Finite Group Databasebeta

← #16927854

Subgroups — #16927854

Order 4352.

398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14531387C211yesmaximal, characteristic
2#14528864C211yesmaximal, characteristic
3#14526693C214yesmaximal
4C17×#1821C211yesmaximal, characteristic
5#11762773C2212yes—
6#11762695—22no—
7#11762695—22no—
8#11762672C2212yes—
9#11762669C412yes—
10C4×C22⋊Dic17C412yes—
11#11762578—22no—
12C22×C4⋊C4×C17C2211yescharacteristic
13C17×#407C2212yes—
14C17×#343—22no—
15C23×C4×C17C2×C411yescharacteristic
16C23×C4×C17C2×C411yescharacteristic
17C23×C4×C17C2311yescharacteristic
18C2×M16×C17—22no—
19C2×C4⋊C4×C17—24no—
20C2×C4⋊C4×C17D412yes—
21C2×C4⋊C4×C17D412yes—
22C2×C22⋊Dic17C2×C414yes—
23C2×C4⋊Dic17—22no—
24C2×C4×Dic17—22no—
25C2×#63223—22no—
26C17×C22⋊C8—24no—
27#10587502—22no—
28#10587502—22no—
29#10587502—22no—
30#10587502—22no—
31C22⋊#3622—24no—
32C24×C17C22×C411yescharacteristic
33C22×C4×C17—22no—
34C22×C4×C17—22no—
35C22×C4×C17—42no—
36C22×C4×C17—81no—
37C22×C4×C17—81no—
38C22×C4×C17C22⋊C412yes—
39C22×C4×C17C22⋊C412yes—
40C22×C4×C17C2×D411yescharacteristic
41C22×C4×C17C2×D411yescharacteristic
42C22×C4×C17#4114yes—
43C22×Dic17—24no—
44M16×C17—44no—
45C2×C8×C17—42no—
46C4⋊C4×C17—24no—
47C4⋊C4×C17—24no—
48C22⋊Dic17—44no—
49C4⋊Dic17—82no—
50C4×Dic17—82no—
51#63223—44no—
52C2×#3622—42no—
53#8755—171nomaximal, Sylow
54C23×C17—22no—
55C23×C17—41no—
56C23×C17—41no—
57C23×C17C2×C22⋊C411yescharacteristic
58C23×C17#11712yes—
59C2×C4×C17—22no—
60C2×C4×C17—22no—
61C2×C4×C17—22no—
62C2×C4×C17—22no—
63C2×C4×C17—44no—
64C2×C4×C17—42no—
65C2×C4×C17—42no—
66C2×C4×C17—82no—
67C2×C4×C17—82no—
68C2×C4×C17#12312yes—
69C2×C4×C17#12312yes—
70C2×Dic17—44no—
71C2×Dic17—44no—
72C2×Dic17—44no—
73C8×C17—82no—
74#3622—82no—
75#2313—171no—
76#1821—171no—
77#1821D1711yescharacteristic
78#1306—174no—
79C22×C17—21no—
80C22×C17—21no—
81C22×C17—22no—
82C22×C17—22no—
83C22×C17—22no—
84C22×C17—44no—
85C22×C17#38111yescharacteristic
86C22×C17#41012yes—
87C4×C17—22no—
88C4×C17—22no—
89C4×C17—42no—
90C4×C17—42no—
91Dic17—84no—
92C22×C4⋊C4C2×D1711yescharacteristic
93#407—172no—
94#407C2×D1712yes—
95#387—342no—
96#387—342no—
97#381—172no—
98#380—172no—
99C4×C22⋊C4—172no—
100#343—22no—
101#343—342no—
102C2×C17—22no—
103C2×C17—42no—
104C2×C17#182011yescharacteristic
105C2×C17#182911yescharacteristic
106C2×C17#183011yescharacteristic
107C23×C4C4×D1711yescharacteristic
108C23×C4C4×D1711yescharacteristic
109C23×C4C22×D1711yescharacteristic
110C2×M16—22no—
111C2×M16—342no—
112C2×C4⋊C4—24no—
113C2×C4⋊C4—342no—
114C2×C4⋊C4D6812yes—
115C2×C4⋊C4C22⋊D1712yes—
116C2×C22⋊C4—174no—
117C2×C42—342no—
118C22⋊C8—24no—
119C22⋊C8—344no—
120#95—342no—
121#95—342no—
122#95—342no—
123#95—342no—
124C17#875511yescharacteristic, complemented, Sylow
125C24C2×C4×D1711yescharacteristic
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—42no—
129C22×C4—81no—
130C22×C4—81no—
131C22×C4—344no—
132C22×C4#6322712yes—
133C22×C4#6322712yes—
134C22×C4C2×D6811yescharacteristic
135C22×C4#6325414yes—
136C22×C4C2×C22⋊D1711yescharacteristic
137M16—44no—
138M16—684no—
139C2×C8—42no—
140C2×C8—682no—
141C4⋊C4—24no—
142C4⋊C4—24no—
143C4⋊C4—1362no—
144C22⋊C4—684no—
145C42—1362no—
146C23—22no—
147C23—41no—
148C23—41no—
149C23#1058756312yes—
150C23C2×#6322711yescharacteristic
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—44no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—684no—
161C2×C4—684no—
162C2×C4—684no—
163C2×C4#1058757212yes—
164C2×C4#1058762112yes—
165C8—82no—
166C8—1362no—
167C22—21no—
168C22—21no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—44no—
173C22#1176267011yescharacteristic
174C22#1176278212yes—
175C4—22no—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—1364no—
180C2—22no—
181C2—42no—
182C2#1452885911yescharacteristic
183C2#1452889311yescharacteristic
184C2#1452889611yescharacteristic
subgroupG/H
centerC22#11762670
commutator, prime radicalC24×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×#1821C2
socleC22×C17#381
cosocleC23×C4×C17C23
hypercenter#1821D17
hypocenterC17#8755
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
124. C17#8755semidirect

Maximal subgroups

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

subgroupindex
#145313872
#145288642
#145266932
C17×#18212
#875517