Subgroups — #16834646

Order 3712.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272096	C₂	1	1	yes	maximal, characteristic, complemented
2	#14272090	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271596	C₂	1	1	yes	maximal, characteristic
4	#11745281	—	2	1	no	—
5	#11745210	—	2	1	no	—
6	C₂₉×Q₃₂	C₄	1	1	yes	characteristic, complemented
7	#11745176	—	2	1	no	—
8	D₄₆₄	C₄	1	1	yes	characteristic, complemented
9	C₁₆×D₂₉	C₂²	1	1	yes	characteristic
10	#11745144	—	2	1	no	—
11	#90809	—	4	1	no	—
12	C₄⋊#1181	—	4	1	no	—
13	Q₁₆×C₂₉	—	2	1	no	—
14	#90784	—	4	1	no	—
15	D₂₃₂	—	2	1	no	—
16	C₈×D₂₉	D₄	1	1	yes	characteristic
17	C₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
18	#90768	D₄	1	1	yes	characteristic
19	C₂×#1181	—	8	1	no	—
20	Q₈×C₂₉	—	4	1	no	—
21	D₁₁₆	—	4	1	no	—
22	D₁₁₆	—	8	1	no	—
23	C₄×D₂₉	—	8	1	no	—
24	C₄×D₂₉	D₈	1	1	yes	characteristic
25	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	#6597	SD₁₆	1	1	yes	characteristic
27	#1418	—	29	1	no	maximal, Sylow
28	C₂×D₂₉	—	8	1	no	—
29	C₂×D₂₉	D₁₆	1	1	yes	characteristic
30	#1181	—	16	1	no	—
31	C₄×C₂₉	—	8	1	no	—
32	C₄×C₂₉	#102	1	1	yes	characteristic
33	Dic₂₉	SD₃₂	1	1	yes	characteristic
34	#508	—	29	1	no	—
35	M₆₄	—	29	1	no	—
36	#367	—	29	1	no	—
37	C₂×C₂₉	#357	1	1	yes	characteristic
38	D₂₉	—	2	1	no	—
39	D₂₉	—	16	1	no	—
40	#135	—	58	1	no	—
41	Q₃₂	#1181	1	1	yes	characteristic, complemented
42	SD₃₂	—	58	1	no	—
43	D₁₆	—	29	1	no	—
44	C₂×C₁₆	—	29	1	no	—
45	#107	—	58	1	no	—
46	C₃₂	—	58	1	no	—
47	C₂₉	#1418	1	1	yes	characteristic, complemented, Sylow
48	#41	—	116	1	no	—
49	Q₁₆	—	2	1	no	—
50	SD₁₆	—	116	1	no	—
51	D₈	—	58	1	no	—
52	C₂×C₈	—	29	1	no	—
53	C₄⋊C₄	—	116	1	no	—
54	C₁₆	—	29	1	no	—
55	C₁₆	C₂×#1181	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	D₄	—	116	1	no	—
58	D₄	—	232	1	no	—
59	C₂×C₄	—	29	1	no	—
60	C₂×C₄	—	232	1	no	—
61	C₂×C₄	—	232	1	no	—
62	C₈	—	29	1	no	—
63	C₈	C₂²⋊#1181	1	1	yes	characteristic
64	C₂²	—	29	1	no	—
65	C₂²	—	232	1	no	—
66	C₄	—	8	1	no	—
67	C₄	—	29	1	no	—
68	C₄	—	464	1	no	—
69	C₄	#11745223	1	1	yes	characteristic
70	C₂	—	58	1	no	—
71	C₂	—	464	1	no	—
72	C₂	#14272075	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272075
commutator	C₁₆×C₂₉	C₂×C₄
Frattini	C₁₆	C₂×#1181
Fitting	C₂₉×Q₃₂	C₄
socle	C₂×C₂₉	#357
prime radical	#14271596	C₂
cosocle	C₁₆×D₂₉	C₂²
hypercenter	Q₃₂	#1181
hypocenter	C₂₉	#1418
LCS	G ▷ C₁₆×C₂₉ ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #14272096	C₂	semidirect
2. #14272090	C₂	semidirect
6. C₂₉×Q₃₂	C₄	semidirect
8. D₄₆₄	C₄	semidirect
41. Q₃₂	#1181	semidirect
47. C₂₉	#1418	semidirect

Maximal subgroups

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

subgroup	index
#14272096	2
#14272090	2
#14271596	2
#1418	29