Group #16835909 — subgroups

Subgroups — #16835909

Order 3712.

126 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 64 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	#14272084	C₂	1	1	yes	maximal, characteristic
2	#14272084	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#90770	C₂	1	1	yes	maximal, characteristic
4	#14272052	C₂	1	1	yes	maximal, characteristic
5	#14272051	C₂	1	1	yes	maximal, characteristic
6	#14272049	C₂	1	1	yes	maximal, characteristic
7	#14271287	C₂	1	1	yes	maximal, characteristic
8	C₄×Dic₅₈	C₄	1	1	yes	characteristic
9	C₂×#90770	C₂²	1	1	yes	characteristic
10	C₂×#90770	C₂²	1	1	yes	characteristic
11	C₂×#90770	C₂²	1	1	yes	characteristic
12	C₂×#90770	C₂²	1	1	yes	characteristic
13	C₂₉×C₄⋊C₈	C₄	1	1	yes	characteristic
14	#11745162	C₄	1	1	yes	characteristic
15	#11745162	C₄	1	1	yes	characteristic
16	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
17	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
18	C₄×#6597	C₂²	1	1	yes	characteristic
19	C₂×Dic₅₈	C₈	1	1	yes	characteristic
20	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
23	C₄⋊Dic₂₉	C₈	1	1	yes	characteristic
24	#90779	C₈	1	1	yes	characteristic
25	#90779	C₈	1	1	yes	characteristic
26	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂×#6597	C₂×C₄	1	1	yes	characteristic
29	C₂×#6597	C₂³	1	1	yes	characteristic
30	#90770	—	2	1	no	—
31	#90770	—	2	1	no	—
32	#90770	—	2	1	no	—
33	#90770	Q₈	1	2	yes	complemented
34	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₂₉	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₂₉	C₂×C₈	1	1	yes	characteristic
39	C₂×Dic₂₉	C₂×C₈	1	1	yes	characteristic
40	C₂×Dic₂₉	C₂×C₈	1	1	yes	characteristic
41	Dic₅₈	—	2	2	no	—
42	C₈×C₂₉	—	2	1	no	—
43	C₈×C₂₉	—	2	1	no	—
44	#6597	—	2	1	no	—
45	#6597	C₂×Q₈	1	1	yes	characteristic
46	#6597	#41	1	1	yes	characteristic
47	#2183	—	29	1	no	maximal, Sylow
48	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
49	C₄×C₂₉	—	2	1	no	—
50	C₄×C₂₉	—	2	1	no	—
51	C₄×C₂₉	C₄×Q₈	1	1	yes	characteristic
52	C₄×C₂₉	#131	1	1	yes	characteristic
53	Dic₂₉	—	2	1	no	—
54	Dic₂₉	—	2	1	no	—
55	Dic₂₉	—	2	1	no	—
56	Dic₂₉	M₃₂	1	2	yes	—
57	C₈×Q₈	—	29	1	no	—
58	C₄⋊C₁₆	—	29	1	no	—
59	C₄⋊C₁₆	—	29	1	no	—
60	C₄⋊C₁₆	—	29	1	no	—
61	#346	—	29	1	no	—
62	#346	—	29	1	no	—
63	C₄×C₁₆	—	29	1	no	—
64	C₂×C₂₉	C₈×Q₈	1	1	yes	characteristic
65	C₂×C₂₉	C₂×M₃₂	1	1	yes	characteristic
66	C₂×C₂₉	#504	1	1	yes	characteristic
67	C₄×Q₈	—	29	1	no	—
68	C₂×C₁₆	—	29	1	no	—
69	C₂×C₁₆	—	29	1	no	—
70	C₂×C₁₆	—	29	1	no	—
71	C₂×C₁₆	—	29	1	no	—
72	C₄⋊C₈	—	29	1	no	—
73	C₄⋊C₈	—	29	1	no	—
74	C₄⋊C₈	#1181	1	1	yes	characteristic
75	C₄×C₈	—	29	1	no	—
76	C₄×C₈	—	29	1	no	—
77	C₄×C₈	—	29	1	no	—
78	C₂₉	#2183	1	1	yes	characteristic, complemented, Sylow
79	C₂×Q₈	—	29	1	no	—
80	C₂×C₈	—	29	1	no	—
81	C₂×C₈	—	29	1	no	—
82	C₂×C₈	C₂×#1181	1	1	yes	characteristic
83	C₂×C₈	C₂×#1181	1	1	yes	characteristic
84	C₄⋊C₄	—	29	1	no	—
85	C₄⋊C₄	—	29	1	no	—
86	C₄⋊C₄	—	29	1	no	—
87	C₄²	—	29	1	no	—
88	C₄²	—	29	1	no	—
89	C₄²	C₂×#1181	1	1	yes	characteristic
90	C₁₆	—	29	2	no	—
91	C₁₆	—	58	1	no	—
92	C₁₆	—	58	1	no	—
93	C₁₆	—	58	1	no	—
94	Q₈	—	58	2	no	—
95	C₂×C₄	—	29	1	no	—
96	C₂×C₄	—	29	1	no	—
97	C₂×C₄	—	29	1	no	—
98	C₂×C₄	—	29	1	no	—
99	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
100	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
101	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	2	1	no	—
104	C₈	—	29	1	no	—
105	C₈	—	29	1	no	—
106	C₈	—	58	1	no	—
107	C₂²	C₂×D₂₉⋊C₈	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	29	2	no	—
111	C₄	—	58	1	no	—
112	C₄	—	58	1	no	—
113	C₄	—	58	1	no	—
114	C₄	#11745346	1	1	yes	characteristic
115	C₄	Q₈×#1181	1	1	yes	characteristic
116	C₂	#14272212	1	1	yes	characteristic
117	C₂	D₂₉⋊M₃₂	1	1	yes	characteristic
118	C₂	#14272222	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272084

C₂

yes

maximal, characteristic

#14272084

C₂

yes

maximal, characteristic

C₄⋊#90770

C₂

yes

maximal, characteristic

#14272052

C₂

yes

maximal, characteristic

#14272051

C₂

yes

maximal, characteristic

#14272049

C₂

yes

maximal, characteristic

#14271287

C₂

yes

maximal, characteristic

C₄×Dic₅₈

C₄

yes

characteristic

C₂×#90770

C₂²

yes

characteristic

C₂×#90770

C₂²

yes

characteristic

C₂×#90770

C₂²

yes

characteristic

C₂×#90770

C₂²

yes

characteristic

C₂₉×C₄⋊C₈

C₄

yes

characteristic

#11745162

C₄

yes

characteristic

#11745162

C₄

yes

characteristic

C₈×Dic₂₉

C₂²

yes

characteristic

C₈×Dic₂₉

C₂²

yes

characteristic

C₄×#6597

C₂²

yes

characteristic

C₂×Dic₅₈

C₈

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄⋊Dic₂₉

C₈

yes

characteristic

#90779

C₈

yes

characteristic

#90779

C₈

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

C₂³

yes

—

—

—

Q₈

yes

complemented

C₂×C₄×C₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂×C₈

yes

characteristic

C₂×Dic₂₉

C₂×C₈

yes

characteristic

C₂×Dic₂₉

C₂×C₈

yes

characteristic

C₂×Dic₂₉

C₂×C₈

yes

characteristic

Dic₅₈

—

C₈×C₂₉

—

C₈×C₂₉

—

#6597

—

#6597

C₂×Q₈

yes

yes

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄×Q₈

yes

characteristic

C₄×C₂₉

#131

yes

characteristic

Dic₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

M₃₂

yes

—

C₈×Q₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

#346

—

#346

—

C₄×C₁₆

—

C₂×C₂₉

C₈×Q₈

yes

characteristic

C₂×C₂₉

C₂×M₃₂

yes

characteristic

C₂×C₂₉

#504

yes

characteristic

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#1181

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂₉

#2183

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₂₉⋊C₈

yes

characteristic

100

C₂×C₄

D₂₉⋊C₈

yes

characteristic

101

C₂×C₄

C₂²×#1181

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

—

107

C₂²

C₂×D₂₉⋊C₈

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

#11745346

yes

characteristic

115

C₄

Q₈×#1181

yes

characteristic

116

C₂

#14272212

yes

characteristic

117

C₂

D₂₉⋊M₃₂

yes

characteristic

118

C₂

#14272222

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator, socle, prime radical	C₂²×C₂₉	C₂²×C₈
Fitting	C₂₉×C₄⋊C₈	C₄
cosocle	C₂×#6597	C₂³
hypercenter	C₄⋊C₈	#1181
hypocenter	C₂₉	#2183
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#1181

commutator, socle, prime radical

C₂²×C₂₉

C₂²×C₈

Fitting

C₂₉×C₄⋊C₈

C₄

C₂³

C₄⋊C₈

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

N	H ≅ G/N	type
33. #90770	Q₈	semidirect
78. C₂₉	#2183	semidirect

H ≅ G/N

type

33. #90770

Q₈

semidirect

78. C₂₉

#2183

semidirect

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

subgroup	index
#14272084	2
C₄⋊#90770	2
#14272052	2
#14272051	2
#14272049	2
#14271287	2
#2183	29

subgroup

index

Subgroups — #16835909

Conjugacy classes of subgroups

Complements

Maximal subgroups