Finite Group Databasebeta

← #17958135

Subgroups — #17958135

Order 4352.

686 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 112 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, complemented
2#14543708C214yesmaximal, complemented
3#14531366C211yesmaximal, characteristic
4#11763825—22no—
5#11763654—22no—
6#11763652C2214yes—
7C2×#10587612C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762712—22no—
10#11762712—22no—
11#11762665C412yes—
12#11762665C2212yes—
13C23×D4×C17C411yescharacteristic
14C25×C17C2×C412yes—
15C22×D4×C17—21no—
16C22×D4×C17—21no—
17C22×D4×C17—22no—
18C22×D4×C17—42no—
19C22×D4×C17—42no—
20C22×D4×C17C814yescomplemented
21C23×C4×C17C2×C411yescharacteristic
22C2×C22⋊Dic17—24no—
23C2×C22⋊Dic17—24no—
24C2×C22⋊Dic17C2×C412yes—
25C2×C22⋊Dic17C2×C411yescharacteristic
26C2×C22⋊Dic17C2311yescharacteristic
27#10587612—42no—
28#10587612—42no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17D412yes—
31C2×C4×Dic17—21no—
32C2×C4×Dic17D412yes—
33C22⋊#3624—24no—
34C4⋊#3624—42no—
35C4×#3624—42no—
36C24×C17—22no—
37C24×C17—22no—
38C24×C17—42no—
39C24×C17—42no—
40C24×C17—84no—
41C24×C17C2×C814yes—
42C24×C17C22×C411yescharacteristic
43C2×D4×C17—24no—
44C2×D4×C17—24no—
45C2×D4×C17—42no—
46C2×D4×C17—42no—
47C2×D4×C17—48no—
48C2×D4×C17—48no—
49C2×D4×C17—42no—
50C2×D4×C17—42no—
51C22×C4×C17—22no—
52C22×C4×C17—22no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C2×C812yes—
56C22×C4×C17M1612yes—
57C22×Dic17—22no—
58C22×Dic17C22⋊C412yes—
59C22×Dic17C2×D412yes—
60C2×#3624—44no—
61C22⋊Dic17—41no—
62C22⋊Dic17—41no—
63C22⋊Dic17—42no—
64C22⋊Dic17—84no—
65C22⋊Dic17—84no—
66C4⋊Dic17—42no—
67C4⋊Dic17—42no—
68C4×Dic17—22no—
69C4×Dic17—22no—
70C4×Dic17—42no—
71#11427—171nomaximal, Sylow
72C23×C17—21no—
73C23×C17—21no—
74C23×C17—24no—
75C23×C17—42no—
76C23×C17—44no—
77C23×C17—44no—
78C23×C17—44no—
79C23×C17—44no—
80C23×C17—42no—
81C23×C17—42no—
82C23×C17—84no—
83C23×C17—84no—
84C23×C17—88no—
85C23×C17—88no—
86C23×C17C2×C22⋊C411yescharacteristic
87C23×C17C22×C811yescharacteristic
88C23×C17C2×M1611yescharacteristic
89D4×C17—48no—
90D4×C17—48no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—24no—
94C2×C4×C17—24no—
95C2×C4×C17C22⋊C812yes—
96C2×C4×C17C22⋊C812yes—
97C2×C4×C17#9912yes—
98C2×C4×C17#10012yes—
99C2×Dic17—22no—
100C2×Dic17—22no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103C2×Dic17—44no—
104C2×Dic17—42no—
105#3624—84no—
106#2309—171no—
107#1458—172no—
108#1316—174no—
109C22×C17—22no—
110C22×C17—21no—
111C22×C17—21no—
112C22×C17—41no—
113C22×C17—41no—
114C22×C17—42no—
115C22×C17—44no—
116C22×C17—44no—
117C22×C17—42no—
118C22×C17—44no—
119C22×C17—84no—
120C22×C17—88no—
121C22×C17—88no—
122C22×C17—84no—
123C22×C17C2×C22⋊C811yescharacteristic
124C22×C17C2×#9911yescharacteristic
125C22×C17C2×#10011yescharacteristic
126C4×C17—22no—
127C4×C17#32314yes—
128Dic17—42no—
129Dic17—42no—
130Dic17—82no—
131C23×D4#59511yescharacteristic
132C2×#117—171no—
133C2×#117—171no—
134#431—342no—
135#390—342no—
136#390—342no—
137#379—172no—
138#379—172no—
139#324—342no—
140#323—174no—
141C2×C17—21no—
142C2×C17—21no—
143C2×C17—41no—
144C2×C17—41no—
145C2×C17—84no—
146C2×C17C2×#32311yescharacteristic
147C2×C17#212212yes—
148C25C2×#59512yes—
149C22×D4—22no—
150C22×D4—21no—
151C22×D4—21no—
152C22×D4—42no—
153C22×D4—42no—
154C22×D4#362414yescomplemented
155C23×C4C2×#59511yescharacteristic
156#117—682no—
157#117—682no—
158C2×C4⋊C4—172no—
159C2×C4⋊C4—341no—
160C2×C22⋊C4—171no—
161C2×C22⋊C4—171no—
162C2×C22⋊C4—172no—
163C2×C22⋊C4—344no—
164C2×C22⋊C4—344no—
165C2×C42—172no—
166C2×C42—341no—
167C4⋊C8—682no—
168C22⋊C8—344no—
169C4×C8—682no—
170C17#1142711yescharacteristic, complemented, Sylow
171C24—22no—
172C24—22no—
173C24—42no—
174C24—42no—
175C24—84no—
176C24C2×#362414yes—
177C24C22×#59511yescharacteristic
178C2×D4—24no—
179C2×D4—24no—
180C2×D4—42no—
181C2×D4—42no—
182C2×D4—48no—
183C2×D4—48no—
184C2×D4—42no—
185C2×D4—42no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—172no—
189C22×C4—172no—
190C22×C4—342no—
191C22×C4C2×#362412yes—
192C22×C4#6324712yes—
193C22×C4C22⋊#59511yescharacteristic
194C22×C4C22⋊#59511yescharacteristic
195C2×C8—684no—
196C4⋊C4—682no—
197C4⋊C4—682no—
198C22⋊C4—681no—
199C22⋊C4—681no—
200C22⋊C4—682no—
201C22⋊C4—1364no—
202C22⋊C4—1364no—
203C42—342no—
204C42—342no—
205C42—682no—
206C23—21no—
207C23—21no—
208C23—24no—
209C23—42no—
210C23—44no—
211C23—44no—
212C23—44no—
213C23—44no—
214C23—42no—
215C23—42no—
216C23—84no—
217C23—84no—
218C23—88no—
219C23—88no—
220C23C22×#362411yescharacteristic
221C23C2×#6324711yescharacteristic
222C23C2×C22⋊#59511yescharacteristic
223D4—48no—
224D4—48no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—24no—
228C2×C4—24no—
229C2×C4—342no—
230C2×C4—342no—
231C2×C4—682no—
232C2×C4—682no—
233C2×C4—684no—
234C2×C4—682no—
235C2×C4#1058755112yes—
236C2×C4C22⋊#362412yes—
237C2×C4C22⋊#362412yes—
238C2×C4#1058755312yes—
239C8—1364no—
240C22—22no—
241C22—21no—
242C22—21no—
243C22—41no—
244C22—41no—
245C22—42no—
246C22—44no—
247C22—44no—
248C22—42no—
249C22—44no—
250C22—84no—
251C22—88no—
252C22—88no—
253C22—84no—
254C22C2×C22⋊#362411yescharacteristic
255C22C2×#1058755111yescharacteristic
256C22C2×#1058755311yescharacteristic
257C4—22no—
258C4—682no—
259C4—682no—
260C4—1362no—
261C4#1176365214yes—
262C2—21no—
263C2—21no—
264C2—41no—
265C2—41no—
266C2—84no—
267C2C2×#1176365211yescharacteristic
268C2#1454504312yes—
subgroupG/H
centerC22C2×#10587551
commutatorC23×C17C22×C8
FrattiniC24C22×#595
Fitting, prime radicalC23×D4×C17C4
socleC22×C17C2×#99
cosocleC2×C22⋊Dic17C23
hypercenterC23×D4#595
hypocenterC17#11427
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #14544015C2semidirect
2. #14543708C2semidirect
20. C22×D4×C17C8semidirect
154. C22×D4#3624semidirect
170. C17#11427semidirect

Maximal subgroups

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

subgroupindex
#145440152
#145437082
#145313662
#1142717