Group #14544440 — subgroups

Subgroups — #14544440

Order 2176.

328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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	#11763768	C₂	1	1	yes	maximal, characteristic
2	C₂×#10587532	C₂	1	2	yes	maximal
3	C₂×C₈×#595	C₂	1	2	yes	maximal
4	#11763745	C₂	1	1	yes	maximal, characteristic
5	C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×#595	C₂²	1	2	yes	—
7	C₂×#63242	C₂²	1	2	yes	—
8	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
10	C₄²×D₁₇	C₂²	1	1	yes	characteristic
11	(C₂×#595)⋊C₄	C₄	1	4	yes	—
12	#10587542	C₄	1	4	yes	complemented
13	#10587532	C₄	1	8	yes	complemented
14	C₈×#595	C₄	1	8	yes	complemented
15	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic, complemented
16	C₈×Dic₁₇	C₄	1	1	yes	characteristic, complemented
17	C₈×Dic₁₇	C₄	1	1	yes	characteristic, complemented
18	C₄×#3622	C₄	1	1	yes	characteristic, complemented
19	C₂²×#595	C₂×C₄	1	4	yes	—
20	C₂×C₄×D₁₇	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
22	C₂×#3624	C₂×C₄	1	4	yes	—
23	C₄×#595	C₂×C₄	1	4	yes	—
24	C₄×#595	C₂×C₄	1	4	yes	—
25	#63242	C₂×C₄	1	4	yes	—
26	#63242	C₂×C₄	1	4	yes	—
27	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
32	C₂×#3622	C₂×C₄	1	1	yes	characteristic
33	C₂×#3622	C₂×C₄	1	1	yes	characteristic
34	C₈×D₁₇	C₂×C₄	1	4	yes	—
35	C₈×D₁₇	C₂×C₄	1	4	yes	—
36	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×#595	—	2	8	no	—
38	C₂×#595	C₄²	1	8	yes	—
39	C₂×C₄×C₁₇	C₄²	1	2	yes	—
40	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₁₇	C₄²	1	2	yes	—
42	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
43	C₄×D₁₇	—	2	4	no	—
44	C₄×D₁₇	C₂²×C₄	1	2	yes	—
45	C₄×D₁₇	C₂²×C₄	1	2	yes	—
46	#3624	C₄²	1	8	yes	—
47	C₈×C₁₇	C₄²	1	2	yes	—
48	C₈×C₁₇	C₄²	1	2	yes	—
49	#3622	C₄²	1	2	yes	—
50	#3622	C₄²	1	2	yes	—
51	#1726	—	17	1	no	maximal, Sylow
52	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
53	C₂×D₁₇	C₂×C₄²	1	2	yes	—
54	C₂×D₁₇	#131	1	4	yes	—
55	#595	—	2	8	no	—
56	C₄×C₁₇	—	2	2	no	—
57	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
58	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
59	Dic₁₇	—	2	2	no	—
60	Dic₁₇	C₂×C₄²	1	2	yes	—
61	C₂×#97	—	17	2	no	—
62	C₂×#97	—	17	1	no	—
63	C₂×C₄×C₈	—	17	2	no	—
64	C₂×C₄×C₈	—	17	1	no	—
65	#376	—	17	1	no	—
66	C₂×C₁₇	C₄³	1	1	yes	characteristic
67	C₂×C₁₇	#405	1	2	yes	—
68	D₁₇	#405	1	4	yes	—
69	C₂²×C₈	—	17	2	no	—
70	C₂²×C₈	—	17	1	no	—
71	C₂²×C₈	—	17	1	no	—
72	C₂×C₄²	—	17	2	no	—
73	C₂×C₄²	—	17	1	no	—
74	#97	—	17	8	no	—
75	#97	—	17	4	no	—
76	C₄×C₈	—	17	8	no	—
77	C₄×C₈	—	17	1	no	—
78	C₄×C₈	—	17	1	no	—
79	C₄×C₈	—	17	1	no	—
80	C₄×C₈	#595	1	1	yes	characteristic, complemented
81	#95	—	17	4	no	—
82	C₁₇	#1726	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₄	—	17	1	no	—
84	C₂²×C₄	—	17	4	no	—
85	C₂²×C₄	—	17	2	no	—
86	C₂×C₈	—	17	4	no	—
87	C₂×C₈	—	17	4	no	—
88	C₂×C₈	—	17	4	no	—
89	C₂×C₈	—	17	1	no	—
90	C₂×C₈	—	17	1	no	—
91	C₂×C₈	—	17	4	no	—
92	C₂×C₈	—	17	4	no	—
93	C₂×C₈	C₂×#595	1	1	yes	characteristic
94	C₂×C₈	C₂×#595	1	1	yes	characteristic
95	C₄²	—	17	4	no	—
96	C₄²	—	17	4	no	—
97	C₄²	—	17	2	no	—
98	C₄²	—	17	1	no	—
99	C₄²	C₂×#595	1	1	yes	characteristic
100	C₂³	—	17	1	no	—
101	C₂×C₄	—	17	1	no	—
102	C₂×C₄	—	17	2	no	—
103	C₂×C₄	—	17	2	no	—
104	C₂×C₄	—	17	8	no	—
105	C₂×C₄	—	17	2	no	—
106	C₂×C₄	—	34	4	no	—
107	C₂×C₄	—	34	8	no	—
108	C₂×C₄	C₄×#595	1	2	yes	—
109	C₂×C₄	C₂²×#595	1	1	yes	characteristic
110	C₈	—	17	8	no	—
111	C₈	—	17	2	no	—
112	C₈	—	17	2	no	—
113	C₈	C₄×#595	1	2	yes	—
114	C₈	C₄×#595	1	2	yes	—
115	C₂²	—	17	2	no	—
116	C₂²	—	17	4	no	—
117	C₂²	C₂×C₄×#595	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	17	2	no	—
120	C₄	—	34	8	no	—
121	C₄	—	34	2	no	—
122	C₄	C₂×C₄×#595	1	1	yes	characteristic
123	C₄	C₂×C₄×#595	1	1	yes	characteristic
124	C₂	—	17	4	no	—
125	C₂	C₄²×#595	1	1	yes	characteristic
126	C₂	#11763772	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11763768

C₂

yes

maximal, characteristic

C₂×#10587532

C₂

yes

maximal

C₂×C₈×#595

C₂

yes

maximal

#11763745

C₂

yes

maximal, characteristic

C₄×C₈×D₁₇

C₂

yes

maximal, characteristic

C₂×C₄×#595

C₂²

yes

—

C₂×#63242

C₂²

yes

—

C₂×C₈×D₁₇

C₂²

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

C₄²×D₁₇

C₂²

yes

characteristic

(C₂×#595)⋊C₄

C₄

yes

—

#10587542

C₄

yes

complemented

#10587532

C₄

yes

complemented

C₈×#595

C₄

yes

complemented

C₄×C₈×C₁₇

C₄

yes

characteristic, complemented

C₈×Dic₁₇

C₄

yes

characteristic, complemented

C₈×Dic₁₇

C₄

yes

characteristic, complemented

C₄×#3622

C₄

yes

characteristic, complemented

C₂²×#595

C₂×C₄

yes

—

C₂×C₄×D₁₇

C₂×C₄

yes

—

C₂×C₄×D₁₇

C₂³

yes

characteristic

C₂×#3624

C₂×C₄

yes

—

C₄×#595

C₂×C₄

yes

—

C₄×#595

C₂×C₄

yes

—

#63242

C₂×C₄

yes

—

#63242

C₂×C₄

yes

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

—

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

—

C₈×D₁₇

C₂×C₄

yes

—

C₂²×D₁₇

C₂²×C₄

yes

characteristic

C₂×#595

—

C₂×#595

C₄²

yes

—

C₂×C₄×C₁₇

C₄²

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₄²

yes

—

C₂×Dic₁₇

C₂²×C₄

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

C₂²×C₄

yes

—

C₄×D₁₇

C₂²×C₄

yes

—

#3624

C₄²

yes

—

C₈×C₁₇

C₄²

yes

—

C₈×C₁₇

C₄²

yes

—

#3622

C₄²

yes

—

#3622

C₄²

yes

—

#1726

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄²

yes

characteristic

C₂×D₁₇

C₂×C₄²

yes

—

C₂×D₁₇

#131

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄²

yes

characteristic

C₄×C₁₇

C₂×C₄²

yes

characteristic

Dic₁₇

—

Dic₁₇

C₂×C₄²

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

C₂×C₁₇

C₄³

yes

characteristic

C₂×C₁₇

#405

yes

—

D₁₇

#405

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#595

yes

characteristic, complemented

#95

—

C₁₇

#1726

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

100

C₂³

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₄×#595

yes

—

109

C₂×C₄

C₂²×#595

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

C₄×#595

yes

—

114

C₈

C₄×#595

yes

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×C₄×#595

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

C₂×C₄×#595

yes

characteristic

123

C₄

C₂×C₄×#595

yes

characteristic

124

C₂

—

125

C₂

C₄²×#595

yes

characteristic

126

C₂

#11763772

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×#595
commutator	C₂×C₁₇	C₄³
Frattini	C₂×C₄	C₂²×#595
Fitting	C₄×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄²
prime radical	C₂²×D₁₇	C₂²×C₄
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1726
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#595

commutator

C₂×C₁₇

C₄³

Frattini

C₂×C₄

C₂²×#595

Fitting

C₄×C₈×C₁₇

C₄

socle

C₂²×C₁₇

C₂×C₄²

prime radical

C₂²×D₁₇

C₂²×C₄

cosocle

C₂×C₄×D₁₇

C₂³

C₄×C₈

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
12. #10587542	C₄	semidirect
13. #10587532	C₄	semidirect
14. C₈×#595	C₄	semidirect
15. C₄×C₈×C₁₇	C₄	semidirect
16. C₈×Dic₁₇	C₄	semidirect
17. C₈×Dic₁₇	C₄	semidirect
18. C₄×#3622	C₄	semidirect
80. C₄×C₈	#595	semidirect
82. C₁₇	#1726	semidirect

H ≅ G/N

type

12. #10587542

C₄

semidirect

13. #10587532

C₄

semidirect

14. C₈×#595

C₄

semidirect

15. C₄×C₈×C₁₇

C₄

semidirect

16. C₈×Dic₁₇

C₄

semidirect

17. C₈×Dic₁₇

C₄

semidirect

18. C₄×#3622

C₄

semidirect

80. C₄×C₈

#595

semidirect

82. C₁₇

#1726

semidirect

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

subgroup	index
#11763768	2
C₂×#10587532	2
C₂×C₈×#595	2
#11763745	2
C₄×C₈×D₁₇	2
#1726	17

subgroup

index

C₂×C₈×#595

C₄×C₈×D₁₇

Subgroups — #14544440

Conjugacy classes of subgroups

Complements

Maximal subgroups