Finite Group Databasebeta

← #46822584

Subgroups — #46822584

Order 34432.

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

normal subgroups only

This group has 546 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×SD16×D269C212yesmaximal, complemented
2#31771270C211yesmaximal, characteristic, complemented
3D4×D1076C211yesmaximal, characteristic
4#31770979C211yesmaximal, characteristic, complemented
5#31770837C212yesmaximal, complemented
6#31770806C211yesmaximal, characteristic, complemented
7#31770754C212yesmaximal, complemented
8#31770745C212yesmaximal, complemented
9C4×#16864390C211yesmaximal, characteristic, complemented
10#31770670C211yesmaximal, characteristic, complemented
11#461×C269C211yesmaximal, characteristic, complemented
12C2×Q8×D269C2212yescomplemented
13C22×D1076—21no—
14C2×D4×D269C2212yes—
15C2×#16864391C2212yescomplemented
16C2×#16864390C2211yescharacteristic
17C2×#16864389C2212yescomplemented
18C2×#16864389C2212yescomplemented
19SD16×D269—28no—
20C2×C8×D269C2212yescomplemented
21#22575452—21no—
22#22575450C2211yescharacteristic
23#22575431—22no—
24#22575429C2212yescomplemented
25#22575428C2212yes—
26#22575427—21no—
27#22575423—22no—
28C4×Dic538C2211yescharacteristic, complemented
29C4×D1076C2211yescharacteristic
30#22575415—21no—
31#22575384C2211yescharacteristic, complemented
32#22575376C2211yescharacteristic, complemented
33#22575375C2212yescomplemented
34#22575374C2211yescharacteristic
35#22575365C2212yescomplemented
36C4×#14524130C2211yescharacteristic, complemented
37C2×SD16×C269C2212yes—
38C4⋊Q8×C269C2211yescharacteristic, complemented
39C4×D4×C269C2211yescharacteristic
40C4⋊C8×C269C2211yescharacteristic, complemented
41#103×C269C2212yescomplemented
42C23×D269—22no—
43C2×Dic538—22no—
44C2×Dic538C2311yescharacteristic
45Q8×D269—24no—
46Q8×D269—42no—
47C2×D1076—22no—
48C2×D1076—21no—
49C2×D1076—21no—
50C2×D1076—44no—
51C2×D1076D411yescharacteristic
52C2×D1076C2312yes—
53C2×C22⋊D269—22no—
54D4×D269—24no—
55D4×D269—42no—
56C2×C4×D269—22no—
57C2×C4×D269C2312yes—
58#16864391—24no—
59#16864390D414yescomplemented
60#16864389—24no—
61#16864389—42no—
62C2×#14524130C2311yescharacteristic
63C2×#14524130C2311yescharacteristic
64C8×D269—24no—
65C4⋊Dic269D411yescharacteristic
66C4⋊Dic269C2311yescharacteristic
67#16864381—22no—
68#16864381—21no—
69#16864379—22no—
70#16864379—22no—
71#16864379D412yes—
72C4×Dic269—21no—
73C2×Q8×C269C2312yes—
74C2×D4×C269C2311yescharacteristic
75C22×C4×C269—21no—
76SD16×C269—24no—
77C2×C8×C269C2312yes—
78C4⋊C4×C269—21no—
79C4⋊C4×C269—21no—
80C4⋊C4×C269C2311yescharacteristic
81C22⋊C4×C269—21no—
82C42×C269C2311yescharacteristic
83C22×D269—22no—
84C22×D269—44no—
85C22×D269—44no—
86C22×D269—82no—
87C22×D269C2×D412yes—
88Dic538—21no—
89Dic538—44no—
90Dic538C2×D412yescomplemented
91D1076—22no—
92D1076—22no—
93D1076—44no—
94D1076—42no—
95D1076—81no—
96D1076SD1614yescomplemented
97C22⋊D269—44no—
98C2×Dic269—21no—
99C2×Dic269—21no—
100C2×Dic269C2×D412yes—
101C4×D269—22no—
102C4×D269—22no—
103C4×D269—44no—
104#14524130—21no—
105#14524130C2×D412yescomplemented
106C23×C269—21no—
107Q8×C269—22no—
108Q8×C269—22no—
109D4×C269—21no—
110D4×C269C2×D412yes—
111C2×C4×C269—21no—
112C2×C4×C269—22no—
113C2×C4×C269—42no—
114C2×C4×C269C2×D411yescharacteristic
115C2×C4×C269C2×D411yescharacteristic
116C2×C4×C269C2411yescharacteristic
117C8×C269—22no—
118C22×C269—22no—
119C22×C269—41no—
120C22×C269—41no—
121C22×C269C22×D411yescharacteristic
122C2×D269—22no—
123C2×D269—22no—
124C2×D269—42no—
125C2×D269—42no—
126C2×D269—42no—
127C2×D269—88no—
128C2×D269C2×SD1614yescomplemented
129C4×C269—21no—
130C4×C269—42no—
131C4×C269—41no—
132C4×C269C2×SD1612yescomplemented
133C4×C269C22×D411yescharacteristic
134C4×C269H(5,𝔽2)11yescharacteristic
135Dic269—22no—
136Dic269—22no—
137Dic269—41no—
138C2×C269—42no—
139C2×C269D4211yescharacteristic
140C2×C269C22×SD1611yescharacteristic
141C2×C269#57711yescharacteristic
142D269—24no—
143D269—82no—
144C269D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—2691nomaximal, Sylow
146C22×SD16—2692no—
147D4×Q8—2691no—
148D42—2691no—
149#492—2691no—
150#465—2692no—
151#461D26911yescharacteristic, complemented
152#460—2691no—
153#450—2692no—
154#448—2692no—
155C4×SD16—2691no—
156C8×D4—2691no—
157C22×Q8—2692no—
158C22×D4—2692no—
159C22×D4—5381no—
160C2×SD16—2691no—
161C2×SD16—2692no—
162C2×SD16—2692no—
163C2×SD16—2692no—
164C2×SD16—5388no—
165C2×SD16C2×D26912yes—
166C22×C8—2692no—
167C4⋊Q8—5381no—
168C4⋊Q8C2×D26911yescharacteristic, complemented
169#127—2691no—
170C22⋊Q8—2692no—
171C22⋊Q8—5382no—
172#121—2692no—
173#121—5381no—
174#120—5382no—
175C4×Q8—2691no—
176C4×D4—2691no—
177C4×D4—5381no—
178C4×D4C2×D26911yescharacteristic
179#106—2691no—
180C4⋊C8C2×D26911yescharacteristic, complemented
181#103—2691no—
182#103C2×D26912yescomplemented
183#102—2691no—
184#102—2692no—
185C22⋊C8—2692no—
186C4×C8—2691no—
187C24—5382no—
188C2×Q8—2691no—
189C2×Q8—5382no—
190C2×Q8—5384no—
191C2×Q8—10762no—
192C2×Q8C22×D26912yes—
193C2×D4—2691no—
194C2×D4—2692no—
195C2×D4—5382no—
196C2×D4—5382no—
197C2×D4—5384no—
198C2×D4—5381no—
199C2×D4—5381no—
200C2×D4—10764no—
201C2×D4—10762no—
202C2×D4C22×D26911yescharacteristic
203C22×C4—21no—
204C22×C4—2692no—
205C22×C4—5382no—
206SD16—24no—
207SD16—2694no—
208SD16—5384no—
209SD16—5384no—
210SD16—10762no—
211C2×C8—2691no—
212C2×C8—2691no—
213C2×C8—5384no—
214C2×C8C22×D26912yes—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—2691no—
218C4⋊C4—2691no—
219C4⋊C4—5382no—
220C4⋊C4—5381no—
221C4⋊C4C22×D26911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—2692no—
224C22⋊C4—5382no—
225C22⋊C4—5382no—
226C42—5381no—
227C42C22×D26911yescharacteristic
228C23—21no—
229C23—2692no—
230C23—5382no—
231C23—10764no—
232C23—10764no—
233C23—21522no—
234Q8—22no—
235Q8—22no—
236Q8—2692no—
237Q8—5381no—
238Q8—10764no—
239D4—21no—
240D4—2694no—
241D4—5382no—
242D4—5382no—
243D4—10764no—
244D4—10764no—
245D4—10762no—
246D4—21521no—
247D4D4×D26912yes—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—2692no—
252C2×C4—5381no—
253C2×C4—5382no—
254C2×C4—5382no—
255C2×C4—5381no—
256C2×C4—10764no—
257C2×C4D4×D26911yescharacteristic
258C2×C4D4×D26911yescharacteristic
259C2×C4C23×D26911yescharacteristic
260C8—22no—
261C8—2692no—
262C8—5381no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—2694no—
267C22—5382no—
268C22—5382no—
269C22—10762no—
270C22—10762no—
271C22—10762no—
272C22—21528no—
273C22C2×D4×D26911yescharacteristic
274C4—21no—
275C4—42no—
276C4—41no—
277C4—5382no—
278C4—5382no—
279C4—10761no—
280C4SD16×D26912yescomplemented
281C4C2×D4×D26911yescharacteristic
282C4#2257549911yescharacteristic
283C2—42no—
284C2—5384no—
285C2—21522no—
286C2#3177123911yescharacteristic
287C2C2×SD16×D26911yescharacteristic
288C2#3177141411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#461×C269C2
socleC22×C269C22×D4
prime radicalD4×D1076C2
hypercenter#461D269
hypocenterC269D4×SD16
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D269C2semidirect
2. #31771270C2semidirect
4. #31770979C2semidirect
5. #31770837C2semidirect
6. #31770806C2semidirect
7. #31770754C2semidirect
8. #31770745C2semidirect
9. C4×#16864390C2semidirect
10. #31770670C2semidirect
11. #461×C269C2semidirect
12. C2×Q8×D269C22semidirect
15. C2×#16864391C22semidirect
17. C2×#16864389C22semidirect
18. C2×#16864389C22semidirect
20. C2×C8×D269C22semidirect
24. #22575429C22semidirect
28. C4×Dic538C22semidirect
31. #22575384C22semidirect
32. #22575376C22semidirect
33. #22575375C22semidirect
35. #22575365C22semidirect
36. C4×#14524130C22semidirect
38. C4⋊Q8×C269C22semidirect
40. C4⋊C8×C269C22semidirect
41. #103×C269C22semidirect
59. #16864390D4semidirect
90. Dic538C2×D4semidirect
96. D1076SD16semidirect
105. #14524130C2×D4semidirect
128. C2×D269C2×SD16semidirect
132. C4×C269C2×SD16semidirect
144. C269D4×SD16semidirect
151. #461D269semidirect
168. C4⋊Q8C2×D269semidirect
180. C4⋊C8C2×D269semidirect
182. #103C2×D269semidirect
280. C4SD16×D269semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D2692
#317712702
D4×D10762
#317709792
#317708372
#317708062
#317707542
#317707452
C4×#168643902
#317706702
#461×C2692
D4×SD16269