Group #15771897 — subgroups

Subgroups — #15771897

Order 3328.

354 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 199 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	C₄×#88038	C₂	1	2	yes	maximal
2	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#13112753	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×#1055	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1311	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88038	C₄	1	4	yes	—
7	C₄×C₈×D₁₃	C₄	1	2	yes	—
8	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
10	C₈²×C₁₃	C₂²	1	1	yes	characteristic
11	#11718094	C₄	1	4	yes	—
12	C₄×#6090	C₂²	1	2	yes	—
13	C₈×#1055	C₄	1	2	yes	—
14	C₈×#1055	C₂²	1	1	yes	characteristic
15	C₂×C₈×D₁₃	C₈	1	4	yes	—
16	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
17	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
19	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₈×Dic₁₃	C₈	1	4	yes	—
22	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
23	C₂×#6090	C₂×C₄	1	4	yes	—
24	C₄×#1055	C₂×C₄	1	1	yes	characteristic
25	C₄×#1055	C₂×C₄	1	2	yes	—
26	#88038	C₈	1	16	yes	complemented
27	C₈×M₃₂	—	13	1	no	maximal, Sylow
28	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
29	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
30	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
31	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
32	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
34	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
35	C₂×#1055	C₄²	1	2	yes	—
36	C₂×#1055	C₂×C₈	1	4	yes	—
37	C₈×D₁₃	—	2	8	no	—
38	C₈×D₁₃	C₂×C₈	1	8	yes	—
39	C₁₃×C₁₆	C₂×C₈	1	8	yes	complemented
40	#6090	C₂×C₈	1	8	yes	complemented
41	C₄×M₃₂	—	13	2	no	—
42	C₂×C₈²	—	13	1	no	—
43	#1311	—	13	1	no	—
44	#1311	D₁₃	1	1	yes	characteristic, complemented
45	C₈×C₁₆	—	13	2	no	—
46	C₂²×D₁₃	C₄×C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
48	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
49	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
50	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
51	C₄×D₁₃	—	2	4	no	—
52	C₄×D₁₃	C₄×C₈	1	4	yes	—
53	C₈×C₁₃	—	2	4	no	—
54	C₈×C₁₃	C₂²×C₈	1	4	yes	—
55	#1055	C₄×C₈	1	4	yes	—
56	#1055	M₃₂	1	8	yes	complemented
57	C₂×M₃₂	—	13	4	no	—
58	C₂×C₄×C₈	—	13	2	no	—
59	C₂×C₄×C₈	—	13	1	no	—
60	#346	—	13	4	no	—
61	C₄×C₁₆	—	13	2	no	—
62	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
63	C₈²	—	13	2	no	—
64	C₈²	—	13	1	no	—
65	C₈²	C₂×D₁₃	1	1	yes	characteristic
66	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
67	C₂×D₁₃	—	2	2	no	—
68	C₂×D₁₃	C₈²	1	2	yes	—
69	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
70	C₄×C₁₃	C₂×M₃₂	1	4	yes	—
71	Dic₁₃	—	2	2	no	—
72	Dic₁₃	C₈²	1	2	yes	—
73	C₂²×C₈	—	13	2	no	—
74	C₂²×C₈	—	13	4	no	—
75	C₂×C₄²	—	13	1	no	—
76	M₃₂	—	13	16	no	—
77	C₂×C₁₆	—	13	4	no	—
78	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
79	C₄×C₈	—	13	4	no	—
80	C₄×C₈	—	13	2	no	—
81	C₄×C₈	—	13	1	no	—
82	C₄×C₈	—	13	2	no	—
83	C₄×C₈	C₄×D₁₃	1	2	yes	—
84	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
85	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
86	C₂×C₁₃	C₄×M₃₂	1	2	yes	—
87	D₁₃	—	2	2	no	—
88	C₂²×C₄	—	13	1	no	—
89	C₂²×C₄	—	13	2	no	—
90	C₂×C₈	—	13	2	no	—
91	C₂×C₈	—	13	4	no	—
92	C₂×C₈	—	13	8	no	—
93	C₂×C₈	—	26	8	no	—
94	C₂×C₈	C₈×D₁₃	1	4	yes	—
95	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
96	C₄²	—	13	1	no	—
97	C₄²	—	13	2	no	—
98	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
99	C₁₆	—	13	8	no	—
100	C₁₆	C₈×D₁₃	1	8	yes	complemented
101	C₁₃	C₈×M₃₂	1	1	yes	characteristic, complemented, Sylow
102	C₂³	—	13	1	no	—
103	C₂×C₄	—	13	1	no	—
104	C₂×C₄	—	13	4	no	—
105	C₂×C₄	—	13	2	no	—
106	C₂×C₄	—	26	4	no	—
107	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
108	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
109	C₈	—	2	4	no	—
110	C₈	—	13	8	no	—
111	C₈	—	13	4	no	—
112	C₈	C₂×C₈×D₁₃	1	4	yes	—
113	C₂²	—	13	2	no	—
114	C₂²	—	26	2	no	—
115	C₂²	C₄×C₈×D₁₃	1	1	yes	characteristic
116	C₄	—	13	2	no	—
117	C₄	—	26	2	no	—
118	C₄	C₄×C₈×D₁₃	1	2	yes	—
119	C₄	D₁₃×M₃₂	1	4	yes	—
120	C₂	—	26	2	no	—
121	C₂	C₈²×D₁₃	1	1	yes	characteristic
122	C₂	#13116429	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#88038

C₂

yes

maximal

C₈²×D₁₃

C₂

yes

maximal, characteristic

#13112753

C₂

yes

maximal, characteristic, complemented

C₁₆×#1055

C₂

yes

maximal, complemented

C₁₃×#1311

C₂

yes

maximal, characteristic, complemented

C₂×#88038

C₄

yes

—

C₄×C₈×D₁₃

C₄

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

C₄×C₁₃×C₁₆

C₂²

yes

—

C₈²×C₁₃

C₂²

yes

characteristic

#11718094

C₄

yes

—

C₄×#6090

C₂²

yes

—

C₈×#1055

C₄

yes

—

C₈×#1055

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₈

yes

—

C₂×C₈×D₁₃

C₂×C₄

yes

—

C₄²×D₁₃

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂³

yes

characteristic

C₈×Dic₁₃

C₈

yes

—

C₈×Dic₁₃

C₂×C₄

yes

—

C₂×#6090

C₂×C₄

yes

—

C₄×#1055

C₂×C₄

yes

characteristic

C₄×#1055

C₂×C₄

yes

—

#88038

C₈

yes

complemented

C₈×M₃₂

—

maximal, Sylow

C₂×C₄×D₁₃

C₄²

yes

characteristic

C₂×C₄×D₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₄²

yes

characteristic

C₄×Dic₁₃

C₂×C₈

yes

—

C₂×#1055

C₄²

yes

—

C₂×#1055

C₂×C₈

yes

—

C₈×D₁₃

—

C₈×D₁₃

C₂×C₈

yes

—

C₁₃×C₁₆

C₂×C₈

yes

complemented

#6090

C₂×C₈

yes

complemented

C₄×M₃₂

—

C₂×C₈²

—

#1311

—

#1311

D₁₃

yes

characteristic, complemented

C₈×C₁₆

—

C₂²×D₁₃

C₄×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₂×Dic₁₃

C₄×C₈

yes

—

C₂×Dic₁₃

C₄×C₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

C₄×C₈

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₂²×C₈

yes

—

#1055

C₄×C₈

yes

—

#1055

M₃₂

yes

complemented

C₂×M₃₂

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₁₃

yes

—

C₈²

—

C₈²

—

C₈²

C₂×D₁₃

yes

characteristic

C₂²×C₁₃

C₂×C₄×C₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₈²

yes

—

C₄×C₁₃

C₂×C₄×C₈

yes

—

C₄×C₁₃

C₂×M₃₂

yes

—

Dic₁₃

—

Dic₁₃

C₈²

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₄×D₁₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₃

yes

—

C₄×C₈

C₂²×D₁₃

yes

characteristic

C₂×C₁₃

C₂×C₈²

yes

characteristic

C₂×C₁₃

C₄×M₃₂

yes

—

D₁₃

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₈×D₁₃

yes

—

C₂×C₈

C₂×C₄×D₁₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂×C₄×D₁₃

yes

characteristic

C₁₆

—

100

C₁₆

C₈×D₁₃

yes

complemented

101

C₁₃

C₈×M₃₂

yes

characteristic, complemented, Sylow

102

C₂³

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₄²×D₁₃

yes

characteristic

108

C₂×C₄

C₂×C₈×D₁₃

yes

—

109

C₈

—

110

C₈

—

111

C₈

—

112

C₈

C₂×C₈×D₁₃

yes

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₄×C₈×D₁₃

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

C₄×C₈×D₁₃

yes

—

119

C₄

D₁₃×M₃₂

yes

—

120

C₂

—

121

C₂

C₈²×D₁₃

yes

characteristic

122

C₂

#13116429

yes

—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₁₃
commutator	C₂×C₁₃	C₂×C₈²
Fitting	C₁₃×#1311	C₂
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	#1311	D₁₃
hypocenter	C₁₃	C₈×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ #1311

subgroup

G/H

center, Frattini

C₄×C₈

C₂²×D₁₃

commutator

C₂×C₁₃

C₂×C₈²

Fitting

C₁₃×#1311

C₂

socle

C₂²×C₁₃

C₂×C₄×C₈

prime radical

C₂²×D₁₃

C₄×C₈

cosocle

C₄×C₈×C₁₃

C₂³

hypercenter

#1311

D₁₃

hypocenter

C₁₃

C₈×M₃₂

LCS

G ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄×C₈ ◁ #1311

N	H ≅ G/N	type
3. #13112753	C₂	semidirect
4. C₁₆×#1055	C₂	semidirect
5. C₁₃×#1311	C₂	semidirect
26. #88038	C₈	semidirect
39. C₁₃×C₁₆	C₂×C₈	semidirect
40. #6090	C₂×C₈	semidirect
44. #1311	D₁₃	semidirect
56. #1055	M₃₂	semidirect
100. C₁₆	C₈×D₁₃	semidirect
101. C₁₃	C₈×M₃₂	semidirect

H ≅ G/N

type

3. #13112753

C₂

semidirect

4. C₁₆×#1055

C₂

semidirect

5. C₁₃×#1311

C₂

semidirect

26. #88038

C₈

semidirect

39. C₁₃×C₁₆

C₂×C₈

semidirect

40. #6090

C₂×C₈

semidirect

44. #1311

D₁₃

semidirect

56. #1055

M₃₂

semidirect

100. C₁₆

C₈×D₁₃

semidirect

101. C₁₃

C₈×M₃₂

semidirect

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

subgroup	index
C₄×#88038	2
C₈²×D₁₃	2
#13112753	2
C₁₆×#1055	2
C₁₃×#1311	2
C₈×M₃₂	13

subgroup

index

C₄×#88038

C₈²×D₁₃

#13112753

C₁₆×#1055

C₁₃×#1311

C₈×M₃₂

Subgroups — #15771897

Conjugacy classes of subgroups

Complements

Maximal subgroups