Finite Group Databasebeta

← #17961430

Subgroups — #17961430

Order 4352.

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

normal subgroups only

This group has 468 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
1C2×#11763719C212yesmaximal
2#14544650C212yesmaximal
3#14543882C212yesmaximal
4C4×#10587630C211yesmaximal, characteristic
5#11763812—22no—
6C2×#10587545C2214yes—
7#11763719—24no—
8#11763689—22no—
9C2×#10587630C2211yescharacteristic
10C2×C4×Dic34C2211yescharacteristic
11#11762716C411yescharacteristic
12#11762714C2211yescharacteristic
13#11762704—22no—
14#11762678C411yescharacteristic
15C4×#63225—22no—
16C42×Dic17C411yescharacteristic
17C2×C4×Q8×C17C411yescharacteristic
18C22×Q8×C17C2×C411yescharacteristic
19C22×Dic34C2311yescharacteristic
20C2×#63247—24no—
21C4×Q8×C17—41no—
22C4×Q8×C17—41no—
23C2×C4⋊C4×C17—21no—
24C2×C4⋊C4×C17C2×C411yescharacteristic
25C2×C42×C17—21no—
26C2×C42×C17C2×C411yescharacteristic
27#10587630—22no—
28#10587630D412yes—
29#10587630Q812yes—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×#63225—22no—
32C2×#63225—22no—
33C2×#63225D412yes—
34C2×C4×Dic17—21no—
35C2×C4×Dic17—21no—
36C2×C4×Dic17C2×C411yescharacteristic
37C2×C4×Dic17C2×C411yescharacteristic
38C2×C4×Dic17D412yes—
39C4×Dic34—41no—
40C4×Dic34—41no—
41#10587545—24no—
42#10587545—24no—
43#10587544—42no—
44C4⋊#3624—42no—
45#10587502—22no—
46#10587502—22no—
47C2×Q8×C17—21no—
48C2×Q8×C17—41no—
49C2×Q8×C17—41no—
50C2×Q8×C17C4⋊C412yes—
51C22×C4×C17—21no—
52C22×C4×C17—21no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22×C411yescharacteristic
56C22×Dic17—21no—
57C22×Dic17—21no—
58C22×Dic17C22⋊C412yes—
59C22×Dic17C2×D412yes—
60C2×Dic34—41no—
61C2×Dic34—41no—
62C2×Dic34C2×D411yescharacteristic
63C2×Dic34C2×Q811yescharacteristic
64C2×Dic34#4112yes—
65#63247—44no—
66#63247—44no—
67C2×#3624—44no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—42no—
70C42×C17—21no—
71C42×C17—21no—
72C42×C17—41no—
73C42×C17—41no—
74C4⋊Dic17—41no—
75#63225—24no—
76#63225—24no—
77#63225—42no—
78#63225—44no—
79C4×Dic17—24no—
80C4×Dic17—22no—
81C4×Dic17—22no—
82C4×Dic17—21no—
83C4×Dic17—42no—
84C4×Dic17—41no—
85C4×Dic17C4⋊C412yes—
86#12802—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88Q8×C17—42no—
89Q8×C17—42no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—22no—
93C2×C4×C17—22no—
94C2×C4×C17—21no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—42no—
99C2×C4×C17—41no—
100C2×C4×C17#9911yescharacteristic
101C2×C4×C17#9911yescharacteristic
102C2×C4×C17C2×C4⋊C411yescharacteristic
103C2×C4×C17#11711yescharacteristic
104C2×Dic17—22no—
105C2×Dic17—22no—
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—22no—
109C2×Dic17—22no—
110C2×Dic17—22no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—42no—
114C2×Dic17#12112yes—
115C2×Dic17C22⋊Q812yes—
116Dic34—41no—
117Dic34—41no—
118Dic34—42no—
119#3624—84no—
120C4×C4⋊Q8—171no—
121C2×#356—172no—
122#1801—172no—
123#1394—172no—
124C22×C17—21no—
125C22×C17—21no—
126C22×C17#38011yescharacteristic
127C22×C17C2×#9911yescharacteristic
128C22×C17#41011yescharacteristic
129C4×C17—21no—
130C4×C17—21no—
131C4×C17—21no—
132C4×C17—42no—
133C4×C17—41no—
134C4×C17—81no—
135C4×C17#35612yescomplemented
136Dic17—24no—
137Dic17—22no—
138Dic17—22no—
139Dic17—42no—
140Dic17—42no—
141C2×C4⋊Q8—171no—
142C2×C4×Q8—171no—
143C2×C4×Q8#59511yescharacteristic
144#423—342no—
145C2×#101—174no—
146#391—171no—
147#391—171no—
148#389—342no—
149#384—171no—
150C4×C4⋊C4—342no—
151C43—171no—
152#356—344no—
153#343—342no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17#179911yescharacteristic
157C2×C17C2×#35611yescharacteristic
158C2×C17#213211yescharacteristic
159C22×Q8—171no—
160C22×Q8C2×#59511yescharacteristic
161C2×M16—344no—
162C4⋊Q8—172no—
163C4⋊Q8—172no—
164C4⋊Q8—342no—
165C4×Q8—41no—
166C4×Q8—41no—
167C4×Q8—681no—
168C4×Q8—681no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—172no—
171C2×C4⋊C4—171no—
172C2×C4⋊C4—342no—
173C2×C4⋊C4—342no—
174C2×C4⋊C4C2×#59511yescharacteristic
175C2×C42—21no—
176C2×C42—171no—
177C2×C42—172no—
178C2×C42—171no—
179C2×C42—341no—
180C2×C42—341no—
181C2×C42C2×#59511yescharacteristic
182C4⋊C8—682no—
183C4⋊C8—682no—
184#101—344no—
185#101—344no—
186#95—342no—
187#95—342no—
188C17#1280211yescharacteristic, complemented, Sylow
189C2×Q8—21no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—171no—
193C2×Q8—171no—
194C2×Q8—172no—
195C2×Q8—681no—
196C2×Q8—681no—
197C2×Q8C4⋊#59512yes—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—172no—
201C22×C4—172no—
202C22×C4—341no—
203C22×C4—341no—
204C22×C4C22⋊#59511yescharacteristic
205C22×C4C22⋊#59511yescharacteristic
206C22×C4C22×#59511yescharacteristic
207M16—684no—
208M16—684no—
209C2×C8—684no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—344no—
213C4⋊C4—344no—
214C4⋊C4—682no—
215C4⋊C4—681no—
216C4⋊C4—684no—
217C42—21no—
218C42—21no—
219C42—41no—
220C42—41no—
221C42—172no—
222C42—344no—
223C42—341no—
224C42—342no—
225C42—342no—
226C42—681no—
227C42—682no—
228C23C2×C22⋊#59511yescharacteristic
229Q8—42no—
230Q8—42no—
231Q8—681no—
232Q8—681no—
233Q8—682no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—172no—
245C2×C4—172no—
246C2×C4—342no—
247C2×C4—342no—
248C2×C4—342no—
249C2×C4—342no—
250C2×C4—342no—
251C2×C4—342no—
252C2×C4—342no—
253C2×C4—681no—
254C2×C4—681no—
255C2×C4—682no—
256C2×C4#1058755111yescharacteristic
257C2×C4#1058755111yescharacteristic
258C2×C4C2×C4⋊#59511yescharacteristic
259C2×C4#1058767711yescharacteristic
260C8—1364no—
261C22—21no—
262C22—21no—
263C22#1176375111yescharacteristic
264C22C2×#1058755111yescharacteristic
265C22#1176378811yescharacteristic
266C4—21no—
267C4—21no—
268C4—21no—
269C4—42no—
270C4—41no—
271C4—81no—
272C4—344no—
273C4—342no—
274C4—342no—
275C4—682no—
276C4—682no—
277C4#1176371912yescomplemented
278C2—21no—
279C2—21no—
280C2#1454464411yescharacteristic
281C2C2×#1176371911yescharacteristic
282C2#1454507511yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C4×Q8×C17C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Dic34C23
hypercenterC2×C4×Q8#595
hypocenterC17#12802
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
135. C4×C17#356semidirect
188. C17#12802semidirect
277. C4#11763719semidirect

Maximal subgroups

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

subgroupindex
C2×#117637192
#145446502
#145438822
C4×#105876302
#1280217