Subgroups — #16817463

Order 3712.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic
2	#14270914	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#346	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₁₆	C₄	1	1	yes	characteristic
5	C₄×Dic₅₈	—	2	1	no	—
6	C₂×C₁₆×C₂₉	—	2	1	no	—
7	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	#11745166	C₄	1	1	yes	characteristic
9	#11745164	—	2	1	no	—
10	C₄⋊#6597	—	2	1	no	—
11	C₂×Dic₅₈	—	2	1	no	—
12	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₄²×C₂₉	D₄	1	1	yes	characteristic
15	C₄⋊Dic₂₉	—	2	1	no	—
16	#90779	—	4	1	no	—
17	C₄×Dic₂₉	—	4	1	no	—
18	C₂×#6597	—	4	1	no	—
19	Dic₁₁₆	—	2	1	no	—
20	Dic₁₁₆	C₈	1	2	yes	complemented
21	C₁₆×C₂₉	—	2	2	no	—
22	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
24	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
25	C₂×Dic₂₉	—	4	1	no	—
26	C₂×Dic₂₉	—	4	1	no	—
27	Dic₅₈	—	2	2	no	—
28	Dic₅₈	—	4	1	no	—
29	C₈×C₂₉	—	2	1	no	—
30	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
31	C₈×C₂₉	M₁₆	1	1	yes	characteristic
32	#6597	—	8	1	no	—
33	#1334	—	29	1	no	maximal, Sylow
34	C₂²×C₂₉	#102	1	1	yes	characteristic
35	C₄×C₂₉	—	2	1	no	—
36	C₄×C₂₉	—	2	1	no	—
37	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₄×C₂₉	#104	1	1	yes	characteristic
39	Dic₂₉	—	4	2	no	—
40	Dic₂₉	—	8	1	no	—
41	C₄×Q₁₆	—	29	1	no	—
42	#346	D₂₉	1	1	yes	characteristic
43	#334	—	29	1	no	—
44	C₂×C₂₉	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₂₉	#360	1	1	yes	characteristic
46	C₂×C₂₉	#362	1	1	yes	characteristic
47	C₂×Q₁₆	—	29	1	no	—
48	C₄×Q₈	—	58	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	#107	—	29	1	no	—
51	C₄⋊C₈	—	58	1	no	—
52	#103	—	58	1	no	—
53	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
54	C₂₉	#1334	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₈	—	58	1	no	—
56	Q₁₆	—	29	2	no	—
57	Q₁₆	—	58	1	no	—
58	C₂×C₈	—	116	1	no	—
59	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
60	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
61	C₄⋊C₄	—	58	1	no	—
62	C₄⋊C₄	—	116	1	no	—
63	C₄²	—	116	1	no	—
64	C₄²	D₁₁₆	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	Q₈	—	58	2	no	—
67	Q₈	—	116	1	no	—
68	C₂×C₄	—	116	1	no	—
69	C₂×C₄	—	116	1	no	—
70	C₂×C₄	#90773	1	1	yes	characteristic
71	C₂×C₄	D₂₃₂	1	1	yes	characteristic
72	C₂×C₄	#90781	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	232	1	no	—
75	C₈	C₈×D₂₉	1	1	yes	characteristic
76	C₈	#90772	1	1	yes	characteristic
77	C₂²	#11745169	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	2	1	no	—
80	C₄	—	116	2	no	—
81	C₄	—	232	1	no	—
82	C₄	#11745153	1	1	yes	characteristic
83	C₄	#11745168	1	1	yes	characteristic
84	C₂	#14270892	1	1	yes	characteristic
85	C₂	#14270974	1	1	yes	characteristic
86	C₂	#14270980	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745169
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#346	C₂
socle, prime radical	C₂²×C₂₉	#102
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#346	D₂₉
hypocenter	C₂₉	#1334
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
20. Dic₁₁₆	C₈	semidirect
54. C₂₉	#1334	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₁₁₆	2
#14270914	2
C₂₉×#346	2
#1334	29