Finite Group Databasebeta

← #46822717

Subgroups — #46822717

Order 34432.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771293C211yesmaximal, characteristic, complemented
2#31771250C211yesmaximal, characteristic
3#31770962C211yesmaximal, characteristic, complemented
4#31770937C211yesmaximal, characteristic, complemented
5#31770932C211yesmaximal, characteristic, complemented
6#31770847C211yesmaximal, characteristic, complemented
7#31770835C211yesmaximal, characteristic, complemented
8#31770828C211yesmaximal, characteristic, complemented
9#31770768C211yesmaximal, characteristic, complemented
10#31770757C211yesmaximal, characteristic, complemented
11C4×#16864390C211yesmaximal, characteristic, complemented
12#31770670C211yesmaximal, characteristic, complemented
13#31770598C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15#478×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×D4×D269C2211yescharacteristic
18C2×Dic1076C2211yescharacteristic, complemented
19C2×#16864391C2211yescharacteristic
20C2×#16864390C2211yescharacteristic
21C2×C8×D269C2211yescharacteristic
22C2×C8×D269C2211yescharacteristic, complemented
23#22575448—21no—
24#22575444—21no—
25#22575441C2211yescharacteristic
26#22575438—21no—
27#22575437—21no—
28#22575433C2211yescharacteristic
29#22575433C2211yescharacteristic
30#22575433C2211yescharacteristic, complemented
31#22575428C2211yescharacteristic
32#22575427—21no—
33#22575423—21no—
34C4×Dic538C2211yescharacteristic, complemented
35C4×D1076C2211yescharacteristic
36#22575411—21no—
37#22575411C2211yescharacteristic, complemented
38C4⋊C4×D269C2211yescharacteristic
39C2×#16864379—21no—
40#22575384C2211yescharacteristic, complemented
41#22575378C2211yescharacteristic, complemented
42#22575376C2211yescharacteristic, complemented
43#22575376C2211yescharacteristic, complemented
44#22575376C2211yescharacteristic, complemented
45#22575375C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic, complemented
51C4×#14524130C2211yescharacteristic, complemented
52#125×C269C2211yescharacteristic, complemented
53C4×D4×C269C2211yescharacteristic
54#107×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56C4⋊C8×C269C2211yescharacteristic, complemented
57#102×C269C2211yescharacteristic
58#102×C269C2211yescharacteristic
59C23×D269—21no—
60#16864401—22no—
61#16864401—41no—
62C2×Dic538C2311yescharacteristic
63C2×Dic538C2311yescharacteristic
64C2×D1076—21no—
65C2×D1076D411yescharacteristic
66C2×D1076C2311yescharacteristic
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69D4×D269—22no—
70D4×D269—41no—
71C22×Dic269—21no—
72C2×C4×D269—21no—
73C2×C4×D269C2311yescharacteristic
74C2×C4×D269C2311yescharacteristic
75Dic1076—41no—
76#16864391—41no—
77#16864390—22no—
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C8×D269—41no—
81C8×D269—41no—
82C4⋊Dic269—21no—
83C4⋊Dic269—21no—
84C4⋊Dic269—21no—
85C4⋊Dic269D411yescharacteristic
86C4⋊Dic269C2311yescharacteristic
87#16864381—21no—
88#16864381—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379D411yescharacteristic
97#16864379D411yescharacteristic
98C4×Dic269—21no—
99C4×Dic269—21no—
100C2×D4×C269C2311yescharacteristic
101C22×C4×C269—21no—
102C2×C8×C269C2311yescharacteristic
103C2×C8×C269C2311yescharacteristic
104C4⋊C4×C269—21no—
105C4⋊C4×C269—21no—
106C4⋊C4×C269C2311yescharacteristic
107C4⋊C4×C269C2311yescharacteristic
108C4⋊C4×C269C2311yescharacteristic
109C22⋊C4×C269—21no—
110C42×C269C2311yescharacteristic
111C22×D269—21no—
112C22×D269—42no—
113C22×D269—42no—
114C22×D269—81no—
115C22×D269C2×D411yescharacteristic
116C22×D269C2×D411yescharacteristic
117Dic538—21no—
118Dic538—21no—
119Dic538—21no—
120Dic538—21no—
121D1076—22no—
122D1076—21no—
123D1076—21no—
124D1076—81no—
125C22⋊D269—42no—
126C22⋊D269—42no—
127C2×Dic269—21no—
128C2×Dic269—21no—
129C2×Dic269—21no—
130C2×Dic269—42no—
131C2×Dic269C2×D411yescharacteristic
132C2×Dic269C2×D411yescharacteristic
133C4×D269—21no—
134C4×D269—21no—
135C4×D269—21no—
136C4×D269—21no—
137C4×D269—42no—
138#14524130—21no—
139#14524130—21no—
140C23×C269—21no—
141D4×C269—21no—
142D4×C269#4112yes—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—81no—
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269C2411yescharacteristic
150C8×C269—21no—
151C8×C269—21no—
152C22×C269—22no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269C22×D411yescharacteristic
156C2×D269—21no—
157C2×D269—21no—
158C2×D269—21no—
159C2×D269—21no—
160C2×D269—21no—
161C2×D269—41no—
162C2×D269—41no—
163C2×D269—41no—
164C2×D269—84no—
165C2×D269#13512yes—
166C4×C269—21no—
167C4×C269—21no—
168C4×C269—41no—
169C4×C269—41no—
170C4×C269—41no—
171C4×C269C2×#4111yescharacteristic
172C4×C269H(5,𝔽2)11yescharacteristic
173Dic269—21no—
174Dic269—21no—
175Dic269—41no—
176Dic269—41no—
177Dic269—41no—
178C2×C269—42no—
179C2×C269#54611yescharacteristic
180C2×C269C2×#13511yescharacteristic
181C2×C269#57711yescharacteristic
182D269—22no—
183D269—41no—
184D269—81no—
185C269#329611yescharacteristic, complemented, Sylow
186#3296—2691nomaximal, Sylow
187#552—2691no—
188#546—2691no—
189#488—2691no—
190#483—2691no—
191#482—2691no—
192#478D26911yescharacteristic, complemented
193#467—2691no—
194#465—2691no—
195#464—2691no—
196#452—2691no—
197#450—2691no—
198C4×SD16—2691no—
199C8×D4—2691no—
200#416—2691no—
201C2×#102—2691no—
202C2×#41—2691no—
203C22×D4—2691no—
204C2×Q16—2691no—
205C2×SD16—2691no—
206C2×SD16—2691no—
207C22×C8—2691no—
208C22×C8—2691no—
209#126—5381no—
210#125—5381no—
211#125C2×D26911yescharacteristic, complemented
212#124—2691no—
213#123—5381no—
214#123—5381no—
215C22⋊Q8—2691no—
216C22⋊Q8—2691no—
217C22⋊Q8—2691no—
218#121—2691no—
219#121—5381no—
220#120—5381no—
221C4×Q8—2691no—
222C4×D4—2691no—
223C4×D4C2×D26911yescharacteristic
224#117—2691no—
225#117—5381no—
226C2×C4⋊C4—2691no—
227C2×C22⋊C4—5381no—
228#107C2×D26911yescharacteristic, complemented
229#106—2691no—
230#106C2×D26911yescharacteristic, complemented
231C4⋊C8C2×D26911yescharacteristic, complemented
232#103—2691no—
233#103—2691no—
234#103—2691no—
235#103—2691no—
236#102—2691no—
237#102—2691no—
238#102—2691no—
239#102—2691no—
240#102C2×D26911yescharacteristic
241#102C2×D26911yescharacteristic
242C22⋊C8—2691no—
243C22⋊C8—2691no—
244C4×C8—2691no—
245C24—5381no—
246#41—5382no—
247#41—10761no—
248C2×Q8—2691no—
249C2×Q8—2691no—
250C2×D4—2691no—
251C2×D4—2691no—
252C2×D4—5381no—
253C2×D4—5381no—
254C2×D4—5382no—
255C2×D4—5381no—
256C2×D4—10761no—
257C2×D4C22×D26911yescharacteristic
258C22×C4—21no—
259C22×C4—2691no—
260C22×C4—2691no—
261C22×C4—5381no—
262C22×C4—5381no—
263Q16—10761no—
264SD16—5382no—
265SD16—10761no—
266C2×C8—2691no—
267C2×C8—2691no—
268C2×C8—10761no—
269C2×C8—10761no—
270C2×C8C22×D26911yescharacteristic
271C2×C8C22×D26911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—2691no—
275C4⋊C4—2691no—
276C4⋊C4—5381no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4—5381no—
280C4⋊C4—5381no—
281C4⋊C4C22×D26911yescharacteristic
282C4⋊C4C22×D26911yescharacteristic
283C4⋊C4C22×D26911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—2691no—
286C22⋊C4—2691no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4—5381no—
292C22⋊C4—5381no—
293C22⋊C4—5381no—
294C42—5381no—
295C42—5381no—
296C42C22×D26911yescharacteristic
297C23—21no—
298C23—2691no—
299C23—2691no—
300C23—5381no—
301C23—10762no—
302C23—10762no—
303C23—21521no—
304Q8—5381no—
305Q8—5381no—
306Q8—5381no—
307Q8—5381no—
308D4—21no—
309D4—5382no—
310D4—5381no—
311D4—5381no—
312D4—10762no—
313D4—10762no—
314D4—21521no—
315D4#1686440312yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—2691no—
321C2×C4—2691no—
322C2×C4—5381no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—5381no—
326C2×C4—5381no—
327C2×C4—5381no—
328C2×C4—5381no—
329C2×C4—10762no—
330C2×C4—10762no—
331C2×C4D4×D26911yescharacteristic
332C2×C4D4×D26911yescharacteristic
333C2×C4C23×D26911yescharacteristic
334C8—21no—
335C8—21no—
336C8—5381no—
337C8—5381no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—2692no—
342C22—5381no—
343C22—5381no—
344C22—5381no—
345C22—5381no—
346C22—5381no—
347C22—10761no—
348C22—10761no—
349C22—10761no—
350C22—21524no—
351C22C2×D4×D26911yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—5381no—
358C4—5381no—
359C4—10761no—
360C4—10761no—
361C4—10761no—
362C4C2×#1686440311yescharacteristic
363C4#2257549911yescharacteristic
364C2—42no—
365C2—5382no—
366C2—10761no—
367C2—21521no—
368C2#3177124611yescharacteristic
369C2#135×D26911yescharacteristic
370C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#478×C269C2
socleC22×C269C22×D4
prime radical#31771250C2
hypercenter#478D269
hypocenterC269#3296
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
1. #31771293C2semidirect
3. #31770962C2semidirect
4. #31770937C2semidirect
5. #31770932C2semidirect
6. #31770847C2semidirect
7. #31770835C2semidirect
8. #31770828C2semidirect
9. #31770768C2semidirect
10. #31770757C2semidirect
11. C4×#16864390C2semidirect
12. #31770670C2semidirect
13. #31770598C2semidirect
14. #102×D269C2semidirect
15. #478×C269C2semidirect
18. C2×Dic1076C22semidirect
22. C2×C8×D269C22semidirect
30. #22575433C22semidirect
34. C4×Dic538C22semidirect
37. #22575411C22semidirect
40. #22575384C22semidirect
41. #22575378C22semidirect
42. #22575376C22semidirect
43. #22575376C22semidirect
44. #22575376C22semidirect
50. #22575365C22semidirect
51. C4×#14524130C22semidirect
52. #125×C269C22semidirect
54. #107×C269C22semidirect
55. #106×C269C22semidirect
56. C4⋊C8×C269C22semidirect
185. C269#3296semidirect
192. #478D269semidirect
211. #125C2×D269semidirect
228. #107C2×D269semidirect
230. #106C2×D269semidirect
231. C4⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712932
#317712502
#317709622
#317709372
#317709322
#317708472
#317708352
#317708282
#317707682
#317707572
C4×#168643902
#317706702
#317705982
#102×D2692
#478×C2692
#3296269