Finite Group Databasebeta

← #13073963

Subgroups — #13073963

Order 1408.

584 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D11C211yesmaximal, characteristic
3#10622826C211yesmaximal, characteristic
4#10622826C211yesmaximal, characteristic
5#10622825C211yesmaximal, characteristic, complemented
6#10622823C211yesmaximal, characteristic, complemented
7#10622823C211yesmaximal, characteristic, complemented
8#10622607C212yesmaximal, complemented
9#10622602C212yesmaximal, complemented
10#10622597C212yesmaximal, complemented
11#10622591C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C22×C22⋊D11C2211yescharacteristic
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4—24no—
18C2×C11×C4⋊C4C2212yes—
19C2×C11×C4⋊C4C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23C4×C22⋊D11—24no—
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×C4⋊Dic11C2212yes—
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C22×C4×C11—22no—
40C22×C4×C11—24no—
41C22×C4×C11—22no—
42C22×C4×C11—42no—
43C22×C4×C11—42no—
44C22×C4×C11D414yes—
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2312yes—
49C2×C22⋊D11—22no—
50C2×C22⋊D11—22no—
51C2×C22⋊D11Q814yes—
52C22×Dic11C2312yes—
53C22×Dic11C2312yes—
54C22×Dic11C2311yescharacteristic
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2311yescharacteristic
57C2×C4×D11—22no—
58C2×C4×D11—42no—
59C11×C4⋊C4—24no—
60C11×C4⋊C4—24no—
61C22⋊Dic11—22no—
62C22⋊Dic11—22no—
63C22⋊Dic11—22no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—24no—
66(C2×D11)⋊C4—42no—
67C4⋊Dic11—42no—
68Dic11⋊C4—22no—
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—28no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—44no—
93C2×C4×C11—44no—
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2×D412yes—
96C2×C4×C11#4114yes—
97C22⋊D11—28no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11C2×Q812yes—
111C4×D11—44no—
112C2×C4×D4—111no—
113C22×C4⋊C4D1111yescharacteristic, complemented
114#398—112no—
115#396—112no—
116#387—112no—
117#386—111no—
118#386—111no—
119#385—111no—
120#385—111no—
121#385—112no—
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×#4112yes—
131C22×C11C2×#4111yescharacteristic
132C22×C11H(5,𝔽2)12yes—
133C2×D11—22no—
134C2×D11—24no—
135C2×D11—41no—
136C2×D11—41no—
137C2×D11—42no—
138C4×C11—24no—
139C4×C11—22no—
140C4×C11—22no—
141C4×C11—42no—
142Dic11—22no—
143Dic11—41no—
144Dic11—41no—
145Dic11—42no—
146Dic11—42no—
147C22×D4—111no—
148C23×C4—111no—
149C23×C4C2×D1111yescharacteristic
150C23×C4C2×D1111yescharacteristic
151C23×C4C2×D1111yescharacteristic
152C4×D4—224no—
153C2×C4⋊C4—24no—
154C2×C4⋊C4—111no—
155C2×C4⋊C4—112no—
156C2×C4⋊C4—112no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4C2×D1112yes—
159C2×C4⋊C4C2×D1112yes—
160C2×C22⋊C4—111no—
161C2×C22⋊C4—111no—
162C2×C22⋊C4—111no—
163C2×C22⋊C4—111no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C42—111no—
167#95—112no—
168#95—112no—
169#95—112no—
170#95—112no—
171#95—112no—
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—24no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—111no—
190C22×C4—112no—
191C22×C4—112no—
192C22×C4—111no—
193C22×C4—111no—
194C22×C4—222no—
195C22×C4—442no—
196C22×C4C22⋊D1114yes—
197C22×C4C22×D1112yes—
198C22×C4C22×D1112yes—
199C22×C4C22×D1111yescharacteristic
200C22×C4C22×D1111yescharacteristic
201C4⋊C4—24no—
202C4⋊C4—24no—
203C4⋊C4—224no—
204C4⋊C4—222no—
205C4⋊C4—442no—
206C4⋊C4—442no—
207C22⋊C4—222no—
208C22⋊C4—222no—
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—222no—
219C23—222no—
220C23—221no—
221C23—221no—
222C23Q8×D1112yes—
223C23#434312yes—
224C23C2×C22⋊D1112yes—
225C23C23×D1111yescharacteristic
226D4—228no—
227C2×C4—28no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—44no—
236C2×C4—44no—
237C2×C4—112no—
238C2×C4—221no—
239C2×C4—221no—
240C2×C4—222no—
241C2×C4—222no—
242C2×C4—222no—
243C2×C4—222no—
244C2×C4—222no—
245C2×C4—222no—
246C2×C4—222no—
247C2×C4—222no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—444no—
251C2×C4#433914yes—
252C2×C4C2×C22⋊D1112yes—
253C2×C4C2×C22⋊D1112yes—
254C22—24no—
255C22—24no—
256C22—22no—
257C22—22no—
258C22—224no—
259C22—222no—
260C22—442no—
261C22—441no—
262C22—441no—
263C22#6699914yes—
264C22C2×#433912yes—
265C22#6703712yes—
266C22C2×Q8×D1111yescharacteristic
267C22C2×#434311yescharacteristic
268C22C22×C22⋊D1111yescharacteristic
269C4—24no—
270C4—22no—
271C4—22no—
272C4—42no—
273C4—222no—
274C4—442no—
275C4—442no—
276C4—441no—
277C4—441no—
278C2—24no—
279C2—442no—
280C2#1062304212yes—
281C2#1062304512yes—
282C2#1062332211yescharacteristic
283C2#1062333511yescharacteristic
284C2C2×#6699911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC22×C11×C4⋊C4C2
prime radicalC22×C22⋊D11C22
hypercenterC22×C4⋊C4D11
hypocenterC11#2579
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C11×C4⋊C4C2semidirect
5. #10622825C2semidirect
6. #10622823C2semidirect
7. #10622823C2semidirect
8. #10622607C2semidirect
9. #10622602C2semidirect
10. #10622597C2semidirect
11. #10622591C2semidirect
113. C22×C4⋊C4D11semidirect
214. C11#2579semidirect

Maximal subgroups

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

subgroupindex
C22×C11×C4⋊C42
C2×C4×C22⋊D112
#106228262
#106228252
#106228232
#106226072
#106226022
#106225972
#106225912
#257911