	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
59	C₄⋊C₄	—	29	1	no	—
60	C₄⋊C₄	—	58	1	no	—
61	C₄²	—	58	1	no	—
62	C₄²	C₄×D₂₉	1	1	yes	characteristic
63	C₁₆	—	2	2	no	—
64	C₁₆	—	116	1	no	—
65	Q₈	—	29	2	no	—
66	Q₈	—	58	1	no	—
67	C₂×C₄	—	58	1	no	—
68	C₂×C₄	—	58	1	no	—
69	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
70	C₂×C₄	#90772	1	1	yes	characteristic
71	C₂×C₄	#90781	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	116	1	no	—
74	C₈	#90773	1	1	yes	characteristic
75	C₈	Dic₁₁₆	1	1	yes	characteristic
76	C₂²	#11745168	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	58	2	no	—
79	C₄	—	116	1	no	—
80	C₄	C₁₆×D₂₉	1	1	yes	characteristic
81	C₄	#11745146	1	1	yes	characteristic
82	C₄	#11745153	1	1	yes	characteristic
83	C₄	#11745164	1	1	yes	characteristic
84	C₂	#14270895	1	1	yes	characteristic
85	C₂	#14270942	1	1	yes	characteristic
86	C₂	#14270946	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₁₁₆
commutator	C₄×C₂₉	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₄×C₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂²⋊C₈
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	Q₈⋊C₁₆
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
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. Dic₅₈	C₁₆	semidirect
54. C₂₉	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×Dic₅₈	2
C₄⋊#90768	2
C₄×C₁₆×C₂₉	2
Q₈⋊C₁₆	29