Group #16950674 — subgroups

Subgroups — #16950674

Order 4352.

322 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 171 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×C₄⋊#63214	C₂	1	2	yes	maximal
2	#14526862	C₂	1	4	yes	maximal
3	C₁₇×#1726	C₂	1	1	yes	maximal, characteristic
4	C₂²×#63214	C₂²	1	4	yes	—
5	C₄⋊#63214	—	2	4	no	—
6	C₂×C₁₇×#97	C₄	1	2	yes	—
7	C₂×C₁₇×#97	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
10	C₁₇×#376	C₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
14	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₁₇×#97	—	2	4	no	—
17	C₁₇×#97	—	2	2	no	—
18	C₄×C₈×C₁₇	—	2	4	no	—
19	C₄×C₈×C₁₇	D₄	1	2	yes	—
20	C₄×C₈×C₁₇	Q₈	1	2	yes	—
21	C₁₇×#95	C₈	1	4	yes	—
22	C₂×#63214	—	2	4	no	—
23	C₂×#63214	—	2	8	no	—
24	C₂²×C₄×C₁₇	C₂×C₈	1	4	yes	—
25	C₂²×C₄×C₁₇	C₂×C₈	1	2	yes	—
26	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₇	—	2	2	no	—
28	C₂×C₈×C₁₇	—	2	2	no	—
29	C₂×C₈×C₁₇	—	2	2	no	—
30	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₇	M₁₆	1	4	yes	—
32	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₈×C₁₇	#41	1	4	yes	—
35	C₄²×C₁₇	—	2	2	no	—
36	C₄²×C₁₇	—	2	2	no	—
37	C₄²×C₁₇	C₄⋊C₄	1	2	yes	—
38	C₄²×C₁₇	M₁₆	1	2	yes	—
39	#63214	—	4	4	no	—
40	#12880	—	17	1	no	maximal, Sylow
41	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
42	C₂×C₄×C₁₇	—	2	4	no	—
43	C₂×C₄×C₁₇	—	2	4	no	—
44	C₂×C₄×C₁₇	—	2	8	no	—
45	C₂×C₄×C₁₇	C₄⋊C₈	1	4	yes	—
46	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₇	#117	1	2	yes	—
48	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
49	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
50	C₈×C₁₇	—	2	2	no	—
51	C₈×C₁₇	—	2	4	no	—
52	C₈×C₁₇	#124	1	2	yes	—
53	C₈×C₁₇	#125	1	2	yes	—
54	C₂×C₄⋊C₁₆	—	17	2	no	—
55	#1726	D₁₇	1	1	yes	characteristic
56	#1374	—	17	4	no	—
57	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
58	C₂²×C₁₇	#431	1	2	yes	—
59	C₂²×C₁₇	#504	1	4	yes	—
60	C₄×C₁₇	—	2	4	no	—
61	C₄×C₁₇	—	4	4	no	—
62	C₄×C₁₇	#382	1	1	yes	characteristic
63	C₄×C₁₇	#423	1	1	yes	characteristic
64	C₄×C₁₇	#432	1	2	yes	—
65	C₂²×C₁₆	—	17	4	no	—
66	C₂×#97	Dic₁₇	1	2	yes	—
67	C₂×#97	Dic₁₇	1	1	yes	characteristic
68	C₂×C₄×C₈	C₂×D₁₇	1	2	yes	—
69	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
70	#376	Dic₁₇	1	1	yes	characteristic
71	C₄⋊C₁₆	—	34	4	no	—
72	C₂×C₁₇	#1831	1	1	yes	characteristic
73	C₂×C₁₇	#2151	1	2	yes	—
74	C₂×C₁₇	#2164	1	4	yes	—
75	C₂²×C₈	C₂×Dic₁₇	1	2	yes	—
76	C₂²×C₈	C₂×Dic₁₇	1	1	yes	characteristic
77	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
78	C₂×C₄²	C₂×Dic₁₇	1	2	yes	—
79	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
80	C₂×C₁₆	—	34	4	no	—
81	C₂×C₁₆	—	34	8	no	—
82	#97	—	2	4	no	—
83	#97	—	2	2	no	—
84	C₄×C₈	—	2	4	no	—
85	C₄×C₈	Dic₃₄	1	2	yes	—
86	C₄×C₈	D₆₈	1	2	yes	—
87	#95	#3622	1	4	yes	—
88	C₁₇	#12880	1	1	yes	characteristic, complemented, Sylow
89	C₂²×C₄	C₂×#3622	1	4	yes	—
90	C₂²×C₄	C₂×#3622	1	2	yes	—
91	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	#63223	1	4	yes	—
96	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
97	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
98	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
99	C₂×C₈	#63252	1	4	yes	—
100	C₄²	—	2	2	no	—
101	C₄²	—	2	2	no	—
102	C₄²	#63223	1	2	yes	—
103	C₄²	C₄⋊Dic₁₇	1	2	yes	—
104	C₁₆	—	68	4	no	—
105	C₂³	C₂²×#3622	1	1	yes	characteristic
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	2	8	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	C₄⋊#3622	1	4	yes	—
110	C₂×C₄	C₂×#63223	1	2	yes	—
111	C₂×C₄	C₂×#63223	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
113	C₂×C₄	#10587612	1	2	yes	—
114	C₈	—	2	2	no	—
115	C₈	—	2	4	no	—
116	C₈	#10587556	1	2	yes	—
117	C₈	#10587561	1	2	yes	—
118	C₂²	C₂×C₄⋊#3622	1	1	yes	characteristic
119	C₂²	#11762862	1	2	yes	—
120	C₂²	#11763226	1	4	yes	—
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	#11762675	1	1	yes	characteristic
124	C₄	#11762833	1	1	yes	characteristic
125	C₄	#11762866	1	2	yes	—
126	C₂	#14528901	1	1	yes	characteristic
127	C₂	#14530543	1	2	yes	—
128	C₂	#14530591	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#63214

C₂

yes

maximal

#14526862

C₂

yes

maximal

C₁₇×#1726

C₂

yes

maximal, characteristic

C₂²×#63214

C₂²

yes

—

C₄⋊#63214

—

C₂×C₁₇×#97

C₄

yes

—

C₂×C₁₇×#97

C₄

yes

characteristic

C₂×C₄×C₈×C₁₇

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×#376

C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

—

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄²×C₁₇

C₂×C₄

yes

—

C₂×C₄²×C₁₇

C₂×C₄

yes

characteristic

C₁₇×#97

—

C₁₇×#97

—

C₄×C₈×C₁₇

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

Q₈

yes

—

C₁₇×#95

C₈

yes

—

C₂×#63214

—

C₂×#63214

—

C₂²×C₄×C₁₇

C₂×C₈

yes

—

C₂²×C₄×C₁₇

C₂×C₈

yes

—

C₂²×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₇

#41

yes

—

C₄²×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

C₄⋊C₄

yes

—

C₄²×C₁₇

M₁₆

yes

—

#63214

—

#12880

—

maximal, Sylow

C₂³×C₁₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

#117

yes

—

C₂×C₄×C₁₇

C₂×M₁₆

yes

—

C₂×C₄×C₁₇

C₂×M₁₆

yes

characteristic

C₈×C₁₇

—

C₈×C₁₇

—

C₈×C₁₇

#124

yes

—

C₈×C₁₇

#125

yes

—

C₂×C₄⋊C₁₆

—

#1726

D₁₇

yes

characteristic

#1374

—

C₂²×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₇

#431

yes

—

C₂²×C₁₇

#504

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

C₂²×C₁₆

—

C₂×#97

Dic₁₇

yes

—

C₂×#97

Dic₁₇

yes

characteristic

C₂×C₄×C₈

C₂×D₁₇

yes

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

#376

Dic₁₇

yes

characteristic

C₄⋊C₁₆

—

C₂×C₁₇

#1831

yes

characteristic

C₂×C₁₇

#2151

yes

—

C₂×C₁₇

#2164

yes

—

C₂²×C₈

C₂×Dic₁₇

yes

—

C₂²×C₈

C₂×Dic₁₇

yes

characteristic

C₂²×C₈

C₂²×D₁₇

yes

characteristic

C₂×C₄²

C₂×Dic₁₇

yes

—

C₂×C₄²

C₂×Dic₁₇

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₃₄

yes

—

C₄×C₈

D₆₈

yes

—

#95

#3622

yes

—

C₁₇

#12880

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×#3622

yes

—

C₂²×C₄

C₂×#3622

yes

—

C₂²×C₄

C₂²×Dic₁₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#63223

yes

—

C₂×C₈

C₄⋊Dic₁₇

yes

—

C₂×C₈

C₂×Dic₃₄

yes

characteristic

C₂×C₈

C₂×D₆₈

yes

characteristic

C₂×C₈

#63252

yes

—

100

C₄²

—

101

C₄²

—

102

C₄²

#63223

yes

—

103

C₄²

C₄⋊Dic₁₇

yes

—

104

C₁₆

—

105

C₂³

C₂²×#3622

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₄⋊#3622

yes

—

110

C₂×C₄

C₂×#63223

yes

—

111

C₂×C₄

C₂×#63223

yes

characteristic

112

C₂×C₄

C₂×C₄⋊Dic₁₇

yes

characteristic

113

C₂×C₄

#10587612

yes

—

114

C₈

—

115

C₈

—

116

C₈

#10587556

yes

—

117

C₈

#10587561

yes

—

118

C₂²

C₂×C₄⋊#3622

yes

characteristic

119

C₂²

#11762862

yes

—

120

C₂²

#11763226

yes

—

121

C₄

—

122

C₄

—

123

C₄

#11762675

yes

characteristic

124

C₄

#11762833

yes

characteristic

125

C₄

#11762866

yes

—

126

C₂

#14528901

yes

characteristic

127

C₂

#14530543

yes

—

128

C₂

#14530591

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂²×C₈
Fitting	C₁₇×#1726	C₂
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#1726	D₁₇
hypocenter	C₁₇	#12880
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₁₇

commutator, socle, prime radical

C₂³×C₁₇

C₂²×C₈

Fitting

C₁₇×#1726

C₂

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂³×C₁₇ ▷ C₁₇

C₁ ◁ C₂²×C₈ ◁ #1726

N	H ≅ G/N	type
88. C₁₇	#12880	semidirect

H ≅ G/N

type

88. C₁₇

#12880

semidirect

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

subgroup	index
C₂×C₄⋊#63214	2
#14526862	2
C₁₇×#1726	2
#12880	17

subgroup

index

C₂×C₄⋊#63214

#14526862

C₁₇×#1726

#12880

Subgroups — #16950674

Conjugacy classes of subgroups

Complements

Maximal subgroups