Subgroups — #16834398

Order 3712.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272184	C₂	1	2	yes	maximal
2	#14271186	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₂₉	C₄	1	1	yes	characteristic
4	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
5	C₂×#90777	C₄	1	1	yes	characteristic
6	C₂²⋊#6599	C₄	1	4	yes	—
7	#11745218	—	2	2	no	—
8	C₄⋊#6599	—	2	2	no	—
9	#11745162	—	2	2	no	—
10	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
12	C₂×#6599	—	2	4	no	—
13	M₁₆×C₂₉	—	4	1	no	—
14	C₂×C₈×C₂₉	—	2	1	no	—
15	C₄×Dic₂₉	D₄	1	1	yes	characteristic
16	C₄×Dic₂₉	D₄	1	2	yes	—
17	C₄×Dic₂₉	Q₈	1	1	yes	characteristic
18	#90777	—	4	1	no	—
19	C₂×#6597	—	2	1	no	—
20	C₂³×C₂₉	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×Dic₂₉	—	4	2	no	—
26	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
27	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
28	#6599	—	4	4	no	—
29	C₈×C₂₉	—	4	1	no	—
30	#6597	—	4	1	no	—
31	#1307	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	—	2	1	no	—
33	C₂²×C₂₉	—	2	2	no	—
34	C₂²×C₂₉	#95	1	1	yes	characteristic
35	C₄×C₂₉	—	2	1	no	—
36	C₄×C₂₉	#100	1	1	yes	characteristic
37	C₄×C₂₉	#101	1	1	yes	characteristic
38	Dic₂₉	—	2	2	no	—
39	Dic₂₉	—	2	2	no	—
40	#432	—	29	2	no	—
41	#423	—	29	1	no	—
42	C₂×C₂₉	—	4	1	no	—
43	C₂×C₂₉	#343	1	1	yes	characteristic
44	C₂×C₂₉	#344	1	2	yes	—
45	C₂×M₁₆	—	29	1	no	—
46	C₂×M₁₆	#1181	1	1	yes	characteristic
47	C₂×C₄²	—	29	1	no	—
48	C₄⋊C₈	—	58	2	no	—
49	C₄⋊C₈	—	58	2	no	—
50	C₂²⋊C₈	—	29	4	no	—
51	#97	—	58	2	no	—
52	C₂₉	#1307	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₄	—	29	2	no	—
54	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
55	M₁₆	—	4	1	no	—
56	M₁₆	—	116	1	no	—
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	—	58	4	no	—
59	C₂×C₈	—	58	1	no	—
60	C₄²	—	29	1	no	—
61	C₄²	—	29	1	no	—
62	C₄²	—	29	2	no	—
63	C₂³	C₄×#1181	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	29	2	no	—
67	C₂×C₄	—	29	2	no	—
68	C₂×C₄	—	116	2	no	—
69	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
71	C₈	—	4	1	no	—
72	C₈	—	116	4	no	—
73	C₈	—	116	1	no	—
74	C₂²	—	2	1	no	—
75	C₂²	—	2	2	no	—
76	C₂²	(C₂×#1181)⋊C₄	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	58	2	no	—
79	C₄	—	58	2	no	—
80	C₄	#11745221	1	1	yes	characteristic
81	C₄	#11745229	1	1	yes	characteristic
82	C₂	—	4	1	no	—
83	C₂	#14272043	1	1	yes	characteristic
84	C₂	#14272046	1	2	yes	—

	subgroup	G/H
center	C₂²	(C₂×#1181)⋊C₄
commutator, prime radical	C₂³×C₂₉	C₄²
Frattini	C₂²×C₄	C₂×#1181
Fitting	C₂×M₁₆×C₂₉	C₄
socle	C₂²×C₂₉	#95
cosocle	C₂×C₄×Dic₂₉	C₂²
hypercenter	C₂×M₁₆	#1181
hypocenter	C₂₉	#1307
LCS	G ▷ C₂³×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
52. C₂₉	#1307	semidirect

Maximal subgroups

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

subgroup	index
#14272184	2
#14271186	2
#1307	29