Finite Group Databasebeta

← #46809403

Subgroups — #46809403

Order 34432.

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

normal subgroups only

This group has 294 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
1C22⋊Q8×D269C211yesmaximal, characteristic
2#31770567C211yesmaximal, characteristic
3#31770452C211yesmaximal, characteristic
4#31770343C211yesmaximal, characteristic, complemented
5#31770342C211yesmaximal, characteristic, complemented
6#31770341C211yesmaximal, characteristic, complemented
7#328×C269C211yesmaximal, characteristic, complemented
8C2×Q8×D269C411yescharacteristic, complemented
9C22×C4×D269C2211yescharacteristic
10C2×#16864385—21no—
11#22575433C411yescharacteristic, complemented
12#22575432C2211yescharacteristic
13#22575431—21no—
14#22575430—21no—
15#22575429C411yescharacteristic, complemented
16C4⋊C4×D269—21no—
17C4⋊C4×D269C411yescharacteristic, complemented
18C2×#16864379—21no—
19C22⋊C4×D269—21no—
20C2×C4×Dic269—21no—
21C22⋊#14524130C2211yescharacteristic
22#22575365—21no—
23#22575360C2211yescharacteristic
24C22⋊Q8×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic
26#95×C269C2211yescharacteristic
27C23×D269D411yescharacteristic
28C2×Dic538—21no—
29C2×Dic538C2×C411yescharacteristic
30Q8×D269—42no—
31C22×Dic269—21no—
32C22×Dic269D411yescharacteristic
33C2×C4×D269—21no—
34C2×C4×D269—21no—
35C2×C4×D269—42no—
36C2×C4×D269C2×C411yescharacteristic
37C2×C4×D269C2×C411yescharacteristic
38C2×C4×D269D411yescharacteristic
39C2×C4×D269D411yescharacteristic
40#16864385—42no—
41C2×#14524130—21no—
42C4⋊Dic269—21no—
43C4⋊Dic269C2×C411yescharacteristic
44#16864381—21no—
45#16864381—21no—
46#16864381—21no—
47C22⋊Dic269—21no—
48#16864379—24no—
49#16864379—21no—
50#16864379—21no—
51C4×Dic269—42no—
52C2×Q8×C269C2×C411yescharacteristic
53C22×C4×C269—21no—
54C22×C4×C269C2311yescharacteristic
55C2×C8×C269—21no—
56C4⋊C4×C269—21no—
57C4⋊C4×C269C2×C411yescharacteristic
58C22⋊C4×C269—21no—
59C22×D269—21no—
60C22×D269—21no—
61C22×D269—22no—
62C22×D269—41no—
63C22×D269C22⋊C411yescharacteristic
64C22×D269C22⋊C411yescharacteristic
65Dic538—42no—
66Dic538—41no—
67C2×Dic269—22no—
68C2×Dic269—22no—
69C2×Dic269—21no—
70C2×Dic269—21no—
71C2×Dic269—41no—
72C2×Dic269—41no—
73C2×Dic269C22⋊C411yescharacteristic
74C2×Dic269C22⋊C411yescharacteristic
75C4×D269—22no—
76C4×D269—22no—
77C4×D269—41no—
78C4×D269—41no—
79C4×D269—42no—
80C4×D269—42no—
81#14524130—41no—
82C23×C269C2×D411yescharacteristic
83Q8×C269—41no—
84C2×C4×C269—22no—
85C2×C4×C269—21no—
86C2×C4×C269—21no—
87C2×C4×C269—41no—
88C2×C4×C269—41no—
89C2×C4×C269—41no—
90C2×C4×C269C22×C411yescharacteristic
91C2×C4×C269C2×D411yescharacteristic
92C8×C269—41no—
93C22×C269—21no—
94C22×C269—21no—
95C22×C269C2×C22⋊C411yescharacteristic
96C22×C269#13711yescharacteristic
97C22×C269#13711yescharacteristic
98C2×D269—21no—
99C2×D269—21no—
100C2×D269—21no—
101C2×D269—21no—
102C2×D269—21no—
103C2×D269—42no—
104C2×D269—42no—
105C2×D269#10412yes—
106C4×C269—21no—
107C4×C269—21no—
108C4×C269—42no—
109C4×C269—41no—
110C4×C269—41no—
111Dic269—21no—
112Dic269—42no—
113Dic269—41no—
114Dic269—41no—
115Dic269#9912yes—
116C2×C269—21no—
117C2×C269—21no—
118C2×C269C2×#9911yescharacteristic
119C2×C269#41911yescharacteristic
120C2×C269C2×#10411yescharacteristic
121D269—22no—
122D269—41no—
123C269#150811yescharacteristic, complemented, Sylow
124#1508—2691nomaximal, Sylow
125C2×C22⋊Q8—2691no—
126#407—2691no—
127C4×C22⋊C4—2691no—
128#328—2691no—
129#328—2691no—
130#328—2691no—
131#328D26911yescharacteristic, complemented
132C22×Q8—2691no—
133C23×C4—2691no—
134C2×M16—5381no—
135C22⋊Q8—2691no—
136C22⋊Q8—2691no—
137C22⋊Q8—2691no—
138C22⋊Q8—5381no—
139C22⋊Q8—5381no—
140C22⋊Q8C2×D26911yescharacteristic
141C2×C4⋊C4—2691no—
142C2×C4⋊C4—5381no—
143C2×C22⋊C4—5381no—
144C2×C22⋊C4—5381no—
145C2×C42—5381no—
146C22⋊C8—2691no—
147C22⋊C8—5381no—
148C22⋊C8C2×D26911yescharacteristic
149#95—2691no—
150#95C2×D26911yescharacteristic
151C24—2691no—
152C2×Q8—2691no—
153C2×Q8—5381no—
154C2×Q8—10762no—
155C2×Q8C4×D26911yescharacteristic
156C22×C4—21no—
157C22×C4—2691no—
158C22×C4—2691no—
159C22×C4—2691no—
160C22×C4—2691no—
161C22×C4—2691no—
162C22×C4—5381no—
163C22×C4—5381no—
164C22×C4—5381no—
165C22×C4—10762no—
166C22×C4C22×D26911yescharacteristic
167M16—10762no—
168C2×C8—21no—
169C2×C8—5381no—
170C4⋊C4—21no—
171C4⋊C4—2691no—
172C4⋊C4—5381no—
173C4⋊C4—5381no—
174C4⋊C4—5381no—
175C4⋊C4—5381no—
176C4⋊C4C4×D26911yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—5381no—
179C22⋊C4—5381no—
180C22⋊C4—5384no—
181C22⋊C4—5381no—
182C42—10762no—
183C23—2691no—
184C23—2691no—
185C23—5382no—
186C23—5381no—
187C23—5381no—
188C23—10761no—
189C23D4×D26911yescharacteristic
190Q8—41no—
191Q8—10761no—
192Q8—10762no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—2691no—
200C2×C4—2691no—
201C2×C4—5382no—
202C2×C4—5382no—
203C2×C4—5382no—
204C2×C4—5382no—
205C2×C4—5381no—
206C2×C4—5381no—
207C2×C4—10761no—
208C2×C4—10761no—
209C2×C4—10762no—
210C2×C4—10762no—
211C2×C4—10761no—
212C2×C4—10761no—
213C2×C4C2×C4×D26911yescharacteristic
214C2×C4D4×D26911yescharacteristic
215C8—41no—
216C8—10761no—
217C22—21no—
218C22—21no—
219C22—2692no—
220C22—5381no—
221C22—5381no—
222C22—5381no—
223C22—5381no—
224C22—5381no—
225C22—10762no—
226C22—10762no—
227C22C22⋊C4×D26911yescharacteristic
228C22#2257548211yescharacteristic
229C22#2257548511yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—41no—
235C4—2692no—
236C4—5381no—
237C4—10762no—
238C4—10761no—
239C4—10761no—
240C2—21no—
241C2—21no—
242C2—5382no—
243C2—10761no—
244C2#99×D26911yescharacteristic
245C2#3177061211yescharacteristic
246C2#104×D26911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#328×C269C2
socleC22×C269C2×C22⋊C4
prime radicalC23×D269D4
cosocleC22×C4×C269C23
hypercenter#328D269
hypocenterC269#1508
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
4. #31770343C2semidirect
5. #31770342C2semidirect
6. #31770341C2semidirect
7. #328×C269C2semidirect
8. C2×Q8×D269C4semidirect
11. #22575433C4semidirect
15. #22575429C4semidirect
17. C4⋊C4×D269C4semidirect
123. C269#1508semidirect
131. #328D269semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D2692
#317705672
#317704522
#317703432
#317703422
#317703412
#328×C2692
#1508269