Finite Group Databasebeta

← #13073968

Subgroups — #13073968

Order 1408.

584 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 153 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×Dic11⋊C4C211yesmaximal, characteristic, complemented
2C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3C11×#385C211yesmaximal, characteristic, complemented
4#10622826C211yesmaximal, characteristic
5#10622602C212yesmaximal, complemented
6#10622593C212yesmaximal, complemented
7#10622571C211yesmaximal, characteristic
8#10622559C211yesmaximal, characteristic, complemented
9#10622555C211yesmaximal, characteristic, complemented
10#10622289C212yesmaximal, complemented
11#10622265C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C23×Dic11C2211yescharacteristic
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C22⋊Dic11C2211yescharacteristic
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×Dic11⋊C4—24no—
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31(C22⋊D11)⋊C4—24no—
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C22×C4×C11—22no—
40C22×C4×C11—42no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—22no—
46C2×C22⋊D11—22no—
47C2×C22⋊D11Q814yes—
48C22×Dic11—24no—
49C22×Dic11—22no—
50C22×Dic11—42no—
51C22×Dic11D414yes—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2312yes—
57C2×C4×D11—22no—
58C2×C4×D11—42no—
59C11×C4⋊C4—42no—
60C11×C22⋊C4—22no—
61C11×C22⋊C4—22no—
62C22⋊Dic11—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—42no—
66Dic11⋊C4—22no—
67Dic11⋊C4—24no—
68Dic11⋊C4—24no—
69Dic11⋊C4—24no—
70Dic11⋊C4—42no—
71C4×Dic11—22no—
72#2579—111nomaximal, Sylow
73C23×C11—22no—
74C23×C11—22no—
75C23×C11C2×D412yes—
76C23×C11C2×Q812yes—
77C23×C11#4112yes—
78C23×C11C2411yescharacteristic
79C22×D11—21no—
80C22×D11—22no—
81C22×D11—21no—
82C22×D11—22no—
83C22×D11C2×Q812yes—
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—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—44no—
95C22⋊D11—28no—
96C2×Dic11—28no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—21no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—44no—
107C2×Dic11C2×D412yes—
108C2×Dic11C2×D412yes—
109C2×Dic11C2×Q812yes—
110C2×Dic11#4114yes—
111C4×D11—44no—
112C2×C4×D4—111no—
113C22×C4⋊C4—111no—
114#398—112no—
115#396—112no—
116#387—112no—
117#386—111no—
118#386—111no—
119#385—112no—
120#385—111no—
121#385D1111yescharacteristic, complemented
122#380—111no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11—24no—
126C22×C11—24no—
127C22×C11C22⋊Q814yes—
128C22×C11C22×D411yescharacteristic
129C22×C11C22×Q811yescharacteristic
130C22×C11C2×#4111yescharacteristic
131C22×C11C2×#4112yes—
132C22×C11H(5,𝔽2)12yes—
133C2×D11—22no—
134C2×D11—24no—
135C2×D11—41no—
136C2×D11—41no—
137C2×D11—42no—
138C4×C11—41no—
139C4×C11—42no—
140C4×C11—41no—
141C4×C11—42no—
142Dic11—22no—
143Dic11—24no—
144Dic11—22no—
145Dic11—22no—
146Dic11—42no—
147C22×D4—111no—
148C23×C4—111no—
149C23×C4—111no—
150C23×C4—111no—
151C23×C4C2×D1111yescharacteristic
152C4×D4—224no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—112no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4—224no—
159C2×C4⋊C4C2×D1112yes—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—111no—
162C2×C22⋊C4—112no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4C2×D1111yescharacteristic
165C2×C22⋊C4C2×D1111yescharacteristic
166C2×C42—111no—
167#95—112no—
168#95—112no—
169#95—112no—
170#95—112no—
171#95C2×D1112yes—
172C2×C11—24no—
173C2×C11C2×C22⋊Q811yescharacteristic
174C2×C11#52511yescharacteristic
175C2×C11#53411yescharacteristic
176C2×C11#55312yes—
177C2×C11#55412yes—
178D11—42no—
179C24—111no—
180C24C22×D1111yescharacteristic
181C2×D4—114no—
182C2×D4—222no—
183C2×D4—222no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4—111no—
187C22×C4—111no—
188C22×C4—112no—
189C22×C4—111no—
190C22×C4—114no—
191C22×C4—112no—
192C22×C4—222no—
193C22×C4—224no—
194C22×C4—222no—
195C22×C4—442no—
196C22×C4—442no—
197C22×C4C22×D1112yes—
198C22×C4C22×D1111yescharacteristic
199C22×C4C22×D1112yes—
200C22×C4C22×D1111yescharacteristic
201C4⋊C4—42no—
202C4⋊C4—224no—
203C4⋊C4—224no—
204C4⋊C4—222no—
205C4⋊C4—224no—
206C4⋊C4—442no—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—222no—
210C22⋊C4—224no—
211C22⋊C4—222no—
212C22⋊C4—442no—
213C42—222no—
214C11#257911yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—112no—
218C23—221no—
219C23—221no—
220C23—222no—
221C23—222no—
222C23#433912yes—
223C23D4×D1112yes—
224C23Q8×D1112yes—
225C23C23×D1111yescharacteristic
226D4—228no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—112no—
239C2×C4—112no—
240C2×C4—112no—
241C2×C4—114no—
242C2×C4—228no—
243C2×C4—221no—
244C2×C4—221no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—222no—
249C2×C4—222no—
250C2×C4—222no—
251C2×C4—222no—
252C2×C4—444no—
253C2×C4—444no—
254C22—24no—
255C22—22no—
256C22—24no—
257C22—22no—
258C22—222no—
259C22—224no—
260C22—442no—
261C22—441no—
262C22—441no—
263C22#6694914yes—
264C22C2×#433911yescharacteristic
265C22C2×D4×D1111yescharacteristic
266C22#6703712yes—
267C22C2×Q8×D1111yescharacteristic
268C22#41×D1112yes—
269C4—42no—
270C4—42no—
271C4—41no—
272C4—41no—
273C4—222no—
274C4—222no—
275C4—222no—
276C4—224no—
277C4—442no—
278C2—24no—
279C2—442no—
280C2C2×#6694911yescharacteristic
281C2#1062307112yes—
282C2#1062312011yescharacteristic
283C2#1062316712yes—
284C2#1062318711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
prime radicalC22×C22⋊D11C22
hypercenter#385D11
hypocenterC11#2579
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C22×Dic11⋊C4C2semidirect
3. C11×#385C2semidirect
5. #10622602C2semidirect
6. #10622593C2semidirect
8. #10622559C2semidirect
9. #10622555C2semidirect
10. #10622289C2semidirect
11. #10622265C2semidirect
121. #385D11semidirect
214. C11#2579semidirect

Maximal subgroups

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

subgroupindex
C22×Dic11⋊C42
C2×(C22⋊D11)⋊C42
C11×#3852
#106228262
#106226022
#106225932
#106225712
#106225592
#106225552
#106222892
#106222652
#257911