Group #16818849 — subgroups

Subgroups — #16818849

Order 3712.

188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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	#14271360	C₂	1	2	yes	maximal, complemented
2	C₈×Dic₅₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#14270916	C₂	1	1	yes	maximal, characteristic, complemented
4	#14270907	C₂	1	2	yes	maximal, complemented
5	C₂₉×#493	C₂	1	1	yes	maximal, characteristic
6	C₂×D₈×C₂₉	—	2	1	no	—
7	C₂×D₈×C₂₉	—	2	1	no	—
8	C₂₉×#127	C₂²	1	2	yes	—
9	C₂×#90783	—	2	2	no	—
10	C₄×Dic₅₈	C₂²	1	1	yes	characteristic
11	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#11745180	—	2	2	no	—
13	#11745162	—	2	1	no	—
14	C₈×Dic₂₉	—	2	1	no	—
15	C₄⋊#6597	C₂²	1	1	yes	characteristic
16	C₄⋊#6597	C₂²	1	2	yes	—
17	C₂×D₄×C₂₉	—	2	2	no	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×D₄×C₂₉	—	2	2	no	—
20	C₂×Dic₅₈	D₄	1	1	yes	characteristic
21	D₈×C₂₉	—	4	2	no	—
22	D₈×C₂₉	—	4	2	no	—
23	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
25	C₄²×C₂₉	C₂³	1	1	yes	characteristic
26	#90783	—	4	4	no	—
27	C₄⋊Dic₂₉	D₄	1	1	yes	characteristic
28	#90779	—	2	1	no	—
29	C₄×Dic₂₉	—	2	1	no	—
30	C₂×#6597	—	2	2	no	—
31	C₂×#6597	—	2	1	no	—
32	C₂³×C₂₉	—	4	2	no	—
33	D₄×C₂₉	—	4	2	no	—
34	D₄×C₂₉	—	4	2	no	—
35	D₄×C₂₉	—	4	2	no	—
36	D₄×C₂₉	—	4	2	no	—
37	D₄×C₂₉	—	8	2	no	—
38	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₂₉	#41	1	1	yes	characteristic
41	C₂×Dic₂₉	—	2	1	no	—
42	C₂×Dic₂₉	—	2	1	no	—
43	Dic₅₈	—	2	1	no	—
44	Dic₅₈	D₈	1	2	yes	complemented
45	C₈×C₂₉	—	2	1	no	—
46	C₈×C₂₉	SD₁₆	1	2	yes	complemented
47	#6597	—	4	2	no	—
48	#6597	—	4	1	no	—
49	#1668	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	—	8	2	no	—
51	C₂²×C₂₉	—	8	2	no	—
52	C₂²×C₂₉	—	8	2	no	—
53	C₂²×C₂₉	#121	1	1	yes	characteristic
54	C₄×C₂₉	—	2	1	no	—
55	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
56	C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
57	C₄×C₂₉	#135	1	1	yes	characteristic
58	C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
59	Dic₂₉	—	2	2	no	—
60	Dic₂₉	—	4	1	no	—
61	#493	D₂₉	1	1	yes	characteristic
62	#460	—	29	2	no	—
63	C₈×Q₈	—	29	1	no	—
64	#335	—	29	1	no	—
65	#331	—	29	2	no	—
66	C₂×C₂₉	—	16	2	no	—
67	C₂×C₂₉	#460	1	1	yes	characteristic
68	C₂×C₂₉	#466	1	1	yes	characteristic
69	C₂×C₂₉	#472	1	1	yes	characteristic
70	C₂×SD₁₆	—	58	2	no	—
71	C₂×D₈	—	2	1	no	—
72	C₂×D₈	—	2	1	no	—
73	#127	C₂×D₂₉	1	2	yes	—
74	C₄×Q₈	—	29	1	no	—
75	C₄⋊C₈	—	29	1	no	—
76	C₄⋊C₈	—	29	2	no	—
77	C₄⋊C₈	—	58	1	no	—
78	#102	—	58	2	no	—
79	C₄×C₈	—	58	1	no	—
80	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
81	C₂₉	#1668	1	1	yes	characteristic, complemented, Sylow
82	C₂×Q₈	—	29	1	no	—
83	C₂×D₄	—	2	2	no	—
84	C₂×D₄	—	2	2	no	—
85	C₂×D₄	—	2	2	no	—
86	SD₁₆	—	116	4	no	—
87	D₈	—	4	2	no	—
88	D₈	—	4	2	no	—
89	C₂×C₈	—	58	2	no	—
90	C₂×C₈	—	58	1	no	—
91	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
92	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
93	C₄⋊C₄	—	29	1	no	—
94	C₄⋊C₄	—	58	1	no	—
95	C₄²	—	58	1	no	—
96	C₄²	C₂²×D₂₉	1	1	yes	characteristic
97	C₂³	—	4	2	no	—
98	Q₈	—	29	2	no	—
99	Q₈	—	58	1	no	—
100	D₄	—	4	2	no	—
101	D₄	—	4	2	no	—
102	D₄	—	4	2	no	—
103	D₄	—	4	2	no	—
104	D₄	—	8	2	no	—
105	C₂×C₄	—	58	1	no	—
106	C₂×C₄	—	58	1	no	—
107	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
108	C₂×C₄	#90807	1	1	yes	characteristic
109	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
110	C₈	—	2	1	no	—
111	C₈	—	116	1	no	—
112	C₈	—	116	2	no	—
113	C₈	#90783	1	2	yes	complemented
114	C₂²	—	8	2	no	—
115	C₂²	—	8	2	no	—
116	C₂²	—	8	2	no	—
117	C₂²	#11745300	1	1	yes	characteristic
118	C₄	—	2	1	no	—
119	C₄	—	58	2	no	—
120	C₄	—	116	1	no	—
121	C₄	D₈×D₂₉	1	1	yes	characteristic
122	C₄	#11745274	1	1	yes	characteristic
123	C₄	#11745294	1	1	yes	characteristic
124	C₄	C₂×#90783	1	1	yes	characteristic
125	C₂	—	16	2	no	—
126	C₂	#14271360	1	1	yes	characteristic
127	C₂	#14271396	1	1	yes	characteristic
128	C₂	#14271430	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14271360

C₂

yes

maximal, complemented

C₈×Dic₅₈

C₂

yes

maximal, characteristic, complemented

#14270916

C₂

yes

maximal, characteristic, complemented

#14270907

C₂

yes

maximal, complemented

C₂₉×#493

C₂

yes

maximal, characteristic

C₂×D₈×C₂₉

—

C₂×D₈×C₂₉

—

C₂₉×#127

C₂²

yes

—

C₂×#90783

—

C₄×Dic₅₈

C₂²

yes

characteristic

C₄×C₈×C₂₉

C₂²

yes

characteristic

#11745180

—

#11745162

—

C₈×Dic₂₉

—

C₄⋊#6597

C₂²

yes

characteristic

C₄⋊#6597

C₂²

yes

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×Dic₅₈

D₄

yes

characteristic

D₈×C₂₉

—

D₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

characteristic

C₂×C₈×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

C₂³

yes

characteristic

#90783

—

C₄⋊Dic₂₉

D₄

yes

characteristic

#90779

—

C₄×Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

Dic₅₈

—

Dic₅₈

D₈

yes

complemented

C₈×C₂₉

—

C₈×C₂₉

SD₁₆

yes

—

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#121

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

C₂×D₈

yes

characteristic

C₄×C₂₉

C₂×SD₁₆

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

#493

D₂₉

yes

characteristic

#460

—

C₈×Q₈

—

#335

—

#331

—

C₂×C₂₉

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

#127

C₂×D₂₉

yes

—

C₄×Q₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#102

—

C₄×C₈

—

C₄×C₈

C₂×D₂₉

yes

characteristic

C₂₉

#1668

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

116

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₂₉

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

100

D₄

—

101

D₄

—

102

D₄

—

103

D₄

—

104

D₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

D₄×D₂₉

yes

characteristic

108

C₂×C₄

#90807

yes

characteristic

109

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

110

C₈

—

111

C₈

—

116

—

112

C₈

—

116

—

113

C₈

#90783

yes

complemented

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

#11745300

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

116

—

121

C₄

D₈×D₂₉

yes

characteristic

122

C₄

#11745274

yes

characteristic

123

C₄

#11745294

yes

characteristic

124

C₄

C₂×#90783

yes

characteristic

125

C₂

—

126

C₂

#14271360

yes

characteristic

127

C₂

#14271396

yes

characteristic

128

C₂

#14271430

yes

characteristic

	subgroup	G/H
center	C₂²	#11745300
commutator, cosocle	C₄²×C₂₉	C₂³
Frattini	C₄²	C₂²×D₂₉
Fitting, prime radical	C₂₉×#493	C₂
socle	C₂²×C₂₉	#121
hypercenter	#493	D₂₉
hypocenter	C₂₉	#1668
LCS	G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#11745300

commutator, cosocle

C₄²×C₂₉

C₂³

Frattini

C₄²

C₂²×D₂₉

Fitting, prime radical

C₂₉×#493

C₂

C₂²×C₂₉

D₂₉

C₂₉

G ▷ C₄²×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. #14271360	C₂	semidirect
2. C₈×Dic₅₈	C₂	semidirect
3. #14270916	C₂	semidirect
4. #14270907	C₂	semidirect
44. Dic₅₈	D₈	semidirect
46. C₈×C₂₉	SD₁₆	semidirect
81. C₂₉	#1668	semidirect
113. C₈	#90783	semidirect

H ≅ G/N

type

1. #14271360

C₂

semidirect

2. C₈×Dic₅₈

C₂

semidirect

3. #14270916

C₂

semidirect

4. #14270907

C₂

semidirect

44. Dic₅₈

D₈

semidirect

46. C₈×C₂₉

SD₁₆

semidirect

81. C₂₉

#1668

semidirect

113. C₈

#90783

semidirect

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

subgroup	index
#14271360	2
C₈×Dic₅₈	2
#14270916	2
#14270907	2
C₂₉×#493	2
#1668	29

subgroup

index

C₈×Dic₅₈

C₂₉×#493

Subgroups — #16818849

Conjugacy classes of subgroups

Complements

Maximal subgroups