Finite Group Databasebeta

← #13073084

Subgroups — #13073084

Order 1408.

708 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 169 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×#66948C211yesmaximal, characteristic
2C2×#66947C214yesmaximal, complemented
3C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4C11×#384C211yesmaximal, characteristic, complemented
5#10622605C214yesmaximal, complemented
6#10622601C211yesmaximal, characteristic, complemented
7#10622589C211yesmaximal, characteristic, complemented
8#10622552C211yesmaximal, characteristic, complemented
9C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
10C22×D44C2212yes—
11C22×D44C2211yescharacteristic
12C22×C4×D11C2212yes—
13C22×C4×D11C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2214yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C42×C11C2211yescharacteristic
18C2×(C2×D11)⋊C4C2214yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2214yes—
25C2×C4×Dic11C2211yescharacteristic
26#66948—24no—
27#66947—216no—
28C4⋊C4×D11—24no—
29C11⋊#95C2212yes—
30C23×D11C2312yes—
31C23×D11C2311yescharacteristic
32C22×C4×C11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2311yescharacteristic
38C22×Dic11C2312yes—
39C2×D44—28no—
40C2×D44—24no—
41C2×D44—22no—
42C2×D44—22no—
43C2×D44—22no—
44C2×C4×D11—24no—
45C2×C4×D11—28no—
46C2×C4×D11—22no—
47C2×C4×D11—22no—
48C2×C4×D11D414yes—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—28no—
51C11×C4⋊C4—22no—
52C42×C11—22no—
53(C2×D11)⋊C4—28no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—28no—
56(C2×D11)⋊C4D418yescomplemented
57C4⋊Dic11—22no—
58Dic11⋊C4—24no—
59Dic11⋊C4—28no—
60C4×Dic11—22no—
61#2501—111nomaximal, Sylow
62C23×C11C2411yescharacteristic
63C22×D11—21no—
64C22×D11—21no—
65C22×D11—22no—
66C22×D11—24no—
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11—24no—
71C22×D11C2×D414yes—
72C22×D11C2×D412yes—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—24no—
77C2×C4×C11—24no—
78C2×C4×C11—22no—
79C2×C4×C11C2×D414yes—
80C2×C4×C11C2×D412yes—
81C2×C4×C11#4112yes—
82C2×C4×C11#4112yes—
83C2×Dic11—22no—
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—24no—
89C2×Dic11C2×D414yes—
90C2×Dic11C2×D412yes—
91D44—48no—
92D44—44no—
93C4×D11—28no—
94C4×D11—48no—
95C2×#123—114no—
96C2×#121—111no—
97C22×C4⋊C4—111no—
98#399—114no—
99#390—111no—
100#390—111no—
101#384—111no—
102#384D1111yescharacteristic, complemented
103C4×C22⋊C4—111no—
104C22×C11C22×D411yescharacteristic
105C22×C11C22×D412yes—
106C22×C11C2×#4111yescharacteristic
107C22×C11C2×#4111yescharacteristic
108C22×C112−1+412yes—
109C2×D11—22no—
110C2×D11—22no—
111C2×D11—24no—
112C2×D11—24no—
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—42no—
116C2×D11—44no—
117C2×D11—44no—
118C2×D11#12714yes—
119C4×C11—24no—
120C4×C11—42no—
121C4×C11—42no—
122C4×C11#12314yescomplemented
123Dic11—22no—
124Dic11—24no—
125Dic11—42no—
126C22×D4—112no—
127C22×D4—111no—
128C23×C4—111no—
129C23×C4—112no—
130#123—2216no—
131#121—224no—
132C2×C4⋊C4—111no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—114no—
135C2×C4⋊C4—224no—
136C2×C4⋊C4C2×D1111yescharacteristic
137C2×C4⋊C4C2×D1111yescharacteristic
138C2×C4⋊C4C2×D1114yes—
139C2×C22⋊C4—112no—
140C2×C22⋊C4—112no—
141C2×C22⋊C4—114no—
142C2×C22⋊C4—114no—
143C2×C42—111no—
144C2×C42C2×D1111yescharacteristic
145#95—112no—
146C2×C11C2×#12311yescharacteristic
147C2×C11C2×#12711yescharacteristic
148C2×C11#53611yescharacteristic
149C2×C11#54712yes—
150C2×C11#54712yes—
151D11—24no—
152D11—82no—
153C24—111no—
154C24—112no—
155C2×D4—224no—
156C2×D4—228no—
157C2×D4—222no—
158C2×D4—222no—
159C2×D4—222no—
160C22×C4—111no—
161C22×C4—112no—
162C22×C4—114no—
163C22×C4—112no—
164C22×C4—224no—
165C22×C4—228no—
166C22×C4—222no—
167C22×C4—222no—
168C22×C4C22×D1112yes—
169C22×C4C22×D1112yes—
170C22×C4C22×D1112yes—
171C22×C4C22×D1111yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—28no—
175C4⋊C4—224no—
176C4⋊C4—228no—
177C4⋊C4—222no—
178C22⋊C4—118no—
179C22⋊C4—224no—
180C22⋊C4—228no—
181C22⋊C4—228no—
182C42—22no—
183C42—222no—
184C11#250111yescharacteristic, complemented, Sylow
185C23—114no—
186C23—112no—
187C23—221no—
188C23—221no—
189C23—222no—
190C23—222no—
191C23—224no—
192C23—222no—
193C23—222no—
194C23—224no—
195C23C23×D1111yescharacteristic
196D4—448no—
197D4—444no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—24no—
204C2×C4—114no—
205C2×C4—112no—
206C2×C4—221no—
207C2×C4—222no—
208C2×C4—221no—
209C2×C4—222no—
210C2×C4—228no—
211C2×C4—224no—
212C2×C4—222no—
213C2×C4—448no—
214C2×C4#433912yes—
215C2×C4D4×D1114yes—
216C2×C4D4×D1112yes—
217C2×C4#434312yes—
218C22—114no—
219C22—222no—
220C22—224no—
221C22—222no—
222C22—224no—
223C22—442no—
224C22—442no—
225C22—444no—
226C22—442no—
227C22—444no—
228C22C2×#433911yescharacteristic
229C22C2×D4×D1111yescharacteristic
230C22C2×D4×D1112yes—
231C22C2×#434311yescharacteristic
232C22#6704012yes—
233C4—24no—
234C4—42no—
235C4—42no—
236C4—224no—
237C4—222no—
238C4—442no—
239C4#6694714yescomplemented
240C2—224no—
241C2—882no—
242C2C2×#6694711yescharacteristic
243C2#1062303812yes—
244C2D11×#12711yescharacteristic
245C2#1062325511yescharacteristic
246C2#1062325712yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#384C2
prime radicalC2×#66948C2
hypercenter#384D11
hypocenterC11#2501
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#66947C2semidirect
3. C2×C4⋊C4×D11C2semidirect
4. C11×#384C2semidirect
5. #10622605C2semidirect
6. #10622601C2semidirect
7. #10622589C2semidirect
8. #10622552C2semidirect
9. C4×(C2×D11)⋊C4C2semidirect
56. (C2×D11)⋊C4D4semidirect
102. #384D11semidirect
122. C4×C11#123semidirect
184. C11#2501semidirect
239. C4#66947semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669472
C2×C4⋊C4×D112
C11×#3842
#106226052
#106226012
#106225892
#106225522
C4×(C2×D11)⋊C42
#250111