Finite Group Databasebeta

← #17958159

Subgroups — #17958159

Order 4352.

526 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544018C212yesmaximal
2#14543715C212yesmaximal, complemented
3#14543714C212yesmaximal, complemented
4#14531367C211yesmaximal, characteristic
5#11763826—22no—
6#11763654C2214yes—
7#11763653—22no—
8C22×Q8×D17C411yescharacteristic
9C2×#10587578C2211yescharacteristic
10C2×#10587558C411yescharacteristic
11#11762716C2211yescharacteristic
12#11762715C2211yescharacteristic
13#11762714C411yescharacteristic
14#11762713—22no—
15#11762671—22no—
16C17×#391C411yescharacteristic
17C22×Q8×C17C2×C411yescharacteristic
18C2×Q8×D17—22no—
19C2×Q8×D17—42no—
20C2×Q8×D17—42no—
21C2×Q8×D17C814yescomplemented
22C22×C4×D17—21no—
23C22×C4×D17C2×C411yescharacteristic
24C22×Dic34—21no—
25C22×Dic34C2×C411yescharacteristic
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C42×C17C2×C411yescharacteristic
28C2×#63227—21no—
29C2×#63227D412yes—
30C2×C4⋊Dic17C2311yescharacteristic
31C2×#63225—21no—
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34#10587578—42no—
35#10587558—42no—
36C22⋊#3624—24no—
37#10587544—42no—
38C4×#3624—42no—
39C17×#95—22no—
40#10587502—22no—
41#10587502—22no—
42#10587502—22no—
43C23×D17C22⋊C411yescharacteristic
44C2×Q8×C17—21no—
45C2×Q8×C17—41no—
46C2×Q8×C17—41no—
47C2×Q8×C17C2×C812yes—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17C22⋊C412yes—
51C22×C4×C17C22×C411yescharacteristic
52C22×Dic17—21no—
53C22×Dic17—21no—
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D412yes—
56Q8×D17—48no—
57Q8×D17—48no—
58C2×C4×D17—22no—
59C2×C4×D17—22no—
60C2×C4×D17—24no—
61C2×C4×D17—42no—
62C2×C4×D17—42no—
63C2×C4×D17C2×C812yes—
64C2×C4×D17M1612yes—
65C2×Dic34—21no—
66C2×Dic34—24no—
67C2×Dic34—42no—
68C2×Dic34—42no—
69C2×Dic34—41no—
70C2×Dic34—41no—
71C2×Dic34C2×C812yes—
72C2×#3624—44no—
73C4⋊C4×C17—41no—
74C42×C17—41no—
75#63227—42no—
76#63227—42no—
77C4⋊Dic17—41no—
78#63225—42no—
79C4×Dic17—22no—
80C4×Dic17—22no—
81C4×Dic17—41no—
82#11434—171nomaximal, Sylow
83C23×C17C2×C22⋊C411yescharacteristic
84C22×D17—21no—
85C22×D17—21no—
86C22×D17—41no—
87C22×D17—41no—
88C22×D17C22⋊C812yes—
89Q8×C17—42no—
90Q8×C17—42no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—22no—
94C2×C4×C17—22no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17—42no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17C22×C811yescharacteristic
102C2×C4×C17C2×M1611yescharacteristic
103C2×Dic17—22no—
104C2×Dic17—22no—
105C2×Dic17—41no—
106C2×Dic17—41no—
107C2×Dic17—42no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—41no—
111C2×Dic17C22⋊C812yes—
112C2×Dic17#9912yes—
113C2×Dic17#10012yes—
114C4×D17—24no—
115C4×D17—24no—
116C4×D17—48no—
117Dic34—42no—
118Dic34—48no—
119Dic34—42no—
120#3624—84no—
121#2310—171no—
122#1458—172no—
123#1319—172no—
124#1319—172no—
125C22×C17—21no—
126C22×C17—21no—
127C22×C17C2×C22⋊C811yescharacteristic
128C22×C17C2×#9911yescharacteristic
129C22×C17C2×#10011yescharacteristic
130C2×D17—22no—
131C2×D17—42no—
132C2×D17—41no—
133C2×D17—41no—
134C2×D17—42no—
135C4×C17—21no—
136C4×C17—21no—
137C4×C17—42no—
138C4×C17—42no—
139C4×C17—81no—
140Dic17—42no—
141Dic17—42no—
142Dic17—81no—
143Dic17#32314yes—
144C23×Q8—171no—
145C2×#117—171no—
146C2×#117—171no—
147#431—342no—
148#391—171no—
149#391—171no—
150#391—171no—
151#391—342no—
152#391#59511yescharacteristic
153#381—342no—
154#324—174no—
155#323—342no—
156C2×C17—21no—
157C2×C17—21no—
158C2×C17C2×#32311yescharacteristic
159C2×C17#212911yescharacteristic
160C2×C17#213511yescharacteristic
161D17—42no—
162C22×Q8—174no—
163C22×Q8—171no—
164C22×Q8—341no—
165C22×Q8—342no—
166C22×Q8—682no—
167C22×Q8—682no—
168C22×Q8C2×#59511yescharacteristic
169C23×C4—171no—
170C23×C4—341no—
171#117—682no—
172#117—682no—
173C2×C4⋊C4—171no—
174C2×C4⋊C4—341no—
175C2×C4⋊C4C2×#59511yescharacteristic
176C2×C22⋊C4—172no—
177C2×C22⋊C4—341no—
178C2×C42—172no—
179C2×C42—171no—
180C2×C42C2×#59511yescharacteristic
181C4⋊C8—682no—
182C22⋊C8—344no—
183C4×C8—682no—
184#95—22no—
185#95—342no—
186#95—342no—
187#95—342no—
188C17#1143411yescharacteristic, complemented, Sylow
189C24—171no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—172no—
194C2×Q8—344no—
195C2×Q8—341no—
196C2×Q8—681no—
197C2×Q8—681no—
198C2×Q8—682no—
199C2×Q8—682no—
200C2×Q8—688no—
201C2×Q8—688no—
202C2×Q8#6324212yes—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—171no—
206C22×C4—172no—
207C22×C4—172no—
208C22×C4—172no—
209C22×C4—342no—
210C22×C4—342no—
211C22×C4—344no—
212C22×C4—341no—
213C22×C4—341no—
214C22×C4—682no—
215C22×C4—682no—
216C22×C4C22⋊#59512yes—
217C22×C4C22×#59511yescharacteristic
218C2×C8—684no—
219C4⋊C4—41no—
220C4⋊C4—681no—
221C4⋊C4—682no—
222C22⋊C4—682no—
223C22⋊C4—682no—
224C42—41no—
225C42—342no—
226C42—342no—
227C42—681no—
228C23—172no—
229C23—341no—
230C23—341no—
231C23—681no—
232C23—681no—
233C23C2×C22⋊#59511yescharacteristic
234Q8—42no—
235Q8—42no—
236Q8—682no—
237Q8—682no—
238Q8—688no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—172no—
250C2×C4—172no—
251C2×C4—172no—
252C2×C4—344no—
253C2×C4—344no—
254C2×C4—342no—
255C2×C4—342no—
256C2×C4—688no—
257C2×C4—681no—
258C2×C4—681no—
259C2×C4—682no—
260C2×C4—681no—
261C2×C4—681no—
262C2×C4—681no—
263C2×C4C2×#6324211yescharacteristic
264C2×C4D17⋊M1611yescharacteristic
265C8—1364no—
266C22—21no—
267C22—21no—
268C22—342no—
269C22—682no—
270C22—682no—
271C22—681no—
272C22—681no—
273C22#1176377711yescharacteristic
274C22D17⋊#9911yescharacteristic
275C22D17⋊#10011yescharacteristic
276C4—21no—
277C4—21no—
278C4—42no—
279C4—42no—
280C4—81no—
281C4—174no—
282C4—682no—
283C4—682no—
284C4—1361no—
285C2—21no—
286C2—21no—
287C2—682no—
288C2#1454401011yescharacteristic
289C2#1454506711yescharacteristic
290C2#1454508711yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#391C4
socleC22×C17C2×#99
prime radicalC23×D17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenter#391#595
hypocenterC17#11434
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. #14543715C2semidirect
3. #14543714C2semidirect
21. C2×Q8×D17C8semidirect
188. C17#11434semidirect

Maximal subgroups

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

subgroupindex
#145440182
#145437152
#145437142
#145313672
#1143417