Finite Group Databasebeta

← #46822906

Subgroups — #46822906

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
2#31770969C211yesmaximal, characteristic, complemented
3#31770926C211yesmaximal, characteristic, complemented
4#31770916C211yesmaximal, characteristic, complemented
5#31770905C211yesmaximal, characteristic, complemented
6#31770849C211yesmaximal, characteristic, complemented
7#31770832C211yesmaximal, characteristic, complemented
8#31770802C211yesmaximal, characteristic, complemented
9#31770756C211yesmaximal, characteristic, complemented
10#31770756C211yesmaximal, characteristic, complemented
11#31770705C211yesmaximal, characteristic, complemented
12#31770677C211yesmaximal, characteristic, complemented
13#31770610C211yesmaximal, characteristic, complemented
14C2×#22575374C211yesmaximal, characteristic, complemented
15D42×C269C211yesmaximal, characteristic
16C2×#16864390C2211yescharacteristic
17C2×#16864390C2211yescharacteristic, complemented
18C2×#16864390C2211yescharacteristic, complemented
19C2×#16864386C2211yescharacteristic, complemented
20C22×#14524130C2211yescharacteristic, complemented
21#22575446—21no—
22#22575445C2211yescharacteristic, complemented
23#22575443—21no—
24#22575434—21no—
25#22575432C2211yescharacteristic, complemented
26#22575432C2211yescharacteristic, complemented
27C4×Dic538C2211yescharacteristic, complemented
28#22575412C2211yescharacteristic, complemented
29#22575409—21no—
30C2×C4⋊Dic269C2211yescharacteristic, complemented
31#22575386C2211yescharacteristic, complemented
32#22575386C2211yescharacteristic, complemented
33#22575384C2211yescharacteristic, complemented
34C4⋊#14524130C2211yescharacteristic, complemented
35#22575376C2211yescharacteristic, complemented
36#22575374C2211yescharacteristic
37#22575374C2211yescharacteristic
38#22575374C2211yescharacteristic
39#22575374C2211yescharacteristic, complemented
40#22575374C2211yescharacteristic, complemented
41#22575374C2211yescharacteristic, complemented
42#22575374C2211yescharacteristic, complemented
43#22575374C2211yescharacteristic, complemented
44#22575374C2211yescharacteristic, complemented
45C22⋊#14524130C2211yescharacteristic, complemented
46C22⋊#14524130C2211yescharacteristic, complemented
47#22575364C2211yescharacteristic, complemented
48C22×D4×C269—21no—
49C22×D4×C269C2211yescharacteristic
50C22×D4×C269C2211yescharacteristic
51#127×C269C2211yescharacteristic
52#121×C269—21no—
53#121×C269C2211yescharacteristic
54#121×C269C2211yescharacteristic
55#120×C269—21no—
56#120×C269—21no—
57C4×D4×C269C2211yescharacteristic
58C4×D4×C269C2211yescharacteristic
59C2×Dic538C2311yescharacteristic
60C22×Dic269—21no—
61#16864390—22no—
62#16864390—41no—
63#16864390—41no—
64#16864386—41no—
65C2×#14524130—41no—
66C2×#14524130C2311yescharacteristic
67C2×#14524130C2311yescharacteristic
68C2×#14524130C2311yescharacteristic
69C2×#14524130C2311yescharacteristic
70C4⋊Dic269—21no—
71C4⋊Dic269C2311yescharacteristic
72C4⋊Dic269C2311yescharacteristic
73C4⋊Dic269C2311yescharacteristic
74#16864381—21no—
75#16864381—21no—
76#16864381—21no—
77#16864381—21no—
78#16864381—21no—
79C22⋊Dic269—21no—
80C22⋊Dic269—21no—
81C22⋊Dic269—21no—
82C4×Dic269—21no—
83C4×Dic269—21no—
84C24×C269—21no—
85C24×C269—21no—
86C2×D4×C269—22no—
87C2×D4×C269—22no—
88C2×D4×C269—21no—
89C2×D4×C269—21no—
90C2×D4×C269—21no—
91C2×D4×C269—21no—
92C2×D4×C269—21no—
93C2×D4×C269—21no—
94C2×D4×C269—41no—
95C2×D4×C269—41no—
96C2×D4×C269—44no—
97C2×D4×C269D411yescharacteristic
98C2×D4×C269C2311yescharacteristic
99C2×D4×C269C2311yescharacteristic
100C2×D4×C269C2311yescharacteristic
101C22×C4×C269—21no—
102C22×C4×C269C2311yescharacteristic
103C22×C4×C269C2311yescharacteristic
104C4⋊C4×C269D411yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C22⋊C4×C269—21no—
108C22⋊C4×C269—21no—
109C22⋊C4×C269D411yescharacteristic
110C22⋊C4×C269D411yescharacteristic
111C42×C269C2311yescharacteristic
112Dic538—21no—
113Dic538—21no—
114C2×Dic269—21no—
115C2×Dic269—21no—
116C2×Dic269—21no—
117C2×Dic269—21no—
118C2×Dic269—42no—
119#14524130—21no—
120#14524130—21no—
121#14524130—21no—
122#14524130—21no—
123C23×C269—21no—
124C23×C269—21no—
125C23×C269—21no—
126C23×C269—42no—
127C23×C269—42no—
128C23×C269—42no—
129C23×C269—42no—
130C23×C269—81no—
131C23×C269—81no—
132C23×C269C2×D411yescharacteristic
133C23×C269C2×D411yescharacteristic
134D4×C269—22no—
135D4×C269—21no—
136D4×C269—21no—
137D4×C269—21no—
138D4×C269—21no—
139D4×C269—21no—
140D4×C269—42no—
141D4×C269—42no—
142D4×C269—42no—
143D4×C269—42no—
144D4×C269—42no—
145D4×C269—81no—
146D4×C269#4112yes—
147C2×C4×C269—21no—
148C2×C4×C269—21no—
149C2×C4×C269—21no—
150C2×C4×C269—21no—
151C2×C4×C269—21no—
152C2×C4×C269—42no—
153C2×C4×C269C2×D411yescharacteristic
154C2×C4×C269C2×D411yescharacteristic
155C2×C4×C269C2×D411yescharacteristic
156C2×C4×C269C2×D411yescharacteristic
157C2×C4×C269C2411yescharacteristic
158C22×C269—21no—
159C22×C269—21no—
160C22×C269—21no—
161C22×C269—22no—
162C22×C269—21no—
163C22×C269—21no—
164C22×C269—41no—
165C22×C269—41no—
166C22×C269—41no—
167C22×C269—41no—
168C22×C269—41no—
169C22×C269—41no—
170C22×C269—41no—
171C22×C269—41no—
172C22×C269—84no—
173C22×C269—84no—
174C22×C269AGL(1,ℤ/8)12yes—
175C22×C269C22×D411yescharacteristic
176C4×C269—21no—
177C4×C269—21no—
178C4×C269—21no—
179C4×C269—21no—
180C4×C269—41no—
181C4×C269C2×#4111yescharacteristic
182C4×C269H(5,𝔽2)11yescharacteristic
183Dic269—41no—
184Dic269—41no—
185Dic269—41no—
186Dic269—41no—
187C2×C269—22no—
188C2×C269—41no—
189C2×C269—42no—
190C2×C269—81no—
191C2×C269—81no—
192C2×C269#54611yescharacteristic
193C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C269#57711yescharacteristic
195C269#331011yescharacteristic, complemented, Sylow
196#3310—2691nomaximal, Sylow
197#552—2691no—
198D42D26911yescharacteristic
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#435—2691no—
210#418—2691no—
211C2×#102—2691no—
212C22×D4—21no—
213C22×D4C2×D26911yescharacteristic
214C22×D4C2×D26911yescharacteristic
215C2×SD16—2691no—
216C2×SD16—2691no—
217C2×SD16—2691no—
218C2×M16—2691no—
219C22×C8—2691no—
220#127C2×D26911yescharacteristic
221#126—5381no—
222#125—2691no—
223#125—5381no—
224#123—5381no—
225C22⋊Q8—2691no—
226C22⋊Q8—2691no—
227#121—21no—
228#121C2×D26911yescharacteristic
229#121C2×D26911yescharacteristic
230#120—21no—
231#120—21no—
232C4×Q8—2691no—
233C4×D4C2×D26911yescharacteristic
234C4×D4C2×D26911yescharacteristic
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#102—2691no—
251#102—2691no—
252C22⋊C8—2691no—
253C22⋊C8—2691no—
254#97—2691no—
255C24—21no—
256C24—21no—
257C2×Q8—2691no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D26911yescharacteristic
270C2×D4C22×D26911yescharacteristic
271C2×D4C22×D26911yescharacteristic
272C2×D4C22×D26911yescharacteristic
273C22×C4—21no—
274C22×C4—5381no—
275C22×C4C22×D26911yescharacteristic
276C22×C4C22×D26911yescharacteristic
277SD16—5382no—
278SD16—10761no—
279SD16—10761no—
280M16—10761no—
281C2×C8—2691no—
282C2×C8—2691no—
283C2×C8—2691no—
284C2×C8—2691no—
285C2×C8—10761no—
286C4⋊C4—2691no—
287C4⋊C4—2691no—
288C4⋊C4—2691no—
289C4⋊C4—5381no—
290C4⋊C4—5381no—
291C4⋊C4—5381no—
292C4⋊C4—5381no—
293C4⋊C4—5381no—
294C4⋊C4—5381no—
295C4⋊C4C22⋊D26911yescharacteristic
296C4⋊C4C22×D26911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—5381no—
301C22⋊C4—5381no—
302C22⋊C4—5381no—
303C22⋊C4C22⋊D26911yescharacteristic
304C22⋊C4C22⋊D26911yescharacteristic
305C42—5381no—
306C42—5381no—
307C42C22×D26911yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D26911yescharacteristic
318C23C2×C22⋊D26911yescharacteristic
319Q8—5381no—
320Q8—5381no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#1686440112yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—5381no—
341C2×C4—5381no—
342C2×C4—5381no—
343C2×C4—5381no—
344C2×C4—10762no—
345C2×C4C2×C22⋊D26911yescharacteristic
346C2×C4C2×C22⋊D26911yescharacteristic
347C2×C4C2×C22⋊D26911yescharacteristic
348C2×C4C2×C22⋊D26911yescharacteristic
349C2×C4C23×D26911yescharacteristic
350C8—5381no—
351C8—5381no—
352C8—5381no—
353C8—5381no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#2257547912yes—
371C22C22×C22⋊D26911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—10761no—
378C4—10761no—
379C4—10761no—
380C4—10761no—
381C4C2×#1686440111yescharacteristic
382C4#2257549811yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#3177124911yescharacteristic
389C2C2×#2257547911yescharacteristic
390C2#3177141611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting, prime radicalD42×C269C2
socleC22×C269C22×D4
hypercenterD42D269
hypocenterC269#3310
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #31771295C2semidirect
2. #31770969C2semidirect
3. #31770926C2semidirect
4. #31770916C2semidirect
5. #31770905C2semidirect
6. #31770849C2semidirect
7. #31770832C2semidirect
8. #31770802C2semidirect
9. #31770756C2semidirect
10. #31770756C2semidirect
11. #31770705C2semidirect
12. #31770677C2semidirect
13. #31770610C2semidirect
14. C2×#22575374C2semidirect
17. C2×#16864390C22semidirect
18. C2×#16864390C22semidirect
19. C2×#16864386C22semidirect
20. C22×#14524130C22semidirect
22. #22575445C22semidirect
25. #22575432C22semidirect
26. #22575432C22semidirect
27. C4×Dic538C22semidirect
28. #22575412C22semidirect
30. C2×C4⋊Dic269C22semidirect
31. #22575386C22semidirect
32. #22575386C22semidirect
33. #22575384C22semidirect
34. C4⋊#14524130C22semidirect
35. #22575376C22semidirect
39. #22575374C22semidirect
40. #22575374C22semidirect
41. #22575374C22semidirect
42. #22575374C22semidirect
43. #22575374C22semidirect
44. #22575374C22semidirect
45. C22⋊#14524130C22semidirect
46. C22⋊#14524130C22semidirect
47. #22575364C22semidirect
195. C269#3310semidirect

Maximal subgroups

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

subgroupindex
#317712952
#317709692
#317709262
#317709162
#317709052
#317708492
#317708322
#317708022
#317707562
#317707052
#317706772
#317706102
C2×#225753742
D42×C2692
#3310269