Finite Group Databasebeta

← #46823457

Subgroups — #46823457

Order 34432.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771296C211yesmaximal, characteristic
2#31771293C211yesmaximal, characteristic
3#31771004C211yesmaximal, characteristic, complemented
4#31770949C211yesmaximal, characteristic, complemented
5#31770944C211yesmaximal, characteristic, complemented
6#31770942C211yesmaximal, characteristic, complemented
7#31770939C211yesmaximal, characteristic, complemented
8#31770913C211yesmaximal, characteristic, complemented
9#31770862C211yesmaximal, characteristic, complemented
10#31770862C211yesmaximal, characteristic, complemented
11C4×#16864392C211yesmaximal, characteristic, complemented
12#31770682C211yesmaximal, characteristic
13#31770646C211yesmaximal, characteristic, complemented
14#31770644C211yesmaximal, characteristic, complemented
15#479×C269C211yesmaximal, characteristic, complemented
16C2×#16864392C2211yescharacteristic
17C2×#16864385C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19#22575448—21no—
20#22575447—21no—
21#22575445C2211yescharacteristic
22#22575444—21no—
23#22575443—21no—
24#22575438—21no—
25#22575438—21no—
26#22575433C2211yescharacteristic
27#22575433C2211yescharacteristic
28#22575429C2211yescharacteristic
29#22575429C2211yescharacteristic
30C4×Dic538C2211yescharacteristic
31C4×D1076C2211yescharacteristic
32#22575411—21no—
33#22575411C2211yescharacteristic
34#22575411C2211yescharacteristic
35#22575410—21no—
36C4⋊C4×D269C2211yescharacteristic
37C4⋊C4×D269C2211yescharacteristic
38#22575387C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575386C2211yescharacteristic
41#22575386C2211yescharacteristic
42#22575385C2211yescharacteristic
43#22575384C2211yescharacteristic
44#22575384C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575377C2211yescharacteristic
48#22575376C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic
51C4×#14524130C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59C2×Dic538C2311yescharacteristic
60C2×D1076D411yescharacteristic
61C2×C4×D269—21no—
62C2×C4×D269—21no—
63C2×C4×D269C2311yescharacteristic
64C2×C4×D269C2311yescharacteristic
65#16864392—22no—
66#16864385—22no—
67#16864385—22no—
68C2×#14524130C2311yescharacteristic
69C2×#14524130C2311yescharacteristic
70C4⋊Dic269—21no—
71C4⋊Dic269—21no—
72C4⋊Dic269D411yescharacteristic
73C4⋊Dic269C2311yescharacteristic
74C4⋊Dic269C2311yescharacteristic
75C4⋊Dic269C2311yescharacteristic
76#16864381—21no—
77#16864381—21no—
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864379—21no—
84#16864379—21no—
85#16864379—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379D411yescharacteristic
90#16864379D411yescharacteristic
91C4×Dic269—21no—
92C4×Dic269—21no—
93C4×Dic269—21no—
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×D269C2×D411yescharacteristic
106C22×D269C2×D411yescharacteristic
107Dic538—21no—
108Dic538—21no—
109D1076—41no—
110C2×Dic269—21no—
111C2×Dic269—21no—
112C2×Dic269—21no—
113C2×Dic269—21no—
114C2×Dic269C2×D411yescharacteristic
115C2×Dic269C2×D411yescharacteristic
116C4×D269—21no—
117C4×D269—21no—
118C4×D269—21no—
119C4×D269—21no—
120C4×D269—42no—
121C4×D269—42no—
122#14524130—21no—
123#14524130#4112yes—
124Q8×C269—21no—
125Q8×C269—21no—
126C2×C4×C269—21no—
127C2×C4×C269—21no—
128C2×C4×C269—21no—
129C2×C4×C269—21no—
130C2×C4×C269C2×D411yescharacteristic
131C2×C4×C269C2×D411yescharacteristic
132C2×C4×C269C2411yescharacteristic
133C8×C269—21no—
134C8×C269—21no—
135C22×C269C22×D411yescharacteristic
136C2×D269—21no—
137C2×D269—21no—
138C2×D269—21no—
139C2×D269—21no—
140C2×D269—21no—
141C2×D269—21no—
142C4×C269—21no—
143C4×C269—21no—
144C4×C269—41no—
145C4×C269—41no—
146C4×C269—41no—
147C4×C269—41no—
148C4×C269C2×#4111yescharacteristic
149C4×C2692−1+411yescharacteristic
150Dic269—21no—
151Dic269—21no—
152Dic269—41no—
153Dic269—41no—
154Dic269—41no—
155Dic269—41no—
156C2×C269#54711yescharacteristic
157C2×C269#57511yescharacteristic
158C2×C269#57811yescharacteristic
159D269—41no—
160D269—41no—
161C269#335211yescharacteristic, complemented, Sylow
162#3352—2691nomaximal, Sylow
163#552—2691no—
164#552—2691no—
165#499—2691no—
166#485—2691no—
167#485—2691no—
168#484—2691no—
169#484—2691no—
170#479—2691no—
171#479D26911yescharacteristic, complemented
172#470—2691no—
173#470—2691no—
174C4×Q16—2691no—
175#436—2691no—
176#428—2691no—
177#428—2691no—
178C2×Q16—2691no—
179C2×M16—2691no—
180C2×M16—2691no—
181#126—5381no—
182#126—5381no—
183#125—2691no—
184#125—5381no—
185#125—5381no—
186#125C2×D26911yescharacteristic
187#123—5381no—
188#123—5381no—
189C22⋊Q8—2691no—
190C22⋊Q8—2691no—
191C22⋊Q8—2691no—
192C22⋊Q8—2691no—
193C4×Q8—2691no—
194C4×Q8C2×D26911yescharacteristic
195C4×D4—2691no—
196#117—2691no—
197#117—2691no—
198#117—5381no—
199#117—5381no—
200C2×C4⋊C4—2691no—
201C2×C4⋊C4—2691no—
202#107—2691no—
203#107—2691no—
204#107—2691no—
205#107—2691no—
206#107C2×D26911yescharacteristic
207#106—2691no—
208#106—2691no—
209#106—2691no—
210#106C2×D26911yescharacteristic
211C4⋊C8C2×D26911yescharacteristic
212#103—2691no—
213#103—2691no—
214#103—2691no—
215#103—2691no—
216#103C2×D26911yescharacteristic
217#103C2×D26911yescharacteristic
218C22⋊C8—2691no—
219C22⋊C8—2691no—
220C4×C8—2691no—
221C2×Q8—2691no—
222C2×Q8C22×D26911yescharacteristic
223C2×D4—2691no—
224C22×C4—2691no—
225C22×C4—2691no—
226C22×C4—5381no—
227C22×C4—5381no—
228Q16—5382no—
229M16—5382no—
230M16—5382no—
231C2×C8—2691no—
232C2×C8—2691no—
233C2×C8C22×D26911yescharacteristic
234C2×C8C22×D26911yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
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⋊C4C22×D26911yescharacteristic
252C4⋊C4C22×D26911yescharacteristic
253C4⋊C4C22×D26911yescharacteristic
254C22⋊C4—2691no—
255C22⋊C4—2691no—
256C22⋊C4—5381no—
257C22⋊C4—5381no—
258C22⋊C4—5381no—
259C22⋊C4—5381no—
260C22⋊C4—5381no—
261C22⋊C4—5381no—
262C42—21no—
263C42—5381no—
264C42—5381no—
265C42—5381no—
266C42C22×D26911yescharacteristic
267C23—2691no—
268C23—2691no—
269Q8—21no—
270Q8—21no—
271Q8—5381no—
272Q8—5381no—
273D4—10761no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—2691no—
279C2×C4—2691no—
280C2×C4—5381no—
281C2×C4—5381no—
282C2×C4—5381no—
283C2×C4—5381no—
284C2×C4—5381no—
285C2×C4—5381no—
286C2×C4—5381no—
287C2×C4—5381no—
288C2×C4—10762no—
289C2×C4—10762no—
290C2×C4D4×D26911yescharacteristic
291C2×C4D4×D26911yescharacteristic
292C2×C4C23×D26911yescharacteristic
293C8—21no—
294C8—21no—
295C8—2692no—
296C8—5381no—
297C22—5381no—
298C22—5381no—
299C22—5381no—
300C22—5381no—
301C22—5381no—
302C22—5381no—
303C22C2×D4×D26911yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—5381no—
311C4—5381no—
312C4—10761no—
313C4—10761no—
314C4—10761no—
315C4—10761no—
316C4#41×D26911yescharacteristic
317C4#2257550111yescharacteristic
318C2—10761no—
319C2—10761no—
320C2#3177125711yescharacteristic
321C2#3177140211yescharacteristic
322C2#3177142111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#479×C269C2
socleC22×C269C22×D4
prime radicalC2×D1076D4
hypercenter#479D269
hypocenterC269#3352
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
3. #31771004C2semidirect
4. #31770949C2semidirect
5. #31770944C2semidirect
6. #31770942C2semidirect
7. #31770939C2semidirect
8. #31770913C2semidirect
9. #31770862C2semidirect
10. #31770862C2semidirect
11. C4×#16864392C2semidirect
13. #31770646C2semidirect
14. #31770644C2semidirect
15. #479×C269C2semidirect
161. C269#3352semidirect
171. #479D269semidirect

Maximal subgroups

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

subgroupindex
#317712962
#317712932
#317710042
#317709492
#317709442
#317709422
#317709392
#317709132
#317708622
C4×#168643922
#317706822
#317706462
#317706442
#479×C2692
#3352269