Finite Group Databasebeta

← #13073531

Subgroups — #13073531

Order 1408.

788 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66983C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C2×#66948C211yesmaximal, characteristic, complemented
4C2×#66946C211yesmaximal, characteristic, complemented
5C2×#66937C212yesmaximal, complemented
6C11×#380C211yesmaximal, characteristic, complemented
7#10622600C211yesmaximal, characteristic, complemented
8#10622589C211yesmaximal, characteristic, complemented
9#10622572C212yesmaximal, complemented
10#10622285C212yesmaximal, complemented
11#10622280C212yesmaximal, complemented
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×C22⋊D11C2211yescharacteristic
15C22×D44C2212yes—
16C22×D44C2211yescharacteristic
17C22×C4×D11C2212yes—
18C22×C4×D11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2212yes—
22C2×C22⋊Dic11C2211yescharacteristic
23#66983—24no—
24C4×C22⋊D11—24no—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×Dic11⋊C4C2212yes—
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2212yes—
34C2×C4×Dic11C2211yescharacteristic
35#66948—24no—
36#66946—24no—
37#66937—28no—
38C11×#95C2212yes—
39C11⋊#95C2212yes—
40C24×C11C2311yescharacteristic
41C23×D11C2312yes—
42C23×D11C2311yescharacteristic
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11C2312yes—
47C22×C4×C11C2311yescharacteristic
48C22×C4×C11C2312yes—
49C22×C4×C11C2311yescharacteristic
50C2×C22⋊D11—22no—
51C2×C22⋊D11—22no—
52C2×C22⋊D11—24no—
53C2×C22⋊D11—24no—
54C2×C22⋊D11—42no—
55C2×C22⋊D11D414yescomplemented
56C22×Dic11C2311yescharacteristic
57C22×Dic11C2312yes—
58C22×Dic11C2311yescharacteristic
59C22×Dic11C2311yescharacteristic
60C2×D44—24no—
61C2×D44—24no—
62C2×D44—22no—
63C2×D44—22no—
64C2×D44—42no—
65C2×D44D414yescomplemented
66C2×C4×D11—24no—
67C2×C4×D11—24no—
68C2×C4×D11—24no—
69C2×C4×D11—22no—
70C2×C4×D11—22no—
71C2×C4×D11—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C22⋊C4—24no—
75C22⋊Dic11—22no—
76(C2×D11)⋊C4—24no—
77(C2×D11)⋊C4—22no—
78(C2×D11)⋊C4—24no—
79(C2×D11)⋊C4—24no—
80(C2×D11)⋊C4—24no—
81C4⋊Dic11—22no—
82Dic11⋊C4—24no—
83Dic11⋊C4—22no—
84Dic11⋊C4—42no—
85C4×Dic11D414yescomplemented
86#2537—111nomaximal, Sylow
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11C2×D412yes—
94C23×C11C2411yescharacteristic
95C22×D11—22no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—22no—
99C22×D11—21no—
100C22×D11—22no—
101C22×D11—22no—
102C22×D11—21no—
103C22×D11—21no—
104C22×D11—22no—
105C22×D11—21no—
106C22×D11—22no—
107C22×D11C2×D412yes—
108C22×D11C2×D414yes—
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—44no—
119C2×C4×C11C2×D412yes—
120C2×C4×C11C2×D412yes—
121C2×C4×C11#4112yes—
122C22⋊D11—28no—
123C22⋊D11—48no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—22no—
127C2×Dic11—21no—
128C2×Dic11—22no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—22no—
132C2×Dic11C2×D412yes—
133C2×Dic11C2×D412yes—
134C2×Dic11C2×D412yes—
135C2×Dic11#4112yes—
136D44—28no—
137D44—48no—
138C4×D11—44no—
139C4×D11—48no—
140C2×#121—111no—
141C2×#121—111no—
142C2×#121—112no—
143C2×C4×D4—111no—
144C2×C4×D4—111no—
145#394—112no—
146#394—112no—
147#384—111no—
148#380—111no—
149#380—112no—
150#380D1111yescharacteristic, complemented
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—22no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11C22×D411yescharacteristic
159C22×C11C22×D411yescharacteristic
160C22×C11C22×D411yescharacteristic
161C22×C11C2×#4111yescharacteristic
162C22×C11C2×#4111yescharacteristic
163C22×C11H(5,𝔽2)11yescharacteristic
164C22×C112−1+411yescharacteristic
165C2×D11—24no—
166C2×D11—22no—
167C2×D11—22no—
168C2×D11—24no—
169C2×D11—22no—
170C2×D11—24no—
171C2×D11—41no—
172C2×D11—42no—
173C2×D11—42no—
174C2×D11—41no—
175C2×D11—42no—
176C2×D11—41no—
177C2×D11—42no—
178C2×D11—41no—
179C4×C11—41no—
180C4×C11—42no—
181C4×C11—42no—
182C4×C11#12114yescomplemented
183Dic11—22no—
184Dic11—41no—
185Dic11—42no—
186Dic11#12114yescomplemented
187C22×D4—111no—
188C22×D4—112no—
189C22×D4—111no—
190C22×D4—112no—
191C23×C4—112no—
192C23×C4—111no—
193C23×C4C2×D1111yescharacteristic
194#121—228no—
195#121—224no—
196#121—224no—
197C4×D4—224no—
198C4×D4—224no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—112no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—112no—
203C2×C4⋊C4C2×D1111yescharacteristic
204C2×C4⋊C4C2×D1111yescharacteristic
205C2×C22⋊C4—111no—
206C2×C22⋊C4—112no—
207C2×C22⋊C4—111no—
208C2×C22⋊C4—112no—
209C2×C22⋊C4—112no—
210C2×C22⋊C4—112no—
211C2×C22⋊C4C2×D1112yes—
212C2×C42—111no—
213#95—112no—
214#95C2×D1112yes—
215C2×C11—42no—
216C2×C11C2×#12111yescharacteristic
217C2×C11C2×#12111yescharacteristic
218C2×C11#53711yescharacteristic
219C2×C11D4211yescharacteristic
220C2×C11#54711yescharacteristic
221C2×C11#54711yescharacteristic
222C2×C11#55511yescharacteristic
223D11—44no—
224D11—42no—
225C24—111no—
226C24—112no—
227C24C22×D1111yescharacteristic
228C2×D4—114no—
229C2×D4—114no—
230C2×D4—224no—
231C2×D4—224no—
232C2×D4—222no—
233C2×D4—222no—
234C2×D4—224no—
235C2×D4—224no—
236C2×D4—222no—
237C2×D4—222no—
238C2×D4—442no—
239C2×D4—442no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—112no—
247C22×C4—224no—
248C22×C4—224no—
249C22×C4—224no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—222no—
253C22×C4C22×D1112yes—
254C22×C4C22×D1111yescharacteristic
255C22×C4C22×D1112yes—
256C22×C4C22×D1111yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—222no—
260C4⋊C4—224no—
261C4⋊C4—222no—
262C4⋊C4—442no—
263C22⋊C4—24no—
264C22⋊C4—224no—
265C22⋊C4—222no—
266C22⋊C4—224no—
267C22⋊C4—224no—
268C22⋊C4—224no—
269C22⋊C4—222no—
270C42—114no—
271C11#253711yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—114no—
279C23—112no—
280C23—221no—
281C23—222no—
282C23—222no—
283C23—221no—
284C23—221no—
285C23—222no—
286C23—221no—
287C23—222no—
288C23—222no—
289C23—221no—
290C23—221no—
291C23—222no—
292C23D4×D1112yes—
293C23C23×D1111yescharacteristic
294D4—228no—
295D4—228no—
296D4—448no—
297D4—448no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—44no—
308C2×C4—112no—
309C2×C4—112no—
310C2×C4—112no—
311C2×C4—112no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—222no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—448no—
321C2×C4—444no—
322C2×C4#433912yes—
323C2×C4D4×D1112yes—
324C2×C4D4×D1112yes—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—224no—
333C22—222no—
334C22—222no—
335C22—222no—
336C22—224no—
337C22—224no—
338C22—441no—
339C22—442no—
340C22—441no—
341C22—442no—
342C22—442no—
343C22—442no—
344C22—441no—
345C22—441no—
346C22C2×#433911yescharacteristic
347C22C2×D4×D1111yescharacteristic
348C22C2×D4×D1111yescharacteristic
349C22C2×D4×D1111yescharacteristic
350C22#6704011yescharacteristic
351C22#41×D1111yescharacteristic
352C22#6704211yescharacteristic
353C4—41no—
354C4—42no—
355C4—42no—
356C4—114no—
357C4—222no—
358C4—441no—
359C4—442no—
360C4#6693714yescomplemented
361C2—42no—
362C2—444no—
363C2—442no—
364C2C2×#6693711yescharacteristic
365C2#1062303811yescharacteristic
366C2#1062306311yescharacteristic
367C2D11×#12111yescharacteristic
368C2#1062314011yescharacteristic
369C2#1062316011yescharacteristic
370C2#1062316211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
hypercenter#380D11
hypocenterC11#2537
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#66983C2semidirect
2. C2×C4×C22⋊D11C2semidirect
3. C2×#66948C2semidirect
4. C2×#66946C2semidirect
5. C2×#66937C2semidirect
6. C11×#380C2semidirect
7. #10622600C2semidirect
8. #10622589C2semidirect
9. #10622572C2semidirect
10. #10622285C2semidirect
11. #10622280C2semidirect
55. C2×C22⋊D11D4semidirect
65. C2×D44D4semidirect
85. C4×Dic11D4semidirect
150. #380D11semidirect
182. C4×C11#121semidirect
186. Dic11#121semidirect
271. C11#2537semidirect
360. C4#66937semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C2×C4×C22⋊D112
C2×#669482
C2×#669462
C2×#669372
C11×#3802
#106226002
#106225892
#106225722
#106222852
#106222802
#253711