Group #14544703 — subgroups

Subgroups — #14544703

Order 2176.

172 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 62 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	D₁₇⋊#108	C₂	1	1	yes	maximal, characteristic
2	#11763819	C₂	1	1	yes	maximal, characteristic
3	#11763691	C₂	1	2	yes	maximal
4	#11763676	C₂	1	2	yes	maximal
5	#11762763	C₂	1	1	yes	maximal, characteristic
6	#10587677	C₂²	1	2	yes	—
7	D₁₇⋊M₁₆	C₂²	1	2	yes	—
8	C₂×#63218	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
10	#10587558	C₂²	1	1	yes	characteristic
11	#10587536	—	2	1	no	—
12	#10587535	—	2	1	no	—
13	#10587534	—	2	1	no	—
14	#10587533	—	2	1	no	—
15	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic, complemented
16	#10587486	C₄	1	1	yes	characteristic, complemented
17	C₈×Dic₁₇	C₄	1	1	yes	characteristic, complemented
18	#10587474	C₄	1	1	yes	characteristic, complemented
19	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
20	C₂²⋊#595	—	2	2	no	—
21	#63247	—	2	2	no	—
22	C₄⋊#595	—	2	2	no	—
23	C₄×#595	—	2	2	no	—
24	#63243	—	2	2	no	—
25	#63242	—	2	2	no	—
26	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
28	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
29	#63227	—	2	1	no	—
30	#63225	—	2	1	no	—
31	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂×#3622	C₂×C₄	1	1	yes	characteristic
33	C₂×#3622	C₂×C₄	1	1	yes	characteristic
34	#63218	—	2	1	no	—
35	#63218	—	2	1	no	—
36	C₈×D₁₇	D₄	1	1	yes	characteristic
37	C₈×D₁₇	D₄	1	1	yes	characteristic
38	C₈×D₁₇	Q₈	1	1	yes	characteristic
39	C₈×D₁₇	Q₈	1	1	yes	characteristic
40	C₂²×D₁₇	#41	1	1	yes	characteristic
41	C₂×#595	—	4	2	no	—
42	C₂×C₄×C₁₇	—	2	1	no	—
43	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
44	C₂×Dic₁₇	—	2	1	no	—
45	C₂×Dic₁₇	#41	1	1	yes	characteristic
46	C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
47	C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
48	C₄×D₁₇	#41	1	1	yes	characteristic
49	C₄×D₁₇	#41	1	1	yes	characteristic
50	#3624	—	4	2	no	—
51	C₈×C₁₇	—	2	1	no	—
52	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
53	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
54	#3622	—	2	1	no	—
55	#3622	C₄⋊C₄	1	1	yes	characteristic
56	#3622	C₄⋊C₄	1	1	yes	characteristic
57	#1833	—	17	1	no	maximal, Sylow
58	C₂²×C₁₇	#117	1	1	yes	characteristic
59	C₂×D₁₇	—	4	1	no	—
60	C₂×D₁₇	#124	1	1	yes	characteristic
61	C₂×D₁₇	#125	1	1	yes	characteristic
62	#595	—	8	2	no	—
63	C₄×C₁₇	—	4	1	no	—
64	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₄×C₁₇	#117	1	1	yes	characteristic
66	Dic₁₇	—	4	1	no	—
67	Dic₁₇	#124	1	1	yes	characteristic
68	Dic₁₇	#125	1	1	yes	characteristic
69	C₂×#108	—	17	1	no	—
70	#427	—	17	1	no	—
71	#405	—	17	1	no	—
72	#344	—	17	2	no	—
73	H(3,ℤ/4)	—	17	2	no	—
74	C₂×C₁₇	—	2	1	no	—
75	C₂×C₁₇	#382	1	1	yes	characteristic
76	D₁₇	—	2	1	no	—
77	D₁₇	—	2	1	no	—
78	C₂×M₁₆	—	17	1	no	—
79	C₂×M₁₆	—	17	2	no	—
80	C₂²×C₈	—	17	1	no	—
81	#117	—	17	1	no	—
82	#117	—	17	2	no	—
83	#108	—	34	1	no	—
84	#108	—	34	1	no	—
85	#107	—	34	1	no	—
86	#106	—	34	1	no	—
87	#97	—	17	1	no	—
88	#97	—	17	1	no	—
89	C₄×C₈	—	17	1	no	—
90	C₄×C₈	#595	1	1	yes	characteristic, complemented
91	C₁₇	#1833	1	1	yes	characteristic, complemented, Sylow
92	C₂²×C₄	—	17	1	no	—
93	M₁₆	—	34	1	no	—
94	M₁₆	—	34	1	no	—
95	M₁₆	—	34	2	no	—
96	M₁₆	—	34	2	no	—
97	C₂×C₈	—	17	1	no	—
98	C₂×C₈	—	17	1	no	—
99	C₂×C₈	—	17	1	no	—
100	C₂×C₈	—	17	1	no	—
101	C₂×C₈	—	17	1	no	—
102	C₂×C₈	—	17	1	no	—
103	C₂×C₈	—	34	2	no	—
104	C₂×C₈	C₂×#595	1	1	yes	characteristic
105	C₂×C₈	C₂×#595	1	1	yes	characteristic
106	C₄⋊C₄	—	34	1	no	—
107	C₄⋊C₄	—	34	2	no	—
108	C₂²⋊C₄	—	34	1	no	—
109	C₂²⋊C₄	—	34	2	no	—
110	C₄²	—	17	1	no	—
111	C₄²	—	34	2	no	—
112	C₄²	C₂×#595	1	1	yes	characteristic
113	C₂³	—	17	1	no	—
114	C₂×C₄	—	2	1	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	—	34	1	no	—
121	C₂×C₄	—	68	2	no	—
122	C₂×C₄	C₂²×#595	1	1	yes	characteristic
123	C₈	—	2	1	no	—
124	C₈	—	17	1	no	—
125	C₈	—	17	1	no	—
126	C₈	—	34	1	no	—
127	C₈	—	68	2	no	—
128	C₈	C₄⋊#595	1	1	yes	characteristic
129	C₈	C₄⋊#595	1	1	yes	characteristic
130	C₂²	—	17	1	no	—
131	C₂²	—	17	1	no	—
132	C₂²	—	68	1	no	—
133	C₂²	#10587677	1	1	yes	characteristic
134	C₄	—	4	1	no	—
135	C₄	—	17	1	no	—
136	C₄	—	17	1	no	—
137	C₄	—	68	1	no	—
138	C₄	—	136	2	no	—
139	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
140	C₄	#10587677	1	1	yes	characteristic
141	C₂	—	2	1	no	—
142	C₂	—	34	1	no	—
143	C₂	—	34	1	no	—
144	C₂	#11763753	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₁₇⋊#108

C₂

yes

maximal, characteristic

#11763819

C₂

yes

maximal, characteristic

#11763691

C₂

yes

maximal

#11763676

C₂

yes

maximal

#11762763

C₂

yes

maximal, characteristic

#10587677

C₂²

yes

—

D₁₇⋊M₁₆

C₂²

yes

—

C₂×#63218

C₂²

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

#10587558

C₂²

yes

—

—

—

—

C₄×C₈×C₁₇

C₄

yes

characteristic, complemented

#10587486

C₄

yes

characteristic, complemented

C₈×Dic₁₇

C₄

yes

characteristic, complemented

#10587474

C₄

yes

characteristic, complemented

C₂×C₄×D₁₇

C₂³

yes

characteristic

C₂²⋊#595

—

—

—

—

—

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₄

yes

characteristic

#63227

—

#63225

—

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

#63218

—

#63218

—

C₈×D₁₇

D₄

yes

characteristic

C₈×D₁₇

D₄

yes

characteristic

C₈×D₁₇

Q₈

yes

characteristic

C₈×D₁₇

Q₈

yes

C₂²×D₁₇

yes

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

#41

yes

characteristic

C₄×D₁₇

C₂×D₄

yes

characteristic

C₄×D₁₇

C₂×Q₈

yes

C₄×D₁₇

yes

C₄×D₁₇

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₄⋊C₄

yes

characteristic

C₈×C₁₇

C₄⋊C₄

yes

characteristic

#3622

—

#3622

C₄⋊C₄

yes

characteristic

#3622

C₄⋊C₄

yes

—

C₂²×C₁₇

yes

C₂×D₁₇

—

C₂×D₁₇

yes

C₂×D₁₇

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₇

#117

yes

characteristic

Dic₁₇

—

Dic₁₇

yes

Dic₁₇

yes

—

—

—

—

—

C₂×C₁₇

—

C₂×C₁₇

#382

yes

characteristic

D₁₇

—

D₁₇

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

—

—

—

—

—

—

—

—

C₄×C₈

—

C₄×C₈

#595

yes

characteristic, complemented

C₁₇

#1833

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₂×#595

yes

characteristic

105

C₂×C₈

C₂×#595

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₄²

C₂×#595

yes

characteristic

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

C₂²×#595

yes

characteristic

123

C₈

—

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

C₄⋊#595

yes

characteristic

129

C₈

C₄⋊#595

yes

characteristic

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

#10587677

yes

characteristic

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

136

—

139

C₄

C₂×C₄⋊#595

yes

characteristic

140

C₄

#10587677

yes

characteristic

141

C₂

—

142

C₂

—

143

C₂

—

144

C₂

#11763753

yes

characteristic

	subgroup	G/H
center	C₄	#10587677
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₄×C₈×C₁₇	C₄
socle	C₂×C₁₇	#382
prime radical	C₂²×D₁₇	#41
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1833
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₄

#10587677

commutator

C₂×C₄×C₁₇

C₂²×C₄

Frattini

C₂×C₄

C₂²×#595

Fitting

C₄×C₈×C₁₇

C₄

C₂×C₁₇

C₂²×D₁₇

C₂×C₄×D₁₇

C₂³

C₄×C₈

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
15. C₄×C₈×C₁₇	C₄	semidirect
16. #10587486	C₄	semidirect
17. C₈×Dic₁₇	C₄	semidirect
18. #10587474	C₄	semidirect
90. C₄×C₈	#595	semidirect
91. C₁₇	#1833	semidirect

H ≅ G/N

type

15. C₄×C₈×C₁₇

C₄

semidirect

16. #10587486

C₄

semidirect

17. C₈×Dic₁₇

C₄

semidirect

18. #10587474

C₄

semidirect

90. C₄×C₈

#595

semidirect

91. C₁₇

#1833

semidirect

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

subgroup	index
D₁₇⋊#108	2
#11763819	2
#11763691	2
#11763676	2
#11762763	2
#1833	17

subgroup

index

D₁₇⋊#108

Subgroups — #14544703

Conjugacy classes of subgroups

Complements

Maximal subgroups