Finite Group Databasebeta

← #13072918

Subgroups — #13072918

Order 1408.

624 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 173 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×C11×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#66982C212yesmaximal
3C2×C4×C22⋊D11C211yesmaximal, characteristic
4#10622825C211yesmaximal, characteristic, complemented
5#10622824C212yesmaximal, complemented
6#10622606C212yesmaximal, complemented
7#10622600C212yesmaximal, complemented
8#10622593C212yesmaximal, complemented
9#10622586C212yesmaximal, complemented
10C23×C4×C11C2212yes—
11C23×C4×C11C2211yescharacteristic
12C22×C22⋊D11C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C2×C11×C4⋊C4—24no—
15C2×C11×C4⋊C4C2212yes—
16C2×C11×C4⋊C4C2212yes—
17C2×C22⋊Dic11C2211yescharacteristic
18C2×C22⋊Dic11C2212yes—
19#66982—28no—
20C4×C22⋊D11—24no—
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2214yes—
23C2×C4⋊Dic11C2212yes—
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2214yes—
26C2×C4×Dic11C2211yescharacteristic
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C11⋊#95C2212yes—
30C24×C11C2311yescharacteristic
31C23×D11C2311yescharacteristic
32C22×C4×C11—24no—
33C22×C4×C11—24no—
34C22×C4×C11—24no—
35C22×C4×C11—24no—
36C22×C4×C11D414yes—
37C22×C4×C11C2314yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C2×C22⋊D11—22no—
41C2×C22⋊D11—22no—
42C2×C22⋊D11D414yes—
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2314yes—
46C22×Dic11C2311yescharacteristic
47C2×C4×D11—22no—
48C2×C4×D11—24no—
49C11×C4⋊C4—24no—
50C11×C4⋊C4—24no—
51C22⋊Dic11—22no—
52C22⋊Dic11—24no—
53(C2×D11)⋊C4—28no—
54(C2×D11)⋊C4—22no—
55C4⋊Dic11—24no—
56Dic11⋊C4—28no—
57Dic11⋊C4—22no—
58C4×Dic11—22no—
59#2486—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11—22no—
62C23×C11C2×D412yes—
63C23×C11C2×D412yes—
64C23×C11#4112yes—
65C23×C11C2411yescharacteristic
66C22×D11—21no—
67C22×D11—22no—
68C22×D11—21no—
69C22×D11—22no—
70C22×D11C2×D412yes—
71C2×C4×C11—22no—
72C2×C4×C11—28no—
73C2×C4×C11—24no—
74C2×C4×C11—24no—
75C2×C4×C11—24no—
76C2×C4×C11—48no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2×D412yes—
79C2×C4×C11#4114yes—
80C22⋊D11—28no—
81C2×Dic11—21no—
82C2×Dic11—21no—
83C2×Dic11—21no—
84C2×Dic11—24no—
85C2×Dic11—21no—
86C2×Dic11—24no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—24no—
90C2×Dic11C2×D412yes—
91C4×D11—44no—
92C2×#123—112no—
93C2×C4×D4—111no—
94C22×C4⋊C4D1111yescharacteristic, complemented
95#398—112no—
96#397—112no—
97#389—112no—
98#381—112no—
99#380—111no—
100#380—112no—
101C22×C11—22no—
102C22×C11—22no—
103C22×C11—24no—
104C22×C11—24no—
105C22×C11#12114yes—
106C22×C11C22×D411yescharacteristic
107C22×C11C22×D411yescharacteristic
108C22×C11C2×#4112yes—
109C22×C11C2×#4111yescharacteristic
110C22×C112−1+412yes—
111C2×D11—22no—
112C2×D11—24no—
113C2×D11—41no—
114C2×D11—41no—
115C2×D11—42no—
116C4×C11—22no—
117C4×C11—44no—
118C4×C11#12314yescomplemented
119Dic11—22no—
120Dic11—41no—
121Dic11—41no—
122Dic11—44no—
123C22×D4—111no—
124C23×C4—111no—
125C23×C4C2×D1112yes—
126C23×C4C2×D1111yescharacteristic
127#123—228no—
128C4×D4—224no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—111no—
131C2×C4⋊C4—114no—
132C2×C4⋊C4—112no—
133C2×C4⋊C4C2×D1112yes—
134C2×C4⋊C4C2×D1112yes—
135C2×C22⋊C4—111no—
136C2×C22⋊C4—112no—
137C2×C22⋊C4—111no—
138C2×C22⋊C4—114no—
139C2×C42—111no—
140#95—114no—
141#95—112no—
142#95—114no—
143C2×C11—24no—
144C2×C11C2×#12111yescharacteristic
145C2×C11C2×#12311yescharacteristic
146C2×C11#53611yescharacteristic
147C2×C11#54712yes—
148C2×C11#55212yes—
149D11—42no—
150C24—111no—
151C24C22×D1111yescharacteristic
152C2×D4—114no—
153C2×D4—222no—
154C2×D4—222no—
155C22×C4—24no—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—111no—
160C22×C4—111no—
161C22×C4—111no—
162C22×C4—114no—
163C22×C4—224no—
164C22×C4—222no—
165C22×C4C22⋊D1114yes—
166C22×C4C22×D1114yes—
167C22×C4C22×D1111yescharacteristic
168C22×C4C22×D1111yescharacteristic
169C4⋊C4—24no—
170C4⋊C4—24no—
171C4⋊C4—228no—
172C4⋊C4—224no—
173C4⋊C4—222no—
174C22⋊C4—228no—
175C22⋊C4—224no—
176C22⋊C4—222no—
177C22⋊C4—222no—
178C42—222no—
179C11#248611yescharacteristic, complemented, Sylow
180C23—22no—
181C23—22no—
182C23—112no—
183C23—222no—
184C23—221no—
185C23—222no—
186C23—221no—
187C23D4×D1112yes—
188C23#434112yes—
189C23C2×C22⋊D1112yes—
190C23C23×D1111yescharacteristic
191D4—228no—
192C2×C4—22no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—48no—
198C2×C4—112no—
199C2×C4—221no—
200C2×C4—221no—
201C2×C4—224no—
202C2×C4—222no—
203C2×C4—224no—
204C2×C4—224no—
205C2×C4—222no—
206C2×C4—221no—
207C2×C4—221no—
208C2×C4—444no—
209C2×C4#433914yes—
210C2×C4C2×C22⋊D1112yes—
211C2×C4C2×C22⋊D1112yes—
212C22—24no—
213C22—24no—
214C22—22no—
215C22—22no—
216C22—224no—
217C22—222no—
218C22—442no—
219C22—441no—
220C22—441no—
221C22#6699114yes—
222C22C2×#433912yes—
223C22C2×D4×D1111yescharacteristic
224C22C2×#434111yescharacteristic
225C22#6704012yes—
226C22C22×C22⋊D1111yescharacteristic
227C4—22no—
228C4—44no—
229C4—222no—
230C4—444no—
231C4—441no—
232C4—441no—
233C4#6698214yescomplemented
234C2—24no—
235C2—442no—
236C2#1062303812yes—
237C2#1062304412yes—
238C2C2×#6698211yescharacteristic
239C2C2×#6699111yescharacteristic
240C2#1062334711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C11×C4⋊C4C2
prime radicalC22×C22⋊D11C22
hypercenterC22×C4⋊C4D11
hypocenterC11#2486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊C4C2semidirect
4. #10622825C2semidirect
5. #10622824C2semidirect
6. #10622606C2semidirect
7. #10622600C2semidirect
8. #10622593C2semidirect
9. #10622586C2semidirect
94. C22×C4⋊C4D11semidirect
118. C4×C11#123semidirect
179. C11#2486semidirect
233. C4#66982semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊C42
C2×#669822
C2×C4×C22⋊D112
#106228252
#106228242
#106226062
#106226002
#106225932
#106225862
#248611