Group #14544996 — subgroups

Subgroups — #14544996

Order 2176.

184 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 96 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×#10587529	C₂	1	1	yes	maximal, characteristic
2	#11763772	C₂	1	1	yes	maximal, characteristic
3	#11763696	C₂	1	2	yes	maximal, complemented
4	C₁₆×#595	C₂	1	2	yes	maximal, complemented
5	M₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
6	#10587677	C₄	1	1	yes	characteristic
7	D₁₇⋊M₁₆	C₄	1	1	yes	characteristic
8	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
9	C₂×#63216	C₄	1	2	yes	complemented
10	#10587532	C₄	1	2	yes	—
11	C₈×#595	C₂²	1	2	yes	—
12	#10587529	C₄	1	2	yes	complemented
13	#10587529	C₂²	1	1	yes	characteristic
14	#10587529	C₂²	1	1	yes	characteristic
15	C₁₇×M₃₂	C₄	1	1	yes	characteristic, complemented
16	#10587483	C₄	1	1	yes	characteristic, complemented
17	#10587469	C₄	1	2	yes	complemented
18	C₁₆×D₁₇	C₂²	1	2	yes	—
19	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂²⋊#595	C₈	1	2	yes	—
21	#63247	C₈	1	2	yes	—
22	C₄⋊#595	C₈	1	2	yes	—
23	C₄×#595	C₂×C₄	1	2	yes	—
24	#63243	C₈	1	2	yes	—
25	#63242	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
27	C₂×#3622	C₂×C₄	1	1	yes	characteristic
28	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
29	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
30	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
31	C₈×D₁₇	C₂³	1	1	yes	characteristic
32	#63216	C₂×C₄	1	2	yes	—
33	#63216	C₂×C₄	1	2	yes	—
34	C₁₆×C₁₇	C₂×C₄	1	2	yes	—
35	#63214	C₂×C₄	1	2	yes	—
36	C₂²×D₁₇	C₂×C₈	1	1	yes	characteristic
37	C₂×#595	C₂×C₈	1	4	yes	—
38	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
39	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
40	C₄×D₁₇	C₄²	1	1	yes	characteristic
41	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
42	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
43	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
44	#3624	C₂×C₈	1	4	yes	—
45	C₈×C₁₇	C₄²	1	1	yes	characteristic
46	C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
47	#3622	C₄²	1	1	yes	characteristic
48	#3622	C₂²×C₄	1	1	yes	characteristic
49	#2108	—	17	1	no	maximal, Sylow
50	C₂²×C₁₇	C₄×C₈	1	1	yes	characteristic
51	C₂×D₁₇	—	2	2	no	—
52	C₂×D₁₇	C₄×C₈	1	1	yes	characteristic
53	C₂×D₁₇	C₂²×C₈	1	1	yes	characteristic
54	#595	—	2	4	no	—
55	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
56	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
57	Dic₁₇	C₄×C₈	1	1	yes	characteristic
58	Dic₁₇	C₂²×C₈	1	1	yes	characteristic
59	C₂×M₃₂	—	17	1	no	—
60	C₂²×C₁₆	—	17	1	no	—
61	#405	—	17	1	no	—
62	#346	—	17	2	no	—
63	C₄×C₁₆	—	17	2	no	—
64	C₂×C₁₇	—	2	1	no	—
65	C₂×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
66	D₁₇	—	2	1	no	—
67	D₁₇	#504	1	2	yes	—
68	C₂×M₁₆	—	17	1	no	—
69	C₂²×C₈	—	17	1	no	—
70	#117	—	17	1	no	—
71	M₃₂	—	17	1	no	—
72	M₃₂	—	17	2	no	—
73	M₃₂	#595	1	1	yes	characteristic, complemented
74	C₂×C₁₆	—	17	1	no	—
75	C₂×C₁₆	—	17	1	no	—
76	C₂×C₁₆	—	17	2	no	—
77	C₂×C₁₆	—	17	2	no	—
78	C₂×C₁₆	—	17	2	no	—
79	#97	—	17	2	no	—
80	C₄×C₈	—	17	2	no	—
81	C₁₇	#2108	1	1	yes	characteristic, complemented, Sylow
82	C₂²×C₄	—	17	1	no	—
83	M₁₆	—	17	2	no	—
84	M₁₆	—	17	2	no	—
85	C₂×C₈	—	17	2	no	—
86	C₂×C₈	—	17	1	no	—
87	C₂×C₈	—	17	1	no	—
88	C₂×C₈	—	17	1	no	—
89	C₂×C₈	—	17	1	no	—
90	C₂×C₈	—	17	1	no	—
91	C₂×C₈	C₂×#595	1	1	yes	characteristic
92	C₄⋊C₄	—	17	2	no	—
93	C₂²⋊C₄	—	17	2	no	—
94	C₄²	—	17	2	no	—
95	C₁₆	—	17	2	no	—
96	C₁₆	—	17	2	no	—
97	C₁₆	—	17	2	no	—
98	C₁₆	C₂×#595	1	2	yes	—
99	C₂³	—	17	1	no	—
100	C₂×C₄	—	17	1	no	—
101	C₂×C₄	—	17	1	no	—
102	C₂×C₄	—	17	1	no	—
103	C₂×C₄	—	17	1	no	—
104	C₂×C₄	—	17	1	no	—
105	C₂×C₄	—	17	4	no	—
106	C₂×C₄	C₄×#595	1	1	yes	characteristic
107	C₈	—	17	4	no	—
108	C₈	—	17	1	no	—
109	C₈	—	17	1	no	—
110	C₈	C₄×#595	1	1	yes	characteristic
111	C₈	C₂²×#595	1	1	yes	characteristic
112	C₂²	—	17	1	no	—
113	C₂²	—	17	1	no	—
114	C₂²	—	34	2	no	—
115	C₂²	C₈×#595	1	1	yes	characteristic
116	C₄	—	17	1	no	—
117	C₄	—	17	1	no	—
118	C₄	—	34	4	no	—
119	C₄	C₈×#595	1	1	yes	characteristic
120	C₄	C₂×C₄×#595	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	17	2	no	—
123	C₂	—	34	1	no	—
124	C₂	C₂×C₈×#595	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587529

C₂

yes

maximal, characteristic

#11763772

C₂

yes

maximal, characteristic

#11763696

C₂

yes

maximal, complemented

C₁₆×#595

C₂

yes

maximal, complemented

M₃₂×D₁₇

C₂

yes

maximal, characteristic

#10587677

C₄

yes

characteristic

D₁₇⋊M₁₆

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

C₂×#63216

C₄

yes

complemented

#10587532

C₄

yes

—

C₈×#595

C₂²

yes

—

#10587529

C₄

yes

complemented

#10587529

C₂²

yes

characteristic

#10587529

C₂²

yes

characteristic

C₁₇×M₃₂

C₄

yes

characteristic, complemented

#10587483

C₄

yes

characteristic, complemented

#10587469

C₄

yes

complemented

C₁₆×D₁₇

C₂²

yes

—

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂²⋊#595

C₈

yes

—

#63247

C₈

yes

—

C₄⋊#595

C₈

yes

—

C₄×#595

C₂×C₄

yes

—

#63243

C₈

yes

—

#63242

C₂×C₄

yes

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂³

yes

characteristic

#63216

C₂×C₄

yes

—

#63216

C₂×C₄

yes

—

C₁₆×C₁₇

C₂×C₄

yes

—

#63214

C₂×C₄

yes

—

C₂²×D₁₇

C₂×C₈

yes

characteristic

C₂×#595

C₂×C₈

yes

—

C₂×C₄×C₁₇

C₄²

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

C₄²

yes

characteristic

C₄×D₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

C₂²×C₄

yes

characteristic

#3624

C₂×C₈

yes

—

C₈×C₁₇

C₄²

yes

characteristic

C₈×C₁₇

C₂²×C₄

yes

characteristic

#3622

C₄²

yes

characteristic

#3622

C₂²×C₄

yes

characteristic

#2108

—

maximal, Sylow

C₂²×C₁₇

C₄×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₄×C₈

yes

characteristic

C₂×D₁₇

C₂²×C₈

yes

characteristic

#595

—

C₄×C₁₇

C₄×C₈

yes

characteristic

C₄×C₁₇

C₂×C₄²

yes

characteristic

Dic₁₇

C₄×C₈

yes

characteristic

Dic₁₇

C₂²×C₈

yes

characteristic

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

C₄×C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₄×C₈

yes

characteristic

D₁₇

—

D₁₇

#504

yes

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

M₃₂

—

M₃₂

#595

yes

characteristic, complemented

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₁₇

#2108

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

C₂×#595

yes

—

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₄×#595

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

C₄×#595

yes

characteristic

111

C₈

C₂²×#595

yes

characteristic

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₈×#595

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

C₈×#595

yes

characteristic

120

C₄

C₂×C₄×#595

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

124

C₂

C₂×C₈×#595

yes

characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#595
commutator, socle	C₂×C₁₇	C₂×C₄×C₈
Fitting	C₁₇×M₃₂	C₄
prime radical	C₂²×D₁₇	C₂×C₈
cosocle	C₈×D₁₇	C₂³
hypercenter	M₃₂	#595
hypocenter	C₁₇	#2108
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ M₃₂

subgroup

G/H

center, Frattini

C₈

C₂²×#595

commutator, socle

C₂×C₁₇

C₂×C₄×C₈

Fitting

C₁₇×M₃₂

C₄

prime radical

C₂²×D₁₇

C₂×C₈

cosocle

C₈×D₁₇

C₂³

M₃₂

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₈ ◁ M₃₂

N	H ≅ G/N	type
3. #11763696	C₂	semidirect
4. C₁₆×#595	C₂	semidirect
9. C₂×#63216	C₄	semidirect
12. #10587529	C₄	semidirect
15. C₁₇×M₃₂	C₄	semidirect
16. #10587483	C₄	semidirect
17. #10587469	C₄	semidirect
73. M₃₂	#595	semidirect
81. C₁₇	#2108	semidirect

H ≅ G/N

type

3. #11763696

C₂

semidirect

4. C₁₆×#595

C₂

semidirect

9. C₂×#63216

C₄

semidirect

12. #10587529

C₄

semidirect

15. C₁₇×M₃₂

C₄

semidirect

16. #10587483

C₄

semidirect

17. #10587469

C₄

semidirect

73. M₃₂

#595

semidirect

81. C₁₇

#2108

semidirect

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

subgroup	index
C₂×#10587529	2
#11763772	2
#11763696	2
C₁₆×#595	2
M₃₂×D₁₇	2
#2108	17

subgroup

index

C₂×#10587529

#11763772

#11763696

C₁₆×#595

M₃₂×D₁₇

#2108

Subgroups — #14544996

Conjugacy classes of subgroups

Complements

Maximal subgroups