Finite Group Databasebeta

← #46823669

Subgroups — #46823669

Order 34432.

340 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771333C211yesmaximal, characteristic, complemented
2#31771311C211yesmaximal, characteristic
3#31770975C211yesmaximal, characteristic, complemented
4#31770972C211yesmaximal, characteristic, complemented
5#31770954C211yesmaximal, characteristic, complemented
6#31770915C211yesmaximal, characteristic, complemented
7#31770899C211yesmaximal, characteristic, complemented
8#31770811C211yesmaximal, characteristic
9#31770809C211yesmaximal, characteristic
10#31770809C211yesmaximal, characteristic
11#31770734C211yesmaximal, characteristic, complemented
12#31770704C211yesmaximal, characteristic
13#31770703C211yesmaximal, characteristic
14#31770692C211yesmaximal, characteristic
15#479×C269C211yesmaximal, characteristic, complemented
16C2×#16864391C2211yescharacteristic
17C2×#16864391C2211yescharacteristic
18C2×#16864389C2211yescharacteristic
19#22575453C2211yescharacteristic
20#22575452C2211yescharacteristic
21#22575451C2211yescharacteristic
22#22575451C2211yescharacteristic
23#22575445—21no—
24#22575444C2211yescharacteristic
25#22575443—21no—
26#22575443—21no—
27#22575433—21no—
28#22575431—21no—
29#22575431—21no—
30C4×Dic538—21no—
31C4×Dic538C2211yescharacteristic
32#22575418C2211yescharacteristic
33#22575418C2211yescharacteristic
34C4×D1076C2211yescharacteristic
35#22575415C2211yescharacteristic
36#22575415C2211yescharacteristic
37C4⋊C4×D269—21no—
38#22575386C2211yescharacteristic
39#22575382C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575377C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575376C2211yescharacteristic
46#22575376C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575364C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538D411yescharacteristic
61C2×Dic538C2311yescharacteristic
62C2×Dic538C2311yescharacteristic
63C2×D1076C2311yescharacteristic
64C2×C4×D269—21no—
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67#16864391—22no—
68#16864391—22no—
69#16864389—22no—
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C4⋊Dic269—21no—
73C4⋊Dic269—21no—
74C4⋊Dic269—21no—
75C4⋊Dic269D411yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77#16864381—21no—
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381D411yescharacteristic
86#16864381D411yescharacteristic
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90C4×Dic269—21no—
91C4×Dic269—21no—
92C4×Dic269C2311yescharacteristic
93C4×Dic269C2311yescharacteristic
94C2×Q8×C269C2311yescharacteristic
95C2×C8×C269C2311yescharacteristic
96C2×C8×C269C2311yescharacteristic
97C4⋊C4×C269—21no—
98C4⋊C4×C269—21no—
99C4⋊C4×C269—21no—
100C4⋊C4×C269C2311yescharacteristic
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C42×C269—21no—
104C42×C269C2311yescharacteristic
105C22×D269—21no—
106Dic538—22no—
107Dic538—21no—
108Dic538—21no—
109Dic538—21no—
110Dic538—21no—
111Dic538—81no—
112D1076—21no—
113D1076#4112yes—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269C2×D411yescharacteristic
118C2×Dic269C2×D411yescharacteristic
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C4×D269—42no—
122C4×D269—81no—
123C4×D269—81no—
124#14524130—21no—
125#14524130—21no—
126Q8×C269—21no—
127Q8×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269C2×D411yescharacteristic
133C2×C4×C269C2×D411yescharacteristic
134C2×C4×C269C2411yescharacteristic
135C8×C269—21no—
136C8×C269—21no—
137C22×C269C22×D411yescharacteristic
138C2×D269—22no—
139C2×D269—41no—
140C2×D269—41no—
141C4×C269—21no—
142C4×C269—21no—
143C4×C269—41no—
144C4×C269—41no—
145C4×C269—41no—
146C4×C269—41no—
147C4×C269C2×#4111yescharacteristic
148C4×C2692−1+411yescharacteristic
149Dic269—21no—
150Dic269—21no—
151Dic269—21no—
152Dic269—41no—
153Dic269—41no—
154Dic269—41no—
155Dic269#13712yes—
156C2×C269#54811yescharacteristic
157C2×C269C2×#13711yescharacteristic
158C2×C269#57711yescharacteristic
159D269—42no—
160C269#337211yescharacteristic, complemented, Sylow
161#3372—2691nomaximal, Sylow
162#557—2691no—
163#554—2691no—
164#491—2691no—
165#491—2691no—
166#487—2691no—
167#479—2691no—
168#479D26911yescharacteristic, complemented
169#477—2691no—
170#461—2691no—
171#461—2691no—
172#461—2691no—
173#446—2691no—
174#440—2691no—
175#440—2691no—
176C4×SD16—2691no—
177C2×SD16—2691no—
178C2×SD16—2691no—
179C2×SD16—2691no—
180C4⋊Q8—2691no—
181C4⋊Q8—2691no—
182C4⋊Q8—2691no—
183C4⋊Q8—2691no—
184#125—2691no—
185#125—5381no—
186#125—5381no—
187#125—5381no—
188#125C2×D26911yescharacteristic
189C22⋊Q8—5381no—
190C22⋊Q8—5381no—
191C22⋊Q8—5381no—
192C4×Q8—2691no—
193C4×Q8—2691no—
194C4×Q8—2691no—
195C4×Q8—5381no—
196C4×Q8C2×D26911yescharacteristic
197C4×D4—2691no—
198C4×D4—2691no—
199C4×D4—2691no—
200C2×C4⋊C4—5381no—
201#107—2691no—
202#107C2×D26911yescharacteristic
203#106C2×D26911yescharacteristic
204C4⋊C8—2691no—
205C4⋊C8—2691no—
206C4⋊C8C2×D26911yescharacteristic
207#103—2691no—
208#103—2691no—
209#103—2691no—
210#103—2691no—
211#103—2691no—
212#103—2691no—
213#103—2691no—
214#103C2×D26911yescharacteristic
215#103C2×D26911yescharacteristic
216#102—2691no—
217#97—2691no—
218#97—2691no—
219C4×C8—2691no—
220C2×Q8—2691no—
221C2×Q8—2691no—
222C2×Q8—2691no—
223C2×Q8—5381no—
224C2×Q8C22×D26911yescharacteristic
225C2×D4—2691no—
226C22×C4—5381no—
227C22×C4—5381no—
228C22×C4—5381no—
229SD16—5382no—
230SD16—5382no—
231SD16—5382no—
232C2×C8—2691no—
233C2×C8—2691no—
234C2×C8C22×D26911yescharacteristic
235C2×C8C22×D26911yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—2691no—
240C4⋊C4—2691no—
241C4⋊C4—2691no—
242C4⋊C4—2691no—
243C4⋊C4—5381no—
244C4⋊C4—5381no—
245C4⋊C4—5381no—
246C4⋊C4—5381no—
247C4⋊C4—5381no—
248C4⋊C4—5381no—
249C4⋊C4—5381no—
250C4⋊C4—5381no—
251C4⋊C4—5381no—
252C4⋊C4—5381no—
253C4⋊C4—5381no—
254C4⋊C4C22×D26911yescharacteristic
255C4⋊C4C22×D26911yescharacteristic
256C4⋊C4C22×D26911yescharacteristic
257C22⋊C4—5381no—
258C22⋊C4—5381no—
259C22⋊C4—5381no—
260C42—21no—
261C42—2691no—
262C42—2691no—
263C42—5381no—
264C42—5381no—
265C42C22×D26911yescharacteristic
266C23—5381no—
267Q8—21no—
268Q8—21no—
269Q8—5382no—
270Q8—5381no—
271Q8—5381no—
272Q8—5381no—
273Q8—5381no—
274Q8—21521no—
275D4—2692no—
276D4—5381no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—2691no—
282C2×C4—2691no—
283C2×C4—2691no—
284C2×C4—2691no—
285C2×C4—5381no—
286C2×C4—5381no—
287C2×C4—5381no—
288C2×C4—10762no—
289C2×C4—21521no—
290C2×C4—21521no—
291C2×C4D4×D26911yescharacteristic
292C2×C4D4×D26911yescharacteristic
293C2×C4C23×D26911yescharacteristic
294C8—21no—
295C8—21no—
296C8—5381no—
297C8—5381no—
298C22—5382no—
299C22—10761no—
300C22—10761no—
301C22C2×D4×D26911yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—2692no—
309C4—5381no—
310C4—5381no—
311C4—5381no—
312C4—10761no—
313C4—10761no—
314C4—10761no—
315C4#41×D26911yescharacteristic
316C4#2257550111yescharacteristic
317C2—10762no—
318C2#3177126511yescharacteristic
319C2#137×D26911yescharacteristic
320C2#3177141211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#479×C269C2
socleC22×C269C22×D4
prime radicalC2×D1076C23
hypercenter#479D269
hypocenterC269#3372
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #31771333C2semidirect
3. #31770975C2semidirect
4. #31770972C2semidirect
5. #31770954C2semidirect
6. #31770915C2semidirect
7. #31770899C2semidirect
11. #31770734C2semidirect
15. #479×C269C2semidirect
160. C269#3372semidirect
168. #479D269semidirect

Maximal subgroups

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

subgroupindex
#317713332
#317713112
#317709752
#317709722
#317709542
#317709152
#317708992
#317708112
#317708092
#317707342
#317707042
#317707032
#317706922
#479×C2692
#3372269