Finite Group Databasebeta

← #13074956

Subgroups — #13074956

Order 1408.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#66949C212yesmaximal, complemented
2C2×#66947C212yesmaximal
3C11×#384C211yesmaximal, characteristic, complemented
4#10622606C212yesmaximal, complemented
5#10622604C211yesmaximal, characteristic
6#10622602C212yesmaximal, complemented
7#10622593C212yesmaximal, complemented
8#10622592C211yesmaximal, characteristic, complemented
9#10622553C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×C4×D11C2212yes—
12C22×Dic22C2211yescharacteristic
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C42×C11C2211yescharacteristic
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26#66949—28no—
27#66947—28no—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C11⋊#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C23×D11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C2×D44—24no—
43C2×D44—41no—
44C2×C4×D11—24no—
45C2×C4×D11—24no—
46C2×C4×D11—42no—
47C2×Dic22—24no—
48C2×Dic22—41no—
49C11×C4⋊C4—24no—
50C11×C4⋊C4—24no—
51C11×C4⋊C4—41no—
52C11×C4⋊C4—41no—
53C42×C11—22no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—24no—
56(C2×D11)⋊C4—24no—
57(C2×D11)⋊C4—24no—
58(C2×D11)⋊C4D418yes—
59Dic11⋊C4—24no—
60Dic11⋊C4—24no—
61Dic11⋊C4—24no—
62#2680—111nomaximal, Sylow
63C23×C11C2411yescharacteristic
64C22×D11—22no—
65C22×D11—22no—
66C22×D11—22no—
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11C2×D414yes—
71C2×C4×C11—22no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11C2×D414yes—
83C2×C4×C11#4112yes—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11C2×D414yes—
93D44—44no—
94C4×D11—48no—
95Dic22—44no—
96C2×#123—112no—
97C2×C22⋊Q8—112no—
98#398—112no—
99#397—112no—
100#395—111no—
101#394—111no—
102#388—112no—
103#385—112no—
104#384D1111yescharacteristic, complemented
105C22×C11C22×D412yes—
106C22×C11C2×#4111yescharacteristic
107C22×C11H(5,𝔽2)11yescharacteristic
108C22×C112−1+411yescharacteristic
109C22×C112−1+412yes—
110C2×D11—24no—
111C2×D11—24no—
112C2×D11—24no—
113C2×D11—42no—
114C2×D11—42no—
115C2×D11—42no—
116C2×D11—42no—
117C4×C11—22no—
118C4×C11—24no—
119C4×C11—41no—
120C4×C11—42no—
121C4×C11—41no—
122Dic11—24no—
123Dic11—42no—
124Dic11—42no—
125C22×Q8—111no—
126C22×D4—111no—
127C23×C4—112no—
128#123—228no—
129C22⋊Q8—228no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—112no—
133C2×C4⋊C4C2×D1112yes—
134C2×C4⋊C4C2×D1112yes—
135C2×C4⋊C4C2×D1111yescharacteristic
136C2×C4⋊C4C2×D1111yescharacteristic
137C2×C22⋊C4—112no—
138C2×C22⋊C4—112no—
139C2×C22⋊C4—112no—
140C2×C22⋊C4—112no—
141C2×C22⋊C4—112no—
142C2×C42C2×D1111yescharacteristic
143#95—112no—
144#95—112no—
145#95—112no—
146#95—111no—
147#95—111no—
148C2×C11#53612yes—
149C2×C11#53911yescharacteristic
150C2×C11D4211yescharacteristic
151C2×C11#54712yes—
152C2×C11#56311yescharacteristic
153D11—44no—
154C24—112no—
155C2×Q8—224no—
156C2×Q8—441no—
157C2×D4—224no—
158C2×D4—441no—
159C22×C4—112no—
160C22×C4—112no—
161C22×C4—112no—
162C22×C4—224no—
163C22×C4—224no—
164C22×C4—442no—
165C22×C4C22×D1111yescharacteristic
166C22×C4C22×D1112yes—
167C22×C4C22×D1111yescharacteristic
168C22×C4C22×D1111yescharacteristic
169C22×C4C22×D1112yes—
170C4⋊C4—24no—
171C4⋊C4—24no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—224no—
175C4⋊C4—224no—
176C4⋊C4—224no—
177C22⋊C4—118no—
178C22⋊C4—224no—
179C22⋊C4—224no—
180C22⋊C4—224no—
181C22⋊C4—224no—
182C42—22no—
183C11#268011yescharacteristic, complemented, Sylow
184C23—114no—
185C23—222no—
186C23—222no—
187C23—222no—
188C23—222no—
189C23—222no—
190C23—222no—
191C23C23×D1111yescharacteristic
192Q8—444no—
193D4—444no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—114no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—448no—
215C2×C4#433912yes—
216C2×C4D4×D1114yes—
217C22—224no—
218C22—224no—
219C22—224no—
220C22—442no—
221C22—442no—
222C22—442no—
223C22—442no—
224C22C2×#433911yescharacteristic
225C22C2×D4×D1112yes—
226C22#6703711yescharacteristic
227C22#6704011yescharacteristic
228C22#6704012yes—
229C4—24no—
230C4—22no—
231C4—42no—
232C4—41no—
233C4—41no—
234C4—224no—
235C4—442no—
236C4—442no—
237C2—444no—
238C2#1062303812yes—
239C2#1062304611yescharacteristic
240C2#1062324811yescharacteristic
241C2#1062325512yes—
242C2#1062326611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#384C2
prime radicalC22×D44C22
hypercenter#384D11
hypocenterC11#2680
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#66949C2semidirect
3. C11×#384C2semidirect
4. #10622606C2semidirect
6. #10622602C2semidirect
7. #10622593C2semidirect
8. #10622592C2semidirect
9. #10622553C2semidirect
104. #384D11semidirect
183. C11#2680semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×#669472
C11×#3842
#106226062
#106226042
#106226022
#106225932
#106225922
#106225532
#268011