Finite Group Databasebeta

← #46809440

Subgroups — #46809440

Order 34432.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#31771118C211yesmaximal, characteristic
2C22⋊C8×D269C211yesmaximal, characteristic, complemented
3#31770467C211yesmaximal, characteristic, complemented
4#31770342C211yesmaximal, characteristic, complemented
5#31770340C211yesmaximal, characteristic, complemented
6#31770338C211yesmaximal, characteristic, complemented
7#328×C269C211yesmaximal, characteristic, complemented
8C2×#16864403C411yescharacteristic, complemented
9C22×C4×D269C2211yescharacteristic
10C2×C8×D269—21no—
11#22575438—21no—
12#22575429C411yescharacteristic, complemented
13#22575428C411yescharacteristic, complemented
14#22575427C2211yescharacteristic
15#22575423—21no—
16#22575415—21no—
17#22575413—21no—
18#22575411C411yescharacteristic, complemented
19C2×#16864379—21no—
20C22⋊#14524130C2211yescharacteristic
21#22575365—21no—
22#22575360—21no—
23#22575360C2211yescharacteristic
24C22⋊Q8×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic
26#95×C269C2211yescharacteristic
27C23×D269D411yescharacteristic
28#16864403—42no—
29C2×D1076—21no—
30C2×D1076—21no—
31C2×D1076C2×C411yescharacteristic
32C2×C22⋊D269—21no—
33C22×Dic269—21no—
34C22×Dic269D411yescharacteristic
35C2×C4×D269—21no—
36C2×C4×D269—42no—
37C2×C4×D269C2×C411yescharacteristic
38C2×C4×D269C2×C411yescharacteristic
39C2×C4×D269D411yescharacteristic
40C2×C4×D269D411yescharacteristic
41C2×#14524130—21no—
42C8×D269—42no—
43C4⋊Dic269C2×C411yescharacteristic
44#16864381—21no—
45#16864379—21no—
46#16864379—21no—
47#16864379—21no—
48#16864379—21no—
49#16864379—42no—
50C4×Dic269—21no—
51C2×Q8×C269C2×C411yescharacteristic
52C22×C4×C269—21no—
53C22×C4×C269C2311yescharacteristic
54C2×C8×C269—21no—
55C4⋊C4×C269—21no—
56C4⋊C4×C269C2×C411yescharacteristic
57C22⋊C4×C269—21no—
58C22×D269—21no—
59C22×D269—21no—
60C22×D269—22no—
61C22×D269—21no—
62C22×D269—41no—
63C22×D269C22⋊C411yescharacteristic
64C22×D269C22⋊C411yescharacteristic
65D1076—41no—
66D1076—42no—
67D1076—42no—
68C22⋊D269—41no—
69C22⋊D269—41no—
70C2×Dic269—21no—
71C2×Dic269—41no—
72C2×Dic269—41no—
73C2×Dic269—41no—
74C2×Dic269—41no—
75C2×Dic269C22⋊C411yescharacteristic
76C2×Dic269C22⋊C411yescharacteristic
77C4×D269—22no—
78C4×D269—22no—
79C4×D269—41no—
80C4×D269—41no—
81C4×D269—42no—
82#14524130—41no—
83C23×C269C2×D411yescharacteristic
84Q8×C269—41no—
85C2×C4×C269—21no—
86C2×C4×C269—21no—
87C2×C4×C269—41no—
88C2×C4×C269—41no—
89C2×C4×C269—41no—
90C2×C4×C269—41no—
91C2×C4×C269C22×C411yescharacteristic
92C2×C4×C269C2×D411yescharacteristic
93C8×C269—41no—
94C22×C269—21no—
95C22×C269—21no—
96C22×C269C2×C22⋊C411yescharacteristic
97C22×C269#13511yescharacteristic
98C22×C269#13511yescharacteristic
99C2×D269—21no—
100C2×D269—21no—
101C2×D269—21no—
102C2×D269—21no—
103C2×D269—21no—
104C2×D269—42no—
105C2×D269—42no—
106C2×D269—41no—
107C2×D269—41no—
108C2×D269—41no—
109C2×D269#9912yes—
110C4×C269—21no—
111C4×C269—21no—
112C4×C269—41no—
113C4×C269—41no—
114C4×C269—81no—
115Dic269—21no—
116Dic269—21no—
117Dic269—41no—
118Dic269—81no—
119C2×C269—21no—
120C2×C269—21no—
121C2×C269C2×#9911yescharacteristic
122C2×C269#41611yescharacteristic
123C2×C269#42111yescharacteristic
124D269—22no—
125D269—41no—
126D269—81no—
127C269#151611yescharacteristic, complemented, Sylow
128#1516—2691nomaximal, Sylow
129#525—2691no—
130C2×C22⋊C8—2691no—
131#381—2691no—
132#328—2691no—
133#328D26911yescharacteristic, complemented
134#327—2691no—
135#327—2691no—
136C2×#41—2691no—
137C23×C4—2691no—
138C22×C8—5381no—
139#123—5381no—
140C22⋊Q8—2691no—
141C22⋊Q8C2×D26911yescharacteristic
142#121—2691no—
143#121—2691no—
144#120—5381no—
145C4×D4—5381no—
146C4×D4—5381no—
147#117—2691no—
148C2×C22⋊C4—5381no—
149C22⋊C8—2691no—
150C22⋊C8—5381no—
151C22⋊C8C2×D26911yescharacteristic
152#95—2691no—
153#95—5381no—
154#95C2×D26911yescharacteristic
155C24—2691no—
156#41—10762no—
157C2×Q8C4×D26911yescharacteristic
158C2×D4—2691no—
159C2×D4—5381no—
160C2×D4—5381no—
161C2×D4—5381no—
162C22×C4—21no—
163C22×C4—2691no—
164C22×C4—2691no—
165C22×C4—2691no—
166C22×C4—2691no—
167C22×C4—2691no—
168C22×C4—5381no—
169C22×C4—5381no—
170C22×C4—10762no—
171C22×C4C22×D26911yescharacteristic
172C2×C8—21no—
173C2×C8—5381no—
174C2×C8—10762no—
175C4⋊C4—21no—
176C4⋊C4—2691no—
177C4⋊C4—5381no—
178C4⋊C4C4×D26911yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—5381no—
181C22⋊C4—5381no—
182C22⋊C4—5381no—
183C22⋊C4—5381no—
184C22⋊C4—10762no—
185C42—5381no—
186C23—2691no—
187C23—2691no—
188C23—5382no—
189C23—5381no—
190C23—5381no—
191C23—5381no—
192C23—10761no—
193C23D4×D26911yescharacteristic
194Q8—41no—
195D4—10761no—
196D4—10762no—
197D4—10762no—
198D4—10761no—
199D4—10761no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—2691no—
207C2×C4—2691no—
208C2×C4—5382no—
209C2×C4—5382no—
210C2×C4—5381no—
211C2×C4—10761no—
212C2×C4—10761no—
213C2×C4—10762no—
214C2×C4—10761no—
215C2×C4—10761no—
216C2×C4—10761no—
217C2×C4—10761no—
218C2×C4C2×C4×D26911yescharacteristic
219C2×C4D4×D26911yescharacteristic
220C8—41no—
221C8—10761no—
222C22—21no—
223C22—21no—
224C22—2692no—
225C22—5381no—
226C22—5381no—
227C22—5381no—
228C22—5381no—
229C22—5381no—
230C22—10762no—
231C22—10762no—
232C22—10761no—
233C22—10761no—
234C22—10761no—
235C22C22⋊C4×D26911yescharacteristic
236C22#2257547411yescharacteristic
237C22#2257547611yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—81no—
243C4—5381no—
244C4—5381no—
245C4—10761no—
246C4—21521no—
247C2—21no—
248C2—21no—
249C2—5382no—
250C2—10761no—
251C2—21521no—
252C2#99×D26911yescharacteristic
253C2#3177060011yescharacteristic
254C2#3177062011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#328×C269C2
socleC22×C269C2×C22⋊C4
prime radical#31771118C2
cosocleC22×C4×C269C23
hypercenter#328D269
hypocenterC269#1516
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D269C2semidirect
3. #31770467C2semidirect
4. #31770342C2semidirect
5. #31770340C2semidirect
6. #31770338C2semidirect
7. #328×C269C2semidirect
8. C2×#16864403C4semidirect
12. #22575429C4semidirect
13. #22575428C4semidirect
18. #22575411C4semidirect
127. C269#1516semidirect
133. #328D269semidirect

Maximal subgroups

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

subgroupindex
#317711182
C22⋊C8×D2692
#317704672
#317703422
#317703402
#317703382
#328×C2692
#1516269