Finite Group Databasebeta

← #13071990

Subgroups — #13071990

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×D4×C11C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic, complemented
3C2×#67006C211yesmaximal, characteristic, complemented
4C22×C22⋊Dic11C211yesmaximal, characteristic, complemented
5C2×#66992C212yesmaximal, complemented
6#10622860C211yesmaximal, characteristic, complemented
7#10622836C212yesmaximal, complemented
8#10622835C212yesmaximal, complemented
9#10622833C212yesmaximal, complemented
10#10622826C211yesmaximal, characteristic, complemented
11#10622823C211yesmaximal, characteristic, complemented
12C25×C11C2211yescharacteristic
13C25×C11C2211yescharacteristic
14C22×D4×C11—24no—
15C22×D4×C11—28no—
16C22×D4×C11C2212yes—
17C22×D4×C11C2212yes—
18C23×C4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic, complemented
21C22×C22⋊D11C2212yescomplemented
22C22×C22⋊D11C2211yescharacteristic, complemented
23C23×Dic11C2212yescomplemented
24#67006—24no—
25#67006—24no—
26C2×C22⋊Dic11—24no—
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊Dic11C2212yescomplemented
31C2×C22⋊Dic11C2211yescharacteristic, complemented
32C2×C22⋊Dic11C2212yescomplemented
33C2×C22⋊Dic11C2211yescharacteristic, complemented
34C2×C22⋊Dic11C2212yescomplemented
35C2×C22⋊Dic11C2212yescomplemented
36#66992—28no—
37C2×(C2×D11)⋊C4C2212yescomplemented
38C2×Dic11⋊C4C2212yescomplemented
39C11⋊#95C2212yescomplemented
40C11⋊#95C2212yescomplemented
41C24×C11—22no—
42C24×C11—24no—
43C24×C11—24no—
44C24×C11—22no—
45C24×C11—22no—
46C24×C11—22no—
47C24×C11—22no—
48C24×C11—42no—
49C24×C11—42no—
50C24×C11D414yescomplemented
51C24×C11C2311yescharacteristic
52C24×C11C2312yes—
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C23×D11C2311yescharacteristic
56C2×D4×C11—232no—
57C2×D4×C11—24no—
58C2×D4×C11—24no—
59C2×D4×C11—24no—
60C2×D4×C11—24no—
61C2×D4×C11—24no—
62C2×D4×C11D418yescomplemented
63C22×C4×C11—22no—
64C22×C4×C11—24no—
65C22×C4×C11C2312yes—
66C2×C22⋊D11—24no—
67C2×C22⋊D11—24no—
68C2×C22⋊D11—24no—
69C2×C22⋊D11—22no—
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—22no—
73C2×C22⋊D11—22no—
74C2×C22⋊D11—42no—
75C2×C22⋊D11—42no—
76C22×Dic11—24no—
77C22×Dic11—24no—
78C22×Dic11—42no—
79C22×Dic11C2311yescharacteristic
80C22×Dic11C2311yescharacteristic
81C22×Dic11C2312yes—
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2312yes—
84C22⋊Dic11—24no—
85C22⋊Dic11—24no—
86C22⋊Dic11—24no—
87C22⋊Dic11—22no—
88C22⋊Dic11—22no—
89C22⋊Dic11—22no—
90C22⋊Dic11—22no—
91C22⋊Dic11—42no—
92C22⋊Dic11D414yescomplemented
93(C2×D11)⋊C4—24no—
94Dic11⋊C4—24no—
95#2410—111nomaximal, Sylow
96C23×C11—21no—
97C23×C11—22no—
98C23×C11—21no—
99C23×C11—22no—
100C23×C11—22no—
101C23×C11—28no—
102C23×C11—28no—
103C23×C11—28no—
104C23×C11—21no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11—21no—
110C23×C11—22no—
111C23×C11—22no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—44no—
115C23×C11—48no—
116C23×C11—48no—
117C23×C11—48no—
118C23×C11—48no—
119C23×C11—44no—
120C23×C11—44no—
121C23×C11C2×D412yes—
122C23×C11C2×D412yes—
123C23×C11C2×D414yes—
124C23×C11C2×D412yes—
125C23×C11C2×D414yes—
126C23×C11C2×D412yes—
127C23×C11#4112yes—
128C23×C11C2411yescharacteristic
129C22×D11—22no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—22no—
134D4×C11—216no—
135D4×C11—216no—
136C2×C4×C11—28no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11C2×D414yes—
140C22⋊D11—48no—
141C22⋊D11—44no—
142C22⋊D11—44no—
143C22⋊D11—44no—
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—48no—
157C2×Dic11C2×D414yescomplemented
158C23×D4D1111yescharacteristic, complemented
159C2×#121—112no—
160C2×#120—111no—
161C2×#120—111no—
162C22×C22⋊C4—111no—
163#394—112no—
164#392—112no—
165#386—112no—
166#386—111no—
167#385—111no—
168#379—111no—
169C22×C11—22no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—24no—
174C22×C11—24no—
175C22×C11—24no—
176C22×C11—24no—
177C22×C11—22no—
178C22×C11—24no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—24no—
182C22×C11—24no—
183C22×C11—416no—
184C22×C11—416no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11#12014yescomplemented
192C22×C11#12114yescomplemented
193C22×C11C22×D411yescharacteristic
194C22×C11C22×D411yescharacteristic
195C22×C11C22×D412yes—
196C22×C11C2×#4111yescharacteristic
197C22×C11H(5,𝔽2)12yes—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—42no—
202C2×D11—42no—
203C4×C11—24no—
204Dic11—24no—
205Dic11—41no—
206Dic11—41no—
207Dic11—41no—
208Dic11—42no—
209C25C2×D1111yescharacteristic
210C25C2×D1111yescharacteristic
211C22×D4—24no—
212C22×D4—28no—
213C22×D4—111no—
214C22×D4—111no—
215C22×D4—112no—
216C22×D4—111no—
217C22×D4C2×D1112yes—
218C22×D4C2×D1112yes—
219C23×C4—112no—
220C23×C4C2×D1111yescharacteristic
221#121—228no—
222#120—224no—
223#120—224no—
224C2×C4⋊C4—112no—
225C2×C22⋊C4—111no—
226C2×C22⋊C4—111no—
227C2×C22⋊C4—112no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—112no—
231C2×C22⋊C4—111no—
232C2×C22⋊C4—112no—
233C2×C22⋊C4—112no—
234C2×C22⋊C4—112no—
235C2×C22⋊C4—224no—
236#95—112no—
237#95—112no—
238C2×C11—24no—
239C2×C11—24no—
240C2×C11—42no—
241C2×C11—44no—
242C2×C11C2×#12011yescharacteristic
243C2×C11C2×#12111yescharacteristic
244C2×C11#53411yescharacteristic
245C2×C11D4212yes—
246C2×C11#54612yes—
247D11—81no—
248C24—22no—
249C24—22no—
250C24—24no—
251C24—24no—
252C24—22no—
253C24—22no—
254C24—22no—
255C24—42no—
256C24—42no—
257C24—111no—
258C24C22⋊D1114yescomplemented
259C24C22×D1111yescharacteristic
260C24C22×D1112yes—
261C24C22×D1111yescharacteristic
262C24C22×D1111yescharacteristic
263C2×D4—232no—
264C2×D4—24no—
265C2×D4—24no—
266C2×D4—24no—
267C2×D4—24no—
268C2×D4—24no—
269C2×D4—224no—
270C2×D4—222no—
271C2×D4—222no—
272C2×D4—222no—
273C2×D4—222no—
274C2×D4—222no—
275C2×D4—224no—
276C2×D4—224no—
277C2×D4—442no—
278C2×D4—442no—
279C2×D4C22⋊D1118yescomplemented
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—112no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—112no—
286C22×C4—111no—
287C22×C4—224no—
288C22×C4—224no—
289C22×C4—442no—
290C22×C4C22×D1112yes—
291C4⋊C4—224no—
292C22⋊C4—114no—
293C22⋊C4—224no—
294C22⋊C4—224no—
295C22⋊C4—222no—
296C22⋊C4—222no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C22⋊C4—224no—
300C22⋊C4—224no—
301C22⋊C4—442no—
302C11#241011yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—22no—
306C23—22no—
307C23—22no—
308C23—28no—
309C23—28no—
310C23—28no—
311C23—21no—
312C23—22no—
313C23—21no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—44no—
322C23—48no—
323C23—48no—
324C23—48no—
325C23—48no—
326C23—44no—
327C23—44no—
328C23—221no—
329C23—221no—
330C23—222no—
331C23—222no—
332C23—221no—
333C23D4×D1112yes—
334C23#434112yes—
335C23C2×C22⋊D1112yes—
336C23C2×C22⋊D1114yes—
337C23C2×C22⋊D1112yes—
338C23C2×C22⋊D1112yes—
339C23C2×C22⋊D1114yes—
340C23C23×D1111yescharacteristic
341D4—216no—
342D4—216no—
343D4—448no—
344D4—444no—
345D4—444no—
346D4—444no—
347C2×C4—28no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—114no—
351C2×C4—222no—
352C2×C4—222no—
353C2×C4—222no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—222no—
357C2×C4—222no—
358C2×C4—222no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—222no—
363C2×C4—448no—
364C2×C4C2×C22⋊D1114yes—
365C22—24no—
366C22—24no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—24no—
371C22—24no—
372C22—22no—
373C22—24no—
374C22—22no—
375C22—22no—
376C22—24no—
377C22—22no—
378C22—24no—
379C22—416no—
380C22—416no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22—442no—
388C22—441no—
389C22—441no—
390C22—442no—
391C22—441no—
392C22#6699214yescomplemented
393C22#6700614yescomplemented
394C22C2×D4×D1111yescharacteristic
395C22C2×#434111yescharacteristic
396C22#6703712yes—
397C22C22×C22⋊D1112yes—
398C22C22×C22⋊D1111yescharacteristic
399C4—24no—
400C4—224no—
401C4—442no—
402C4—441no—
403C4—441no—
404C4—441no—
405C2—24no—
406C2—24no—
407C2—44no—
408C2—42no—
409C2—881no—
410C2D4×C22⋊D1112yes—
411C2C2×#6699211yescharacteristic
412C2#1062333511yescharacteristic
413C2#1062333712yes—
414C2C2×#6700611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC23×D4×C11C2
hypercenterC23×D4D11
hypocenterC11#2410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×D4×C11C2semidirect
2. C2×#67006C2semidirect
3. C2×#67006C2semidirect
4. C22×C22⋊Dic11C2semidirect
5. C2×#66992C2semidirect
6. #10622860C2semidirect
7. #10622836C2semidirect
8. #10622835C2semidirect
9. #10622833C2semidirect
10. #10622826C2semidirect
11. #10622823C2semidirect
20. C22×C22⋊D11C22semidirect
21. C22×C22⋊D11C22semidirect
22. C22×C22⋊D11C22semidirect
23. C23×Dic11C22semidirect
30. C2×C22⋊Dic11C22semidirect
31. C2×C22⋊Dic11C22semidirect
32. C2×C22⋊Dic11C22semidirect
33. C2×C22⋊Dic11C22semidirect
34. C2×C22⋊Dic11C22semidirect
35. C2×C22⋊Dic11C22semidirect
37. C2×(C2×D11)⋊C4C22semidirect
38. C2×Dic11⋊C4C22semidirect
39. C11⋊#95C22semidirect
40. C11⋊#95C22semidirect
50. C24×C11D4semidirect
62. C2×D4×C11D4semidirect
92. C22⋊Dic11D4semidirect
157. C2×Dic11C2×D4semidirect
158. C23×D4D11semidirect
191. C22×C11#120semidirect
192. C22×C11#121semidirect
258. C24C22⋊D11semidirect
279. C2×D4C22⋊D11semidirect
302. C11#2410semidirect
392. C22#66992semidirect
393. C22#67006semidirect

Maximal subgroups

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

subgroupindex
C23×D4×C112
C2×#670062
C22×C22⋊Dic112
C2×#669922
#106228602
#106228362
#106228352
#106228332
#106228262
#106228232
#241011