Finite Group Databasebeta

← #17949795

Subgroups — #17949795

Order 4352.

608 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 106 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#14544712C212yesmaximal, complemented
2#14543601C212yesmaximal, complemented
3#14543600C212yesmaximal, complemented
4C4×#10587626C211yesmaximal, characteristic
5#11763675—22no—
6#11763675—22no—
7#11763675C2214yes—
8C2×#10587626C411yescharacteristic
9C2×C4×D68C411yescharacteristic
10C2×C4×C22⋊D17—22no—
11#11762712C2211yescharacteristic
12#11762710C2211yescharacteristic
13#11762709—22no—
14#11762678C411yescharacteristic
15C42×Dic17C2211yescharacteristic
16C2×C4×D4×C17C411yescharacteristic
17C22×D4×C17C2×C411yescharacteristic
18C23×C4×C17—21no—
19C22×C22⋊D17—22no—
20C22×D68C2×C411yescharacteristic
21C22×C4×D17—21no—
22C22×#3624—24no—
23C4×D4×C17—42no—
24C2×C4⋊C4×C17C2×C411yescharacteristic
25C2×C22⋊C4×C17—21no—
26C2×C42×C17C2×C411yescharacteristic
27C2×C22⋊Dic17—22no—
28#10587626—22no—
29#10587626C814yescomplemented
30C4×C22⋊D17—48no—
31C2×#63227—21no—
32C2×#63227—22no—
33C2×C4⋊Dic17C2×C411yescharacteristic
34C2×#63225—22no—
35C2×C4×Dic17C2×C411yescharacteristic
36C2×C4×Dic17D412yes—
37C2×C4×Dic17D412yes—
38C2×C4×Dic17C2311yescharacteristic
39C4×D68—42no—
40C24×C17—21no—
41C23×D17—21no—
42C2×D4×C17—21no—
43C2×D4×C17—41no—
44C2×D4×C17—41no—
45C2×D4×C17C2×C812yes—
46C22×C4×C17—21no—
47C22×C4×C17—44no—
48C22×C4×C17—42no—
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22×C411yescharacteristic
52C2×C22⋊D17—28no—
53C2×C22⋊D17—44no—
54C2×C22⋊D17—44no—
55C22×Dic17—21no—
56C22×Dic17C22⋊C412yes—
57C22×Dic17C2×D412yes—
58C2×D68—21no—
59C2×D68—41no—
60C2×D68—41no—
61C2×D68C2×C812yes—
62C2×C4×D17—44no—
63C2×C4×D17—42no—
64C2×#3624—44no—
65C2×#3624—44no—
66C2×#3624—44no—
67C4⋊C4×C17—41no—
68C22⋊C4×C17—42no—
69C42×C17—22no—
70C22⋊Dic17—44no—
71#63227—42no—
72#63227—44no—
73C4⋊Dic17—41no—
74#63225—44no—
75C4×Dic17—24no—
76C4×Dic17—42no—
77C4×Dic17—41no—
78C4×Dic17C2×C812yes—
79C4×Dic17M1612yes—
80#7603—171nomaximal, Sylow
81C23×C17—22no—
82C23×C17—41no—
83C23×C17—41no—
84C23×C17—42no—
85C23×C17—42no—
86C23×C17C2×C22⋊C411yescharacteristic
87C22×D17—22no—
88C22×D17—41no—
89C22×D17—41no—
90C22×D17—42no—
91C22×D17—42no—
92D4×C17—42no—
93D4×C17—42no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—22no—
97C2×C4×C17—21no—
98C2×C4×C17—22no—
99C2×C4×C17—41no—
100C2×C4×C17—42no—
101C2×C4×C17—84no—
102C2×C4×C17#10012yes—
103C2×C4×C17C22×C811yescharacteristic
104C2×C4×C17C2×M1611yescharacteristic
105C22⋊D17—416no—
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—22no—
109C2×Dic17—22no—
110C2×Dic17—41no—
111C2×Dic17—42no—
112C2×Dic17C22⋊C814yes—
113C2×Dic17AGL(1,ℤ/8)14yes—
114D68—42no—
115D68—42no—
116C4×D17—84no—
117#3624—84no—
118C4×#127—171no—
119#1839—172no—
120#1270—172no—
121#1270—172no—
122C22×C17—42no—
123C22×C17—44no—
124C22×C17—81no—
125C22×C17—81no—
126C22×C17—82no—
127C22×C17C2×C22⋊C811yescharacteristic
128C22×C17#41011yescharacteristic
129C22×C17C2×#10011yescharacteristic
130C22×C17#41812yes—
131C22×C17#42112yes—
132C2×D17—42no—
133C2×D17—44no—
134C2×D17—81no—
135C2×D17—81no—
136C2×D17—82no—
137C4×C17—22no—
138C4×C17—21no—
139C4×C17—21no—
140C4×C17—41no—
141C4×C17—81no—
142Dic17—24no—
143Dic17—24no—
144Dic17—81no—
145C2×#127—171no—
146C2×C4×D4—171no—
147C2×C4×D4—342no—
148C2×C4×D4#59511yescharacteristic
149#390—171no—
150#390—171no—
151#390—342no—
152#384—171no—
153C43—171no—
154#336—174no—
155#336—342no—
156#336—342no—
157C2×C17—82no—
158C2×C17#146011yescharacteristic
159C2×C17#147812yes—
160C2×C17#151412yes—
161C2×C17#153611yescharacteristic
162C2×C17#155511yescharacteristic
163D17—82no—
164C22×D4—171no—
165C22×D4—342no—
166C22×D4C2×#59511yescharacteristic
167C23×C4—21no—
168C23×C4—341no—
169C22×C8—344no—
170#127—174no—
171#127—342no—
172C4×D4—42no—
173C4×D4—682no—
174C4×D4—688no—
175C2×C4⋊C4—171no—
176C2×C4⋊C4—342no—
177C2×C4⋊C4C2×#59511yescharacteristic
178C2×C22⋊C4—21no—
179C2×C22⋊C4—342no—
180C2×C22⋊C4—342no—
181C2×C22⋊C4—341no—
182C2×C42—171no—
183C2×C42—172no—
184C2×C42—172no—
185C2×C42—171no—
186C2×C42C2×#59511yescharacteristic
187C17#760311yescharacteristic, complemented, Sylow
188C24—21no—
189C24—341no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—172no—
194C2×D4—348no—
195C2×D4—341no—
196C2×D4—681no—
197C2×D4—681no—
198C2×D4—684no—
199C2×D4—684no—
200C2×D4#6324212yes—
201C22×C4—21no—
202C22×C4—44no—
203C22×C4—42no—
204C22×C4—172no—
205C22×C4—172no—
206C22×C4—341no—
207C22×C4—684no—
208C22×C4—682no—
209C22×C4C22⋊#59511yescharacteristic
210C22×C4C22⋊#59511yescharacteristic
211C22×C4C22×#59511yescharacteristic
212C2×C8—684no—
213C2×C8—684no—
214C2×C8—684no—
215C4⋊C4—41no—
216C4⋊C4—681no—
217C4⋊C4—684no—
218C22⋊C4—42no—
219C22⋊C4—682no—
220C22⋊C4—684no—
221C22⋊C4—684no—
222C42—22no—
223C42—172no—
224C42—172no—
225C42—344no—
226C42—681no—
227C42—682no—
228C23—22no—
229C23—41no—
230C23—41no—
231C23—42no—
232C23—42no—
233C23—342no—
234C23—681no—
235C23—681no—
236C23—682no—
237C23—682no—
238C23C2×C22⋊#59511yescharacteristic
239D4—42no—
240D4—42no—
241D4—682no—
242D4—682no—
243D4—6816no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—84no—
252C2×C4—174no—
253C2×C4—174no—
254C2×C4—342no—
255C2×C4—342no—
256C2×C4—342no—
257C2×C4—342no—
258C2×C4—681no—
259C2×C4—682no—
260C2×C4—1364no—
261C2×C4#1058755312yes—
262C2×C4C2×#6324211yescharacteristic
263C2×C4D17⋊M1611yescharacteristic
264C8—1364no—
265C22—42no—
266C22—44no—
267C22—82no—
268C22—81no—
269C22—81no—
270C22—682no—
271C22—684no—
272C22—1362no—
273C22—1361no—
274C22—1361no—
275C22#1176377711yescharacteristic
276C22#1176378811yescharacteristic
277C22C2×#1058755311yescharacteristic
278C22#1176380112yes—
279C22#1176380612yes—
280C4—21no—
281C4—21no—
282C4—22no—
283C4—41no—
284C4—81no—
285C4—344no—
286C4—344no—
287C4—1361no—
288C2—82no—
289C2—1362no—
290C2#1454402311yescharacteristic
291C2#1454408412yes—
292C2#1454420312yes—
293C2#1454427211yescharacteristic
294C2#1454431111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC2×C4×D4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587626C4
cosocleC2×C4×Dic17C23
hypercenterC2×C4×D4#595
hypocenterC17#7603
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14544712C2semidirect
2. #14543601C2semidirect
3. #14543600C2semidirect
29. #10587626C8semidirect
187. C17#7603semidirect

Maximal subgroups

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

subgroupindex
#145447122
#145436012
#145436002
C4×#105876262
#760317