Finite Group Databasebeta

← #46809451

Subgroups — #46809451

Order 34432.

340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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#121×D269C211yesmaximal, characteristic
2C22⋊C8×D269C211yesmaximal, characteristic, complemented
3#31770464C211yesmaximal, characteristic, complemented
4#31770340C211yesmaximal, characteristic, complemented
5#31770339C211yesmaximal, characteristic, complemented
6#31770338C211yesmaximal, characteristic, complemented
7#327×C269C211yesmaximal, characteristic, complemented
8C2×D4×D269—21no—
9C2×D4×D269C411yescharacteristic, complemented
10C22×C4×D269C2211yescharacteristic
11C2×C8×D269—21no—
12#22575428C411yescharacteristic, complemented
13#22575427C2211yescharacteristic
14#22575426—21no—
15#22575425—21no—
16#22575424C411yescharacteristic, complemented
17C2×#16864381—21no—
18C4⋊C4×D269C411yescharacteristic, complemented
19C2×#16864379—21no—
20C22⋊C4×D269—21no—
21C22⋊#14524130C2211yescharacteristic, complemented
22#22575365—21no—
23#22575360C2211yescharacteristic, complemented
24#121×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic, complemented
26#95×C269C2211yescharacteristic, complemented
27C23×D269—21no—
28C23×D269D411yescharacteristic
29C2×D1076—21no—
30C2×D1076C2×C411yescharacteristic
31C2×C22⋊D269—21no—
32C2×C22⋊D269—21no—
33C2×C22⋊D269—21no—
34D4×D269—42no—
35D4×D269—42no—
36D4×D269—42no—
37C22×Dic269—21no—
38C22×Dic269D411yescharacteristic
39C2×C4×D269—21no—
40C2×C4×D269—42no—
41C2×C4×D269C2×C411yescharacteristic
42C2×C4×D269C2×C411yescharacteristic
43C2×C4×D269D411yescharacteristic
44C2×C4×D269D411yescharacteristic
45C2×#14524130—21no—
46C8×D269—42no—
47C4⋊Dic269C2×C411yescharacteristic
48#16864381—21no—
49#16864381—42no—
50C22⋊Dic269—21no—
51#16864379—21no—
52#16864379—21no—
53#16864379—42no—
54C2×D4×C269—21no—
55C2×D4×C269C2×C411yescharacteristic
56C22×C4×C269—21no—
57C22×C4×C269C2311yescharacteristic
58C2×C8×C269—21no—
59C4⋊C4×C269C2×C411yescharacteristic
60C22⋊C4×C269—21no—
61C22×D269—21no—
62C22×D269—41no—
63C22×D269—41no—
64C22×D269—42no—
65C22×D269—42no—
66C22×D269—42no—
67C22×D269C22⋊C411yescharacteristic
68C22×D269C22⋊C411yescharacteristic
69C22×D269D812yes—
70C22×D269SD1612yes—
71D1076—41no—
72D1076—42no—
73C22⋊D269—41no—
74C22⋊D269—41no—
75C22⋊D269—42no—
76C22⋊D269—42no—
77C2×Dic269—22no—
78C2×Dic269—21no—
79C2×Dic269—41no—
80C2×Dic269—41no—
81C2×Dic269—41no—
82C2×Dic269C22⋊C411yescharacteristic
83C2×Dic269C22⋊C411yescharacteristic
84C4×D269—22no—
85C4×D269—22no—
86C4×D269—41no—
87C4×D269—41no—
88C4×D269—42no—
89#14524130—41no—
90C23×C269—21no—
91C23×C269C2×D411yescharacteristic
92D4×C269—41no—
93D4×C269—41no—
94D4×C269—41no—
95C2×C4×C269—21no—
96C2×C4×C269—41no—
97C2×C4×C269—41no—
98C2×C4×C269—41no—
99C2×C4×C269—41no—
100C2×C4×C269C22×C411yescharacteristic
101C2×C4×C269C2×D411yescharacteristic
102C8×C269—41no—
103C22×C269—21no—
104C22×C269—21no—
105C22×C269—41no—
106C22×C269—41no—
107C22×C269—41no—
108C22×C269C2×C22⋊C411yescharacteristic
109C22×C269C2×D811yescharacteristic
110C22×C269C2×SD1611yescharacteristic
111C2×D269—21no—
112C2×D269—21no—
113C2×D269—21no—
114C2×D269—21no—
115C2×D269—42no—
116C2×D269—42no—
117C2×D269—41no—
118C2×D269—41no—
119C2×D269—41no—
120C2×D269—84no—
121C2×D269#10212yes—
122C2×D269#10212yes—
123C4×C269—21no—
124C4×C269—21no—
125C4×C269—41no—
126C4×C269—81no—
127Dic269—21no—
128Dic269—41no—
129Dic269—81no—
130Dic269#9912yes—
131C2×C269—21no—
132C2×C269—21no—
133C2×C269—81no—
134C2×C269C2×#9911yescharacteristic
135C2×C269C2×#10211yescharacteristic
136C2×C269#42111yescharacteristic
137D269—22no—
138D269—22no—
139D269—81no—
140C269#151911yescharacteristic, complemented, Sylow
141#1519—2691nomaximal, Sylow
142C2×#121—2691no—
143C2×C22⋊C8—2691no—
144#380—2691no—
145#327—2691no—
146#327—2691no—
147#327—2691no—
148#327D26911yescharacteristic, complemented
149C22×D4—2691no—
150C22×D4—5381no—
151C23×C4—2691no—
152C22×C8—5381no—
153#121—2691no—
154#121—2691no—
155#121—2691no—
156#121—5381no—
157#121—5381no—
158#121C2×D26911yescharacteristic
159C2×C4⋊C4—2691no—
160C2×C4⋊C4—5381no—
161C2×C22⋊C4—5381no—
162C2×C22⋊C4—5381no—
163C22⋊C8—2691no—
164C22⋊C8—5381no—
165C22⋊C8C2×D26911yescharacteristic, complemented
166#95—2691no—
167#95C2×D26911yescharacteristic, complemented
168C24—2691no—
169C24—5381no—
170C2×D4—21no—
171C2×D4—2691no—
172C2×D4—5381no—
173C2×D4—5381no—
174C2×D4—5381no—
175C2×D4—5381no—
176C2×D4—10762no—
177C2×D4—10762no—
178C2×D4—10762no—
179C2×D4C4×D26911yescharacteristic
180C22×C4—21no—
181C22×C4—2691no—
182C22×C4—2691no—
183C22×C4—2691no—
184C22×C4—2691no—
185C22×C4—2691no—
186C22×C4—5381no—
187C22×C4—5381no—
188C22×C4—10762no—
189C22×C4C22×D26911yescharacteristic
190C2×C8—21no—
191C2×C8—5381no—
192C2×C8—10762no—
193C4⋊C4—2691no—
194C4⋊C4—5381no—
195C4⋊C4—10762no—
196C4⋊C4C4×D26911yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—5381no—
199C22⋊C4—5381no—
200C22⋊C4—5381no—
201C22⋊C4—10762no—
202C23—21no—
203C23—2691no—
204C23—2691no—
205C23—2692no—
206C23—2692no—
207C23—5381no—
208C23—10761no—
209C23—10761no—
210C23—10762no—
211C23—10762no—
212C23—10762no—
213C23D4×D26911yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—10761no—
218D4—10762no—
219D4—10762no—
220D4—10762no—
221D4—10761no—
222D4—10761no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—2691no—
229C2×C4—2691no—
230C2×C4—5382no—
231C2×C4—5382no—
232C2×C4—5382no—
233C2×C4—5381no—
234C2×C4—10761no—
235C2×C4—10761no—
236C2×C4—10762no—
237C2×C4—10761no—
238C2×C4—10761no—
239C2×C4—10761no—
240C2×C4C2×C4×D26911yescharacteristic
241C2×C4D4×D26911yescharacteristic
242C8—41no—
243C8—10761no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—2692no—
250C22—2692no—
251C22—5381no—
252C22—5381no—
253C22—5381no—
254C22—5381no—
255C22—10762no—
256C22—10762no—
257C22—10761no—
258C22—10761no—
259C22—10761no—
260C22—21524no—
261C22C22⋊C4×D26911yescharacteristic
262C22D8×D26911yescharacteristic
263C22SD16×D26911yescharacteristic
264C4—21no—
265C4—21no—
266C4—41no—
267C4—81no—
268C4—2692no—
269C4—5381no—
270C4—10761no—
271C4—21521no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—5382no—
276C2—5382no—
277C2—21521no—
278C2#99×D26911yescharacteristic
279C2#102×D26911yescharacteristic
280C2#3177062011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#327×C269C2
socleC22×C269C2×C22⋊C4
prime radical#121×D269C2
cosocleC22×C4×C269C23
hypercenter#327D269
hypocenterC269#1519
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. C22⋊C8×D269C2semidirect
3. #31770464C2semidirect
4. #31770340C2semidirect
5. #31770339C2semidirect
6. #31770338C2semidirect
7. #327×C269C2semidirect
9. C2×D4×D269C4semidirect
12. #22575428C4semidirect
16. #22575424C4semidirect
18. C4⋊C4×D269C4semidirect
21. C22⋊#14524130C22semidirect
23. #22575360C22semidirect
25. C22⋊C8×C269C22semidirect
26. #95×C269C22semidirect
140. C269#1519semidirect
148. #327D269semidirect
165. C22⋊C8C2×D269semidirect
167. #95C2×D269semidirect

Maximal subgroups

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

subgroupindex
#121×D2692
C22⋊C8×D2692
#317704642
#317703402
#317703392
#317703382
#327×C2692
#1519269