Finite Group Databasebeta

← #46809232

Subgroups — #46809232

Order 34432.

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

normal subgroups only

This group has 280 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
1C2×#22575438C211yesmaximal, characteristic
2#31770567C211yesmaximal, characteristic, complemented
3C22⋊C8×D269C211yesmaximal, characteristic, complemented
4#31770331C211yesmaximal, characteristic, complemented
5#31770328C211yesmaximal, characteristic, complemented
6#31770328C211yesmaximal, characteristic, complemented
7#324×C269C211yesmaximal, characteristic, complemented
8C22×D1076C411yescharacteristic
9C22×C4×D269C2211yescharacteristic
10C2×#16864385—21no—
11C2×C8×D269—21no—
12#22575438—21no—
13#22575438—21no—
14#22575438—21no—
15#22575438—21no—
16C2×#16864381C411yescharacteristic
17C2×#16864379C411yescharacteristic
18C2×#16864379C411yescharacteristic
19C2×#16864379C2211yescharacteristic
20C22⋊#14524130C2211yescharacteristic
21C22⋊#14524130C2211yescharacteristic
22#22575365—21no—
23#22575365—21no—
24C2×C4⋊C4×C269C2211yescharacteristic
25C22⋊C8×C269C2211yescharacteristic
26C22⋊C8×C269C2211yescharacteristic
27C23×D269C2×C411yescharacteristic
28C23×D269C2×C411yescharacteristic
29C2×D1076—21no—
30C2×D1076—21no—
31C2×D1076—42no—
32C22×Dic269C2×C411yescharacteristic
33C22×Dic269C2×C411yescharacteristic
34C2×C4×D269—42no—
35C2×C4×D269D411yescharacteristic
36C2×C4×D269D411yescharacteristic
37C2×C4×D269D411yescharacteristic
38C2×C4×D269D411yescharacteristic
39#16864385—42no—
40C2×#14524130—21no—
41C2×#14524130—21no—
42C8×D269—42no—
43#16864381—21no—
44#16864381—21no—
45#16864379—21no—
46#16864379—21no—
47#16864379—21no—
48#16864379—21no—
49#16864379—21no—
50#16864379—21no—
51C22×C4×C269C2×C411yescharacteristic
52C22×C4×C269C2×C411yescharacteristic
53C22×C4×C269C2311yescharacteristic
54C2×C8×C269—21no—
55C2×C8×C269—21no—
56C4⋊C4×C269—21no—
57C4⋊C4×C269—21no—
58C22×D269—21no—
59C22×D269—21no—
60C22×D269—22no—
61C22×D269—21no—
62C22×D269—21no—
63C22×D269—21no—
64C22×D269—41no—
65C22×D269—41no—
66C22×D269—41no—
67C22×D269C22⋊C411yescharacteristic
68C22×D269C22⋊C411yescharacteristic
69D1076—42no—
70D1076—42no—
71C2×Dic269—21no—
72C2×Dic269—41no—
73C2×Dic269—41no—
74C2×Dic269C22⋊C411yescharacteristic
75C2×Dic269C22⋊C411yescharacteristic
76C4×D269—22no—
77C4×D269—22no—
78C4×D269—41no—
79C4×D269—41no—
80#14524130—41no—
81#14524130—41no—
82C23×C269C22×C411yescharacteristic
83C2×C4×C269—21no—
84C2×C4×C269—21no—
85C2×C4×C269—21no—
86C2×C4×C269—21no—
87C2×C4×C269—41no—
88C2×C4×C269—41no—
89C2×C4×C269C2×D411yescharacteristic
90C2×C4×C269C2×D411yescharacteristic
91C8×C269—41no—
92C8×C269—41no—
93C22×C269—21no—
94C22×C269—21no—
95C22×C269C2×C22⋊C411yescharacteristic
96C22×C269#13111yescharacteristic
97C22×C269#13111yescharacteristic
98C2×D269—21no—
99C2×D269—21no—
100C2×D269—21no—
101C2×D269—21no—
102C2×D269—21no—
103C2×D269—42no—
104C2×D269—42no—
105C2×D269—41no—
106C2×D269—41no—
107C2×D269—41no—
108C2×D269—81no—
109C2×D269—81no—
110C2×D269#9912yes—
111C4×C269—21no—
112C4×C269—21no—
113C4×C269—41no—
114C4×C269—41no—
115Dic269—21no—
116Dic269—21no—
117Dic269—41no—
118C2×C269—21no—
119C2×C269—21no—
120C2×C269#40811yescharacteristic
121C2×C269C2×#9911yescharacteristic
122C2×C269#41311yescharacteristic
123D269—22no—
124D269—41no—
125D269—81no—
126C269#146811yescharacteristic, complemented, Sylow
127#1468—2691nomaximal, Sylow
128C2×#123—2691no—
129#407—2691no—
130C2×C22⋊C8—2691no—
131#324—2691no—
132#324D26911yescharacteristic, complemented
133#323—2691no—
134#323—2691no—
135C22×D4—2691no—
136C23×C4—2691no—
137C2×M16—5381no—
138C22×C8—5381no—
139#123—5381no—
140#123—5381no—
141#123—5381no—
142#123—5381no—
143C2×C4⋊C4—2691no—
144C2×C4⋊C4C2×D26911yescharacteristic
145C2×C22⋊C4—2691no—
146C2×C22⋊C4—2691no—
147C2×C22⋊C4—2691no—
148C22⋊C8—2691no—
149C22⋊C8—2691no—
150C22⋊C8—5381no—
151C22⋊C8—5381no—
152C22⋊C8C2×D26911yescharacteristic
153C22⋊C8C2×D26911yescharacteristic
154C24—2691no—
155C24—2691no—
156C2×D4—5381no—
157C2×D4—5381no—
158C2×D4—10762no—
159C22×C4—2691no—
160C22×C4—2691no—
161C22×C4—2691no—
162C22×C4—2691no—
163C22×C4—2691no—
164C22×C4—2691no—
165C22×C4—10762no—
166C22×C4C4×D26911yescharacteristic
167C22×C4C4×D26911yescharacteristic
168C22×C4C22×D26911yescharacteristic
169M16—10762no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—5381no—
173C2×C8—5381no—
174C2×C8—10762no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—5381no—
178C4⋊C4—5381no—
179C22⋊C4—5381no—
180C22⋊C4—5381no—
181C22⋊C4—5381no—
182C22⋊C4—5381no—
183C22⋊C4—5381no—
184C22⋊C4—5381no—
185C23—2691no—
186C23—2691no—
187C23—5382no—
188C23—5381no—
189C23—5381no—
190C23—5381no—
191C23—5381no—
192C23—5381no—
193C23—10761no—
194C23—10761no—
195C23—10761no—
196C23C2×C4×D26911yescharacteristic
197D4—10762no—
198D4—10762no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—2691no—
206C2×C4—2691no—
207C2×C4—5382no—
208C2×C4—5382no—
209C2×C4—5381no—
210C2×C4—10761no—
211C2×C4—10761no—
212C2×C4—10761no—
213C2×C4—10761no—
214C2×C4D4×D26911yescharacteristic
215C2×C4D4×D26911yescharacteristic
216C8—41no—
217C8—41no—
218C8—10761no—
219C8—10761no—
220C22—21no—
221C22—21no—
222C22—2692no—
223C22—5381no—
224C22—5381no—
225C22—5381no—
226C22—5381no—
227C22—5381no—
228C22—10762no—
229C22—10762no—
230C22—10761no—
231C22—10761no—
232C22—10761no—
233C22—21521no—
234C22—21521no—
235C22C22⋊C4×D26911yescharacteristic
236C22#2257545911yescharacteristic
237C22#2257546111yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—5381no—
243C4—5381no—
244C4—10761no—
245C2—21no—
246C2—21no—
247C2—5382no—
248C2—10761no—
249C2—21521no—
250C2#3177057011yescharacteristic
251C2#99×D26911yescharacteristic
252C2#3177058811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D269
commutatorC23×C269C22×C4
FrattiniC22×C4C22×D269
Fitting#324×C269C2
socleC22×C269C2×C22⋊C4
prime radicalC22×D1076C4
cosocleC22×C4×C269C23
hypercenter#324D269
hypocenterC269#1468
LCSG ▷ C23×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #31770567C2semidirect
3. C22⋊C8×D269C2semidirect
4. #31770331C2semidirect
5. #31770328C2semidirect
6. #31770328C2semidirect
7. #324×C269C2semidirect
126. C269#1468semidirect
132. #324D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754382
#317705672
C22⋊C8×D2692
#317703312
#317703282
#324×C2692
#1468269