Finite Group Databasebeta

← #17953669

Subgroups — #17953669

Order 4352.

566 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 76 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#14544618C212yesmaximal
2#14543687C214yesmaximal
3#14531369C211yesmaximal, characteristic
4C2×#10587545—24no—
5#11763779C2214yes—
6C23×Dic34C2211yescharacteristic
7C2×#10587563C412yes—
8#11762713—24no—
9#11762672C411yescharacteristic
10#11762670C2212yes—
11C17×#381C411yescharacteristic
12C23×C4×C17C2×C411yescharacteristic
13C23×Dic17C2×C411yescharacteristic
14C23×Dic17C2311yescharacteristic
15C22×Dic34—24no—
16C22×Dic34—44no—
17C22×Dic34D414yes—
18C2×#63247—24no—
19C2×C22⋊C4×C17C2×C412yes—
20C2×C22⋊Dic17C2×C412yes—
21C2×#63225—22no—
22C2×C4×Dic17—22no—
23#10587563—44no—
24C22⋊#3624—28no—
25#10587545—48no—
26C17×#95—22no—
27#10587502—22no—
28#10587502—24no—
29C24×C17C22×C411yescharacteristic
30C22×C4×C17—22no—
31C22×C4×C17—22no—
32C22×C4×C17—42no—
33C22×C4×C17C22⋊C412yes—
34C22×Dic17—22no—
35C22×Dic17—24no—
36C22×Dic17—22no—
37C22×Dic17—42no—
38C22×Dic17C22⋊C412yes—
39C22×Dic17C2×D412yes—
40C22×Dic17#4114yes—
41C2×Dic34—28no—
42C2×Dic34—28no—
43C2×Dic34—44no—
44C2×Dic34—416no—
45#63247—48no—
46C2×#3624—44no—
47C22⋊C4×C17—42no—
48C22⋊Dic17—42no—
49#63225—44no—
50C4×Dic17—44no—
51#8753—171nomaximal, Sylow
52C23×C17—22no—
53C23×C17—42no—
54C23×C17C2×C22⋊C411yescharacteristic
55C23×C17#11712yes—
56C2×C4×C17—22no—
57C2×C4×C17—24no—
58C2×C4×C17—44no—
59C2×C4×C17—44no—
60C2×C4×C17—42no—
61C2×Dic17—28no—
62C2×Dic17—22no—
63C2×Dic17—24no—
64C2×Dic17—22no—
65C2×Dic17—44no—
66C2×Dic17—44no—
67C2×Dic17—42no—
68C2×Dic17#9914yes—
69C2×Dic17#12314yes—
70Dic34—416no—
71#3624—84no—
72#2310—171no—
73#1784—172no—
74#1306—174no—
75C22×C17—22no—
76C22×C17—22no—
77C22×C17—24no—
78C22×C17—44no—
79C22×C17#38111yescharacteristic
80C22×C17C2×#9912yes—
81C4×C17—42no—
82C4×C17—82no—
83Dic17—24no—
84Dic17—24no—
85Dic17—82no—
86C23×Q8—171no—
87C2×#117—172no—
88C2×#101—344no—
89#407—174no—
90#391—344no—
91#381—171no—
92#381—172no—
93#381#59511yescharacteristic
94C2×C17—22no—
95C2×C17—42no—
96C2×C17#181911yescharacteristic
97C2×C17#183012yes—
98C22×Q8—174no—
99C22×Q8—344no—
100C22×Q8—684no—
101C23×C4—171no—
102C23×C4—171no—
103C23×C4C2×#59511yescharacteristic
104C2×M16—344no—
105#117—684no—
106C2×C4⋊C4—342no—
107C2×C22⋊C4—172no—
108C2×C22⋊C4C2×#59512yes—
109C2×C42—342no—
110#101—688no—
111C22⋊C8—348no—
112#95—22no—
113#95—344no—
114#95—342no—
115C17#875311yescharacteristic, complemented, Sylow
116C24C22×#59511yescharacteristic
117C2×Q8—348no—
118C2×Q8—348no—
119C2×Q8—684no—
120C2×Q8—6816no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—42no—
124C22×C4—172no—
125C22×C4—172no—
126C22×C4—174no—
127C22×C4—344no—
128C22×C4—342no—
129C22×C4—342no—
130C22×C4—682no—
131C22×C4C22⋊#59512yes—
132M16—688no—
133C2×C8—684no—
134C4⋊C4—684no—
135C22⋊C4—42no—
136C22⋊C4—682no—
137C42—684no—
138C23—22no—
139C23—42no—
140C23#1058767712yes—
141C23C2×C22⋊#59511yescharacteristic
142Q8—6816no—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—44no—
146C2×C4—44no—
147C2×C4—42no—
148C2×C4—174no—
149C2×C4—174no—
150C2×C4—348no—
151C2×C4—342no—
152C2×C4—342no—
153C2×C4—344no—
154C2×C4—684no—
155C2×C4—684no—
156C2×C4—682no—
157C8—1364no—
158C22—22no—
159C22—22no—
160C22—24no—
161C22—44no—
162C22#1176375211yescharacteristic
163C22D17⋊#9912yes—
164C4—42no—
165C4—82no—
166C4—344no—
167C4—344no—
168C4—1362no—
169C2—22no—
170C2—42no—
171C2#1454468011yescharacteristic
172C2#1454469812yes—
subgroupG/H
centerC22#11763752
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC17×#381C4
socleC22×C17#381
cosocleC23×Dic17C23
hypercenter#381#595
hypocenterC17#8753
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
115. C17#8753semidirect

Maximal subgroups

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

subgroupindex
#145446182
#145436872
#145313692
#875317