Finite Group Databasebeta

← #46820688

Subgroups — #46820688

Order 34432.

376 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#31771161C211yesmaximal, characteristic
2C4×Q8×D269C211yesmaximal, characteristic
3#31770913C211yesmaximal, characteristic, complemented
4#31770912C211yesmaximal, characteristic, complemented
5#31770909C211yesmaximal, characteristic, complemented
6#31770899C211yesmaximal, characteristic, complemented
7#31770898C211yesmaximal, characteristic, complemented
8#31770889C211yesmaximal, characteristic, complemented
9#31770888C211yesmaximal, characteristic, complemented
10#31770646C211yesmaximal, characteristic
11#31770644C211yesmaximal, characteristic
12#31770627C211yesmaximal, characteristic
13#31770612C211yesmaximal, characteristic
14#31770612C211yesmaximal, characteristic
15#479×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269C2211yescharacteristic
17C2×#16864385C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19#22575452C2211yescharacteristic
20#22575452C2211yescharacteristic
21#22575445C2211yescharacteristic
22#22575431—21no—
23#22575431—21no—
24Q8×Dic269C2211yescharacteristic
25C4×Dic538—21no—
26C4×Dic538C2211yescharacteristic
27#22575418—21no—
28#22575418—21no—
29#22575418—21no—
30#22575418C2211yescharacteristic
31#22575411C2211yescharacteristic
32#22575411C2211yescharacteristic
33C4⋊C4×D269—21no—
34C4⋊C4×D269C2211yescharacteristic
35C42×D269—21no—
36C42×D269C2211yescharacteristic
37#22575387C2211yescharacteristic
38#22575386C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575385C2211yescharacteristic
41#22575384C2211yescharacteristic
42#22575384C2211yescharacteristic
43C4⋊#14524130C2211yescharacteristic
44#22575382C2211yescharacteristic
45#22575382C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575378C2211yescharacteristic
48#22575377C2211yescharacteristic
49#22575377C2211yescharacteristic
50#22575376C2211yescharacteristic
51#22575376C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#103×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic
59C2×Dic538—21no—
60C2×Dic538—21no—
61C2×Dic538—21no—
62C2×Dic538C2311yescharacteristic
63Q8×D269—22no—
64Q8×D269Q814yescomplemented
65C2×C4×D269—21no—
66C2×C4×D269—21no—
67C2×C4×D269D411yescharacteristic
68C2×C4×D269D411yescharacteristic
69C2×C4×D269C2311yescharacteristic
70#16864385—22no—
71#16864385—22no—
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C4⋊Dic269—21no—
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864379—21no—
86#16864379—21no—
87C4×Dic269—21no—
88C4×Dic269—21no—
89C4×Dic269—21no—
90C4×Dic269—21no—
91C4×Dic269—21no—
92C4×Dic269D411yescharacteristic
93C4×Dic269D411yescharacteristic
94C4×Dic269C2311yescharacteristic
95C2×Q8×C269C2311yescharacteristic
96C2×C8×C269C2311yescharacteristic
97C2×C8×C269C2311yescharacteristic
98C4⋊C4×C269—21no—
99C4⋊C4×C269—21no—
100C4⋊C4×C269—21no—
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C4⋊C4×C269C2311yescharacteristic
104C42×C269—21no—
105C42×C269C2311yescharacteristic
106C22×D269C2×D411yescharacteristic
107Dic538—21no—
108Dic538—24no—
109Dic538—42no—
110Dic538—42no—
111Dic538C2×Q812yes—
112C2×Dic269—21no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269C2×D411yescharacteristic
117C2×Dic269C2×D411yescharacteristic
118C2×Dic269C2×D411yescharacteristic
119C4×D269—24no—
120C4×D269—22no—
121C4×D269—41no—
122C4×D269—42no—
123C4×D269C2×Q812yes—
124C4×D269#4112yes—
125#14524130—21no—
126#14524130—21no—
127Q8×C269—21no—
128Q8×C269C2×Q812yes—
129C2×C4×C269—21no—
130C2×C4×C269—21no—
131C2×C4×C269—21no—
132C2×C4×C269—21no—
133C2×C4×C269C2×D411yescharacteristic
134C2×C4×C269C2×D411yescharacteristic
135C2×C4×C269C2411yescharacteristic
136C8×C269—21no—
137C8×C269—21no—
138C22×C269C22×D411yescharacteristic
139C2×D269—21no—
140C2×D269—21no—
141C2×D269C22⋊Q812yes—
142C4×C269—22no—
143C4×C269—21no—
144C4×C269—21no—
145C4×C269—41no—
146C4×C269—41no—
147C4×C269—41no—
148C4×C269C22×Q811yescharacteristic
149C4×C269C2×#4111yescharacteristic
150Dic269—22no—
151Dic269—21no—
152Dic269—41no—
153Dic269—41no—
154Dic269—41no—
155Dic269C22⋊Q812yes—
156Dic269#13712yes—
157C2×C269C2×C22⋊Q811yescharacteristic
158C2×C269C2×#13711yescharacteristic
159C2×C269#57511yescharacteristic
160D269—22no—
161C269#307811yescharacteristic, complemented, Sylow
162#3078—2691nomaximal, Sylow
163#533—2691no—
164C2×C4×Q8—2691no—
165#479—2691no—
166#479—2691no—
167#479—2691no—
168#479D26911yescharacteristic, complemented
169#477—2691no—
170#477—2691no—
171#475—2691no—
172#475—2691no—
173#428—2691no—
174#428—2691no—
175#423—2691no—
176#419—2691no—
177#419—2691no—
178C22×Q8—2691no—
179C2×M16—2691no—
180C2×M16—2691no—
181C4⋊Q8—2691no—
182C4⋊Q8—2691no—
183#125—2691no—
184#125C2×D26911yescharacteristic
185C22⋊Q8—5381no—
186C22⋊Q8—5381no—
187C4×Q8—2691no—
188C4×Q8—2691no—
189C4×Q8—2691no—
190C4×Q8—5381no—
191C4×Q8—5381no—
192C4×Q8—5381no—
193C4×Q8—5381no—
194C4×Q8C2×D26911yescharacteristic
195#117—2691no—
196#117—2691no—
197C2×C4⋊C4—2691no—
198C2×C4⋊C4—5381no—
199C2×C42—2691no—
200C2×C42—5381no—
201#107—2691no—
202#107—2691no—
203#107—2691no—
204#107C2×D26911yescharacteristic
205#106—2691no—
206#106—2691no—
207#106—2691no—
208#106C2×D26911yescharacteristic
209C4⋊C8—2691no—
210C4⋊C8—2691no—
211C4⋊C8—2691no—
212C4⋊C8C2×D26911yescharacteristic
213#103—2691no—
214#103—2691no—
215#103—2691no—
216#103—2691no—
217#103—2691no—
218#103—2691no—
219#103C2×D26911yescharacteristic
220#103C2×D26911yescharacteristic
221C2×Q8—2694no—
222C2×Q8—2691no—
223C2×Q8—5381no—
224C2×Q8—5381no—
225C2×Q8—5381no—
226C2×Q8—5382no—
227C2×Q8C22×D26911yescharacteristic
228C22×C4—2691no—
229C22×C4—2691no—
230C22×C4—2691no—
231C22×C4—5381no—
232C22×C4—5381no—
233M16—5382no—
234M16—5382no—
235C2×C8—2691no—
236C2×C8—2691no—
237C2×C8C22×D26911yescharacteristic
238C2×C8C22×D26911yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—2691no—
243C4⋊C4—2691no—
244C4⋊C4—2691no—
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⋊C4C22×D26911yescharacteristic
254C4⋊C4C22×D26911yescharacteristic
255C4⋊C4C22×D26911yescharacteristic
256C22⋊C4—5381no—
257C22⋊C4—5381no—
258C42—21no—
259C42—2691no—
260C42—2691no—
261C42—2691no—
262C42—5381no—
263C42—5381no—
264C42—5381no—
265C42—5381no—
266C42—5381no—
267C42C22×D26911yescharacteristic
268C23—2691no—
269Q8—21no—
270Q8—2692no—
271Q8—5384no—
272Q8—5381no—
273Q8—10762no—
274Q8—10762no—
275Q8Q8×D26912yes—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—2691no—
281C2×C4—2691no—
282C2×C4—2692no—
283C2×C4—2692no—
284C2×C4—2691no—
285C2×C4—5382no—
286C2×C4—5384no—
287C2×C4—5381no—
288C2×C4—5381no—
289C2×C4—5381no—
290C2×C4—5381no—
291C2×C4—10761no—
292C2×C4—10762no—
293C2×C4D4×D26911yescharacteristic
294C2×C4D4×D26911yescharacteristic
295C2×C4C23×D26911yescharacteristic
296C8—21no—
297C8—21no—
298C8—5381no—
299C8—5381no—
300C22—2692no—
301C22—5381no—
302C22—5381no—
303C22C2×D4×D26911yescharacteristic
304C4—21no—
305C4—21no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—2692no—
311C4—2692no—
312C4—5381no—
313C4—5382no—
314C4—10761no—
315C4—10761no—
316C4—10761no—
317C4C2×Q8×D26911yescharacteristic
318C4#41×D26911yescharacteristic
319C2—5382no—
320C2C22⋊Q8×D26911yescharacteristic
321C2#137×D26911yescharacteristic
322C2#3177140211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#479×C269C2
socleC22×C269C22×D4
prime radicalC22×D269C2×D4
hypercenter#479D269
hypocenterC269#3078
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. #31770913C2semidirect
4. #31770912C2semidirect
5. #31770909C2semidirect
6. #31770899C2semidirect
7. #31770898C2semidirect
8. #31770889C2semidirect
9. #31770888C2semidirect
15. #479×C269C2semidirect
64. Q8×D269Q8semidirect
161. C269#3078semidirect
168. #479D269semidirect

Maximal subgroups

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

subgroupindex
#317711612
C4×Q8×D2692
#317709132
#317709122
#317709092
#317708992
#317708982
#317708892
#317708882
#317706462
#317706442
#317706272
#317706122
#479×C2692
#3078269