Subgroups — #16834496

Order 3712.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272055	C₂	1	2	yes	maximal, complemented
2	#14271529	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#125	C₄	1	1	yes	characteristic
4	#11745236	C₄	1	1	yes	characteristic
5	#11745214	—	2	2	no	—
6	#11745157	—	2	2	no	—
7	#11745151	C₂²	1	1	yes	characteristic
8	C₂×D₁₁₆	—	2	1	no	—
9	C₂×D₁₁₆	—	4	1	no	—
10	C₄⋊C₄×C₂₉	—	2	1	no	—
11	C₄⋊C₄×C₂₉	—	4	1	no	—
12	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×#6597	D₄	1	2	yes	—
14	#90770	—	2	4	no	—
15	C₂²×D₂₉	—	4	1	no	—
16	C₂×C₄×C₂₉	—	2	1	no	—
17	C₂×C₄×C₂₉	—	4	1	no	—
18	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
19	D₁₁₆	—	4	2	no	—
20	D₁₁₆	—	8	2	no	—
21	#6597	—	2	2	no	—
22	#1355	—	29	1	no	maximal, Sylow
23	C₂²×C₂₉	#100	1	1	yes	characteristic
24	C₂×D₂₉	—	8	2	no	—
25	C₂×D₂₉	—	8	1	no	—
26	C₄×C₂₉	—	4	1	no	—
27	C₄×C₂₉	—	8	1	no	—
28	C₄×C₂₉	#104	1	2	yes	—
29	#490	—	29	1	no	—
30	#347	—	29	2	no	—
31	C₂×C₂₉	—	2	1	no	—
32	C₂×C₂₉	#329	1	1	yes	characteristic
33	D₂₉	—	16	1	no	—
34	#127	—	29	1	no	—
35	#125	#1181	1	1	yes	characteristic
36	M₃₂	—	58	2	no	—
37	#102	—	58	2	no	—
38	#97	—	29	1	no	—
39	C₂₉	#1355	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₄	—	58	1	no	—
41	C₂×D₄	—	116	1	no	—
42	C₂×C₈	—	29	2	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	4	1	no	—
45	C₄²	C₂×#1181	1	1	yes	characteristic
46	C₁₆	—	58	4	no	—
47	C₂³	—	116	1	no	—
48	D₄	—	116	2	no	—
49	D₄	—	232	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
53	C₈	—	58	2	no	—
54	C₂²	—	232	2	no	—
55	C₂²	—	232	1	no	—
56	C₂²	#11745229	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	1	no	—
59	C₄	#11745226	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	464	1	no	—
62	C₂	#14272019	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272019
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄²	C₂×#1181
Fitting	C₂₉×#125	C₄
socle	C₂×C₂₉	#329
prime radical	#11745236	C₄
cosocle	#11745151	C₂²
hypercenter	#125	#1181
hypocenter	C₂₉	#1355
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #14272055	C₂	semidirect
39. C₂₉	#1355	semidirect

Maximal subgroups

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

subgroup	index
#14272055	2
#14271529	2
#1355	29