Finite Group Databasebeta

← #46823447

Subgroups — #46823447

Order 34432.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771301C211yesmaximal, characteristic
2#31771295C211yesmaximal, characteristic, complemented
3#31771007C211yesmaximal, characteristic, complemented
4#31770947C211yesmaximal, characteristic, complemented
5#31770936C211yesmaximal, characteristic, complemented
6#31770930C211yesmaximal, characteristic, complemented
7#31770924C211yesmaximal, characteristic, complemented
8#31770913C211yesmaximal, characteristic, complemented
9#31770906C211yesmaximal, characteristic, complemented
10#31770851C211yesmaximal, characteristic, complemented
11#31770851C211yesmaximal, characteristic, complemented
12C4×#16864391C211yesmaximal, characteristic, complemented
13#31770647C211yesmaximal, characteristic, complemented
14#31770647C211yesmaximal, characteristic, complemented
15#436×C269C211yesmaximal, characteristic, complemented
16C2×#16864391C2211yescharacteristic
17#22575448—21no—
18#22575446—21no—
19#22575445C2211yescharacteristic
20#22575445C2211yescharacteristic
21#22575443—21no—
22#22575435—21no—
23#22575434—21no—
24#22575432C2211yescharacteristic
25#22575432C2211yescharacteristic
26#22575427C2211yescharacteristic
27#22575427C2211yescharacteristic
28#22575425—21no—
29C4×Dic538C2211yescharacteristic
30C4×D1076C2211yescharacteristic
31#22575413—21no—
32#22575412C2211yescharacteristic
33#22575412C2211yescharacteristic
34#22575409—21no—
35C2×C4⋊Dic269C2211yescharacteristic
36C2×C4⋊Dic269C2211yescharacteristic
37#22575387C2211yescharacteristic
38#22575387C2211yescharacteristic
39#22575387C2211yescharacteristic
40#22575387C2211yescharacteristic
41#22575385C2211yescharacteristic
42#22575385C2211yescharacteristic
43#22575385C2211yescharacteristic
44#22575385C2211yescharacteristic
45#22575385C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575378C2211yescharacteristic
48#22575378C2211yescharacteristic
49#22575375C2211yescharacteristic
50#22575375C2211yescharacteristic
51#22575375C2211yescharacteristic
52C2×M16×C269C2211yescharacteristic
53C2×M16×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55C4⋊C8×C269C2211yescharacteristic
56C22⋊C8×C269C2211yescharacteristic
57C22⋊C8×C269C2211yescharacteristic
58C4×C8×C269C2211yescharacteristic
59C2×Dic538C2311yescharacteristic
60C2×D1076C2311yescharacteristic
61C2×C22⋊D269—21no—
62C2×C22⋊D269—21no—
63C22×Dic269—21no—
64C22×Dic269—21no—
65C2×C4×D269—21no—
66#16864391—22no—
67C4⋊Dic269—21no—
68C4⋊Dic269—21no—
69C4⋊Dic269C2311yescharacteristic
70C4⋊Dic269C2311yescharacteristic
71C4⋊Dic269C2311yescharacteristic
72C4⋊Dic269C2311yescharacteristic
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—
82C22⋊Dic269—21no—
83C22⋊Dic269—21no—
84C22⋊Dic269—21no—
85C22⋊Dic269—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269—21no—
92C2×D4×C269D411yescharacteristic
93C22×C4×C269C2311yescharacteristic
94C22×C4×C269C2311yescharacteristic
95M16×C269—22no—
96M16×C269—22no—
97C2×C8×C269C2311yescharacteristic
98C2×C8×C269C2311yescharacteristic
99C2×C8×C269C2311yescharacteristic
100C2×C8×C269C2311yescharacteristic
101C4⋊C4×C269D411yescharacteristic
102C22⋊C4×C269D411yescharacteristic
103C22⋊C4×C269D411yescharacteristic
104C42×C269C2311yescharacteristic
105C22×D269—21no—
106Dic538—21no—
107Dic538—21no—
108D1076—21no—
109D1076—21no—
110C22⋊D269—42no—
111C22⋊D269—81no—
112C2×Dic269—21no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—21no—
119C2×Dic269—42no—
120C2×Dic269—81no—
121C4×D269—81no—
122C23×C269C2×D411yescharacteristic
123C23×C269C2×D411yescharacteristic
124D4×C269—41no—
125C2×C4×C269—21no—
126C2×C4×C269—21no—
127C2×C4×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269C2×D411yescharacteristic
130C2×C4×C269C2×D411yescharacteristic
131C2×C4×C269C2×D411yescharacteristic
132C2×C4×C269C2×D411yescharacteristic
133C2×C4×C269C2411yescharacteristic
134C8×C269—21no—
135C8×C269—21no—
136C8×C269—21no—
137C8×C269#4112yes—
138C22×C269—21no—
139C22×C269—21no—
140C22×C269—21no—
141C22×C269—21no—
142C22×C269—21no—
143C22×C269—21no—
144C22×C269C22×D411yescharacteristic
145C2×D269—41no—
146C2×D269—41no—
147C2×D269—41no—
148C4×C269—21no—
149C4×C269—21no—
150C4×C269—21no—
151C4×C269—21no—
152C4×C269C2×#4111yescharacteristic
153C4×C2692−1+411yescharacteristic
154Dic269—41no—
155Dic269—41no—
156Dic269—41no—
157Dic269—41no—
158Dic269—41no—
159Dic269—41no—
160Dic269—41no—
161C2×C269—41no—
162C2×C269—41no—
163C2×C269#54711yescharacteristic
164C2×C269#57511yescharacteristic
165C2×C269#57711yescharacteristic
166D269—81no—
167C269#335111yescharacteristic, complemented, Sylow
168#3351—2691nomaximal, Sylow
169#553—2691no—
170#552—2691no—
171#499—2691no—
172#485—2691no—
173#483—2691no—
174#482—2691no—
175#481—2691no—
176#479—2691no—
177#478—2691no—
178#468—2691no—
179#468—2691no—
180C4×SD16—2691no—
181#436D26911yescharacteristic, complemented
182#428—2691no—
183#428—2691no—
184C2×SD16—2691no—
185C2×M16C2×D26911yescharacteristic
186C2×M16C2×D26911yescharacteristic
187#126—5381no—
188#126—5381no—
189#125—2691no—
190#125—2691no—
191#125—5381no—
192#123—5381no—
193#123—5381no—
194C22⋊Q8—2691no—
195C22⋊Q8—2691no—
196#121—2691no—
197#121—2691no—
198#121—5381no—
199C4×Q8—2691no—
200C4×D4—2691no—
201C4×D4—5381no—
202C4×D4C2×D26911yescharacteristic
203#117—2691no—
204#117—2691no—
205#117—5381no—
206C2×C4⋊C4—2691no—
207C2×C4⋊C4—2691no—
208#107—2691no—
209#107—2691no—
210#107—2691no—
211#107—2691no—
212#106—2691no—
213#106—2691no—
214#106—2691no—
215#106—2691no—
216#106—2691no—
217C4⋊C8C2×D26911yescharacteristic
218#103—2691no—
219#103—2691no—
220#103—2691no—
221#102—2691no—
222#102—2691no—
223#102—2691no—
224C22⋊C8C2×D26911yescharacteristic
225C22⋊C8C2×D26911yescharacteristic
226C4×C8C2×D26911yescharacteristic
227C2×Q8—2691no—
228C2×D4—2691no—
229C2×D4—5381no—
230C2×D4—5381no—
231C2×D4D107611yescharacteristic
232C22×C4—5381no—
233C22×C4—5381no—
234C22×C4—5381no—
235C22×C4C22×D26911yescharacteristic
236C22×C4C22×D26911yescharacteristic
237SD16—5382no—
238M16—22no—
239M16—22no—
240C2×C8C22×D26911yescharacteristic
241C2×C8C22×D26911yescharacteristic
242C2×C8C22×D26911yescharacteristic
243C2×C8C22×D26911yescharacteristic
244C4⋊C4—2691no—
245C4⋊C4—2691no—
246C4⋊C4—2691no—
247C4⋊C4—2691no—
248C4⋊C4—2691no—
249C4⋊C4—2691no—
250C4⋊C4—5381no—
251C4⋊C4—5381no—
252C4⋊C4—5381no—
253C4⋊C4—5381no—
254C4⋊C4—5381no—
255C4⋊C4—5381no—
256C4⋊C4—5381no—
257C4⋊C4—5381no—
258C4⋊C4—5381no—
259C4⋊C4D107611yescharacteristic
260C22⋊C4—5381no—
261C22⋊C4—5381no—
262C22⋊C4—5381no—
263C22⋊C4—5381no—
264C22⋊C4—5381no—
265C22⋊C4—5381no—
266C22⋊C4—5381no—
267C22⋊C4D107611yescharacteristic
268C22⋊C4D107611yescharacteristic
269C42—5381no—
270C42—5381no—
271C42—5381no—
272C42C22×D26911yescharacteristic
273C23—5381no—
274C23C2×D107611yescharacteristic
275C23C2×D107611yescharacteristic
276Q8—5381no—
277Q8—5381no—
278D4—41no—
279D4—5381no—
280D4—5381no—
281D4—10762no—
282D4—21521no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—5381no—
288C2×C4—5381no—
289C2×C4—5381no—
290C2×C4—5381no—
291C2×C4—5381no—
292C2×C4—5381no—
293C2×C4—5381no—
294C2×C4—10762no—
295C2×C4—21521no—
296C2×C4—21521no—
297C2×C4C2×D107611yescharacteristic
298C2×C4C2×D107611yescharacteristic
299C2×C4C2×D107611yescharacteristic
300C2×C4C2×D107611yescharacteristic
301C2×C4C23×D26911yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8#1686440112yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—10761no—
313C22—10761no—
314C22—10761no—
315C22C22×D107611yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—10761no—
321C4—10761no—
322C4—10761no—
323C4—10761no—
324C4—10761no—
325C4—10761no—
326C4—10761no—
327C4C2×#1686440111yescharacteristic
328C4#2257550011yescharacteristic
329C2—41no—
330C2—41no—
331C2—21521no—
332C2#3177125911yescharacteristic
333C2#3177140511yescharacteristic
334C2#3177141711yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#436×C269C2
socleC22×C269C22×D4
prime radical#31771301C2
hypercenter#436D269
hypocenterC269#3351
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
2. #31771295C2semidirect
3. #31771007C2semidirect
4. #31770947C2semidirect
5. #31770936C2semidirect
6. #31770930C2semidirect
7. #31770924C2semidirect
8. #31770913C2semidirect
9. #31770906C2semidirect
10. #31770851C2semidirect
11. #31770851C2semidirect
12. C4×#16864391C2semidirect
13. #31770647C2semidirect
14. #31770647C2semidirect
15. #436×C269C2semidirect
167. C269#3351semidirect
181. #436D269semidirect

Maximal subgroups

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

subgroupindex
#317713012
#317712952
#317710072
#317709472
#317709362
#317709302
#317709242
#317709132
#317709062
#317708512
C4×#168643912
#317706472
#436×C2692
#3351269