Group #14544966 — subgroups

Subgroups — #14544966

Order 2176.

252 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 78 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	C₄×#63242	C₂	1	1	yes	maximal, characteristic
2	#11763753	C₂	1	1	yes	maximal, characteristic
3	#11763682	C₂	1	4	yes	maximal
4	#125×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊#595	C₂²	1	2	yes	—
6	C₂×#63242	C₂²	1	2	yes	—
7	C₁₇×#125	C₄	1	1	yes	characteristic, complemented
8	C₄⋊C₄×D₁₇	—	2	2	no	—
9	C₄⋊C₄×D₁₇	C₂²	1	2	yes	—
10	#10587576	C₄	1	2	yes	complemented
11	#10587575	—	2	2	no	—
12	C₄²×D₁₇	C₂²	1	1	yes	characteristic
13	#10587556	C₄	1	1	yes	characteristic, complemented
14	(C₂×#595)⋊C₄	—	2	2	no	—
15	C₄×#3624	—	2	2	no	—
16	C₂²×#595	—	2	2	no	—
17	C₂×C₄×D₁₇	—	2	2	no	—
18	C₂×C₄×D₁₇	D₄	1	2	yes	—
19	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
20	C₂×#3624	—	2	2	no	—
21	C₄⋊#595	—	2	4	no	—
22	#63242	—	2	2	no	—
23	#63242	Q₈	1	4	yes	—
24	C₄⋊C₄×C₁₇	—	2	2	no	—
25	C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
26	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
27	C₄⋊Dic₁₇	—	2	2	no	—
28	C₄⋊Dic₁₇	C₂×C₄	1	2	yes	—
29	#63225	—	2	2	no	—
30	#63225	—	2	2	no	—
31	#63225	—	2	2	no	—
32	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
33	C₄×Dic₁₇	D₄	1	2	yes	—
34	C₂²×D₁₇	C₂×D₄	1	1	yes	characteristic
35	C₂×#595	—	4	2	no	—
36	C₂×#595	—	4	4	no	—
37	C₂×C₄×C₁₇	—	2	2	no	—
38	C₂×C₄×C₁₇	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₁₇	—	2	2	no	—
41	C₂×Dic₁₇	C₂²⋊C₄	1	2	yes	—
42	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
43	C₄×D₁₇	—	2	4	no	—
44	C₄×D₁₇	—	4	4	no	—
45	C₄×D₁₇	C₂×Q₈	1	2	yes	—
46	C₄×D₁₇	#41	1	2	yes	—
47	#3624	—	2	4	no	—
48	#1991	—	17	1	no	maximal, Sylow
49	C₂²×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
50	C₂×D₁₇	#124	1	1	yes	characteristic
51	C₂×D₁₇	C₄⋊Q₈	1	1	yes	characteristic
52	C₂×D₁₇	#135	1	4	yes	—
53	#595	—	8	2	no	—
54	C₄×C₁₇	—	2	2	no	—
55	C₄×C₁₇	—	4	2	no	—
56	C₄×C₁₇	C₄×Q₈	1	2	yes	—
57	Dic₁₇	—	2	2	no	—
58	Dic₁₇	—	4	2	no	—
59	Dic₁₇	C₂²⋊Q₈	1	2	yes	—
60	C₂×#125	—	17	1	no	—
61	C₂×C₄×C₈	—	17	1	no	—
62	#382	—	17	1	no	—
63	#340	—	17	4	no	—
64	C₂×C₁₇	#391	1	1	yes	characteristic
65	C₂×C₁₇	#416	1	2	yes	—
66	D₁₇	#488	1	2	yes	—
67	D₁₇	#499	1	2	yes	—
68	C₂²×C₈	—	17	2	no	—
69	#125	—	17	2	no	—
70	#125	—	17	1	no	—
71	#125	—	34	2	no	—
72	#125	#595	1	1	yes	characteristic, complemented
73	C₂×C₄⋊C₄	—	17	2	no	—
74	C₂×C₄⋊C₄	—	17	2	no	—
75	C₂×C₄⋊C₄	—	34	2	no	—
76	C₂×C₄²	—	17	1	no	—
77	C₄×C₈	—	34	2	no	—
78	#95	—	34	2	no	—
79	C₁₇	#1991	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₄	—	17	1	no	—
81	C₂²×C₄	—	17	2	no	—
82	C₂²×C₄	—	34	2	no	—
83	C₂²×C₄	—	34	2	no	—
84	C₂×C₈	—	17	4	no	—
85	C₂×C₈	—	34	2	no	—
86	C₂×C₈	—	34	2	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	17	2	no	—
89	C₄⋊C₄	—	34	2	no	—
90	C₄⋊C₄	—	34	2	no	—
91	C₄⋊C₄	—	34	2	no	—
92	C₄⋊C₄	—	34	4	no	—
93	C₄⋊C₄	—	34	2	no	—
94	C₄⋊C₄	C₂×#595	1	2	yes	—
95	C₄²	—	17	2	no	—
96	C₄²	—	17	1	no	—
97	C₄²	C₂×#595	1	1	yes	characteristic
98	C₂³	—	17	1	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	17	1	no	—
101	C₂×C₄	—	17	2	no	—
102	C₂×C₄	—	17	2	no	—
103	C₂×C₄	—	17	2	no	—
104	C₂×C₄	—	34	4	no	—
105	C₂×C₄	—	34	2	no	—
106	C₂×C₄	—	68	4	no	—
107	C₂×C₄	—	68	2	no	—
108	C₂×C₄	—	68	4	no	—
109	C₂×C₄	C₂²⋊#595	1	2	yes	—
110	C₂×C₄	C₂²×#595	1	1	yes	characteristic
111	C₈	—	34	4	no	—
112	C₂²	—	17	1	no	—
113	C₂²	—	17	1	no	—
114	C₂²	—	17	4	no	—
115	C₂²	C₂×C₂²⋊#595	1	1	yes	characteristic
116	C₄	—	2	2	no	—
117	C₄	—	4	2	no	—
118	C₄	—	17	2	no	—
119	C₄	—	34	2	no	—
120	C₄	—	68	2	no	—
121	C₄	—	136	2	no	—
122	C₄	Q₈×#595	1	2	yes	—
123	C₂	—	17	2	no	—
124	C₂	—	17	2	no	—
125	C₂	(C₂×#595)⋊Q₈	1	1	yes	characteristic
126	C₂	#11763799	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#63242

C₂

yes

maximal, characteristic

#11763753

C₂

yes

maximal, characteristic

#11763682

C₂

yes

maximal

#125×D₁₇

C₂

yes

maximal, characteristic

C₂×C₄⋊#595

C₂²

yes

—

C₂×#63242

C₂²

yes

—

C₁₇×#125

C₄

yes

characteristic, complemented

C₄⋊C₄×D₁₇

—

C₄⋊C₄×D₁₇

C₂²

yes

—

#10587576

C₄

yes

complemented

#10587575

—

C₄²×D₁₇

C₂²

yes

characteristic

#10587556

C₄

yes

characteristic, complemented

(C₂×#595)⋊C₄

—

C₄×#3624

—

C₂²×#595

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

D₄

yes

—

C₂×C₄×D₁₇

C₂³

yes

—

—

—

Q₈

yes

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

C₂×C₄

yes

—

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

C₂×C₄

yes

—

#63225

—

#63225

—

#63225

—

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

D₄

yes

—

C₂²×D₁₇

C₂×D₄

yes

characteristic

C₂×#595

—

C₂×#595

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²⋊C₄

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂²⋊C₄

yes

—

C₂×Dic₁₇

C₂×D₄

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

C₂×Q₈

yes

—

C₄×D₁₇

#41

yes

—

#3624

—

#1991

—

maximal, Sylow

C₂²×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₁₇

#124

yes

characteristic

C₂×D₁₇

C₄⋊Q₈

yes

characteristic

C₂×D₁₇

#135

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

C₄×Q₈

yes

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

C₂²⋊Q₈

yes

—

C₂×#125

—

C₂×C₄×C₈

—

#382

—

#340

—

C₂×C₁₇

#391

yes

characteristic

C₂×C₁₇

#416

yes

—

D₁₇

#488

yes

—

D₁₇

#499

yes

—

C₂²×C₈

—

—

—

—

yes

characteristic, complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄×C₈

—

#95

—

C₁₇

#1991

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#595

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂²⋊#595

yes

—

110

C₂×C₄

C₂²×#595

yes

characteristic

111

C₈

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂×C₂²⋊#595

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

136

—

122

C₄

Q₈×#595

yes

—

123

C₂

—

124

C₂

—

125

C₂

(C₂×#595)⋊Q₈

yes

characteristic

126

C₂

#11763799

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₁₇×#125	C₄
socle	C₂²×C₁₇	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₇	C₂×D₄
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	#125	#595
hypocenter	C₁₇	#1991
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

subgroup

G/H

center

C₂²

C₂×C₂²⋊#595

commutator

C₂×C₄×C₁₇

C₂²×C₄

Frattini

C₂×C₄

C₂²×#595

Fitting

C₁₇×#125

C₄

socle

C₂²×C₁₇

C₂×C₂²⋊C₄

prime radical

C₂²×D₁₇

C₂×D₄

cosocle

C₂×C₄×D₁₇

C₂³

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #125

N	H ≅ G/N	type
7. C₁₇×#125	C₄	semidirect
10. #10587576	C₄	semidirect
13. #10587556	C₄	semidirect
72. #125	#595	semidirect
79. C₁₇	#1991	semidirect

H ≅ G/N

type

7. C₁₇×#125

C₄

semidirect

10. #10587576

C₄

semidirect

13. #10587556

C₄

semidirect

72. #125

#595

semidirect

79. C₁₇

#1991

semidirect

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

subgroup	index
C₄×#63242	2
#11763753	2
#11763682	2
#125×D₁₇	2
#1991	17

subgroup

index

#125×D₁₇

Subgroups — #14544966

Conjugacy classes of subgroups

Complements

Maximal subgroups