Finite Group Databasebeta

← #46823452

Subgroups — #46823452

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#31771305C211yesmaximal, characteristic
2#31771293C211yesmaximal, characteristic, complemented
3#31771004C211yesmaximal, characteristic, complemented
4#31770948C211yesmaximal, characteristic, complemented
5#31770937C211yesmaximal, characteristic, complemented
6#31770927C211yesmaximal, characteristic, complemented
7#31770922C211yesmaximal, characteristic, complemented
8#31770913C211yesmaximal, characteristic, complemented
9#31770850C211yesmaximal, characteristic, complemented
10#31770850C211yesmaximal, characteristic, complemented
11C4×#16864390C211yesmaximal, characteristic, complemented
12#31770682C211yesmaximal, characteristic, complemented
13#31770646C211yesmaximal, characteristic, complemented
14#31770644C211yesmaximal, characteristic, complemented
15#478×C269C211yesmaximal, characteristic, complemented
16C2×#16864390C2211yescharacteristic
17C2×#16864385C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19#22575448—21no—
20#22575446—21no—
21#22575445C2211yescharacteristic
22#22575444—21no—
23#22575438—21no—
24#22575436—21no—
25#22575433C2211yescharacteristic
26#22575433C2211yescharacteristic
27#22575426—21no—
28#22575424C2211yescharacteristic
29#22575424C2211yescharacteristic
30C4×Dic538C2211yescharacteristic
31C4×D1076C2211yescharacteristic
32C4×C22⋊D269—21no—
33#22575411—21no—
34#22575411C2211yescharacteristic
35#22575411C2211yescharacteristic
36C4⋊C4×D269C2211yescharacteristic
37C4⋊C4×D269C2211yescharacteristic
38#22575387C2211yescharacteristic
39#22575386C2211yescharacteristic
40#22575386C2211yescharacteristic
41#22575385C2211yescharacteristic
42#22575384C2211yescharacteristic
43#22575384C2211yescharacteristic
44#22575384C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575378C2211yescharacteristic
47#22575376C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic
51C4×#14524130C2211yescharacteristic
52#125×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic
55#106×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C2×Dic538C2311yescharacteristic
60C2×D1076D411yescharacteristic
61C2×C22⋊D269—21no—
62C2×C22⋊D269—21no—
63C2×C4×D269—21no—
64C2×C4×D269—21no—
65C2×C4×D269C2311yescharacteristic
66C2×C4×D269C2311yescharacteristic
67#16864390—22no—
68#16864385—22no—
69#16864385—22no—
70C2×#14524130C2311yescharacteristic
71C2×#14524130C2311yescharacteristic
72C4⋊Dic269—21no—
73C4⋊Dic269—21no—
74C4⋊Dic269D411yescharacteristic
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381—21no—
82#16864381—21no—
83C22⋊Dic269—21no—
84C22⋊Dic269—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×D4×C269C2311yescharacteristic
95C22×C4×C269—21no—
96C2×C8×C269C2311yescharacteristic
97C2×C8×C269C2311yescharacteristic
98C4⋊C4×C269—21no—
99C4⋊C4×C269—21no—
100C4⋊C4×C269C2311yescharacteristic
101C4⋊C4×C269C2311yescharacteristic
102C4⋊C4×C269C2311yescharacteristic
103C22⋊C4×C269—21no—
104C42×C269C2311yescharacteristic
105C22×D269C2×D411yescharacteristic
106C22×D269C2×D411yescharacteristic
107Dic538—21no—
108Dic538—21no—
109D1076—41no—
110C22⋊D269—42no—
111C22⋊D269—81no—
112C2×Dic269—21no—
113C2×Dic269—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269C2×D411yescharacteristic
117C2×Dic269C2×D411yescharacteristic
118C4×D269—21no—
119C4×D269—21no—
120C4×D269—21no—
121C4×D269—21no—
122C4×D269—42no—
123C4×D269—81no—
124#14524130—21no—
125#14524130#4112yes—
126C23×C269—21no—
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—21no—
143C2×D269—21no—
144C2×D269—21no—
145C2×D269—21no—
146C2×D269—21no—
147C2×D269—21no—
148C4×C269—21no—
149C4×C269—21no—
150C4×C269—41no—
151C4×C269—41no—
152C4×C269—41no—
153C4×C269C2×#4111yescharacteristic
154C4×C2692−1+411yescharacteristic
155Dic269—21no—
156Dic269—21no—
157Dic269—41no—
158Dic269—41no—
159Dic269—41no—
160Dic269—41no—
161C2×C269—81no—
162C2×C269#54711yescharacteristic
163C2×C269#57511yescharacteristic
164C2×C269#57711yescharacteristic
165D269—41no—
166D269—41no—
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#478D26911yescharacteristic, complemented
178#468—2691no—
179#468—2691no—
180C4×SD16—2691no—
181#436—2691no—
182#428—2691no—
183#428—2691no—
184C2×SD16—2691no—
185C2×M16—2691no—
186C2×M16—2691no—
187#126—5381no—
188#126—5381no—
189#125—2691no—
190#125—5381no—
191#125C2×D26911yescharacteristic
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#107C2×D26911yescharacteristic
212#106—2691no—
213#106—2691no—
214#106—2691no—
215#106—2691no—
216#106C2×D26911yescharacteristic
217C4⋊C8C2×D26911yescharacteristic
218#103—2691no—
219#103—2691no—
220#103—2691no—
221#102—2691no—
222#102C2×D26911yescharacteristic
223#102C2×D26911yescharacteristic
224C22⋊C8—2691no—
225C22⋊C8—2691no—
226C4×C8—2691no—
227C2×Q8—2691no—
228C2×D4—2691no—
229C2×D4—5381no—
230C2×D4—5381no—
231C2×D4C22×D26911yescharacteristic
232C22×C4—21no—
233C22×C4—2691no—
234C22×C4—2691no—
235C22×C4—5381no—
236C22×C4—5381no—
237SD16—5382no—
238M16—5382no—
239M16—5382no—
240C2×C8—2691no—
241C2×C8—2691no—
242C2×C8C22×D26911yescharacteristic
243C2×C8C22×D26911yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
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⋊C4C22×D26911yescharacteristic
258C4⋊C4C22×D26911yescharacteristic
259C4⋊C4C22×D26911yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—2691no—
262C22⋊C4—2691no—
263C22⋊C4—5381no—
264C22⋊C4—5381no—
265C22⋊C4—5381no—
266C22⋊C4—5381no—
267C22⋊C4—5381no—
268C22⋊C4—5381no—
269C42—5381no—
270C42—5381no—
271C42—5381no—
272C42C22×D26911yescharacteristic
273C23—21no—
274C23—2691no—
275C23—2691no—
276Q8—5381no—
277Q8—5381no—
278D4—21no—
279D4—21no—
280D4—10761no—
281D4—10762no—
282D4—21521no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—2691no—
288C2×C4—2691no—
289C2×C4—5381no—
290C2×C4—5381no—
291C2×C4—5381no—
292C2×C4—5381no—
293C2×C4—5381no—
294C2×C4—5381no—
295C2×C4—5381no—
296C2×C4—5381no—
297C2×C4—10762no—
298C2×C4—21521no—
299C2×C4D4×D26911yescharacteristic
300C2×C4D4×D26911yescharacteristic
301C2×C4C23×D26911yescharacteristic
302C8—21no—
303C8—21no—
304C8—2692no—
305C8—5381no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—5381no—
310C22—5381no—
311C22—5381no—
312C22—5381no—
313C22—5381no—
314C22—5381no—
315C22C2×D4×D26911yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—5381no—
322C4—5381no—
323C4—10761no—
324C4—10761no—
325C4—10761no—
326C4—10761no—
327C4#41×D26911yescharacteristic
328C4#2257550111yescharacteristic
329C2—81no—
330C2—10761no—
331C2—10761no—
332C2#3177125711yescharacteristic
333C2#3177140211yescharacteristic
334C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#478×C269C2
socleC22×C269C22×D4
prime radical#31771305C2
hypercenter#478D269
hypocenterC269#3351
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
2. #31771293C2semidirect
3. #31771004C2semidirect
4. #31770948C2semidirect
5. #31770937C2semidirect
6. #31770927C2semidirect
7. #31770922C2semidirect
8. #31770913C2semidirect
9. #31770850C2semidirect
10. #31770850C2semidirect
11. C4×#16864390C2semidirect
12. #31770682C2semidirect
13. #31770646C2semidirect
14. #31770644C2semidirect
15. #478×C269C2semidirect
167. C269#3351semidirect
177. #478D269semidirect

Maximal subgroups

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

subgroupindex
#317713052
#317712932
#317710042
#317709482
#317709372
#317709272
#317709222
#317709132
#317708502
C4×#168643902
#317706822
#317706462
#317706442
#478×C2692
#3351269