Finite Group Databasebeta

← #46822567

Subgroups — #46822567

Order 34432.

526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22575476C211yesmaximal, characteristic, complemented
2C22×D2152C211yesmaximal, characteristic, complemented
3#31771246C212yesmaximal, complemented
4#31770990C211yesmaximal, characteristic, complemented
5#31770842C211yesmaximal, characteristic, complemented
6#31770823C212yesmaximal, complemented
7#31770755C212yesmaximal, complemented
8#31770753C212yesmaximal, complemented
9#31770687C211yesmaximal, characteristic, complemented
10C8×C22⋊D269C211yesmaximal, characteristic, complemented
11#467×C269C211yesmaximal, characteristic, complemented
12C2×#16864403C2212yescomplemented
13C22×D1076C2212yes—
14#22575476—24no—
15C2×#16864389C2212yescomplemented
16C2×#16864389C2212yescomplemented
17C2×D2152—24no—
18C2×D2152C2211yescharacteristic
19C2×D2152C2212yes—
20C2×D2152C2211yescharacteristic
21C2×C8×D269C2211yescharacteristic, complemented
22#22575442C2212yescomplemented
23#22575438—22no—
24#22575428—22no—
25#22575428C2212yescomplemented
26#22575423—22no—
27#22575415C2212yescomplemented
28C4×C22⋊D269C2211yescharacteristic
29C22⋊C4×D269—22no—
30#22575382C2211yescharacteristic, complemented
31#22575373C2212yescomplemented
32#22575373C2212yescomplemented
33C22⋊#14524130C2211yescharacteristic
34#22575365C2211yescharacteristic, complemented
35C8×Dic269C2211yescharacteristic, complemented
36C2×Q16×C269C2211yescharacteristic, complemented
37C22×C8×C269C2211yescharacteristic
38C22⋊Q8×C269C2212yes—
39#107×C269C2211yescharacteristic, complemented
40#103×C269C2212yescomplemented
41C23×D269—22no—
42#16864403—24no—
43#16864403—42no—
44C2×D1076—24no—
45C2×D1076—22no—
46C2×D1076—22no—
47C2×D1076—22no—
48C2×D1076—42no—
49C2×D1076C2312yes—
50C2×D1076C2312yes—
51C2×C22⋊D269D411yescharacteristic
52C2×C4×D269—22no—
53C2×C4×D269—22no—
54C2×C4×D269C2311yescharacteristic
55#16864389—24no—
56#16864389—42no—
57D2152—24no—
58D2152—22no—
59D2152D414yescomplemented
60C2×#14524130C2311yescharacteristic
61C2×#14524130C2311yescharacteristic
62C8×D269—22no—
63#16864381D411yescharacteristic
64C22⋊Dic269D411yescharacteristic
65#16864379—22no—
66#16864379—22no—
67#16864379—22no—
68#16864379—22no—
69#16864379D411yescharacteristic
70C4×Dic269C2311yescharacteristic
71C2×Q8×C269C2312yes—
72C22×C4×C269C2311yescharacteristic
73Q16×C269—22no—
74C2×C8×C269—22no—
75C2×C8×C269C2311yescharacteristic
76C2×C8×C269C2311yescharacteristic
77C4⋊C4×C269—22no—
78C4⋊C4×C269C2312yes—
79C22⋊C4×C269—22no—
80C22×D269—22no—
81C22×D269—22no—
82C22×D269—44no—
83C22×D269—44no—
84C22×D269—82no—
85C22×D269C2×D411yescharacteristic
86D1076—22no—
87D1076—22no—
88D1076—22no—
89D1076—44no—
90D1076—44no—
91D1076—82no—
92D1076C2×D414yes—
93C22⋊D269—22no—
94C2×Dic269C2×D411yescharacteristic
95C2×Dic269C2×D411yescharacteristic
96C2×Dic269C2×D411yescharacteristic
97C4×D269—21no—
98C4×D269—21no—
99C4×D269—44no—
100C4×D269—82no—
101#14524130—21no—
102#14524130—21no—
103C23×C269C2×D411yescharacteristic
104Q8×C269—22no—
105Q8×C269—22no—
106C2×C4×C269—21no—
107C2×C4×C269—21no—
108C2×C4×C269—22no—
109C2×C4×C269—22no—
110C2×C4×C269C2×D411yescharacteristic
111C2×C4×C269C2411yescharacteristic
112C8×C269—21no—
113C8×C269C2×D412yes—
114C22×C269—21no—
115C22×C269—21no—
116C22×C269#13512yescomplemented
117C22×C269C22×D411yescharacteristic
118C2×D269—21no—
119C2×D269—24no—
120C2×D269—21no—
121C2×D269—21no—
122C2×D269—42no—
123C2×D269—42no—
124C2×D269—42no—
125C2×D269—42no—
126C2×D269—42no—
127C2×D269—88no—
128C4×C269—21no—
129C4×C269—42no—
130C4×C269—42no—
131C4×C269C22×D411yescharacteristic
132C4×C269H(5,𝔽2)11yescharacteristic
133Dic269—21no—
134Dic269—21no—
135Dic269—21no—
136C2×C269—22no—
137C2×C269D4211yescharacteristic
138C2×C269C2×#13511yescharacteristic
139C2×C269#57611yescharacteristic
140D269—41no—
141D269—44no—
142D269—82no—
143C269#328011yescharacteristic, complemented, Sylow
144#3280—2691nomaximal, Sylow
145C2×#135—2691no—
146C22×D8—2691no—
147#546—2692no—
148#495—2691no—
149#467D26911yescharacteristic, complemented
150#466—2691no—
151#463—2692no—
152#450—2692no—
153#449—2692no—
154C4×D8—2691no—
155C8×D4—2691no—
156C2×#41—2692no—
157C22×D4—2692no—
158#135—5384no—
159C2×Q16C2×D26911yescharacteristic, complemented
160C2×SD16—2692no—
161C2×SD16—2692no—
162C2×D8—2691no—
163C2×D8—2692no—
164C2×D8—2691no—
165C2×D8—5384no—
166C22×C8—2691no—
167C22×C8C2×D26911yescharacteristic
168#124—2692no—
169#123—5382no—
170C22⋊Q8C2×D26912yes—
171#121—2692no—
172#121—5382no—
173#120—5382no—
174C4×D4—2691no—
175C4×D4—2692no—
176C2×C22⋊C4—5382no—
177#107C2×D26911yescharacteristic, complemented
178C4⋊C8—2691no—
179#103C2×D26912yescomplemented
180#102—2692no—
181#102—2692no—
182C22⋊C8—2691no—
183C22⋊C8—2691no—
184C4×C8—2691no—
185C24—5382no—
186#41—5384no—
187#41—10762no—
188C2×Q8C22×D26912yes—
189C2×D4—2691no—
190C2×D4—2692no—
191C2×D4—2692no—
192C2×D4—5384no—
193C2×D4—5382no—
194C2×D4—5382no—
195C2×D4—5382no—
196C2×D4—10762no—
197C22×C4—2691no—
198C22×C4—5382no—
199C22×C4—5382no—
200C22×C4C22×D26911yescharacteristic
201Q16—22no—
202SD16—5384no—
203SD16—10762no—
204D8—2694no—
205D8—5384no—
206D8—5382no—
207C2×C8—22no—
208C2×C8—2691no—
209C2×C8—2691no—
210C2×C8—5382no—
211C2×C8C22×D26911yescharacteristic
212C2×C8C22×D26911yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—2691no—
215C4⋊C4C22×D26912yes—
216C22⋊C4—22no—
217C22⋊C4—2691no—
218C22⋊C4—2691no—
219C22⋊C4—5382no—
220C22⋊C4—5382no—
221C22⋊C4—5382no—
222C22⋊C4—5382no—
223C42—2691no—
224C23—2691no—
225C23—5382no—
226C23—5382no—
227C23—10764no—
228C23—10764no—
229C23—21522no—
230C23D4×D26911yescharacteristic
231Q8—22no—
232Q8—22no—
233D4—2694no—
234D4—5382no—
235D4—5382no—
236D4—5382no—
237D4—5382no—
238D4—10764no—
239D4—10764no—
240D4—21522no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—2691no—
246C2×C4—2691no—
247C2×C4—2691no—
248C2×C4—5381no—
249C2×C4—5381no—
250C2×C4—10764no—
251C2×C4—21522no—
252C2×C4D4×D26911yescharacteristic
253C2×C4C23×D26911yescharacteristic
254C8—21no—
255C8—5381no—
256C8—5381no—
257C8D4×D26912yes—
258C22—21no—
259C22—21no—
260C22—5381no—
261C22—5381no—
262C22—5384no—
263C22—5381no—
264C22—10762no—
265C22—10762no—
266C22—10762no—
267C22—10762no—
268C22—10762no—
269C22—21528no—
270C22#2257547612yescomplemented
271C22C2×D4×D26911yescharacteristic
272C4—21no—
273C4—42no—
274C4—42no—
275C4—5381no—
276C4—5381no—
277C4—5381no—
278C4C2×D4×D26911yescharacteristic
279C4#2257549911yescharacteristic
280C2—22no—
281C2—10761no—
282C2—10764no—
283C2—21522no—
284C2#3177123911yescharacteristic
285C2C2×#2257547611yescharacteristic
286C2#3177140711yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#467×C269C2
socleC22×C269C22×D4
hypercenter#467D269
hypocenterC269#3280
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#22575476C2semidirect
2. C22×D2152C2semidirect
3. #31771246C2semidirect
4. #31770990C2semidirect
5. #31770842C2semidirect
6. #31770823C2semidirect
7. #31770755C2semidirect
8. #31770753C2semidirect
9. #31770687C2semidirect
10. C8×C22⋊D269C2semidirect
11. #467×C269C2semidirect
12. C2×#16864403C22semidirect
15. C2×#16864389C22semidirect
16. C2×#16864389C22semidirect
21. C2×C8×D269C22semidirect
22. #22575442C22semidirect
25. #22575428C22semidirect
27. #22575415C22semidirect
30. #22575382C22semidirect
31. #22575373C22semidirect
32. #22575373C22semidirect
34. #22575365C22semidirect
35. C8×Dic269C22semidirect
36. C2×Q16×C269C22semidirect
39. #107×C269C22semidirect
40. #103×C269C22semidirect
59. D2152D4semidirect
116. C22×C269#135semidirect
143. C269#3280semidirect
149. #467D269semidirect
159. C2×Q16C2×D269semidirect
177. #107C2×D269semidirect
179. #103C2×D269semidirect
270. C22#22575476semidirect

Maximal subgroups

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

subgroupindex
C2×#225754762
C22×D21522
#317712462
#317709902
#317708422
#317708232
#317707552
#317707532
#317706872
C8×C22⋊D2692
#467×C2692
#3280269