Finite Group Databasebeta

← #13073607

Subgroups — #13073607

Order 1408.

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

normal subgroups only

This group has 604 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×#66941C211yesmaximal, characteristic, complemented
2C2×#66938C212yesmaximal
3C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic
4C11×#397C211yesmaximal, characteristic, complemented
5#10622606C211yesmaximal, characteristic, complemented
6#10622566C211yesmaximal, characteristic, complemented
7#10622555C212yesmaximal, complemented
8#10622287C211yesmaximal, characteristic, complemented
9#10622280C212yesmaximal, complemented
10#10622262C211yesmaximal, characteristic, complemented
11#10622259C212yesmaximal, complemented
12C22×C22⋊D11C2211yescharacteristic
13C23×Dic11C2211yescharacteristic
14C22×C4×D11C2211yescharacteristic
15C22×Dic22C2212yes—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C22⋊Dic11C2212yes—
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2212yes—
28C2×C4×Dic11C2211yescharacteristic
29#66941—24no—
30#66938—28no—
31(C22⋊D11)⋊C4—24no—
32C11×#95C2212yes—
33C11×#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C11⋊#95C2211yescharacteristic
38C24×C11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—22no—
45C2×C22⋊D11—22no—
46C2×C22⋊D11D414yes—
47C22×Dic11—22no—
48C22×Dic11—24no—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2312yes—
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C2×C4×D11—22no—
55C2×C4×D11—24no—
56C2×Dic22—24no—
57C2×Dic22—24no—
58C2×Dic22—24no—
59C11×C4⋊C4—22no—
60C11×C22⋊C4—24no—
61C11×C22⋊C4—22no—
62C22⋊Dic11—24no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—22no—
66C4⋊Dic11—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—24no—
69Dic11⋊C4—24no—
70C4×Dic11—24no—
71C4×Dic11D414yes—
72#2547—111nomaximal, Sylow
73C23×C11—21no—
74C23×C11—22no—
75C23×C11—21no—
76C23×C11—22no—
77C23×C11C2×D412yes—
78C23×C11C2411yescharacteristic
79C22×D11—21no—
80C22×D11—22no—
81C22×D11—21no—
82C22×D11—22no—
83C22×D11C2×D412yes—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11C2×D412yes—
94C22⋊D11—28no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—44no—
104C2×Dic11C2×D412yes—
105C2×Dic11C2×D412yes—
106C2×Dic11C2×D412yes—
107C2×Dic11#4112yes—
108C2×Dic11#4114yes—
109C4×D11—44no—
110Dic22—48no—
111C2×C4⋊Q8—111no—
112C2×#124—112no—
113C2×C4×D4—111no—
114#397—111no—
115#397—111no—
116#397—111no—
117#397D1111yescharacteristic, complemented
118#391—112no—
119#380—112no—
120#380—112no—
121C4×C4⋊C4—111no—
122C22×C11—22no—
123C22×C11—24no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—42no—
127C22×C11C22×D411yescharacteristic
128C22×C11C22×D411yescharacteristic
129C22×C11C2×#4111yescharacteristic
130C22×C11C2×#4112yes—
131C22×C112−1+412yes—
132C2×D11—22no—
133C2×D11—24no—
134C2×D11—41no—
135C2×D11—41no—
136C2×D11—42no—
137C4×C11—22no—
138C4×C11—42no—
139C4×C11—41no—
140C4×C11—42no—
141Dic11—42no—
142Dic11—41no—
143Dic11—42no—
144Dic11#12114yes—
145Dic11#12414yescomplemented
146C22×Q8—112no—
147C22×D4—111no—
148C23×C4—111no—
149C23×C4—111no—
150C4⋊Q8—224no—
151#124—228no—
152C4×D4—224no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—112no—
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C22⋊C4—112no—
159C2×C22⋊C4—111no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4—112no—
162C2×C22⋊C4C2×D1111yescharacteristic
163C2×C22⋊C4C2×D1112yes—
164C2×C42—111no—
165C2×C42—112no—
166#95—111no—
167#95—112no—
168#95—112no—
169#95—112no—
170#95C2×D1111yescharacteristic
171#95C2×D1112yes—
172C2×C11—42no—
173C2×C11C2×#12111yescharacteristic
174C2×C11C2×#12411yescharacteristic
175C2×C11#53611yescharacteristic
176C2×C11#54712yes—
177C2×C11#55612yes—
178D11—42no—
179C24—111no—
180C24C22×D1111yescharacteristic
181C2×Q8—224no—
182C2×Q8—224no—
183C2×Q8—224no—
184C2×D4—114no—
185C2×D4—222no—
186C2×D4—222no—
187C22×C4—111no—
188C22×C4—111no—
189C22×C4—111no—
190C22×C4—112no—
191C22×C4—112no—
192C22×C4—222no—
193C22×C4—224no—
194C22×C4—222no—
195C22×C4—224no—
196C22×C4C22×D1111yescharacteristic
197C22×C4C22×D1112yes—
198C22×C4C22×D1112yes—
199C22×C4C22×D1111yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—222no—
202C4⋊C4—224no—
203C4⋊C4—224no—
204C4⋊C4—222no—
205C22⋊C4—24no—
206C22⋊C4—22no—
207C22⋊C4—224no—
208C22⋊C4—224no—
209C22⋊C4—224no—
210C22⋊C4—222no—
211C42—114no—
212C42—224no—
213C11#254711yescharacteristic, complemented, Sylow
214C23—21no—
215C23—22no—
216C23—21no—
217C23—22no—
218C23—112no—
219C23—221no—
220C23—222no—
221C23—221no—
222C23—222no—
223C23D4×D1112yes—
224C23C23×D1111yescharacteristic
225Q8—448no—
226D4—228no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—112no—
237C2×C4—112no—
238C2×C4—112no—
239C2×C4—114no—
240C2×C4—112no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—221no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—222no—
249C2×C4—444no—
250C2×C4—444no—
251C2×C4D4×D1112yes—
252C22—22no—
253C22—24no—
254C22—42no—
255C22—41no—
256C22—41no—
257C22—222no—
258C22—224no—
259C22—442no—
260C22—441no—
261C22—441no—
262C22C2×D4×D1111yescharacteristic
263C22C2×D4×D1111yescharacteristic
264C22#41×D1111yescharacteristic
265C22#41×D1112yes—
266C22#6704312yes—
267C4—22no—
268C4—42no—
269C4—42no—
270C4—41no—
271C4—114no—
272C4—114no—
273C4—442no—
274C4—442no—
275C4—441no—
276C2—42no—
277C2—442no—
278C2D11×#12111yescharacteristic
279C2#1062317911yescharacteristic
280C2#1062318612yes—
281C2D11×#12411yescharacteristic
282C2#1062323312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC22×C22⋊D11C22
hypercenter#397D11
hypocenterC11#2547
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#66941C2semidirect
4. C11×#397C2semidirect
5. #10622606C2semidirect
6. #10622566C2semidirect
7. #10622555C2semidirect
8. #10622287C2semidirect
9. #10622280C2semidirect
10. #10622262C2semidirect
11. #10622259C2semidirect
117. #397D11semidirect
145. Dic11#124semidirect
213. C11#2547semidirect

Maximal subgroups

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

subgroupindex
C2×#669412
C2×#669382
C2×(C22⋊D11)⋊C42
C11×#3972
#106226062
#106225662
#106225552
#106222872
#106222802
#106222622
#106222592
#254711