Finite Group Databasebeta

← #17958192

Subgroups — #17958192

Order 4352.

510 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 98 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#14544013C212yesmaximal
2#14543725C212yesmaximal, complemented
3#14543724C212yesmaximal, complemented
4D17×#382C211yesmaximal, characteristic
5#11763777—22no—
6#11763655—22no—
7#11763654C2214yes—
8C2×C4⋊C4×D17C411yescharacteristic
9C2×C4⋊C4×D17C2211yescharacteristic
10C2×C42×D17C411yescharacteristic
11#11762675C2211yescharacteristic
12#11762674C411yescharacteristic
13#11762674C2211yescharacteristic
14#11762673—22no—
15#95×D17—22no—
16C17×#382C411yescharacteristic
17C22×C4×D17—21no—
18C22×C4×D17—21no—
19C22×C4×D17C2×C411yescharacteristic
20C22×C4×D17D412yes—
21C2×#63242—42no—
22C2×C4⋊C4×C17C2×C411yescharacteristic
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C42×C17C2×C411yescharacteristic
25C2×C4⋊Dic17C2×C411yescharacteristic
26C2×C4⋊Dic17C2311yescharacteristic
27C2×#63225—21no—
28C2×#63225D412yes—
29C2×C4×Dic17—21no—
30C2×C4×Dic17C2×C411yescharacteristic
31C4⋊C4×D17—41no—
32C4⋊C4×D17—41no—
33C4⋊C4×D17—41no—
34C4⋊C4×D17—41no—
35C42×D17—22no—
36C42×D17C814yescomplemented
37C22⋊#3624—24no—
38#10587543—42no—
39C17×#95—22no—
40#10587502—22no—
41#10587502—22no—
42#10587502—22no—
43C23×D17C22⋊C411yescharacteristic
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17C22⋊C412yes—
47C22×C4×C17C22×C411yescharacteristic
48C22×Dic17—21no—
49C22×Dic17—21no—
50C22×Dic17C22⋊C411yescharacteristic
51C22×Dic17C2×D412yes—
52C2×C4×D17—21no—
53C2×C4×D17—21no—
54C2×C4×D17—22no—
55C2×C4×D17—24no—
56C2×C4×D17—22no—
57C2×C4×D17—22no—
58C2×C4×D17—42no—
59C2×C4×D17—42no—
60C2×C4×D17—44no—
61C2×C4×D17—44no—
62C2×C4×D17—41no—
63C2×C4×D17—41no—
64C2×C4×D17C2×C812yes—
65C2×C4×D17M1612yes—
66C2×#3624—44no—
67#63242—84no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—41no—
70C42×C17—21no—
71C42×C17C2×C812yescomplemented
72C4⋊Dic17—41no—
73C4⋊Dic17—41no—
74#63225—42no—
75#63225—42no—
76C4×Dic17—21no—
77C4×Dic17—24no—
78C4×Dic17C2×C812yescomplemented
79C2×#1324—171nomaximal, Sylow
80C23×C17C2×C22⋊C411yescharacteristic
81C22×D17—22no—
82C22×D17—22no—
83C22×D17C22⋊C812yes—
84C22×D17#9911yescharacteristic
85C22×D17#9911yescharacteristic
86C22×D17#10112yes—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—22no—
90C2×C4×C17—22no—
91C2×C4×C17—41no—
92C2×C4×C17—41no—
93C2×C4×C17—42no—
94C2×C4×C17—42no—
95C2×C4×C17—41no—
96C2×C4×C17C22×C811yescharacteristic
97C2×C4×C17C2×M1611yescharacteristic
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—22no—
101C2×Dic17—22no—
102C2×Dic17—41no—
103C2×Dic17—41no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17—41no—
107C2×Dic17C22⋊C812yes—
108C4×D17—22no—
109C4×D17—22no—
110C4×D17—22no—
111C4×D17—22no—
112C4×D17—48no—
113C4×D17—44no—
114C4×D17—82no—
115C4×D17—82no—
116C4×D17—82no—
117#3624—84no—
118C2×#382—171no—
119C2×#324—172no—
120#1324—172no—
121#1324—172no—
122C22×C17—21no—
123C22×C17—21no—
124C22×C17C2×C22⋊C811yescharacteristic
125C22×C17C2×#9911yescharacteristic
126C22×C17C2×#10111yescharacteristic
127C2×D17—21no—
128C2×D17—21no—
129C2×D17—24no—
130C2×D17—24no—
131C2×D17#32412yes—
132C2×D17#32412yes—
133C2×D17#35412yes—
134C2×D17#35512yes—
135C4×C17—21no—
136C4×C17—21no—
137C4×C17—42no—
138C4×C17—42no—
139C4×C17—81no—
140Dic17—22no—
141Dic17—42no—
142Dic17—42no—
143Dic17—81no—
144C22×C4⋊C4—171no—
145C22×C4⋊C4—171no—
146C22×C42—171no—
147C2×C22⋊C8—342no—
148#382—171no—
149#382—171no—
150#382—171no—
151#382—342no—
152#382#59511yescharacteristic
153C2×#95—342no—
154#324—174no—
155#324—342no—
156C2×C17—21no—
157C2×C17—21no—
158C2×C17C2×#32411yescharacteristic
159C2×C17C2×#35411yescharacteristic
160C2×C17C2×#35511yescharacteristic
161D17—22no—
162D17#132414yescomplemented
163C23×C4—171no—
164C23×C4—172no—
165C23×C4—341no—
166C23×C4—341no—
167C22×C8—682no—
168C2×C4⋊C4—172no—
169C2×C4⋊C4—171no—
170C2×C4⋊C4—171no—
171C2×C4⋊C4—341no—
172C2×C4⋊C4—681no—
173C2×C4⋊C4—681no—
174C2×C4⋊C4—681no—
175C2×C4⋊C4—681no—
176C2×C4⋊C4C2×#59511yescharacteristic
177C2×C4⋊C4C2×#59511yescharacteristic
178C2×C42—171no—
179C2×C42—174no—
180C2×C42—342no—
181C2×C42—341no—
182C2×C42C2×#59511yescharacteristic
183C22⋊C8—344no—
184C22⋊C8—682no—
185#95—22no—
186#95—342no—
187#95—342no—
188#95—342no—
189C17C2×#132411yescharacteristic, complemented, Sylow
190C24—171no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—171no—
194C22×C4—172no—
195C22×C4—172no—
196C22×C4—172no—
197C22×C4—341no—
198C22×C4—341no—
199C22×C4—342no—
200C22×C4—344no—
201C22×C4—342no—
202C22×C4—342no—
203C22×C4—341no—
204C22×C4—341no—
205C22×C4—682no—
206C22×C4—682no—
207C22×C4—684no—
208C22×C4—681no—
209C22×C4—681no—
210C22×C4—684no—
211C22×C4C22⋊#59512yes—
212C22×C4C22×#59511yescharacteristic
213C2×C8—684no—
214C2×C8—1364no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—682no—
218C4⋊C4—681no—
219C4⋊C4—681no—
220C4⋊C4—682no—
221C42—21no—
222C42—172no—
223C42—344no—
224C42—341no—
225C42#6324212yescomplemented
226C23—171no—
227C23—172no—
228C23—171no—
229C23—172no—
230C23—342no—
231C23—342no—
232C23C2×C22⋊#59511yescharacteristic
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—172no—
243C2×C4—342no—
244C2×C4—342no—
245C2×C4—342no—
246C2×C4—342no—
247C2×C4—341no—
248C2×C4—341no—
249C2×C4—342no—
250C2×C4—342no—
251C2×C4—684no—
252C2×C4—688no—
253C2×C4—681no—
254C2×C4—681no—
255C2×C4—682no—
256C2×C4—682no—
257C2×C4—681no—
258C2×C4—1362no—
259C2×C4—1362no—
260C2×C4—1362no—
261C2×C4C2×#6324211yescharacteristic
262C2×C4D17⋊M1611yescharacteristic
263C8—1364no—
264C22—21no—
265C22—21no—
266C22—172no—
267C22—172no—
268C22—172no—
269C22—172no—
270C22—344no—
271C22—344no—
272C22—341no—
273C22—341no—
274C22#1176377711yescharacteristic
275C22D17⋊#9911yescharacteristic
276C22D17⋊#10111yescharacteristic
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—81no—
282C4—342no—
283C4—682no—
284C4—682no—
285C4—1361no—
286C2—21no—
287C2—21no—
288C2—174no—
289C2—342no—
290C2#1454401311yescharacteristic
291C2D17⋊#35411yescharacteristic
292C2D17⋊#35511yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#382C4
socleC22×C17C2×#99
prime radicalC23×D17C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenter#382#595
hypocenterC17C2×#1324
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #14543725C2semidirect
3. #14543724C2semidirect
36. C42×D17C8semidirect
71. C42×C17C2×C8semidirect
78. C4×Dic17C2×C8semidirect
162. D17#1324semidirect
189. C17C2×#1324semidirect
225. C42#63242semidirect

Maximal subgroups

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

subgroupindex
#145440132
#145437252
#145437242
D17×#3822
C2×#132417