Finite Group Databasebeta

← #13073969

Subgroups — #13073969

Order 1408.

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

normal subgroups only

This group has 564 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×Q8×Dic11C211yesmaximal, characteristic, complemented
2C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3C11×#393C211yesmaximal, characteristic, complemented
4#10622844C211yesmaximal, characteristic, complemented
5#10622570C212yesmaximal
6#10622563C212yesmaximal, complemented
7#10622562C211yesmaximal, characteristic, complemented
8#10622290C211yesmaximal, characteristic, complemented
9#10622281C212yesmaximal, complemented
10#10622263C211yesmaximal, characteristic, complemented
11#10622260C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C23×Dic11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C2×C11×C22⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C22⋊Dic11C2212yes—
19Q8×Dic11—24no—
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2212yes—
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2212yes—
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×C4×Dic11C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31(C22⋊D11)⋊C4—24no—
32C11×#95C2212yes—
33C11×#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C2×Q8×C11—22no—
40C2×Q8×C11—24no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2312yes—
45C2×C22⋊D11—22no—
46C2×C22⋊D11—22no—
47C2×C22⋊D11Q814yescomplemented
48C22×Dic11—22no—
49C22×Dic11—42no—
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C2×C4×D11—22no—
56C2×C4×D11—42no—
57C11×C22⋊C4—22no—
58C11×C22⋊C4—24no—
59C22⋊Dic11—42no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—24no—
62(C2×D11)⋊C4—42no—
63C4⋊Dic11—24no—
64C4⋊Dic11—22no—
65C4⋊Dic11—42no—
66Dic11⋊C4—22no—
67Dic11⋊C4—24no—
68Dic11⋊C4—42no—
69C4×Dic11—24no—
70C4×Dic11D414yes—
71#2580—111nomaximal, Sylow
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11C2×Q812yes—
77C23×C11C2411yescharacteristic
78C22×D11—21no—
79C22×D11—22no—
80C22×D11—21no—
81C22×D11—22no—
82C22×D11C2×Q812yes—
83Q8×C11—28no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11C2×D412yes—
93C2×C4×C11#4114yes—
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—22no—
104C2×Dic11—44no—
105C2×Dic11C2×D412yes—
106C2×Dic11C2×D412yes—
107C2×Dic11C2×Q812yes—
108C2×Dic11#4112yes—
109C4×D11—44no—
110C2×C4×Q8—111no—
111C2×C4×D4—111no—
112#399—111no—
113#399—111no—
114#393—111no—
115#393D1111yescharacteristic, complemented
116#390—112no—
117#389—112no—
118#385—112no—
119#385—112no—
120#382—111no—
121C22×C11—22no—
122C22×C11—24no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—42no—
126C22×C11C22×D411yescharacteristic
127C22×C11C22×Q811yescharacteristic
128C22×C11C2×#4112yes—
129C22×C11C2×#4111yescharacteristic
130C22×C11H(5,𝔽2)12yes—
131C2×D11—22no—
132C2×D11—24no—
133C2×D11—41no—
134C2×D11—41no—
135C2×D11—42no—
136C4×C11—22no—
137C4×C11—24no—
138C4×C11—41no—
139C4×C11—42no—
140Dic11—22no—
141Dic11—42no—
142Dic11—41no—
143Dic11—42no—
144Dic11C22⋊Q814yes—
145C22×Q8C2×D1111yescharacteristic
146C22×D4—111no—
147C23×C4—111no—
148C23×C4—111no—
149C4×Q8—224no—
150C4×D4—224no—
151C2×C4⋊C4—111no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4—112no—
157C2×C22⋊C4—111no—
158C2×C22⋊C4—112no—
159C2×C22⋊C4—112no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4C2×D1111yescharacteristic
162C2×C22⋊C4C2×D1112yes—
163C2×C42—111no—
164C2×C42—112no—
165#95—112no—
166#95—111no—
167#95—112no—
168#95C2×D1111yescharacteristic
169#95C2×D1112yes—
170C2×C11—42no—
171C2×C11C2×C22⋊Q811yescharacteristic
172C2×C11#52511yescharacteristic
173C2×C11#53511yescharacteristic
174C2×C11#55412yes—
175C2×C11#55912yes—
176D11—42no—
177C24—111no—
178C24C22×D1111yescharacteristic
179C2×Q8—22no—
180C2×Q8—24no—
181C2×D4—114no—
182C2×D4—222no—
183C2×D4—222no—
184C22×C4—111no—
185C22×C4—111no—
186C22×C4—112no—
187C22×C4—111no—
188C22×C4—112no—
189C22×C4—222no—
190C22×C4—222no—
191C22×C4—442no—
192C22×C4—442no—
193C22×C4C22×D1112yes—
194C22×C4C22×D1111yescharacteristic
195C22×C4C22×D1111yescharacteristic
196C22×C4C22×D1112yes—
197C4⋊C4—222no—
198C4⋊C4—224no—
199C4⋊C4—224no—
200C4⋊C4—222no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C22⋊C4—22no—
204C22⋊C4—24no—
205C22⋊C4—222no—
206C22⋊C4—224no—
207C22⋊C4—442no—
208C22⋊C4—442no—
209C42—114no—
210C42—224no—
211C11#258011yescharacteristic, complemented, Sylow
212C23—21no—
213C23—22no—
214C23—21no—
215C23—22no—
216C23—112no—
217C23—221no—
218C23—222no—
219C23—221no—
220C23—222no—
221C23Q8×D1112yes—
222C23C23×D1111yescharacteristic
223Q8—28no—
224D4—228no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—112no—
234C2×C4—112no—
235C2×C4—112no—
236C2×C4—112no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—221no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—444no—
247C2×C4—444no—
248C2×C4D4×D1112yes—
249C2×C4#434114yes—
250C22—22no—
251C22—24no—
252C22—41no—
253C22—41no—
254C22—42no—
255C22—222no—
256C22—224no—
257C22—441no—
258C22—441no—
259C22—442no—
260C22C2×D4×D1111yescharacteristic
261C22C2×#434112yes—
262C22C2×Q8×D1111yescharacteristic
263C22#41×D1111yescharacteristic
264C22#6704212yes—
265C4—22no—
266C4—24no—
267C4—41no—
268C4—42no—
269C4—114no—
270C4—222no—
271C4—441no—
272C4—442no—
273C4—442no—
274C2—42no—
275C2—442no—
276C2#1062311711yescharacteristic
277C2D11×C22⋊Q811yescharacteristic
278C2#1062316612yes—
279C2#1062320511yescharacteristic
280C2#1062321212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC22×C22⋊D11C22
hypercenter#393D11
hypocenterC11#2580
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic11C2semidirect
3. C11×#393C2semidirect
4. #10622844C2semidirect
6. #10622563C2semidirect
7. #10622562C2semidirect
8. #10622290C2semidirect
9. #10622281C2semidirect
10. #10622263C2semidirect
11. #10622260C2semidirect
47. C2×C22⋊D11Q8semidirect
115. #393D11semidirect
211. C11#2580semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic112
C2×(C22⋊D11)⋊C42
C11×#3932
#106228442
#106225702
#106225632
#106225622
#106222902
#106222812
#106222632
#106222602
#258011