Finite Group Databasebeta

← #46820360

Subgroups — #46820360

Order 34432.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575477C212yesmaximal, complemented
2#127×D269C211yesmaximal, characteristic, complemented
3C4×#16864401C211yesmaximal, characteristic, complemented
4#31770806C211yesmaximal, characteristic, complemented
5#31770804C212yesmaximal, complemented
6#31770802C211yesmaximal, characteristic, complemented
7#31770800C211yesmaximal, characteristic, complemented
8#31770798C212yesmaximal, complemented
9#31770627C211yesmaximal, characteristic, complemented
10#31770608C212yesmaximal, complemented
11#459×C269C211yesmaximal, characteristic, complemented
12C2×#16864401C2211yescharacteristic
13C2×D4×D269—21no—
14C2×D4×D269—21no—
15C2×D4×D269C2212yes—
16#22575477—28no—
17C2×#16864391C2212yescomplemented
18C2×#16864390C2212yescomplemented
19C2×#16864387C2212yescomplemented
20C2×#16864385C2212yes—
21#22575450C2211yescharacteristic
22#22575449—21no—
23#22575449—21no—
24#22575449C2212yes—
25C4×Dic538C2211yescharacteristic, complemented
26#22575418C2211yescharacteristic, complemented
27D4×Dic269C2211yescharacteristic, complemented
28C4×C22⋊D269—21no—
29#22575413—21no—
30#22575411C2211yescharacteristic
31#22575409—21no—
32C2×C4×Dic269—21no—
33C42×D269C2211yescharacteristic
34C4⋊#14524130C2211yescharacteristic, complemented
35#22575382C2212yescomplemented
36#22575375C2212yescomplemented
37#22575374C2212yescomplemented
38#22575373C2212yescomplemented
39C2×D8×C269C2212yescomplemented
40#127×C269C2211yescharacteristic
41C4×D4×C269C2211yescharacteristic, complemented
42C4⋊C8×C269C2211yescharacteristic, complemented
43#102×C269C2212yescomplemented
44C23×D269—22no—
45#16864401—22no—
46#16864401D414yescomplemented
47C2×Dic538C2311yescharacteristic
48C2×D1076—21no—
49C2×D1076—21no—
50C2×D1076C2312yes—
51C2×C22⋊D269—21no—
52C2×C22⋊D269—22no—
53C2×C22⋊D269—22no—
54C2×C22⋊D269—22no—
55D4×D269—24no—
56D4×D269—24no—
57D4×D269—44no—
58D4×D269—44no—
59C22×Dic269—21no—
60C22×Dic269—21no—
61C2×C4×D269D411yescharacteristic
62C2×C4×D269D411yescharacteristic
63C2×C4×D269C2311yescharacteristic
64#16864391—24no—
65#16864390—24no—
66#16864387—24no—
67#16864385—24no—
68C2×#14524130C2312yes—
69C4⋊Dic269C2311yescharacteristic
70#16864381—21no—
71#16864381—21no—
72C22⋊Dic269—21no—
73#16864379—21no—
74C4×Dic269—21no—
75C4×Dic269—21no—
76C4×Dic269—21no—
77C4×Dic269D411yescharacteristic
78C4×Dic269D411yescharacteristic
79C4×Dic269C2311yescharacteristic
80C2×D4×C269—21no—
81C2×D4×C269—21no—
82C2×D4×C269C2312yes—
83C2×D4×C269C2311yescharacteristic
84C22×C4×C269—21no—
85D8×C269—24no—
86C2×C8×C269C2312yes—
87C4⋊C4×C269C2311yescharacteristic
88C22⋊C4×C269—21no—
89C42×C269C2311yescharacteristic
90C22×D269—22no—
91C22×D269—44no—
92C22×D269—44no—
93C22×D269—44no—
94C22×D269C2×D411yescharacteristic
95Dic538—21no—
96Dic538C2×D412yescomplemented
97D1076—22no—
98D1076—22no—
99D1076—42no—
100D1076—42no—
101C22⋊D269—24no—
102C22⋊D269—44no—
103C22⋊D269—44no—
104C22⋊D269—44no—
105C2×Dic269—21no—
106C2×Dic269—24no—
107C2×Dic269—21no—
108C2×Dic269—42no—
109C2×Dic269C2×D411yescharacteristic
110C2×Dic269C2×D411yescharacteristic
111C2×Dic269C2×D411yescharacteristic
112C4×D269—22no—
113C4×D269—22no—
114C4×D269C2×D412yes—
115C4×D269#4112yes—
116#14524130—22no—
117C23×C269—21no—
118C23×C269—22no—
119D4×C269—22no—
120D4×C269—21no—
121D4×C269—22no—
122D4×C269—42no—
123D4×C269—42no—
124D4×C269C2×D412yescomplemented
125C2×C4×C269—21no—
126C2×C4×C269—42no—
127C2×C4×C269C2×D411yescharacteristic
128C2×C4×C269C2×D411yescharacteristic
129C2×C4×C269C2411yescharacteristic
130C8×C269—22no—
131C22×C269—22no—
132C22×C269—41no—
133C22×C269—41no—
134C22×C269—42no—
135C22×C269—42no—
136C22×C269—42no—
137C22×C269C22×D411yescharacteristic
138C2×D269—21no—
139C2×D269—21no—
140C2×D269—42no—
141C2×D269—42no—
142C2×D269—42no—
143C2×D269—88no—
144C2×D269#12112yes—
145C4×C269—21no—
146C4×C269—41no—
147C4×C269AGL(1,ℤ/8)12yescomplemented
148C4×C269C22×D411yescharacteristic
149C4×C269C2×#4111yescharacteristic
150Dic269—22no—
151Dic269—21no—
152Dic269—41no—
153Dic269#12112yes—
154Dic269AGL(1,ℤ/8)12yescomplemented
155C2×C269—42no—
156C2×C269—82no—
157C2×C269C2×#12111yescharacteristic
158C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
159C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
160D269—22no—
161D269—82no—
162C269#303811yescharacteristic, complemented, Sylow
163#3038—2691nomaximal, Sylow
164C2×AGL(1,ℤ/8)—2692no—
165C2×#127—2691no—
166C4×#41—2691no—
167#460—2691no—
168#460—2691no—
169#460—2692no—
170#459—2692no—
171#459—2691no—
172#459D26911yescharacteristic, complemented
173#423—2691no—
174#418—2692no—
175C2×#41—2691no—
176C22×D4—2692no—
177C22×D4—5381no—
178C22×D4—5381no—
179AGL(1,ℤ/8)—5388no—
180C2×SD16—2692no—
181C2×SD16—2692no—
182C2×D8—2692no—
183C2×D8C2×D26912yescomplemented
184C2×M16—2692no—
185#127—2692no—
186#127—2691no—
187#127—5381no—
188#127—5381no—
189#127C2×D26911yescharacteristic
190C4×Q8—2691no—
191C4×Q8—2691no—
192C4×D4—2691no—
193C4×D4—5381no—
194C4×D4—5381no—
195C4×D4C2×D26911yescharacteristic, complemented
196#117—2691no—
197#117—5381no—
198C2×C42—2691no—
199C2×C42—5381no—
200C4⋊C8—2692no—
201C4⋊C8—2691no—
202C4⋊C8C2×D26911yescharacteristic, complemented
203#102—2692no—
204#102—2692no—
205#102—2692no—
206#102C2×D26912yescomplemented
207C24—5382no—
208#41—2694no—
209#41—5382no—
210C2×Q8—2691no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—2692no—
214C2×D4—5384no—
215C2×D4—5384no—
216C2×D4—5382no—
217C2×D4—5382no—
218C2×D4—5382no—
219C2×D4—5381no—
220C2×D4—5381no—
221C2×D4—5381no—
222C2×D4—10764no—
223C2×D4—10764no—
224C2×D4C22×D26912yes—
225C2×D4C22×D26911yescharacteristic
226C22×C4—21no—
227C22×C4—2691no—
228C22×C4—2691no—
229C22×C4—2691no—
230C22×C4—5381no—
231C22×C4—5381no—
232SD16—5384no—
233SD16—5384no—
234D8—24no—
235D8—5384no—
236M16—5384no—
237C2×C8—2692no—
238C2×C8C22×D26912yes—
239C4⋊C4—2691no—
240C4⋊C4—5381no—
241C4⋊C4—5381no—
242C4⋊C4C22×D26911yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—5381no—
245C22⋊C4—5381no—
246C42—2691no—
247C42—2691no—
248C42—2691no—
249C42—5381no—
250C42—5381no—
251C42—5381no—
252C42C22×D26911yescharacteristic
253C23—21no—
254C23—22no—
255C23—2691no—
256C23—5382no—
257C23—10764no—
258C23—10764no—
259C23—10764no—
260Q8—2692no—
261Q8—5381no—
262D4—22no—
263D4—21no—
264D4—22no—
265D4—42no—
266D4—42no—
267D4—5384no—
268D4—5382no—
269D4—5382no—
270D4—10762no—
271D4—10764no—
272D4—10764no—
273D4—10764no—
274D4—10762no—
275D4D4×D26912yescomplemented
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—2691no—
279C2×C4—2691no—
280C2×C4—2692no—
281C2×C4—2692no—
282C2×C4—2691no—
283C2×C4—5382no—
284C2×C4—5384no—
285C2×C4—5381no—
286C2×C4—5382no—
287C2×C4—5381no—
288C2×C4—10762no—
289C2×C4D4×D26911yescharacteristic
290C2×C4D4×D26911yescharacteristic
291C2×C4C23×D26911yescharacteristic
292C8—22no—
293C8—5382no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—2692no—
301C22—5381no—
302C22—5381no—
303C22—10762no—
304C22—10762no—
305C22—10762no—
306C22—21528no—
307C22C2×D4×D26911yescharacteristic
308C4—21no—
309C4—41no—
310C4—2692no—
311C4—2692no—
312C4—5382no—
313C4—5381no—
314C4—10761no—
315C4#2257547712yescomplemented
316C4C2×D4×D26911yescharacteristic
317C4#41×D26911yescharacteristic
318C2—42no—
319C2—82no—
320C2—5382no—
321C2—21522no—
322C2#121×D26911yescharacteristic
323C2AGL(1,ℤ/8)×D26911yescharacteristic
324C2C2×#2257547711yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#459×C269C2
socleC22×C269C22×D4
hypercenter#459D269
hypocenterC269#3038
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#22575477C2semidirect
2. #127×D269C2semidirect
3. C4×#16864401C2semidirect
4. #31770806C2semidirect
5. #31770804C2semidirect
6. #31770802C2semidirect
7. #31770800C2semidirect
8. #31770798C2semidirect
9. #31770627C2semidirect
10. #31770608C2semidirect
11. #459×C269C2semidirect
17. C2×#16864391C22semidirect
18. C2×#16864390C22semidirect
19. C2×#16864387C22semidirect
25. C4×Dic538C22semidirect
26. #22575418C22semidirect
27. D4×Dic269C22semidirect
34. C4⋊#14524130C22semidirect
35. #22575382C22semidirect
36. #22575375C22semidirect
37. #22575374C22semidirect
38. #22575373C22semidirect
39. C2×D8×C269C22semidirect
41. C4×D4×C269C22semidirect
42. C4⋊C8×C269C22semidirect
43. #102×C269C22semidirect
46. #16864401D4semidirect
96. Dic538C2×D4semidirect
124. D4×C269C2×D4semidirect
147. C4×C269AGL(1,ℤ/8)semidirect
154. Dic269AGL(1,ℤ/8)semidirect
162. C269#3038semidirect
172. #459D269semidirect
183. C2×D8C2×D269semidirect
195. C4×D4C2×D269semidirect
202. C4⋊C8C2×D269semidirect
206. #102C2×D269semidirect
275. D4D4×D269semidirect
315. C4#22575477semidirect

Maximal subgroups

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

subgroupindex
C2×#225754772
#127×D2692
C4×#168644012
#317708062
#317708042
#317708022
#317708002
#317707982
#317706272
#317706082
#459×C2692
#3038269