Finite Group Databasebeta

← #13071986

Subgroups — #13071986

Order 1408.

1246 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊D11C211yesmaximal, characteristic, complemented
2C2×C11×#120C211yesmaximal, characteristic, complemented
3C2×#66991C212yesmaximal, complemented
4C2×#66990C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
6#10622860C211yesmaximal, characteristic, complemented
7#10622836C212yesmaximal, complemented
8#10622833C211yesmaximal, characteristic, complemented
9#10622574C212yesmaximal, complemented
10#10622569C212yesmaximal, complemented
11#10622563C211yesmaximal, characteristic, complemented
12C25×C11C2211yescharacteristic
13C24×D11C2211yescharacteristic
14C22×D4×C11C2211yescharacteristic
15C22×D4×C11C2212yescomplemented
16C22×C22⋊D11—24no—
17C22×C22⋊D11—28no—
18C22×C22⋊D11C2212yes—
19C22×C22⋊D11C2212yes—
20C22×C22⋊D11C2211yescharacteristic, complemented
21C22×C22⋊D11C2211yescharacteristic, complemented
22C23×Dic11C2211yescharacteristic
23C22×C4×D11C2212yescomplemented
24C11×#120—24no—
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2212yescomplemented
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2212yescomplemented
30C2×C22⋊Dic11C2212yescomplemented
31C2×C22⋊Dic11C2212yescomplemented
32#66991—28no—
33#66990—24no—
34C2×(C2×D11)⋊C4C2212yescomplemented
35C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
36C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
37C2×C4⋊Dic11C2212yescomplemented
38C22⋊C4×D11—24no—
39C11⋊#95C2212yescomplemented
40C11⋊#95C2212yescomplemented
41C24×C11—24no—
42C24×C11—22no—
43C24×C11—22no—
44C24×C11—22no—
45C24×C11—42no—
46C24×C11C2311yescharacteristic
47C24×C11C2312yes—
48C24×C11C2311yescharacteristic
49C23×D11—22no—
50C23×D11—22no—
51C23×D11—24no—
52C23×D11—42no—
53C23×D11D414yescomplemented
54C23×D11C2311yescharacteristic
55C23×D11C2311yescharacteristic
56C2×D4×C11—22no—
57C2×D4×C11—24no—
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—24no—
61C2×D4×C11—42no—
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2312yes—
64C2×C22⋊D11—232no—
65C2×C22⋊D11—24no—
66C2×C22⋊D11—24no—
67C2×C22⋊D11—24no—
68C2×C22⋊D11—24no—
69C2×C22⋊D11—24no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—24no—
73C2×C22⋊D11—42no—
74C2×C22⋊D11D418yescomplemented
75C22×Dic11—24no—
76C22×Dic11—22no—
77C22×Dic11C2311yescharacteristic
78C22×Dic11C2312yes—
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2312yes—
81C2×C4×D11—24no—
82C2×C4×D11—24no—
83C2×C4×D11—42no—
84C11×C22⋊C4—24no—
85C11×C22⋊C4D414yescomplemented
86C22⋊Dic11—24no—
87C22⋊Dic11—22no—
88C22⋊Dic11—22no—
89C22⋊Dic11—24no—
90C22⋊Dic11—42no—
91(C2×D11)⋊C4—22no—
92(C2×D11)⋊C4—22no—
93(C2×D11)⋊C4—24no—
94C4⋊Dic11—24no—
95#2410—111nomaximal, Sylow
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—28no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—22no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—22no—
105C23×C11—22no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—22no—
110C23×C11—48no—
111C23×C11—48no—
112C23×C11—44no—
113C23×C11—44no—
114C23×C11C2×D414yes—
115C23×C11C2×D412yes—
116C23×C11C2×D412yes—
117C23×C11#4112yes—
118C23×C11C2411yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—22no—
122C22×D11—28no—
123C22×D11—21no—
124C22×D11—22no—
125C22×D11—21no—
126C22×D11—22no—
127C22×D11—28no—
128C22×D11—44no—
129C22×D11—48no—
130C22×D11—48no—
131C22×D11C2×D412yes—
132C22×D11C2×D412yes—
133C22×D11C2×D414yes—
134D4×C11—48no—
135D4×C11—44no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11C2×D414yescomplemented
142C22⋊D11—216no—
143C22⋊D11—216no—
144C22⋊D11—44no—
145C22⋊D11—44no—
146C2×Dic11—28no—
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11C2×D414yes—
157C4×D11—48no—
158C23×D4—111no—
159C2×#121—112no—
160C2×#120—111no—
161C2×#120D1111yescharacteristic, complemented
162C22×C22⋊C4—111no—
163#394—112no—
164#392—112no—
165#386—111no—
166#386—112no—
167#385—111no—
168#379—111no—
169C22×C11—22no—
170C22×C11—22no—
171C22×C11—24no—
172C22×C11—24no—
173C22×C11—24no—
174C22×C11—24no—
175C22×C11—24no—
176C22×C11—416no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11#12114yescomplemented
187C22×C11C22×D411yescharacteristic
188C22×C11C22×D412yes—
189C22×C11C22×D411yescharacteristic
190C22×C11C2×#4111yescharacteristic
191C22×C11H(5,𝔽2)12yes—
192C2×D11—22no—
193C2×D11—22no—
194C2×D11—24no—
195C2×D11—24no—
196C2×D11—22no—
197C2×D11—22no—
198C2×D11—22no—
199C2×D11—416no—
200C2×D11—42no—
201C2×D11—42no—
202C2×D11#12014yescomplemented
203C4×C11—24no—
204C4×C11—41no—
205Dic11—24no—
206Dic11—41no—
207Dic11—41no—
208Dic11—42no—
209C25—111no—
210C25C2×D1111yescharacteristic
211C22×D4—112no—
212C22×D4—111no—
213C22×D4—112no—
214C22×D4—111no—
215C22×D4—228no—
216C22×D4—224no—
217C22×D4C2×D1111yescharacteristic
218C22×D4C2×D1112yescomplemented
219C23×C4—111no—
220C23×C4—112no—
221#121—228no—
222#120—24no—
223#120—224no—
224C2×C4⋊C4—112no—
225C2×C22⋊C4—111no—
226C2×C22⋊C4—111no—
227C2×C22⋊C4—112no—
228C2×C22⋊C4—112no—
229C2×C22⋊C4—112no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—111no—
232C2×C22⋊C4—112no—
233C2×C22⋊C4—224no—
234C2×C22⋊C4C2×D1111yescharacteristic
235C2×C22⋊C4C2×D1112yescomplemented
236#95—112no—
237#95—112no—
238C2×C11—24no—
239C2×C11—44no—
240C2×C11—81no—
241C2×C11C2×#12011yescharacteristic
242C2×C11C2×#12111yescharacteristic
243C2×C11#53411yescharacteristic
244C2×C11D4212yes—
245C2×C11#54612yes—
246D11—24no—
247D11—42no—
248C24—24no—
249C24—22no—
250C24—22no—
251C24—22no—
252C24—42no—
253C24—111no—
254C24—111no—
255C24—114no—
256C24—224no—
257C24—222no—
258C24—222no—
259C24—442no—
260C24C22×D1111yescharacteristic
261C24C22×D1112yes—
262C24C22×D1111yescharacteristic
263C2×D4—22no—
264C2×D4—24no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—24no—
268C2×D4—42no—
269C2×D4—118no—
270C2×D4—224no—
271C2×D4—224no—
272C2×D4—224no—
273C2×D4—224no—
274C2×D4—2232no—
275C2×D4—224no—
276C2×D4—222no—
277C2×D4—222no—
278C2×D4—224no—
279C2×D4—442no—
280C22×C4—112no—
281C22×C4—111no—
282C22×C4—112no—
283C22×C4—111no—
284C22×C4—224no—
285C22×C4—224no—
286C22×C4—222no—
287C22×C4—224no—
288C22×C4—442no—
289C22×C4C22×D1111yescharacteristic
290C22×C4C22×D1112yes—
291C4⋊C4—224no—
292C22⋊C4—24no—
293C22⋊C4—222no—
294C22⋊C4—222no—
295C22⋊C4—224no—
296C22⋊C4—222no—
297C22⋊C4—224no—
298C22⋊C4—222no—
299C22⋊C4—224no—
300C22⋊C4—442no—
301C22⋊C4C22⋊D1114yescomplemented
302C11#241011yescharacteristic, complemented, Sylow
303C23—22no—
304C23—22no—
305C23—28no—
306C23—22no—
307C23—22no—
308C23—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—21no—
314C23—21no—
315C23—22no—
316C23—21no—
317C23—48no—
318C23—48no—
319C23—44no—
320C23—44no—
321C23—112no—
322C23—114no—
323C23—112no—
324C23—228no—
325C23—221no—
326C23—222no—
327C23—221no—
328C23—228no—
329C23—222no—
330C23—221no—
331C23—222no—
332C23—221no—
333C23—444no—
334C23—448no—
335C23—448no—
336C23D4×D1114yes—
337C23D4×D1112yes—
338C23#434112yes—
339C23C2×C22⋊D1112yes—
340C23C23×D1111yescharacteristic
341D4—48no—
342D4—44no—
343D4—2216no—
344D4—2216no—
345D4—444no—
346D4—444no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—114no—
353C2×C4—228no—
354C2×C4—222no—
355C2×C4—222no—
356C2×C4—222no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—448no—
364C2×C4C2×C22⋊D1114yescomplemented
365C22—24no—
366C22—22no—
367C22—22no—
368C22—24no—
369C22—24no—
370C22—24no—
371C22—24no—
372C22—416no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—41no—
378C22—42no—
379C22—41no—
380C22—41no—
381C22—42no—
382C22—114no—
383C22—222no—
384C22—224no—
385C22—222no—
386C22—224no—
387C22—222no—
388C22—222no—
389C22—222no—
390C22—4416no—
391C22—442no—
392C22—442no—
393C22#6699114yescomplemented
394C22C2×D4×D1111yescharacteristic
395C22C2×D4×D1112yes—
396C22C2×#434111yescharacteristic
397C22#6703712yes—
398C22C22×C22⋊D1111yescharacteristic
399C4—24no—
400C4—41no—
401C4—224no—
402C4—442no—
403C4—441no—
404C4—441no—
405C2—24no—
406C2—44no—
407C2—81no—
408C2—224no—
409C2—442no—
410C2D11×#12011yescharacteristic
411C2#1062312011yescharacteristic
412C2#1062312212yes—
413C2C2×#6699111yescharacteristic
414C2D4×C22⋊D1112yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#120C2
hypercenterC2×#120D11
hypocenterC11#2410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D11C2semidirect
2. C2×C11×#120C2semidirect
3. C2×#66991C2semidirect
4. C2×#66990C2semidirect
5. C2×C22⋊C4×D11C2semidirect
6. #10622860C2semidirect
7. #10622836C2semidirect
8. #10622833C2semidirect
9. #10622574C2semidirect
10. #10622569C2semidirect
11. #10622563C2semidirect
15. C22×D4×C11C22semidirect
20. C22×C22⋊D11C22semidirect
21. C22×C22⋊D11C22semidirect
23. C22×C4×D11C22semidirect
26. C2×C11×C22⋊C4C22semidirect
29. C2×C22⋊Dic11C22semidirect
30. C2×C22⋊Dic11C22semidirect
31. C2×C22⋊Dic11C22semidirect
34. C2×(C2×D11)⋊C4C22semidirect
35. C2×(C2×D11)⋊C4C22semidirect
36. C2×(C2×D11)⋊C4C22semidirect
37. C2×C4⋊Dic11C22semidirect
39. C11⋊#95C22semidirect
40. C11⋊#95C22semidirect
53. C23×D11D4semidirect
74. C2×C22⋊D11D4semidirect
85. C11×C22⋊C4D4semidirect
141. C2×C4×C11C2×D4semidirect
161. C2×#120D11semidirect
186. C22×C11#121semidirect
202. C2×D11#120semidirect
218. C22×D4C2×D11semidirect
235. C2×C22⋊C4C2×D11semidirect
301. C22⋊C4C22⋊D11semidirect
302. C11#2410semidirect
364. C2×C4C2×C22⋊D11semidirect
393. C22#66991semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D112
C2×C11×#1202
C2×#669912
C2×#669902
C2×C22⋊C4×D112
#106228602
#106228362
#106228332
#106225742
#106225692
#106225632
#241011