Finite Group Databasebeta

← #13076294

Subgroups — #13076294

Order 1408.

448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 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×#394C211yesmaximal, characteristic
2#10622833C212yesmaximal
3#10622599C211yesmaximal, characteristic, complemented
4#10622590C211yesmaximal, characteristic, complemented
5#10622565C212yesmaximal, complemented
6#10622563C212yesmaximal, complemented
7#10622563C212yesmaximal, complemented
8#10622557C212yesmaximal, complemented
9#10622272C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C4⋊Dic11C2212yes—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23C11×#95C2211yescharacteristic
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C24×C11C2312yes—
32C2×D4×C11—24no—
33C2×D4×C11—41no—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C22×Dic11—42no—
39C22×Dic11—42no—
40C22×Dic11—42no—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C11×C4⋊C4—41no—
46C11×C22⋊C4—24no—
47C11×C22⋊C4—24no—
48C22⋊Dic11—24no—
49C22⋊Dic11—42no—
50C22⋊Dic11—42no—
51C4⋊Dic11—41no—
52C4⋊Dic11—42no—
53C4⋊Dic11—41no—
54Dic11⋊C4—42no—
55C4×Dic11—22no—
56#2782—111nomaximal, Sylow
57C23×C11—22no—
58C23×C11—22no—
59C23×C11—22no—
60C23×C11—22no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11#4114yes—
64C23×C11C2411yescharacteristic
65D4×C11—44no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
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—21no—
75C2×C4×C11#4112yes—
76C2×Dic11—22no—
77C2×Dic11—22no—
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—
87C2×Dic11—22no—
88C2×Dic11—48no—
89#400—111no—
90#400—112no—
91#397—112no—
92#394D1111yescharacteristic
93#388—112no—
94#386—112no—
95#385—112no—
96#385—112no—
97#382—111no—
98C22×C11—24no—
99C22×C11—24no—
100C22×C11—24no—
101C22×C11—42no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11C2×#4112yes—
106C22×C11C2×#4111yescharacteristic
107C22×C11H(5,𝔽2)11yescharacteristic
108C22×C11H(5,𝔽2)12yes—
109C22×C112−1+411yescharacteristic
110C4×C11—22no—
111C4×C11—41no—
112C4×C11—41no—
113C4×C11—42no—
114Dic11—42no—
115Dic11—42no—
116Dic11—42no—
117Dic11—42no—
118C22×D4C2×D1111yescharacteristic
119C23×C4—112no—
120C2×C4⋊C4—111no—
121C2×C4⋊C4—111no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4—112no—
124C2×C4⋊C4C2×D1111yescharacteristic
125C2×C22⋊C4—112no—
126C2×C22⋊C4—112no—
127C2×C22⋊C4—112no—
128C2×C22⋊C4C2×D1112yes—
129C2×C22⋊C4C2×D1112yes—
130C2×C42—111no—
131#95—112no—
132#95—112no—
133#95—112no—
134#95—112no—
135#95—112no—
136#95—112no—
137#95—111no—
138#95C2×D1111yescharacteristic
139C2×C11—44no—
140C2×C11#53911yescharacteristic
141C2×C11#53912yes—
142C2×C11#55111yescharacteristic
143C2×C11#55312yes—
144C2×C11H(3,𝔽4)11yescharacteristic
145C24C22×D1112yes—
146C2×D4—24no—
147C2×D4—41no—
148C22×C4—112no—
149C22×C4—112no—
150C22×C4—112no—
151C22×C4—112no—
152C22×C4—442no—
153C22×C4—442no—
154C22×C4—442no—
155C22×C4C22×D1111yescharacteristic
156C22×C4C22×D1111yescharacteristic
157C22×C4C22×D1112yes—
158C22×C4C22×D1111yescharacteristic
159C4⋊C4—41no—
160C4⋊C4—442no—
161C4⋊C4—441no—
162C4⋊C4—441no—
163C4⋊C4—442no—
164C22⋊C4—24no—
165C22⋊C4—24no—
166C22⋊C4—224no—
167C22⋊C4—442no—
168C22⋊C4—442no—
169C42—222no—
170C11#278211yescharacteristic, complemented, Sylow
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23#434114yes—
178C23C23×D1111yescharacteristic
179D4—44no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—222no—
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#434112yes—
203C22—24no—
204C22—24no—
205C22—24no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22C2×#434112yes—
211C22C2×#434111yescharacteristic
212C22#6703711yescharacteristic
213C22#6704212yes—
214C22#6704311yescharacteristic
215C4—22no—
216C4—41no—
217C4—41no—
218C4—42no—
219C4—442no—
220C4—442no—
221C4—442no—
222C4—442no—
223C2—44no—
224C2#1062311811yescharacteristic
225C2#1062313311yescharacteristic
226C2#1062314912yes—
227C2#1062319612yes—
228C2#1062321411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC22×D4×C11C22
hypercenter#394D11
hypocenterC11#2782
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
3. #10622599C2semidirect
4. #10622590C2semidirect
5. #10622565C2semidirect
6. #10622563C2semidirect
7. #10622563C2semidirect
8. #10622557C2semidirect
9. #10622272C2semidirect
170. C11#2782semidirect

Maximal subgroups

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

subgroupindex
C11×#3942
#106228332
#106225992
#106225902
#106225652
#106225632
#106225572
#106222722
#278211