Subgroups — #16817633

Order 3712.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271579	C₂	1	1	yes	maximal, characteristic
2	#14270997	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745263	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
6	#11745160	C₄	1	1	yes	characteristic
7	#11745146	—	2	1	no	—
8	C₁₆×D₂₉	—	2	1	no	—
9	C₂₉×C₃₂	—	2	1	no	—
10	#11745142	—	2	1	no	—
11	#90805	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
13	#90777	C₈	1	1	yes	characteristic
14	#90772	—	2	1	no	—
15	C₈×D₂₉	—	2	1	no	—
16	C₁₆×C₂₉	D₄	1	1	yes	characteristic
17	C₁₆×C₂₉	D₄	1	1	yes	characteristic
18	#90768	—	2	1	no	—
19	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
20	C₂²⋊D₂₉	—	2	1	no	—
21	D₁₁₆	C₁₆	1	1	yes	characteristic
22	C₄×D₂₉	—	2	1	no	—
23	Dic₅₈	C₁₆	1	1	yes	characteristic
24	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₂₉	M₁₆	1	1	yes	characteristic
26	#6597	—	2	1	no	—
27	#1401	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	M₃₂	1	1	yes	characteristic
29	C₂×D₂₉	—	2	1	no	—
30	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
32	Dic₂₉	—	2	1	no	—
33	#504	—	29	1	no	—
34	M₆₄	—	29	1	no	—
35	C₂×C₃₂	D₂₉	1	1	yes	characteristic, complemented
36	C₂×C₂₉	—	2	1	no	—
37	C₂×C₂₉	C₂²⋊C₁₆	1	1	yes	characteristic
38	D₂₉	—	4	1	no	—
39	#131	—	29	1	no	—
40	M₃₂	—	29	1	no	—
41	M₃₂	—	58	1	no	—
42	C₂×C₁₆	—	58	1	no	—
43	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
44	C₃₂	—	2	1	no	—
45	C₃₂	—	58	1	no	—
46	C₂₉	#1401	1	1	yes	characteristic, complemented, Sylow
47	#41	—	29	1	no	—
48	M₁₆	—	29	1	no	—
49	M₁₆	—	58	1	no	—
50	C₂×C₈	—	58	1	no	—
51	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
52	C₁₆	—	58	1	no	—
53	C₁₆	D₁₁₆	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₂₉	1	1	yes	characteristic
55	Q₈	—	29	1	no	—
56	D₄	—	29	1	no	—
57	D₄	—	58	1	no	—
58	C₂×C₄	—	58	1	no	—
59	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
60	C₈	—	58	1	no	—
61	C₈	#90772	1	1	yes	characteristic
62	C₈	#90781	1	1	yes	characteristic
63	C₂²	—	58	1	no	—
64	C₂²	#11745146	1	1	yes	characteristic
65	C₄	—	58	1	no	—
66	C₄	C₁₆×D₂₉	1	1	yes	characteristic
67	C₄	#11745168	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	116	1	no	—
70	C₂	#14270942	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₁₁₆
commutator	C₄×C₂₉	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₂₉
Fitting	C₂×C₂₉×C₃₂	C₂
socle	C₂×C₂₉	C₂²⋊C₁₆
prime radical	#90805	C₈
cosocle	C₂×C₁₆×C₂₉	C₂²
hypercenter	C₂×C₃₂	D₂₉
hypocenter	C₂₉	#1401
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #14270997	C₂	semidirect
3. C₂×C₂₉×C₃₂	C₂	semidirect
35. C₂×C₃₂	D₂₉	semidirect
46. C₂₉	#1401	semidirect

Maximal subgroups

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

subgroup	index
#14271579	2
#14270997	2
C₂×C₂₉×C₃₂	2
#1401	29