Group #14544891 — subgroups

Subgroups — #14544891

Order 2176.

208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 70 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	C₂×#10587535	C₂	1	1	yes	maximal, characteristic
2	#11763816	C₂	1	2	yes	maximal
3	C₂×C₈×#595	C₂	1	1	yes	maximal, characteristic
4	#11763679	C₂	1	2	yes	maximal
5	#11762844	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×#595	C₂²	1	1	yes	characteristic
7	C₂×#63243	C₂²	1	2	yes	—
8	C₂×#63242	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
10	#10587578	C₂²	1	2	yes	—
11	#10587544	—	2	2	no	—
12	C₄⋊#3624	—	2	2	no	—
13	#10587535	—	2	2	no	—
14	C₈×#595	—	2	2	no	—
15	C₁₇×#106	C₄	1	1	yes	characteristic, complemented
16	#10587488	C₄	1	1	yes	characteristic, complemented
17	#10587478	C₄	1	2	yes	complemented
18	C₂²×#595	—	2	1	no	—
19	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
20	C₂×#3624	—	2	2	no	—
21	C₂×#3624	D₄	1	2	yes	—
22	C₄×#595	—	2	1	no	—
23	C₄×#595	Q₈	1	2	yes	—
24	#63243	—	2	2	no	—
25	#63243	—	2	2	no	—
26	#63242	—	2	1	no	—
27	#63242	—	2	1	no	—
28	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
29	C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
30	#63227	—	2	2	no	—
31	C₄⋊Dic₁₇	C₂×C₄	1	2	yes	—
32	C₄×Dic₁₇	—	2	2	no	—
33	C₂×#3622	C₂×C₄	1	1	yes	characteristic
34	C₈×D₁₇	D₄	1	2	yes	—
35	C₈×D₁₇	Q₈	1	2	yes	—
36	C₂²×D₁₇	#41	1	1	yes	characteristic
37	C₂×#595	—	2	4	no	—
38	C₂×#595	—	2	2	no	—
39	C₂×C₄×C₁₇	—	2	2	no	—
40	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₁₇	—	2	2	no	—
42	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
43	C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
44	C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
45	C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
46	C₄×D₁₇	#41	1	1	yes	characteristic
47	#3624	—	2	2	no	—
48	#3624	—	4	2	no	—
49	C₈×C₁₇	C₄⋊C₄	1	2	yes	—
50	#3622	C₄⋊C₄	1	2	yes	—
51	#1945	—	17	1	no	maximal, Sylow
52	C₂²×C₁₇	C₄×D₄	1	1	yes	characteristic
53	C₂×D₁₇	—	2	2	no	—
54	C₂×D₁₇	C₂²⋊Q₈	1	1	yes	characteristic
55	C₂×D₁₇	#125	1	1	yes	characteristic
56	#595	—	2	4	no	—
57	C₄×C₁₇	—	4	2	no	—
58	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
60	Dic₁₇	—	4	2	no	—
61	Dic₁₇	#121	1	1	yes	characteristic
62	Dic₁₇	C₄⋊Q₈	1	1	yes	characteristic
63	C₂×#108	—	17	1	no	—
64	#427	—	17	1	no	—
65	#424	—	17	2	no	—
66	C₂×C₄×C₈	—	17	1	no	—
67	#339	—	17	2	no	—
68	C₂×C₁₇	#389	1	1	yes	characteristic
69	C₂×C₁₇	#443	1	2	yes	—
70	D₁₇	—	2	1	no	—
71	D₁₇	—	2	1	no	—
72	C₂×M₁₆	—	17	2	no	—
73	C₂²×C₈	—	17	1	no	—
74	C₂²×C₈	—	17	1	no	—
75	#117	—	17	2	no	—
76	C₂×C₄²	—	17	1	no	—
77	#108	—	34	2	no	—
78	#107	—	17	2	no	—
79	#106	—	17	1	no	—
80	#106	#595	1	1	yes	characteristic, complemented
81	C₄⋊C₈	—	34	2	no	—
82	C₄⋊C₈	—	34	2	no	—
83	C₄×C₈	—	34	2	no	—
84	C₁₇	#1945	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₄	—	17	1	no	—
86	C₂²×C₄	—	34	1	no	—
87	M₁₆	—	34	2	no	—
88	M₁₆	—	34	2	no	—
89	C₂×C₈	—	17	1	no	—
90	C₂×C₈	—	17	2	no	—
91	C₂×C₈	—	17	2	no	—
92	C₂×C₈	—	17	2	no	—
93	C₂×C₈	—	34	1	no	—
94	C₂×C₈	—	34	1	no	—
95	C₂×C₈	—	34	2	no	—
96	C₂×C₈	C₂×#595	1	1	yes	characteristic
97	C₄⋊C₄	—	17	2	no	—
98	C₄⋊C₄	C₂×#595	1	2	yes	—
99	C₂²⋊C₄	—	34	2	no	—
100	C₄²	—	17	2	no	—
101	C₄²	—	34	2	no	—
102	C₄²	—	34	1	no	—
103	C₂³	—	17	1	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	17	1	no	—
106	C₂×C₄	—	17	1	no	—
107	C₂×C₄	—	17	1	no	—
108	C₂×C₄	—	17	1	no	—
109	C₂×C₄	—	17	1	no	—
110	C₂×C₄	—	34	2	no	—
111	C₂×C₄	—	34	4	no	—
112	C₂×C₄	—	34	2	no	—
113	C₂×C₄	C₂²×#595	1	1	yes	characteristic
114	C₈	—	17	2	no	—
115	C₈	—	34	2	no	—
116	C₈	—	68	2	no	—
117	C₈	C₄⋊#595	1	2	yes	—
118	C₂²	—	17	1	no	—
119	C₂²	—	17	1	no	—
120	C₂²	—	34	2	no	—
121	C₂²	D₄×#595	1	1	yes	characteristic
122	C₄	—	4	2	no	—
123	C₄	—	17	1	no	—
124	C₄	—	17	1	no	—
125	C₄	—	34	4	no	—
126	C₄	—	68	2	no	—
127	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
128	C₄	Q₈×#595	1	1	yes	characteristic
129	C₂	—	34	1	no	—
130	C₂	—	34	1	no	—
131	C₂	#11763760	1	1	yes	characteristic
132	C₂	#11763852	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587535

C₂

yes

maximal, characteristic

#11763816

C₂

yes

maximal

C₂×C₈×#595

C₂

yes

maximal, characteristic

#11763679

C₂

yes

maximal

#11762844

C₂

yes

maximal, characteristic

C₂×C₄×#595

C₂²

yes

characteristic

C₂×#63243

C₂²

yes

—

C₂×#63242

C₂²

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

#10587578

C₂²

yes

—

—

—

—

—

C₁₇×#106

C₄

yes

characteristic, complemented

#10587488

C₄

yes

characteristic, complemented

#10587478

C₄

yes

complemented

C₂²×#595

—

C₂×C₄×D₁₇

C₂³

yes

characteristic

C₂×#3624

—

C₂×#3624

D₄

yes

—

C₄×#595

—

C₄×#595

Q₈

yes

—

—

—

—

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄⋊C₄×C₁₇

C₂×C₄

yes

—

#63227

—

C₄⋊Dic₁₇

C₂×C₄

yes

—

C₄×Dic₁₇

—

C₂×#3622

C₂×C₄

yes

characteristic

C₈×D₁₇

D₄

yes

—

C₈×D₁₇

Q₈

yes

—

C₂²×D₁₇

yes

—

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂×D₄

yes

characteristic

C₄×D₁₇

C₂×D₄

yes

characteristic

C₄×D₁₇

C₂×Q₈

yes

characteristic

C₄×D₁₇

C₂×Q₈

yes

C₄×D₁₇

yes

—

—

C₈×C₁₇

C₄⋊C₄

yes

—

#3622

C₄⋊C₄

yes

—

#1945

—

maximal, Sylow

C₂²×C₁₇

C₄×D₄

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₂²⋊Q₈

yes

C₂×D₁₇

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₇

C₄×Q₈

yes

characteristic

Dic₁₇

—

Dic₁₇

#121

yes

characteristic

Dic₁₇

C₄⋊Q₈

yes

—

—

—

C₂×C₄×C₈

—

#339

—

C₂×C₁₇

#389

yes

characteristic

C₂×C₁₇

#443

yes

—

D₁₇

—

D₁₇

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₁₇

#1945

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×#595

yes

—

C₂²⋊C₄

—

100

C₄²

—

101

C₄²

—

102

C₄²

—

103

C₂³

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₂²×#595

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

C₄⋊#595

yes

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

D₄×#595

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

C₂×C₄⋊#595

yes

characteristic

128

C₄

Q₈×#595

yes

characteristic

129

C₂

—

130

C₂

—

131

C₂

#11763760

yes

characteristic

132

C₂

#11763852

yes

—

	subgroup	G/H
center	C₂²	D₄×#595
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₁₇×#106	C₄
socle	C₂²×C₁₇	C₄×D₄
prime radical	C₂²×D₁₇	#41
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	#106	#595
hypocenter	C₁₇	#1945
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

subgroup

G/H

center

C₂²

D₄×#595

commutator

C₂×C₄×C₁₇

C₂²×C₄

Frattini

C₂×C₄

C₂²×#595

Fitting

C₁₇×#106

C₄

socle

C₂²×C₁₇

C₄×D₄

prime radical

C₂²×D₁₇

#41

cosocle

C₂×C₄×D₁₇

C₂³

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

N	H ≅ G/N	type
15. C₁₇×#106	C₄	semidirect
16. #10587488	C₄	semidirect
17. #10587478	C₄	semidirect
80. #106	#595	semidirect
84. C₁₇	#1945	semidirect

H ≅ G/N

type

15. C₁₇×#106

C₄

semidirect

16. #10587488

C₄

semidirect

17. #10587478

C₄

semidirect

80. #106

#595

semidirect

84. C₁₇

#1945

semidirect

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

subgroup	index
C₂×#10587535	2
#11763816	2
C₂×C₈×#595	2
#11763679	2
#11762844	2
#1945	17

subgroup

index

C₂×C₈×#595

Subgroups — #14544891

Conjugacy classes of subgroups

Complements

Maximal subgroups