Finite Group Databasebeta

← #17958403

Subgroups — #17958403

Order 4352.

814 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 88 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#14544032C212yesmaximal, complemented
2#14543712C214yesmaximal, complemented
3C2×#11762712C211yesmaximal, characteristic
4#11763779—22no—
5#11763654—22no—
6#11763654C2214yescomplemented
7C22×C4⋊Dic17C2211yescharacteristic
8C22×C22⋊Dic17—22no—
9C22×C4×Dic17C411yescharacteristic
10#11762712—22no—
11#11762712C412yes—
12#11762712C2212yes—
13C23×D4×C17C411yescharacteristic
14C25×C17—21no—
15C22×D4×C17—24no—
16C22×D4×C17—21no—
17C22×D4×C17—41no—
18C22×D4×C17—41no—
19C22×D4×C17—42no—
20C22×D4×C17C2×C412yes—
21C23×C4×C17C2×C411yescharacteristic
22C23×Dic17—21no—
23C23×Dic17D412yes—
24C2×#63247—42no—
25C2×C22⋊Dic17—24no—
26C2×C22⋊Dic17—24no—
27C2×C22⋊Dic17—48no—
28C2×C4⋊Dic17—41no—
29C2×C4⋊Dic17—41no—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×C4⋊Dic17D412yes—
32C2×C4⋊Dic17C2311yescharacteristic
33C2×C4×Dic17—21no—
34C2×C4×Dic17—42no—
35C2×C4×Dic17C2×C412yes—
36C22⋊#3624—24no—
37C22⋊#3624—42no—
38C24×C17—24no—
39C24×C17—22no—
40C24×C17—42no—
41C24×C17—44no—
42C24×C17—44no—
43C24×C17—41no—
44C24×C17—41no—
45C24×C17C22⋊C411yescharacteristic
46C2×D4×C17—24no—
47C2×D4×C17—22no—
48C2×D4×C17—42no—
49C2×D4×C17—42no—
50C2×D4×C17—48no—
51C2×D4×C17—48no—
52C2×D4×C17—42no—
53C2×D4×C17—42no—
54C2×D4×C17M1614yescomplemented
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—22no—
58C22×C4×C17—22no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—24no—
62C22×Dic17—22no—
63C22×Dic17—22no—
64C22×Dic17—22no—
65C22×Dic17—42no—
66C22×Dic17—42no—
67C22×Dic17—44no—
68C22×Dic17C22⋊C412yes—
69C22×Dic17C2×D412yes—
70#63247—84no—
71C2×#3624—44no—
72C22⋊Dic17—48no—
73C22⋊Dic17—48no—
74C4⋊Dic17—41no—
75C4⋊Dic17—42no—
76C4⋊Dic17—41no—
77C4×Dic17—42no—
78C4×Dic17—42no—
79#11505—171nomaximal, Sylow
80C23×C17—22no—
81C23×C17—22no—
82C23×C17—21no—
83C23×C17—21no—
84C23×C17—24no—
85C23×C17—44no—
86C23×C17—44no—
87C23×C17—44no—
88C23×C17—416no—
89C23×C17—44no—
90C23×C17—42no—
91C23×C17—42no—
92C23×C17—88no—
93C23×C17—82no—
94C23×C17—82no—
95C23×C17—82no—
96C23×C17—82no—
97C23×C17#9911yescharacteristic
98C23×C17#9911yescharacteristic
99C23×C17C2×C22⋊C411yescharacteristic
100D4×C17—44no—
101D4×C17—48no—
102D4×C17—44no—
103C2×C4×C17—24no—
104C2×C4×C17—24no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17#10012yes—
110C2×C4×C17C2×M1612yes—
111C2×Dic17—24no—
112C2×Dic17—22no—
113C2×Dic17—22no—
114C2×Dic17—48no—
115C2×Dic17—42no—
116C2×Dic17—44no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C2×Dic17—42no—
120C2×Dic17—82no—
121#3624—84no—
122C2×#390—171no—
123#1463—172no—
124#1318—174no—
125C22×C17—24no—
126C22×C17—24no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17—21no—
133C22×C17—48no—
134C22×C17—44no—
135C22×C17—84no—
136C22×C17—88no—
137C22×C17—88no—
138C22×C17—82no—
139C22×C17—82no—
140C22×C17#35312yes—
141C22×C17#35512yes—
142C22×C17#40711yescharacteristic
143C22×C17C2×#9911yescharacteristic
144C22×C17C2×#10011yescharacteristic
145C4×C17—22no—
146C4×C17—22no—
147Dic17—44no—
148Dic17—42no—
149Dic17—42no—
150C23×D4#59511yescharacteristic
151C22×C4⋊C4—171no—
152C22×C22⋊C4—342no—
153C22×C42—171no—
154#407—342no—
155#390—172no—
156#390—172no—
157#390—342no—
158#324—174no—
159#324—342no—
160C2×C17—21no—
161C2×C17—21no—
162C2×C17—22no—
163C2×C17—22no—
164C2×C17—84no—
165C2×C17#146211yescharacteristic
166C2×C17C2×#35311yescharacteristic
167C2×C17C2×#35511yescharacteristic
168C25—21no—
169C22×D4—24no—
170C22×D4—21no—
171C22×D4—41no—
172C22×D4—41no—
173C22×D4—42no—
174C22×D4C2×#59512yes—
175C23×C4—172no—
176C23×C4—341no—
177C23×C4C2×#59511yescharacteristic
178C2×M16—682no—
179C2×C4⋊C4—172no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4—171no—
182C2×C4⋊C4—681no—
183C2×C4⋊C4—681no—
184C2×C22⋊C4—344no—
185C2×C22⋊C4—344no—
186C2×C22⋊C4—688no—
187C2×C42—172no—
188C2×C42—341no—
189C2×C42—682no—
190C22⋊C8—344no—
191C22⋊C8—682no—
192C17#1150511yescharacteristic, complemented, Sylow
193C24—24no—
194C24—22no—
195C24—44no—
196C24—42no—
197C24—44no—
198C24—41no—
199C24—41no—
200C24C22⋊#59511yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—48no—
206C2×D4—48no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4#6324714yescomplemented
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—172no—
215C22×C4—172no—
216C22×C4—344no—
217C22×C4—342no—
218C22×C4—342no—
219C22×C4—342no—
220C22×C4—682no—
221C22×C4—682no—
222C22×C4—684no—
223C22×C4C22⋊#59511yescharacteristic
224C22×C4C22×#59511yescharacteristic
225M16—1364no—
226C2×C8—684no—
227C4⋊C4—682no—
228C4⋊C4—681no—
229C4⋊C4—681no—
230C22⋊C4—688no—
231C22⋊C4—688no—
232C42—682no—
233C42—682no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—24no—
239C23—44no—
240C23—44no—
241C23—44no—
242C23—416no—
243C23—44no—
244C23—42no—
245C23—42no—
246C23—88no—
247C23—82no—
248C23—82no—
249C23—82no—
250C23—82no—
251C23#1058755111yescharacteristic
252C23#1058755111yescharacteristic
253C23C2×C22⋊#59511yescharacteristic
254D4—44no—
255D4—44no—
256D4—48no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—344no—
264C2×C4—342no—
265C2×C4—342no—
266C2×C4—688no—
267C2×C4—682no—
268C2×C4—684no—
269C2×C4—682no—
270C2×C4—682no—
271C2×C4—682no—
272C2×C4—1362no—
273C2×C4#1058755312yes—
274C2×C4C2×#6324712yes—
275C8—1364no—
276C22—24no—
277C22—24no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—48no—
285C22—44no—
286C22—84no—
287C22—88no—
288C22—88no—
289C22—82no—
290C22—82no—
291C22#1176371312yes—
292C22#1176371712yes—
293C22#1176377911yescharacteristic
294C22C2×#1058755111yescharacteristic
295C22C2×#1058755311yescharacteristic
296C4—22no—
297C4—22no—
298C4—684no—
299C4—682no—
300C4—682no—
301C2—21no—
302C2—21no—
303C2—22no—
304C2—22no—
305C2—84no—
306C2#1454402911yescharacteristic
307C2C2×#1176371311yescharacteristic
308C2C2×#1176371711yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC23×D4×C17C4
socleC22×C17C2×#99
cosocleC2×C4⋊Dic17C23
hypercenterC23×D4#595
hypocenterC17#11505
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #14544032C2semidirect
2. #14543712C2semidirect
6. #11763654C22semidirect
54. C2×D4×C17M16semidirect
192. C17#11505semidirect
209. C2×D4#63247semidirect

Maximal subgroups

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

subgroupindex
#145440322
#145437122
C2×#117627122
#1150517