Finite Group Databasebeta

← #13076290

Subgroups — #13076290

Order 1408.

448 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C11×#382C211yesmaximal, characteristic, complemented
2#10622604C211yesmaximal, characteristic
3#10622602C212yesmaximal, complemented
4#10622599C211yesmaximal, characteristic, complemented
5#10622553C212yesmaximal, complemented
6#10622288C212yesmaximal, complemented
7#10622281C212yesmaximal, complemented
8#10622278C212yesmaximal
9#10622271C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×C4×D11C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×(C2×D11)⋊C4C2212yes—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C11×#95C2212yes—
24C11×#95C2212yes—
25C11⋊#95C2211yescharacteristic
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C23×D11C2312yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×D44—24no—
41C2×D44—41no—
42C2×C4×D11—42no—
43C2×C4×D11—42no—
44C2×C4×D11—42no—
45C11×C4⋊C4—41no—
46C11×C4⋊C4—41no—
47C42×C11—22no—
48(C2×D11)⋊C4—24no—
49(C2×D11)⋊C4—24no—
50(C2×D11)⋊C4—24no—
51(C2×D11)⋊C4—42no—
52(C2×D11)⋊C4—42no—
53C4⋊Dic11—41no—
54Dic11⋊C4—42no—
55Dic11⋊C4—42no—
56#2782—111nomaximal, Sylow
57C23×C11C2411yescharacteristic
58C22×D11—22no—
59C22×D11—22no—
60C22×D11—22no—
61C22×D11—22no—
62C22×D11—22no—
63C22×D11—22no—
64C22×D11#4114yes—
65C2×C4×C11—21no—
66C2×C4×C11—21no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—21no—
77C2×C4×C11#4112yes—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87D44—44no—
88C4×D11—48no—
89#400—111no—
90#400—112no—
91#397—112no—
92#394—111no—
93#388—112no—
94#386—112no—
95#385—112no—
96#385—112no—
97#382D1111yescharacteristic, complemented
98C22×C11C2×#4111yescharacteristic
99C22×C11C2×#4112yes—
100C22×C11H(5,𝔽2)11yescharacteristic
101C22×C11H(5,𝔽2)12yes—
102C22×C112−1+411yescharacteristic
103C2×D11—24no—
104C2×D11—24no—
105C2×D11—24no—
106C2×D11—42no—
107C2×D11—42no—
108C2×D11—42no—
109C2×D11—42no—
110C4×C11—22no—
111C4×C11—41no—
112C4×C11—41no—
113C4×C11—42no—
114C4×C11—42no—
115Dic11—42no—
116Dic11—42no—
117Dic11—42no—
118C22×D4—111no—
119C23×C4—112no—
120C2×C4⋊C4—112no—
121C2×C4⋊C4—111no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4C2×D1111yescharacteristic
124C2×C4⋊C4C2×D1111yescharacteristic
125C2×C22⋊C4—112no—
126C2×C22⋊C4—112no—
127C2×C22⋊C4—112no—
128C2×C22⋊C4—112no—
129C2×C22⋊C4—112no—
130C2×C42C2×D1111yescharacteristic
131#95—112no—
132#95—112no—
133#95—112no—
134#95—112no—
135#95—111no—
136#95—111no—
137#95C2×D1112yes—
138#95C2×D1112yes—
139C2×C11#53911yescharacteristic
140C2×C11#53912yes—
141C2×C11#55111yescharacteristic
142C2×C11#55312yes—
143C2×C11H(3,𝔽4)11yescharacteristic
144D11—44no—
145C24—112no—
146C2×D4—224no—
147C2×D4—441no—
148C22×C4—112no—
149C22×C4—112no—
150C22×C4—112no—
151C22×C4—442no—
152C22×C4—442no—
153C22×C4—442no—
154C22×C4C22×D1111yescharacteristic
155C22×C4C22×D1112yes—
156C22×C4C22×D1111yescharacteristic
157C22×C4C22×D1112yes—
158C22×C4C22×D1111yescharacteristic
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—442no—
162C4⋊C4—442no—
163C4⋊C4—441no—
164C22⋊C4—224no—
165C22⋊C4—224no—
166C22⋊C4—224no—
167C22⋊C4—442no—
168C22⋊C4—442no—
169C42—22no—
170C11#278211yescharacteristic, complemented, Sylow
171C23—114no—
172C23—222no—
173C23—222no—
174C23—222no—
175C23—222no—
176C23—222no—
177C23—222no—
178C23C23×D1111yescharacteristic
179D4—444no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—448no—
202C2×C4#433912yes—
203C22—224no—
204C22—224no—
205C22—224no—
206C22—442no—
207C22—442no—
208C22—442no—
209C22—442no—
210C22C2×#433911yescharacteristic
211C22#6703711yescharacteristic
212C22#6704011yescharacteristic
213C22#41×D1112yes—
214C22#6704212yes—
215C4—22no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—442no—
221C4—442no—
222C4—442no—
223C2—444no—
224C2#1062304611yescharacteristic
225C2#1062306112yes—
226C2#1062321011yescharacteristic
227C2#1062321411yescharacteristic
228C2#1062322312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#382C2
prime radicalC22×D44C22
hypercenter#382D11
hypocenterC11#2782
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C11×#382C2semidirect
3. #10622602C2semidirect
4. #10622599C2semidirect
5. #10622553C2semidirect
6. #10622288C2semidirect
7. #10622281C2semidirect
9. #10622271C2semidirect
97. #382D11semidirect
170. C11#2782semidirect

Maximal subgroups

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

subgroupindex
C11×#3822
#106226042
#106226022
#106225992
#106225532
#106222882
#106222812
#106222782
#106222712
#278211