Finite Group Databasebeta

← #46822908

Subgroups — #46822908

Order 34432.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771295C211yesmaximal, characteristic, complemented
2D4×D1076C211yesmaximal, characteristic
3#31770970C211yesmaximal, characteristic, complemented
4#31770930C211yesmaximal, characteristic, complemented
5#31770919C211yesmaximal, characteristic, complemented
6#31770906C211yesmaximal, characteristic, complemented
7#31770851C211yesmaximal, characteristic, complemented
8#31770834C211yesmaximal, characteristic, complemented
9#31770806C211yesmaximal, characteristic, complemented
10#31770758C211yesmaximal, characteristic, complemented
11#31770758C211yesmaximal, characteristic, complemented
12#31770707C211yesmaximal, characteristic, complemented
13#31770611C211yesmaximal, characteristic, complemented
14C2×#22575375C211yesmaximal, characteristic, complemented
15#435×C269C211yesmaximal, characteristic, complemented
16C22×D1076C2211yescharacteristic
17C22×D1076C2211yescharacteristic
18C2×D4×D269—21no—
19C2×#16864391C2211yescharacteristic
20C2×#16864391C2211yescharacteristic, complemented
21C2×#16864391C2211yescharacteristic, complemented
22#22575450C2211yescharacteristic
23#22575446—21no—
24#22575445C2211yescharacteristic, complemented
25#22575443—21no—
26#22575434—21no—
27#22575432C2211yescharacteristic, complemented
28#22575432C2211yescharacteristic, complemented
29#22575428—21no—
30#22575427C2211yescharacteristic
31#22575427C2211yescharacteristic
32#22575423—21no—
33#22575423—21no—
34C4×Dic538C2211yescharacteristic, complemented
35C4×D1076C2211yescharacteristic
36#22575412C2211yescharacteristic, complemented
37#22575409—21no—
38C2×C4⋊Dic269C2211yescharacteristic, complemented
39#22575387C2211yescharacteristic, complemented
40#22575387C2211yescharacteristic, complemented
41#22575385C2211yescharacteristic, complemented
42#22575378C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575375C2211yescharacteristic
46#22575375C2211yescharacteristic, complemented
47#22575375C2211yescharacteristic, complemented
48#22575375C2211yescharacteristic, complemented
49#22575375C2211yescharacteristic, complemented
50#22575375C2211yescharacteristic, complemented
51#22575375C2211yescharacteristic, complemented
52C2×M16×C269C2211yescharacteristic, complemented
53C22×C8×C269C2211yescharacteristic, complemented
54C4×D4×C269C2211yescharacteristic
55C4⋊C8×C269C2211yescharacteristic, complemented
56C22⋊C8×C269C2211yescharacteristic, complemented
57C22⋊C8×C269C2211yescharacteristic, complemented
58#97×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60C23×D269—21no—
61C2×Dic538C2311yescharacteristic
62C2×D1076—22no—
63C2×D1076—22no—
64C2×D1076—21no—
65C2×D1076—21no—
66C2×D1076—21no—
67C2×D1076—21no—
68C2×D1076—41no—
69C2×D1076—41no—
70C2×D1076C2311yescharacteristic
71C2×D1076C2311yescharacteristic
72C2×D1076C2311yescharacteristic
73C2×C22⋊D269—21no—
74C2×C22⋊D269—21no—
75D4×D269—44no—
76C22×Dic269—21no—
77C2×C4×D269—21no—
78#16864391—22no—
79#16864391—41no—
80#16864391—41no—
81C4⋊Dic269—21no—
82C4⋊Dic269C2311yescharacteristic
83C4⋊Dic269C2311yescharacteristic
84C4⋊Dic269C2311yescharacteristic
85C4⋊Dic269C2311yescharacteristic
86#16864381—21no—
87#16864381—21no—
88#16864381—21no—
89#16864381—21no—
90#16864381—21no—
91C22⋊Dic269—21no—
92C22⋊Dic269—21no—
93C22⋊Dic269—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379—21no—
97C4×Dic269—21no—
98C4×Dic269—21no—
99C2×D4×C269D411yescharacteristic
100C22×C4×C269C2311yescharacteristic
101C22×C4×C269C2311yescharacteristic
102M16×C269—41no—
103C2×C8×C269—41no—
104C2×C8×C269C2311yescharacteristic
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C2×C8×C269C2311yescharacteristic
108C4⋊C4×C269D411yescharacteristic
109C22⋊C4×C269D411yescharacteristic
110C22⋊C4×C269D411yescharacteristic
111C42×C269C2311yescharacteristic
112C22×D269—21no—
113C22×D269—21no—
114C22×D269—21no—
115C22×D269—42no—
116C22×D269—42no—
117C22×D269—42no—
118C22×D269—42no—
119C22×D269—81no—
120C22×D269—81no—
121Dic538—21no—
122Dic538—21no—
123D1076—21no—
124D1076—21no—
125D1076—21no—
126D1076—21no—
127D1076—21no—
128D1076—42no—
129D1076—42no—
130D1076—42no—
131D1076—81no—
132D1076#4112yes—
133C22⋊D269—42no—
134C22⋊D269—42no—
135C2×Dic269—21no—
136C2×Dic269—21no—
137C2×Dic269—21no—
138C2×Dic269—21no—
139C2×Dic269—21no—
140C2×Dic269—42no—
141C4×D269—42no—
142C23×C269C2×D411yescharacteristic
143C23×C269C2×D411yescharacteristic
144D4×C269—22no—
145C2×C4×C269—21no—
146C2×C4×C269—21no—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269C2×D411yescharacteristic
150C2×C4×C269C2×D411yescharacteristic
151C2×C4×C269C2×D411yescharacteristic
152C2×C4×C269C2×D411yescharacteristic
153C2×C4×C269C2411yescharacteristic
154C8×C269—21no—
155C8×C269—21no—
156C8×C269—21no—
157C8×C269—21no—
158C22×C269—21no—
159C22×C269—21no—
160C22×C269—21no—
161C22×C269—21no—
162C22×C269—21no—
163C22×C269AGL(1,ℤ/8)12yes—
164C22×C269C22×D411yescharacteristic
165C2×D269—22no—
166C2×D269—41no—
167C2×D269—41no—
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—41no—
171C2×D269—41no—
172C2×D269—41no—
173C2×D269—41no—
174C2×D269—84no—
175C2×D269—84no—
176C4×C269—21no—
177C4×C269—21no—
178C4×C269—21no—
179C4×C269—21no—
180C4×C269C2×#4111yescharacteristic
181C4×C269H(5,𝔽2)11yescharacteristic
182Dic269—41no—
183Dic269—41no—
184Dic269—41no—
185Dic269—41no—
186Dic269—41no—
187C2×C269—22no—
188C2×C269—41no—
189C2×C269#54611yescharacteristic
190C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C269#57711yescharacteristic
192D269—42no—
193D269—81no—
194D269—81no—
195C269#331011yescharacteristic, complemented, Sylow
196#3310—2691nomaximal, Sylow
197#552—2691no—
198D42—2691no—
199#490—2691no—
200#482—2691no—
201#480—2691no—
202#478—2691no—
203#468—2691no—
204#465—2691no—
205#460—2691no—
206#450—2691no—
207#450—2691no—
208#440—2691no—
209#435D26911yescharacteristic, complemented
210#418—2691no—
211C2×#102—2691no—
212C22×D4—2691no—
213C22×D4—2691no—
214C22×D4—5381no—
215C2×SD16—2691no—
216C2×SD16—2691no—
217C2×SD16—2691no—
218C2×M16C2×D26911yescharacteristic, complemented
219C22×C8C2×D26911yescharacteristic, complemented
220#127—2691no—
221#126—5381no—
222#125—2691no—
223#125—5381no—
224#123—5381no—
225C22⋊Q8—2691no—
226C22⋊Q8—2691no—
227#121—2691no—
228#121—2691no—
229#121—5381no—
230#120—5381no—
231#120—5381no—
232C4×Q8—2691no—
233C4×D4—2691no—
234C4×D4C2×D26911yescharacteristic
235#117—2691no—
236#117—5381no—
237C2×C4⋊C4—2691no—
238#107—2691no—
239#107—2691no—
240#106—2691no—
241C4⋊C8C2×D26911yescharacteristic, complemented
242#103—2691no—
243#102—2691no—
244#102—2691no—
245#102—2691no—
246#102—2691no—
247#102—2691no—
248#102—2691no—
249#102—2691no—
250#102—2691no—
251#102—2691no—
252C22⋊C8C2×D26911yescharacteristic, complemented
253C22⋊C8C2×D26911yescharacteristic, complemented
254#97C2×D26911yescharacteristic, complemented
255C24—5381no—
256C24—5381no—
257C2×Q8—2691no—
258C2×D4—2691no—
259C2×D4—2691no—
260C2×D4—2691no—
261C2×D4—5382no—
262C2×D4—5382no—
263C2×D4—5381no—
264C2×D4—5381no—
265C2×D4—5381no—
266C2×D4—5381no—
267C2×D4—5381no—
268C2×D4—5381no—
269C2×D4—10761no—
270C2×D4—10761no—
271C2×D4—10764no—
272C2×D4D107611yescharacteristic
273C22×C4—5381no—
274C22×C4—5381no—
275C22×C4C22×D26911yescharacteristic
276C22×C4C22×D26911yescharacteristic
277SD16—5382no—
278SD16—10761no—
279SD16—10761no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D26911yescharacteristic
283C2×C8C22×D26911yescharacteristic
284C2×C8C22×D26911yescharacteristic
285C2×C8C22×D26911yescharacteristic
286C4⋊C4—2691no—
287C4⋊C4—2691no—
288C4⋊C4—2691no—
289C4⋊C4—2691no—
290C4⋊C4—5381no—
291C4⋊C4—5381no—
292C4⋊C4—5381no—
293C4⋊C4—5381no—
294C4⋊C4—5381no—
295C4⋊C4—5381no—
296C4⋊C4D107611yescharacteristic
297C22⋊C4—5381no—
298C22⋊C4—5381no—
299C22⋊C4—5381no—
300C22⋊C4—5381no—
301C22⋊C4—5381no—
302C22⋊C4—5381no—
303C22⋊C4D107611yescharacteristic
304C22⋊C4D107611yescharacteristic
305C42—5381no—
306C42—5381no—
307C42C22×D26911yescharacteristic
308C23—5381no—
309C23—5381no—
310C23—5381no—
311C23—10762no—
312C23—10762no—
313C23—10762no—
314C23—10762no—
315C23—21521no—
316C23—21521no—
317C23C2×D107611yescharacteristic
318C23C2×D107611yescharacteristic
319Q8—5381no—
320Q8—5381no—
321D4—22no—
322D4—2692no—
323D4—5381no—
324D4—5381no—
325D4—5381no—
326D4—5381no—
327D4—5381no—
328D4—10762no—
329D4—10762no—
330D4—10762no—
331D4—10762no—
332D4—10762no—
333D4—21521no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—5381no—
339C2×C4—5381no—
340C2×C4—5381no—
341C2×C4—5381no—
342C2×C4—5381no—
343C2×C4—10762no—
344C2×C4—10762no—
345C2×C4C2×D107611yescharacteristic
346C2×C4C2×D107611yescharacteristic
347C2×C4C2×D107611yescharacteristic
348C2×C4C2×D107611yescharacteristic
349C2×C4C23×D26911yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—5382no—
360C22—10761no—
361C22—10761no—
362C22—10761no—
363C22—10761no—
364C22—10761no—
365C22—10761no—
366C22—10761no—
367C22—10761no—
368C22—21524no—
369C22—21524no—
370C22#2257548112yes—
371C22C22×D107611yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—10761no—
377C4—10761no—
378C4—10761no—
379C4—10761no—
380C4—10761no—
381C4#41×D26911yescharacteristic
382C4#2257549811yescharacteristic
383C2—22no—
384C2—41no—
385C2—10762no—
386C2—21521no—
387C2—21521no—
388C2#3177125011yescharacteristic
389C2C2×#2257548111yescharacteristic
390C2#3177141711yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#435×C269C2
socleC22×C269C22×D4
prime radicalD4×D1076C2
hypercenter#435D269
hypocenterC269#3310
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #31771295C2semidirect
3. #31770970C2semidirect
4. #31770930C2semidirect
5. #31770919C2semidirect
6. #31770906C2semidirect
7. #31770851C2semidirect
8. #31770834C2semidirect
9. #31770806C2semidirect
10. #31770758C2semidirect
11. #31770758C2semidirect
12. #31770707C2semidirect
13. #31770611C2semidirect
14. C2×#22575375C2semidirect
15. #435×C269C2semidirect
20. C2×#16864391C22semidirect
21. C2×#16864391C22semidirect
24. #22575445C22semidirect
27. #22575432C22semidirect
28. #22575432C22semidirect
34. C4×Dic538C22semidirect
36. #22575412C22semidirect
38. C2×C4⋊Dic269C22semidirect
39. #22575387C22semidirect
40. #22575387C22semidirect
41. #22575385C22semidirect
42. #22575378C22semidirect
46. #22575375C22semidirect
47. #22575375C22semidirect
48. #22575375C22semidirect
49. #22575375C22semidirect
50. #22575375C22semidirect
51. #22575375C22semidirect
52. C2×M16×C269C22semidirect
53. C22×C8×C269C22semidirect
55. C4⋊C8×C269C22semidirect
56. C22⋊C8×C269C22semidirect
57. C22⋊C8×C269C22semidirect
58. #97×C269C22semidirect
195. C269#3310semidirect
209. #435D269semidirect
218. C2×M16C2×D269semidirect
219. C22×C8C2×D269semidirect
241. C4⋊C8C2×D269semidirect
252. C22⋊C8C2×D269semidirect
253. C22⋊C8C2×D269semidirect
254. #97C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712952
D4×D10762
#317709702
#317709302
#317709192
#317709062
#317708512
#317708342
#317708062
#317707582
#317707072
#317706112
C2×#225753752
#435×C2692
#3310269