Group #11763521 — subgroups

Subgroups — #11763521

Order 1088.

236 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 95 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	C₁₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	#10587633	C₂	1	1	yes	maximal, characteristic, complemented
3	#10587630	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587625	C₂	1	2	yes	maximal, complemented
5	#10587571	C₂	1	2	yes	maximal, complemented
6	#10587570	C₂	1	2	yes	maximal, complemented
7	#10587567	C₂	1	2	yes	maximal, complemented
8	#10587563	C₂	1	2	yes	maximal, complemented
9	#10587558	C₂	1	2	yes	maximal, complemented
10	C₂×Q₈×C₁₇	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₁₇	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊D₁₇	C₂²	1	2	yes	—
13	C₂×C₂²⋊D₁₇	C₂²	1	2	yes	—
14	C₂²×Dic₁₇	C₂²	1	2	yes	—
15	C₂×D₆₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₁₇	C₂²	1	2	yes	—
17	C₂×Dic₃₄	C₂²	1	1	yes	characteristic
18	C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
19	C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
20	C₄²×C₁₇	C₂²	1	1	yes	characteristic
21	C₂²⋊Dic₁₇	C₂²	1	2	yes	—
22	#63227	C₂²	1	2	yes	—
23	#63227	C₂²	1	2	yes	—
24	#63227	C₂²	1	2	yes	—
25	#63225	C₂²	1	2	yes	—
26	#63225	C₂²	1	2	yes	—
27	#63225	C₂²	1	2	yes	—
28	C₄×Dic₁₇	C₂²	1	2	yes	—
29	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
30	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
31	C₂³×C₁₇	C₂³	1	2	yes	—
32	C₂²×D₁₇	C₂³	1	2	yes	—
33	Q₈×C₁₇	—	4	1	no	—
34	D₄×C₁₇	—	4	1	no	—
35	C₂×C₄×C₁₇	C₂³	1	2	yes	—
36	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
37	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
38	C₂×C₄×C₁₇	C₂³	1	1	yes	characteristic
39	C₂²⋊D₁₇	—	2	4	no	—
40	C₂²⋊D₁₇	—	4	2	no	—
41	C₂×Dic₁₇	—	2	4	no	—
42	C₂×Dic₁₇	C₂³	1	2	yes	—
43	C₂×Dic₁₇	C₂³	1	2	yes	—
44	C₂×Dic₁₇	C₂³	1	2	yes	—
45	D₆₈	—	4	1	no	—
46	C₄×D₁₇	—	2	4	no	—
47	Dic₃₄	—	4	1	no	—
48	C₂²×C₁₇	—	2	2	no	—
49	C₂²×C₁₇	—	2	2	no	—
50	C₂²×C₁₇	—	2	2	no	—
51	C₂²×C₁₇	C₂⁴	1	1	yes	characteristic
52	C₂×D₁₇	—	2	2	no	—
53	C₂×D₁₇	—	2	2	no	—
54	C₂×D₁₇	—	2	2	no	—
55	C₄×C₁₇	—	2	2	no	—
56	C₄×C₁₇	—	2	1	no	—
57	C₄×C₁₇	—	2	1	no	—
58	C₄×C₁₇	—	2	1	no	—
59	Dic₁₇	—	2	2	no	—
60	Dic₁₇	—	2	2	no	—
61	Dic₁₇	#41	1	4	yes	—
62	#555	—	17	1	no	maximal, Sylow
63	C₂×C₁₇	—	4	2	no	—
64	C₂×C₁₇	C₂×#41	1	2	yes	—
65	C₂×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
66	D₁₇	—	4	2	no	—
67	C₄⋊Q₈	—	17	1	no	—
68	#124	—	17	1	no	—
69	#124	—	17	2	no	—
70	#124	D₁₇	1	1	yes	characteristic, complemented
71	#121	—	17	2	no	—
72	#121	—	17	2	no	—
73	C₄×D₄	—	17	2	no	—
74	#117	—	17	2	no	—
75	#117	—	17	2	no	—
76	C₁₇	#555	1	1	yes	characteristic, complemented, Sylow
77	C₂×Q₈	—	17	1	no	—
78	C₂×Q₈	C₂×D₁₇	1	1	yes	characteristic
79	C₂×D₄	—	17	2	no	—
80	C₂×D₄	—	17	2	no	—
81	C₂×D₄	—	17	1	no	—
82	C₂×D₄	C₂×D₁₇	1	1	yes	characteristic
83	C₂²×C₄	—	17	2	no	—
84	C₂²×C₄	—	17	2	no	—
85	C₄⋊C₄	—	17	2	no	—
86	C₄⋊C₄	—	17	2	no	—
87	C₄⋊C₄	—	17	2	no	—
88	C₂²⋊C₄	—	17	2	no	—
89	C₂²⋊C₄	—	17	2	no	—
90	C₂²⋊C₄	—	17	2	no	—
91	C₂²⋊C₄	—	17	2	no	—
92	C₂²⋊C₄	C₂×D₁₇	1	2	yes	—
93	C₂²⋊C₄	C₂×D₁₇	1	2	yes	—
94	C₄²	—	17	1	no	—
95	C₄²	—	17	2	no	—
96	C₄²	—	17	1	no	—
97	C₄²	C₂×D₁₇	1	1	yes	characteristic
98	C₂³	—	17	2	no	—
99	C₂³	C₂²×D₁₇	1	2	yes	—
100	Q₈	—	4	1	no	—
101	Q₈	—	68	1	no	—
102	D₄	—	4	1	no	—
103	D₄	—	34	4	no	—
104	D₄	—	68	1	no	—
105	D₄	—	68	2	no	—
106	C₂×C₄	—	17	2	no	—
107	C₂×C₄	—	17	2	no	—
108	C₂×C₄	—	17	2	no	—
109	C₂×C₄	—	34	4	no	—
110	C₂×C₄	—	34	4	no	—
111	C₂×C₄	C₂²×D₁₇	1	2	yes	—
112	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
113	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
114	C₂×C₄	C₂²×D₁₇	1	1	yes	characteristic
115	C₂²	—	2	2	no	—
116	C₂²	—	2	2	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	34	2	no	—
119	C₂²	—	34	2	no	—
120	C₂²	—	34	2	no	—
121	C₂²	C₂³×D₁₇	1	1	yes	characteristic
122	C₄	—	2	1	no	—
123	C₄	—	2	1	no	—
124	C₄	—	2	1	no	—
125	C₄	—	2	2	no	—
126	C₄	—	17	4	no	—
127	C₄	—	34	2	no	—
128	C₄	—	34	2	no	—
129	C₂	—	4	2	no	—
130	C₂	—	68	2	no	—
131	C₂	#10587691	1	1	yes	characteristic
132	C₂	#41×D₁₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₇×#124

C₂

yes

maximal, characteristic, complemented

#10587633

C₂

yes

maximal, characteristic, complemented

#10587630

C₂

yes

maximal, characteristic, complemented

#10587625

C₂

yes

maximal, complemented

#10587571

C₂

yes

maximal, complemented

#10587570

C₂

yes

maximal, complemented

#10587567

C₂

yes

maximal, complemented

#10587563

C₂

yes

maximal, complemented

#10587558

C₂

yes

maximal, complemented

C₂×Q₈×C₁₇

C₂²

yes

characteristic

C₂×D₄×C₁₇

C₂²

yes

characteristic

C₂×C₂²⋊D₁₇

C₂²

yes

—

C₂×C₂²⋊D₁₇

C₂²

yes

—

C₂²×Dic₁₇

C₂²

yes

—

C₂×D₆₈

C₂²

yes

characteristic

C₂×C₄×D₁₇

C₂²

yes

—

C₂×Dic₃₄

C₂²

yes

characteristic

C₂²⋊C₄×C₁₇

C₂²

yes

—

C₂²⋊C₄×C₁₇

C₂²

yes

—

C₄²×C₁₇

C₂²

yes

characteristic

C₂²⋊Dic₁₇

C₂²

yes

—

#63227

C₂²

yes

—

#63227

C₂²

yes

—

#63227

C₂²

yes

—

#63225

C₂²

yes

—

#63225

C₂²

yes

—

#63225

C₂²

yes

—

C₄×Dic₁₇

C₂²

yes

—

C₄×Dic₁₇

C₂²

yes

characteristic

C₄×Dic₁₇

C₂²

yes

characteristic

C₂³×C₁₇

C₂³

yes

—

C₂²×D₁₇

C₂³

yes

—

Q₈×C₁₇

—

D₄×C₁₇

—

C₂×C₄×C₁₇

C₂³

yes

—

C₂×C₄×C₁₇

C₂³

yes

characteristic

C₂×C₄×C₁₇

C₂³

yes

characteristic

C₂×C₄×C₁₇

C₂³

yes

characteristic

C₂²⋊D₁₇

—

C₂²⋊D₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂³

yes

—

C₂×Dic₁₇

C₂³

yes

—

C₂×Dic₁₇

C₂³

yes

—

D₆₈

—

C₄×D₁₇

—

Dic₃₄

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

C₂⁴

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

#41

yes

—

#555

—

maximal, Sylow

C₂×C₁₇

—

C₂×C₁₇

C₂×#41

yes

—

C₂×C₁₇

H(5,𝔽₂)

yes

characteristic

D₁₇

—

C₄⋊Q₈

—

#124

—

#124

—

#124

D₁₇

yes

characteristic, complemented

#121

—

#121

—

C₄×D₄

—

#117

—

#117

—

C₁₇

#555

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂×D₁₇

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×D₁₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×D₁₇

yes

—

C₂²⋊C₄

C₂×D₁₇

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×D₁₇

yes

characteristic

C₂³

—

C₂³

C₂²×D₁₇

yes

—

100

Q₈

—

101

Q₈

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₂²×D₁₇

yes

—

112

C₂×C₄

C₂²×D₁₇

yes

characteristic

113

C₂×C₄

C₂²×D₁₇

yes

characteristic

114

C₂×C₄

C₂²×D₁₇

yes

characteristic

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂³×D₁₇

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₂

—

130

C₂

—

131

C₂

#10587691

yes

characteristic

132

C₂

#41×D₁₇

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁴
Fitting	C₁₇×#124	C₂
hypercenter	#124	D₁₇
hypocenter	C₁₇	#555
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #124

subgroup

G/H

center, Frattini

C₂²

C₂³×D₁₇

commutator, socle, cosocle

C₂²×C₁₇

C₂⁴

Fitting

C₁₇×#124

C₂

D₁₇

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂² ◁ #124

N	H ≅ G/N	type
1. C₁₇×#124	C₂	semidirect
2. #10587633	C₂	semidirect
3. #10587630	C₂	semidirect
4. #10587625	C₂	semidirect
5. #10587571	C₂	semidirect
6. #10587570	C₂	semidirect
7. #10587567	C₂	semidirect
8. #10587563	C₂	semidirect
9. #10587558	C₂	semidirect
70. #124	D₁₇	semidirect
76. C₁₇	#555	semidirect

H ≅ G/N

type

1. C₁₇×#124

C₂

semidirect

2. #10587633

C₂

semidirect

3. #10587630

C₂

semidirect

4. #10587625

C₂

semidirect

5. #10587571

C₂

semidirect

6. #10587570

C₂

semidirect

7. #10587567

C₂

semidirect

8. #10587563

C₂

semidirect

9. #10587558

C₂

semidirect

70. #124

D₁₇

semidirect

76. C₁₇

#555

semidirect

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

subgroup	index
C₁₇×#124	2
#10587633	2
#10587630	2
#10587625	2
#10587571	2
#10587570	2
#10587567	2
#10587563	2
#10587558	2
#555	17

subgroup

index

C₁₇×#124

Subgroups — #11763521

Conjugacy classes of subgroups

Complements

Maximal subgroups