Finite Group Databasebeta

← #46822576

Subgroups — #46822576

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
2Q8×D1076C211yesmaximal, characteristic, complemented
3#31771240C211yesmaximal, characteristic
4#31770977C211yesmaximal, characteristic, complemented
5#31770833C212yesmaximal, complemented
6#31770811C211yesmaximal, characteristic, complemented
7#31770757C212yesmaximal, complemented
8#31770742C212yesmaximal, complemented
9C4×#16864389C211yesmaximal, characteristic, complemented
10#31770670C211yesmaximal, characteristic, complemented
11#460×C269C211yesmaximal, characteristic, complemented
12C2×Q8×D269C2212yescomplemented
13C2×D4×D269—21no—
14C2×D4×D269C2212yes—
15C2×#16864391C2212yes—
16C2×#16864390C2212yescomplemented
17C2×#16864390C2212yescomplemented
18C2×#16864389C2211yescharacteristic
19SD16×D269—28no—
20C2×C8×D269C2212yescomplemented
21#22575453—21no—
22#22575453C2211yescharacteristic, complemented
23#22575433—22no—
24#22575433C2212yescomplemented
25#22575424—21no—
26#22575424C2212yes—
27#22575421—22no—
28C4×D1076—21no—
29C4×D1076C2211yescharacteristic
30C4×D1076C2211yescharacteristic
31#22575384C2211yescharacteristic, complemented
32#22575378C2212yescomplemented
33#22575377C2211yescharacteristic, complemented
34#22575373C2211yescharacteristic
35#22575365C2212yescomplemented
36C4×#14524130C2211yescharacteristic, complemented
37C2×SD16×C269C2212yescomplemented
38#127×C269C2211yescharacteristic
39C4×Q8×C269C2211yescharacteristic, complemented
40C4⋊C8×C269C2211yescharacteristic, complemented
41#102×C269C2212yescomplemented
42C23×D269—22no—
43C2×Dic538—22no—
44C2×Dic538C2312yes—
45Q8×D269—24no—
46Q8×D269—42no—
47C2×D1076D411yescharacteristic
48C2×D1076C2311yescharacteristic
49C2×C22⋊D269—22no—
50C2×C22⋊D269—22no—
51D4×D269—24no—
52D4×D269—42no—
53D4×D269—44no—
54C2×C4×D269—22no—
55C2×C4×D269—21no—
56C2×C4×D269C2312yes—
57#16864391—24no—
58#16864390—24no—
59#16864390—42no—
60#16864389D414yescomplemented
61C2×#14524130C2311yescharacteristic
62C2×#14524130C2311yescharacteristic
63C8×D269—24no—
64C4⋊Dic269—22no—
65C4⋊Dic269—21no—
66C4⋊Dic269—21no—
67C4⋊Dic269D411yescharacteristic
68C4⋊Dic269C2311yescharacteristic
69C22⋊Dic269—22no—
70#16864379—22no—
71#16864379—21no—
72#16864379D412yes—
73C2×Q8×C269C2311yescharacteristic
74C2×D4×C269—21no—
75C2×D4×C269—21no—
76C2×D4×C269C2312yes—
77SD16×C269—24no—
78C2×C8×C269C2312yes—
79C4⋊C4×C269—21no—
80C4⋊C4×C269C2311yescharacteristic
81C42×C269—21no—
82C42×C269C2311yescharacteristic
83C22×D269—21no—
84C22×D269—44no—
85C22×D269—44no—
86C22×D269—82no—
87C22×D269C2×D412yes—
88Dic538—22no—
89Dic538—22no—
90Dic538—44no—
91D1076—21no—
92D1076SD1614yescomplemented
93D1076C2×D412yes—
94C22⋊D269—44no—
95C22⋊D269—44no—
96C2×Dic269—21no—
97C2×Dic269—22no—
98C2×Dic269C2×D412yes—
99C4×D269—22no—
100C4×D269—22no—
101C4×D269—44no—
102C4×D269—42no—
103#14524130—21no—
104#14524130C2×D412yescomplemented
105C23×C269—22no—
106Q8×C269—21no—
107Q8×C269C2×D412yescomplemented
108D4×C269—22no—
109D4×C269—22no—
110D4×C269—42no—
111D4×C269—81no—
112C2×C4×C269—21no—
113C2×C4×C269—21no—
114C2×C4×C269C2×D411yescharacteristic
115C2×C4×C269C2×D411yescharacteristic
116C2×C4×C269C2411yescharacteristic
117C8×C269—22no—
118C22×C269—42no—
119C22×C269—42no—
120C22×C269—42no—
121C22×C269C22×D411yescharacteristic
122C2×D269—22no—
123C2×D269—22no—
124C2×D269—22no—
125C2×D269—41no—
126C2×D269—41no—
127C2×D269—88no—
128C2×D269C2×SD1614yescomplemented
129C4×C269—22no—
130C4×C269—21no—
131C4×C269—41no—
132C4×C269C2×SD1612yescomplemented
133C4×C269C22×D411yescharacteristic
134C4×C269H(5,𝔽2)11yescharacteristic
135Dic269—22no—
136Dic269—42no—
137Dic269—41no—
138C2×C269—82no—
139C2×C269D4211yescharacteristic
140C2×C269C22×SD1611yescharacteristic
141C2×C269#57711yescharacteristic
142D269—24no—
143D269—42no—
144C269D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—2691nomaximal, Sylow
146C22×SD16—2692no—
147D4×Q8—2691no—
148D42—2691no—
149#492—2691no—
150#465—2692no—
151#461—2691no—
152#460D26911yescharacteristic, complemented
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×D26912yescomplemented
166C22×C8—2692no—
167C4⋊Q8—2691no—
168C4⋊Q8—5381no—
169#127C2×D26911yescharacteristic
170C22⋊Q8—2692no—
171C22⋊Q8—5382no—
172#121—2692no—
173#121—5381no—
174#120—5382no—
175C4×Q8C2×D26911yescharacteristic, complemented
176C4×D4—2691no—
177C4×D4—2691no—
178C4×D4—5381no—
179#106—2691no—
180C4⋊C8C2×D26911yescharacteristic, complemented
181#103—2691no—
182#103—2692no—
183#102—2691no—
184#102C2×D26912yescomplemented
185C22⋊C8—2692no—
186C4×C8—2691no—
187C24—5382no—
188C2×Q8—2692no—
189C2×Q8—5382no—
190C2×Q8—5384no—
191C2×Q8—10762no—
192C2×Q8C22×D26911yescharacteristic
193C2×D4—21no—
194C2×D4—21no—
195C2×D4—2691no—
196C2×D4—2691no—
197C2×D4—5382no—
198C2×D4—5384no—
199C2×D4—5382no—
200C2×D4—10762no—
201C2×D4—10764no—
202C2×D4C22×D26912yes—
203C22×C4—2692no—
204C22×C4—5382no—
205C22×C4—5381no—
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—2691no—
217C4⋊C4—2691no—
218C4⋊C4—5382no—
219C4⋊C4—5381no—
220C4⋊C4—5381no—
221C4⋊C4C22×D26911yescharacteristic
222C22⋊C4—2692no—
223C22⋊C4—5382no—
224C22⋊C4—5382no—
225C22⋊C4—5381no—
226C42—21no—
227C42C22×D26911yescharacteristic
228C23—22no—
229C23—2692no—
230C23—5381no—
231C23—10764no—
232C23—10764no—
233C23—21522no—
234Q8—21no—
235Q8—5382no—
236Q8—5382no—
237Q8—10764no—
238Q8D4×D26912yescomplemented
239D4—22no—
240D4—22no—
241D4—42no—
242D4—81no—
243D4—2694no—
244D4—2692no—
245D4—5381no—
246D4—10764no—
247D4—10764no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—2692no—
251C2×C4—5382no—
252C2×C4—5382no—
253C2×C4—5381no—
254C2×C4—5382no—
255C2×C4—10764no—
256C2×C4—10762no—
257C2×C4D4×D26911yescharacteristic
258C2×C4D4×D26911yescharacteristic
259C2×C4C23×D26911yescharacteristic
260C8—22no—
261C8—2692no—
262C8—5381no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—2694no—
267C22—5382no—
268C22—5382no—
269C22—5382no—
270C22—10761no—
271C22—10761no—
272C22—21528no—
273C22C2×D4×D26911yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—5382no—
278C4—10762no—
279C4—10761no—
280C4SD16×D26912yescomplemented
281C4C2×D4×D26911yescharacteristic
282C4#2257549911yescharacteristic
283C2—82no—
284C2—5384no—
285C2—10762no—
286C2#3177123911yescharacteristic
287C2C2×SD16×D26911yescharacteristic
288C2#3177141511yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#460×C269C2
socleC22×C269C22×D4
prime radical#31771240C2
hypercenter#460D269
hypocenterC269D4×SD16
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D269C2semidirect
2. Q8×D1076C2semidirect
4. #31770977C2semidirect
5. #31770833C2semidirect
6. #31770811C2semidirect
7. #31770757C2semidirect
8. #31770742C2semidirect
9. C4×#16864389C2semidirect
10. #31770670C2semidirect
11. #460×C269C2semidirect
12. C2×Q8×D269C22semidirect
16. C2×#16864390C22semidirect
17. C2×#16864390C22semidirect
20. C2×C8×D269C22semidirect
22. #22575453C22semidirect
24. #22575433C22semidirect
31. #22575384C22semidirect
32. #22575378C22semidirect
33. #22575377C22semidirect
35. #22575365C22semidirect
36. C4×#14524130C22semidirect
37. C2×SD16×C269C22semidirect
39. C4×Q8×C269C22semidirect
40. C4⋊C8×C269C22semidirect
41. #102×C269C22semidirect
60. #16864389D4semidirect
92. D1076SD16semidirect
104. #14524130C2×D4semidirect
107. Q8×C269C2×D4semidirect
128. C2×D269C2×SD16semidirect
132. C4×C269C2×SD16semidirect
144. C269D4×SD16semidirect
152. #460D269semidirect
165. C2×SD16C2×D269semidirect
175. C4×Q8C2×D269semidirect
180. C4⋊C8C2×D269semidirect
184. #102C2×D269semidirect
238. Q8D4×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
Q8×D10762
#317712402
#317709772
#317708332
#317708112
#317707572
#317707422
C4×#168643892
#317706702
#460×C2692
D4×SD16269