Group #14544592 — subgroups

Subgroups — #14544592

Order 2176.

224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 90 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	#11763774	C₂	1	2	yes	maximal
3	C₂×#10587532	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	#10587542	—	2	2	no	—
12	C₄×#3624	—	2	2	no	—
13	#10587536	C₄	1	4	yes	complemented
14	#10587532	C₄	1	4	yes	complemented
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	C₂×C₄	1	2	yes	—
24	#63243	—	2	2	no	—
25	#63243	C₂×C₄	1	4	yes	—
26	#63242	C₂×C₄	1	2	yes	—
27	#63242	Q₈	1	2	yes	—
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	C₂×C₄	1	2	yes	—
35	C₈×D₁₇	C₂×C₄	1	2	yes	—
36	C₂²×D₁₇	#41	1	1	yes	characteristic
37	C₂×#595	—	2	2	no	—
38	C₂×#595	—	4	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	C₂²×C₄	1	1	yes	characteristic
44	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
45	C₄×D₁₇	C₂×Q₈	1	1	yes	characteristic
46	C₄×D₁₇	#41	1	1	yes	characteristic
47	#3624	—	2	4	no	—
48	#3624	C₄⋊C₄	1	4	yes	—
49	C₈×C₁₇	C₄²	1	2	yes	—
50	#3622	C₄²	1	2	yes	—
51	#1773	—	17	1	no	maximal, Sylow
52	C₂²×C₁₇	C₄×D₄	1	1	yes	characteristic
53	C₂×D₁₇	—	2	2	no	—
54	C₂×D₁₇	#117	1	1	yes	characteristic
55	C₂×D₁₇	C₄×Q₈	1	1	yes	characteristic
56	#595	—	4	2	no	—
57	C₄×C₁₇	—	4	2	no	—
58	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
59	C₄×C₁₇	C₄×Q₈	1	1	yes	characteristic
60	Dic₁₇	—	4	2	no	—
61	Dic₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
62	Dic₁₇	C₄×D₄	1	1	yes	characteristic
63	C₂×#108	—	17	1	no	—
64	#427	—	17	1	no	—
65	#405	—	17	2	no	—
66	C₂×#97	—	17	1	no	—
67	#339	—	17	2	no	—
68	C₂×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₁₇	#444	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	—	17	4	no	—
78	#107	—	17	2	no	—
79	#106	—	17	1	no	—
80	#106	#595	1	1	yes	characteristic, complemented
81	#97	—	17	4	no	—
82	#97	—	34	2	no	—
83	C₄×C₈	—	34	2	no	—
84	C₁₇	#1773	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₄	—	17	1	no	—
86	C₂²×C₄	—	34	1	no	—
87	M₁₆	—	17	4	no	—
88	M₁₆	—	34	2	no	—
89	C₂×C₈	—	17	2	no	—
90	C₂×C₈	—	17	2	no	—
91	C₂×C₈	—	17	2	no	—
92	C₂×C₈	—	17	1	no	—
93	C₂×C₈	—	17	2	no	—
94	C₂×C₈	—	17	2	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	2	no	—
112	C₂×C₄	—	68	2	no	—
113	C₂×C₄	C₂²×#595	1	1	yes	characteristic
114	C₈	—	17	4	no	—
115	C₈	—	17	2	no	—
116	C₈	—	34	4	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	—	68	2	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	C₄⋊C₄×#595	1	1	yes	characteristic
132	C₂	#11763854	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587536

C₂

yes

maximal, characteristic

#11763774

C₂

yes

maximal

C₂×#10587532

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

—

#10587542

—

C₄×#3624

—

#10587536

C₄

yes

complemented

#10587532

C₄

yes

complemented

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

C₂×C₄

yes

—

#63243

—

#63243

C₂×C₄

yes

—

#63242

C₂×C₄

yes

—

#63242

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

C₂×C₄

yes

—

C₈×D₁₇

C₂×C₄

yes

—

C₂²×D₁₇

yes

—

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂×D₄

yes

characteristic

C₄×D₁₇

C₂²×C₄

yes

characteristic

C₄×D₁₇

C₂²×C₄

yes

characteristic

C₄×D₁₇

C₂×Q₈

yes

C₄×D₁₇

yes

—

C₄⋊C₄

yes

—

C₈×C₁₇

C₄²

yes

—

#3622

C₄²

yes

—

#1773

—

maximal, Sylow

C₂²×C₁₇

C₄×D₄

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

#117

yes

characteristic

C₂×D₁₇

C₄×Q₈

yes

characteristic

#595

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄²

yes

characteristic

C₄×C₁₇

C₄×Q₈

yes

characteristic

Dic₁₇

—

Dic₁₇

C₂×C₄⋊C₄

yes

characteristic

Dic₁₇

C₄×D₄

yes

—

—

—

C₂×#97

—

#339

—

C₂×C₁₇

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₇

#444

yes

—

D₁₇

—

D₁₇

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

#117

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

#97

—

#97

—

C₄×C₈

—

C₁₇

#1773

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

C₄⋊C₄×#595

yes

characteristic

132

C₂

#11763854

yes

—

	subgroup	G/H
center	C₂²	D₄×#595
commutator	C₄×C₁₇	C₂×C₄²
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	#1773
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

subgroup

G/H

center

C₂²

D₄×#595

commutator

C₄×C₁₇

C₂×C₄²

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 ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

N	H ≅ G/N	type
13. #10587536	C₄	semidirect
14. #10587532	C₄	semidirect
15. C₁₇×#106	C₄	semidirect
16. #10587488	C₄	semidirect
17. #10587478	C₄	semidirect
80. #106	#595	semidirect
84. C₁₇	#1773	semidirect

H ≅ G/N

type

13. #10587536

C₄

semidirect

14. #10587532

C₄

semidirect

15. C₁₇×#106

C₄

semidirect

16. #10587488

C₄

semidirect

17. #10587478

C₄

semidirect

80. #106

#595

semidirect

84. C₁₇

#1773

semidirect

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

subgroup	index
C₂×#10587536	2
#11763774	2
C₂×#10587532	2
#11763679	2
#11762844	2
#1773	17

subgroup

index

Subgroups — #14544592

Conjugacy classes of subgroups

Complements

Maximal subgroups