Group #16820273 — subgroups

Subgroups — #16820273

Order 3712.

196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14271205	C₂	1	2	yes	maximal
2	C₂×#11745165	C₂	1	1	yes	maximal, characteristic
3	#14271118	C₂	1	1	yes	maximal, characteristic
4	#14270931	C₂	1	2	yes	maximal
5	C₂×C₂₉×#108	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	#11745288	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
10	C₂×#90777	C₂²	1	1	yes	characteristic
11	C₂₉×#108	C₄	1	4	yes	complemented
12	#11745166	—	2	2	no	—
13	#11745165	—	2	1	no	—
14	#11745165	—	2	1	no	—
15	#11745165	—	2	2	no	—
16	#11745163	—	2	1	no	—
17	C₈×Dic₂₉	—	2	1	no	—
18	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₂₉	—	2	2	no	—
20	M₁₆×C₂₉	—	2	2	no	—
21	M₁₆×C₂₉	C₂×C₄	1	4	yes	—
22	C₂×C₈×C₂₉	—	2	2	no	—
23	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
25	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₂₉	Q₈	1	2	yes	—
27	C₂²⋊Dic₂₉	—	2	1	no	—
28	C₄⋊Dic₂₉	—	2	2	no	—
29	C₄⋊Dic₂₉	—	2	2	no	—
30	C₄⋊Dic₂₉	D₄	1	2	yes	—
31	C₄×Dic₂₉	—	2	1	no	—
32	#90777	—	2	1	no	—
33	#90777	Q₈	1	2	yes	—
34	C₂×#6597	—	2	1	no	—
35	C₂³×C₂₉	#41	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
42	C₂×Dic₂₉	—	2	2	no	—
43	C₂×Dic₂₉	—	4	2	no	—
44	C₂×Dic₂₉	—	8	2	no	—
45	C₈×C₂₉	—	2	4	no	—
46	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
47	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
48	#6597	—	2	2	no	—
49	#1951	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	—	2	2	no	—
51	C₂²×C₂₉	C₄×Q₈	1	1	yes	characteristic
52	C₂²×C₂₉	#121	1	1	yes	characteristic
53	C₂²×C₂₉	#125	1	1	yes	characteristic
54	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
56	C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
57	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
58	Dic₂₉	—	4	2	no	—
59	Dic₂₉	—	8	2	no	—
60	C₂×#108	D₂₉	1	1	yes	characteristic
61	#428	—	29	2	no	—
62	C₂×#106	—	29	1	no	—
63	#405	—	29	1	no	—
64	#343	—	29	2	no	—
65	C₂×C₂₉	—	2	1	no	—
66	C₂×C₂₉	—	2	1	no	—
67	C₂×C₂₉	#389	1	1	yes	characteristic
68	C₂×C₂₉	#471	1	2	yes	—
69	C₂×M₁₆	—	29	1	no	—
70	C₂×M₁₆	C₂×D₂₉	1	2	yes	—
71	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
72	#117	—	29	1	no	—
73	C₂×C₄⋊C₄	—	29	2	no	—
74	#108	Dic₂₉	1	4	yes	complemented
75	#107	—	58	2	no	—
76	#106	—	58	2	no	—
77	#106	—	58	1	no	—
78	#106	—	58	1	no	—
79	#97	—	58	1	no	—
80	C₄×C₈	—	58	1	no	—
81	C₂₉	#1951	1	1	yes	characteristic, complemented, Sylow
82	C₂²×C₄	—	58	2	no	—
83	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
84	M₁₆	—	2	2	no	—
85	M₁₆	—	29	2	no	—
86	M₁₆	—	58	1	no	—
87	M₁₆	C₂×Dic₂₉	1	4	yes	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	58	1	no	—
90	C₂×C₈	Dic₅₈	1	2	yes	—
91	C₂×C₈	D₁₁₆	1	1	yes	characteristic
92	C₂×C₈	D₁₁₆	1	1	yes	characteristic
93	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
94	C₄⋊C₄	—	29	2	no	—
95	C₄⋊C₄	—	58	2	no	—
96	C₄⋊C₄	—	58	2	no	—
97	C₂²⋊C₄	—	58	1	no	—
98	C₄²	—	58	1	no	—
99	C₂³	#90809	1	1	yes	characteristic
100	C₂×C₄	—	58	2	no	—
101	C₂×C₄	—	116	2	no	—
102	C₂×C₄	—	232	2	no	—
103	C₂×C₄	C₂×Dic₅₈	1	1	yes	characteristic
104	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
105	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
106	C₂×C₄	#90807	1	1	yes	characteristic
107	C₂×C₄	Q₈×D₂₉	1	1	yes	characteristic
108	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
109	C₈	—	2	4	no	—
110	C₈	—	58	2	no	—
111	C₈	C₄⋊Dic₂₉	1	2	yes	—
112	C₈	C₄⋊Dic₂₉	1	2	yes	—
113	C₂²	—	2	2	no	—
114	C₂²	#11745252	1	1	yes	characteristic
115	C₂²	#11745257	1	1	yes	characteristic
116	C₂²	Q₈×Dic₂₉	1	1	yes	characteristic
117	C₄	—	116	2	no	—
118	C₄	—	232	2	no	—
119	C₄	#11745250	1	1	yes	characteristic
120	C₄	#11745259	1	1	yes	characteristic
121	C₄	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
122	C₄	D₄×Dic₂₉	1	1	yes	characteristic
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	#14271062	1	1	yes	characteristic
126	C₂	#14271427	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271205

C₂

yes

maximal

C₂×#11745165

C₂

yes

maximal, characteristic

#14271118

C₂

yes

maximal, characteristic

#14270931

C₂

yes

maximal

C₂×C₂₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

#11745288

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90777

C₂²

yes

characteristic

C₂₉×#108

C₄

yes

—

—

—

—

—

C₈×Dic₂₉

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂×C₄

yes

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

Q₈

yes

—

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

D₄

yes

—

C₄×Dic₂₉

—

#90777

—

#90777

Q₈

yes

—

C₂×#6597

—

C₂³×C₂₉

#41

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

C₈×C₂₉

C₄⋊C₄

yes

—

C₈×C₂₉

C₄⋊C₄

yes

—

#6597

—

#1951

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₄×Q₈

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₉

C₄×D₄

yes

characteristic

C₄×C₂₉

C₂²⋊Q₈

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

Dic₂₉

—

Dic₂₉

—

C₂×#108

D₂₉

yes

—

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#389

yes

characteristic

C₂×C₂₉

#471

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₂₉

yes

—

C₂²×C₈

C₂×D₂₉

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#108

Dic₂₉

yes

—

—

—

—

—

C₄×C₈

—

C₂₉

#1951

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

C₂×Dic₂₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₅₈

yes

—

C₂×C₈

D₁₁₆

yes

characteristic

C₂×C₈

D₁₁₆

yes

characteristic

C₂×C₈

C₂×Dic₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#90809

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

116

—

102

C₂×C₄

—

232

—

103

C₂×C₄

C₂×Dic₅₈

yes

characteristic

104

C₂×C₄

C₂×D₁₁₆

yes

characteristic

105

C₂×C₄

D₄×D₂₉

yes

characteristic

106

C₂×C₄

#90807

yes

characteristic

107

C₂×C₄

Q₈×D₂₉

yes

characteristic

108

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

109

C₈

—

110

C₈

—

111

C₈

C₄⋊Dic₂₉

yes

—

112

C₈

C₄⋊Dic₂₉

yes

—

113

C₂²

—

114

C₂²

#11745252

yes

characteristic

115

C₂²

#11745257

yes

characteristic

116

C₂²

Q₈×Dic₂₉

yes

characteristic

117

C₄

—

116

—

118

C₄

—

232

—

119

C₄

#11745250

yes

characteristic

120

C₄

#11745259

yes

characteristic

121

C₄

C₂×C₄⋊Dic₂₉

yes

characteristic

122

C₄

D₄×Dic₂₉

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

#14271062

yes

characteristic

126

C₂

#14271427

yes

—

	subgroup	G/H
center	C₂²	#11745257
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×#108	C₂
socle	C₂²×C₂₉	#121
prime radical	C₂³×C₂₉	#41
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×#108	D₂₉
hypocenter	C₂₉	#1951
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂²

#11745257

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×#108

C₂

C₂²×C₂₉

C₂³×C₂₉

C₂²×C₄×C₂₉

C₂³

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
11. C₂₉×#108	C₄	semidirect
74. #108	Dic₂₉	semidirect
81. C₂₉	#1951	semidirect

H ≅ G/N

type

11. C₂₉×#108

C₄

semidirect

74. #108

Dic₂₉

semidirect

81. C₂₉

#1951

semidirect

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

subgroup	index
#14271205	2
C₂×#11745165	2
#14271118	2
#14270931	2
C₂×C₂₉×#108	2
#1951	29

subgroup

index

C₂×C₂₉×#108

Subgroups — #16820273

Conjugacy classes of subgroups

Complements

Maximal subgroups