Finite Group Databasebeta

← #46820974

Subgroups — #46820974

Order 34432.

488 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771152C211yesmaximal, characteristic, complemented
2C4×D4×D269C211yesmaximal, characteristic, complemented
3#31770925C211yesmaximal, characteristic, complemented
4#31770922C211yesmaximal, characteristic, complemented
5#31770894C211yesmaximal, characteristic, complemented
6#31770893C211yesmaximal, characteristic, complemented
7#31770799C211yesmaximal, characteristic, complemented
8#31770798C211yesmaximal, characteristic, complemented
9#31770740C211yesmaximal, characteristic, complemented
10#31770737C211yesmaximal, characteristic, complemented
11#31770718C211yesmaximal, characteristic, complemented
12#31770715C211yesmaximal, characteristic, complemented
13#31770715C211yesmaximal, characteristic, complemented
14#31770660C211yesmaximal, characteristic, complemented
15#442×C269C211yesmaximal, characteristic, complemented
16C2×#16864402—21no—
17C2×D4×D269C2211yescharacteristic
18C22×C4×D269—21no—
19C2×D2152C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21C2×#16864387C2211yescharacteristic
22#22575452C2211yescharacteristic, complemented
23#22575449C2211yescharacteristic, complemented
24#22575439—21no—
25#22575428C2211yescharacteristic
26#22575426—21no—
27#22575424C2211yescharacteristic
28C4×D1076C2211yescharacteristic
29C4×D1076C2211yescharacteristic, complemented
30D4×Dic269C2211yescharacteristic
31#22575415C2211yescharacteristic
32C4×C22⋊D269—21no—
33C4×C22⋊D269—21no—
34#22575413—21no—
35C4⋊C4×D269C2211yescharacteristic
36C22⋊C4×D269—21no—
37C42×D269C2211yescharacteristic
38#22575385C2211yescharacteristic, complemented
39#22575384C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575382C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic
44#22575375C2211yescharacteristic, complemented
45#22575374C2211yescharacteristic
46#22575374C2211yescharacteristic, complemented
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic, complemented
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575364C2211yescharacteristic, complemented
52C2×D8×C269C2211yescharacteristic
53C4×D4×C269C2211yescharacteristic
54C4×D4×C269C2211yescharacteristic, complemented
55#106×C269C2211yescharacteristic, complemented
56#102×C269C2211yescharacteristic
57#102×C269C2211yescharacteristic, complemented
58#97×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60#16864402—44no—
61C2×Dic538—21no—
62C2×D1076—21no—
63C2×D1076C2311yescharacteristic
64C2×D1076C2311yescharacteristic
65C2×C22⋊D269—21no—
66C2×C22⋊D269—21no—
67C2×C22⋊D269—21no—
68C2×C22⋊D269—21no—
69D4×D269—22no—
70D4×D269—22no—
71C22×Dic269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269—21no—
76C2×C4×D269—44no—
77C2×C4×D269D411yescharacteristic
78C2×C4×D269D411yescharacteristic
79C2×C4×D269C2311yescharacteristic
80D2152—22no—
81#16864387—22no—
82#16864387—22no—
83C2×#14524130C2311yescharacteristic
84C2×#14524130C2311yescharacteristic
85C4⋊Dic269C2311yescharacteristic
86C4⋊Dic269C2311yescharacteristic
87#16864381—21no—
88#16864381—21no—
89C22⋊Dic269—21no—
90C22⋊Dic269—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95C4×Dic269D411yescharacteristic
96C4×Dic269D411yescharacteristic
97C4×Dic269C2311yescharacteristic
98C2×D4×C269C2311yescharacteristic
99C2×D4×C269C2311yescharacteristic
100C22×C4×C269—21no—
101C22×C4×C269—21no—
102D8×C269—22no—
103C2×C8×C269C2311yescharacteristic
104C2×C8×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C4⋊C4×C269C2311yescharacteristic
107C22⋊C4×C269—21no—
108C22⋊C4×C269—21no—
109C42×C269C2311yescharacteristic
110C22×D269—24no—
111C22×D269—21no—
112C22×D269—21no—
113C22×D269—42no—
114C22×D269—42no—
115C22×D269C2×D411yescharacteristic
116Dic538—42no—
117D1076—21no—
118D1076—21no—
119D1076—21no—
120D1076—42no—
121D1076#4112yescomplemented
122C22⋊D269—24no—
123C22⋊D269—42no—
124C22⋊D269—42no—
125C22⋊D269—42no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—42no—
129C2×Dic269C2×D411yescharacteristic
130C2×Dic269C2×D411yescharacteristic
131C2×Dic269C2×D411yescharacteristic
132C4×D269—22no—
133C4×D269—21no—
134C4×D269—21no—
135C4×D269—22no—
136C4×D269—42no—
137C4×D269—42no—
138C4×D269—42no—
139C4×D269—42no—
140#14524130—21no—
141#14524130—21no—
142C23×C269—21no—
143C23×C269—21no—
144D4×C269—21no—
145D4×C269—21no—
146D4×C269—21no—
147D4×C269#4112yescomplemented
148C2×C4×C269—21no—
149C2×C4×C269—21no—
150C2×C4×C269—42no—
151C2×C4×C269—42no—
152C2×C4×C269C2×D411yescharacteristic
153C2×C4×C269C2×D411yescharacteristic
154C2×C4×C269C2411yescharacteristic
155C8×C269—21no—
156C8×C269—21no—
157C22×C269—22no—
158C22×C269—41no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269—41no—
162C22×C269—41no—
163C22×C269C22×D411yescharacteristic
164C2×D269—21no—
165C2×D269—21no—
166C2×D269—22no—
167C2×D269—48no—
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—41no—
171C2×D269—41no—
172C2×D269—41no—
173C2×D269AGL(1,ℤ/8)12yes—
174C4×C269—21no—
175C4×C269—21no—
176C4×C269—41no—
177C4×C269—41no—
178C4×C269C2×#4111yescharacteristic
179C4×C269C2×#4111yescharacteristic
180Dic269—21no—
181Dic269—21no—
182Dic269—41no—
183Dic269—41no—
184Dic269AGL(1,ℤ/8)12yes—
185C2×C269—42no—
186C2×C269—81no—
187C2×C269#52511yescharacteristic
188C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
190D269—22no—
191D269—42no—
192D269—81no—
193C269#310911yescharacteristic, complemented, Sylow
194#3109—2691nomaximal, Sylow
195#532—2691no—
196C2×C4×D4—2691no—
197#481—2691no—
198#481—2691no—
199#476—2691no—
200#476—2691no—
201#459—2691no—
202#459—2691no—
203#447—2691no—
204#447—2691no—
205#442—2691no—
206#442—2691no—
207#442—2691no—
208#442D26911yescharacteristic, complemented
209#432—2691no—
210C2×#41—5381no—
211C22×D4—2691no—
212C23×C4—5381no—
213C2×D8—2691no—
214C2×D8—2691no—
215C2×D8—2691no—
216C2×D8C2×D26911yescharacteristic
217C4⋊Q8—2691no—
218#127—2691no—
219#124—5381no—
220#121—2691no—
221#121—2691no—
222#121—5381no—
223C4×D4—2691no—
224C4×D4—2691no—
225C4×D4—2691no—
226C4×D4—2691no—
227C4×D4—5381no—
228C4×D4—5381no—
229C4×D4—5381no—
230C4×D4C2×D26911yescharacteristic
231C4×D4C2×D26911yescharacteristic, complemented
232C2×C4⋊C4—2691no—
233C2×C22⋊C4—5381no—
234C2×C42—2691no—
235#106—2691no—
236#106—2691no—
237#106—2691no—
238#106C2×D26911yescharacteristic, complemented
239C4⋊C8—2691no—
240C4⋊C8—2691no—
241#102—2691no—
242#102—2691no—
243#102—2691no—
244#102—2691no—
245#102—2691no—
246#102—2691no—
247#102C2×D26911yescharacteristic
248#102C2×D26911yescharacteristic, complemented
249C22⋊C8—2691no—
250C22⋊C8—2691no—
251#97—2691no—
252#97C2×D26911yescharacteristic, complemented
253C24—5381no—
254#41—10764no—
255C2×Q8—5381no—
256C2×D4—2691no—
257C2×D4—2691no—
258C2×D4—5381no—
259C2×D4—5381no—
260C2×D4—5381no—
261C2×D4—5381no—
262C2×D4—5382no—
263C2×D4—5382no—
264C2×D4—5381no—
265C2×D4C22×D26911yescharacteristic
266C2×D4C22×D26911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—2691no—
270C22×C4—2691no—
271C22×C4—2691no—
272C22×C4—5381no—
273C22×C4—5381no—
274C22×C4—5381no—
275C22×C4—5381no—
276C22×C4—5381no—
277C22×C4—10764no—
278D8—22no—
279D8—5382no—
280D8—5382no—
281D8—5382no—
282C2×C8—2691no—
283C2×C8—2691no—
284C2×C8C22×D26911yescharacteristic
285C2×C8C22×D26911yescharacteristic
286C4⋊C4—2691no—
287C4⋊C4—2691no—
288C4⋊C4—5381no—
289C4⋊C4—5381no—
290C4⋊C4C22×D26911yescharacteristic
291C4⋊C4C22×D26911yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C22⋊C4—5381no—
299C22⋊C4—5381no—
300C42—2691no—
301C42—2691no—
302C42—2691no—
303C42C22×D26911yescharacteristic
304C23—21no—
305C23—21no—
306C23—2691no—
307C23—5384no—
308C23—5381no—
309C23—5381no—
310C23—10762no—
311C23—10762no—
312Q8—10762no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—2692no—
317D4—5384no—
318D4—5381no—
319D4—5381no—
320D4—5381no—
321D4—10762no—
322D4—10762no—
323D4—10762no—
324D4—10762no—
325D4#1686440212yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—2691no—
331C2×C4—2691no—
332C2×C4—2691no—
333C2×C4—5382no—
334C2×C4—5382no—
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—10762no—
344C2×C4D4×D26911yescharacteristic
345C2×C4D4×D26911yescharacteristic
346C2×C4C23×D26911yescharacteristic
347C8—21no—
348C8—21no—
349C8—5381no—
350C8—5381no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—2692no—
358C22—5381no—
359C22—5381no—
360C22—5382no—
361C22—10768no—
362C22—10761no—
363C22—10761no—
364C22—10761no—
365C22—10761no—
366C22—10761no—
367C22C2×D4×D26911yescharacteristic
368C4—21no—
369C4—21no—
370C4—41no—
371C4—41no—
372C4—2692no—
373C4—5381no—
374C4—5381no—
375C4—10761no—
376C4—10761no—
377C4#41×D26911yescharacteristic
378C4C2×#1686440211yescharacteristic
379C2—42no—
380C2—81no—
381C2—5382no—
382C2—10762no—
383C2—21521no—
384C2#3177111411yescharacteristic
385C2AGL(1,ℤ/8)×D26911yescharacteristic
386C2AGL(1,ℤ/8)×D26911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#442×C269C2
socleC22×C269C22×D4
hypercenter#442D269
hypocenterC269#3109
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #31771152C2semidirect
2. C4×D4×D269C2semidirect
3. #31770925C2semidirect
4. #31770922C2semidirect
5. #31770894C2semidirect
6. #31770893C2semidirect
7. #31770799C2semidirect
8. #31770798C2semidirect
9. #31770740C2semidirect
10. #31770737C2semidirect
11. #31770718C2semidirect
12. #31770715C2semidirect
13. #31770715C2semidirect
14. #31770660C2semidirect
15. #442×C269C2semidirect
22. #22575452C22semidirect
23. #22575449C22semidirect
29. C4×D1076C22semidirect
38. #22575385C22semidirect
39. #22575384C22semidirect
40. #22575384C22semidirect
41. #22575382C22semidirect
42. #22575382C22semidirect
44. #22575375C22semidirect
46. #22575374C22semidirect
48. #22575373C22semidirect
51. #22575364C22semidirect
54. C4×D4×C269C22semidirect
55. #106×C269C22semidirect
57. #102×C269C22semidirect
58. #97×C269C22semidirect
121. D1076#41semidirect
147. D4×C269#41semidirect
193. C269#3109semidirect
208. #442D269semidirect
231. C4×D4C2×D269semidirect
238. #106C2×D269semidirect
248. #102C2×D269semidirect
252. #97C2×D269semidirect
325. D4#16864402semidirect

Maximal subgroups

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

subgroupindex
#317711522
C4×D4×D2692
#317709252
#317709222
#317708942
#317708932
#317707992
#317707982
#317707402
#317707372
#317707182
#317707152
#317706602
#442×C2692
#3109269