Subgroups — #16817528

Order 3712.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271540	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×D₂₃₂	—	2	1	no	—
5	C₂×D₂₃₂	—	2	1	no	—
6	#11745236	C₄	1	2	yes	—
7	C₂₉×M₃₂	—	2	1	no	—
8	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	#11745160	—	2	1	no	—
10	C₂×D₁₁₆	—	2	2	no	—
11	C₂×D₁₁₆	—	4	2	no	—
12	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
15	D₂₃₂	—	4	1	no	—
16	D₂₃₂	—	4	1	no	—
17	D₂₃₂	—	4	1	no	—
18	D₂₃₂	—	4	1	no	—
19	C₁₆×C₂₉	—	4	1	no	—
20	#90768	—	4	1	no	—
21	C₂²×D₂₉	—	4	2	no	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
24	D₁₁₆	—	4	2	no	—
25	D₁₁₆	—	4	2	no	—
26	D₁₁₆	—	8	4	no	—
27	C₈×C₂₉	D₈	1	1	yes	characteristic
28	C₈×C₂₉	D₈	1	1	yes	characteristic
29	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
30	C₈×C₂₉	SD₁₆	1	1	yes	characteristic
31	#1357	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	#100	1	1	yes	characteristic
33	C₂×D₂₉	—	8	4	no	—
34	C₂×D₂₉	—	8	2	no	—
35	C₄×C₂₉	—	2	2	no	—
36	C₄×C₂₉	#102	1	1	yes	characteristic
37	C₄×C₂₉	#102	1	1	yes	characteristic
38	#493	—	29	1	no	—
39	#364	—	29	1	no	—
40	#364	D₂₉	1	1	yes	characteristic, complemented
41	C₂×C₂₉	—	2	1	no	—
42	C₂×C₂₉	#331	1	1	yes	characteristic
43	D₂₉	—	16	2	no	—
44	C₂×D₈	—	58	1	no	—
45	C₂×D₈	—	58	1	no	—
46	#127	—	29	2	no	—
47	M₃₂	—	2	1	no	—
48	M₃₂	—	58	1	no	—
49	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
50	C₂₉	#1357	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₄	—	58	2	no	—
52	C₂×D₄	—	116	2	no	—
53	D₈	—	116	1	no	—
54	D₈	—	116	1	no	—
55	D₈	—	116	1	no	—
56	D₈	—	116	1	no	—
57	C₂×C₈	D₁₁₆	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
59	C₄²	C₄×D₂₉	1	1	yes	characteristic
60	C₁₆	—	4	1	no	—
61	C₁₆	—	116	1	no	—
62	C₂³	—	116	2	no	—
63	D₄	—	116	2	no	—
64	D₄	—	116	2	no	—
65	D₄	—	232	4	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	#90781	1	1	yes	characteristic
68	C₈	#90773	1	1	yes	characteristic
69	C₈	D₂₃₂	1	1	yes	characteristic
70	C₈	#90782	1	1	yes	characteristic
71	C₈	#90784	1	1	yes	characteristic
72	C₂²	—	232	4	no	—
73	C₂²	—	232	2	no	—
74	C₂²	#11745171	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#11745157	1	1	yes	characteristic
77	C₄	#11745169	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	464	2	no	—
80	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	#14271540	C₂
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#364	D₂₉
hypocenter	C₂₉	#1357
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
40. #364	D₂₉	semidirect
50. C₂₉	#1357	semidirect

Maximal subgroups

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

subgroup	index
#14271540	2
#14270984	2
C₂₉×#364	2
#1357	29