Finite Group Databasebeta

← #46822848

Subgroups — #46822848

Order 34432.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771259C211yesmaximal, characteristic, complemented
2#31771251C211yesmaximal, characteristic, complemented
3#31770965C211yesmaximal, characteristic, complemented
4#31770936C211yesmaximal, characteristic, complemented
5#31770924C211yesmaximal, characteristic, complemented
6#31770896C211yesmaximal, characteristic, complemented
7#31770858C211yesmaximal, characteristic, complemented
8#31770834C211yesmaximal, characteristic, complemented
9#31770821C211yesmaximal, characteristic, complemented
10#31770752C211yesmaximal, characteristic, complemented
11#31770741C211yesmaximal, characteristic, complemented
12#31770718C211yesmaximal, characteristic, complemented
13#31770607C211yesmaximal, characteristic, complemented
14C2×#22575375C211yesmaximal, characteristic, complemented
15#435×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864401—21no—
18C22×D1076C2211yescharacteristic
19C2×#16864391C2211yescharacteristic, complemented
20C2×D2152C2211yescharacteristic
21C2×D2152C2211yescharacteristic
22#22575453C2211yescharacteristic, complemented
23#22575441C2211yescharacteristic
24#22575438—21no—
25#22575437—21no—
26#22575437—21no—
27#22575433—21no—
28#22575432C2211yescharacteristic
29#22575427C2211yescharacteristic
30#22575427C2211yescharacteristic
31#22575427C2211yescharacteristic, complemented
32#22575426—21no—
33#22575421—21no—
34C4×D1076C2211yescharacteristic
35C4×D1076C2211yescharacteristic, complemented
36C2×C4⋊Dic269C2211yescharacteristic
37C2×C4⋊Dic269C2211yescharacteristic, complemented
38C22⋊C4×D269—21no—
39#22575385C2211yescharacteristic, complemented
40#22575385C2211yescharacteristic, complemented
41#22575385C2211yescharacteristic, complemented
42#22575378C2211yescharacteristic, complemented
43#22575378C2211yescharacteristic, complemented
44#22575378C2211yescharacteristic, complemented
45#22575375C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575375C2211yescharacteristic
48#22575375C2211yescharacteristic
49#22575375C2211yescharacteristic
50#22575375C2211yescharacteristic
51#22575375C2211yescharacteristic, complemented
52C2×M16×C269C2211yescharacteristic, complemented
53C22×C8×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic
55C4⋊C8×C269C2211yescharacteristic, complemented
56C22⋊C8×C269C2211yescharacteristic
57C22⋊C8×C269C2211yescharacteristic, complemented
58#97×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60#16864402—22no—
61#16864402—41no—
62#16864401—44no—
63C2×Dic538—21no—
64C2×Dic538C2311yescharacteristic
65C2×D1076—22no—
66C2×D1076—21no—
67C2×D1076—41no—
68C2×D1076C2311yescharacteristic
69C2×D1076C2311yescharacteristic
70C2×D1076C2311yescharacteristic
71C2×C22⋊D269—21no—
72C2×C22⋊D269—21no—
73C2×C22⋊D269—21no—
74C2×C22⋊D269—21no—
75C22×Dic269—21no—
76C22×Dic269—21no—
77C2×C4×D269—21no—
78C2×C4×D269—21no—
79C2×C4×D269—21no—
80#16864391—41no—
81D2152—22no—
82D2152—41no—
83C4⋊Dic269—21no—
84C4⋊Dic269—21no—
85C4⋊Dic269—21no—
86C4⋊Dic269C2311yescharacteristic
87C4⋊Dic269C2311yescharacteristic
88C4⋊Dic269C2311yescharacteristic
89C4⋊Dic269C2311yescharacteristic
90#16864381—21no—
91C22⋊Dic269—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379—21no—
97#16864379—21no—
98#16864379—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—81no—
118Dic538—21no—
119Dic538—21no—
120Dic538—42no—
121D1076—21no—
122D1076—21no—
123D1076—21no—
124D1076—21no—
125D1076—21no—
126D1076—42no—
127D1076#4112yescomplemented
128C22⋊D269—42no—
129C22⋊D269—42no—
130C22⋊D269—42no—
131C22⋊D269—81no—
132C2×Dic269—21no—
133C2×Dic269—21no—
134C2×Dic269—21no—
135C2×Dic269—21no—
136C2×Dic269—21no—
137C2×Dic269—42no—
138C2×Dic269—42no—
139C4×D269—42no—
140C4×D269—42no—
141C4×D269—81no—
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—
175C4×C269—21no—
176C4×C269—21no—
177C4×C269—21no—
178C4×C269—21no—
179C4×C269C2×#4111yescharacteristic
180C4×C269H(5,𝔽2)11yescharacteristic
181Dic269—41no—
182Dic269—41no—
183Dic269—41no—
184Dic269—41no—
185Dic269—41no—
186C2×C269—22no—
187C2×C269—41no—
188C2×C269#54611yescharacteristic
189C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C269#57711yescharacteristic
191D269—42no—
192D269—81no—
193D269—81no—
194C269#330611yescharacteristic, complemented, Sylow
195#3306—2691nomaximal, Sylow
196#547—2691no—
197#546—2691no—
198#489—2691no—
199#483—2691no—
200#481—2691no—
201#476—2691no—
202#469—2691no—
203#465—2691no—
204#463—2691no—
205#449—2691no—
206#447—2691no—
207#442—2691no—
208#435D26911yescharacteristic, complemented
209#417—2691no—
210C2×#102—2691no—
211C2×#41—2691no—
212C2×#41—5381no—
213C22×D4—2691no—
214C2×SD16—2691no—
215C2×D8—2691no—
216C2×D8—2691no—
217C2×M16C2×D26911yescharacteristic, complemented
218C22×C8C2×D26911yescharacteristic
219C4⋊Q8—2691no—
220#124—2691no—
221#123—5381no—
222#123—5381no—
223#123—5381no—
224C22⋊Q8—2691no—
225C22⋊Q8—5381no—
226#121—2691no—
227#121—2691no—
228#121—2691no—
229#121—5381no—
230#120—5381no—
231C4×D4—2691no—
232C4×D4—2691no—
233C4×D4C2×D26911yescharacteristic
234C2×C4⋊C4—2691no—
235C2×C4⋊C4—2691no—
236C2×C22⋊C4—5381no—
237#106—2691no—
238#106—2691no—
239#106—2691no—
240C4⋊C8C2×D26911yescharacteristic, complemented
241#103—2691no—
242#103—2691no—
243#103—2691no—
244#102—2691no—
245#102—2691no—
246#102—2691no—
247#102—2691no—
248#102—2691no—
249#102—2691no—
250#102—2691no—
251C22⋊C8C2×D26911yescharacteristic
252C22⋊C8C2×D26911yescharacteristic, complemented
253#97C2×D26911yescharacteristic, complemented
254C24—5381no—
255#41—5382no—
256#41—10761no—
257#41—10764no—
258C2×Q8—2691no—
259C2×Q8—5381no—
260C2×D4—2691no—
261C2×D4—2691no—
262C2×D4—2691no—
263C2×D4—5382no—
264C2×D4—5381no—
265C2×D4—5381no—
266C2×D4—5381no—
267C2×D4—5381no—
268C2×D4—5381no—
269C2×D4—10761no—
270C2×D4D107611yescharacteristic
271C22×C4—5381no—
272C22×C4—5381no—
273C22×C4—5381no—
274C22×C4—5381no—
275C22×C4—5381no—
276C22×C4C22×D26911yescharacteristic
277C22×C4C22×D26911yescharacteristic
278SD16—10761no—
279D8—5382no—
280D8—10761no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D26911yescharacteristic
284C2×C8C22×D26911yescharacteristic
285C2×C8C22×D26911yescharacteristic
286C2×C8C22×D26911yescharacteristic
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⋊C4D107611yescharacteristic
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C22⋊C4—5381no—
299C22⋊C4—5381no—
300C22⋊C4—5381no—
301C22⋊C4—5381no—
302C22⋊C4—5381no—
303C22⋊C4—5381no—
304C22⋊C4D107611yescharacteristic
305C22⋊C4D107611yescharacteristic
306C42C22×D26911yescharacteristic
307C23—5381no—
308C23—5381no—
309C23—5381no—
310C23—10762no—
311C23—10762no—
312C23—21521no—
313C23C2×D107611yescharacteristic
314C23C2×D107611yescharacteristic
315Q8—5381no—
316Q8—5381no—
317Q8—10762no—
318D4—22no—
319D4—2692no—
320D4—5381no—
321D4—5381no—
322D4—5381no—
323D4—5381no—
324D4—5381no—
325D4—10762no—
326D4—10762no—
327D4—10762no—
328D4—10762no—
329D4—21521no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—5381no—
335C2×C4—5381no—
336C2×C4—5381no—
337C2×C4—5381no—
338C2×C4—5381no—
339C2×C4—10762no—
340C2×C4—10762no—
341C2×C4—10762no—
342C2×C4—10762no—
343C2×C4—21521no—
344C2×C4C2×D107611yescharacteristic
345C2×C4C2×D107611yescharacteristic
346C2×C4C2×D107611yescharacteristic
347C2×C4C2×D107611yescharacteristic
348C2×C4C23×D26911yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—5382no—
359C22—10761no—
360C22—10761no—
361C22—10761no—
362C22—10761no—
363C22—10761no—
364C22—10761no—
365C22—10761no—
366C22—10761no—
367C22—21524no—
368C22#2257548112yes—
369C22C22×D107611yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—10761no—
375C4—10761no—
376C4—10761no—
377C4—10761no—
378C4—10761no—
379C4#41×D26911yescharacteristic
380C4#2257549811yescharacteristic
381C2—22no—
382C2—41no—
383C2—10762no—
384C2—21521no—
385C2—21521no—
386C2#3177125011yescharacteristic
387C2C2×#2257548111yescharacteristic
388C2#3177141711yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#435×C269C2
socleC22×C269C22×D4
hypercenter#435D269
hypocenterC269#3306
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. #31771259C2semidirect
2. #31771251C2semidirect
3. #31770965C2semidirect
4. #31770936C2semidirect
5. #31770924C2semidirect
6. #31770896C2semidirect
7. #31770858C2semidirect
8. #31770834C2semidirect
9. #31770821C2semidirect
10. #31770752C2semidirect
11. #31770741C2semidirect
12. #31770718C2semidirect
13. #31770607C2semidirect
14. C2×#22575375C2semidirect
15. #435×C269C2semidirect
19. C2×#16864391C22semidirect
22. #22575453C22semidirect
31. #22575427C22semidirect
35. C4×D1076C22semidirect
37. C2×C4⋊Dic269C22semidirect
39. #22575385C22semidirect
40. #22575385C22semidirect
41. #22575385C22semidirect
42. #22575378C22semidirect
43. #22575378C22semidirect
44. #22575378C22semidirect
51. #22575375C22semidirect
52. C2×M16×C269C22semidirect
55. C4⋊C8×C269C22semidirect
57. C22⋊C8×C269C22semidirect
58. #97×C269C22semidirect
127. D1076#41semidirect
194. C269#3306semidirect
208. #435D269semidirect
217. C2×M16C2×D269semidirect
240. C4⋊C8C2×D269semidirect
252. C22⋊C8C2×D269semidirect
253. #97C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317712592
#317712512
#317709652
#317709362
#317709242
#317708962
#317708582
#317708342
#317708212
#317707522
#317707412
#317707182
#317706072
C2×#225753752
#435×C2692
#3306269