Finite Group Databasebeta

← #13074410

Subgroups — #13074410

Order 1408.

548 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66948C211yesmaximal, characteristic
2C2×#66925C211yesmaximal, characteristic, complemented
3C11×#389C211yesmaximal, characteristic, complemented
4#10622605C212yesmaximal, complemented
5#10622604C212yesmaximal, complemented
6#10622601C211yesmaximal, characteristic, complemented
7#10622600C211yesmaximal, characteristic, complemented
8#10622586C211yesmaximal, characteristic, complemented
9#10622552C211yesmaximal, characteristic, complemented
10#10622288C212yesmaximal, complemented
11#10622285C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×D44C2212yes—
14C22×C4×D11C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18C2×C42×C11C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×C4⋊Dic11C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2211yescharacteristic
32#66948—24no—
33#66925—24no—
34C11×#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C23×D11C2312yes—
38C23×D11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×D44—24no—
49C2×D44—22no—
50C2×D44—22no—
51C2×D44—22no—
52C2×D44—42no—
53C2×D44—42no—
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×C4×D11D414yes—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—42no—
60C42×C11—22no—
61(C2×D11)⋊C4—24no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—42no—
65(C2×D11)⋊C4—42no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—42no—
68(C2×D11)⋊C4—42no—
69C4⋊Dic11—22no—
70Dic11⋊C4—22no—
71Dic11⋊C4—22no—
72Dic11⋊C4—42no—
73C4×Dic11—22no—
74#2624—111nomaximal, Sylow
75C23×C11C2411yescharacteristic
76C22×D11—21no—
77C22×D11—21no—
78C22×D11—21no—
79C22×D11—21no—
80C22×D11—21no—
81C22×D11—21no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—22no—
86C22×D11—22no—
87C22×D11—22no—
88C22×D11—22no—
89C22×D11C2×D412yes—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11C2×D412yes—
103C2×C4×C11#4112yes—
104C2×C4×C11#4112yes—
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—21no—
108C2×Dic11—21no—
109C2×Dic11—22no—
110C2×Dic11—21no—
111C2×Dic11—22no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—22no—
115C2×Dic11—21no—
116C2×Dic11C2×D412yes—
117D44—48no—
118D44—44no—
119C4×D11—28no—
120C2×#121—111no—
121C2×#117—111no—
122#399—112no—
123#397—112no—
124#394—112no—
125#394—112no—
126#390—111no—
127#390—111no—
128#389—111no—
129#389D1111yescharacteristic, complemented
130#380—111no—
131C22×C11C22×D411yescharacteristic
132C22×C11C2×#4111yescharacteristic
133C22×C11C2×#4111yescharacteristic
134C22×C11H(5,𝔽2)11yescharacteristic
135C22×C11H(5,𝔽2)11yescharacteristic
136C22×C11H(5,𝔽2)11yescharacteristic
137C22×C112−1+411yescharacteristic
138C2×D11—22no—
139C2×D11—22no—
140C2×D11—22no—
141C2×D11—41no—
142C2×D11—41no—
143C2×D11—41no—
144C2×D11—41no—
145C2×D11—42no—
146C2×D11—42no—
147C2×D11—42no—
148C2×D11—42no—
149C2×D11—42no—
150C2×D11—42no—
151C2×D11—42no—
152C4×C11—41no—
153C4×C11—42no—
154C4×C11—41no—
155C4×C11—42no—
156C4×C11#12314yes—
157Dic11—22no—
158Dic11—41no—
159Dic11—41no—
160Dic11—42no—
161C22×D4—111no—
162C22×D4—112no—
163C23×C4—111no—
164#121—224no—
165#117—224no—
166C2×C4⋊C4—111no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—111no—
169C2×C4⋊C4—112no—
170C2×C4⋊C4C2×D1111yescharacteristic
171C2×C4⋊C4C2×D1111yescharacteristic
172C2×C4⋊C4C2×D1112yes—
173C2×C22⋊C4—111no—
174C2×C22⋊C4—111no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4—112no—
177C2×C22⋊C4—112no—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—112no—
180C2×C22⋊C4—112no—
181C2×C42—111no—
182C2×C42C2×D1111yescharacteristic
183#95—112no—
184#95—112no—
185#95C2×D1112yes—
186C2×C11C2×#12311yescharacteristic
187C2×C11#53511yescharacteristic
188C2×C11#53711yescharacteristic
189C2×C11#54011yescharacteristic
190C2×C11#54011yescharacteristic
191C2×C11#54211yescharacteristic
192C2×C11#54211yescharacteristic
193D11—42no—
194D11—82no—
195C24—111no—
196C24—112no—
197C2×D4—224no—
198C2×D4—222no—
199C2×D4—222no—
200C2×D4—222no—
201C2×D4—442no—
202C2×D4—442no—
203C22×C4—111no—
204C22×C4—114no—
205C22×C4—111no—
206C22×C4—112no—
207C22×C4—111no—
208C22×C4—222no—
209C22×C4—222no—
210C22×C4C22×D1112yes—
211C22×C4C22×D1112yes—
212C22×C4C22×D1111yescharacteristic
213C22×C4C22×D1111yescharacteristic
214C22×C4C22×D1111yescharacteristic
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—42no—
218C4⋊C4—222no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4—442no—
222C22⋊C4—224no—
223C22⋊C4—222no—
224C22⋊C4—222no—
225C22⋊C4—442no—
226C22⋊C4—442no—
227C22⋊C4—442no—
228C22⋊C4—442no—
229C22⋊C4—442no—
230C42—22no—
231C42—222no—
232C11#262411yescharacteristic, complemented, Sylow
233C23—112no—
234C23—221no—
235C23—221no—
236C23—221no—
237C23—221no—
238C23—221no—
239C23—221no—
240C23—222no—
241C23—222no—
242C23—222no—
243C23—222no—
244C23—222no—
245C23—222no—
246C23—222no—
247C23C23×D1111yescharacteristic
248D4—448no—
249D4—444no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—112no—
263C2×C4—221no—
264C2×C4—221no—
265C2×C4—228no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—222no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—222no—
273C2×C4—222no—
274C2×C4—221no—
275C2×C4#433912yes—
276C2×C4D4×D1112yes—
277C2×C4#434312yes—
278C22—222no—
279C22—222no—
280C22—222no—
281C22—441no—
282C22—441no—
283C22—441no—
284C22—441no—
285C22—442no—
286C22—442no—
287C22—442no—
288C22—442no—
289C22—442no—
290C22—442no—
291C22—442no—
292C22C2×#433911yescharacteristic
293C22C2×D4×D1111yescharacteristic
294C22#6703711yescharacteristic
295C22C2×#434311yescharacteristic
296C22#6704011yescharacteristic
297C22#6704211yescharacteristic
298C22#6704211yescharacteristic
299C4—42no—
300C4—42no—
301C4—41no—
302C4—41no—
303C4—222no—
304C4—441no—
305C4—441no—
306C4—442no—
307C4#6694714yes—
308C2—442no—
309C2—882no—
310C2C2×#6694711yescharacteristic
311C2#1062309311yescharacteristic
312C2#1062311311yescharacteristic
313C2#1062313811yescharacteristic
314C2#1062316011yescharacteristic
315C2#1062322911yescharacteristic
316C2#1062326411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
prime radicalC2×#66948C2
hypercenter#389D11
hypocenterC11#2624
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×#66925C2semidirect
3. C11×#389C2semidirect
4. #10622605C2semidirect
5. #10622604C2semidirect
6. #10622601C2semidirect
7. #10622600C2semidirect
8. #10622586C2semidirect
9. #10622552C2semidirect
10. #10622288C2semidirect
11. #10622285C2semidirect
129. #389D11semidirect
232. C11#2624semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669252
C11×#3892
#106226052
#106226042
#106226012
#106226002
#106225862
#106225522
#106222882
#106222852
#262411