Group #17960412 — subgroups

Subgroups — #17960412

Order 4352.

226 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 62 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	#14544434	C₂	1	2	yes	maximal, complemented
2	#14543808	C₂	1	1	yes	maximal, characteristic, complemented
3	#14543742	C₂	1	2	yes	maximal, complemented
4	#14543700	C₂	1	1	yes	maximal, characteristic, complemented
5	#14530660	C₂	1	1	yes	maximal, characteristic
6	#11763844	—	2	2	no	—
7	#11763698	C₂²	1	1	yes	characteristic
8	#11763670	C₂²	1	2	yes	—
9	D₄⋊#3624	—	2	2	no	—
10	#11763650	C₂²	1	1	yes	characteristic
11	D₈×Dic₁₇	C₂²	1	2	yes	—
12	#11762637	C₄	1	1	yes	characteristic
13	#11762610	C₄	1	2	yes	—
14	#11762584	C₂²	1	1	yes	characteristic
15	C₂×C₁₇×D₁₆	C₄	1	1	yes	characteristic
16	C₂×#63247	—	4	2	no	—
17	C₂×D₈×C₁₇	C₂×C₄	1	2	yes	—
18	D₄×Dic₁₇	—	2	2	no	—
19	C₂²⋊#3624	—	4	2	no	—
20	C₄⋊#3624	—	2	2	no	—
21	C₄×#3624	D₄	1	2	yes	—
22	C₂×#63216	—	2	1	no	—
23	C₁₇×D₁₆	—	2	2	no	—
24	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
25	#10587503	—	2	2	no	—
26	#10587489	C₂×C₄	1	2	yes	—
27	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
28	C₂×#63214	C₂×C₄	1	1	yes	characteristic
29	C₂×D₄×C₁₇	—	2	2	no	—
30	C₂²×Dic₁₇	—	4	2	no	—
31	#63247	—	8	4	no	—
32	C₂×#3624	—	2	2	no	—
33	C₂×#3624	—	4	2	no	—
34	D₈×C₁₇	—	2	2	no	—
35	D₈×C₁₇	—	2	2	no	—
36	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₂²⋊Dic₁₇	—	4	2	no	—
38	C₄⋊Dic₁₇	—	2	2	no	—
39	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
40	C₂×#3622	#41	1	1	yes	characteristic
41	#63216	—	4	1	no	—
42	C₁₆×C₁₇	M₁₆	1	2	yes	complemented
43	#63214	—	2	1	no	—
44	#12089	—	17	1	no	maximal, Sylow
45	C₂³×C₁₇	—	4	2	no	—
46	D₄×C₁₇	—	4	2	no	—
47	D₄×C₁₇	—	4	2	no	—
48	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
49	C₂×Dic₁₇	—	4	2	no	—
50	C₂×Dic₁₇	—	8	2	no	—
51	C₂×Dic₁₇	—	8	2	no	—
52	C₂×Dic₁₇	AGL(1,ℤ/8)	1	2	yes	—
53	#3624	—	4	2	no	—
54	#3624	—	8	2	no	—
55	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
56	C₈×C₁₇	#131	1	1	yes	characteristic
57	#3622	—	2	1	no	—
58	#2177	—	17	1	no	—
59	#1594	—	17	2	no	—
60	#1368	—	17	1	no	—
61	#1333	—	17	2	no	—
62	#1313	—	17	1	no	—
63	C₂²×C₁₇	—	8	2	no	—
64	C₂²×C₁₇	—	8	2	no	—
65	C₂²×C₁₇	—	8	2	no	—
66	C₂²×C₁₇	#442	1	1	yes	characteristic
67	C₄×C₁₇	#436	1	1	yes	characteristic
68	C₄×C₁₇	#444	1	1	yes	characteristic
69	Dic₁₇	—	2	2	no	—
70	Dic₁₇	—	8	2	no	—
71	C₂×D₁₆	#595	1	1	yes	characteristic
72	C₄×D₈	—	17	2	no	—
73	#436	—	34	2	no	—
74	#367	—	17	1	no	—
75	#357	—	17	2	no	—
76	#346	—	17	1	no	—
77	#346	—	17	1	no	—
78	#334	—	17	2	no	—
79	D₄⋊C₈	—	34	2	no	—
80	#322	—	17	1	no	—
81	C₂×C₁₇	—	16	2	no	—
82	C₂×C₁₇	#1594	1	1	yes	characteristic
83	C₂×C₁₇	AGL(1,ℤ/16)	1	2	yes	—
84	C₂×D₈	C₂×#595	1	2	yes	—
85	C₂×M₁₆	—	68	2	no	—
86	C₄×D₄	—	34	2	no	—
87	D₁₆	—	2	2	no	—
88	C₂×C₁₆	—	17	1	no	—
89	C₂×C₁₆	—	34	1	no	—
90	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
91	#107	—	17	2	no	—
92	C₄⋊C₈	—	34	2	no	—
93	#102	—	34	2	no	—
94	C₂²⋊C₈	—	68	2	no	—
95	C₄×C₈	—	17	1	no	—
96	C₄×C₈	—	17	2	no	—
97	C₁₇	#12089	1	1	yes	characteristic, complemented, Sylow
98	C₂×D₄	—	2	2	no	—
99	C₂²×C₄	—	68	2	no	—
100	D₈	—	2	2	no	—
101	D₈	—	2	2	no	—
102	M₁₆	—	136	4	no	—
103	C₂×C₈	—	17	1	no	—
104	C₂×C₈	—	34	2	no	—
105	C₂×C₈	—	68	2	no	—
106	C₂×C₈	C₂²×#595	1	1	yes	characteristic
107	C₄⋊C₄	—	34	2	no	—
108	C₂²⋊C₄	—	68	2	no	—
109	C₄²	—	17	1	no	—
110	C₁₆	—	34	1	no	—
111	C₁₆	—	68	1	no	—
112	C₁₆	#63247	1	2	yes	complemented
113	C₂³	—	4	2	no	—
114	D₄	—	4	2	no	—
115	D₄	—	4	2	no	—
116	C₂×C₄	—	17	2	no	—
117	C₂×C₄	—	68	2	no	—
118	C₂×C₄	—	136	2	no	—
119	C₂×C₄	—	136	2	no	—
120	C₂×C₄	D₄×#595	1	1	yes	characteristic
121	C₈	—	34	1	no	—
122	C₈	—	68	2	no	—
123	C₈	—	136	2	no	—
124	C₈	#10587678	1	1	yes	characteristic
125	C₈	C₂×#63247	1	1	yes	characteristic
126	C₂²	—	8	2	no	—
127	C₂²	—	8	2	no	—
128	C₂²	—	8	2	no	—
129	C₂²	#11763850	1	1	yes	characteristic
130	C₄	—	34	2	no	—
131	C₄	—	136	2	no	—
132	C₄	#11763844	1	1	yes	characteristic
133	C₄	#11763856	1	1	yes	characteristic
134	C₂	—	16	2	no	—
135	C₂	#14544434	1	1	yes	characteristic
136	C₂	#14545193	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14544434

C₂

yes

maximal, complemented

#14543808

C₂

yes

maximal, characteristic, complemented

#14543742

C₂

yes

maximal, complemented

#14543700

C₂

yes

maximal, characteristic, complemented

#14530660

C₂

yes

maximal, characteristic

#11763844

—

#11763698

C₂²

yes

characteristic

#11763670

C₂²

yes

—

D₄⋊#3624

—

#11763650

C₂²

yes

characteristic

D₈×Dic₁₇

C₂²

yes

—

#11762637

C₄

yes

characteristic

#11762610

C₄

yes

—

#11762584

C₂²

yes

characteristic

C₂×C₁₇×D₁₆

C₄

yes

characteristic

C₂×#63247

—

C₂×D₈×C₁₇

C₂×C₄

yes

—

D₄×Dic₁₇

—

C₂²⋊#3624

—

C₄⋊#3624

—

C₄×#3624

D₄

yes

—

C₂×#63216

—

C₁₇×D₁₆

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

#10587503

—

#10587489

C₂×C₄

yes

—

C₈×Dic₁₇

C₂³

yes

characteristic

C₂×#63214

C₂×C₄

yes

characteristic

C₂×D₄×C₁₇

—

C₂²×Dic₁₇

—

#63247

—

C₂×#3624

—

C₂×#3624

—

D₈×C₁₇

—

D₈×C₁₇

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂²⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₄×Dic₁₇

C₂×D₄

yes

yes

—

C₁₆×C₁₇

M₁₆

yes

—

—

C₂³×C₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

C₂×C₄×C₁₇

C₄×D₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

AGL(1,ℤ/8)

yes

—

#3624

—

#3624

—

C₈×C₁₇

C₂×M₁₆

yes

C₈×C₁₇

yes

—

—

—

—

—

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

—

C₂×D₁₆

#595

yes

characteristic

C₄×D₈

—

—

—

—

—

—

—

D₄⋊C₈

—

#322

—

C₂×C₁₇

—

C₂×C₁₇

#1594

yes

characteristic

C₂×C₁₇

AGL(1,ℤ/16)

yes

—

C₂×D₈

C₂×#595

yes

—

C₂×M₁₆

—

C₄×D₄

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#595

yes

characteristic

#107

—

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₇

#12089

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂²×C₄

—

100

D₈

—

101

D₈

—

102

M₁₆

—

136

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂²×#595

yes

characteristic

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₁₆

—

111

C₁₆

—

112

C₁₆

#63247

yes

complemented

113

C₂³

—

114

D₄

—

115

D₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

136

—

119

C₂×C₄

—

136

—

120

C₂×C₄

D₄×#595

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

136

—

124

C₈

#10587678

yes

characteristic

125

C₈

C₂×#63247

yes

characteristic

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#11763850

yes

characteristic

130

C₄

—

131

C₄

—

136

—

132

C₄

#11763844

yes

characteristic

133

C₄

#11763856

yes

characteristic

134

C₂

—

135

C₂

#14544434

yes

characteristic

136

C₂

#14545193

yes

—

	subgroup	G/H
center	C₂²	#11763850
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×#595
Fitting, prime radical	C₂×C₁₇×D₁₆	C₄
socle	C₂²×C₁₇	#442
cosocle	C₈×Dic₁₇	C₂³
hypercenter	C₂×D₁₆	#595
hypocenter	C₁₇	#12089
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

#11763850

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×#595

Fitting, prime radical

C₂×C₁₇×D₁₆

C₄

socle

C₂²×C₁₇

#442

cosocle

C₈×Dic₁₇

C₂³

C₂×D₁₆

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. #14544434	C₂	semidirect
2. #14543808	C₂	semidirect
3. #14543742	C₂	semidirect
4. #14543700	C₂	semidirect
42. C₁₆×C₁₇	M₁₆	semidirect
97. C₁₇	#12089	semidirect
112. C₁₆	#63247	semidirect

H ≅ G/N

type

1. #14544434

C₂

semidirect

2. #14543808

C₂

semidirect

3. #14543742

C₂

semidirect

4. #14543700

C₂

semidirect

42. C₁₆×C₁₇

M₁₆

semidirect

97. C₁₇

#12089

semidirect

112. C₁₆

#63247

semidirect

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

subgroup	index
#14544434	2
#14543808	2
#14543742	2
#14543700	2
#14530660	2
#12089	17

subgroup

index

Subgroups — #17960412

Conjugacy classes of subgroups

Complements

Maximal subgroups