Finite Group Databasebeta

← #46823667

Subgroups — #46823667

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#31771314C211yesmaximal, characteristic
3#31770974C211yesmaximal, characteristic, complemented
4#31770972C211yesmaximal, characteristic, complemented
5#31770954C211yesmaximal, characteristic, complemented
6#31770912C211yesmaximal, characteristic, complemented
7#31770911C211yesmaximal, characteristic, complemented
8#31770899C211yesmaximal, characteristic, complemented
9#31770810C211yesmaximal, characteristic
10#31770808C211yesmaximal, characteristic
11#31770808C211yesmaximal, characteristic
12#31770733C211yesmaximal, characteristic, complemented
13#31770702C211yesmaximal, characteristic
14#31770696C211yesmaximal, characteristic
15#440×C269C211yesmaximal, characteristic
16C2×#16864390C2211yescharacteristic
17C2×#16864390C2211yescharacteristic
18#22575453C2211yescharacteristic
19#22575452C2211yescharacteristic
20#22575451C2211yescharacteristic
21#22575451C2211yescharacteristic
22#22575445—21no—
23#22575445C2211yescharacteristic
24#22575444C2211yescharacteristic
25#22575443—21no—
26#22575443—21no—
27#22575432—21no—
28#22575430—21no—
29#22575430—21no—
30C4×Dic538—21no—
31C4×Dic538C2211yescharacteristic
32#22575418C2211yescharacteristic
33#22575418C2211yescharacteristic
34D4×Dic269C2211yescharacteristic
35D4×Dic269C2211yescharacteristic
36C2×#16864381—21no—
37#22575386C2211yescharacteristic
38#22575384C2211yescharacteristic
39C4⋊#14524130C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575377C2211yescharacteristic
48#22575376C2211yescharacteristic
49#22575376C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C2×SD16×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55#107×C269C2211yescharacteristic
56#103×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538D411yescharacteristic
61C2×Dic538C2311yescharacteristic
62C2×Dic538C2311yescharacteristic
63C22×Dic269—21no—
64C22×Dic269—21no—
65#16864390—22no—
66#16864390—22no—
67C2×#14524130C2311yescharacteristic
68C2×#14524130C2311yescharacteristic
69C4⋊Dic269—21no—
70C4⋊Dic269—21no—
71C4⋊Dic269—21no—
72C4⋊Dic269D411yescharacteristic
73C4⋊Dic269C2311yescharacteristic
74C4⋊Dic269C2311yescharacteristic
75#16864381—21no—
76#16864381—21no—
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
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269C2311yescharacteristic
92C4×Dic269C2311yescharacteristic
93C2×Q8×C269C2311yescharacteristic
94C2×D4×C269C2311yescharacteristic
95C22×C4×C269—21no—
96SD16×C269—22no—
97C2×C8×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C4⋊C4×C269—21no—
100C4⋊C4×C269C2311yescharacteristic
101C4⋊C4×C269C2311yescharacteristic
102C22⋊C4×C269—21no—
103C42×C269—21no—
104C42×C269C2311yescharacteristic
105Dic538—22no—
106Dic538—21no—
107Dic538—21no—
108Dic538—21no—
109Dic538—21no—
110Dic538—81no—
111C2×Dic269—21no—
112C2×Dic269—21no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—42no—
116C2×Dic269—81no—
117C2×Dic269C2×D411yescharacteristic
118C2×Dic269C2×D411yescharacteristic
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121#14524130—21no—
122#14524130—21no—
123C23×C269—21no—
124Q8×C269—21no—
125Q8×C269—21no—
126D4×C269—21no—
127D4×C269#4112yes—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—81no—
132C2×C4×C269C2×D411yescharacteristic
133C2×C4×C269C2×D411yescharacteristic
134C2×C4×C269C2411yescharacteristic
135C8×C269—21no—
136C8×C269—21no—
137C22×C269—22no—
138C22×C269—41no—
139C22×C269—41no—
140C22×C269C22×D411yescharacteristic
141C4×C269—21no—
142C4×C269—21no—
143C4×C269—41no—
144C4×C269—41no—
145C4×C269—41no—
146C4×C269C2×#4111yescharacteristic
147C4×C2692−1+411yescharacteristic
148Dic269—21no—
149Dic269—21no—
150Dic269—21no—
151Dic269—41no—
152Dic269—41no—
153Dic269—41no—
154Dic269—41no—
155Dic269#13712yes—
156C2×C269—42no—
157C2×C269#54811yescharacteristic
158C2×C269C2×#13711yescharacteristic
159C2×C269#57711yescharacteristic
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#479—2691no—
169#477—2691no—
170#461—2691no—
171#461—2691no—
172#461—2691no—
173#446—2691no—
174#440—2691no—
175#440D26911yescharacteristic
176C4×SD16—2691no—
177C2×SD16—2691no—
178C2×SD16—2691no—
179C2×SD16C2×D26911yescharacteristic
180C4⋊Q8—2691no—
181C4⋊Q8—2691no—
182C4⋊Q8—2691no—
183C4⋊Q8—2691no—
184#125—2691no—
185#125—2691no—
186#125—5381no—
187#125—5381no—
188#125—5381no—
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×D4C2×D26911yescharacteristic
200C2×C4⋊C4—5381no—
201#107—2691no—
202#107C2×D26911yescharacteristic
203#106—2691no—
204C4⋊C8—2691no—
205C4⋊C8—2691no—
206C4⋊C8—2691no—
207#103—2691no—
208#103—2691no—
209#103—2691no—
210#103—2691no—
211#103—2691no—
212#103—2691no—
213#103—2691no—
214#103—2691no—
215#103C2×D26911yescharacteristic
216#102C2×D26911yescharacteristic
217#97—2691no—
218#97C2×D26911yescharacteristic
219C4×C8—2691no—
220C2×Q8—2691no—
221C2×Q8—2691no—
222C2×Q8—2691no—
223C2×Q8—5381no—
224C2×Q8C22×D26911yescharacteristic
225C2×D4C22×D26911yescharacteristic
226C22×C4—21no—
227C22×C4—5381no—
228C22×C4—5381no—
229SD16—22no—
230SD16—5382no—
231SD16—5382no—
232C2×C8—2691no—
233C2×C8—2691no—
234C2×C8C22×D26911yescharacteristic
235C2×C8C22×D26911yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—2691no—
238C4⋊C4—2691no—
239C4⋊C4—2691no—
240C4⋊C4—2691no—
241C4⋊C4—2691no—
242C4⋊C4—5381no—
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⋊C4—5381no—
255C4⋊C4C22×D26911yescharacteristic
256C4⋊C4C22×D26911yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—5381no—
259C22⋊C4—5381no—
260C42—21no—
261C42—2691no—
262C42—2691no—
263C42—5381no—
264C42—5381no—
265C42C22×D26911yescharacteristic
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—5382no—
270Q8—5381no—
271Q8—5381no—
272Q8—5381no—
273Q8—5381no—
274Q8—21521no—
275D4—21no—
276D4#1686440212yes—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—2691no—
282C2×C4—2691no—
283C2×C4—2691no—
284C2×C4—2691no—
285C2×C4—5381no—
286C2×C4—5381no—
287C2×C4—5381no—
288C2×C4—5381no—
289C2×C4—10762no—
290C2×C4—21521no—
291C2×C4D4×D26911yescharacteristic
292C2×C4D4×D26911yescharacteristic
293C2×C4C23×D26911yescharacteristic
294C8—21no—
295C8—21no—
296C8—5381no—
297C8—5381no—
298C22—22no—
299C22—41no—
300C22—41no—
301C22C2×D4×D26911yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—2692no—
308C4—5381no—
309C4—5381no—
310C4—5381no—
311C4—10761no—
312C4—10761no—
313C4—10761no—
314C4—10761no—
315C4C2×#1686440211yescharacteristic
316C4#2257550011yescharacteristic
317C2—42no—
318C2#3177126411yescharacteristic
319C2#137×D26911yescharacteristic
320C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#440×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×C269C23
hypercenter#440D269
hypocenterC269#3372
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #31771333C2semidirect
3. #31770974C2semidirect
4. #31770972C2semidirect
5. #31770954C2semidirect
6. #31770912C2semidirect
7. #31770911C2semidirect
8. #31770899C2semidirect
12. #31770733C2semidirect
160. C269#3372semidirect

Maximal subgroups

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

subgroupindex
#317713332
#317713142
#317709742
#317709722
#317709542
#317709122
#317709112
#317708992
#317708102
#317708082
#317707332
#317707022
#317706962
#440×C2692
#3372269