Finite Group Databasebeta

← #13072919

Subgroups — #13072919

Order 1408.

624 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 151 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×#66947C212yesmaximal
2C2×#66946C211yesmaximal, characteristic
3C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4C11×#398C211yesmaximal, characteristic, complemented
5#10622606C211yesmaximal, characteristic, complemented
6#10622596C211yesmaximal, characteristic, complemented
7#10622585C212yesmaximal, complemented
8#10622287C211yesmaximal, characteristic, complemented
9#10622280C212yesmaximal, complemented
10#10622280C211yesmaximal, characteristic, complemented
11#10622277C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11C2212yes—
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×C4⋊Dic11C2211yescharacteristic
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2211yescharacteristic
29#66947—28no—
30#66946—24no—
31C4⋊C4×D11—24no—
32C11×#95C2212yes—
33C11×#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2211yescharacteristic
38C23×D11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C22×Dic11C2311yescharacteristic
49C2×D44—22no—
50C2×D44—22no—
51C2×D44D414yes—
52C2×C4×D11—24no—
53C2×C4×D11—22no—
54C2×C4×D11—24no—
55C2×C4×D11—24no—
56C2×C4×D11—24no—
57C2×C4×D11—24no—
58C2×C4×D11D414yes—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—22no—
61C11×C4⋊C4—24no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—22no—
67C4⋊Dic11—22no—
68Dic11⋊C4—24no—
69Dic11⋊C4—24no—
70Dic11⋊C4—24no—
71C4×Dic11—22no—
72#2486—111nomaximal, Sylow
73C23×C11C2411yescharacteristic
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—21no—
77C22×D11—22no—
78C22×D11—21no—
79C22×D11—22no—
80C22×D11C2×D412yes—
81C22×D11C2×D412yes—
82C22×D11C2×D412yes—
83C22×D11#4112yes—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11C2×D412yes—
96C2×C4×C11C2×D412yes—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11C2×D412yes—
106C2×Dic11#4114yes—
107D44—28no—
108C4×D11—28no—
109C4×D11—48no—
110C4×D11—44no—
111C2×#123—112no—
112C2×C4×D4—111no—
113C22×C4⋊C4—111no—
114#398—111no—
115#398D1111yescharacteristic, complemented
116#397—111no—
117#397—111no—
118#389—112no—
119#381—112no—
120#380—112no—
121#380—111no—
122C22×C11C22×D411yescharacteristic
123C22×C11C22×D411yescharacteristic
124C22×C11C2×#4111yescharacteristic
125C22×C11C2×#4112yes—
126C22×C112−1+412yes—
127C2×D11—22no—
128C2×D11—22no—
129C2×D11—24no—
130C2×D11—24no—
131C2×D11—22no—
132C2×D11—24no—
133C2×D11—41no—
134C2×D11—41no—
135C2×D11—42no—
136C2×D11#12114yes—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—42no—
140C4×C11—41no—
141C4×C11—42no—
142Dic11—42no—
143Dic11—41no—
144Dic11—42no—
145Dic11#12314yescomplemented
146C22×D4—111no—
147C23×C4—111no—
148C23×C4—112no—
149C23×C4—111no—
150#123—228no—
151C4×D4—224no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4—224no—
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C4⋊C4C2×D1111yescharacteristic
159C2×C4⋊C4C2×D1112yes—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—111no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C42—111no—
166#95—112no—
167#95—111no—
168#95—112no—
169#95—112no—
170#95C2×D1112yes—
171#95C2×D1111yescharacteristic
172C2×C11C2×#12111yescharacteristic
173C2×C11C2×#12311yescharacteristic
174C2×C11#53611yescharacteristic
175C2×C11#54712yes—
176C2×C11#55212yes—
177D11—24no—
178D11—42no—
179C24—111no—
180C24—111no—
181C2×D4—114no—
182C2×D4—222no—
183C2×D4—222no—
184C22×C4—111no—
185C22×C4—114no—
186C22×C4—111no—
187C22×C4—112no—
188C22×C4—112no—
189C22×C4—224no—
190C22×C4—222no—
191C22×C4—224no—
192C22×C4—224no—
193C22×C4—224no—
194C22×C4—224no—
195C22×C4C22×D1111yescharacteristic
196C22×C4C22×D1112yes—
197C22×C4C22×D1112yes—
198C22×C4C22×D1111yescharacteristic
199C22×C4C22×D1111yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—24no—
203C4⋊C4—224no—
204C4⋊C4—224no—
205C4⋊C4—222no—
206C4⋊C4—224no—
207C22⋊C4—222no—
208C22⋊C4—224no—
209C22⋊C4—224no—
210C22⋊C4—224no—
211C22⋊C4—222no—
212C42—222no—
213C11#248611yescharacteristic, complemented, Sylow
214C23—112no—
215C23—112no—
216C23—112no—
217C23—112no—
218C23—222no—
219C23—222no—
220C23—221no—
221C23—222no—
222C23—222no—
223C23—221no—
224C23C23×D1111yescharacteristic
225D4—228no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—112no—
238C2×C4—114no—
239C2×C4—228no—
240C2×C4—221no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—444no—
249C2×C4—448no—
250C2×C4D4×D1112yes—
251C2×C4D4×D1112yes—
252C22—114no—
253C22—222no—
254C22—224no—
255C22—222no—
256C22—224no—
257C22—222no—
258C22—224no—
259C22—441no—
260C22—441no—
261C22—442no—
262C22C2×D4×D1111yescharacteristic
263C22C2×D4×D1111yescharacteristic
264C22#6704012yes—
265C22#41×D1111yescharacteristic
266C22#41×D1112yes—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—42no—
271C4—41no—
272C4—114no—
273C4—441no—
274C4—442no—
275C4—442no—
276C2—224no—
277C2—442no—
278C2D11×#12111yescharacteristic
279C2#1062316212yes—
280C2D11×#12311yescharacteristic
281C2#1062322412yes—
282C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#398C2
prime radicalC22×D44C22
hypercenter#398D11
hypocenterC11#2486
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D11C2semidirect
4. C11×#398C2semidirect
5. #10622606C2semidirect
6. #10622596C2semidirect
7. #10622585C2semidirect
8. #10622287C2semidirect
9. #10622280C2semidirect
10. #10622280C2semidirect
11. #10622277C2semidirect
115. #398D11semidirect
145. Dic11#123semidirect
213. C11#2486semidirect

Maximal subgroups

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

subgroupindex
C2×#669472
C2×#669462
C2×C4⋊C4×D112
C11×#3982
#106226062
#106225962
#106225852
#106222872
#106222802
#106222772
#248611