Group #14544604 — subgroups

Subgroups — #14544604

Order 2176.

220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 92 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×#10587536	C₂	1	1	yes	maximal, characteristic
2	C₂×#10587535	C₂	1	1	yes	maximal, characteristic
3	C₄×#63243	C₂	1	2	yes	maximal
4	#11763685	C₂	1	2	yes	maximal
5	#97×D₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#63243	C₂²	1	2	yes	—
7	C₂×#63243	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	#10587542	—	2	2	no	—
12	C₄×#3624	—	2	2	no	—
13	#10587536	C₄	1	4	yes	complemented
14	#10587535	C₄	1	4	yes	complemented
15	C₁₇×#97	C₄	1	1	yes	characteristic
16	#10587486	C₄	1	1	yes	characteristic
17	#10587486	C₄	1	1	yes	characteristic
18	#10587474	C₄	1	1	yes	characteristic
19	C₂×C₄×D₁₇	Q₈	1	2	yes	—
20	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
21	C₂×#3624	—	2	2	no	—
22	C₂×#3624	—	2	2	no	—
23	#63243	—	2	2	no	—
24	#63243	—	2	2	no	—
25	#63243	C₂×C₄	1	4	yes	—
26	#63243	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	D₄	1	2	yes	—
32	C₂×#3622	C₂×C₄	1	1	yes	characteristic
33	C₂×#3622	C₂×C₄	1	1	yes	characteristic
34	C₈×D₁₇	—	2	1	no	—
35	C₈×D₁₇	—	2	1	no	—
36	C₈×D₁₇	C₂×C₄	1	2	yes	—
37	C₈×D₁₇	C₂×C₄	1	2	yes	—
38	C₂²×D₁₇	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
42	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
43	C₄×D₁₇	—	4	2	no	—
44	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
45	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
46	C₄×D₁₇	#41	1	1	yes	characteristic
47	C₄×D₁₇	#41	1	1	yes	characteristic
48	#3624	—	2	4	no	—
49	#3624	—	2	4	no	—
50	C₈×C₁₇	—	2	1	no	—
51	C₈×C₁₇	C₄²	1	2	yes	—
52	#3622	—	2	1	no	—
53	#3622	C₄²	1	2	yes	—
54	#1778	—	17	1	no	maximal, Sylow
55	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×D₁₇	—	2	2	no	—
57	C₂×D₁₇	C₄×Q₈	1	1	yes	characteristic
58	C₂×D₁₇	C₄×Q₈	1	1	yes	characteristic
59	C₄×C₁₇	—	2	2	no	—
60	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
61	C₄×C₁₇	#117	1	1	yes	characteristic
62	Dic₁₇	—	2	2	no	—
63	Dic₁₇	C₄×D₄	1	1	yes	characteristic
64	Dic₁₇	C₄×D₄	1	1	yes	characteristic
65	C₂×#108	—	17	1	no	—
66	C₂×#108	—	17	1	no	—
67	C₄×M₁₆	—	17	2	no	—
68	C₂×#97	—	17	1	no	—
69	#341	—	17	2	no	—
70	C₂×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₁₇	#430	1	2	yes	—
72	D₁₇	—	2	1	no	—
73	D₁₇	—	2	1	no	—
74	C₂×M₁₆	—	17	2	no	—
75	C₂×M₁₆	—	17	2	no	—
76	C₂²×C₈	—	17	1	no	—
77	C₂²×C₈	—	17	1	no	—
78	C₂×C₄²	—	17	1	no	—
79	#108	—	17	4	no	—
80	#108	—	17	4	no	—
81	#97	—	17	1	no	—
82	#97	—	17	1	no	—
83	#97	—	17	1	no	—
84	#97	—	34	2	no	—
85	#97	#595	1	1	yes	characteristic
86	C₄×C₈	—	34	2	no	—
87	C₁₇	#1778	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄	—	17	1	no	—
89	C₂²×C₄	—	17	2	no	—
90	M₁₆	—	17	4	no	—
91	M₁₆	—	17	4	no	—
92	M₁₆	—	34	2	no	—
93	M₁₆	—	34	2	no	—
94	C₂×C₈	—	17	1	no	—
95	C₂×C₈	—	17	2	no	—
96	C₂×C₈	—	17	2	no	—
97	C₂×C₈	—	17	1	no	—
98	C₂×C₈	—	34	1	no	—
99	C₂×C₈	—	34	1	no	—
100	C₂×C₈	—	34	2	no	—
101	C₂×C₈	—	34	2	no	—
102	C₂×C₈	C₂×#595	1	1	yes	characteristic
103	C₂×C₈	C₂×#595	1	1	yes	characteristic
104	C₄²	—	17	2	no	—
105	C₄²	—	17	1	no	—
106	C₄²	C₂×#595	1	1	yes	characteristic
107	C₂³	—	17	1	no	—
108	C₂×C₄	—	17	1	no	—
109	C₂×C₄	—	17	1	no	—
110	C₂×C₄	—	17	1	no	—
111	C₂×C₄	—	17	1	no	—
112	C₂×C₄	—	17	1	no	—
113	C₂×C₄	—	17	2	no	—
114	C₂×C₄	—	68	2	no	—
115	C₂×C₄	C₄⋊#595	1	2	yes	—
116	C₂×C₄	C₂²×#595	1	1	yes	characteristic
117	C₈	—	2	1	no	—
118	C₈	—	17	2	no	—
119	C₈	—	34	4	no	—
120	C₈	—	34	4	no	—
121	C₈	—	34	1	no	—
122	C₈	C₄×#595	1	2	yes	—
123	C₂²	—	17	1	no	—
124	C₂²	—	17	1	no	—
125	C₂²	—	34	2	no	—
126	C₂²	C₂×C₄⋊#595	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	17	1	no	—
129	C₄	—	17	1	no	—
130	C₄	—	34	2	no	—
131	C₄	C₂×C₄×#595	1	1	yes	characteristic
132	C₄	#10587677	1	1	yes	characteristic
133	C₂	—	34	1	no	—
134	C₂	—	34	1	no	—
135	C₂	C₄×C₄⋊#595	1	1	yes	characteristic
136	C₂	#11763824	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587536

C₂

yes

maximal, characteristic

C₂×#10587535

C₂

yes

maximal, characteristic

C₄×#63243

C₂

yes

maximal

#11763685

C₂

yes

maximal

#97×D₁₇

C₂

yes

maximal, characteristic

C₂×#63243

C₂²

yes

—

C₂×#63243

C₂²

yes

—

C₂×C₈×D₁₇

C₂²

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

C₄²×D₁₇

C₂²

yes

—

—

C₄

yes

complemented

#10587535

C₄

yes

complemented

C₁₇×#97

C₄

yes

characteristic

#10587486

C₄

yes

characteristic

#10587486

C₄

yes

characteristic

#10587474

C₄

yes

characteristic

C₂×C₄×D₁₇

Q₈

yes

—

C₂×C₄×D₁₇

C₂³

yes

—

—

—

—

C₂×C₄

yes

—

#63243

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

D₄

yes

—

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₈×D₁₇

—

C₈×D₁₇

—

C₈×D₁₇

C₂×C₄

yes

—

C₈×D₁₇

C₂×C₄

yes

—

C₂²×D₁₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₄⋊C₄

yes

—

C₂×Dic₁₇

C₂×D₄

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

C₂²×C₄

yes

characteristic

C₄×D₁₇

C₂²×C₄

yes

C₄×D₁₇

yes

C₄×D₁₇

yes

—

—

C₈×C₁₇

—

C₈×C₁₇

C₄²

yes

—

#3622

—

#3622

C₄²

yes

—

#1778

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₄×Q₈

yes

characteristic

C₂×D₁₇

C₄×Q₈

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄²

yes

characteristic

C₄×C₁₇

#117

yes

characteristic

Dic₁₇

—

Dic₁₇

C₄×D₄

yes

characteristic

Dic₁₇

C₄×D₄

yes

characteristic

C₂×#108

—

C₂×#108

—

C₄×M₁₆

—

C₂×#97

—

#341

—

C₂×C₁₇

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₇

#430

yes

—

D₁₇

—

D₁₇

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

—

—

—

—

—

—

yes

C₄×C₈

—

C₁₇

#1778

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

C₂×#595

yes

characteristic

103

C₂×C₈

C₂×#595

yes

characteristic

104

C₄²

—

105

C₄²

—

106

C₄²

C₂×#595

yes

characteristic

107

C₂³

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

C₄⋊#595

yes

—

116

C₂×C₄

C₂²×#595

yes

characteristic

117

C₈

—

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

122

C₈

C₄×#595

yes

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

C₂×C₄⋊#595

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

C₂×C₄×#595

yes

characteristic

132

C₄

#10587677

yes

characteristic

133

C₂

—

134

C₂

—

135

C₂

C₄×C₄⋊#595

yes

characteristic

136

C₂

#11763824

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#595
commutator	C₄×C₁₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×#595
Fitting	C₁₇×#97	C₄
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₇	C₂×Q₈
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	#97	#595
hypocenter	C₁₇	#1778
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#595

commutator

C₄×C₁₇

C₂×C₄²

Frattini

C₂×C₄

C₂²×#595

Fitting

C₁₇×#97

C₄

socle

C₂²×C₁₇

C₂×C₄⋊C₄

prime radical

C₂²×D₁₇

C₂×Q₈

cosocle

C₂×C₄×D₁₇

C₂³

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
13. #10587536	C₄	semidirect
14. #10587535	C₄	semidirect
87. C₁₇	#1778	semidirect

H ≅ G/N

type

13. #10587536

C₄

semidirect

14. #10587535

C₄

semidirect

87. C₁₇

#1778

semidirect

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

subgroup	index
C₂×#10587536	2
C₂×#10587535	2
C₄×#63243	2
#11763685	2
#97×D₁₇	2
#1778	17

subgroup

index

#97×D₁₇

Subgroups — #14544604

Conjugacy classes of subgroups

Complements

Maximal subgroups