Group #16954810 — subgroups

Subgroups — #16954810

Order 4352.

206 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 147 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×#11762643	C₂	1	1	yes	maximal, characteristic
2	C₂²×#10587465	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10587465	C₂	1	4	yes	maximal, complemented
4	C₁₇×#2108	C₂	1	1	yes	maximal, characteristic
5	#11762643	—	2	2	no	—
6	C₂×#10587465	—	2	2	no	—
7	C₂×#10587465	C₂²	1	2	yes	—
8	C₂×#10587465	C₂²	1	2	yes	—
9	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic
10	C₂²×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
11	C₁₇×#405	C₄	1	1	yes	characteristic
12	C₁₇×#346	C₄	1	2	yes	—
13	C₄×C₁₆×C₁₇	C₂²	1	2	yes	—
14	C₂×M₁₆×C₁₇	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₁₇×#117	C₈	1	1	yes	characteristic
17	C₁₇×M₃₂	—	2	2	no	—
18	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
19	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₆×C₁₇	D₄	1	2	yes	—
21	C₂×C₁₆×C₁₇	Q₈	1	2	yes	—
22	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
23	C₁₇×#97	C₈	1	2	yes	—
24	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
25	#10587465	—	2	2	no	—
26	#10587465	—	2	2	no	—
27	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
28	M₁₆×C₁₇	—	2	2	no	—
29	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
30	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
31	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
33	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
34	C₄⋊C₄×C₁₇	C₁₆	1	2	yes	—
35	C₂²⋊C₄×C₁₇	C₁₆	1	2	yes	—
36	C₄²×C₁₇	C₂×C₈	1	2	yes	—
37	C₁₆×C₁₇	—	2	2	no	—
38	C₁₆×C₁₇	C₄⋊C₄	1	2	yes	—
39	C₁₆×C₁₇	C₂×D₄	1	1	yes	characteristic
40	C₁₆×C₁₇	C₂×Q₈	1	1	yes	characteristic
41	#13628	—	17	1	no	maximal, Sylow
42	C₂³×C₁₇	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₇	C₄⋊C₈	1	2	yes	—
44	C₂×C₄×C₁₇	C₂×C₁₆	1	4	yes	—
45	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
46	C₂×C₄×C₁₇	M₃₂	1	2	yes	—
47	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
48	C₈×C₁₇	—	2	2	no	—
49	C₈×C₁₇	C₄⋊C₈	1	2	yes	—
50	C₈×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
52	C₂×M₆₄	—	17	1	no	—
53	C₂²×C₃₂	—	17	1	no	—
54	#2108	D₁₇	1	1	yes	characteristic
55	C₄⋊C₃₂	—	17	4	no	—
56	C₂²×C₁₇	—	2	2	no	—
57	C₂²×C₁₇	C₄⋊C₁₆	1	2	yes	—
58	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
59	C₄×C₁₇	—	2	4	no	—
60	C₄×C₁₇	C₄⋊C₁₆	1	2	yes	—
61	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
62	C₄×C₁₇	C₂×M₃₂	1	1	yes	characteristic
63	C₂×M₃₂	Dic₁₇	1	1	yes	characteristic
64	C₂²×C₁₆	C₂×D₁₇	1	1	yes	characteristic
65	#405	Dic₁₇	1	1	yes	characteristic
66	M₆₄	—	34	2	no	—
67	C₂×C₃₂	—	17	2	no	—
68	C₂×C₃₂	—	17	2	no	—
69	C₂×C₃₂	—	34	2	no	—
70	#346	Dic₁₇	1	2	yes	—
71	C₄×C₁₆	C₂×D₁₇	1	2	yes	—
72	C₂×C₁₇	—	2	2	no	—
73	C₂×C₁₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic
74	C₂×C₁₇	#2258	1	2	yes	—
75	C₂×M₁₆	#3622	1	1	yes	characteristic
76	C₂²×C₈	C₂×Dic₁₇	1	1	yes	characteristic
77	#117	#3622	1	1	yes	characteristic
78	M₃₂	—	2	2	no	—
79	C₂×C₁₆	Dic₃₄	1	2	yes	—
80	C₂×C₁₆	D₆₈	1	2	yes	—
81	C₂×C₁₆	C₂×Dic₁₇	1	2	yes	—
82	C₂×C₁₆	C₂×Dic₁₇	1	1	yes	characteristic
83	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
84	#97	#3622	1	2	yes	—
85	C₄×C₈	C₂×Dic₁₇	1	2	yes	—
86	C₃₂	—	34	2	no	—
87	C₃₂	—	34	2	no	—
88	C₁₇	#13628	1	1	yes	characteristic, complemented, Sylow
89	C₂²×C₄	C₂×#3622	1	1	yes	characteristic
90	M₁₆	—	2	2	no	—
91	C₂×C₈	C₂×#3622	1	2	yes	—
92	C₂×C₈	C₂×#3622	1	1	yes	characteristic
93	C₂×C₈	#63223	1	2	yes	—
94	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
95	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
96	C₄⋊C₄	#63214	1	2	yes	—
97	C₂²⋊C₄	#63214	1	2	yes	—
98	C₄²	C₂×#3622	1	2	yes	—
99	C₁₆	—	2	2	no	—
100	C₁₆	C₄⋊Dic₁₇	1	2	yes	—
101	C₁₆	C₂×Dic₃₄	1	1	yes	characteristic
102	C₁₆	C₂×D₆₈	1	1	yes	characteristic
103	C₂³	C₂×#63214	1	1	yes	characteristic
104	C₂×C₄	C₄⋊#3622	1	2	yes	—
105	C₂×C₄	C₂×#63214	1	4	yes	—
106	C₂×C₄	C₂×#63214	1	1	yes	characteristic
107	C₂×C₄	#10587483	1	2	yes	—
108	C₂×C₄	C₂²×#3622	1	1	yes	characteristic
109	C₈	—	2	2	no	—
110	C₈	C₄⋊#3622	1	2	yes	—
111	C₈	C₂×#63223	1	1	yes	characteristic
112	C₈	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
113	C₂²	—	2	2	no	—
114	C₂²	C₄⋊#63214	1	2	yes	—
115	C₂²	C₂²×#63214	1	1	yes	characteristic
116	C₄	—	2	4	no	—
117	C₄	C₄⋊#63214	1	2	yes	—
118	C₄	C₂×C₄⋊#3622	1	1	yes	characteristic
119	C₄	C₂×#10587483	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₂×C₄⋊#63214	1	1	yes	characteristic
122	C₂	#14531078	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11762643

C₂

yes

maximal, characteristic

C₂²×#10587465

C₂

yes

maximal, characteristic

C₄⋊#10587465

C₂

yes

maximal, complemented

C₁₇×#2108

C₂

yes

maximal, characteristic

#11762643

—

C₂×#10587465

—

C₂×#10587465

C₂²

yes

—

C₂×#10587465

C₂²

yes

—

C₂×C₁₇×M₃₂

C₄

yes

characteristic

C₂²×C₁₆×C₁₇

C₂²

yes

characteristic

C₁₇×#405

C₄

yes

characteristic

C₁₇×#346

C₄

yes

—

C₄×C₁₆×C₁₇

C₂²

yes

—

C₂×M₁₆×C₁₇

C₈

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₁₇×#117

C₈

yes

characteristic

C₁₇×M₃₂

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₇

D₄

yes

—

C₂×C₁₆×C₁₇

Q₈

yes

—

C₂×C₁₆×C₁₇

C₂³

yes

characteristic

C₁₇×#97

C₈

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

#10587465

—

#10587465

—

C₂²×C₄×C₁₇

C₂×C₈

yes

characteristic

M₁₆×C₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄⋊C₄×C₁₇

C₁₆

yes

—

C₂²⋊C₄×C₁₇

C₁₆

yes

—

C₄²×C₁₇

C₂×C₈

yes

—

C₁₆×C₁₇

—

C₁₆×C₁₇

C₄⋊C₄

yes

—

C₁₆×C₁₇

C₂×D₄

yes

characteristic

C₁₆×C₁₇

C₂×Q₈

yes

characteristic

#13628

—

maximal, Sylow

C₂³×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

C₂×C₁₆

yes

—

C₂×C₄×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

M₃₂

yes

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₈×C₁₇

—

C₈×C₁₇

C₄⋊C₈

yes

—

C₈×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₈×C₁₇

C₂×M₁₆

yes

characteristic

C₂×M₆₄

—

C₂²×C₃₂

—

#2108

D₁₇

yes

characteristic

C₄⋊C₃₂

—

C₂²×C₁₇

—

C₂²×C₁₇

C₄⋊C₁₆

yes

—

C₂²×C₁₇

C₂²×C₁₆

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

C₄⋊C₁₆

yes

—

C₄×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₇

C₂×M₃₂

yes

characteristic

C₂×M₃₂

Dic₁₇

yes

characteristic

C₂²×C₁₆

C₂×D₁₇

yes

characteristic

#405

Dic₁₇

yes

characteristic

M₆₄

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

#346

Dic₁₇

yes

—

C₄×C₁₆

C₂×D₁₇

yes

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₁₇

#2258

yes

—

C₂×M₁₆

#3622

yes

characteristic

C₂²×C₈

C₂×Dic₁₇

yes

yes

M₃₂

—

C₂×C₁₆

Dic₃₄

yes

—

C₂×C₁₆

D₆₈

yes

—

C₂×C₁₆

C₂×Dic₁₇

yes

—

C₂×C₁₆

C₂×Dic₁₇

yes

characteristic

C₂×C₁₆

C₂²×D₁₇

yes

characteristic

#97

#3622

yes

—

C₄×C₈

C₂×Dic₁₇

yes

—

C₃₂

—

C₃₂

—

C₁₇

#13628

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×#3622

yes

characteristic

M₁₆

—

C₂×C₈

C₂×#3622

yes

—

C₂×C₈

C₂×#3622

yes

characteristic

C₂×C₈

#63223

yes

—

C₂×C₈

C₄⋊Dic₁₇

yes

—

C₂×C₈

C₂²×Dic₁₇

yes

characteristic

C₄⋊C₄

#63214

yes

—

C₂²⋊C₄

#63214

yes

—

C₄²

C₂×#3622

yes

—

C₁₆

—

100

C₁₆

C₄⋊Dic₁₇

yes

—

101

C₁₆

C₂×Dic₃₄

yes

characteristic

102

C₁₆

C₂×D₆₈

yes

characteristic

103

C₂³

C₂×#63214

yes

characteristic

104

C₂×C₄

C₄⋊#3622

yes

—

105

C₂×C₄

C₂×#63214

yes

—

106

C₂×C₄

C₂×#63214

yes

characteristic

107

C₂×C₄

#10587483

yes

—

108

C₂×C₄

C₂²×#3622

yes

characteristic

109

C₈

—

110

C₈

C₄⋊#3622

yes

—

111

C₈

C₂×#63223

yes

characteristic

112

C₈

C₂×C₄⋊Dic₁₇

yes

characteristic

113

C₂²

—

114

C₂²

C₄⋊#63214

yes

—

115

C₂²

C₂²×#63214

yes

characteristic

116

C₄

—

117

C₄

C₄⋊#63214

yes

—

118

C₄

C₂×C₄⋊#3622

yes

characteristic

119

C₄

C₂×#10587483

yes

characteristic

120

C₂

—

121

C₂

C₂×C₄⋊#63214

yes

characteristic

122

C₂

#14531078

yes

—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂²×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₁₆
Fitting	C₁₇×#2108	C₂
prime radical	C₂³×C₁₇	C₂×C₁₆
cosocle	C₂×C₁₆×C₁₇	C₂³
hypercenter	#2108	D₁₇
hypocenter	C₁₇	#13628
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₆ ◁ #2108

subgroup

G/H

center, Frattini

C₂×C₁₆

C₂²×D₁₇

commutator, socle

C₂²×C₁₇

C₂²×C₁₆

Fitting

C₁₇×#2108

C₂

prime radical

C₂³×C₁₇

C₂×C₁₆

cosocle

C₂×C₁₆×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₁₆ ◁ #2108

N	H ≅ G/N	type
3. C₄⋊#10587465	C₂	semidirect
88. C₁₇	#13628	semidirect

H ≅ G/N

type

3. C₄⋊#10587465

C₂

semidirect

88. C₁₇

#13628

semidirect

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

subgroup	index
C₂×#11762643	2
C₂²×#10587465	2
C₄⋊#10587465	2
C₁₇×#2108	2
#13628	17

subgroup

index

C₁₇×#2108

Subgroups — #16954810

Conjugacy classes of subgroups

Complements

Maximal subgroups