Finite Group Databasebeta

← #46809386

Subgroups — #46809386

Order 34432.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#31771115C211yesmaximal, characteristic
2#31770567C211yesmaximal, characteristic, complemented
3#95×D269C211yesmaximal, characteristic, complemented
4#31770343C211yesmaximal, characteristic, complemented
5#31770341C211yesmaximal, characteristic, complemented
6#31770339C211yesmaximal, characteristic, complemented
7#327×C269C211yesmaximal, characteristic, complemented
8C2×#16864401C411yescharacteristic, complemented
9C22×C4×D269—21no—
10C22×C4×D269C2211yescharacteristic
11C2×#16864385—21no—
12#22575435—21no—
13#22575433C411yescharacteristic, complemented
14#22575432C2211yescharacteristic
15#22575424C411yescharacteristic, complemented
16#22575421—21no—
17D4×Dic269—21no—
18#22575413—21no—
19#22575411C411yescharacteristic, complemented
20C22⋊#14524130C2211yescharacteristic
21#22575365—21no—
22#22575360—21no—
23#22575360C2211yescharacteristic
24#121×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic
26#95×C269C2211yescharacteristic
27C23×D269D411yescharacteristic
28#16864401—42no—
29C2×Dic538C2×C411yescharacteristic, complemented
30C2×C22⋊D269—21no—
31C2×C22⋊D269—21no—
32C22×Dic269—21no—
33C22×Dic269—21no—
34C22×Dic269D411yescharacteristic
35C2×C4×D269—24no—
36C2×C4×D269—42no—
37C2×C4×D269—42no—
38C2×C4×D269—42no—
39C2×C4×D269C2×C411yescharacteristic
40C2×C4×D269C2×C411yescharacteristic
41C2×C4×D269D411yescharacteristic
42C2×C4×D269D411yescharacteristic
43#16864385—42no—
44C2×#14524130—21no—
45C4⋊Dic269—21no—
46C4⋊Dic269C2×C411yescharacteristic, complemented
47#16864381—21no—
48C22⋊Dic269—21no—
49C22⋊Dic269—21no—
50#16864379—21no—
51#16864379—21no—
52C4×Dic269—21no—
53C2×D4×C269—21no—
54C2×D4×C269C2×C411yescharacteristic, complemented
55C22×C4×C269—21no—
56C22×C4×C269C2311yescharacteristic
57C2×C8×C269—21no—
58C4⋊C4×C269C2×C411yescharacteristic, complemented
59C22⋊C4×C269—21no—
60C22×D269—21no—
61C22×D269—21no—
62C22×D269—22no—
63C22×D269—22no—
64C22×D269C22⋊C411yescharacteristic
65C22×D269C22⋊C411yescharacteristic
66Dic538—41no—
67C22⋊D269—42no—
68C22⋊D269—42no—
69C2×Dic269—22no—
70C2×Dic269—21no—
71C2×Dic269—21no—
72C2×Dic269—41no—
73C2×Dic269—42no—
74C2×Dic269—41no—
75C2×Dic269—41no—
76C2×Dic269C22⋊C411yescharacteristic
77C2×Dic269C22⋊C411yescharacteristic
78C4×D269—22no—
79C4×D269—22no—
80C4×D269—41no—
81C4×D269—41no—
82C4×D269—48no—
83#14524130—41no—
84C23×C269—21no—
85C23×C269C2×D411yescharacteristic
86D4×C269—41no—
87D4×C269—41no—
88D4×C269—41no—
89C2×C4×C269—22no—
90C2×C4×C269—21no—
91C2×C4×C269—41no—
92C2×C4×C269—41no—
93C2×C4×C269—41no—
94C2×C4×C269C22×C411yescharacteristic
95C2×C4×C269C2×D411yescharacteristic
96C8×C269—41no—
97C22×C269—21no—
98C22×C269—21no—
99C22×C269—41no—
100C22×C269—41no—
101C22×C269—41no—
102C22×C269C2×C22⋊C411yescharacteristic
103C22×C269AGL(1,ℤ/8)11yescharacteristic
104C22×C269#13711yescharacteristic
105C2×D269—24no—
106C2×D269—24no—
107C2×D269—21no—
108C2×D269—21no—
109C2×D269—21no—
110C2×D269—21no—
111C2×D269#9912yes—
112C2×D269#10412yes—
113C4×C269—21no—
114C4×C269—21no—
115C4×C269—42no—
116C4×C269—41no—
117Dic269—21no—
118Dic269—21no—
119Dic269—42no—
120Dic269—41no—
121Dic269—41no—
122C2×C269—21no—
123C2×C269—21no—
124C2×C269—81no—
125C2×C269C2×#9911yescharacteristic
126C2×C269#41711yescharacteristic
127C2×C269C2×#10411yescharacteristic
128D269—22no—
129D269—22no—
130C269#150411yescharacteristic, complemented, Sylow
131#1504—2691nomaximal, Sylow
132#525—2691no—
133#407—2691no—
134C2×#95—2691no—
135#328—2691no—
136#328—2691no—
137#327—2691no—
138#327D26911yescharacteristic, complemented
139C2×#41—2691no—
140C23×C4—2691no—
141C23×C4—5381no—
142C2×M16—5381no—
143#123—5381no—
144C22⋊Q8—2691no—
145C22⋊Q8—2691no—
146#121—2691no—
147#121C2×D26911yescharacteristic
148#120—5381no—
149C4×D4—5381no—
150C4×D4—5381no—
151#117—2691no—
152C22⋊C8—2691no—
153C22⋊C8—5381no—
154C22⋊C8C2×D26911yescharacteristic
155#95—2691no—
156#95—5381no—
157#95C2×D26911yescharacteristic
158C24—2691no—
159#41—10762no—
160C2×Q8—2691no—
161C2×D4—21no—
162C2×D4—5381no—
163C2×D4—5381no—
164C2×D4C4×D26911yescharacteristic, complemented
165C22×C4—21no—
166C22×C4—2691no—
167C22×C4—2691no—
168C22×C4—2691no—
169C22×C4—2691no—
170C22×C4—2691no—
171C22×C4—5384no—
172C22×C4—5381no—
173C22×C4—5381no—
174C22×C4—10762no—
175C22×C4—10762no—
176C22×C4—10762no—
177C22×C4C22×D26911yescharacteristic
178M16—10762no—
179C2×C8—21no—
180C2×C8—5381no—
181C4⋊C4—2691no—
182C4⋊C4—5381no—
183C4⋊C4—5381no—
184C4⋊C4C4×D26911yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—5381no—
187C22⋊C4—5381no—
188C22⋊C4—5381no—
189C22⋊C4—5381no—
190C42—5381no—
191C23—21no—
192C23—2691no—
193C23—2691no—
194C23—5382no—
195C23—5382no—
196C23—5381no—
197C23—5381no—
198C23D4×D26911yescharacteristic
199Q8—10761no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—10762no—
204D4—10762no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—2691no—
211C2×C4—2691no—
212C2×C4—5382no—
213C2×C4—5382no—
214C2×C4—5382no—
215C2×C4—5381no—
216C2×C4—5381no—
217C2×C4—10761no—
218C2×C4—10761no—
219C2×C4—10768no—
220C2×C4—10761no—
221C2×C4—10762no—
222C2×C4—10761no—
223C2×C4—10761no—
224C2×C4C2×C4×D26911yescharacteristic
225C2×C4D4×D26911yescharacteristic
226C8—41no—
227C8—10761no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—2692no—
234C22—2692no—
235C22—5384no—
236C22—5384no—
237C22—5381no—
238C22—5381no—
239C22—5381no—
240C22—5381no—
241C22C22⋊C4×D26911yescharacteristic
242C22#2257547711yescharacteristic
243C22#2257548211yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—5381no—
249C4—5381no—
250C4—10762no—
251C4—10761no—
252C4—10761no—
253C2—21no—
254C2—21no—
255C2—81no—
256C2—5382no—
257C2—5382no—
258C2#99×D26911yescharacteristic
259C2#3177060311yescharacteristic
260C2#104×D26911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#327×C269C2
socleC22×C269C2×C22⋊C4
prime radical#31771115C2
cosocleC22×C4×C269C23
hypercenter#327D269
hypocenterC269#1504
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #31770567C2semidirect
3. #95×D269C2semidirect
4. #31770343C2semidirect
5. #31770341C2semidirect
6. #31770339C2semidirect
7. #327×C269C2semidirect
8. C2×#16864401C4semidirect
13. #22575433C4semidirect
15. #22575424C4semidirect
19. #22575411C4semidirect
29. C2×Dic538C2×C4semidirect
46. C4⋊Dic269C2×C4semidirect
54. C2×D4×C269C2×C4semidirect
58. C4⋊C4×C269C2×C4semidirect
130. C269#1504semidirect
138. #327D269semidirect
164. C2×D4C4×D269semidirect
184. C4⋊C4C4×D269semidirect

Maximal subgroups

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

subgroupindex
#317711152
#317705672
#95×D2692
#317703432
#317703412
#317703392
#327×C2692
#1504269