Finite Group Databasebeta

← #13074399

Subgroups — #13074399

Order 1408.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#66982C211yesmaximal, characteristic
2C22×C4⋊Dic11C211yesmaximal, characteristic, complemented
3C11×#381C211yesmaximal, characteristic, complemented
4#10622571C212yesmaximal
5#10622563C212yesmaximal, complemented
6#10622290C212yesmaximal, complemented
7#10622287C212yesmaximal, complemented
8#10622274C212yesmaximal, complemented
9#10622272C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×C22⋊D11C2211yescharacteristic
12C23×Dic11C2212yes—
13C2×C11×C22⋊C4C2212yes—
14C2×C22⋊Dic11C2211yescharacteristic
15#66982—24no—
16C2×(C2×D11)⋊C4C2211yescharacteristic
17C2×(C2×D11)⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C4C2214yes—
19C2×C4⋊Dic11—24no—
20C2×C4⋊Dic11C2212yes—
21C2×C4⋊Dic11C2212yes—
22C2×C4⋊Dic11C2214yes—
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C11×#95C2212yes—
26C11×#95C2212yes—
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C24×C11C2311yescharacteristic
30C23×D11C2311yescharacteristic
31C22×C4×C11—24no—
32C22×C4×C11D414yes—
33C22×C4×C11C2314yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C2×C22⋊D11—22no—
37C2×C22⋊D11—24no—
38C22×Dic11—24no—
39C22×Dic11—44no—
40C22×Dic11C2311yescharacteristic
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2314yes—
43C22×Dic11C2311yescharacteristic
44C11×C22⋊C4—24no—
45C22⋊Dic11—22no—
46(C2×D11)⋊C4—22no—
47(C2×D11)⋊C4—22no—
48(C2×D11)⋊C4—44no—
49C4⋊Dic11—24no—
50C4⋊Dic11—24no—
51C4⋊Dic11—44no—
52Dic11⋊C4—22no—
53Dic11⋊C4—22no—
54#2623—111nomaximal, Sylow
55C23×C11—22no—
56C23×C11—22no—
57C23×C11C2×D412yes—
58C23×C11#4114yes—
59C23×C11C2411yescharacteristic
60C22×D11—21no—
61C22×D11—22no—
62C22×D11—22no—
63C22×D11—22no—
64C2×C4×C11—28no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—24no—
68C2×C4×C11—24no—
69C2×C4×C11—24no—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×D412yes—
72C22⋊D11—44no—
73C2×Dic11—21no—
74C2×Dic11—21no—
75C2×Dic11—21no—
76C2×Dic11—24no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—24no—
80C2×Dic11—24no—
81C2×Dic11—22no—
82C2×Dic11—48no—
83C2×#123—111no—
84C22×C4⋊C4—111no—
85#400—112no—
86#399—112no—
87#398—112no—
88#397—112no—
89#386—112no—
90#385—112no—
91#381D1111yescharacteristic, complemented
92C22×C11—22no—
93C22×C11—22no—
94C22×C11—28no—
95C22×C11#12314yes—
96C22×C11C22×D411yescharacteristic
97C22×C11C2×#4112yes—
98C22×C11H(5,𝔽2)12yes—
99C22×C112−1+412yes—
100C2×D11—41no—
101C2×D11—41no—
102C2×D11—41no—
103C2×D11—44no—
104C4×C11—22no—
105C4×C11—22no—
106C4×C11—44no—
107Dic11—41no—
108Dic11—41no—
109Dic11—44no—
110Dic11—41no—
111C22×D4—111no—
112C23×C4—112no—
113C23×C4C2×D1111yescharacteristic
114#123—224no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—111no—
118C2×C4⋊C4—111no—
119C2×C4⋊C4—114no—
120C2×C4⋊C4—224no—
121C2×C22⋊C4—111no—
122C2×C22⋊C4—111no—
123C2×C22⋊C4—111no—
124C2×C22⋊C4—114no—
125C2×C22⋊C4C2×D1112yes—
126#95—114no—
127#95—114no—
128#95C2×D1112yes—
129#95C2×D1112yes—
130C2×C11—24no—
131C2×C11C2×#12311yescharacteristic
132C2×C11#53511yescharacteristic
133C2×C11#53611yescharacteristic
134C2×C11#53914yes—
135D11—81no—
136C24—111no—
137C24C22×D1111yescharacteristic
138C2×D4—222no—
139C2×D4—224no—
140C22×C4—24no—
141C22×C4—111no—
142C22×C4—111no—
143C22×C4—114no—
144C22×C4—111no—
145C22×C4—224no—
146C22×C4—444no—
147C22×C4D4414yes—
148C22×C4C22×D1114yes—
149C22×C4C22×D1111yescharacteristic
150C22×C4C22×D1111yescharacteristic
151C4⋊C4—224no—
152C4⋊C4—224no—
153C4⋊C4—222no—
154C4⋊C4—222no—
155C4⋊C4—444no—
156C22⋊C4—24no—
157C22⋊C4—222no—
158C22⋊C4—222no—
159C22⋊C4—222no—
160C22⋊C4—444no—
161C11#262311yescharacteristic, complemented, Sylow
162C23—22no—
163C23—22no—
164C23—221no—
165C23—222no—
166C23—222no—
167C23—222no—
168C23C2×D4412yes—
169C23#434114yes—
170C23C23×D1111yescharacteristic
171D4—444no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—221no—
179C2×C4—221no—
180C2×C4—224no—
181C2×C4—221no—
182C2×C4—222no—
183C2×C4—224no—
184C2×C4—222no—
185C2×C4—224no—
186C2×C4—222no—
187C2×C4—448no—
188C2×C4C2×D4412yes—
189C2×C4C2×D4412yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—441no—
194C22—441no—
195C22—441no—
196C22—444no—
197C22#6693914yes—
198C22C22×D4411yescharacteristic
199C22C2×#434112yes—
200C22#6704212yes—
201C22#6704312yes—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—441no—
206C4—444no—
207C4—441no—
208C4—441no—
209C2—24no—
210C2—881no—
211C2C2×#6693911yescharacteristic
212C2#1062305611yescharacteristic
213C2#1062305711yescharacteristic
214C2#1062319614yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC22×C22⋊D11C22
hypercenter#381D11
hypocenterC11#2623
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic11C2semidirect
3. C11×#381C2semidirect
5. #10622563C2semidirect
6. #10622290C2semidirect
7. #10622287C2semidirect
8. #10622274C2semidirect
9. #10622272C2semidirect
91. #381D11semidirect
161. C11#2623semidirect

Maximal subgroups

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

subgroupindex
C2×#669822
C22×C4⋊Dic112
C11×#3812
#106225712
#106225632
#106222902
#106222872
#106222742
#106222722
#262311