Group #14545947 — subgroups

Subgroups — #14545947

Order 2176.

184 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 93 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	#11763928	C₂	1	1	yes	maximal, characteristic
2	C₂×#10587665	C₂	1	1	yes	maximal, characteristic
3	#11763904	C₂	1	2	yes	maximal, complemented
4	#11763902	C₂	1	2	yes	maximal, complemented
5	#11763775	C₂	1	1	yes	maximal, characteristic
6	#10587677	C₄	1	1	yes	characteristic
7	C₂×#63242	C₂²	1	1	yes	characteristic
8	#10587670	C₄	1	2	yes	complemented
9	C₂×#63241	C₄	1	2	yes	complemented
10	#10587666	C₄	1	2	yes	complemented
11	#10587665	C₄	1	2	yes	complemented
12	#10587665	C₂²	1	1	yes	characteristic
13	#10587665	C₂²	1	2	yes	—
14	#10587665	C₂²	1	1	yes	characteristic
15	M₁₆×D₁₇	C₄	1	1	yes	characteristic
16	#10587532	C₄	1	2	yes	—
17	C₈×#595	C₂²	1	2	yes	—
18	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊#595	C₈	1	2	yes	—
20	C₂×#3624	C₂×C₄	1	1	yes	characteristic
21	C₂×#3624	C₂×C₄	1	1	yes	characteristic
22	C₄⋊#595	C₈	1	2	yes	—
23	C₄×#595	C₂×C₄	1	2	yes	—
24	#63242	C₂×C₄	1	1	yes	characteristic
25	#63242	C₂×C₄	1	1	yes	characteristic
26	#63242	C₂×C₄	1	1	yes	characteristic
27	#63242	C₂³	1	1	yes	characteristic
28	#63241	C₂×C₄	1	2	yes	—
29	#63241	C₂×C₄	1	2	yes	—
30	#63241	C₂×C₄	1	4	yes	—
31	M₁₆×C₁₇	C₈	1	1	yes	characteristic
32	#63223	C₈	1	1	yes	characteristic
33	#63218	C₈	1	2	yes	—
34	C₈×D₁₇	C₂×C₄	1	2	yes	—
35	C₂²×D₁₇	C₂×C₈	1	1	yes	characteristic
36	C₂×#595	C₂×C₈	1	4	yes	—
37	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
38	C₂×Dic₁₇	C₄²	1	1	yes	characteristic
39	C₄×D₁₇	C₄²	1	1	yes	characteristic
40	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
41	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
42	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
43	#3624	C₄²	1	1	yes	characteristic
44	#3624	C₄²	1	1	yes	characteristic
45	#3624	C₂²×C₄	1	1	yes	characteristic
46	#3624	C₂²×C₄	1	1	yes	characteristic
47	C₈×C₁₇	C₂×C₈	1	2	yes	—
48	#3622	C₂×C₈	1	2	yes	—
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	C₂²×C₈	1	1	yes	characteristic
57	Dic₁₇	C₄×C₈	1	1	yes	characteristic
58	Dic₁₇	C₂×C₄²	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	2	no	—
72	M₃₂	—	17	2	no	—
73	C₂×C₁₆	—	17	2	no	—
74	C₂×C₁₆	—	17	1	no	—
75	C₂×C₁₆	—	17	2	no	—
76	C₂×C₁₆	—	17	1	no	—
77	C₂×C₁₆	—	17	2	no	—
78	#97	—	17	2	no	—
79	C₄×C₈	—	17	2	no	—
80	C₁₇	#2108	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	—	17	1	no	—
82	M₁₆	—	17	1	no	—
83	M₁₆	—	17	2	no	—
84	M₁₆	#3633	1	1	yes	characteristic
85	C₂×C₈	—	17	1	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	—	17	2	no	—
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	4	no	—
98	C₂³	—	17	1	no	—
99	C₂×C₄	—	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	4	no	—
105	C₂×C₄	C₂×#3633	1	1	yes	characteristic
106	C₈	—	17	1	no	—
107	C₈	—	17	1	no	—
108	C₈	—	17	1	no	—
109	C₈	—	17	1	no	—
110	C₈	—	17	2	no	—
111	C₈	C₂×#3633	1	2	yes	—
112	C₂²	—	17	1	no	—
113	C₂²	—	17	1	no	—
114	C₂²	—	34	2	no	—
115	C₂²	C₄×#3633	1	1	yes	characteristic
116	C₄	—	17	1	no	—
117	C₄	—	17	1	no	—
118	C₄	—	34	4	no	—
119	C₄	C₄×#3633	1	1	yes	characteristic
120	C₄	C₂²×#3633	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	17	2	no	—
123	C₂	—	34	1	no	—
124	C₂	C₂×C₄×#3633	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763928

C₂

yes

maximal, characteristic

C₂×#10587665

C₂

yes

maximal, characteristic

#11763904

C₂

yes

maximal, complemented

#11763902

C₂

yes

maximal, complemented

#11763775

C₂

yes

maximal, characteristic

#10587677

C₄

yes

characteristic

C₂×#63242

C₂²

yes

characteristic

#10587670

C₄

yes

complemented

C₂×#63241

C₄

yes

complemented

#10587666

C₄

yes

complemented

#10587665

C₄

yes

complemented

#10587665

C₂²

yes

characteristic

#10587665

C₂²

yes

—

#10587665

C₂²

yes

characteristic

M₁₆×D₁₇

C₄

yes

characteristic

#10587532

C₄

yes

—

C₈×#595

C₂²

yes

—

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂²⋊#595

C₈

yes

—

C₂×#3624

C₂×C₄

yes

characteristic

C₂×#3624

C₂×C₄

yes

characteristic

C₄⋊#595

C₈

yes

—

C₄×#595

C₂×C₄

yes

—

#63242

C₂×C₄

yes

characteristic

#63242

C₂×C₄

yes

characteristic

#63242

C₂×C₄

yes

characteristic

#63242

C₂³

yes

characteristic

#63241

C₂×C₄

yes

—

#63241

C₂×C₄

yes

—

#63241

C₂×C₄

yes

—

M₁₆×C₁₇

C₈

yes

characteristic

#63223

C₈

yes

characteristic

#63218

C₈

yes

—

C₈×D₁₇

C₂×C₄

yes

—

C₂²×D₁₇

C₂×C₈

yes

characteristic

C₂×#595

C₂×C₈

yes

—

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

C₄²

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

C₄²

yes

characteristic

#3624

C₄²

yes

characteristic

#3624

C₂²×C₄

yes

characteristic

#3624

C₂²×C₄

yes

characteristic

C₈×C₁₇

C₂×C₈

yes

—

#3622

C₂×C₈

yes

—

#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

C₂²×C₈

yes

characteristic

Dic₁₇

C₄×C₈

yes

characteristic

Dic₁₇

C₂×C₄²

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

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

C₄×C₈

—

C₁₇

#2108

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

#3633

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×#3633

yes

characteristic

106

C₈

—

107

C₈

—

108

C₈

—

109

C₈

—

110

C₈

—

111

C₈

C₂×#3633

yes

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₄×#3633

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

C₄×#3633

yes

characteristic

120

C₄

C₂²×#3633

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

124

C₂

C₂×C₄×#3633

yes

characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#3633
commutator, socle	C₂×C₁₇	C₂×C₄×C₈
Fitting	M₁₆×C₁₇	C₈
prime radical	C₂²×D₁₇	C₂×C₈
cosocle	#63242	C₂³
hypercenter	M₁₆	#3633
hypocenter	C₁₇	#2108
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ M₁₆

subgroup

G/H

center, Frattini

C₄

C₂²×#3633

commutator, socle

C₂×C₁₇

C₂×C₄×C₈

Fitting

M₁₆×C₁₇

C₈

prime radical

C₂²×D₁₇

C₂×C₈

C₂³

M₁₆

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₄ ◁ M₁₆

N	H ≅ G/N	type
3. #11763904	C₂	semidirect
4. #11763902	C₂	semidirect
8. #10587670	C₄	semidirect
9. C₂×#63241	C₄	semidirect
10. #10587666	C₄	semidirect
11. #10587665	C₄	semidirect
80. C₁₇	#2108	semidirect

H ≅ G/N

type

3. #11763904

C₂

semidirect

4. #11763902

C₂

semidirect

8. #10587670

C₄

semidirect

9. C₂×#63241

C₄

semidirect

10. #10587666

C₄

semidirect

11. #10587665

C₄

semidirect

80. C₁₇

#2108

semidirect

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

subgroup	index
#11763928	2
C₂×#10587665	2
#11763904	2
#11763902	2
#11763775	2
#2108	17

subgroup

index

Subgroups — #14545947

Conjugacy classes of subgroups

Complements

Maximal subgroups