Group #16946344 — subgroups

Subgroups — #16946344

Order 4352.

198 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 77 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	#14527693	C₂	1	2	yes	maximal
2	#14526850	C₂	1	1	yes	maximal, characteristic
3	#14526754	C₂	1	2	yes	maximal
4	#14526704	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#2176	C₂	1	1	yes	maximal, characteristic
6	#11762940	—	2	2	no	—
7	#11762585	C₂²	1	1	yes	characteristic
8	#11762560	C₂²	1	2	yes	—
9	Q₈⋊#3622	—	2	2	no	—
10	#11762530	C₂²	1	1	yes	characteristic
11	C₂×C₁₇×Q₃₂	C₄	1	1	yes	characteristic
12	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
13	C₁₇×#367	C₄	1	1	yes	characteristic
14	C₁₇×#358	C₄	1	2	yes	—
15	C₁₇×#346	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₁₇	C₂×C₄	1	2	yes	—
17	C₄×Q₈×C₁₇	—	2	2	no	—
18	C₁₇×Q₃₂	—	2	2	no	—
19	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
21	C₁₇×#107	C₂×C₄	1	2	yes	—
22	C₁₇×#103	—	2	2	no	—
23	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
24	C₂×#63214	—	2	1	no	—
25	C₄⋊#3622	—	2	2	no	—
26	C₄⋊#3622	—	4	2	no	—
27	#10587474	—	4	2	no	—
28	C₄×#3622	D₄	1	2	yes	—
29	C₂×Q₈×C₁₇	—	2	2	no	—
30	Q₁₆×C₁₇	—	2	2	no	—
31	Q₁₆×C₁₇	—	2	2	no	—
32	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
34	C₄⋊C₄×C₁₇	—	2	2	no	—
35	C₄⋊C₄×C₁₇	—	4	2	no	—
36	C₄²×C₁₇	—	4	2	no	—
37	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
38	C₂×#3622	—	2	2	no	—
39	C₂×#3622	—	4	2	no	—
40	C₁₆×C₁₇	—	2	1	no	—
41	C₁₆×C₁₇	M₁₆	1	2	yes	—
42	#63214	—	4	1	no	—
43	#12088	—	17	1	no	maximal, Sylow
44	Q₈×C₁₇	—	4	2	no	—
45	Q₈×C₁₇	—	4	2	no	—
46	C₂×C₄×C₁₇	—	4	2	no	—
47	C₂×C₄×C₁₇	—	4	2	no	—
48	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
50	C₈×C₁₇	—	2	1	no	—
51	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
52	C₈×C₁₇	#131	1	1	yes	characteristic
53	#3622	—	4	2	no	—
54	#3622	—	8	2	no	—
55	#2176	D₁₇	1	1	yes	characteristic
56	#1593	—	17	2	no	—
57	#1368	—	17	1	no	—
58	#1334	—	17	2	no	—
59	#1313	—	17	1	no	—
60	C₂²×C₁₇	#442	1	1	yes	characteristic
61	C₄×C₁₇	—	2	2	no	—
62	C₄×C₁₇	—	8	2	no	—
63	C₄×C₁₇	—	8	2	no	—
64	C₄×C₁₇	#436	1	1	yes	characteristic
65	C₄×C₁₇	#444	1	1	yes	characteristic
66	C₂×Q₃₂	Dic₁₇	1	1	yes	characteristic
67	#446	—	34	2	no	—
68	C₄×Q₁₆	C₂×D₁₇	1	2	yes	—
69	#367	Dic₁₇	1	1	yes	characteristic
70	#358	Dic₁₇	1	2	yes	—
71	#346	—	17	1	no	—
72	#346	C₂×D₁₇	1	1	yes	characteristic
73	#334	—	17	2	no	—
74	Q₈⋊C₈	—	34	2	no	—
75	#322	—	17	1	no	—
76	C₂×C₁₇	#1594	1	1	yes	characteristic
77	C₂×C₁₇	#2180	1	2	yes	—
78	C₂×Q₁₆	C₂×Dic₁₇	1	2	yes	—
79	C₄×Q₈	—	2	2	no	—
80	Q₃₂	—	2	2	no	—
81	C₂×C₁₆	—	34	1	no	—
82	C₂×C₁₆	C₂×Dic₁₇	1	1	yes	characteristic
83	C₂×C₁₆	C₂×Dic₁₇	1	1	yes	characteristic
84	#107	C₂×Dic₁₇	1	2	yes	—
85	C₄⋊C₈	—	34	2	no	—
86	C₄⋊C₈	—	68	2	no	—
87	#103	—	2	2	no	—
88	#97	—	68	2	no	—
89	C₄×C₈	—	17	2	no	—
90	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
91	C₁₇	#12088	1	1	yes	characteristic, complemented, Sylow
92	C₂×Q₈	—	2	2	no	—
93	Q₁₆	—	2	2	no	—
94	Q₁₆	—	2	2	no	—
95	C₂×C₈	—	34	2	no	—
96	C₂×C₈	—	68	2	no	—
97	C₂×C₈	#63254	1	1	yes	characteristic
98	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
99	C₄⋊C₄	—	2	2	no	—
100	C₄⋊C₄	—	4	2	no	—
101	C₄²	—	4	2	no	—
102	C₄²	D₄×D₁₇	1	1	yes	characteristic
103	C₁₆	—	2	1	no	—
104	C₁₆	—	68	1	no	—
105	C₁₆	#63223	1	2	yes	—
106	Q₈	—	4	2	no	—
107	Q₈	—	4	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	4	2	no	—
110	C₂×C₄	#10587597	1	2	yes	—
111	C₂×C₄	D₄×Dic₁₇	1	1	yes	characteristic
112	C₈	—	2	1	no	—
113	C₈	—	68	2	no	—
114	C₈	—	136	2	no	—
115	C₈	C₂×#63223	1	1	yes	characteristic
116	C₈	#10587634	1	1	yes	characteristic
117	C₂²	#11762921	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	8	2	no	—
120	C₄	—	8	2	no	—
121	C₄	#11762887	1	1	yes	characteristic
122	C₄	#11762931	1	1	yes	characteristic
123	C₂	#14527698	1	1	yes	characteristic
124	C₂	#14530676	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14527693

C₂

yes

maximal

#14526850

C₂

yes

maximal, characteristic

#14526754

C₂

yes

maximal

#14526704

C₂

yes

maximal, characteristic

C₁₇×#2176

C₂

yes

maximal, characteristic

#11762940

—

#11762585

C₂²

yes

characteristic

#11762560

C₂²

yes

—

Q₈⋊#3622

—

#11762530

C₂²

yes

characteristic

C₂×C₁₇×Q₃₂

C₄

yes

characteristic

C₄×Q₁₆×C₁₇

C₂²

yes

—

C₁₇×#367

C₄

yes

characteristic

C₁₇×#358

C₄

yes

—

C₁₇×#346

C₂²

yes

characteristic

C₂×Q₁₆×C₁₇

C₂×C₄

yes

—

C₄×Q₈×C₁₇

—

C₁₇×Q₃₂

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₇

C₂×C₄

yes

characteristic

C₁₇×#107

C₂×C₄

yes

—

C₁₇×#103

—

C₄×C₈×C₁₇

C₂³

yes

—

—

—

—

D₄

yes

—

C₂×Q₈×C₁₇

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

#41

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₂×#3622

—

C₂×#3622

—

C₁₆×C₁₇

—

C₁₆×C₁₇

M₁₆

yes

—

#63214

—

#12088

—

maximal, Sylow

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄×D₄

yes

characteristic

C₂×C₄×C₁₇

AGL(1,ℤ/8)

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₂×M₁₆

yes

C₈×C₁₇

yes

—

—

D₁₇

yes

—

—

—

—

C₂²×C₁₇

#442

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₂×Q₃₂

Dic₁₇

yes

characteristic

#446

—

C₄×Q₁₆

C₂×D₁₇

yes

—

#367

Dic₁₇

yes

characteristic

#358

Dic₁₇

yes

—

#346

—

#346

C₂×D₁₇

yes

characteristic

#334

—

Q₈⋊C₈

—

#322

—

C₂×C₁₇

#1594

yes

characteristic

C₂×C₁₇

#2180

yes

—

C₂×Q₁₆

C₂×Dic₁₇

yes

—

C₄×Q₈

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₁₇

yes

characteristic

C₂×C₁₆

C₂×Dic₁₇

yes

characteristic

#107

C₂×Dic₁₇

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

—

C₄×C₈

C₂²×D₁₇

yes

characteristic

C₁₇

#12088

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#63254

yes

characteristic

C₂×C₈

C₂²×Dic₁₇

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

—

102

C₄²

D₄×D₁₇

yes

characteristic

103

C₁₆

—

104

C₁₆

—

105

C₁₆

#63223

yes

—

106

Q₈

—

107

Q₈

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

#10587597

yes

—

111

C₂×C₄

D₄×Dic₁₇

yes

characteristic

112

C₈

—

113

C₈

—

114

C₈

—

136

—

115

C₈

C₂×#63223

yes

characteristic

116

C₈

#10587634

yes

characteristic

117

C₂²

#11762921

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

#11762887

yes

characteristic

122

C₄

#11762931

yes

characteristic

123

C₂

#14527698

yes

characteristic

124

C₂

#14530676

yes

—

	subgroup	G/H
center	C₂²	#11762921
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₁₇×#2176	C₂
socle, prime radical	C₂²×C₁₇	#442
cosocle	C₄×C₈×C₁₇	C₂³
hypercenter	#2176	D₁₇
hypocenter	C₁₇	#12088
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2176

subgroup

G/H

center

C₂²

#11762921

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₄×C₈

C₂²×D₁₇

Fitting

C₁₇×#2176

C₂

socle, prime radical

C₂²×C₁₇

#442

cosocle

C₄×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2176

N	H ≅ G/N	type
91. C₁₇	#12088	semidirect

H ≅ G/N

type

91. C₁₇

#12088

semidirect

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

subgroup	index
#14527693	2
#14526850	2
#14526754	2
#14526704	2
C₁₇×#2176	2
#12088	17

subgroup

index

C₁₇×#2176

Subgroups — #16946344

Conjugacy classes of subgroups

Complements

Maximal subgroups