Subgroups — #16834452

Order 3712.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272052	C₂	1	1	yes	maximal, characteristic
2	#14272024	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₂₉	C₄	1	1	yes	characteristic
5	Q₈×Dic₂₉	—	2	1	no	—
6	C₄⋊#6599	—	2	1	no	—
7	C₂×#90770	—	2	1	no	—
8	#11745183	—	2	1	no	—
9	#11745166	C₄	1	1	yes	characteristic
10	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₂₉	—	2	1	no	—
12	C₂×#6599	—	4	1	no	—
13	Q₁₆×C₂₉	—	2	1	no	—
14	Q₁₆×C₂₉	C₈	1	2	yes	complemented
15	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₂₉	—	2	1	no	—
17	C₄⋊Dic₂₉	—	4	1	no	—
18	C₄×Dic₂₉	—	4	1	no	—
19	C₄×Dic₂₉	D₄	1	1	yes	characteristic
20	C₂×#6597	D₄	1	1	yes	characteristic
21	#90770	—	2	2	no	—
22	Q₈×C₂₉	—	2	2	no	—
23	Q₈×C₂₉	—	4	1	no	—
24	C₂×C₄×C₂₉	—	4	1	no	—
25	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₂₉	—	4	1	no	—
27	C₂×Dic₂₉	D₈	1	1	yes	characteristic
28	C₂×Dic₂₉	SD₁₆	1	1	yes	characteristic
29	#6599	—	8	1	no	—
30	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
31	C₈×C₂₉	M₁₆	1	1	yes	characteristic
32	#6597	—	2	1	no	—
33	#1334	—	29	1	no	maximal, Sylow
34	C₂²×C₂₉	#102	1	1	yes	characteristic
35	C₄×C₂₉	—	4	2	no	—
36	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₂₉	#104	1	1	yes	characteristic
38	Dic₂₉	—	2	1	no	—
39	Dic₂₉	—	2	1	no	—
40	Dic₂₉	—	8	1	no	—
41	C₄×Q₁₆	—	29	1	no	—
42	#346	—	29	1	no	—
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	#1181	1	1	yes	characteristic
48	C₄×Q₈	—	58	1	no	—
49	C₂×C₁₆	—	58	1	no	—
50	#107	—	29	1	no	—
51	C₄⋊C₈	—	58	1	no	—
52	#103	—	58	1	no	—
53	C₄×C₈	—	29	1	no	—
54	C₂₉	#1334	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₈	—	2	1	no	—
56	Q₁₆	—	2	1	no	—
57	Q₁₆	#6599	1	2	yes	complemented
58	C₂×C₈	—	29	1	no	—
59	C₂×C₈	—	116	1	no	—
60	C₂×C₈	C₂×#1181	1	1	yes	characteristic
61	C₄⋊C₄	—	58	1	no	—
62	C₄⋊C₄	—	116	1	no	—
63	C₄²	—	29	1	no	—
64	C₄²	—	116	1	no	—
65	C₁₆	—	58	2	no	—
66	Q₈	—	2	2	no	—
67	Q₈	—	4	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	29	1	no	—
70	C₂×C₄	—	29	1	no	—
71	C₂×C₄	—	116	1	no	—
72	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
73	C₈	—	58	1	no	—
74	C₈	—	232	1	no	—
75	C₈	C₂×#6599	1	1	yes	characteristic
76	C₈	#90800	1	1	yes	characteristic
77	C₂²	#11745223	1	1	yes	characteristic
78	C₄	—	4	2	no	—
79	C₄	—	58	1	no	—
80	C₄	—	58	1	no	—
81	C₄	—	232	1	no	—
82	C₄	#11745224	1	1	yes	characteristic
83	C₄	C₂²⋊#6599	1	1	yes	characteristic
84	C₂	D₄⋊#6599	1	1	yes	characteristic
85	C₂	#14272080	1	1	yes	characteristic
86	C₂	#14272082	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745223
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂×Q₁₆×C₂₉	C₄
socle, prime radical	C₂²×C₂₉	#102
cosocle	C₈×Dic₂₉	C₂²
hypercenter	C₂×Q₁₆	#1181
hypocenter	C₂₉	#1334
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
14. Q₁₆×C₂₉	C₈	semidirect
54. C₂₉	#1334	semidirect
57. Q₁₆	#6599	semidirect

Maximal subgroups

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

subgroup	index
#14272052	2
#14272024	2
Q₁₆×Dic₂₉	2
#1334	29