Subgroups — #16835916

Order 3712.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272096	C₂	1	2	yes	maximal, complemented
2	#14272095	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₉⋊C₃₂	C₂	1	2	yes	maximal, complemented
4	C₂×#11745144	C₂	1	1	yes	maximal, characteristic, complemented
5	#14271581	C₂	1	1	yes	maximal, characteristic
6	#11745263	C₄	1	1	yes	characteristic
7	C₂₉×M₃₂	C₄	1	1	yes	characteristic
8	C₂×#90768	C₂²	1	1	yes	characteristic
9	#11745146	C₄	1	2	yes	—
10	C₁₆×D₂₉	C₂²	1	2	yes	—
11	#11745144	C₂²	1	1	yes	characteristic
12	#11745144	C₂²	1	1	yes	characteristic
13	#11745144	C₂²	1	2	yes	—
14	#90805	C₈	1	1	yes	characteristic
15	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
16	#90777	C₈	1	1	yes	characteristic
17	#90772	C₈	1	2	yes	—
18	C₈×D₂₉	C₂×C₄	1	2	yes	—
19	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
20	#90768	C₂×C₄	1	1	yes	characteristic
21	#90768	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₂₉	C₁₆	1	2	yes	—
24	D₁₁₆	C₁₆	1	1	yes	characteristic
25	C₄×D₂₉	C₂×C₈	1	2	yes	—
26	Dic₅₈	C₁₆	1	1	yes	characteristic
27	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
28	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	#6597	C₂×C₈	1	2	yes	—
30	#2258	—	29	1	no	maximal, Sylow
31	C₂²×C₂₉	C₂×C₁₆	1	1	yes	characteristic
32	C₂×D₂₉	C₂×C₁₆	1	2	yes	—
33	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
34	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
35	Dic₂₉	C₂×C₁₆	1	2	yes	—
36	#504	—	29	1	no	—
37	M₆₄	—	29	1	no	—
38	M₆₄	—	29	2	no	—
39	C₂×C₃₂	—	29	1	no	—
40	C₂×C₃₂	—	29	2	no	—
41	C₂×C₂₉	—	2	1	no	—
42	C₂×C₂₉	C₂²×C₁₆	1	1	yes	characteristic
43	D₂₉	—	2	2	no	—
44	#131	—	29	1	no	—
45	M₃₂	—	29	2	no	—
46	M₃₂	#1181	1	1	yes	characteristic
47	C₂×C₁₆	—	29	1	no	—
48	C₂×C₁₆	—	29	2	no	—
49	C₃₂	—	29	1	no	—
50	C₃₂	—	29	1	no	—
51	C₃₂	—	29	2	no	—
52	C₂₉	#2258	1	1	yes	characteristic, complemented, Sylow
53	#41	—	29	1	no	—
54	M₁₆	—	29	1	no	—
55	M₁₆	—	29	2	no	—
56	C₂×C₈	—	29	2	no	—
57	C₂×C₈	C₂×#1181	1	1	yes	characteristic
58	C₁₆	—	29	1	no	—
59	C₁₆	—	29	1	no	—
60	C₁₆	C₂×#1181	1	2	yes	—
61	Q₈	—	29	1	no	—
62	D₄	—	29	2	no	—
63	D₄	—	29	1	no	—
64	C₂×C₄	—	29	2	no	—
65	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
66	C₈	—	29	2	no	—
67	C₈	D₂₉⋊C₈	1	1	yes	characteristic
68	C₈	C₂²×#1181	1	1	yes	characteristic
69	C₂²	—	29	2	no	—
70	C₂²	D₂₉⋊C₁₆	1	1	yes	characteristic
71	C₄	—	29	2	no	—
72	C₄	D₂₉⋊C₁₆	1	1	yes	characteristic
73	C₄	C₂×D₂₉⋊C₈	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	58	2	no	—
76	C₂	C₂×D₂₉⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#1181
commutator, socle	C₂×C₂₉	C₂²×C₁₆
Fitting	C₂₉×M₃₂	C₄
prime radical	#90805	C₈
cosocle	#90768	C₂³
hypercenter	M₃₂	#1181
hypocenter	C₂₉	#2258
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
1. #14272096	C₂	semidirect
2. #14272095	C₂	semidirect
3. D₂₉⋊C₃₂	C₂	semidirect
4. C₂×#11745144	C₂	semidirect
52. C₂₉	#2258	semidirect

Maximal subgroups

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

subgroup	index
#14272096	2
#14272095	2
D₂₉⋊C₃₂	2
C₂×#11745144	2
#14271581	2
#2258	29