Finite Group Databasebeta

← #17961565

Subgroups — #17961565

Order 4352.

642 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544613C212yesmaximal
2#14543878C214yesmaximal, complemented
3#14531372C211yesmaximal, characteristic
4C2×#10587539C2214yes—
5C2×#10587551—22no—
6#11763752—22no—
7C22×#63252C2211yescharacteristic
8C22×C4⋊Dic17C411yescharacteristic, complemented
9#11762715C412yescomplemented
10#11762711C2212yes—
11#11762686—22no—
12#11762666—22no—
13C2×C17×#117C411yescharacteristic, complemented
14C23×C4×C17C2×C411yescharacteristic
15C22×C22⋊D17D412yes—
16C23×Dic17—21no—
17C2×#63252—24no—
18C2×#63252—42no—
19C2×#63252—42no—
20C22×D68C2311yescharacteristic
21C22×C4×D17D412yes—
22C22×Dic34C2×C411yescharacteristic
23C2×C22⋊#595—24no—
24C17×#117—42no—
25C2×C4⋊C4×C17—21no—
26C2×C22⋊C4×C17—21no—
27C2×C42×C17C2×C412yes—
28C2×#63227—24no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17—42no—
31C2×C4⋊Dic17C2×C412yes—
32#10587551—44no—
33(C2×#595)⋊C4—44no—
34#10587539—28no—
35#10587502—24no—
36C24×C17C22⋊C411yescharacteristic
37C23×D17C2×D412yes—
38C22×#595—44no—
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17C22⋊C411yescharacteristic
44C22×C4×C17C22×C411yescharacteristic
45C2×C22⋊D17—24no—
46C2×C22⋊D17—24no—
47C2×C22⋊D17—42no—
48C22×Dic17—22no—
49C22×Dic17—42no—
50C22×Dic17—82no—
51C22×Dic17C22⋊C412yes—
52#63252—416no—
53C2×D68—41no—
54C2×D68—41no—
55C2×D68#4114yes—
56C2×C4×D17—24no—
57C2×C4×D17—24no—
58C2×C4×D17—42no—
59C2×Dic34—22no—
60C2×Dic34—41no—
61C2×Dic34—41no—
62C22⋊#595—44no—
63C22⋊#595—44no—
64C4⋊C4×C17—42no—
65C22⋊C4×C17—42no—
66C42×C17—42no—
67#63227—84no—
68C4⋊Dic17—42no—
69C4⋊Dic17—42no—
70#12859—171nomaximal, Sylow
71C23×C17—21no—
72C23×C17—21no—
73C23×C17—41no—
74C23×C17—41no—
75C23×C17#9912yes—
76C23×C17C2×C22⋊C411yescharacteristic
77C22×D17—22no—
78C22×D17—22no—
79C22×D17—42no—
80C22×D17—42no—
81C22×D17#12314yes—
82C2×#595—84no—
83C2×#595—84no—
84C2×#595—84no—
85C2×C4×C17—28no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—42no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17#9912yes—
94C2×C4×C17#11712yes—
95C22⋊D17—48no—
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—22no—
99C2×Dic17—44no—
100C2×Dic17—42no—
101C2×Dic17—84no—
102D68—44no—
103C4×D17—48no—
104Dic34—44no—
105#2311—171no—
106#1782—172no—
107#1393—174no—
108C22×C17—21no—
109C22×C17—21no—
110C22×C17—22no—
111C22×C17—42no—
112C22×C17—42no—
113C22×C17—41no—
114C22×C17—41no—
115C22×C17#38111yescharacteristic
116C22×C17C2×#9911yescharacteristic
117C22×C17C2×#9911yescharacteristic
118C2×D17—24no—
119C2×D17—42no—
120C2×D17—42no—
121C2×D17—44no—
122C2×D17—82no—
123#595—164no—
124C4×C17—22no—
125C4×C17—22no—
126C4×C17—82no—
127Dic17—42no—
128Dic17—82no—
129C22×#41—171no—
130C2×#117#59511yescharacteristic, complemented
131C22×C4⋊C4—171no—
132C2×#99—174no—
133C2×#99—342no—
134#391—172no—
135#390—172no—
136#386—342no—
137#381—342no—
138#380—342no—
139C2×C17—21no—
140C2×C17—21no—
141C2×C17—42no—
142C2×C17#181911yescharacteristic
143C2×C17#212811yescharacteristic
144C2×C17#212911yescharacteristic
145D17—44no—
146C2×#41—344no—
147C2×#41—682no—
148C2×#41—682no—
149C22×Q8—171no—
150C22×D4—172no—
151C22×D4—171no—
152C23×C4—172no—
153C23×C4—341no—
154C23×C4C2×#59511yescharacteristic
155#117—42no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—172no—
158C2×C4⋊C4—341no—
159C2×C4⋊C4—682no—
160C2×C22⋊C4—21no—
161C2×C22⋊C4—344no—
162C2×C22⋊C4—344no—
163C2×C42C2×#59512yes—
164#99—348no—
165#99—684no—
166#95—344no—
167#95—684no—
168C17#1285911yescharacteristic, complemented, Sylow
169C24—172no—
170C24C22⋊#59511yescharacteristic
171#41—6816no—
172C2×Q8—342no—
173C2×Q8—681no—
174C2×Q8—681no—
175C2×D4—174no—
176C2×D4—344no—
177C2×D4—344no—
178C2×D4—681no—
179C2×D4—681no—
180C2×D4—682no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—172no—
186C22×C4—344no—
187C22×C4—344no—
188C22×C4—342no—
189C22×C4—682no—
190C22×C4—682no—
191C22×C4—684no—
192C22×C4—1362no—
193C22×C4C22⋊#59511yescharacteristic
194C22×C4C22×#59511yescharacteristic
195C4⋊C4—42no—
196C4⋊C4—682no—
197C4⋊C4—682no—
198C22⋊C4—42no—
199C22⋊C4—684no—
200C22⋊C4—684no—
201C22⋊C4—1364no—
202C42—42no—
203C23—21no—
204C23—21no—
205C23—41no—
206C23—41no—
207C23—174no—
208C23—342no—
209C23—342no—
210C23—682no—
211C23—682no—
212C23#1058755112yes—
213C23C2×C22⋊#59511yescharacteristic
214Q8—684no—
215D4—684no—
216D4—688no—
217C2×C4—28no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—342no—
226C2×C4—342no—
227C2×C4—342no—
228C2×C4—688no—
229C2×C4—684no—
230C2×C4—682no—
231C2×C4—1364no—
232C2×C4—1364no—
233C2×C4—1364no—
234C2×C4—1364no—
235C2×C4#1058753912yes—
236C2×C4#1058767712yes—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—42no—
242C22—41no—
243C22—41no—
244C22—344no—
245C22—684no—
246C22—682no—
247C22—682no—
248C22—1362no—
249C22#1176375211yescharacteristic
250C22C2×#1058755111yescharacteristic
251C22C2×#1058753911yescharacteristic
252C4—22no—
253C4—22no—
254C4—82no—
255C4—2724no—
256C4—682no—
257C4—1362no—
258C2—21no—
259C2—21no—
260C2—42no—
261C2—684no—
262C2#1454467911yescharacteristic
263C2#1454506511yescharacteristic
264C2#1454506811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC22×C17C2×#99
prime radicalC22×#63252C22
cosocleC22×D68C23
hypercenterC2×#117#595
hypocenterC17#12859
LCSG ▷ C22×C4×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
2. #14543878C2semidirect
8. C22×C4⋊Dic17C4semidirect
9. #11762715C4semidirect
13. C2×C17×#117C4semidirect
130. C2×#117#595semidirect
168. C17#12859semidirect

Maximal subgroups

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

subgroupindex
#145446132
#145438782
#145313722
#1285917