Group #16835406 — subgroups

Subgroups — #16835406

Order 3712.

236 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745221	C₂	1	2	yes	maximal
2	#14272044	C₂	1	4	yes	maximal
3	#14271640	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₅₈	C₂²	1	1	yes	characteristic
5	C₂×#90800	C₂²	1	4	yes	—
6	C₂₉×#117	C₄	1	1	yes	characteristic
7	#11745288	C₄	1	1	yes	characteristic
8	#11745249	—	2	2	no	—
9	#11745239	C₄	1	2	yes	—
10	#11745239	C₂²	1	2	yes	—
11	C₄×Dic₅₈	—	2	2	no	—
12	#11745221	—	2	2	no	—
13	#11745221	—	2	2	no	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₅₈	—	2	4	no	—
18	C₂×Dic₅₈	D₄	1	2	yes	—
19	C₂×Dic₅₈	D₄	1	2	yes	—
20	#90800	—	2	4	no	—
21	#90800	—	2	4	no	—
22	C₂×#6599	—	2	4	no	—
23	C₄⋊C₄×C₂₉	—	2	1	no	—
24	C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
25	C₄²×C₂₉	—	2	1	no	—
26	C₂²⋊Dic₂₉	C₂×C₄	1	2	yes	—
27	C₄⋊Dic₂₉	—	2	1	no	—
28	#90779	—	2	2	no	—
29	#90779	—	2	2	no	—
30	C₄×Dic₂₉	—	2	1	no	—
31	C₄×Dic₂₉	—	2	2	no	—
32	C₄×Dic₂₉	—	2	2	no	—
33	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	—	2	2	no	—
36	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×Dic₂₉	—	2	2	no	—
39	C₂×Dic₂₉	—	2	2	no	—
40	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
41	C₂×Dic₂₉	C₂×D₄	1	2	yes	—
42	C₂×Dic₂₉	#41	1	4	yes	—
43	Dic₅₈	—	2	4	no	—
44	Dic₅₈	—	2	4	no	—
45	#6599	—	4	4	no	—
46	#1830	—	29	1	no	maximal, Sylow
47	C₂²×C₂₉	—	4	1	no	—
48	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₂₉	#117	1	2	yes	—
50	C₄×C₂₉	—	2	1	no	—
51	C₄×C₂₉	—	2	1	no	—
52	C₄×C₂₉	—	4	2	no	—
53	Dic₂₉	—	2	2	no	—
54	Dic₂₉	—	4	2	no	—
55	Dic₂₉	#123	1	4	yes	—
56	#519	—	29	1	no	—
57	C₂×#101	—	29	2	no	—
58	#344	—	29	4	no	—
59	C₂×C₂₉	—	2	1	no	—
60	C₂×C₂₉	—	2	2	no	—
61	C₂×C₂₉	#381	1	1	yes	characteristic
62	C₂²×Q₈	—	29	1	no	—
63	C₂×M₁₆	—	29	4	no	—
64	C₄×Q₈	—	58	2	no	—
65	C₄×Q₈	—	58	2	no	—
66	#117	—	29	1	no	—
67	#117	—	29	2	no	—
68	#117	—	29	2	no	—
69	#117	#1181	1	1	yes	characteristic
70	#101	—	58	2	no	—
71	#101	—	58	2	no	—
72	C₂₉	#1830	1	1	yes	characteristic, complemented, Sylow
73	C₂×Q₈	—	29	2	no	—
74	C₂×Q₈	—	29	2	no	—
75	C₂×Q₈	—	58	4	no	—
76	C₂²×C₄	—	29	1	no	—
77	C₂²×C₄	—	29	1	no	—
78	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
79	M₁₆	—	58	4	no	—
80	M₁₆	—	58	4	no	—
81	C₂×C₈	—	58	4	no	—
82	C₄⋊C₄	—	2	1	no	—
83	C₄⋊C₄	—	58	2	no	—
84	C₄⋊C₄	—	58	2	no	—
85	C₄⋊C₄	—	58	1	no	—
86	C₂²⋊C₄	—	29	2	no	—
87	C₂²⋊C₄	C₂×#1181	1	2	yes	—
88	C₄²	—	2	1	no	—
89	C₄²	—	58	2	no	—
90	C₄²	—	58	2	no	—
91	C₄²	—	58	1	no	—
92	C₂³	C₂²×#1181	1	1	yes	characteristic
93	Q₈	—	58	4	no	—
94	Q₈	—	58	4	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	29	4	no	—
98	C₂×C₄	—	29	2	no	—
99	C₂×C₄	—	29	2	no	—
100	C₂×C₄	—	58	2	no	—
101	C₂×C₄	—	58	2	no	—
102	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
103	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
104	C₈	—	116	4	no	—
105	C₂²	—	4	1	no	—
106	C₂²	#11745345	1	2	yes	—
107	C₂²	C₂×C₂²⋊#1181	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	4	2	no	—
111	C₄	—	29	4	no	—
112	C₄	—	58	2	no	—
113	C₄	—	116	2	no	—
114	C₂	—	2	1	no	—
115	C₂	—	2	2	no	—
116	C₂	#14272106	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745221

C₂

yes

maximal

#14272044

C₂

yes

maximal

#14271640

C₂

yes

maximal, characteristic

C₂²×Dic₅₈

C₂²

yes

characteristic

C₂×#90800

C₂²

yes

—

C₂₉×#117

C₄

yes

characteristic

#11745288

C₄

yes

characteristic

#11745249

—

#11745239

C₄

yes

—

#11745239

C₂²

yes

—

C₄×Dic₅₈

—

#11745221

—

#11745221

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂³

yes

characteristic

C₂×Dic₅₈

—

C₂×Dic₅₈

D₄

yes

—

C₂×Dic₅₈

D₄

yes

—

#90800

—

#90800

—

C₂×#6599

—

C₄⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

—

C₂²⋊Dic₂₉

C₂×C₄

yes

—

C₄⋊Dic₂₉

—

#90779

—

#90779

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

—

C₂×Dic₂₉

#41

yes

—

Dic₅₈

—

Dic₅₈

—

#6599

—

#1830

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#123

yes

—

#519

—

C₂×#101

—

#344

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#381

yes

characteristic

C₂²×Q₈

—

C₂×M₁₆

—

C₄×Q₈

—

C₄×Q₈

—

—

—

—

yes

—

—

C₂₉

#1830

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×#1181

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²×#1181

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₂²⋊#1181

yes

characteristic

103

C₂×C₄

C₂²⋊#1181

yes

characteristic

104

C₈

—

116

—

105

C₂²

—

106

C₂²

#11745345

yes

—

107

C₂²

C₂×C₂²⋊#1181

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

116

—

114

C₂

—

115

C₂

—

116

C₂

#14272106

yes

characteristic

	subgroup	G/H
center	C₂	#14272106
commutator, prime radical	C₂³×C₂₉	C₂²×C₄
Frattini	C₂³	C₂²×#1181
Fitting	C₂₉×#117	C₄
socle	C₂×C₂₉	#381
cosocle	C₂²×Dic₂₉	C₂³
hypercenter	#117	#1181
hypocenter	C₂₉	#1830
LCS	G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ #117

subgroup

G/H

center

C₂

#14272106

commutator, prime radical

C₂³×C₂₉

C₂²×C₄

Frattini

C₂³

C₂²×#1181

Fitting

C₂₉×#117

C₄

socle

C₂×C₂₉

#381

cosocle

C₂²×Dic₂₉

C₂³

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂ ◁ C₂³ ◁ #117

N	H ≅ G/N	type
72. C₂₉	#1830	semidirect

H ≅ G/N

type

72. C₂₉

#1830

semidirect

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

subgroup	index
C₂×#11745221	2
#14272044	2
#14271640	2
#1830	29

subgroup

index

Subgroups — #16835406

Conjugacy classes of subgroups

Complements

Maximal subgroups