Subgroups — #16834609

Order 3712.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272095	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11745144	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271580	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#131	C₄	1	1	yes	characteristic
5	#11745160	—	2	1	no	—
6	#11745160	C₄	1	1	yes	characteristic
7	C₂×#90768	—	2	1	no	—
8	C₂×#90768	C₂²	1	1	yes	characteristic
9	#11745144	—	2	1	no	—
10	#11745144	—	2	1	no	—
11	#41×C₂₉	C₈	1	1	yes	characteristic
12	M₁₆×C₂₉	—	2	1	no	—
13	M₁₆×C₂₉	C₈	1	1	yes	characteristic
14	C₂×C₈×C₂₉	—	2	1	no	—
15	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
16	#90768	—	2	1	no	—
17	#90768	D₄	1	1	yes	characteristic
18	#90768	D₄	1	1	yes	characteristic
19	Q₈×C₂₉	C₁₆	1	1	yes	characteristic
20	D₄×C₂₉	—	2	1	no	—
21	D₄×C₂₉	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
24	C₈×C₂₉	—	2	1	no	—
25	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₉	M₁₆	1	1	yes	characteristic
27	#1401	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	—	2	1	no	—
29	C₂²×C₂₉	M₃₂	1	1	yes	characteristic
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₂₉	C₂×C₁₆	1	1	yes	characteristic
33	#504	—	29	1	no	—
34	M₆₄	—	29	1	no	—
35	C₂×C₃₂	—	29	1	no	—
36	C₂×C₂₉	—	2	1	no	—
37	C₂×C₂₉	—	4	1	no	—
38	C₂×C₂₉	C₂²⋊C₁₆	1	1	yes	characteristic
39	#131	#1181	1	1	yes	characteristic
40	M₃₂	—	29	1	no	—
41	M₃₂	—	58	1	no	—
42	C₂×C₁₆	—	29	1	no	—
43	C₂×C₁₆	—	58	1	no	—
44	C₃₂	—	58	1	no	—
45	C₃₂	—	58	1	no	—
46	C₂₉	#1401	1	1	yes	characteristic, complemented, Sylow
47	#41	#6599	1	1	yes	characteristic
48	M₁₆	—	2	1	no	—
49	M₁₆	#6599	1	1	yes	characteristic
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	C₂×#1181	1	1	yes	characteristic
52	C₁₆	—	29	1	no	—
53	C₁₆	—	29	1	no	—
54	C₁₆	—	58	1	no	—
55	Q₈	#90770	1	1	yes	characteristic
56	D₄	—	2	1	no	—
57	D₄	#90770	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₂×#6599	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	#90800	1	1	yes	characteristic
62	C₈	C₂²⋊#1181	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₂²	#11745214	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	C₂×#90770	1	1	yes	characteristic
67	C₄	C₂²⋊#6599	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	C₂²⋊#90770	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#1181
commutator	C₄×C₂₉	C₂×C₁₆
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂₉×#131	C₄
socle	C₂×C₂₉	C₂²⋊C₁₆
prime radical	#41×C₂₉	C₈
cosocle	C₂×#90768	C₂²
hypercenter	#131	#1181
hypocenter	C₂₉	#1401
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #14272095	C₂	semidirect
2. C₂×#11745144	C₂	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
#14272095	2
C₂×#11745144	2
#14271580	2
#1401	29