Finite Group Databasebeta

← #14810466

Subgroups — #14810466

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic, complemented
2C2×#10622680C211yesmaximal, characteristic, complemented
3C2×#10622326C211yesmaximal, characteristic, complemented
4#13076962C211yesmaximal, characteristic
5#13069761C214yesmaximal, complemented
6#13069584C211yesmaximal, characteristic, complemented
7#13068932C214yesmaximal, complemented
8#13068379C211yesmaximal, characteristic, complemented
9C11×#1992C211yesmaximal, characteristic, complemented
10C2×C11×#125C2211yescharacteristic
11D11×#125—24no—
12D11×#125—24no—
13C2×#66948—22no—
14C2×#66948C2212yes—
15C2×C4⋊C4×D11—22no—
16C2×C4⋊C4×D11C2212yes—
17C2×#66943C2212yes—
18C2×#66942—22no—
19C2×#66927C2211yescharacteristic
20C2×C42×D11C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C2×#66885C2214yes—
25C2×(C2×D11)⋊C8C2212yes—
26#10622680—24no—
27#10622601—22no—
28#10622601C2212yes—
29C2×#66873C2214yes—
30C2×#66867C2211yescharacteristic
31#10622326—24no—
32C11×#340C2214yes—
33#10622188C2212yes—
34#10622167C2214yes—
35C22×D44—22no—
36C22×D44—22no—
37C22×D44C2312yes—
38C22×C4×D11—22no—
39C22×C4×D11D412yes—
40C22×C4×D11C2311yescharacteristic
41C22×C8×C11C2312yes—
42C11×#125—22no—
43C11×#125D414yescomplemented
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C42×C11C2311yescharacteristic
49C2×(C2×D11)⋊C4—24no—
50C2×(C2×D11)⋊C4—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11C2312yes—
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4—22no—
55C2×Dic11⋊C4—22no—
56C2×C4×Dic11D412yes—
57C2×C4×Dic11C2311yescharacteristic
58C22×C11⋊C8C2312yes—
59#66948—28no—
60#66948—48no—
61C4⋊C4×D11—216no—
62C4⋊C4×D11—24no—
63C4⋊C4×D11—24no—
64#66943—24no—
65#66943—24no—
66#66942—216no—
67#66927—22no—
68#66927—22no—
69C42×D11—22no—
70C42×D11—22no—
71#66923—22no—
72#66923D414yescomplemented
73C11×#97—22no—
74#66885—28no—
75(C2×D11)⋊C8—24no—
76#66873—28no—
77#66867—22no—
78#25913—111nomaximal, Sylow
79C23×D11—22no—
80C23×D11C2×D411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11C2×D412yes—
87C22×Dic11C2×D411yescharacteristic
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—24no—
91C2×D44—24no—
92C2×D44—44no—
93C2×D44—44no—
94C2×D44—44no—
95C2×D44—48no—
96C2×D44—44no—
97C2×C4×D11—28no—
98C2×C4×D11—24no—
99C2×C4×D11—24no—
100C2×C4×D11—21no—
101C2×C4×D11—21no—
102C2×C4×D11—22no—
103C2×C4×D11—42no—
104C2×C4×D11—44no—
105C2×C4×D11—44no—
106C2×C4×D11#4114yes—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C11×C4⋊C4—28no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—44no—
114C11×C4⋊C4C2×D414yes—
115C42×C11C2×D412yes—
116C42×C11C2×D412yes—
117(C2×D11)⋊C4—48no—
118(C2×D11)⋊C4—44no—
119C4⋊Dic11—28no—
120C4⋊Dic11—22no—
121C4⋊Dic11C2×D414yes—
122Dic11⋊C4—28no—
123Dic11⋊C4—28no—
124Dic11⋊C4—28no—
125C4×Dic11—24no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C22×#125—111no—
132C2×#490—111no—
133C2×#490—111no—
134#2856—111no—
135#2025—114no—
136#1992—111no—
137#1992D1111yescharacteristic, complemented
138#1874—114no—
139#1749—111no—
140C23×C11C22×D411yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—22no—
144C22×D11—42no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—44no—
148C22×D11—44no—
149C22×D11#12412yes—
150C22×D11AGL(1,ℤ/8)14yes—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—24no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—44no—
158C2×C4×C11#12014yes—
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4112yes—
162C2×C4×C112−1+412yes—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—22no—
166C2×Dic11—24no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11#12412yes—
172D44—44no—
173D44—44no—
174D44—88no—
175D44—88no—
176C4×D11—24no—
177C4×D11—24no—
178C4×D11—48no—
179C4×D11—416no—
180C8×C11—42no—
181C11⋊C8—42no—
182C2×#127—111no—
183C2×#125—112no—
184C2×#125—111no—
185C2×#125—222no—
186C2×#125—224no—
187C2×#125—224no—
188C2×#125C2×D1111yescharacteristic
189C2×#121—112no—
190C2×#121—222no—
191C22×C4⋊C4—112no—
192C22×C4⋊C4—222no—
193C22×C42—111no—
194#490—224no—
195#490—224no—
196C2×#102—114no—
197C2×#102—114no—
198C2×C22⋊C8—112no—
199C2×#97—111no—
200C2×#97C2×D1111yescharacteristic
201#390—112no—
202#390—222no—
203#384C2×D1111yescharacteristic
204#340—114no—
205#340C2×D1114yes—
206#336—112no—
207C22×C11C2×#12011yescharacteristic
208C22×C11C2×#12411yescharacteristic
209C22×C11#53611yescharacteristic
210C22×C11C2×AGL(1,ℤ/8)12yes—
211C22×C11#57512yes—
212C2×D11—22no—
213C2×D11—22no—
214C2×D11—24no—
215C2×D11—24no—
216C2×D11—82no—
217C2×D11—82no—
218C2×D11—82no—
219C2×D11—84no—
220C2×D11—84no—
221C2×D11#49014yescomplemented
222C4×C11—24no—
223C4×C11—44no—
224C4×C11—82no—
225C4×C11#54812yes—
226C4×C11#54812yes—
227Dic11—22no—
228Dic11—42no—
229Dic11—44no—
230C22×D4—112no—
231C22×D4—222no—
232C22×D4—222no—
233C23×C4—111no—
234C23×C4—112no—
235C23×C4—222no—
236C22×C8—112no—
237C22×C8C22×D1112yes—
238#127—222no—
239#127—222no—
240#125—22no—
241#125—114no—
242#125—224no—
243#125—2216no—
244#125—224no—
245#125—222no—
246#125D4414yescomplemented
247#121—228no—
248#121—448no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—112no—
252C2×C4⋊C4—224no—
253C2×C4⋊C4—2216no—
254C2×C4⋊C4—222no—
255C2×C4⋊C4—222no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4—224no—
259C2×C4⋊C4C22×D1112yes—
260C2×C4⋊C4C22×D1112yes—
261C2×C22⋊C4—222no—
262C2×C22⋊C4—224no—
263C2×C42—112no—
264C2×C42—111no—
265C2×C42—222no—
266C2×C42—222no—
267C2×C42C22×D1111yescharacteristic
268#102—228no—
269#102—228no—
270C22⋊C8—224no—
271#97—22no—
272#97—222no—
273C2×C11#243611yescharacteristic
274C2×C11#300612yes—
275C2×C11C2×#49011yescharacteristic
276C2×C11#314211yescharacteristic
277C2×C11#323412yes—
278D11—24no—
279D11—162no—
280C24—111no—
281C24—222no—
282C2×D4—222no—
283C2×D4—222no—
284C2×D4—224no—
285C2×D4—224no—
286C2×D4—444no—
287C2×D4—444no—
288C2×D4—444no—
289C2×D4—448no—
290C2×D4—444no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—111no—
294C22×C4—114no—
295C22×C4—112no—
296C22×C4—224no—
297C22×C4—228no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—222no—
301C22×C4—222no—
302C22×C4—224no—
303C22×C4—442no—
304C22×C4—444no—
305C22×C4—444no—
306C22×C4D4×D1112yes—
307C22×C4C23×D1111yescharacteristic
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—222no—
312C2×C8—222no—
313C2×C8—222no—
314C4⋊C4—28no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—44no—
318C4⋊C4—114no—
319C4⋊C4—228no—
320C4⋊C4—228no—
321C4⋊C4—228no—
322C4⋊C4—228no—
323C4⋊C4—222no—
324C4⋊C4C2×D4414yes—
325C22⋊C4—444no—
326C22⋊C4—448no—
327C42—224no—
328C42—221no—
329C42—221no—
330C42C2×D4412yes—
331C42D4×D1112yes—
332C11#2591311yescharacteristic, complemented, Sylow
333C23—114no—
334C23—112no—
335C23—221no—
336C23—221no—
337C23—222no—
338C23—442no—
339C23—442no—
340C23—444no—
341C23—444no—
342C23—442no—
343C23C2×D4×D1111yescharacteristic
344D4—444no—
345D4—444no—
346D4—888no—
347D4—888no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—24no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—112no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—224no—
359C2×C4—224no—
360C2×C4—222no—
361C2×C4—224no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—448no—
365C2×C4—4416no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4#6693514yes—
369C2×C4C22×D4411yescharacteristic
370C2×C4C2×D4×D1111yescharacteristic
371C2×C4#6704012yes—
372C2×C4#41×D1112yes—
373C8—42no—
374C8—442no—
375C22—114no—
376C22—224no—
377C22—222no—
378C22—222no—
379C22—224no—
380C22—884no—
381C22—882no—
382C22—882no—
383C22—882no—
384C22—884no—
385C22C2×#6693511yescharacteristic
386C22D11×#12411yescharacteristic
387C22#1062325511yescharacteristic
388C22D11×AGL(1,ℤ/8)12yes—
389C22#1062330812yes—
390C4—24no—
391C4—44no—
392C4—82no—
393C4—222no—
394C4—442no—
395C4—444no—
396C4#1062310712yes—
397C4#1062316412yes—
398C2—224no—
399C2—1762no—
400C2#1307227311yescharacteristic
401C2#1307786912yes—
402C2D11×#49011yescharacteristic
403C2#1307901811yescharacteristic
404C2#1307980712yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1992C2
socleC23×C11C22×D4
prime radical#13076962C2
hypercenter#1992D11
hypocenterC11#25913
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
1. C2×D11×#125C2semidirect
2. C2×#10622680C2semidirect
3. C2×#10622326C2semidirect
5. #13069761C2semidirect
6. #13069584C2semidirect
7. #13068932C2semidirect
8. #13068379C2semidirect
9. C11×#1992C2semidirect
43. C11×#125D4semidirect
72. #66923D4semidirect
137. #1992D11semidirect
221. C2×D11#490semidirect
246. #125D44semidirect
332. C11#25913semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×#106226802
C2×#106223262
#130769622
#130697612
#130695842
#130689322
#130683792
C11×#19922
#2591311