Finite Group Databasebeta

← #46822899

Subgroups — #46822899

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#31771289C211yesmaximal, characteristic, complemented
2D4×C22⋊D269C211yesmaximal, characteristic
3#31770968C211yesmaximal, characteristic, complemented
4#31770930C211yesmaximal, characteristic, complemented
5#31770917C211yesmaximal, characteristic, complemented
6#31770907C211yesmaximal, characteristic, complemented
7#31770853C211yesmaximal, characteristic, complemented
8#31770831C211yesmaximal, characteristic, complemented
9#31770803C211yesmaximal, characteristic, complemented
10#31770754C211yesmaximal, characteristic, complemented
11#31770706C211yesmaximal, characteristic, complemented
12#31770679C211yesmaximal, characteristic, complemented
13#31770610C211yesmaximal, characteristic, complemented
14#102×D269C211yesmaximal, characteristic, complemented
15#450×C269C211yesmaximal, characteristic, complemented
16C22×C22⋊D269—21no—
17C2×D4×D269C2211yescharacteristic
18C2×#16864389C2211yescharacteristic, complemented
19C2×#16864386C2211yescharacteristic, complemented
20C2×C8×D269C2211yescharacteristic, complemented
21#22575449C2211yescharacteristic
22#22575446—21no—
23#22575444C2211yescharacteristic, complemented
24#22575443—21no—
25#22575435—21no—
26#22575429C2211yescharacteristic, complemented
27#22575427C2211yescharacteristic
28#22575425—21no—
29#22575424C2211yescharacteristic
30#22575422—21no—
31#22575421—21no—
32Q8×Dic269C2211yescharacteristic, complemented
33D4×Dic269C2211yescharacteristic
34C4×C22⋊D269C2211yescharacteristic
35#22575412C2211yescharacteristic, complemented
36#22575411—21no—
37C4⋊C4×D269C2211yescharacteristic, complemented
38#22575387C2211yescharacteristic, complemented
39#22575386C2211yescharacteristic, complemented
40#22575385C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575377C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic, complemented
44#22575375C2211yescharacteristic, complemented
45#22575374C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic, complemented
48#22575374C2211yescharacteristic, complemented
49#22575373C2211yescharacteristic, complemented
50#22575365C2211yescharacteristic, complemented
51#22575363C2211yescharacteristic, complemented
52C22×D4×C269C2211yescharacteristic
53C2×SD16×C269C2211yescharacteristic
54C2×SD16×C269C2211yescharacteristic, complemented
55C22⋊Q8×C269C2211yescharacteristic, complemented
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic, complemented
58C22⋊C8×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60C2×D1076C2311yescharacteristic
61C2×C22⋊D269—21no—
62C2×C22⋊D269—21no—
63C2×C22⋊D269—21no—
64C2×C22⋊D269—21no—
65C2×C22⋊D269—21no—
66C2×C22⋊D269—44no—
67C2×C22⋊D269D411yescharacteristic
68D4×D269—22no—
69D4×D269—41no—
70C22×Dic269—21no—
71C2×C4×D269—21no—
72C2×C4×D269C2311yescharacteristic
73#16864389—41no—
74#16864386—41no—
75C2×#14524130C2311yescharacteristic
76C2×#14524130C2311yescharacteristic
77C8×D269—41no—
78C4⋊Dic269—21no—
79C4⋊Dic269—21no—
80C4⋊Dic269C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86#16864381D411yescharacteristic
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89C22⋊Dic269—21no—
90C22⋊Dic269D411yescharacteristic
91#16864379—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
94C4×Dic269—21no—
95C4×Dic269—21no—
96C4×Dic269C2311yescharacteristic
97C24×C269—21no—
98C2×Q8×C269C2311yescharacteristic
99C2×D4×C269—22no—
100C2×D4×C269—21no—
101C2×D4×C269—41no—
102C2×D4×C269C2311yescharacteristic
103C2×D4×C269C2311yescharacteristic
104C22×C4×C269C2311yescharacteristic
105SD16×C269—22no—
106SD16×C269—41no—
107C2×C8×C269C2311yescharacteristic
108C2×C8×C269C2311yescharacteristic
109C4⋊C4×C269—21no—
110C4⋊C4×C269C2311yescharacteristic
111C22⋊C4×C269—21no—
112C22×D269—21no—
113C22×D269—42no—
114C22×D269—42no—
115C22×D269—81no—
116C22×D269C2×D411yescharacteristic
117D1076—21no—
118D1076—21no—
119C22⋊D269—22no—
120C22⋊D269—42no—
121C22⋊D269—42no—
122C22⋊D269—42no—
123C22⋊D269—42no—
124C22⋊D269—81no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—42no—
129C2×Dic269C2×D411yescharacteristic
130C2×Dic269C2×D411yescharacteristic
131C2×Dic269C2×D411yescharacteristic
132C4×D269—21no—
133C4×D269—21no—
134C4×D269—42no—
135#14524130—21no—
136#14524130—21no—
137C23×C269—21no—
138C23×C269—21no—
139C23×C269—42no—
140C23×C269—42no—
141C23×C269—81no—
142C23×C269C2×D411yescharacteristic
143Q8×C269—21no—
144Q8×C269—21no—
145D4×C269—21no—
146D4×C269—21no—
147D4×C269—21no—
148D4×C269—42no—
149D4×C269#4112yes—
150C2×C4×C269—21no—
151C2×C4×C269—21no—
152C2×C4×C269—21no—
153C2×C4×C269—21no—
154C2×C4×C269C2×D411yescharacteristic
155C2×C4×C269C2411yescharacteristic
156C8×C269—21no—
157C8×C269—21no—
158C22×C269—21no—
159C22×C269—22no—
160C22×C269—21no—
161C22×C269—21no—
162C22×C269—41no—
163C22×C269—41no—
164C22×C269—41no—
165C22×C269—41no—
166C22×C269—41no—
167C22×C269—84no—
168C22×C269C22×D411yescharacteristic
169C2×D269—21no—
170C2×D269—21no—
171C2×D269—41no—
172C2×D269—41no—
173C2×D269—41no—
174C2×D269—84no—
175C2×D269AGL(1,ℤ/8)12yes—
176C4×C269—21no—
177C4×C269—41no—
178C4×C269—41no—
179C4×C269C2×#4111yescharacteristic
180C4×C269H(5,𝔽2)11yescharacteristic
181Dic269—21no—
182Dic269—21no—
183Dic269—21no—
184Dic269—41no—
185Dic269—41no—
186Dic269—41no—
187C2×C269—42no—
188C2×C269—41no—
189C2×C269—81no—
190C2×C269#54611yescharacteristic
191C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C269#57711yescharacteristic
193D269—22no—
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#450D26911yescharacteristic, complemented
208#440—2691no—
209#435—2691no—
210#418—2691no—
211C2×#102—2691no—
212C22×D4—2691no—
213C22×D4—5381no—
214C22×D4C2×D26911yescharacteristic
215C2×SD16—2691no—
216C2×SD16C2×D26911yescharacteristic
217C2×SD16C2×D26911yescharacteristic, complemented
218C2×M16—2691no—
219C22×C8—2691no—
220#127—2691no—
221#126—5381no—
222#125—2691no—
223#125—5381no—
224#123—5381no—
225C22⋊Q8—2691no—
226C22⋊Q8C2×D26911yescharacteristic, complemented
227#121—2691no—
228#121—2691no—
229#121—5381no—
230#120—5381no—
231#120—5381no—
232C4×Q8—2691no—
233C4×D4—2691no—
234C4×D4—2691no—
235#117—2691no—
236#117—5381no—
237C2×C4⋊C4—2691no—
238#107—2691no—
239#107—2691no—
240#106—2691no—
241C4⋊C8—2691no—
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#102C2×D26911yescharacteristic
251#102C2×D26911yescharacteristic, complemented
252C22⋊C8—2691no—
253C22⋊C8C2×D26911yescharacteristic, complemented
254#97—2691no—
255C24—21no—
256C24—5381no—
257C2×Q8C22×D26911yescharacteristic
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—2691no—
262C2×D4—2691no—
263C2×D4—5381no—
264C2×D4—5381no—
265C2×D4—5381no—
266C2×D4—5382no—
267C2×D4—5381no—
268C2×D4—5381no—
269C2×D4—10761no—
270C2×D4—10764no—
271C2×D4C22×D26911yescharacteristic
272C2×D4C22×D26911yescharacteristic
273C22×C4—2691no—
274C22×C4—5381no—
275C22×C4—5381no—
276C22×C4C22×D26911yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—10761no—
280M16—10761no—
281C2×C8—2691no—
282C2×C8—2691no—
283C2×C8—10761no—
284C2×C8C22×D26911yescharacteristic
285C2×C8C22×D26911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—2691no—
288C4⋊C4—2691no—
289C4⋊C4—2691no—
290C4⋊C4—2691no—
291C4⋊C4—5381no—
292C4⋊C4—5381no—
293C4⋊C4—5381no—
294C4⋊C4—5381no—
295C4⋊C4—5381no—
296C4⋊C4C22×D26911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—2691no—
299C22⋊C4—2691no—
300C22⋊C4—5381no—
301C22⋊C4—5381no—
302C22⋊C4—5381no—
303C22⋊C4—5381no—
304C22⋊C4—5381no—
305C42—2691no—
306C42—5381no—
307C42—5381no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—2691no—
314C23—5381no—
315C23—10762no—
316C23—10762no—
317C23—21521no—
318C23D4×D26911yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—5382no—
326D4—5381no—
327D4—5381no—
328D4—10762no—
329D4—10762no—
330D4—10762no—
331D4—10762no—
332D4—21521no—
333D4#1686440112yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—2691no—
339C2×C4—2691no—
340C2×C4—2691no—
341C2×C4—5381no—
342C2×C4—5381no—
343C2×C4—5381no—
344C2×C4—5381no—
345C2×C4—5381no—
346C2×C4—10762no—
347C2×C4—10762no—
348C2×C4D4×D26911yescharacteristic
349C2×C4C23×D26911yescharacteristic
350C8—21no—
351C8—21no—
352C8—5381no—
353C8—5381no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—2692no—
365C22—5381no—
366C22—5381no—
367C22—10761no—
368C22—10761no—
369C22—10761no—
370C22—21524no—
371C22C2×D4×D26911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—5381no—
376C4—5381no—
377C4—5381no—
378C4—10761no—
379C4—10761no—
380C4—10761no—
381C4C2×#1686440111yescharacteristic
382C4#2257549811yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—5382no—
387C2—21521no—
388C2#3177124211yescharacteristic
389C2AGL(1,ℤ/8)×D26911yescharacteristic
390C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#450×C269C2
socleC22×C269C22×D4
prime radicalD4×C22⋊D269C2
hypercenter#450D269
hypocenterC269#3310
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #31771289C2semidirect
3. #31770968C2semidirect
4. #31770930C2semidirect
5. #31770917C2semidirect
6. #31770907C2semidirect
7. #31770853C2semidirect
8. #31770831C2semidirect
9. #31770803C2semidirect
10. #31770754C2semidirect
11. #31770706C2semidirect
12. #31770679C2semidirect
13. #31770610C2semidirect
14. #102×D269C2semidirect
15. #450×C269C2semidirect
18. C2×#16864389C22semidirect
19. C2×#16864386C22semidirect
20. C2×C8×D269C22semidirect
23. #22575444C22semidirect
26. #22575429C22semidirect
32. Q8×Dic269C22semidirect
35. #22575412C22semidirect
37. C4⋊C4×D269C22semidirect
38. #22575387C22semidirect
39. #22575386C22semidirect
40. #22575385C22semidirect
41. #22575382C22semidirect
42. #22575377C22semidirect
43. #22575375C22semidirect
44. #22575375C22semidirect
47. #22575374C22semidirect
48. #22575374C22semidirect
49. #22575373C22semidirect
50. #22575365C22semidirect
51. #22575363C22semidirect
54. C2×SD16×C269C22semidirect
55. C22⋊Q8×C269C22semidirect
57. #102×C269C22semidirect
58. C22⋊C8×C269C22semidirect
195. C269#3310semidirect
207. #450D269semidirect
217. C2×SD16C2×D269semidirect
226. C22⋊Q8C2×D269semidirect
251. #102C2×D269semidirect
253. C22⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712892
D4×C22⋊D2692
#317709682
#317709302
#317709172
#317709072
#317708532
#317708312
#317708032
#317707542
#317707062
#317706792
#317706102
#102×D2692
#450×C2692
#3310269