Finite Group Databasebeta

← #46821027

Subgroups — #46821027

Order 34432.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771142C211yesmaximal, characteristic, complemented
2C4×D4×D269C211yesmaximal, characteristic, complemented
3#31770934C211yesmaximal, characteristic, complemented
4#31770920C211yesmaximal, characteristic, complemented
5#31770908C211yesmaximal, characteristic, complemented
6#31770907C211yesmaximal, characteristic, complemented
7#31770823C211yesmaximal, characteristic, complemented
8#31770822C211yesmaximal, characteristic, complemented
9#31770754C211yesmaximal, characteristic, complemented
10#31770740C211yesmaximal, characteristic
11#31770718C211yesmaximal, characteristic, complemented
12#31770715C211yesmaximal, characteristic, complemented
13#31770703C211yesmaximal, characteristic, complemented
14#31770660C211yesmaximal, characteristic, complemented
15#440×C269C211yesmaximal, characteristic, complemented
16C2×D4×D269C2211yescharacteristic
17C22×C4×D269—21no—
18C2×#16864389C2211yescharacteristic
19C2×D2152C2211yescharacteristic
20C2×#16864387C2211yescharacteristic
21#22575448—21no—
22#22575444C2211yescharacteristic, complemented
23#22575442C2211yescharacteristic, complemented
24#22575438—21no—
25#22575429C2211yescharacteristic
26#22575428C2211yescharacteristic
27C4×D1076—21no—
28C4×D1076C2211yescharacteristic
29C4×D1076C2211yescharacteristic, complemented
30D4×Dic269C2211yescharacteristic
31#22575415C2211yescharacteristic
32C4×C22⋊D269—21no—
33#22575413—21no—
34#22575410—21no—
35C4⋊C4×D269C2211yescharacteristic
36C22⋊C4×D269—21no—
37C42×D269C2211yescharacteristic
38#22575386C2211yescharacteristic, complemented
39#22575385C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575382C2211yescharacteristic, complemented
43#22575377C2211yescharacteristic, complemented
44#22575375C2211yescharacteristic
45#22575375C2211yescharacteristic, complemented
46#22575374C2211yescharacteristic
47#22575373C2211yescharacteristic
48#22575373C2211yescharacteristic, complemented
49#22575365C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575364C2211yescharacteristic, complemented
52C2×SD16×C269C2211yescharacteristic
53C4×Q8×C269C2211yescharacteristic, complemented
54C4×D4×C269C2211yescharacteristic
55#107×C269C2211yescharacteristic, complemented
56#103×C269C2211yescharacteristic, complemented
57#102×C269C2211yescharacteristic
58#97×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60C2×D1076—21no—
61C2×D1076C2311yescharacteristic
62C2×D1076C2311yescharacteristic
63C2×C22⋊D269—21no—
64D4×D269—22no—
65D4×D269—22no—
66C22×Dic269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—44no—
72C2×C4×D269D411yescharacteristic
73C2×C4×D269D411yescharacteristic
74C2×C4×D269C2311yescharacteristic
75#16864389—22no—
76D2152—22no—
77#16864387—22no—
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C4⋊Dic269—21no—
81C4⋊Dic269C2311yescharacteristic
82C4⋊Dic269C2311yescharacteristic
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86C22⋊Dic269—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379—21no—
94C4×Dic269D411yescharacteristic
95C4×Dic269D411yescharacteristic
96C4×Dic269C2311yescharacteristic
97C2×Q8×C269C2311yescharacteristic
98C2×D4×C269C2311yescharacteristic
99C22×C4×C269—21no—
100SD16×C269—22no—
101C2×C8×C269C2311yescharacteristic
102C2×C8×C269C2311yescharacteristic
103C4⋊C4×C269—21no—
104C4⋊C4×C269C2311yescharacteristic
105C4⋊C4×C269C2311yescharacteristic
106C22⋊C4×C269—21no—
107C42×C269—21no—
108C42×C269C2311yescharacteristic
109C22×D269—24no—
110C22×D269—21no—
111C22×D269—21no—
112C22×D269—42no—
113C22×D269—42no—
114C22×D269C2×D411yescharacteristic
115D1076—21no—
116D1076—21no—
117D1076—21no—
118D1076—42no—
119D1076#4112yes—
120C22⋊D269—24no—
121C2×Dic269—21no—
122C2×Dic269—21no—
123C2×Dic269—42no—
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C2×Dic269C2×D411yescharacteristic
127C4×D269—22no—
128C4×D269—21no—
129C4×D269—21no—
130C4×D269—41no—
131C4×D269—42no—
132C4×D269—42no—
133C4×D269—42no—
134C4×D269—42no—
135#14524130—21no—
136#14524130—21no—
137C23×C269—21no—
138Q8×C269—21no—
139Q8×C269—21no—
140D4×C269—21no—
141D4×C269#4112yes—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—42no—
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2411yescharacteristic
149C8×C269—21no—
150C8×C269—21no—
151C22×C269—22no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269C22×D411yescharacteristic
155C2×D269—21no—
156C2×D269—21no—
157C2×D269—22no—
158C2×D269—48no—
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—41no—
162C2×D269—41no—
163C2×D269—41no—
164C2×D269AGL(1,ℤ/8)12yes—
165C4×C269—21no—
166C4×C269—21no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269—41no—
170C4×C269C2×#4111yescharacteristic
171C4×C269C2×#4111yescharacteristic
172Dic269—21no—
173Dic269—21no—
174Dic269—21no—
175Dic269—41no—
176Dic269—41no—
177C2×C269—42no—
178C2×C269#52511yescharacteristic
179C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C269#57511yescharacteristic
181D269—22no—
182D269—42no—
183D269—81no—
184C269#311411yescharacteristic, complemented, Sylow
185#3114—2691nomaximal, Sylow
186#529—2691no—
187C2×C4×D4—2691no—
188#483—2691no—
189#480—2691no—
190#478—2691no—
191#478—2691no—
192#463—2691no—
193#463—2691no—
194#450—2691no—
195#447—2691no—
196#442—2691no—
197#442—2691no—
198#440—2691no—
199#440D26911yescharacteristic, complemented
200#432—2691no—
201C22×D4—2691no—
202C23×C4—5381no—
203C2×SD16—2691no—
204C2×SD16C2×D26911yescharacteristic
205C2×D8—2691no—
206C2×D8—2691no—
207#126—5381no—
208#125—2691no—
209#124—2691no—
210#123—5381no—
211C22⋊Q8—2691no—
212#121—2691no—
213C4×Q8C2×D26911yescharacteristic, complemented
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—2691no—
217C4×D4—2691no—
218C4×D4—5381no—
219C4×D4—5381no—
220C4×D4—5381no—
221C4×D4C2×D26911yescharacteristic
222#117—5381no—
223C2×C4⋊C4—2691no—
224C2×C22⋊C4—5381no—
225C2×C42—2691no—
226#107—2691no—
227#107C2×D26911yescharacteristic, complemented
228#106—2691no—
229#106—2691no—
230C4⋊C8—2691no—
231C4⋊C8—2691no—
232#103—2691no—
233#103C2×D26911yescharacteristic, complemented
234#102—2691no—
235#102—2691no—
236#102—2691no—
237#102—2691no—
238#102—2691no—
239#102C2×D26911yescharacteristic
240C22⋊C8—2691no—
241C22⋊C8—2691no—
242#97—2691no—
243#97C2×D26911yescharacteristic, complemented
244C24—5381no—
245C2×Q8C22×D26911yescharacteristic
246C2×D4—2691no—
247C2×D4—2691no—
248C2×D4—5381no—
249C2×D4—5381no—
250C2×D4—5382no—
251C2×D4—5382no—
252C2×D4C22×D26911yescharacteristic
253C22×C4—21no—
254C22×C4—2691no—
255C22×C4—2691no—
256C22×C4—2691no—
257C22×C4—5381no—
258C22×C4—5381no—
259C22×C4—5381no—
260C22×C4—5381no—
261C22×C4—5381no—
262C22×C4—10764no—
263SD16—22no—
264SD16—5382no—
265D8—5382no—
266D8—5382no—
267C2×C8—2691no—
268C2×C8—2691no—
269C2×C8C22×D26911yescharacteristic
270C2×C8C22×D26911yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—2691no—
273C4⋊C4—2691no—
274C4⋊C4—5381no—
275C4⋊C4—5381no—
276C4⋊C4—5381no—
277C4⋊C4—5381no—
278C4⋊C4C22×D26911yescharacteristic
279C4⋊C4C22×D26911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—5381no—
282C22⋊C4—5381no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C22⋊C4—5381no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C42—21no—
290C42—2691no—
291C42—2691no—
292C42—2691no—
293C42C22×D26911yescharacteristic
294C23—21no—
295C23—2691no—
296C23—5384no—
297C23—5381no—
298C23—5381no—
299C23—10762no—
300C23—10762no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—2692no—
305D4—5384no—
306D4—5381no—
307D4—5381no—
308D4—5381no—
309D4—10762no—
310D4#1686440212yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—2691no—
316C2×C4—2691no—
317C2×C4—2691no—
318C2×C4—5382no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—5381no—
322C2×C4—5381no—
323C2×C4—10761no—
324C2×C4—10762no—
325C2×C4—10762no—
326C2×C4—10762no—
327C2×C4—10762no—
328C2×C4—10762no—
329C2×C4D4×D26911yescharacteristic
330C2×C4D4×D26911yescharacteristic
331C2×C4C23×D26911yescharacteristic
332C8—21no—
333C8—21no—
334C8—5381no—
335C8—5381no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—2692no—
340C22—5381no—
341C22—5381no—
342C22—5382no—
343C22—10768no—
344C22—10761no—
345C22—10761no—
346C22—10761no—
347C22—10761no—
348C22—10761no—
349C22C2×D4×D26911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—5381no—
356C4—5381no—
357C4—5381no—
358C4—10761no—
359C4—10761no—
360C4#41×D26911yescharacteristic
361C4C2×#1686440211yescharacteristic
362C2—42no—
363C2—5382no—
364C2—10762no—
365C2—21521no—
366C2#3177111411yescharacteristic
367C2AGL(1,ℤ/8)×D26911yescharacteristic
368C2#3177140411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#440×C269C2
socleC22×C269C22×D4
prime radical#31770740C2
hypercenter#440D269
hypocenterC269#3114
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #31771142C2semidirect
2. C4×D4×D269C2semidirect
3. #31770934C2semidirect
4. #31770920C2semidirect
5. #31770908C2semidirect
6. #31770907C2semidirect
7. #31770823C2semidirect
8. #31770822C2semidirect
9. #31770754C2semidirect
11. #31770718C2semidirect
12. #31770715C2semidirect
13. #31770703C2semidirect
14. #31770660C2semidirect
15. #440×C269C2semidirect
22. #22575444C22semidirect
23. #22575442C22semidirect
29. C4×D1076C22semidirect
38. #22575386C22semidirect
39. #22575385C22semidirect
40. #22575384C22semidirect
41. #22575382C22semidirect
42. #22575382C22semidirect
43. #22575377C22semidirect
45. #22575375C22semidirect
48. #22575373C22semidirect
51. #22575364C22semidirect
53. C4×Q8×C269C22semidirect
55. #107×C269C22semidirect
56. #103×C269C22semidirect
58. #97×C269C22semidirect
184. C269#3114semidirect
199. #440D269semidirect
213. C4×Q8C2×D269semidirect
227. #107C2×D269semidirect
233. #103C2×D269semidirect
243. #97C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317711422
C4×D4×D2692
#317709342
#317709202
#317709082
#317709072
#317708232
#317708222
#317707542
#317707402
#317707182
#317707152
#317707032
#317706602
#440×C2692
#3114269