Finite Group Databasebeta

← #46822707

Subgroups — #46822707

Order 34432.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771310C211yesmaximal, characteristic, complemented
2#31771239C211yesmaximal, characteristic
3#31770950C211yesmaximal, characteristic, complemented
4#31770925C211yesmaximal, characteristic, complemented
5#31770894C211yesmaximal, characteristic, complemented
6#31770835C211yesmaximal, characteristic, complemented
7#31770832C211yesmaximal, characteristic, complemented
8#31770804C211yesmaximal, characteristic, complemented
9#31770758C211yesmaximal, characteristic, complemented
10#31770757C211yesmaximal, characteristic, complemented
11#31770692C211yesmaximal, characteristic, complemented
12#31770668C211yesmaximal, characteristic, complemented
13C2×#22575373C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15#481×C269C211yesmaximal, characteristic, complemented
16C22×D1076C2211yescharacteristic
17C2×D4×D269—21no—
18C2×D4×D269C2211yescharacteristic
19C2×#16864391C2211yescharacteristic
20C2×#16864391C2211yescharacteristic, complemented
21C2×#16864390C2211yescharacteristic, complemented
22C22×#14524130C2211yescharacteristic, complemented
23C2×C8×D269C2211yescharacteristic, complemented
24#22575452C2211yescharacteristic, complemented
25#22575449C2211yescharacteristic
26#22575443—21no—
27#22575433C2211yescharacteristic, complemented
28#22575432—21no—
29#22575432C2211yescharacteristic, complemented
30#22575431—21no—
31#22575428C2211yescharacteristic
32#22575426—21no—
33#22575423—21no—
34#22575421—21no—
35#22575418C2211yescharacteristic, complemented
36#22575415C2211yescharacteristic
37C4×C22⋊D269—21no—
38C4×C22⋊D269C2211yescharacteristic
39C4⋊C4×D269C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575376C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic
44#22575375C2211yescharacteristic, complemented
45#22575374C2211yescharacteristic, complemented
46#22575373C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic, complemented
49#22575373C2211yescharacteristic, complemented
50#22575365C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52#121×C269C2211yescharacteristic
53C2×C4⋊C4×C269C2211yescharacteristic, complemented
54#106×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56#102×C269C2211yescharacteristic, complemented
57#102×C269C2211yescharacteristic, complemented
58C22⋊C8×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60C23×D269—21no—
61C2×Dic538—21no—
62C2×Dic538C2311yescharacteristic
63C2×D1076—22no—
64C2×D1076—21no—
65C2×D1076—21no—
66C2×D1076—41no—
67C2×D1076C2311yescharacteristic
68C2×D1076C2311yescharacteristic
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71C2×C22⋊D269—21no—
72C2×C22⋊D269D411yescharacteristic
73D4×D269—22no—
74D4×D269—41no—
75D4×D269—44no—
76C2×C4×D269—21no—
77C2×C4×D269—21no—
78C2×C4×D269C2311yescharacteristic
79#16864391—22no—
80#16864391—41no—
81#16864390—41no—
82C2×#14524130—41no—
83C2×#14524130C2311yescharacteristic
84C2×#14524130C2311yescharacteristic
85C8×D269—41no—
86C4⋊Dic269—21no—
87C4⋊Dic269C2311yescharacteristic
88#16864381—21no—
89#16864381—21no—
90#16864381—21no—
91#16864381—21no—
92#16864381D411yescharacteristic
93C22⋊Dic269—21no—
94C22⋊Dic269D411yescharacteristic
95#16864379—21no—
96#16864379—21no—
97#16864379—21no—
98#16864379D411yescharacteristic
99C4×Dic269—21no—
100C4×Dic269C2311yescharacteristic
101C2×D4×C269—21no—
102C2×D4×C269C2311yescharacteristic
103C22×C4×C269—21no—
104C22×C4×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C4⋊C4×C269—21no—
108C4⋊C4×C269C2311yescharacteristic
109C4⋊C4×C269C2311yescharacteristic
110C4⋊C4×C269C2311yescharacteristic
111C22⋊C4×C269—21no—
112C22×D269—21no—
113C22×D269—21no—
114C22×D269—42no—
115C22×D269—42no—
116C22×D269—42no—
117C22×D269—42no—
118C22×D269—81no—
119C22×D269—81no—
120C22×D269C2×D411yescharacteristic
121Dic538—21no—
122Dic538—21no—
123Dic538—81no—
124D1076—21no—
125D1076—21no—
126D1076—21no—
127D1076—42no—
128D1076—42no—
129D1076#4112yes—
130C22⋊D269—42no—
131C22⋊D269—42no—
132C22⋊D269—81no—
133C22⋊D269SD1614yescomplemented
134C2×Dic269—21no—
135C2×Dic269—21no—
136C2×Dic269C2×D411yescharacteristic
137C2×Dic269C2×D411yescharacteristic
138C2×Dic269C2×D411yescharacteristic
139C4×D269—21no—
140C4×D269—21no—
141C4×D269—42no—
142C4×D269—81no—
143#14524130—21no—
144#14524130—21no—
145C23×C269—21no—
146C23×C269C2×D411yescharacteristic
147D4×C269—21no—
148D4×C269—21no—
149D4×C269—42no—
150C2×C4×C269—21no—
151C2×C4×C269—21no—
152C2×C4×C269—21no—
153C2×C4×C269—21no—
154C2×C4×C269—21no—
155C2×C4×C269—81no—
156C2×C4×C269C2×D411yescharacteristic
157C2×C4×C269C2411yescharacteristic
158C8×C269—21no—
159C8×C269—21no—
160C22×C269—21no—
161C22×C269—21no—
162C22×C269—41no—
163C22×C269—41no—
164C22×C269—41no—
165C22×C269C2×SD1612yes—
166C22×C269C22×D411yescharacteristic
167C2×D269—21no—
168C2×D269—21no—
169C2×D269—22no—
170C2×D269—41no—
171C2×D269—41no—
172C2×D269—41no—
173C2×D269—41no—
174C2×D269—41no—
175C2×D269—84no—
176C2×D269—84no—
177C2×D269C2×SD1612yes—
178C4×C269—21no—
179C4×C269—41no—
180C4×C269—41no—
181C4×C269—41no—
182C4×C269C2×#4111yescharacteristic
183C4×C269H(5,𝔽2)11yescharacteristic
184Dic269—21no—
185Dic269—21no—
186Dic269—41no—
187Dic269—41no—
188Dic269C2×SD1612yes—
189C2×C269—22no—
190C2×C269—81no—
191C2×C269#54611yescharacteristic
192C2×C269C22×SD1611yescharacteristic
193C2×C269#57611yescharacteristic
194D269—22no—
195D269—42no—
196D269—81no—
197C269#329511yescharacteristic, complemented, Sylow
198#3295—2691nomaximal, Sylow
199#554—2691no—
200D42—2691no—
201#486—2691no—
202#481—2691no—
203#481D26911yescharacteristic, complemented
204#476—2691no—
205#465—2691no—
206#465—2691no—
207#460—2691no—
208#450—2691no—
209#450—2691no—
210C4×SD16—2691no—
211C8×D4—2691no—
212C2×#102—2691no—
213C2×#102—2691no—
214C22×D4—2691no—
215C22×D4—2691no—
216C22×D4—5381no—
217C2×SD16—2691no—
218C2×SD16—2691no—
219C2×SD16—2691no—
220C22×C8—2691no—
221C22×C8—2691no—
222C4⋊Q8—2691no—
223#127—2691no—
224#125—5381no—
225C22⋊Q8—2691no—
226C22⋊Q8—2691no—
227C22⋊Q8—5381no—
228C22⋊Q8—5381no—
229#121—2691no—
230#121—5381no—
231#121C2×D26911yescharacteristic
232#120—5381no—
233#120—5381no—
234C4×Q8—2691no—
235C4×D4—2691no—
236C4×D4—2691no—
237C4×D4—5381no—
238C2×C4⋊C4—2691no—
239C2×C4⋊C4C2×D26911yescharacteristic, complemented
240#106—2691no—
241#106C2×D26911yescharacteristic, complemented
242#106C2×D26911yescharacteristic, complemented
243C4⋊C8—2691no—
244#103—2691no—
245#102—2691no—
246#102—2691no—
247#102—2691no—
248#102—2691no—
249#102—2691no—
250#102—2691no—
251#102—2691no—
252#102C2×D26911yescharacteristic, complemented
253#102C2×D26911yescharacteristic, complemented
254C22⋊C8—2691no—
255C22⋊C8C2×D26911yescharacteristic, complemented
256C4×C8—2691no—
257C24—5381no—
258C24—5381no—
259C2×Q8—2691no—
260C2×Q8—5381no—
261C2×D4—21no—
262C2×D4—2691no—
263C2×D4—2691no—
264C2×D4—2691no—
265C2×D4—5382no—
266C2×D4—5381no—
267C2×D4—5381no—
268C2×D4—5381no—
269C2×D4—5381no—
270C2×D4—5382no—
271C2×D4—5381no—
272C2×D4—10761no—
273C2×D4—10761no—
274C2×D4—10764no—
275C2×D4C22×D26911yescharacteristic
276C22×C4—21no—
277C22×C4—2691no—
278C22×C4—5381no—
279C22×C4—5381no—
280C22×C4C22×D26911yescharacteristic
281SD16—5382no—
282SD16—10761no—
283SD16—10761no—
284C2×C8—2691no—
285C2×C8—2691no—
286C2×C8—10761no—
287C2×C8—10761no—
288C2×C8C22×D26911yescharacteristic
289C2×C8C22×D26911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—2691no—
292C4⋊C4—2691no—
293C4⋊C4—5381no—
294C4⋊C4—5381no—
295C4⋊C4—5381no—
296C4⋊C4—5381no—
297C4⋊C4—5381no—
298C4⋊C4C22×D26911yescharacteristic
299C4⋊C4C22×D26911yescharacteristic
300C4⋊C4C22×D26911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—2691no—
303C22⋊C4—2691no—
304C22⋊C4—5381no—
305C22⋊C4—5381no—
306C22⋊C4—5381no—
307C22⋊C4—5381no—
308C42—2691no—
309C42—5381no—
310C23—21no—
311C23—2691no—
312C23—5381no—
313C23—5381no—
314C23—10762no—
315C23—10762no—
316C23—10762no—
317C23—10762no—
318C23—21521no—
319C23—21521no—
320C23D4×D26911yescharacteristic
321Q8—5381no—
322Q8—5381no—
323Q8—21521no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—2694no—
328D4—2692no—
329D4—5381no—
330D4—5381no—
331D4—5381no—
332D4—10762no—
333D4—10762no—
334D4—10762no—
335D4—10762no—
336D4—21521no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—81no—
343C2×C4—2691no—
344C2×C4—2691no—
345C2×C4—2691no—
346C2×C4—5381no—
347C2×C4—5381no—
348C2×C4—5381no—
349C2×C4—5381no—
350C2×C4—10762no—
351C2×C4—21521no—
352C2×C4D4×D26911yescharacteristic
353C2×C4C23×D26911yescharacteristic
354C8—21no—
355C8—21no—
356C8—5381no—
357C8—5381no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—2692no—
364C22—5381no—
365C22—5381no—
366C22—5382no—
367C22—10761no—
368C22—10761no—
369C22—10761no—
370C22—10761no—
371C22—10761no—
372C22—21524no—
373C22—21524no—
374C22SD16×D26912yes—
375C22C2×D4×D26911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2692no—
381C4—5381no—
382C4—5381no—
383C4—10761no—
384C4—10761no—
385C4#41×D26911yescharacteristic
386C4#2257549911yescharacteristic
387C2—22no—
388C2—81no—
389C2—5382no—
390C2—10762no—
391C2—21521no—
392C2#3177124711yescharacteristic
393C2C2×SD16×D26911yescharacteristic
394C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#481×C269C2
socleC22×C269C22×D4
prime radical#31771239C2
hypercenter#481D269
hypocenterC269#3295
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #31771310C2semidirect
3. #31770950C2semidirect
4. #31770925C2semidirect
5. #31770894C2semidirect
6. #31770835C2semidirect
7. #31770832C2semidirect
8. #31770804C2semidirect
9. #31770758C2semidirect
10. #31770757C2semidirect
11. #31770692C2semidirect
12. #31770668C2semidirect
13. C2×#22575373C2semidirect
14. #102×D269C2semidirect
15. #481×C269C2semidirect
20. C2×#16864391C22semidirect
21. C2×#16864390C22semidirect
22. C22×#14524130C22semidirect
23. C2×C8×D269C22semidirect
24. #22575452C22semidirect
27. #22575433C22semidirect
29. #22575432C22semidirect
35. #22575418C22semidirect
39. C4⋊C4×D269C22semidirect
40. #22575384C22semidirect
41. #22575382C22semidirect
42. #22575376C22semidirect
44. #22575375C22semidirect
45. #22575374C22semidirect
48. #22575373C22semidirect
49. #22575373C22semidirect
50. #22575365C22semidirect
51. C8×Dic269C22semidirect
53. C2×C4⋊C4×C269C22semidirect
54. #106×C269C22semidirect
55. #106×C269C22semidirect
56. #102×C269C22semidirect
57. #102×C269C22semidirect
58. C22⋊C8×C269C22semidirect
133. C22⋊D269SD16semidirect
197. C269#3295semidirect
203. #481D269semidirect
239. C2×C4⋊C4C2×D269semidirect
241. #106C2×D269semidirect
242. #106C2×D269semidirect
252. #102C2×D269semidirect
253. #102C2×D269semidirect
255. C22⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317713102
#317712392
#317709502
#317709252
#317708942
#317708352
#317708322
#317708042
#317707582
#317707572
#317706922
#317706682
C2×#225753732
#102×D2692
#481×C2692
#3295269