Subgroups — #16834637

Order 3712.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272072	C₂	1	1	yes	maximal, characteristic
2	#14272070	C₂	1	1	yes	maximal, characteristic
3	#14271520	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#125	C₄	1	1	yes	characteristic, complemented
5	#11745237	C₂²	1	1	yes	characteristic
6	#11745221	—	2	1	no	—
7	#11745215	—	2	1	no	—
8	#11745158	—	2	1	no	—
9	#11745157	—	2	1	no	—
10	C₄×#6597	C₄	1	1	yes	characteristic, complemented
11	C₂×D₁₁₆	D₄	1	1	yes	characteristic
12	C₂×Dic₅₈	D₄	1	1	yes	characteristic
13	C₂²⋊#1181	—	4	1	no	—
14	#90800	—	4	1	no	—
15	C₄⋊C₄×C₂₉	—	2	1	no	—
16	C₄⋊C₄×C₂₉	—	4	1	no	—
17	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
18	#90781	—	4	1	no	—
19	C₂×#6597	—	2	1	no	—
20	C₂²×D₂₉	—	2	1	no	—
21	C₂×#1181	—	8	1	no	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	—	4	1	no	—
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×Dic₂₉	—	2	1	no	—
26	D₁₁₆	—	4	1	no	—
27	Dic₅₈	—	4	1	no	—
28	#6599	—	8	1	no	—
29	#6597	—	4	1	no	—
30	#1414	—	29	1	no	maximal, Sylow
31	C₂²×C₂₉	#99	1	1	yes	characteristic
32	C₂×D₂₉	—	4	1	no	—
33	C₂×D₂₉	—	8	1	no	—
34	#1181	—	16	1	no	—
35	C₄×C₂₉	—	2	1	no	—
36	C₄×C₂₉	—	4	1	no	—
37	C₄×C₂₉	—	8	1	no	—
38	Dic₂₉	—	4	1	no	—
39	#488	—	29	1	no	—
40	#355	—	29	1	no	—
41	#354	—	29	1	no	—
42	C₂×C₂₉	—	2	1	no	—
43	C₂×C₂₉	#354	1	1	yes	characteristic
44	D₂₉	—	8	1	no	—
45	#125	#1181	1	1	yes	characteristic, complemented
46	#124	—	29	1	no	—
47	#103	—	58	1	no	—
48	#102	—	58	1	no	—
49	#101	—	58	1	no	—
50	#99	—	58	1	no	—
51	C₄×C₈	—	29	1	no	—
52	C₂₉	#1414	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₈	—	29	1	no	—
54	C₂×D₄	—	29	1	no	—
55	M₁₆	—	116	1	no	—
56	C₂×C₈	—	58	1	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	—	4	1	no	—
59	C₂²⋊C₄	—	116	1	no	—
60	C₂²⋊C₄	—	116	1	no	—
61	C₄²	C₂×#1181	1	1	yes	characteristic
62	C₂³	—	58	1	no	—
63	Q₈	—	116	1	no	—
64	D₄	—	116	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	4	1	no	—
67	C₂×C₄	—	58	1	no	—
68	C₂×C₄	—	232	1	no	—
69	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
70	C₈	—	116	1	no	—
71	C₈	—	232	1	no	—
72	C₂²	—	116	1	no	—
73	C₂²	—	232	1	no	—
74	C₂²	#11745227	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	8	1	no	—
78	C₄	—	116	1	no	—
79	C₄	—	464	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	232	1	no	—
82	C₂	#14272069	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272069
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄²	C₂×#1181
Fitting	C₂₉×#125	C₄
socle	C₂×C₂₉	#354
prime radical	C₂×D₁₁₆	D₄
cosocle	#11745237	C₂²
hypercenter	#125	#1181
hypocenter	C₂₉	#1414
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
4. C₂₉×#125	C₄	semidirect
10. C₄×#6597	C₄	semidirect
45. #125	#1181	semidirect
52. C₂₉	#1414	semidirect

Maximal subgroups

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

subgroup	index
#14272072	2
#14272070	2
#14271520	2
#1414	29