Finite Group Databasebeta

← #46819741

Subgroups — #46819741

Order 34432.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D269C211yesmaximal, characteristic
2#31771081C211yesmaximal, characteristic, complemented
3#31771077C211yesmaximal, characteristic
4#31770707C211yesmaximal, characteristic, complemented
5#31770706C211yesmaximal, characteristic, complemented
6#31770704C211yesmaximal, characteristic, complemented
7#31770696C211yesmaximal, characteristic, complemented
8C4×#16864389C211yesmaximal, characteristic, complemented
9C4×#16864390C211yesmaximal, characteristic, complemented
10#31770690C211yesmaximal, characteristic, complemented
11#31770642C211yesmaximal, characteristic, complemented
12#31770612C211yesmaximal, characteristic, complemented
13#31770608C211yesmaximal, characteristic
14#31770562C211yesmaximal, characteristic, complemented
15#440×C269C211yesmaximal, characteristic, complemented
16C2×Q8×D269C2211yescharacteristic
17C2×D4×D269C2211yescharacteristic
18C2×#16864391C2211yescharacteristic
19C2×#16864390C2211yescharacteristic
20C2×#16864389C2211yescharacteristic
21SD16×D269C418yescomplemented
22C2×#16864385C2211yescharacteristic
23C2×C8×D269C2211yescharacteristic
24Q8×Dic269C2211yescharacteristic, complemented
25C4×Dic538—21no—
26C4×Dic538C2211yescharacteristic, complemented
27#22575418—21no—
28#22575418C2211yescharacteristic, complemented
29C4×D1076C2211yescharacteristic
30D4×Dic269C2211yescharacteristic
31#22575415C2211yescharacteristic
32C4×C22⋊D269—21no—
33#22575413—21no—
34#22575411—21no—
35#22575411C2211yescharacteristic
36#22575411C2211yescharacteristic
37#22575410—21no—
38#22575410C2211yescharacteristic
39C2×#16864379—21no—
40C22⋊C4×D269—21no—
41#22575387C2211yescharacteristic, complemented
42#22575384C2211yescharacteristic, complemented
43#22575384C2211yescharacteristic, complemented
44#22575378C2211yescharacteristic, complemented
45#22575377C2211yescharacteristic, complemented
46#22575376C2211yescharacteristic, complemented
47#22575375C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575373C2211yescharacteristic
50#22575363C2211yescharacteristic, complemented
51C4×#14524130C2211yescharacteristic, complemented
52C8×Dic269C2211yescharacteristic, complemented
53C2×SD16×C269C2211yescharacteristic
54C4×Q8×C269C2211yescharacteristic, complemented
55C4×D4×C269C2211yescharacteristic
56#107×C269C2211yescharacteristic, complemented
57#103×C269C2211yescharacteristic, complemented
58#102×C269C2211yescharacteristic
59#97×C269C2211yescharacteristic, complemented
60C23×D269—21no—
61C2×Dic538—21no—
62C2×Dic538C2311yescharacteristic
63Q8×D269—22no—
64Q8×D269C2×C414yescomplemented
65C2×D1076C2311yescharacteristic
66C2×C22⋊D269—21no—
67D4×D269—22no—
68D4×D269C2×C414yes—
69C22×Dic269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269C2311yescharacteristic
74#16864391C2×C414yescomplemented
75#16864390C2×C414yescomplemented
76#16864389C2×C414yescomplemented
77#16864385—22no—
78C2×#14524130C2311yescharacteristic
79C2×#14524130C2311yescharacteristic
80C8×D269C2×C414yescomplemented
81C4⋊Dic269—21no—
82C4⋊Dic269C2311yescharacteristic
83C4⋊Dic269C2311yescharacteristic
84#16864381—21no—
85#16864381—21no—
86#16864381D411yescharacteristic
87#16864381D411yescharacteristic
88C22⋊Dic269—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92#16864379—21no—
93#16864379D411yescharacteristic
94#16864379D411yescharacteristic
95C4×Dic269—21no—
96C4×Dic269—21no—
97C4×Dic269—21no—
98C4×Dic269—21no—
99C4×Dic269—21no—
100C4×Dic269C2311yescharacteristic
101C2×Q8×C269C2311yescharacteristic
102C2×D4×C269C2311yescharacteristic
103C22×C4×C269—21no—
104SD16×C269C2×C414yescomplemented
105C2×C8×C269C2311yescharacteristic
106C2×C8×C269C2311yescharacteristic
107C4⋊C4×C269—21no—
108C4⋊C4×C269C2311yescharacteristic
109C4⋊C4×C269C2311yescharacteristic
110C22⋊C4×C269—21no—
111C42×C269—21no—
112C42×C269C2311yescharacteristic
113C22×D269—21no—
114C22×D269—24no—
115C22×D269—81no—
116C22×D269—81no—
117C22×D269C2×D411yescharacteristic
118Dic538—21no—
119Dic538—24no—
120Dic538C22×C412yes—
121D1076—21no—
122D1076C22×C412yes—
123C22⋊D269—24no—
124C2×Dic269—21no—
125C2×Dic269—21no—
126C2×Dic269—21no—
127C2×Dic269—81no—
128C2×Dic269C2×D411yescharacteristic
129C2×Dic269C2×D411yescharacteristic
130C2×Dic269C2×D411yescharacteristic
131C4×D269—24no—
132C4×D269—81no—
133C4×D269—81no—
134C4×D269C22×C412yes—
135C4×D269#4112yes—
136#14524130—21no—
137#14524130C22×C412yes—
138C23×C269—21no—
139Q8×C269—21no—
140Q8×C269C22×C412yes—
141D4×C269—21no—
142D4×C269C22×C412yes—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—81no—
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269C2411yescharacteristic
150C8×C269—21no—
151C8×C269C22×C412yes—
152C22×C269—22no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269C22×D411yescharacteristic
156C2×D269—21no—
157C2×D269—21no—
158C2×D269—22no—
159C2×D269—41no—
160C2×D269—41no—
161C2×D269—84no—
162C2×D269C4×D412yes—
163C4×C269—22no—
164C4×C269—21no—
165C4×C269—21no—
166C4×C269—41no—
167C4×C269—41no—
168C4×C269C23×C411yescharacteristic
169C4×C269C2×#4111yescharacteristic
170Dic269—22no—
171Dic269—21no—
172Dic269—21no—
173Dic269—41no—
174Dic269—41no—
175Dic269C4×D412yes—
176C2×C269—42no—
177C2×C269C2×C4×D411yescharacteristic
178C2×C269#57711yescharacteristic
179C2×C269#57711yescharacteristic
180D269—22no—
181D269—42no—
182C269#294911yescharacteristic, complemented, Sylow
183#2949—2691nomaximal, Sylow
184C22×SD16—2691no—
185#519—2691no—
186#518—2691no—
187#440—2691no—
188#440—2691no—
189#440—2691no—
190#440D26911yescharacteristic, complemented
191C4×SD16—2691no—
192C4×SD16—2691no—
193C4×SD16—2691no—
194C4×SD16—2691no—
195#427—2691no—
196#419—2691no—
197#418—2691no—
198#405—2691no—
199C22×Q8—2691no—
200C22×D4—2691no—
201C2×SD16—2691no—
202C2×SD16—2691no—
203C2×SD16—2698no—
204C2×SD16—2691no—
205C2×SD16C2×D26911yescharacteristic
206C2×M16—2691no—
207C22×C8—2691no—
208C4×Q8—2691no—
209C4×Q8—2691no—
210C4×Q8—2691no—
211C4×Q8—5381no—
212C4×Q8—5381no—
213C4×Q8C2×D26911yescharacteristic, complemented
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—2691no—
217C4×D4—5381no—
218C4×D4—5381no—
219C4×D4C2×D26911yescharacteristic
220#117—2691no—
221#117—2691no—
222#117—2691no—
223#117—5381no—
224#117—5381no—
225C2×C22⋊C4—5381no—
226C2×C22⋊C4—5381no—
227#107—2691no—
228#107C2×D26911yescharacteristic, complemented
229#106—2691no—
230#106—2691no—
231#103—2691no—
232#103—2691no—
233#103—2691no—
234#103C2×D26911yescharacteristic, complemented
235#102—2691no—
236#102—2691no—
237#102—2691no—
238#102C2×D26911yescharacteristic
239#97—2691no—
240#97C2×D26911yescharacteristic, complemented
241C4×C8—2691no—
242C4×C8—2691no—
243C24—5381no—
244C2×Q8—2694no—
245C2×Q8—2691no—
246C2×Q8—5381no—
247C2×Q8—5382no—
248C2×Q8C22×D26911yescharacteristic
249C2×D4—2694no—
250C2×D4—2691no—
251C2×D4—5382no—
252C2×D4—5381no—
253C2×D4C22×D26911yescharacteristic
254C22×C4—21no—
255C22×C4—2691no—
256C22×C4—5381no—
257C22×C4—5381no—
258C22×C4—5381no—
259C22×C4—5381no—
260SD16—2694no—
261SD16—2694no—
262SD16—2694no—
263SD16C4×D26914yescomplemented
264M16—5382no—
265C2×C8—2691no—
266C2×C8—2694no—
267C2×C8—2691no—
268C2×C8C22×D26911yescharacteristic
269C2×C8C22×D26911yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—2691no—
272C4⋊C4—2691no—
273C4⋊C4—2691no—
274C4⋊C4—2691no—
275C4⋊C4—5381no—
276C4⋊C4—5381no—
277C4⋊C4—5381no—
278C4⋊C4C22×D26911yescharacteristic
279C4⋊C4C22×D26911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—2691no—
282C22⋊C4—2691no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C22⋊C4—5381no—
287C22⋊C4—5381no—
288C42—21no—
289C42—2691no—
290C42—5381no—
291C42—5381no—
292C42—5381no—
293C42—5381no—
294C42—5381no—
295C42C22×D26911yescharacteristic
296C23—21no—
297C23—2691no—
298C23—5384no—
299C23—5381no—
300C23—21521no—
301C23—21521no—
302Q8—21no—
303Q8—2692no—
304Q8—5384no—
305Q8—5381no—
306Q8C2×C4×D26912yes—
307D4—21no—
308D4—2692no—
309D4—5384no—
310D4—5381no—
311D4C2×C4×D26912yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—2691no—
317C2×C4—2692no—
318C2×C4—2692no—
319C2×C4—2691no—
320C2×C4—2691no—
321C2×C4—5384no—
322C2×C4—5381no—
323C2×C4—5381no—
324C2×C4—5381no—
325C2×C4—21521no—
326C2×C4—21521no—
327C2×C4—21521no—
328C2×C4D4×D26911yescharacteristic
329C2×C4D4×D26911yescharacteristic
330C2×C4C23×D26911yescharacteristic
331C8—21no—
332C8—2692no—
333C8—5381no—
334C8C2×C4×D26912yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—2692no—
339C22—5381no—
340C22—5381no—
341C22—5382no—
342C22—10761no—
343C22—10761no—
344C22—21524no—
345C22C2×D4×D26911yescharacteristic
346C4—21no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—2692no—
352C4—5381no—
353C4—5381no—
354C4—5382no—
355C4—10761no—
356C4—10761no—
357C4C22×C4×D26911yescharacteristic
358C4#41×D26911yescharacteristic
359C2—42no—
360C2—5382no—
361C2—10762no—
362C2C4×D4×D26911yescharacteristic
363C2#3177141411yescharacteristic
364C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
Fitting#440×C269C2
socleC22×C269C22×D4
prime radicalC2×D4×D269C22
cosocleC2×C4×C269C24
hypercenter#440D269
hypocenterC269#2949
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #31771081C2semidirect
4. #31770707C2semidirect
5. #31770706C2semidirect
6. #31770704C2semidirect
7. #31770696C2semidirect
8. C4×#16864389C2semidirect
9. C4×#16864390C2semidirect
10. #31770690C2semidirect
11. #31770642C2semidirect
12. #31770612C2semidirect
14. #31770562C2semidirect
15. #440×C269C2semidirect
21. SD16×D269C4semidirect
24. Q8×Dic269C22semidirect
26. C4×Dic538C22semidirect
28. #22575418C22semidirect
41. #22575387C22semidirect
42. #22575384C22semidirect
43. #22575384C22semidirect
44. #22575378C22semidirect
45. #22575377C22semidirect
46. #22575376C22semidirect
50. #22575363C22semidirect
51. C4×#14524130C22semidirect
52. C8×Dic269C22semidirect
54. C4×Q8×C269C22semidirect
56. #107×C269C22semidirect
57. #103×C269C22semidirect
59. #97×C269C22semidirect
64. Q8×D269C2×C4semidirect
74. #16864391C2×C4semidirect
75. #16864390C2×C4semidirect
76. #16864389C2×C4semidirect
80. C8×D269C2×C4semidirect
104. SD16×C269C2×C4semidirect
182. C269#2949semidirect
190. #440D269semidirect
213. C4×Q8C2×D269semidirect
228. #107C2×D269semidirect
234. #103C2×D269semidirect
240. #97C2×D269semidirect
263. SD16C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D2692
#317710812
#317710772
#317707072
#317707062
#317707042
#317706962
C4×#168643892
C4×#168643902
#317706902
#317706422
#317706122
#317706082
#317705622
#440×C2692
#2949269