Finite Group Databasebeta

← #13072244

Subgroups — #13072244

Order 1408.

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

normal subgroups only

This group has 836 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×#4339C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic, complemented
3C2×#66928C211yesmaximal, characteristic, complemented
4C2×#66922C211yesmaximal, characteristic, complemented
5C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6#10622574C214yesmaximal, complemented
7#10622552C211yesmaximal, characteristic, complemented
8#10622542C211yesmaximal, characteristic, complemented
9#10622281C214yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C2×#4339—24no—
13C2×#4339—24no—
14C2×#4339—24no—
15C22×D44C2211yescharacteristic
16C22×C4×D11C2212yes—
17C22×Dic22C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C42×C11C2211yescharacteristic
21C2×C42×C11C2211yescharacteristic
22C2×C22⋊Dic11C2212yes—
23C2×(C2×D11)⋊C4C2214yes—
24C2×(C2×D11)⋊C4C2214yes—
25C2×C4⋊Dic11C2214yes—
26C2×C4⋊Dic11C2211yescharacteristic
27#66977—24no—
28C2×Dic11⋊C4C2212yes—
29#66928—24no—
30#66922—24no—
31C11×#95C2212yes—
32C11⋊#95C2214yes—
33C24×C11C2311yescharacteristic
34C23×D11C2312yes—
35C22×C4×C11—22no—
36C22×C4×C11—22no—
37C22×C4×C11D414yes—
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C2×C22⋊D11—24no—
43C2×C22⋊D11—24no—
44C2×C22⋊D11—24no—
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48#4339—232no—
49C2×D44—22no—
50C2×D44—22no—
51C2×D44D414yes—
52C2×C4×D11—24no—
53C2×C4×D11—24no—
54C2×C4×D11—24no—
55C2×Dic22—22no—
56C2×Dic22—22no—
57C2×Dic22—22no—
58C2×Dic22—22no—
59C2×Dic22—22no—
60C2×Dic22D414yes—
61C11×C22⋊C4—24no—
62C42×C11—22no—
63C42×C11—22no—
64C22⋊Dic11—24no—
65(C2×D11)⋊C4—28no—
66(C2×D11)⋊C4—28no—
67C4⋊Dic11—28no—
68C4⋊Dic11—22no—
69Dic11⋊C4—24no—
70#2432—111nomaximal, Sylow
71C23×C11—21no—
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11C2×D412yes—
76C23×C11C2411yescharacteristic
77C22×D11—22no—
78C22×D11—22no—
79C22×D11—24no—
80C22×D11—24no—
81C22×D11C2×D414yes—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—28no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×D412yes—
92C2×C4×C11C2×D412yes—
93C2×C4×C11C2×D412yes—
94C2×C4×C11#4114yescomplemented
95C22⋊D11—216no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—24no—
103C2×Dic11C2×D414yes—
104D44—28no—
105C4×D11—216no—
106Dic22—28no—
107Dic22—44no—
108C22×#41—111no—
109C2×C4⋊Q8—111no—
110C2×#124—111no—
111C2×C22⋊Q8—111no—
112#394—114no—
113#391—111no—
114#390—111no—
115#385—114no—
116C4×C22⋊C4D1111yescharacteristic, complemented
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—42no—
121C22×C11—42no—
122C22×C11C22×D411yescharacteristic
123C22×C11C22×D411yescharacteristic
124C22×C11C22×D411yescharacteristic
125C22×C11C2×#4112yes—
126C22×C112−1+412yes—
127C2×D11—24no—
128C2×D11—28no—
129C2×D11—42no—
130C2×D11—42no—
131C2×D11—44no—
132C4×C11—22no—
133C4×C11—24no—
134C4×C11—42no—
135C4×C11#12014yes—
136Dic11—24no—
137Dic11—42no—
138Dic11—42no—
139C2×#41—224no—
140C2×#41—224no—
141C2×#41—224no—
142C22×Q8—111no—
143C22×Q8—111no—
144C22×D4—112no—
145C22×D4—111no—
146C23×C4—112no—
147C23×C4C2×D1111yescharacteristic
148C4⋊Q8—224no—
149#124—224no—
150C22⋊Q8—224no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—111no—
153C2×C4⋊C4—114no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—114no—
156C2×C22⋊C4—114no—
157C2×C22⋊C4C2×D1112yes—
158C2×C42C2×D1111yescharacteristic
159C2×C42C2×D1111yescharacteristic
160#95—114no—
161#95C2×D1112yes—
162C2×C11—42no—
163C2×C11C2×#12011yescharacteristic
164C2×C11#53211yescharacteristic
165C2×C11#53611yescharacteristic
166C2×C11#54712yes—
167C2×C11#54812yes—
168D11—44no—
169C24—112no—
170C24C22×D1111yescharacteristic
171#41—2232no—
172C2×Q8—114no—
173C2×Q8—222no—
174C2×Q8—222no—
175C2×Q8—222no—
176C2×Q8—222no—
177C2×Q8—222no—
178C2×D4—114no—
179C2×D4—224no—
180C2×D4—224no—
181C2×D4—224no—
182C2×D4—222no—
183C2×D4—222no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—112no—
187C22×C4—112no—
188C22×C4—112no—
189C22×C4—224no—
190C22×C4—224no—
191C22×C4—224no—
192C22×C4D4414yes—
193C22×C4C22×D1112yes—
194C22×C4C22×D1111yescharacteristic
195C22×C4C22×D1112yes—
196C22×C4C22×D1111yescharacteristic
197C4⋊C4—228no—
198C4⋊C4—224no—
199C4⋊C4—222no—
200C22⋊C4—24no—
201C22⋊C4—228no—
202C22⋊C4—224no—
203C22⋊C4—228no—
204C42—22no—
205C42—22no—
206C11#243211yescharacteristic, complemented, Sylow
207C23—22no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—114no—
212C23—222no—
213C23—224no—
214C23—222no—
215C23—224no—
216C23C2×D4412yes—
217C23C23×D1111yescharacteristic
218Q8—228no—
219Q8—444no—
220D4—2216no—
221D4—228no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—28no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—114no—
231C2×C4—2216no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—224no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4C2×D4412yes—
240C2×C4C2×D4412yes—
241C2×C4#433914yescomplemented
242C2×C4D4×D1112yes—
243C2×C4D4×D1112yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—224no—
250C22—228no—
251C22—442no—
252C22—442no—
253C22—444no—
254C22C22×D4411yescharacteristic
255C22C2×#433912yes—
256C22C2×D4×D1111yescharacteristic
257C22C2×D4×D1111yescharacteristic
258C22#6704312yes—
259C4—22no—
260C4—24no—
261C4—42no—
262C4—224no—
263C4—442no—
264C4—442no—
265C4#6693514yes—
266C2—42no—
267C2—444no—
268C2#1062300811yescharacteristic
269C2C2×#6693511yescharacteristic
270C2#1062305711yescharacteristic
271C2#1062308212yes—
272C2#1062308312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C22⋊C4C2
prime radicalC22×#4339C2
hypercenterC4×C22⋊C4D11
hypocenterC11#2432
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#66977C2semidirect
3. C2×#66928C2semidirect
4. C2×#66922C2semidirect
5. C4×C11×C22⋊C4C2semidirect
6. #10622574C2semidirect
7. #10622552C2semidirect
8. #10622542C2semidirect
9. #10622281C2semidirect
94. C2×C4×C11#41semidirect
116. C4×C22⋊C4D11semidirect
206. C11#2432semidirect
241. C2×C4#4339semidirect

Maximal subgroups

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

subgroupindex
C22×#43392
C2×#669772
C2×#669282
C2×#669222
C4×C11×C22⋊C42
#106225742
#106225522
#106225422
#106222812
#243211