Finite Group Databasebeta

← #13072414

Subgroups — #13072414

Order 1408.

512 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
1C2×#66928C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic, complemented
3C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
4#10622605C212yesmaximal, complemented
5#10622603C212yesmaximal, complemented
6#10622552C211yesmaximal, characteristic
7#10622552C211yesmaximal, characteristic
8#10622542C211yesmaximal, characteristic, complemented
9#10622541C211yesmaximal, characteristic, complemented
10#10622288C212yesmaximal, complemented
11#10622282C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C42×C11C2211yescharacteristic
17C2×C42×C11C2211yescharacteristic
18C2×C42×C11C2211yescharacteristic
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×C4×Dic11C2212yes—
30#66928—24no—
31C4×Dic22—24no—
32C11×#95C2211yescharacteristic
33C11×#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C23×D11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2312yes—
48C2×D44—22no—
49C2×D44—22no—
50C2×D44—22no—
51C2×Dic22—22no—
52C2×Dic22—22no—
53C2×Dic22D414yes—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—22no—
56C42×C11—22no—
57C42×C11—22no—
58C42×C11—22no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4—24no—
61(C2×D11)⋊C4—24no—
62(C2×D11)⋊C4—24no—
63(C2×D11)⋊C4—42no—
64(C2×D11)⋊C4—42no—
65C4⋊Dic11—22no—
66C4⋊Dic11—22no—
67Dic11⋊C4—24no—
68Dic11⋊C4—42no—
69C4×Dic11—24no—
70#2448—111nomaximal, Sylow
71C23×C11C2411yescharacteristic
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11C2×D412yes—
96C2×C4×C11#4112yes—
97C2×C4×C11#4112yes—
98C2×C4×C11#4112yes—
99C2×C4×C11#4112yes—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11C2×D414yes—
109D44—44no—
110Dic22—28no—
111C2×#124—111no—
112C2×C4×Q8—111no—
113#399—112no—
114#397—112no—
115#391—111no—
116#390—111no—
117#390—111no—
118#389—111no—
119#388—112no—
120#388—112no—
121C4×C4⋊C4D1111yescharacteristic, complemented
122C22×C11C22×D411yescharacteristic
123C22×C11C2×#4111yescharacteristic
124C22×C11C2×#4111yescharacteristic
125C22×C11C2×#4111yescharacteristic
126C22×C11C2×#4111yescharacteristic
127C22×C11H(5,𝔽2)11yescharacteristic
128C22×C112−1+411yescharacteristic
129C2×D11—42no—
130C2×D11—42no—
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—42no—
134C2×D11—42no—
135C2×D11—42no—
136C4×C11—22no—
137C4×C11—22no—
138C4×C11—41no—
139C4×C11—41no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11#12314yes—
143Dic11—24no—
144Dic11—42no—
145Dic11—42no—
146C22×Q8—111no—
147C22×D4—111no—
148#124—224no—
149C4×Q8—224no—
150C2×C4⋊C4—111no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—111no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4C2×D1111yescharacteristic
155C2×C4⋊C4C2×D1111yescharacteristic
156C2×C22⋊C4—112no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—112no—
159C2×C22⋊C4—112no—
160C2×C22⋊C4—112no—
161C2×C22⋊C4—112no—
162C2×C42—112no—
163C2×C42C2×D1111yescharacteristic
164C2×C42C2×D1111yescharacteristic
165C2×C42C2×D1111yescharacteristic
166#95—112no—
167#95—112no—
168#95—112no—
169#95C2×D1111yescharacteristic
170#95C2×D1111yescharacteristic
171C2×C11C2×#12311yescharacteristic
172C2×C11#52911yescharacteristic
173C2×C11#54211yescharacteristic
174C2×C11#54811yescharacteristic
175C2×C11#55011yescharacteristic
176C2×C11#55611yescharacteristic
177C2×C11#55911yescharacteristic
178D11—82no—
179C24—112no—
180C2×Q8—114no—
181C2×Q8—222no—
182C2×Q8—222no—
183C2×D4—222no—
184C2×D4—222no—
185C2×D4—222no—
186C22×C4—112no—
187C22×C4—112no—
188C22×C4—112no—
189C22×C4C22×D1111yescharacteristic
190C22×C4C22×D1111yescharacteristic
191C22×C4C22×D1111yescharacteristic
192C22×C4C22×D1111yescharacteristic
193C22×C4C22×D1111yescharacteristic
194C22×C4C22×D1111yescharacteristic
195C22×C4C22×D1111yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—22no—
198C4⋊C4—224no—
199C4⋊C4—222no—
200C4⋊C4—222no—
201C4⋊C4—442no—
202C22⋊C4—224no—
203C22⋊C4—224no—
204C22⋊C4—224no—
205C22⋊C4—224no—
206C22⋊C4—442no—
207C22⋊C4—442no—
208C42—22no—
209C42—22no—
210C42—22no—
211C42—224no—
212C11#244811yescharacteristic, complemented, Sylow
213C23—222no—
214C23—222no—
215C23—222no—
216C23—222no—
217C23—222no—
218C23—222no—
219C23—222no—
220C23C23×D1111yescharacteristic
221Q8—228no—
222D4—444no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—114no—
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#433912yes—
249C2×C4#433912yes—
250C2×C4#433912yes—
251C2×C4D4×D1112yes—
252C2×C4#434312yes—
253C22—442no—
254C22—442no—
255C22—442no—
256C22—442no—
257C22—442no—
258C22—442no—
259C22—442no—
260C22C2×#433911yescharacteristic
261C22C2×#433911yescharacteristic
262C22C2×#433911yescharacteristic
263C22C2×D4×D1111yescharacteristic
264C22C2×#434311yescharacteristic
265C22#6704211yescharacteristic
266C22#6704311yescharacteristic
267C4—22no—
268C4—22no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—224no—
274C4—442no—
275C4—442no—
276C4#6694714yes—
277C2—882no—
278C2#1062301011yescharacteristic
279C2C2×#6694711yescharacteristic
280C2#1062306511yescharacteristic
281C2#1062308311yescharacteristic
282C2#1062308411yescharacteristic
283C2#1062311511yescharacteristic
284C2#1062311611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C4⋊C4C2
prime radicalC22×D44C22
hypercenterC4×C4⋊C4D11
hypocenterC11#2448
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic22C2semidirect
3. C4×C11×C4⋊C4C2semidirect
4. #10622605C2semidirect
5. #10622603C2semidirect
8. #10622542C2semidirect
9. #10622541C2semidirect
10. #10622288C2semidirect
11. #10622282C2semidirect
121. C4×C4⋊C4D11semidirect
212. C11#2448semidirect

Maximal subgroups

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

subgroupindex
C2×#669282
C2×C4×Dic222
C4×C11×C4⋊C42
#106226052
#106226032
#106225522
#106225422
#106225412
#106222882
#106222822
#244811