Group #14544887 — subgroups

Subgroups — #14544887

Order 2176.

248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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×#10587533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#595	C₂	1	1	yes	maximal, characteristic
3	#11763760	C₂	1	2	yes	maximal
4	#11763682	C₂	1	2	yes	maximal
5	#106×D₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#595	—	2	2	no	—
7	C₂×C₄⋊#595	C₂²	1	2	yes	—
8	C₂×C₄×#595	C₂²	1	1	yes	characteristic
9	C₂×#63242	C₂²	1	1	yes	characteristic
10	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×D₁₇	C₂²	1	2	yes	—
12	(C₂×#595)⋊C₄	—	2	2	no	—
13	#10587533	—	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	#10587479	C₄	1	2	yes	complemented
18	C₂²×#595	—	2	2	no	—
19	C₂²×#595	D₄	1	2	yes	—
20	C₂×C₄×D₁₇	—	2	2	no	—
21	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
22	C₂×#3624	—	2	1	no	—
23	C₄⋊#595	—	2	2	no	—
24	C₄⋊#595	—	2	2	no	—
25	C₄⋊#595	—	4	4	no	—
26	C₄×#595	—	2	1	no	—
27	C₄×#595	—	2	1	no	—
28	#63242	—	2	1	no	—
29	#63242	Q₈	1	2	yes	—
30	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
31	C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
32	C₄⋊Dic₁₇	C₂×C₄	1	2	yes	—
33	#63225	—	2	2	no	—
34	C₂×#3622	C₂×C₄	1	1	yes	characteristic
35	C₈×D₁₇	D₄	1	2	yes	—
36	C₈×D₁₇	Q₈	1	2	yes	—
37	C₂²×D₁₇	C₂×D₄	1	1	yes	characteristic
38	C₂×#595	—	2	2	no	—
39	C₂×#595	—	2	2	no	—
40	C₂×#595	—	4	2	no	—
41	C₂×#595	—	4	2	no	—
42	C₂×#595	—	4	2	no	—
43	C₂×#595	SD₁₆	1	4	yes	—
44	C₂×C₄×C₁₇	—	2	2	no	—
45	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
46	C₂×Dic₁₇	—	2	2	no	—
47	C₂×Dic₁₇	#41	1	1	yes	characteristic
48	C₄×D₁₇	—	4	2	no	—
49	C₄×D₁₇	—	4	2	no	—
50	C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
51	C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
52	C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
53	C₄×D₁₇	#41	1	1	yes	characteristic
54	#3624	—	2	2	no	—
55	C₈×C₁₇	C₄⋊C₄	1	2	yes	complemented
56	#3622	C₄⋊C₄	1	2	yes	complemented
57	#1941	—	17	1	no	maximal, Sylow
58	C₂²×C₁₇	C₄×D₄	1	1	yes	characteristic
59	C₂×D₁₇	#121	1	1	yes	characteristic
60	C₂×D₁₇	C₄⋊Q₈	1	1	yes	characteristic
61	C₂×D₁₇	C₂×SD₁₆	1	2	yes	—
62	C₂×D₁₇	#135	1	2	yes	—
63	#595	—	2	4	no	—
64	#595	—	8	2	no	—
65	C₄×C₁₇	—	4	2	no	—
66	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
68	Dic₁₇	—	4	2	no	—
69	Dic₁₇	C₂²⋊Q₈	1	1	yes	characteristic
70	Dic₁₇	#125	1	1	yes	characteristic
71	C₂×#106	—	17	1	no	—
72	C₂×#106	—	17	1	no	—
73	C₂×C₄×C₈	—	17	1	no	—
74	#389	—	17	2	no	—
75	#340	—	17	2	no	—
76	C₂×C₁₇	#389	1	1	yes	characteristic
77	C₂×C₁₇	C₄×SD₁₆	1	2	yes	—
78	D₁₇	#465	1	2	yes	—
79	D₁₇	#498	1	1	yes	characteristic
80	D₁₇	#499	1	1	yes	characteristic
81	C₂²×C₈	—	17	1	no	—
82	C₂²×C₈	—	17	1	no	—
83	C₂×C₄⋊C₄	—	17	2	no	—
84	C₂×C₄⋊C₄	—	17	2	no	—
85	C₂×C₄⋊C₄	—	34	2	no	—
86	C₂×C₄²	—	17	1	no	—
87	#106	—	17	1	no	—
88	#106	—	17	2	no	—
89	#106	—	34	2	no	—
90	#106	#595	1	1	yes	characteristic, complemented
91	C₄×C₈	—	34	2	no	—
92	#95	—	34	2	no	—
93	C₁₇	#1941	1	1	yes	characteristic, complemented, Sylow
94	C₂²×C₄	—	17	1	no	—
95	C₂²×C₄	—	17	2	no	—
96	C₂²×C₄	—	34	2	no	—
97	C₂²×C₄	—	34	2	no	—
98	C₂×C₈	—	17	1	no	—
99	C₂×C₈	—	17	2	no	—
100	C₂×C₈	—	17	2	no	—
101	C₂×C₈	—	17	2	no	—
102	C₂×C₈	—	34	1	no	—
103	C₂×C₈	—	34	1	no	—
104	C₂×C₈	C₂×#595	1	1	yes	characteristic
105	C₄⋊C₄	—	17	2	no	—
106	C₄⋊C₄	—	34	2	no	—
107	C₄⋊C₄	—	34	2	no	—
108	C₄⋊C₄	—	34	2	no	—
109	C₄⋊C₄	—	68	4	no	—
110	C₄⋊C₄	C₂×#595	1	2	yes	—
111	C₄²	—	34	1	no	—
112	C₄²	—	34	1	no	—
113	C₂³	—	17	1	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	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	4	no	—
121	C₂×C₄	—	34	2	no	—
122	C₂×C₄	—	34	2	no	—
123	C₂×C₄	—	34	2	no	—
124	C₂×C₄	—	68	2	no	—
125	C₂×C₄	—	68	2	no	—
126	C₂×C₄	—	68	2	no	—
127	C₂×C₄	—	68	2	no	—
128	C₂×C₄	—	68	2	no	—
129	C₂×C₄	C₂²×#595	1	1	yes	characteristic
130	C₈	—	17	2	no	—
131	C₈	—	34	2	no	—
132	C₈	C₄⋊#595	1	2	yes	complemented
133	C₂²	—	17	1	no	—
134	C₂²	—	17	1	no	—
135	C₂²	—	17	2	no	—
136	C₂²	—	17	2	no	—
137	C₂²	D₄×#595	1	1	yes	characteristic
138	C₄	—	4	2	no	—
139	C₄	—	17	1	no	—
140	C₄	—	17	1	no	—
141	C₄	—	34	4	no	—
142	C₄	—	68	2	no	—
143	C₄	—	136	2	no	—
144	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
145	C₄	Q₈×#595	1	1	yes	characteristic
146	C₂	—	17	2	no	—
147	C₂	—	17	1	no	—
148	C₂	—	17	1	no	—
149	C₂	#11763760	1	1	yes	characteristic
150	C₂	SD₁₆×#595	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587533

C₂

yes

maximal, characteristic

C₂×C₈×#595

C₂

yes

maximal, characteristic

#11763760

C₂

yes

maximal

#11763682

C₂

yes

maximal

#106×D₁₇

C₂

yes

maximal, characteristic

C₂×C₄⋊#595

—

C₂×C₄⋊#595

C₂²

yes

—

C₂×C₄×#595

C₂²

yes

characteristic

C₂×#63242

C₂²

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

C₄⋊C₄×D₁₇

C₂²

yes

—

(C₂×#595)⋊C₄

—

#10587533

—

C₈×#595

—

C₁₇×#106

C₄

yes

characteristic, complemented

#10587488

C₄

yes

characteristic, complemented

#10587479

C₄

yes

complemented

C₂²×#595

—

C₂²×#595

D₄

yes

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₂³

yes

—

—

—

—

—

—

—

Q₈

yes

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄⋊C₄×C₁₇

C₂×C₄

yes

—

C₄⋊Dic₁₇

C₂×C₄

yes

—

#63225

—

C₂×#3622

C₂×C₄

yes

characteristic

C₈×D₁₇

D₄

yes

—

C₈×D₁₇

Q₈

yes

—

C₂²×D₁₇

C₂×D₄

yes

—

—

—

—

—

SD₁₆

yes

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

#41

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

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

complemented

#3622

C₄⋊C₄

yes

complemented

#1941

—

maximal, Sylow

C₂²×C₁₇

C₄×D₄

yes

characteristic

C₂×D₁₇

#121

yes

characteristic

C₂×D₁₇

C₄⋊Q₈

yes

characteristic

C₂×D₁₇

C₂×SD₁₆

yes

—

C₂×D₁₇

#135

yes

—

#595

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₇

C₄×Q₈

yes

characteristic

Dic₁₇

—

Dic₁₇

C₂²⋊Q₈

yes

Dic₁₇

yes

—

—

C₂×C₄×C₈

—

#389

—

#340

—

C₂×C₁₇

#389

yes

characteristic

C₂×C₁₇

C₄×SD₁₆

yes

—

D₁₇

#465

yes

—

D₁₇

yes

D₁₇

yes

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₄×C₈

—

#95

—

C₁₇

#1941

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₂×#595

yes

characteristic

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

C₂×#595

yes

—

111

C₄²

—

112

C₄²

—

113

C₂³

—

114

C₂×C₄

—

115

C₂×C₄

—

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

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂²×#595

yes

characteristic

130

C₈

—

131

C₈

—

132

C₈

C₄⋊#595

yes

complemented

133

C₂²

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

D₄×#595

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

136

—

144

C₄

C₂×C₄⋊#595

yes

characteristic

145

C₄

Q₈×#595

yes

characteristic

146

C₂

—

147

C₂

—

148

C₂

—

149

C₂

#11763760

yes

characteristic

150

C₂

SD₁₆×#595

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	C₂×D₄
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	#106	#595
hypocenter	C₁₇	#1941
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

C₂×D₄

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. #10587479	C₄	semidirect
55. C₈×C₁₇	C₄⋊C₄	semidirect
56. #3622	C₄⋊C₄	semidirect
90. #106	#595	semidirect
93. C₁₇	#1941	semidirect
132. C₈	C₄⋊#595	semidirect

H ≅ G/N

type

15. C₁₇×#106

C₄

semidirect

16. #10587488

C₄

semidirect

17. #10587479

C₄

semidirect

55. C₈×C₁₇

C₄⋊C₄

semidirect

56. #3622

C₄⋊C₄

semidirect

90. #106

#595

semidirect

93. C₁₇

#1941

semidirect

132. C₈

C₄⋊#595

semidirect

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

subgroup	index
C₂×#10587533	2
C₂×C₈×#595	2
#11763760	2
#11763682	2
#106×D₁₇	2
#1941	17

subgroup

index

C₂×C₈×#595

#106×D₁₇

Subgroups — #14544887

Conjugacy classes of subgroups

Complements

Maximal subgroups