Finite Group Databasebeta

← #13071953

Subgroups — #13071953

Order 1408.

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

normal subgroups only

This group has 864 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
1C22×#4339C211yesmaximal, characteristic
2C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
3C2×#66939C212yesmaximal, complemented
4C11×#381C211yesmaximal, characteristic, complemented
5#10622571C212yesmaximal, complemented
6#10622285C212yesmaximal, complemented
7#10622281C214yesmaximal, complemented
8#10622269C212yesmaximal, complemented
9C23×C4×C11C2211yescharacteristic
10C22×C22⋊D11C2212yes—
11C23×Dic11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C2×#4339—24no—
14C2×#4339—28no—
15C22×D44C2211yescharacteristic
16C22×C4×D11C2212yes—
17C22×Dic22C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×(C2×D11)⋊C4C2214yes—
21C2×C4⋊Dic11C2214yes—
22C2×Dic11⋊C4—24no—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25#66939—28no—
26C11×#95C2212yes—
27C11×#95C2212yes—
28C11⋊#95C2214yes—
29C24×C11C2311yescharacteristic
30C23×D11C2312yes—
31C22×C4×C11—24no—
32C22×C4×C11D414yes—
33C22×C4×C11C2314yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C2×C22⋊D11—24no—
37C2×C22⋊D11—24no—
38C2×C22⋊D11D418yes—
39C22×Dic11—24no—
40C22×Dic11—22no—
41C22×Dic11—24no—
42C22×Dic11—22no—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46#4339—232no—
47C2×D44—24no—
48C2×D44—22no—
49C2×C4×D11—24no—
50C2×C4×D11—24no—
51C2×C4×D11—24no—
52C2×Dic22—24no—
53C2×Dic22—22no—
54C11×C22⋊C4—24no—
55(C2×D11)⋊C4—28no—
56(C2×D11)⋊C4—28no—
57C4⋊Dic11—28no—
58Dic11⋊C4—24no—
59Dic11⋊C4—24no—
60#2406—111nomaximal, Sylow
61C23×C11—22no—
62C23×C11—22no—
63C23×C11C2×D412yes—
64C23×C11C2×D414yes—
65C23×C11C2411yescharacteristic
66C22×D11—22no—
67C22×D11—22no—
68C22×D11—24no—
69C22×D11—24no—
70C22×D11C2×D414yes—
71C2×C4×C11—28no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—24no—
75C2×C4×C11—24no—
76C2×C4×C11—24no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D412yes—
79C22⋊D11—216no—
80C2×Dic11—28no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—24no—
87C2×Dic11—44no—
88C2×Dic11C2×D414yes—
89C2×Dic11#4114yescomplemented
90D44—28no—
91C4×D11—216no—
92Dic22—28no—
93C22×#41—111no—
94C2×#123—112no—
95C22×C4⋊C4—111no—
96#395—112no—
97#394—112no—
98#386—112no—
99#385—114no—
100#381D1111yescharacteristic, complemented
101C22×C11—22no—
102C22×C11—22no—
103C22×C11—28no—
104C22×C11#12014yes—
105C22×C11C22×D411yescharacteristic
106C22×C11C22×D412yes—
107C22×C11C2×#4112yes—
108C22×C112−1+412yes—
109C2×D11—24no—
110C2×D11—28no—
111C2×D11—42no—
112C2×D11—42no—
113C2×D11—44no—
114C4×C11—22no—
115C4×C11—22no—
116C4×C11—44no—
117Dic11—24no—
118Dic11—24no—
119Dic11—42no—
120C2×#41—228no—
121C2×#41—224no—
122C22×Q8—111no—
123C22×D4—112no—
124C22×D4—111no—
125C23×C4—111no—
126C23×C4—111no—
127C23×C4—112no—
128C23×C4C2×D1111yescharacteristic
129#123—228no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—112no—
132C2×C4⋊C4—114no—
133C2×C4⋊C4—224no—
134C2×C22⋊C4—114no—
135C2×C22⋊C4—114no—
136C2×C22⋊C4C2×D1112yes—
137#95—114no—
138#95C2×D1112yes—
139#95C2×D1112yes—
140C2×C11—24no—
141C2×C11C2×#12011yescharacteristic
142C2×C11#52511yescharacteristic
143C2×C11#53611yescharacteristic
144C2×C11#54714yes—
145D11—44no—
146C24—112no—
147C24C22×D1111yescharacteristic
148#41—2232no—
149C2×Q8—224no—
150C2×Q8—222no—
151C2×D4—118no—
152C2×D4—224no—
153C2×D4—224no—
154C2×D4—224no—
155C2×D4—222no—
156C22×C4—24no—
157C22×C4—112no—
158C22×C4—112no—
159C22×C4—112no—
160C22×C4—224no—
161C22×C4—224no—
162C22×C4—224no—
163C22×C4—222no—
164C22×C4—224no—
165C22×C4—222no—
166C22×C4—224no—
167C22×C4D4414yes—
168C22×C4C22×D1114yes—
169C22×C4C22×D1111yescharacteristic
170C22×C4C22×D1111yescharacteristic
171C4⋊C4—228no—
172C4⋊C4—224no—
173C4⋊C4—224no—
174C22⋊C4—24no—
175C22⋊C4—228no—
176C22⋊C4—228no—
177C11#240611yescharacteristic, complemented, Sylow
178C23—22no—
179C23—22no—
180C23—114no—
181C23—222no—
182C23—222no—
183C23—224no—
184C23—224no—
185C23C2×D4412yes—
186C23D4×D1114yes—
187C23C23×D1111yescharacteristic
188Q8—228no—
189D4—228no—
190D4—2216no—
191C2×C4—28no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—114no—
198C2×C4—114no—
199C2×C4—2216no—
200C2×C4—228no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—224no—
207C2×C4—444no—
208C2×C4C2×D4412yes—
209C2×C4C2×D4412yes—
210C22—22no—
211C22—22no—
212C22—28no—
213C22—224no—
214C22—228no—
215C22—442no—
216C22—442no—
217C22—444no—
218C22#6693514yes—
219C22C22×D4411yescharacteristic
220C22C2×D4×D1112yes—
221C22#41×D1112yes—
222C22#6704312yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—224no—
227C4—224no—
228C4—442no—
229C2—24no—
230C2—444no—
231C2C2×#6693511yescharacteristic
232C2#1062305511yescharacteristic
233C2#1062305711yescharacteristic
234C2#1062318614yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC22×#4339C2
hypercenter#381D11
hypocenterC11#2406
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×Dic11⋊C4C2semidirect
3. C2×#66939C2semidirect
4. C11×#381C2semidirect
5. #10622571C2semidirect
6. #10622285C2semidirect
7. #10622281C2semidirect
8. #10622269C2semidirect
89. C2×Dic11#41semidirect
100. #381D11semidirect
177. C11#2406semidirect

Maximal subgroups

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

subgroupindex
C22×#43392
C22×Dic11⋊C42
C2×#669392
C11×#3812
#106225712
#106222852
#106222812
#106222692
#240611