Finite Group Databasebeta

← #46822739

Subgroups — #46822739

Order 34432.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771307C211yesmaximal, characteristic, complemented
2#31771249C211yesmaximal, characteristic, complemented
3#31770958C211yesmaximal, characteristic, complemented
4#31770941C211yesmaximal, characteristic, complemented
5#31770927C211yesmaximal, characteristic, complemented
6#31770903C211yesmaximal, characteristic, complemented
7#31770838C211yesmaximal, characteristic, complemented
8#31770832C211yesmaximal, characteristic, complemented
9#31770818C211yesmaximal, characteristic, complemented
10#31770747C211yesmaximal, characteristic, complemented
11D8×Dic269C211yesmaximal, characteristic, complemented
12#31770668C211yesmaximal, characteristic, complemented
13#31770598C211yesmaximal, characteristic, complemented
14C2×#22575374C211yesmaximal, characteristic, complemented
15#447×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×#16864390C2211yescharacteristic, complemented
18C22×#14524130C2211yescharacteristic
19C2×C8×D269C2211yescharacteristic, complemented
20#22575446—21no—
21#22575444C2211yescharacteristic, complemented
22#22575440C2211yescharacteristic
23#22575437—21no—
24#22575434—21no—
25#22575432C2211yescharacteristic
26#22575425—21no—
27#22575425—21no—
28#22575424C2211yescharacteristic
29#22575424C2211yescharacteristic, complemented
30#22575422—21no—
31D4×Dic269—21no—
32D4×Dic269C2211yescharacteristic
33D4×Dic269C2211yescharacteristic, complemented
34C4×C22⋊D269C2211yescharacteristic
35#22575411C2211yescharacteristic, complemented
36C2×C4⋊Dic269C2211yescharacteristic
37C2×C22⋊Dic269—21no—
38#22575387C2211yescharacteristic, complemented
39#22575387C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575378C2211yescharacteristic, complemented
43#22575378C2211yescharacteristic, complemented
44#22575376C2211yescharacteristic, complemented
45#22575374C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575374C2211yescharacteristic, complemented
50#22575365C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52C22×D4×C269C2211yescharacteristic
53C2×D8×C269C2211yescharacteristic
54C2×D8×C269C2211yescharacteristic
55#121×C269C2211yescharacteristic
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic
59#16864401—22no—
60#16864401—41no—
61C2×Dic538C2311yescharacteristic
62C2×C22⋊D269—21no—
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C2×C22⋊D269D411yescharacteristic
66C22×Dic269—21no—
67C22×Dic269—21no—
68C22×Dic269—21no—
69C22×Dic269—21no—
70C2×C4×D269C2311yescharacteristic
71#16864390—41no—
72C2×#14524130—41no—
73C2×#14524130C2311yescharacteristic
74C2×#14524130C2311yescharacteristic
75C8×D269—41no—
76C4⋊Dic269—21no—
77C4⋊Dic269—21no—
78C4⋊Dic269C2311yescharacteristic
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81#16864381—21no—
82#16864381—21no—
83#16864381D411yescharacteristic
84C22⋊Dic269—21no—
85C22⋊Dic269—21no—
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89C22⋊Dic269—21no—
90C22⋊Dic269—21no—
91C22⋊Dic269D411yescharacteristic
92#16864379—21no—
93#16864379D411yescharacteristic
94C4×Dic269—21no—
95C4×Dic269C2311yescharacteristic
96C24×C269—21no—
97C2×D4×C269—22no—
98C2×D4×C269—21no—
99C2×D4×C269—21no—
100C2×D4×C269—41no—
101C2×D4×C269C2311yescharacteristic
102C2×D4×C269C2311yescharacteristic
103C2×D4×C269C2311yescharacteristic
104C22×C4×C269C2311yescharacteristic
105D8×C269—22no—
106D8×C269—41no—
107C2×C8×C269C2311yescharacteristic
108C2×C8×C269C2311yescharacteristic
109C4⋊C4×C269C2311yescharacteristic
110C22⋊C4×C269—21no—
111C22×D269C2×D411yescharacteristic
112Dic538—21no—
113Dic538—21no—
114C22⋊D269—22no—
115C22⋊D269—42no—
116C22⋊D269—81no—
117C22⋊D269—81no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—21no—
122C2×Dic269—42no—
123C2×Dic269—81no—
124C2×Dic269—81no—
125C2×Dic269—81no—
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C4×D269—21no—
130C4×D269—21no—
131#14524130—21no—
132#14524130—21no—
133C23×C269—21no—
134C23×C269—21no—
135C23×C269—21no—
136C23×C269—42no—
137C23×C269—42no—
138C23×C269—81no—
139C23×C269C2×D411yescharacteristic
140D4×C269—21no—
141D4×C269—21no—
142D4×C269—21no—
143D4×C269—21no—
144D4×C269—21no—
145D4×C269—42no—
146D4×C269—42no—
147D4×C269#4112yes—
148C2×C4×C269—21no—
149C2×C4×C269—21no—
150C2×C4×C269—21no—
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2411yescharacteristic
153C8×C269—21no—
154C8×C269—21no—
155C22×C269—21no—
156C22×C269—21no—
157C22×C269—22no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269—41no—
162C22×C269—41no—
163C22×C269—41no—
164C22×C269—41no—
165C22×C269—41no—
166C22×C269—84no—
167C22×C269#13512yes—
168C22×C269C22×D411yescharacteristic
169C2×D269—21no—
170C2×D269—21no—
171C2×D269—21no—
172C4×C269—21no—
173C4×C269—41no—
174C4×C269C2×#4111yescharacteristic
175C4×C269H(5,𝔽2)11yescharacteristic
176Dic269—21no—
177Dic269—21no—
178Dic269—21no—
179Dic269—41no—
180Dic269—41no—
181Dic269—41no—
182Dic269—41no—
183C2×C269—22no—
184C2×C269—42no—
185C2×C269—81no—
186C2×C269—81no—
187C2×C269#54611yescharacteristic
188C2×C269C2×#13511yescharacteristic
189C2×C269#57611yescharacteristic
190D269—41no—
191C269#329711yescharacteristic, complemented, Sylow
192#3297—2691nomaximal, Sylow
193#553—2691no—
194#546—2691no—
195#488—2691no—
196#484—2691no—
197#482—2691no—
198#478—2691no—
199#466—2691no—
200#465—2691no—
201#463—2691no—
202#449—2691no—
203#447D26911yescharacteristic, complemented
204C4×D8—2691no—
205C8×D4—2691no—
206#416—2691no—
207C2×#102—2691no—
208C2×#41—2691no—
209C22×D4C2×D26911yescharacteristic
210C2×SD16—2691no—
211C2×D8C2×D26911yescharacteristic
212C2×D8C2×D26911yescharacteristic
213C22×C8—2691no—
214C22×C8—2691no—
215#126—5381no—
216#125—2691no—
217#124—2691no—
218#123—5381no—
219#123—5381no—
220C22⋊Q8—2691no—
221#121—2691no—
222#121—2691no—
223#121—5381no—
224#121—5381no—
225#121C2×D26911yescharacteristic
226#120—5381no—
227C4×D4—2691no—
228C4×D4—2691no—
229C4×D4—2691no—
230C4×D4—5381no—
231#117—2691no—
232C2×C4⋊C4—2691no—
233C2×C22⋊C4—5381no—
234#107—2691no—
235#107—2691no—
236#106—2691no—
237C4⋊C8—2691no—
238#103—2691no—
239#103—2691no—
240#103—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244#102—2691no—
245#102—2691no—
246#102C2×D26911yescharacteristic
247#102C2×D26911yescharacteristic
248C22⋊C8—2691no—
249C22⋊C8C2×D26911yescharacteristic
250C4×C8—2691no—
251C24—21no—
252#41—5382no—
253#41—10761no—
254C2×Q8—2691no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—2691no—
260C2×D4—5381no—
261C2×D4—5381no—
262C2×D4—5381no—
263C2×D4C22×D26911yescharacteristic
264C2×D4C22×D26911yescharacteristic
265C2×D4C22×D26911yescharacteristic
266C22×C4—2691no—
267C22×C4—5381no—
268C22×C4—5381no—
269C22×C4—5381no—
270C22×C4—5381no—
271C22×C4C22×D26911yescharacteristic
272SD16—10761no—
273D8—22no—
274D8—41no—
275C2×C8—2691no—
276C2×C8—2691no—
277C2×C8—10761no—
278C2×C8—10761no—
279C2×C8C22×D26911yescharacteristic
280C2×C8C22×D26911yescharacteristic
281C4⋊C4—2691no—
282C4⋊C4—2691no—
283C4⋊C4—2691no—
284C4⋊C4—2691no—
285C4⋊C4—5381no—
286C4⋊C4—5381no—
287C4⋊C4—5381no—
288C4⋊C4—5381no—
289C4⋊C4C22×D26911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2691no—
292C22⋊C4—2691no—
293C22⋊C4—5381no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C22⋊C4—5381no—
299C22⋊C4—5381no—
300C22⋊C4—5381no—
301C42—2691no—
302C42—5381no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—42no—
307C23—42no—
308C23—81no—
309C23—2691no—
310C23D4×D26911yescharacteristic
311Q8—5381no—
312Q8—5381no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—42no—
320D4—5382no—
321D4—10762no—
322D4—21521no—
323D4—21521no—
324D4#1686440112yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—2691no—
329C2×C4—2691no—
330C2×C4—2691no—
331C2×C4—5381no—
332C2×C4—5381no—
333C2×C4—5381no—
334C2×C4—5381no—
335C2×C4—5381no—
336C2×C4—5381no—
337C2×C4—10762no—
338C2×C4—21521no—
339C2×C4—21521no—
340C2×C4—21521no—
341C2×C4D4×D26911yescharacteristic
342C2×C4C23×D26911yescharacteristic
343C8—21no—
344C8—21no—
345C8—5381no—
346C8—5381no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—84no—
359C22—5381no—
360C22—5381no—
361C22—5381no—
362C22#2257547212yes—
363C22C2×D4×D26911yescharacteristic
364C4—21no—
365C4—41no—
366C4—5381no—
367C4—5381no—
368C4—5381no—
369C4—10761no—
370C4—10761no—
371C4—10761no—
372C4—10761no—
373C4C2×#1686440111yescharacteristic
374C4#2257549811yescharacteristic
375C2—22no—
376C2—42no—
377C2—81no—
378C2—81no—
379C2—10761no—
380C2#3177124211yescharacteristic
381C2C2×#2257547211yescharacteristic
382C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#447×C269C2
socleC22×C269C22×D4
hypercenter#447D269
hypocenterC269#3297
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #31771307C2semidirect
2. #31771249C2semidirect
3. #31770958C2semidirect
4. #31770941C2semidirect
5. #31770927C2semidirect
6. #31770903C2semidirect
7. #31770838C2semidirect
8. #31770832C2semidirect
9. #31770818C2semidirect
10. #31770747C2semidirect
11. D8×Dic269C2semidirect
12. #31770668C2semidirect
13. #31770598C2semidirect
14. C2×#22575374C2semidirect
15. #447×C269C2semidirect
17. C2×#16864390C22semidirect
19. C2×C8×D269C22semidirect
21. #22575444C22semidirect
29. #22575424C22semidirect
33. D4×Dic269C22semidirect
35. #22575411C22semidirect
38. #22575387C22semidirect
39. #22575387C22semidirect
40. #22575384C22semidirect
41. #22575382C22semidirect
42. #22575378C22semidirect
43. #22575378C22semidirect
44. #22575376C22semidirect
49. #22575374C22semidirect
50. #22575365C22semidirect
51. C8×Dic269C22semidirect
191. C269#3297semidirect
203. #447D269semidirect

Maximal subgroups

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

subgroupindex
#317713072
#317712492
#317709582
#317709412
#317709272
#317709032
#317708382
#317708322
#317708182
#317707472
D8×Dic2692
#317706682
#317705982
C2×#225753742
#447×C2692
#3297269