Finite Group Databasebeta

← #13074237

Subgroups — #13074237

Order 1408.

582 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×D4×C11C211yesmaximal, characteristic, complemented
2C2×#66929C211yesmaximal, characteristic, complemented
3#10622836C211yesmaximal, characteristic
4#10622835C211yesmaximal, characteristic, complemented
5#10622826C212yesmaximal, complemented
6#10622823C212yesmaximal, complemented
7#10622606C211yesmaximal, characteristic, complemented
8#10622593C211yesmaximal, characteristic, complemented
9#10622570C212yesmaximal, complemented
10#10622558C212yesmaximal, complemented
11#10622545C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2212yes—
14C22×C22⋊D11C2212yes—
15C4×D4×C11—24no—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C42×C11C2211yescharacteristic
19C2×C22⋊Dic11C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2212yes—
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2212yes—
31#66929—24no—
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C23×D11C2311yescharacteristic
39C2×D4×C11—24no—
40C2×D4×C11—22no—
41C22×C4×C11—24no—
42C22×C4×C11—42no—
43C22×C4×C11—42no—
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—24no—
49C2×C22⋊D11—24no—
50C2×C22⋊D11—42no—
51C22×Dic11C2312yes—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2311yescharacteristic
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2312yes—
56C11×C4⋊C4—22no—
57C11×C22⋊C4—24no—
58C42×C11D414yescomplemented
59C22⋊Dic11—24no—
60C22⋊Dic11—24no—
61C22⋊Dic11—42no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—42no—
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—42no—
70C4×Dic11—24no—
71#2603—111nomaximal, Sylow
72C23×C11—22no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11#4114yes—
79C23×C11C2411yescharacteristic
80C22×D11—21no—
81C22×D11—22no—
82C22×D11—22no—
83C22×D11—21no—
84C22×D11—21no—
85D4×C11—28no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—48no—
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2×D412yes—
96C2×C4×C11C2×D412yes—
97C22⋊D11—48no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—21no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—21no—
108C2×Dic11—22no—
109C2×Dic11—21no—
110C2×Dic11#4114yes—
111C2×#126—111no—
112C2×C4×D4D1111yescharacteristic, complemented
113#398—111no—
114#397—111no—
115#394—111no—
116#392—111no—
117#390—112no—
118#388—112no—
119#386—112no—
120#385—112no—
121#376—111no—
122C22×C11—24no—
123C22×C11—24no—
124C22×C11—24no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11C22×D411yescharacteristic
130C22×C11C2×#4112yes—
131C22×C11C2×#4112yes—
132C22×C11H(5,𝔽2)11yescharacteristic
133C22×C11H(5,𝔽2)11yescharacteristic
134C2×D11—41no—
135C2×D11—41no—
136C2×D11—41no—
137C2×D11—42no—
138C2×D11—42no—
139C4×C11—22no—
140C4×C11—22no—
141C4×C11—22no—
142C4×C11—42no—
143Dic11—24no—
144Dic11—41no—
145Dic11—41no—
146Dic11—41no—
147Dic11—42no—
148C22×D4—112no—
149C22×D4C2×D1111yescharacteristic
150C23×C4C2×D1112yes—
151#126—224no—
152C4×D4—24no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—111no—
155C2×C4⋊C4—111no—
156C2×C4⋊C4—112no—
157C2×C4⋊C4C2×D1111yescharacteristic
158C2×C22⋊C4—112no—
159C2×C22⋊C4—112no—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—111no—
162C2×C22⋊C4—111no—
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4C2×D1112yes—
166C2×C42—112no—
167C2×C42C2×D1111yescharacteristic
168#95—112no—
169#95—111no—
170#95—111no—
171#95—112no—
172#95—112no—
173C2×C11—44no—
174C2×C11#52511yescharacteristic
175C2×C11#53211yescharacteristic
176C2×C11#53511yescharacteristic
177C2×C11#55112yes—
178C2×C11#55312yes—
179D11—81no—
180C24—111no—
181C24C22×D1112yes—
182C2×D4—24no—
183C2×D4—22no—
184C2×D4—224no—
185C2×D4—224no—
186C2×D4—442no—
187C22×C4—24no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—112no—
191C22×C4—112no—
192C22×C4—111no—
193C22×C4—111no—
194C22×C4—111no—
195C22×C4C22×D1112yes—
196C22×C4C22×D1111yescharacteristic
197C22×C4C22×D1111yescharacteristic
198C22×C4C22×D1111yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C4⋊C4—222no—
203C4⋊C4—442no—
204C22⋊C4—24no—
205C22⋊C4—224no—
206C22⋊C4—224no—
207C22⋊C4—222no—
208C22⋊C4—222no—
209C22⋊C4—222no—
210C22⋊C4—442no—
211C22⋊C4—442no—
212C42—224no—
213C42C22⋊D1114yescomplemented
214C11#260311yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—222no—
222C23—221no—
223C23—221no—
224C23—222no—
225C23—221no—
226C23#433914yes—
227C23C23×D1111yescharacteristic
228D4—28no—
229D4—448no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—48no—
238C2×C4—114no—
239C2×C4—222no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—221no—
245C2×C4—221no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—221no—
251C2×C4C2×C22⋊D1112yes—
252C2×C4C2×C22⋊D1112yes—
253C2×C4C2×C22⋊D1112yes—
254C22—24no—
255C22—24no—
256C22—24no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—441no—
262C22—442no—
263C22—441no—
264C22—442no—
265C22—441no—
266C22C2×#433912yes—
267C22#6703711yescharacteristic
268C22#6703711yescharacteristic
269C22#41×D1112yes—
270C22C22×C22⋊D1111yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—42no—
275C4—224no—
276C4—441no—
277C4—442no—
278C4—441no—
279C4—441no—
280C2—44no—
281C2—881no—
282C2#1062307112yes—
283C2#1062308712yes—
284C2#1062332211yescharacteristic
285C2#1062333611yescharacteristic
286C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
prime radical#10622836C2
hypercenterC2×C4×D4D11
hypocenterC11#2603
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C11C2semidirect
2. C2×#66929C2semidirect
4. #10622835C2semidirect
5. #10622826C2semidirect
6. #10622823C2semidirect
7. #10622606C2semidirect
8. #10622593C2semidirect
9. #10622570C2semidirect
10. #10622558C2semidirect
11. #10622545C2semidirect
58. C42×C11D4semidirect
112. C2×C4×D4D11semidirect
213. C42C22⋊D11semidirect
214. C11#2603semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C2×#669292
#106228362
#106228352
#106228262
#106228232
#106226062
#106225932
#106225702
#106225582
#106225452
#260311