Finite Group Databasebeta

← #17952562

Subgroups — #17952562

Order 4352.

1030 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 160 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#14544640C212yesmaximal
2C2×#11763669C214yesmaximal, complemented
3C22×#10587630C211yesmaximal, characteristic
4C2×#10587544C2214yes—
5C2×C22⋊#3624—22no—
6#11763675—22no—
7#11763669—28no—
8C23×Dic34C411yescharacteristic
9C2×#10587630—28no—
10C2×#10587630—22no—
11C2×#10587630C412yes—
12C2×#10587630C2212yes—
13C22×#63225—22no—
14C22×C4×Dic17C2211yescharacteristic
15C23×Q8×C17C411yescharacteristic
16C22×Q8×C17—24no—
17C22×Q8×C17—21no—
18C22×Q8×C17—42no—
19C22×Q8×C17—42no—
20C22×Q8×C17C2×C412yes—
21C23×C4×C17—21no—
22C23×C4×C17C2×C411yescharacteristic
23C23×Dic17—21no—
24C23×Dic17D412yes—
25C22×Dic34—21no—
26C22×Dic34—24no—
27C22×Dic34—42no—
28C22×Dic34—42no—
29C22×Dic34C2×C412yes—
30C22×#3624—24no—
31#10587630—216no—
32#10587630—24no—
33#10587630—24no—
34#10587630—24no—
35#10587630D418yes—
36C2×#63225—216no—
37C2×#63225—24no—
38C2×#63225—24no—
39C2×C4×Dic17—24no—
40C2×C4×Dic17C2×C411yescharacteristic
41C2×C4×Dic17D412yes—
42C2×C4×Dic17C2311yescharacteristic
43C22⋊#3624—44no—
44#10587544—28no—
45C24×C17C22⋊C411yescharacteristic
46C2×Q8×C17—24no—
47C2×Q8×C17—22no—
48C2×Q8×C17—416no—
49C2×Q8×C17—42no—
50C2×Q8×C17—42no—
51C2×Q8×C17—42no—
52C2×Q8×C17—42no—
53C2×Q8×C17C22⋊C414yes—
54C22×C4×C17—22no—
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17—24no—
58C22×C4×C17—22no—
59C22×C4×C17—42no—
60C22×C4×C17—42no—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22×C411yescharacteristic
63C22×Dic17—24no—
64C22×Dic17—24no—
65C22×Dic17—24no—
66C22×Dic17—22no—
67C22×Dic17—42no—
68C22×Dic17—42no—
69C22×Dic17C22⋊C412yes—
70C22×Dic17SD1614yes—
71C22×Dic17Q1614yes—
72C22×Dic17C2×D412yes—
73C2×Dic34—24no—
74C2×Dic34—22no—
75C2×Dic34—42no—
76C2×Dic34—416no—
77C2×Dic34—42no—
78C2×Dic34—42no—
79C2×Dic34—42no—
80C2×Dic34C22⋊C414yes—
81C2×#3624—44no—
82C2×#3624—44no—
83C2×#3624—44no—
84#63225—216no—
85#63225—216no—
86C4×Dic17—22no—
87C4×Dic17—24no—
88C4×Dic17C2×D414yes—
89#8342—171nomaximal, Sylow
90C23×C17—21no—
91C23×C17—21no—
92C23×C17—22no—
93C23×C17#10012yes—
94C23×C17#10314yes—
95C23×C17C2×C22⋊C411yescharacteristic
96Q8×C17—44no—
97Q8×C17—48no—
98Q8×C17—44no—
99C2×C4×C17—28no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—24no—
105C2×C4×C17—48no—
106C2×C4×C17—42no—
107C2×C4×C17—42no—
108C2×C4×C17#10012yes—
109C2×C4×C17C2×C22⋊C412yes—
110C2×Dic17—22no—
111C2×Dic17—22no—
112C2×Dic17—28no—
113C2×Dic17—28no—
114C2×Dic17—24no—
115C2×Dic17—48no—
116C2×Dic17—42no—
117C2×Dic17—42no—
118C2×Dic17#10314yes—
119C2×Dic17#12014yes—
120C2×Dic17C2×SD1612yes—
121C2×Dic17C2×Q1612yes—
122C2×Dic17#13714yes—
123Dic34—48no—
124Dic34—44no—
125Dic34—44no—
126#3624—84no—
127C22×C4⋊Q8—171no—
128#1797—172no—
129C2×#333—174no—
130C22×C17—24no—
131C22×C17—22no—
132C22×C17—22no—
133C22×C17—24no—
134C22×C17#33314yescomplemented
135C22×C17#37911yescharacteristic
136C22×C17C2×#10011yescharacteristic
137C22×C17C2×#10011yescharacteristic
138C22×C17C2×#10312yes—
139C22×C17#41912yes—
140C4×C17—22no—
141C4×C17—22no—
142C4×C17—44no—
143Dic17—24no—
144Dic17—44no—
145Dic17#44814yes—
146Dic17#45114yes—
147C23×Q8—171no—
148C23×Q8#59511yescharacteristic
149C2×C4⋊Q8—172no—
150C2×C4⋊Q8—172no—
151C2×C4⋊Q8—342no—
152C2×C4⋊Q8—348no—
153C22×C4⋊C4—342no—
154C22×C42—171no—
155C2×C4⋊C8—174no—
156C2×C22⋊C8—342no—
157#336—342no—
158#333—348no—
159C2×C17—24no—
160C2×C17C2×#33311yescharacteristic
161C2×C17#154812yes—
162C2×C17#155811yescharacteristic
163C2×C17#178311yescharacteristic
164C2×C17#178712yes—
165C22×Q8—24no—
166C22×Q8—21no—
167C22×Q8—42no—
168C22×Q8—42no—
169C22×Q8—172no—
170C22×Q8—344no—
171C22×Q8—341no—
172C22×Q8—682no—
173C22×Q8—682no—
174C22×Q8C2×#59512yes—
175C23×C4—21no—
176C23×C4—172no—
177C23×C4—341no—
178C23×C4C2×#59511yescharacteristic
179C22×C8—344no—
180C4⋊Q8—178no—
181C4⋊Q8—344no—
182C4⋊Q8—344no—
183C4⋊Q8—3416no—
184C4⋊Q8—344no—
185C2×C4⋊C4—344no—
186C2×C4⋊C4—344no—
187C2×C4⋊C4—3416no—
188C2×C42—171no—
189C2×C42—172no—
190C2×C42—171no—
191C2×C42—344no—
192C4⋊C8—348no—
193C22⋊C8—684no—
194C17#834211yescharacteristic, complemented, Sylow
195C24C22⋊#59511yescharacteristic
196C2×Q8—24no—
197C2×Q8—22no—
198C2×Q8—416no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—174no—
204C2×Q8—344no—
205C2×Q8—342no—
206C2×Q8—6816no—
207C2×Q8—682no—
208C2×Q8—682no—
209C2×Q8—682no—
210C2×Q8—682no—
211C2×Q8C22⋊#59514yes—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—172no—
220C22×C4—172no—
221C22×C4—174no—
222C22×C4—174no—
223C22×C4—344no—
224C22×C4—344no—
225C22×C4—344no—
226C22×C4—342no—
227C22×C4—682no—
228C22×C4—682no—
229C22×C4C22⋊#59511yescharacteristic
230C22×C4C22×#59511yescharacteristic
231C2×C8—684no—
232C2×C8—684no—
233C2×C8—684no—
234C4⋊C4—3416no—
235C4⋊C4—3416no—
236C42—174no—
237C42—344no—
238C42—342no—
239C23—21no—
240C23—21no—
241C23—22no—
242C23#1058754914yes—
243C23#1058755312yes—
244C23C2×C22⋊#59511yescharacteristic
245Q8—44no—
246Q8—44no—
247Q8—48no—
248Q8—684no—
249Q8—684no—
250Q8—688no—
251C2×C4—28no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—24no—
257C2×C4—48no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—174no—
261C2×C4—172no—
262C2×C4—172no—
263C2×C4—174no—
264C2×C4—174no—
265C2×C4—348no—
266C2×C4—348no—
267C2×C4—342no—
268C2×C4—342no—
269C2×C4—344no—
270C2×C4—688no—
271C2×C4—682no—
272C2×C4—682no—
273C2×C4#1058755312yes—
274C2×C4C2×C22⋊#59512yes—
275C8—1364no—
276C22—24no—
277C22—22no—
278C22—22no—
279C22—24no—
280C22#1176366914yescomplemented
281C22#1176375011yescharacteristic
282C22C2×#1058755311yescharacteristic
283C22C2×#1058755311yescharacteristic
284C22C2×#1058754912yes—
285C22#1176380212yes—
286C4—22no—
287C4—22no—
288C4—44no—
289C4—174no—
290C4—174no—
291C4—344no—
292C4—684no—
293C2—24no—
294C2C2×#1176366911yescharacteristic
295C2#1454429712yes—
296C2#1454431711yescharacteristic
297C2#1454461611yescharacteristic
298C2#1454462312yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC23×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC23×Q8#595
hypocenterC17#8342
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11763669C2semidirect
134. C22×C17#333semidirect
194. C17#8342semidirect
280. C22#11763669semidirect

Maximal subgroups

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

subgroupindex
#145446402
C2×#117636692
C22×#105876302
#834217