Group #14544589 — subgroups

Subgroups — #14544589

Order 2176.

232 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 88 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	#11763819	C₂	1	1	yes	maximal, characteristic
2	#11763775	C₂	1	2	yes	maximal
3	C₂×C₈×#595	C₂	1	1	yes	maximal, characteristic
4	#11763681	C₂	1	2	yes	maximal
5	#108×D₁₇	C₂	1	1	yes	maximal, characteristic
6	#10587677	C₂²	1	2	yes	—
7	C₂×C₄×#595	C₂²	1	1	yes	characteristic
8	C₂×#63242	C₂²	1	1	yes	characteristic
9	M₁₆×D₁₇	C₂²	1	2	yes	—
10	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
11	#10587534	C₄	1	2	yes	complemented
12	#10587533	C₄	1	2	yes	complemented
13	#10587532	—	2	2	no	—
14	C₈×#595	—	2	2	no	—
15	C₈×#595	C₄	1	2	yes	complemented
16	C₈×#595	C₄	1	2	yes	complemented
17	C₁₇×#108	C₄	1	1	yes	characteristic, complemented
18	#10587493	C₄	1	2	yes	complemented
19	#10587490	C₄	1	1	yes	characteristic, complemented
20	C₂²×#595	—	2	1	no	—
21	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
22	C₂²⋊#595	—	2	2	no	—
23	C₂×#3624	Q₈	1	2	yes	—
24	C₄⋊#595	C₂×C₄	1	4	yes	—
25	C₄×#595	—	2	2	no	—
26	C₄×#595	—	2	1	no	—
27	C₄×#595	C₂×C₄	1	2	yes	—
28	#63242	C₂×C₄	1	2	yes	—
29	#63242	D₄	1	1	yes	characteristic
30	#63242	D₄	1	1	yes	characteristic
31	M₁₆×C₁₇	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
33	#63223	C₂×C₄	1	2	yes	—
34	C₂×#3622	C₂×C₄	1	1	yes	characteristic
35	#63218	—	2	2	no	—
36	C₈×D₁₇	—	2	2	no	—
37	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
38	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
39	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
40	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₁₇	#41	1	1	yes	characteristic
42	C₂×#595	—	2	4	no	—
43	C₂×#595	—	2	2	no	—
44	C₂×#595	—	2	4	no	—
45	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
46	C₂×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
47	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
48	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
49	C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
50	C₄×D₁₇	#41	1	1	yes	characteristic
51	#3624	C₄⋊C₄	1	2	yes	—
52	#3624	C₄⋊C₄	1	2	yes	—
53	C₈×C₁₇	—	2	2	no	—
54	C₈×C₁₇	C₄²	1	1	yes	characteristic
55	C₈×C₁₇	C₄²	1	1	yes	characteristic
56	#3622	—	2	2	no	—
57	#3622	C₄²	1	1	yes	characteristic
58	#3622	C₄²	1	1	yes	characteristic
59	#1772	—	17	1	no	maximal, Sylow
60	C₂²×C₁₇	C₄×Q₈	1	1	yes	characteristic
61	C₂×D₁₇	—	2	2	no	—
62	C₂×D₁₇	#117	1	1	yes	characteristic
63	C₂×D₁₇	C₄×D₄	1	1	yes	characteristic
64	#595	—	2	4	no	—
65	#595	—	4	4	no	—
66	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
67	C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
68	Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
69	Dic₁₇	C₄×Q₈	1	1	yes	characteristic
70	C₂×#108	—	17	1	no	—
71	#427	—	17	1	no	—
72	#405	—	17	2	no	—
73	C₂×C₄×C₈	—	17	1	no	—
74	#339	—	17	2	no	—
75	C₂×C₁₇	—	2	1	no	—
76	C₂×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
77	D₁₇	—	2	1	no	—
78	D₁₇	#443	1	2	yes	—
79	C₂×M₁₆	—	17	2	no	—
80	C₂²×C₈	—	17	1	no	—
81	C₂²×C₈	—	17	1	no	—
82	#117	—	17	2	no	—
83	C₂×C₄²	—	17	1	no	—
84	#108	—	17	2	no	—
85	#108	—	17	1	no	—
86	#108	#595	1	1	yes	characteristic, complemented
87	#107	—	17	2	no	—
88	#106	—	17	2	no	—
89	#97	—	34	2	no	—
90	C₄×C₈	—	17	2	no	—
91	C₄×C₈	—	17	2	no	—
92	C₄×C₈	—	34	2	no	—
93	C₁₇	#1772	1	1	yes	characteristic, complemented, Sylow
94	C₂²×C₄	—	17	1	no	—
95	C₂²×C₄	—	34	1	no	—
96	M₁₆	—	17	2	no	—
97	M₁₆	—	34	2	no	—
98	M₁₆	C₂×#595	1	2	yes	—
99	C₂×C₈	—	17	2	no	—
100	C₂×C₈	—	17	1	no	—
101	C₂×C₈	—	17	1	no	—
102	C₂×C₈	—	17	2	no	—
103	C₂×C₈	—	17	1	no	—
104	C₂×C₈	—	17	1	no	—
105	C₂×C₈	—	17	1	no	—
106	C₂×C₈	—	17	1	no	—
107	C₂×C₈	—	17	1	no	—
108	C₂×C₈	—	34	2	no	—
109	C₂×C₈	C₂×#595	1	1	yes	characteristic
110	C₄⋊C₄	—	17	4	no	—
111	C₂²⋊C₄	—	34	2	no	—
112	C₄²	—	17	2	no	—
113	C₄²	—	34	2	no	—
114	C₄²	—	34	1	no	—
115	C₂³	—	17	1	no	—
116	C₂×C₄	—	17	1	no	—
117	C₂×C₄	—	17	1	no	—
118	C₂×C₄	—	17	1	no	—
119	C₂×C₄	—	17	1	no	—
120	C₂×C₄	—	17	1	no	—
121	C₂×C₄	—	34	2	no	—
122	C₂×C₄	—	34	4	no	—
123	C₂×C₄	—	34	4	no	—
124	C₂×C₄	C₂²×#595	1	1	yes	characteristic
125	C₈	—	2	2	no	—
126	C₈	—	17	2	no	—
127	C₈	—	17	2	no	—
128	C₈	—	17	1	no	—
129	C₈	—	17	1	no	—
130	C₈	—	34	2	no	—
131	C₈	C₄×#595	1	1	yes	characteristic
132	C₈	C₄×#595	1	1	yes	characteristic
133	C₂²	—	17	1	no	—
134	C₂²	—	17	1	no	—
135	C₂²	—	34	2	no	—
136	C₂²	Q₈×#595	1	1	yes	characteristic
137	C₄	—	17	1	no	—
138	C₄	—	17	1	no	—
139	C₄	—	34	4	no	—
140	C₄	—	68	4	no	—
141	C₄	C₂×C₄×#595	1	1	yes	characteristic
142	C₄	D₄×#595	1	1	yes	characteristic
143	C₂	—	2	1	no	—
144	C₂	—	17	2	no	—
145	C₂	—	34	1	no	—
146	C₂	C₄⋊C₄×#595	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763819

C₂

yes

maximal, characteristic

#11763775

C₂

yes

maximal

C₂×C₈×#595

C₂

yes

maximal, characteristic

#11763681

C₂

yes

maximal

#108×D₁₇

C₂

yes

maximal, characteristic

#10587677

C₂²

yes

—

C₂×C₄×#595

C₂²

yes

characteristic

C₂×#63242

C₂²

yes

characteristic

M₁₆×D₁₇

C₂²

yes

—

C₂×C₈×D₁₇

C₂²

yes

characteristic

#10587534

C₄

yes

complemented

#10587533

C₄

yes

—

—

C₄

yes

complemented

C₈×#595

C₄

yes

complemented

C₁₇×#108

C₄

yes

characteristic, complemented

#10587493

C₄

yes

complemented

#10587490

C₄

yes

characteristic, complemented

C₂²×#595

—

C₂×C₄×D₁₇

C₂³

yes

characteristic

C₂²⋊#595

—

C₂×#3624

Q₈

yes

—

C₄⋊#595

C₂×C₄

yes

—

C₄×#595

—

C₄×#595

—

C₄×#595

C₂×C₄

yes

—

#63242

C₂×C₄

yes

—

#63242

D₄

yes

characteristic

#63242

D₄

yes

characteristic

M₁₆×C₁₇

C₂×C₄

yes

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

#63223

C₂×C₄

yes

—

C₂×#3622

C₂×C₄

yes

characteristic

#63218

—

C₈×D₁₇

—

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

C₂²×D₁₇

yes

—

—

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₂×Q₈

yes

characteristic

C₄×D₁₇

C₂²×C₄

yes

characteristic

C₄×D₁₇

C₂²×C₄

yes

characteristic

C₄×D₁₇

C₂×D₄

yes

C₄×D₁₇

yes

C₄⋊C₄

yes

—

#3624

C₄⋊C₄

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₄²

yes

characteristic

C₈×C₁₇

C₄²

yes

characteristic

#3622

—

#3622

C₄²

yes

characteristic

#3622

C₄²

yes

characteristic

#1772

—

maximal, Sylow

C₂²×C₁₇

C₄×Q₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

#117

yes

characteristic

C₂×D₁₇

C₄×D₄

yes

characteristic

#595

—

#595

—

C₄×C₁₇

C₂×C₄²

yes

characteristic

C₄×C₁₇

C₄×D₄

yes

characteristic

Dic₁₇

C₂×C₄⋊C₄

yes

characteristic

Dic₁₇

C₄×Q₈

yes

—

—

—

C₂×C₄×C₈

—

#339

—

C₂×C₁₇

—

C₂×C₁₇

C₄×C₄⋊C₄

yes

characteristic

D₁₇

—

D₁₇

#443

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

#107

—

#106

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₇

#1772

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

C₂×#595

yes

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₂×#595

yes

characteristic

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₂³

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

C₂²×#595

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

C₄×#595

yes

characteristic

132

C₈

C₄×#595

yes

characteristic

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

Q₈×#595

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

C₂×C₄×#595

yes

characteristic

142

C₄

D₄×#595

yes

characteristic

143

C₂

—

144

C₂

—

145

C₂

—

146

C₂

C₄⋊C₄×#595

yes

characteristic

	subgroup	G/H
center	C₄	D₄×#595
commutator	C₄×C₁₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×#595
Fitting	C₁₇×#108	C₄
socle	C₂×C₁₇	C₄×C₄⋊C₄
prime radical	C₂²×D₁₇	#41
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	#108	#595
hypocenter	C₁₇	#1772
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

subgroup

G/H

center

C₄

D₄×#595

commutator

C₄×C₁₇

C₂×C₄²

Frattini

C₂×C₄

C₂²×#595

Fitting

C₁₇×#108

C₄

socle

C₂×C₁₇

C₄×C₄⋊C₄

prime radical

C₂²×D₁₇

#41

cosocle

C₂×C₄×D₁₇

C₂³

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

N	H ≅ G/N	type
11. #10587534	C₄	semidirect
12. #10587533	C₄	semidirect
15. C₈×#595	C₄	semidirect
16. C₈×#595	C₄	semidirect
17. C₁₇×#108	C₄	semidirect
18. #10587493	C₄	semidirect
19. #10587490	C₄	semidirect
86. #108	#595	semidirect
93. C₁₇	#1772	semidirect

H ≅ G/N

type

11. #10587534

C₄

semidirect

12. #10587533

C₄

semidirect

15. C₈×#595

C₄

semidirect

16. C₈×#595

C₄

semidirect

17. C₁₇×#108

C₄

semidirect

18. #10587493

C₄

semidirect

19. #10587490

C₄

semidirect

86. #108

#595

semidirect

93. C₁₇

#1772

semidirect

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

subgroup	index
#11763819	2
#11763775	2
C₂×C₈×#595	2
#11763681	2
#108×D₁₇	2
#1772	17

subgroup

index

C₂×C₈×#595

#108×D₁₇

Subgroups — #14544589

Conjugacy classes of subgroups

Complements

Maximal subgroups