Finite Group Databasebeta

← #13073072

Subgroups — #13073072

Order 1408.

484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#66950C211yesmaximal, characteristic
2C2×#66945C211yesmaximal, characteristic
3C11×#382C211yesmaximal, characteristic, complemented
4#10622589C211yesmaximal, characteristic, complemented
5#10622587C211yesmaximal, characteristic, complemented
6C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#10622542C211yesmaximal, characteristic, complemented
8#10622288C214yesmaximal
9#10622268C214yesmaximal, complemented
10C22×C4×D11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×(C2×D11)⋊C4C2212yes—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20C2×Dic11⋊C4C2214yes—
21C2×C4×Dic11C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23#66950—24no—
24#66945—24no—
25C11×#95C2214yes—
26C11⋊#95C2212yes—
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C23×D11C2311yescharacteristic
30C22×C4×C11C2312yes—
31C22×C4×C11C2312yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×Dic11C2312yes—
35C22×Dic11C2312yes—
36C22×Dic11C2311yescharacteristic
37C22×Dic11C2312yes—
38C2×C4×D11—22no—
39C2×C4×D11—22no—
40C2×C4×D11D414yes—
41C2×Dic22—22no—
42C2×Dic22—22no—
43C2×Dic22—22no—
44C11×C4⋊C4—22no—
45C11×C4⋊C4—22no—
46C42×C11—22no—
47(C2×D11)⋊C4—24no—
48(C2×D11)⋊C4—24no—
49(C2×D11)⋊C4—24no—
50C4⋊Dic11—24no—
51C4⋊Dic11—22no—
52Dic11⋊C4—28no—
53C4×Dic11—24no—
54C4×Dic11—22no—
55#2499—111nomaximal, Sylow
56C23×C11C2411yescharacteristic
57C22×D11—22no—
58C22×D11—21no—
59C22×D11—21no—
60C22×D11—22no—
61C22×D11C2×D412yes—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—24no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—24no—
68C2×C4×C11—22no—
69C2×C4×C11C2×D412yes—
70C2×C4×C11#4112yes—
71C2×C4×C11#4112yes—
72C2×Dic11—22no—
73C2×Dic11—21no—
74C2×Dic11—21no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—24no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11C2×D412yes—
82C2×Dic11#4114yes—
83C4×D11—28no—
84Dic22—44no—
85C2×C22⋊Q8—111no—
86C2×#117—111no—
87#397—114no—
88#391—111no—
89#391—111no—
90#387—114no—
91#384—111no—
92#382D1111yescharacteristic, complemented
93C4×C22⋊C4—111no—
94C22×C11C22×D411yescharacteristic
95C22×C11C2×#4111yescharacteristic
96C22×C11C2×#4111yescharacteristic
97C22×C11C2×#4112yes—
98C22×C112−1+412yes—
99C2×D11—22no—
100C2×D11—22no—
101C2×D11—22no—
102C2×D11—42no—
103C2×D11—42no—
104C4×C11—42no—
105C4×C11—42no—
106C4×C11—42no—
107C4×C11#12314yes—
108Dic11—22no—
109Dic11—24no—
110Dic11—42no—
111Dic11—42no—
112C22×Q8—111no—
113C23×C4—111no—
114C22⋊Q8—224no—
115#117—224no—
116C2×C4⋊C4—111no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—114no—
119C2×C4⋊C4C2×D1111yescharacteristic
120C2×C4⋊C4C2×D1111yescharacteristic
121C2×C22⋊C4—112no—
122C2×C22⋊C4—112no—
123C2×C22⋊C4—112no—
124C2×C42—112no—
125C2×C42—111no—
126C2×C42C2×D1111yescharacteristic
127#95—112no—
128#95—114no—
129#95—114no—
130#95C2×D1114yes—
131C2×C11C2×#12311yescharacteristic
132C2×C11#53211yescharacteristic
133C2×C11#53611yescharacteristic
134C2×C11#55212yes—
135C2×C11#55612yes—
136D11—42no—
137C24—111no—
138C2×Q8—222no—
139C2×Q8—222no—
140C2×Q8—222no—
141C22×C4—112no—
142C22×C4—111no—
143C22×C4—114no—
144C22×C4—112no—
145C22×C4—112no—
146C22×C4—222no—
147C22×C4—222no—
148C22×C4C22×D1112yes—
149C22×C4C22×D1112yes—
150C22×C4C22×D1112yes—
151C22×C4C22×D1111yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—224no—
155C4⋊C4—228no—
156C4⋊C4—222no—
157C22⋊C4—224no—
158C22⋊C4—224no—
159C22⋊C4—224no—
160C42—22no—
161C42—224no—
162C42—222no—
163C11#249911yescharacteristic, complemented, Sylow
164C23—112no—
165C23—221no—
166C23—221no—
167C23—222no—
168C23—222no—
169C23C23×D1111yescharacteristic
170Q8—444no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—112no—
179C2×C4—114no—
180C2×C4—221no—
181C2×C4—222no—
182C2×C4—221no—
183C2×C4—222no—
184C2×C4—228no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—224no—
190C2×C4#433912yes—
191C2×C4D4×D1112yes—
192C2×C4#434312yes—
193C22—222no—
194C22—222no—
195C22—222no—
196C22—442no—
197C22—442no—
198C22C2×#433911yescharacteristic
199C22C2×D4×D1111yescharacteristic
200C22C2×#434311yescharacteristic
201C22#41×D1112yes—
202C22#6704312yes—
203C4—42no—
204C4—42no—
205C4—42no—
206C4—222no—
207C4—224no—
208C4—442no—
209C4—442no—
210C4#6694714yes—
211C2—442no—
212C2C2×#6694711yescharacteristic
213C2#1062306412yes—
214C2#1062319911yescharacteristic
215C2#1062320611yescharacteristic
216C2#1062322512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#382C2
prime radicalC23×D11C23
hypercenter#382D11
hypocenterC11#2499
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
3. C11×#382C2semidirect
4. #10622589C2semidirect
5. #10622587C2semidirect
7. #10622542C2semidirect
9. #10622268C2semidirect
92. #382D11semidirect
163. C11#2499semidirect

Maximal subgroups

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

subgroupindex
C2×#669502
C2×#669452
C11×#3822
#106225892
#106225872
C4×(C2×D11)⋊C42
#106225422
#106222882
#106222682
#249911