Finite Group Databasebeta

← #46823658

Subgroups — #46823658

Order 34432.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771338C211yesmaximal, characteristic
2#31771334C211yesmaximal, characteristic, complemented
3#31770968C211yesmaximal, characteristic
4#31770965C211yesmaximal, characteristic, complemented
5#31770958C211yesmaximal, characteristic, complemented
6#31770911C211yesmaximal, characteristic, complemented
7#31770908C211yesmaximal, characteristic, complemented
8#31770895C211yesmaximal, characteristic, complemented
9#31770827C211yesmaximal, characteristic, complemented
10#31770825C211yesmaximal, characteristic, complemented
11#31770803C211yesmaximal, characteristic
12#31770733C211yesmaximal, characteristic, complemented
13#31770709C211yesmaximal, characteristic, complemented
14#31770690C211yesmaximal, characteristic, complemented
15#440×C269C211yesmaximal, characteristic, complemented
16C2×#16864392C2211yescharacteristic
17C2×#16864389C2211yescharacteristic
18#22575453—21no—
19#22575453C2211yescharacteristic
20#22575449C2211yescharacteristic
21#22575444—21no—
22#22575444—21no—
23#22575444C2211yescharacteristic
24#22575444C2211yescharacteristic
25#22575441C2211yescharacteristic
26#22575440C2211yescharacteristic
27#22575439—21no—
28#22575436—21no—
29#22575435—21no—
30Q8×Dic269C2211yescharacteristic
31Q8×Dic269C2211yescharacteristic
32C4×Dic538—21no—
33C4×Dic538C2211yescharacteristic
34#22575418C2211yescharacteristic
35#22575415C2211yescharacteristic
36C4×C22⋊D269—21no—
37#22575384C2211yescharacteristic
38#22575384C2211yescharacteristic
39C4⋊#14524130C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575382C2211yescharacteristic
42#22575378C2211yescharacteristic
43#22575378C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575373C2211yescharacteristic
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×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C2×C4×D269—21no—
66#16864392—22no—
67#16864389—22no—
68C2×#14524130C2311yescharacteristic
69C2×#14524130C2311yescharacteristic
70C4⋊Dic269—21no—
71C4⋊Dic269—21no—
72C4⋊Dic269—21no—
73C4⋊Dic269—21no—
74C4⋊Dic269—21no—
75C4⋊Dic269D411yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381D411yescharacteristic
82#16864381D411yescharacteristic
83C22⋊Dic269—21no—
84C22⋊Dic269—21no—
85#16864379—21no—
86#16864379—21no—
87#16864379—21no—
88C4×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
105C22×D269—21no—
106Dic538—21no—
107Dic538—21no—
108Dic538—41no—
109Dic538—42no—
110D1076—21no—
111D1076—21no—
112C22⋊D269—42no—
113C22⋊D269—81no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269C2×D411yescharacteristic
118C2×Dic269C2×D411yescharacteristic
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C4×D269—81no—
122#14524130—21no—
123#14524130—21no—
124C23×C269—21no—
125Q8×C269—21no—
126Q8×C269#4112yes—
127D4×C269—21no—
128D4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—81no—
133C2×C4×C269C2×D411yescharacteristic
134C2×C4×C269C2×D411yescharacteristic
135C2×C4×C269C2411yescharacteristic
136C8×C269—21no—
137C8×C269—21no—
138C22×C269—41no—
139C22×C269—41no—
140C22×C269—41no—
141C22×C269C22×D411yescharacteristic
142C2×D269—41no—
143C2×D269—41no—
144C2×D269—41no—
145C4×C269—22no—
146C4×C269—21no—
147C4×C269—21no—
148C4×C269—41no—
149C4×C269—41no—
150C4×C269C2×#4111yescharacteristic
151C4×C2692−1+411yescharacteristic
152Dic269—21no—
153Dic269—21no—
154Dic269—21no—
155Dic269—21no—
156Dic269—41no—
157Dic269—41no—
158Dic269—41no—
159C2×C269—81no—
160C2×C269#54811yescharacteristic
161C2×C269#57511yescharacteristic
162C2×C269#57711yescharacteristic
163D269—81no—
164C269#337111yescharacteristic, complemented, Sylow
165#3371—2691nomaximal, Sylow
166#559—2691no—
167#557—2691no—
168#490—2691no—
169#489—2691no—
170#488—2691no—
171#479—2691no—
172#478—2691no—
173#476—2691no—
174#464—2691no—
175#464—2691no—
176#460—2691no—
177#446—2691no—
178#441—2691no—
179#440D26911yescharacteristic, complemented
180C4×SD16—2691no—
181C2×Q16—2691no—
182C2×SD16—2691no—
183C2×SD16C2×D26911yescharacteristic
184C4⋊Q8—2691no—
185C4⋊Q8—5381no—
186#127—2691no—
187#125—2691no—
188#125—2691no—
189#125—5381no—
190#125—5381no—
191#124—2691no—
192#124—2691no—
193#124—5381no—
194#123—5381no—
195#123—5381no—
196C4×Q8—2691no—
197C4×Q8—2691no—
198C4×Q8—2691no—
199C4×Q8—2691no—
200C4×Q8—5381no—
201C4×Q8C2×D26911yescharacteristic
202C4×D4—2691no—
203C4×D4—5381no—
204C4×D4C2×D26911yescharacteristic
205#107C2×D26911yescharacteristic
206#106—2691no—
207#106—2691no—
208C4⋊C8—2691no—
209C4⋊C8—2691no—
210C4⋊C8—2691no—
211#103—2691no—
212#103—2691no—
213#103—2691no—
214#103C2×D26911yescharacteristic
215#102—2691no—
216#102—2691no—
217#102—2691no—
218#102—2691no—
219#102—2691no—
220#102C2×D26911yescharacteristic
221#97—2691no—
222#97C2×D26911yescharacteristic
223C4×C8—2691no—
224C2×Q8—2691no—
225C2×Q8—2691no—
226C2×Q8—5381no—
227C2×Q8C22×D26911yescharacteristic
228C2×D4—2691no—
229C2×D4—5381no—
230C2×D4—5381no—
231C2×D4C22×D26911yescharacteristic
232C22×C4—21no—
233C22×C4—5381no—
234Q16—5382no—
235SD16—22no—
236SD16—5382no—
237C2×C8—2691no—
238C2×C8—2691no—
239C2×C8C22×D26911yescharacteristic
240C2×C8C22×D26911yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—2691no—
243C4⋊C4—2691no—
244C4⋊C4—2691no—
245C4⋊C4—2691no—
246C4⋊C4—2691no—
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—
260C22⋊C4—5381no—
261C22⋊C4—5381no—
262C22⋊C4—5381no—
263C42—21no—
264C42—2691no—
265C42—2691no—
266C42—5381no—
267C42—5381no—
268C42—5381no—
269C42C22×D26911yescharacteristic
270C23—21no—
271C23—5381no—
272Q8—21no—
273Q8—5381no—
274Q8—5381no—
275Q8—10761no—
276Q8—10762no—
277Q8#1686440212yes—
278D4—21no—
279D4—21no—
280D4—5381no—
281D4—5381no—
282D4—10762no—
283D4—21521no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—81no—
288C2×C4—2691no—
289C2×C4—2691no—
290C2×C4—2691no—
291C2×C4—2691no—
292C2×C4—5381no—
293C2×C4—5381no—
294C2×C4—5381no—
295C2×C4—21521no—
296C2×C4D4×D26911yescharacteristic
297C2×C4D4×D26911yescharacteristic
298C2×C4C23×D26911yescharacteristic
299C8—21no—
300C8—21no—
301C8—5381no—
302C8—5381no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—10761no—
307C22—10761no—
308C22—10761no—
309C22C2×D4×D26911yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—5381no—
316C4—5381no—
317C4—5381no—
318C4—5381no—
319C4—10761no—
320C4—10761no—
321C4—10761no—
322C4C2×#1686440211yescharacteristic
323C4#2257550011yescharacteristic
324C2—81no—
325C2—21521no—
326C2#3177126411yescharacteristic
327C2#3177140411yescharacteristic
328C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#440×C269C2
socleC22×C269C22×D4
prime radical#22575449C22
hypercenter#440D269
hypocenterC269#3371
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
2. #31771334C2semidirect
4. #31770965C2semidirect
5. #31770958C2semidirect
6. #31770911C2semidirect
7. #31770908C2semidirect
8. #31770895C2semidirect
9. #31770827C2semidirect
10. #31770825C2semidirect
12. #31770733C2semidirect
13. #31770709C2semidirect
14. #31770690C2semidirect
15. #440×C269C2semidirect
164. C269#3371semidirect
179. #440D269semidirect

Maximal subgroups

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

subgroupindex
#317713382
#317713342
#317709682
#317709652
#317709582
#317709112
#317709082
#317708952
#317708272
#317708252
#317708032
#317707332
#317707092
#317706902
#440×C2692
#3371269