Finite Group Databasebeta

← #17958140

Subgroups — #17958140

Order 4352.

526 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 104 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#14544015C212yesmaximal
2#14543711C214yesmaximal
3#14531368C211yesmaximal, characteristic
4#11763825—22no—
5#11763654—22no—
6#11763652C2214yes—
7C23×Dic34C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762715—22no—
10#11762714—22no—
11#11762670C412yes—
12#11762670C2212yes—
13C2×C17×#117C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17C2×C412yes—
16C22×Dic34—21no—
17C22×Dic34—21no—
18C22×Dic34—22no—
19C22×Dic34—42no—
20C22×Dic34—42no—
21C22×Dic34C814yescomplemented
22C17×#117—42no—
23C2×C4⋊C4×C17—21no—
24C2×C22⋊C4×C17C2×C412yes—
25C2×C42×C17—21no—
26C2×C22⋊Dic17C2×C411yescharacteristic
27C2×C22⋊Dic17C2311yescharacteristic
28#10587612—42no—
29C2×C4⋊Dic17D412yes—
30C2×C4×Dic17D412yes—
31C22⋊#3624—24no—
32C4⋊#3624—42no—
33C4×#3624—42no—
34#10587502—24no—
35#10587502—24no—
36C24×C17C22×C411yescharacteristic
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17C22⋊C411yescharacteristic
41C22×C4×C17C22⋊C411yescharacteristic
42C22×C4×C17C2×C812yes—
43C22×C4×C17M1612yes—
44C22×Dic17—22no—
45C22×Dic17—22no—
46C22×Dic17—42no—
47C22×Dic17—42no—
48C22×Dic17C22⋊C412yes—
49C22×Dic17C2×C814yes—
50C22×Dic17C2×D412yes—
51C2×Dic34—24no—
52C2×Dic34—24no—
53C2×Dic34—42no—
54C2×Dic34—42no—
55C2×Dic34—48no—
56C2×Dic34—42no—
57C2×Dic34—42no—
58C2×Dic34—48no—
59C2×#3624—44no—
60C4⋊C4×C17—42no—
61C22⋊C4×C17—42no—
62C42×C17—42no—
63C22⋊Dic17—41no—
64C22⋊Dic17—41no—
65C4⋊Dic17—42no—
66C4×Dic17—22no—
67C4×Dic17—22no—
68#11428—171nomaximal, Sylow
69C23×C17—21no—
70C23×C17—21no—
71C23×C17—42no—
72C23×C17C2×C22⋊C411yescharacteristic
73C23×C17C22×C811yescharacteristic
74C23×C17C2×M1611yescharacteristic
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—24no—
78C2×C4×C17—24no—
79C2×C4×C17—44no—
80C2×C4×C17—42no—
81C2×C4×C17C22⋊C812yes—
82C2×C4×C17C22⋊C812yes—
83C2×C4×C17#9912yes—
84C2×C4×C17#10012yes—
85C2×Dic17—24no—
86C2×Dic17—22no—
87C2×Dic17—22no—
88C2×Dic17—44no—
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—44no—
92C2×Dic17—42no—
93C2×Dic17—42no—
94Dic34—48no—
95Dic34—48no—
96#3624—84no—
97#2310—171no—
98#1458—172no—
99#1317—174no—
100C22×C17—22no—
101C22×C17—21no—
102C22×C17—21no—
103C22×C17—41no—
104C22×C17—41no—
105C22×C17—42no—
106C22×C17—42no—
107C22×C17C2×C22⋊C811yescharacteristic
108C22×C17C2×#9911yescharacteristic
109C22×C17C2×#10011yescharacteristic
110C4×C17—22no—
111C4×C17—82no—
112C4×C17#32314yes—
113Dic17—42no—
114Dic17—42no—
115Dic17—44no—
116C23×Q8—171no—
117C2×#117—171no—
118C2×#117#59511yescharacteristic
119#431—342no—
120#391—342no—
121#391—342no—
122#381—172no—
123#381—172no—
124#324—342no—
125#323—174no—
126C2×C17—21no—
127C2×C17—21no—
128C2×C17—41no—
129C2×C17—41no—
130C2×C17C2×#32311yescharacteristic
131C2×C17#212312yes—
132C22×Q8—174no—
133C22×Q8—342no—
134C22×Q8—341no—
135C22×Q8—341no—
136C22×Q8—682no—
137C22×Q8—682no—
138C23×C4—172no—
139C23×C4C2×#59511yescharacteristic
140#117—42no—
141#117—682no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—172no—
144C2×C22⋊C4—171no—
145C2×C22⋊C4—171no—
146C2×C22⋊C4C2×#59512yes—
147C2×C42—21no—
148C2×C42—172no—
149C4⋊C8—682no—
150C22⋊C8—344no—
151C4×C8—682no—
152#95—344no—
153#95—344no—
154C17#1142811yescharacteristic, complemented, Sylow
155C24C22×#59511yescharacteristic
156C2×Q8—344no—
157C2×Q8—344no—
158C2×Q8—688no—
159C2×Q8—682no—
160C2×Q8—682no—
161C2×Q8—688no—
162C2×Q8—682no—
163C2×Q8—682no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—174no—
168C22×C4—172no—
169C22×C4—172no—
170C22×C4—342no—
171C22×C4—342no—
172C22×C4—682no—
173C22×C4—682no—
174C22×C4#6324212yes—
175C22×C4#6324312yes—
176C22×C4C22⋊#59511yescharacteristic
177C22×C4C22⋊#59511yescharacteristic
178C2×C8—684no—
179C4⋊C4—42no—
180C4⋊C4—682no—
181C22⋊C4—42no—
182C22⋊C4—681no—
183C22⋊C4—681no—
184C42—42no—
185C42—342no—
186C42—342no—
187C23—21no—
188C23—21no—
189C23—42no—
190C23C2×#6324211yescharacteristic
191C23C2×#6324311yescharacteristic
192C23C2×C22⋊#59511yescharacteristic
193Q8—688no—
194Q8—688no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—24no—
198C2×C4—24no—
199C2×C4—44no—
200C2×C4—42no—
201C2×C4—344no—
202C2×C4—342no—
203C2×C4—342no—
204C2×C4—684no—
205C2×C4—682no—
206C2×C4—682no—
207C2×C4—684no—
208C2×C4—682no—
209C2×C4—682no—
210C2×C4#1058753912yes—
211C2×C4#1058754312yes—
212C2×C4#1058754312yes—
213C2×C4#1058755312yes—
214C8—1364no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—42no—
221C22—42no—
222C22C2×#1058754311yescharacteristic
223C22C2×#1058753911yescharacteristic
224C22C2×#1058755311yescharacteristic
225C4—22no—
226C4—82no—
227C4—684no—
228C4—682no—
229C4—682no—
230C4#1176365314yes—
231C2—21no—
232C2—21no—
233C2—41no—
234C2—41no—
235C2C2×#1176365311yescharacteristic
236C2#1454504812yes—
subgroupG/H
centerC22C2×#10587539
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC24×C17C22×C4
cosocleC2×C22⋊Dic17C23
hypercenterC2×#117#595
hypocenterC17#11428
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
21. C22×Dic34C8semidirect
154. C17#11428semidirect

Maximal subgroups

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

subgroupindex
#145440152
#145437112
#145313682
#1142817