Finite Group Databasebeta

← #46823660

Subgroups — #46823660

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#31771330C211yesmaximal, characteristic, complemented
3#31770968C211yesmaximal, characteristic
4#31770967C211yesmaximal, characteristic, complemented
5#31770958C211yesmaximal, characteristic, complemented
6#31770915C211yesmaximal, characteristic, complemented
7#31770904C211yesmaximal, characteristic, complemented
8#31770828C211yesmaximal, characteristic, complemented
9#31770826C211yesmaximal, characteristic, complemented
10#31770804C211yesmaximal, characteristic
11#31770734C211yesmaximal, characteristic, complemented
12#31770711C211yesmaximal, characteristic, complemented
13#31770705C211yesmaximal, characteristic, complemented
14#31770692C211yesmaximal, characteristic, complemented
15#476×C269C211yesmaximal, characteristic, complemented
16C2×Dic1076C2211yescharacteristic
17C2×#16864391C2211yescharacteristic
18C2×#16864390C2211yescharacteristic
19#22575451—21no—
20#22575449C2211yescharacteristic
21#22575444C2211yescharacteristic
22#22575444C2211yescharacteristic
23#22575443—21no—
24#22575443—21no—
25#22575441C2211yescharacteristic
26#22575440C2211yescharacteristic
27#22575439—21no—
28#22575436—21no—
29#22575435—21no—
30Q8×Dic269—21no—
31C4×Dic538C2211yescharacteristic
32C4×Dic538C2211yescharacteristic
33#22575418C2211yescharacteristic
34#22575418C2211yescharacteristic
35#22575418C2211yescharacteristic
36#22575415C2211yescharacteristic
37C4×C22⋊D269—21no—
38#22575386C2211yescharacteristic
39#22575382C2211yescharacteristic
40#22575382C2211yescharacteristic
41#22575378C2211yescharacteristic
42#22575376C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575364C2211yescharacteristic
50#22575363C2211yescharacteristic
51C8×Dic269C2211yescharacteristic
52C4⋊Q8×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54#106×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C2×Dic538D411yescharacteristic
60C2×Dic538C2311yescharacteristic
61C2×Dic538C2311yescharacteristic
62C2×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C2×C4×D269—21no—
66Dic1076—22no—
67#16864391—22no—
68#16864390—22no—
69C2×#14524130C2311yescharacteristic
70C2×#14524130C2311yescharacteristic
71C4⋊Dic269—21no—
72C4⋊Dic269—21no—
73C4⋊Dic269D411yescharacteristic
74C4⋊Dic269C2311yescharacteristic
75#16864381—21no—
76#16864381—21no—
77#16864381—21no—
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×Dic269—21no—
92C4×Dic269C2311yescharacteristic
93C4×Dic269C2311yescharacteristic
94C2×Q8×C269—21no—
95C2×D4×C269C2311yescharacteristic
96C22×C4×C269—21no—
97C2×C8×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C4⋊C4×C269—21no—
100C4⋊C4×C269C2311yescharacteristic
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C22⋊C4×C269—21no—
104C42×C269C2311yescharacteristic
105C22×D269—21no—
106Dic538—21no—
107Dic538—21no—
108Dic538—21no—
109Dic538—41no—
110Dic538#4112yes—
111D1076—21no—
112D1076—21no—
113C22⋊D269—42no—
114C22⋊D269—81no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269C2×D411yescharacteristic
119C2×Dic269C2×D411yescharacteristic
120C2×Dic269C2×D411yescharacteristic
121C2×Dic269C2×D411yescharacteristic
122C4×D269—81no—
123#14524130—21no—
124#14524130—21no—
125C23×C269—21no—
126Q8×C269—42no—
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—21no—
146C4×C269—21no—
147C4×C269—41no—
148C4×C269—41no—
149C4×C269—41no—
150C4×C269C2×#4111yescharacteristic
151C4×C2692−1+411yescharacteristic
152Dic269—22no—
153Dic269—21no—
154Dic269—21no—
155Dic269—21no—
156Dic269—21no—
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#476D26911yescharacteristic, complemented
174#464—2691no—
175#464—2691no—
176#460—2691no—
177#446—2691no—
178#441—2691no—
179#440—2691no—
180C4×SD16—2691no—
181C2×Q16—2691no—
182C2×SD16—2691no—
183C2×SD16—2691no—
184C4⋊Q8—5381no—
185C4⋊Q8C2×D26911yescharacteristic
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—2691no—
201C4×Q8—5381no—
202C4×D4—2691no—
203C4×D4—5381no—
204C4×D4C2×D26911yescharacteristic
205#107—2691no—
206#106C2×D26911yescharacteristic
207#106C2×D26911yescharacteristic
208C4⋊C8—2691no—
209C4⋊C8—2691no—
210C4⋊C8C2×D26911yescharacteristic
211#103—2691no—
212#103—2691no—
213#103—2691no—
214#103—2691no—
215#102—2691no—
216#102—2691no—
217#102—2691no—
218#102—2691no—
219#102C2×D26911yescharacteristic
220#102C2×D26911yescharacteristic
221#97—2691no—
222#97—2691no—
223C4×C8—2691no—
224C2×Q8—21no—
225C2×Q8—2691no—
226C2×Q8—2691no—
227C2×Q8—2691no—
228C2×D4—2691no—
229C2×D4—5381no—
230C2×D4—5381no—
231C2×D4C22×D26911yescharacteristic
232C22×C4—21no—
233C22×C4—5381no—
234Q16—5382no—
235SD16—5382no—
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—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—21no—
258C22⋊C4—5381no—
259C22⋊C4—5381no—
260C22⋊C4—5381no—
261C22⋊C4—5381no—
262C22⋊C4—5381no—
263C42—2691no—
264C42—2691no—
265C42—5381no—
266C42—5381no—
267C42—5381no—
268C42—5381no—
269C42C22×D26911yescharacteristic
270C23—21no—
271C23—5381no—
272Q8—42no—
273Q8—2692no—
274Q8—5381no—
275Q8—5381no—
276Q8—5381no—
277Q8—10761no—
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—41no—
313C4—41no—
314C4—41no—
315C4—5381no—
316C4—5381no—
317C4—5381no—
318C4—5381no—
319C4—5382no—
320C4—10761no—
321C4—10761no—
322C4#41×D26911yescharacteristic
323C4#2257550111yescharacteristic
324C2—81no—
325C2—21521no—
326C2#3177126511yescharacteristic
327C2#3177140111yescharacteristic
328C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#476×C269C2
socleC22×C269C22×D4
prime radical#22575449C22
hypercenter#476D269
hypocenterC269#3371
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31771330C2semidirect
4. #31770967C2semidirect
5. #31770958C2semidirect
6. #31770915C2semidirect
7. #31770904C2semidirect
8. #31770828C2semidirect
9. #31770826C2semidirect
11. #31770734C2semidirect
12. #31770711C2semidirect
13. #31770705C2semidirect
14. #31770692C2semidirect
15. #476×C269C2semidirect
164. C269#3371semidirect
173. #476D269semidirect

Maximal subgroups

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

subgroupindex
#317713382
#317713302
#317709682
#317709672
#317709582
#317709152
#317709042
#317708282
#317708262
#317708042
#317707342
#317707112
#317707052
#317706922
#476×C2692
#3371269