Subgroups — #16817532

Order 3712.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271536	C₂	1	1	yes	maximal, characteristic
2	#14270984	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90773	—	2	1	no	—
5	C₂×#90773	—	2	1	no	—
6	#11745236	C₄	1	1	yes	characteristic
7	#11745231	C₄	1	1	yes	characteristic
8	C₂₉×M₃₂	—	2	1	no	—
9	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	#11745160	—	2	1	no	—
11	C₂×D₁₁₆	—	2	1	no	—
12	C₂×D₁₁₆	—	4	1	no	—
13	C₂×Dic₅₈	—	2	1	no	—
14	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₄⋊Dic₂₉	—	4	1	no	—
18	#90773	—	4	1	no	—
19	#90773	—	4	1	no	—
20	#90773	—	4	1	no	—
21	#90773	—	4	1	no	—
22	C₁₆×C₂₉	—	4	1	no	—
23	#90768	—	4	1	no	—
24	C₂²×D₂₉	—	4	1	no	—
25	C₂×C₄×C₂₉	—	2	1	no	—
26	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₂₉	—	4	1	no	—
28	D₁₁₆	—	4	1	no	—
29	D₁₁₆	—	4	1	no	—
30	D₁₁₆	—	8	2	no	—
31	Dic₅₈	—	4	1	no	—
32	Dic₅₈	—	4	1	no	—
33	C₈×C₂₉	D₈	1	1	yes	characteristic
34	C₈×C₂₉	D₈	1	1	yes	characteristic
35	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
36	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
37	#1359	—	29	1	no	maximal, Sylow
38	C₂²×C₂₉	#100	1	1	yes	characteristic
39	C₂×D₂₉	—	8	2	no	—
40	C₂×D₂₉	—	8	1	no	—
41	C₄×C₂₉	—	2	2	no	—
42	C₄×C₂₉	#102	1	1	yes	characteristic
43	C₄×C₂₉	#102	1	1	yes	characteristic
44	Dic₂₉	—	8	1	no	—
45	#492	—	29	1	no	—
46	#364	—	29	1	no	—
47	#364	D₂₉	1	1	yes	characteristic, complemented
48	C₂×C₂₉	—	2	1	no	—
49	C₂×C₂₉	#331	1	1	yes	characteristic
50	D₂₉	—	16	1	no	—
51	C₂×SD₁₆	—	58	1	no	—
52	C₂×SD₁₆	—	58	1	no	—
53	C₄⋊Q₈	—	29	1	no	—
54	#127	—	29	1	no	—
55	M₃₂	—	2	1	no	—
56	M₃₂	—	58	1	no	—
57	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
58	C₂₉	#1359	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₈	—	58	1	no	—
60	C₂×D₄	—	58	1	no	—
61	C₂×D₄	—	116	1	no	—
62	SD₁₆	—	116	1	no	—
63	SD₁₆	—	116	1	no	—
64	SD₁₆	—	116	1	no	—
65	SD₁₆	—	116	1	no	—
66	C₂×C₈	D₁₁₆	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
68	C₄⋊C₄	—	116	1	no	—
69	C₄²	C₄×D₂₉	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	116	1	no	—
72	C₂³	—	116	1	no	—
73	Q₈	—	116	1	no	—
74	Q₈	—	116	1	no	—
75	D₄	—	116	1	no	—
76	D₄	—	116	1	no	—
77	D₄	—	232	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	116	1	no	—
80	C₂×C₄	#90781	1	1	yes	characteristic
81	C₈	#90773	1	1	yes	characteristic
82	C₈	D₂₃₂	1	1	yes	characteristic
83	C₈	#90782	1	1	yes	characteristic
84	C₈	#90784	1	1	yes	characteristic
85	C₂²	—	232	2	no	—
86	C₂²	—	232	1	no	—
87	C₂²	#11745171	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	232	1	no	—
90	C₄	#11745157	1	1	yes	characteristic
91	C₄	#11745169	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	464	1	no	—
94	C₂	#14270906	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270906
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#364	C₂
socle	C₂×C₂₉	#331
prime radical	#11745236	C₄
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#364	D₂₉
hypocenter	C₂₉	#1359
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #14270984	C₂	semidirect
3. C₂₉×#364	C₂	semidirect
47. #364	D₂₉	semidirect
58. C₂₉	#1359	semidirect

Maximal subgroups

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

subgroup	index
#14271536	2
#14270984	2
C₂₉×#364	2
#1359	29