Group #11719476 — subgroups

Subgroups — #11719476

Order 832.

248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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	#88257	C₂	1	2	yes	maximal, complemented
2	C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	#88205	C₂	1	2	yes	maximal, complemented
4	Q₁₆×D₁₃	C₂	1	2	yes	maximal, complemented
5	#88169	C₂	1	4	yes	maximal, complemented
6	#88166	C₂	1	2	yes	maximal, complemented
7	C₂×Dic₅₂	C₂	1	1	yes	maximal, characteristic, complemented
8	#88155	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#41	C₂²	1	2	yes	—
10	Q₈×D₁₃	C₂²	1	4	yes	—
11	#6129	—	2	4	no	—
12	#6129	C₂²	1	4	yes	—
13	#6127	—	2	2	no	—
14	#6127	C₂²	1	1	yes	characteristic
15	C₂×Dic₂₆	—	2	2	no	—
16	C₂×Dic₂₆	C₂²	1	2	yes	—
17	C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₁₃×SD₁₆	C₂²	1	2	yes	—
19	C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	#6107	C₂²	1	4	yes	—
22	#6105	C₂²	1	4	yes	—
23	#6099	C₂²	1	1	yes	characteristic
24	Dic₅₂	C₂²	1	2	yes	—
25	Dic₅₂	C₂²	1	2	yes	—
26	#6094	C₂²	1	2	yes	—
27	C₈×D₁₃	C₂²	1	2	yes	—
28	Q₈×C₁₃	C₂³	1	2	yes	—
29	D₄×C₁₃	—	2	2	no	—
30	D₄×C₁₃	C₂³	1	2	yes	—
31	C₂×C₄×C₁₃	—	2	2	no	—
32	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
33	C₂²⋊D₁₃	—	2	4	no	—
34	C₂²⋊D₁₃	D₄	1	2	yes	—
35	C₂×Dic₁₃	—	2	2	no	—
36	C₂×Dic₁₃	—	2	4	no	—
37	D₅₂	D₄	1	1	yes	characteristic
38	C₄×D₁₃	—	2	4	no	—
39	C₄×D₁₃	C₂³	1	2	yes	—
40	Dic₂₆	—	2	2	no	—
41	Dic₂₆	—	2	4	no	—
42	Dic₂₆	D₄	1	1	yes	characteristic
43	Dic₂₆	C₂³	1	4	yes	—
44	C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₈×C₁₃	C₂³	1	1	yes	characteristic
46	#1055	C₂³	1	2	yes	—
47	#578	—	13	1	no	maximal, Sylow
48	C₂²×C₁₃	—	2	2	no	—
49	C₂²×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×D₁₃	C₂×D₄	1	2	yes	—
51	C₄×C₁₃	—	2	2	no	—
52	C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₄×C₁₃	C₂⁴	1	1	yes	characteristic
54	Dic₁₃	—	2	4	no	—
55	Dic₁₃	C₂×D₄	1	2	yes	—
56	2₋¹⁺⁴	—	13	2	no	—
57	#137	—	13	2	no	—
58	#137	—	13	4	no	—
59	#135	—	13	2	no	—
60	#135	D₁₃	1	1	yes	characteristic, complemented
61	C₂×Q₁₆	—	13	2	no	—
62	C₂×Q₁₆	—	13	1	no	—
63	#131	—	13	1	no	—
64	C₂×C₁₃	—	2	1	no	—
65	C₂×C₁₃	—	4	2	no	—
66	C₂×C₁₃	C₂²×D₄	1	1	yes	characteristic
67	D₁₃	—	2	2	no	—
68	#41	—	13	1	no	—
69	#41	—	13	4	no	—
70	#41	—	26	2	no	—
71	#41	—	26	4	no	—
72	#41	C₂×D₁₃	1	2	yes	—
73	C₂×Q₈	—	13	4	no	—
74	C₂×Q₈	—	13	2	no	—
75	C₂×Q₈	—	26	2	no	—
76	Q₁₆	—	13	4	no	—
77	Q₁₆	—	13	2	no	—
78	Q₁₆	—	13	2	no	—
79	Q₁₆	C₂×D₁₃	1	1	yes	characteristic
80	SD₁₆	—	13	4	no	—
81	SD₁₆	C₂×D₁₃	1	2	yes	—
82	D₈	C₂×D₁₃	1	1	yes	characteristic
83	M₁₆	—	13	1	no	—
84	M₁₆	—	13	2	no	—
85	C₂×C₈	—	13	2	no	—
86	C₂×C₈	C₂×D₁₃	1	1	yes	characteristic
87	C₁₃	#578	1	1	yes	characteristic, complemented, Sylow
88	Q₈	—	13	1	no	—
89	Q₈	—	13	4	no	—
90	Q₈	—	26	4	no	—
91	Q₈	—	26	2	no	—
92	Q₈	C₂²×D₁₃	1	2	yes	—
93	D₄	—	2	2	no	—
94	D₄	—	13	2	no	—
95	D₄	—	13	1	no	—
96	D₄	—	26	4	no	—
97	D₄	C₂²×D₁₃	1	2	yes	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	13	2	no	—
100	C₂×C₄	—	26	4	no	—
101	C₂×C₄	—	26	4	no	—
102	C₂×C₄	—	26	2	no	—
103	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
104	C₈	—	13	2	no	—
105	C₈	C₂²×D₁₃	1	1	yes	characteristic
106	C₈	C₂²×D₁₃	1	1	yes	characteristic
107	C₂²	—	2	2	no	—
108	C₂²	—	13	2	no	—
109	C₂²	D₄×D₁₃	1	1	yes	characteristic
110	C₄	—	2	2	no	—
111	C₄	—	13	2	no	—
112	C₄	—	26	4	no	—
113	C₄	D₄×D₁₃	1	1	yes	characteristic
114	C₄	C₂³×D₁₃	1	1	yes	characteristic
115	C₂	—	2	1	no	—
116	C₂	—	4	2	no	—
117	C₂	—	26	2	no	—
118	C₂	C₂×D₄×D₁₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#88257

C₂

yes

maximal, complemented

C₁₃×#135

C₂

yes

maximal, characteristic, complemented

#88205

C₂

yes

maximal, complemented

Q₁₆×D₁₃

C₂

yes

maximal, complemented

#88169

C₂

yes

maximal, complemented

#88166

C₂

yes

maximal, complemented

C₂×Dic₅₂

C₂

yes

maximal, characteristic, complemented

#88155

C₂

yes

maximal, characteristic, complemented

C₁₃×#41

C₂²

yes

—

Q₈×D₁₃

C₂²

yes

—

#6129

—

#6129

C₂²

yes

—

#6127

—

#6127

C₂²

yes

characteristic

C₂×Dic₂₆

—

C₂×Dic₂₆

C₂²

yes

—

C₁₃×Q₁₆

C₂²

yes

characteristic

C₁₃×SD₁₆

C₂²

yes

—

C₁₃×D₈

C₂²

yes

characteristic

C₂×C₈×C₁₃

C₂²

yes

characteristic

#6107

C₂²

yes

—

#6105

C₂²

yes

—

#6099

C₂²

yes

characteristic

Dic₅₂

C₂²

yes

—

Dic₅₂

C₂²

yes

—

#6094

C₂²

yes

—

C₈×D₁₃

C₂²

yes

—

Q₈×C₁₃

C₂³

yes

—

D₄×C₁₃

—

D₄×C₁₃

C₂³

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂³

yes

characteristic

C₂²⋊D₁₃

—

C₂²⋊D₁₃

D₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

D₅₂

D₄

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

C₂³

yes

—

Dic₂₆

—

Dic₂₆

—

Dic₂₆

D₄

yes

characteristic

Dic₂₆

C₂³

yes

—

C₈×C₁₃

C₂³

yes

characteristic

C₈×C₁₃

C₂³

yes

characteristic

#1055

C₂³

yes

—

#578

—

maximal, Sylow

C₂²×C₁₃

—

C₂²×C₁₃

C₂×D₄

yes

characteristic

C₂×D₁₃

C₂×D₄

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×D₄

yes

characteristic

C₄×C₁₃

C₂⁴

yes

characteristic

Dic₁₃

—

Dic₁₃

C₂×D₄

yes

—

2₋¹⁺⁴

—

—

—

—

D₁₃

yes

characteristic, complemented

C₂×Q₁₆

—

C₂×Q₁₆

—

#131

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

C₂²×D₄

yes

characteristic

D₁₃

—

—

—

—

—

C₂×D₁₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

C₂×D₁₃

yes

characteristic

SD₁₆

—

SD₁₆

C₂×D₁₃

yes

—

D₈

C₂×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂×D₁₃

yes

characteristic

C₁₃

#578

yes

characteristic, complemented, Sylow

Q₈

—

Q₈

—

Q₈

—

Q₈

—

Q₈

C₂²×D₁₃

yes

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

C₂²×D₁₃

yes

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₂²×D₁₃

yes

characteristic

104

C₈

—

105

C₈

C₂²×D₁₃

yes

characteristic

106

C₈

C₂²×D₁₃

yes

characteristic

107

C₂²

—

108

C₂²

—

109

C₂²

D₄×D₁₃

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

D₄×D₁₃

yes

characteristic

114

C₄

C₂³×D₁₃

yes

characteristic

115

C₂

—

116

C₂

—

117

C₂

—

118

C₂

C₂×D₄×D₁₃

yes

characteristic

	subgroup	G/H
center	C₂	C₂×D₄×D₁₃
commutator, cosocle	C₄×C₁₃	C₂⁴
Frattini	C₄	C₂³×D₁₃
Fitting	C₁₃×#135	C₂
socle	C₂×C₁₃	C₂²×D₄
hypercenter	#135	D₁₃
hypocenter	C₁₃	#578
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #135

subgroup

G/H

center

C₂

C₂×D₄×D₁₃

commutator, cosocle

C₄×C₁₃

C₂⁴

Frattini

C₄

C₂³×D₁₃

Fitting

C₁₃×#135

C₂

socle

C₂×C₁₃

C₂²×D₄

D₁₃

C₁₃

G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #135

N	H ≅ G/N	type
1. #88257	C₂	semidirect
2. C₁₃×#135	C₂	semidirect
3. #88205	C₂	semidirect
4. Q₁₆×D₁₃	C₂	semidirect
5. #88169	C₂	semidirect
6. #88166	C₂	semidirect
7. C₂×Dic₅₂	C₂	semidirect
8. #88155	C₂	semidirect
60. #135	D₁₃	semidirect
87. C₁₃	#578	semidirect

H ≅ G/N

type

1. #88257

C₂

semidirect

2. C₁₃×#135

C₂

semidirect

3. #88205

C₂

semidirect

4. Q₁₆×D₁₃

C₂

semidirect

5. #88169

C₂

semidirect

6. #88166

C₂

semidirect

7. C₂×Dic₅₂

C₂

semidirect

8. #88155

C₂

semidirect

60. #135

D₁₃

semidirect

87. C₁₃

#578

semidirect

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

subgroup	index
#88257	2
C₁₃×#135	2
#88205	2
Q₁₆×D₁₃	2
#88169	2
#88166	2
C₂×Dic₅₂	2
#88155	2
#578	13

subgroup

index

C₁₃×#135

Q₁₆×D₁₃

C₂×Dic₅₂

Subgroups — #11719476

Conjugacy classes of subgroups

Complements

Maximal subgroups