Subgroups — #16834510

Order 3712.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272084	C₂	1	1	yes	maximal, characteristic
2	#14272027	C₂	1	1	yes	maximal, characteristic
3	#14271567	C₂	1	1	yes	maximal, characteristic
4	#11745250	—	2	1	no	—
5	C₄⋊#6599	—	2	1	no	—
6	C₂×#90770	—	2	1	no	—
7	C₂₉×#107	C₄	1	1	yes	characteristic
8	#11745166	C₄	1	1	yes	characteristic
9	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
10	#11745155	—	2	1	no	—
11	C₂×Dic₅₈	—	4	1	no	—
12	C₂×#6599	—	4	1	no	—
13	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₄⋊C₄×C₂₉	—	2	1	no	—
15	C₄⋊Dic₂₉	—	2	1	no	—
16	#90779	—	4	1	no	—
17	C₄×Dic₂₉	D₄	1	1	yes	characteristic
18	C₂×#6597	D₄	1	1	yes	characteristic
19	#90770	—	4	1	no	—
20	C₂×C₄×C₂₉	—	4	1	no	—
21	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×Dic₂₉	—	4	1	no	—
23	C₂×Dic₂₉	D₈	1	1	yes	characteristic
24	C₂×Dic₂₉	SD₁₆	1	1	yes	characteristic
25	Dic₅₈	—	8	1	no	—
26	Dic₅₈	—	8	1	no	—
27	#6599	—	8	1	no	—
28	C₈×C₂₉	—	2	1	no	—
29	#6597	SD₁₆	1	1	yes	characteristic
30	#6597	Q₁₆	1	1	yes	characteristic
31	#1364	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	#102	1	1	yes	characteristic
33	C₄×C₂₉	—	8	1	no	—
34	C₄×C₂₉	#101	1	1	yes	characteristic
35	C₄×C₂₉	#103	1	1	yes	characteristic
36	Dic₂₉	—	2	1	no	—
37	Dic₂₉	—	8	1	no	—
38	Dic₂₉	D₁₆	1	1	yes	characteristic
39	Dic₂₉	SD₃₂	1	1	yes	characteristic
40	#500	—	29	1	no	—
41	C₄⋊C₁₆	—	29	1	no	—
42	#335	—	29	1	no	—
43	C₂×C₂₉	#332	1	1	yes	characteristic
44	C₂×C₂₉	#357	1	1	yes	characteristic
45	C₂×C₂₉	#362	1	1	yes	characteristic
46	C₄⋊Q₈	—	58	1	no	—
47	C₂×C₁₆	—	58	1	no	—
48	#107	—	29	1	no	—
49	#107	—	58	1	no	—
50	#107	#1181	1	1	yes	characteristic
51	C₄⋊C₈	—	58	1	no	—
52	C₄×C₈	—	29	1	no	—
53	C₂₉	#1364	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	116	1	no	—
55	C₂×C₈	—	29	1	no	—
56	C₂×C₈	—	116	1	no	—
57	C₂×C₈	C₂×#1181	1	1	yes	characteristic
58	C₄⋊C₄	—	2	1	no	—
59	C₄⋊C₄	—	58	1	no	—
60	C₄⋊C₄	—	116	1	no	—
61	C₄²	—	29	1	no	—
62	C₁₆	—	116	1	no	—
63	Q₈	—	232	1	no	—
64	Q₈	—	232	1	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	29	1	no	—
67	C₂×C₄	—	29	1	no	—
68	C₂×C₄	—	116	1	no	—
69	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	29	1	no	—
72	C₈	—	29	1	no	—
73	C₈	—	232	1	no	—
74	C₂²	#11745223	1	1	yes	characteristic
75	C₄	—	8	1	no	—
76	C₄	—	29	1	no	—
77	C₄	—	29	1	no	—
78	C₄	—	58	1	no	—
79	C₄	—	232	1	no	—
80	C₄	#11745221	1	1	yes	characteristic
81	C₄	#11745225	1	1	yes	characteristic
82	C₂	#14272022	1	1	yes	characteristic
83	C₂	#14272075	1	1	yes	characteristic
84	C₂	#14272082	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745223
commutator	C₂×C₈×C₂₉	C₂×C₄
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂₉×#107	C₄
socle, prime radical	C₂²×C₂₉	#102
cosocle	C₈×Dic₂₉	C₂²
hypercenter	#107	#1181
hypocenter	C₂₉	#1364
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
53. C₂₉	#1364	semidirect

Maximal subgroups

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

subgroup	index
#14272084	2
#14272027	2
#14271567	2
#1364	29