Finite Group Databasebeta

← #14810459

Subgroups — #14810459

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2C2×#10622682C211yesmaximal, characteristic, complemented
3C2×#10622316C211yesmaximal, characteristic, complemented
4#13076969C211yesmaximal, characteristic
5#13069766C214yesmaximal, complemented
6#13069584C211yesmaximal, characteristic, complemented
7#13068922C214yesmaximal
8#13068379C211yesmaximal, characteristic
9C11×#1992C211yesmaximal, characteristic, complemented
10C2×C11×#125C2211yescharacteristic
11D11×#125—24no—
12D11×#125—24no—
13C2×#66950C2212yes—
14C2×C4⋊C4×D11—22no—
15C2×C4⋊C4×D11C2212yes—
16C2×#66943C2212yes—
17C2×#66942—22no—
18C2×C42×D11C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C11×#384C2211yescharacteristic
23C2×(C2×D11)⋊C8C2212yes—
24C2×#66880C2214yes—
25#10622682—24no—
26#10622600—22no—
27#10622598—22no—
28#10622587C2212yes—
29C2×#66874C2214yes—
30C2×#66867C2211yescharacteristic
31#10622316—24no—
32C11×#340C2214yes—
33#10622188C2212yes—
34#10622167C2214yes—
35C22×C4×D11—22no—
36C22×C4×D11D412yes—
37C22×C4×D11C2311yescharacteristic
38C22×Dic22C2312yes—
39C22×C8×C11C2312yes—
40C11×#125—22no—
41C11×#125D414yes—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C42×C11C2311yescharacteristic
47C2×(C2×D11)⋊C4—22no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11C2312yes—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4—22no—
55C2×C4×Dic11D412yes—
56C2×C4×Dic11C2311yescharacteristic
57C22×C11⋊C8C2312yes—
58#66950—28no—
59C4⋊C4×D11—216no—
60C4⋊C4×D11—24no—
61C4⋊C4×D11—24no—
62#66943—24no—
63#66943—24no—
64#66942—216no—
65C42×D11—22no—
66C42×D11—22no—
67#66923—22no—
68#66923D414yes—
69#66922—22no—
70#66922—22no—
71C11×#97—22no—
72C11⋊#95—24no—
73(C2×D11)⋊C8—24no—
74#66880—28no—
75#66874—28no—
76#66867—22no—
77#25912—111nomaximal, Sylow
78C23×D11C2×D411yescharacteristic
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11—22no—
85C22×Dic11C2×D412yes—
86C22×Dic11C2×D411yescharacteristic
87C2×C4×D11—28no—
88C2×C4×D11—24no—
89C2×C4×D11—24no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—22no—
93C2×C4×D11—42no—
94C2×C4×D11—44no—
95C2×C4×D11—44no—
96C2×C4×D11#4114yes—
97C2×Dic22—22no—
98C2×Dic22—22no—
99C2×Dic22—24no—
100C2×Dic22—24no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—44no—
108C11×C4⋊C4C2×D414yes—
109C42×C11C2×D412yes—
110C42×C11C2×D412yes—
111(C2×D11)⋊C4—44no—
112C4⋊Dic11—28no—
113C4⋊Dic11—22no—
114C4⋊Dic11—44no—
115C4⋊Dic11—44no—
116C4⋊Dic11C2×D414yes—
117Dic11⋊C4—28no—
118Dic11⋊C4—28no—
119Dic11⋊C4—28no—
120C4×Dic11—24no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C22×#125—111no—
127C2×#491—111no—
128C2×#491—111no—
129#2857—111no—
130#2026—114no—
131#1992—111no—
132#1992D1111yescharacteristic, complemented
133#1872—114no—
134#1749—111no—
135C23×C11C22×D411yescharacteristic
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—22no—
139C22×D11#12412yes—
140C22×D11#13714yes—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—44no—
148C2×C4×C11#12014yes—
149C2×C4×C11C22×D411yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C2×#4112yes—
152C2×C4×C112−1+412yes—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—22no—
156C2×Dic11—24no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11#12412yes—
165C4×D11—24no—
166C4×D11—24no—
167C4×D11—48no—
168C4×D11—416no—
169Dic22—44no—
170Dic22—44no—
171C8×C11—42no—
172C11⋊C8—42no—
173C2×C4⋊Q8—111no—
174C2×#125—112no—
175C2×#125—111no—
176C2×#125—222no—
177C2×#125—224no—
178C2×#125—224no—
179C2×#125C2×D1111yescharacteristic
180C2×C22⋊Q8—112no—
181C22×C4⋊C4—112no—
182C22×C4⋊C4—222no—
183C22×C42—111no—
184#491—224no—
185#491—224no—
186C2×#103—114no—
187C2×#103—114no—
188C2×C22⋊C8—112no—
189C2×#97—111no—
190C2×#97C2×D1111yescharacteristic
191#391—112no—
192#389—222no—
193#384C2×D1111yescharacteristic
194#380—222no—
195#340—114no—
196#340C2×D1114yes—
197#336—112no—
198C22×C11C2×#12011yescharacteristic
199C22×C11C2×#12411yescharacteristic
200C22×C11#53611yescharacteristic
201C22×C11C2×#13712yes—
202C22×C11#57512yes—
203C2×D11—22no—
204C2×D11—22no—
205C2×D11—24no—
206C2×D11—24no—
207C2×D11#49114yescomplemented
208C4×C11—24no—
209C4×C11—44no—
210C4×C11—82no—
211C4×C11#54812yes—
212C4×C11#54812yes—
213Dic11—22no—
214Dic11—42no—
215Dic11—44no—
216Dic11—82no—
217C22×Q8—112no—
218C23×C4—111no—
219C23×C4—112no—
220C23×C4—222no—
221C22×C8—112no—
222C22×C8C22×D1112yes—
223C4⋊Q8—222no—
224C4⋊Q8—222no—
225#125—22no—
226#125—114no—
227#125—224no—
228#125—2216no—
229#125—224no—
230#125—222no—
231#125D4414yes—
232C22⋊Q8—228no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—112no—
236C2×C4⋊C4—224no—
237C2×C4⋊C4—2216no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4—224no—
243C2×C4⋊C4—222no—
244C2×C4⋊C4—222no—
245C2×C4⋊C4C22×D1112yes—
246C2×C4⋊C4C22×D1112yes—
247C2×C22⋊C4—222no—
248C2×C42—112no—
249C2×C42—111no—
250C2×C42—222no—
251C2×C42—222no—
252C2×C42C22×D1111yescharacteristic
253#103—228no—
254#103—228no—
255C22⋊C8—224no—
256#97—22no—
257#97—222no—
258#95—224no—
259C2×C11#243611yescharacteristic
260C2×C11#300712yes—
261C2×C11C2×#49111yescharacteristic
262C2×C11#314211yescharacteristic
263C2×C11#323612yes—
264D11—24no—
265C24—111no—
266C2×Q8—222no—
267C2×Q8—222no—
268C2×Q8—224no—
269C2×Q8—224no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—111no—
273C22×C4—114no—
274C22×C4—112no—
275C22×C4—224no—
276C22×C4—228no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—222no—
280C22×C4—222no—
281C22×C4—224no—
282C22×C4—222no—
283C22×C4—442no—
284C22×C4—444no—
285C22×C4—444no—
286C22×C4D4×D1112yes—
287C22×C4C23×D1111yescharacteristic
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—222no—
294C4⋊C4—28no—
295C4⋊C4—22no—
296C4⋊C4—24no—
297C4⋊C4—44no—
298C4⋊C4—114no—
299C4⋊C4—228no—
300C4⋊C4—228no—
301C4⋊C4—228no—
302C4⋊C4—228no—
303C4⋊C4—222no—
304C4⋊C4—444no—
305C4⋊C4—444no—
306C4⋊C4C2×D4414yes—
307C22⋊C4—444no—
308C42—224no—
309C42—221no—
310C42—221no—
311C42C2×D4412yes—
312C42D4×D1112yes—
313C11#2591211yescharacteristic, complemented, Sylow
314C23—114no—
315C23—112no—
316C23—221no—
317C23—221no—
318C23—222no—
319C23C2×D4×D1111yescharacteristic
320Q8—444no—
321Q8—444no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4—42no—
329C2×C4—112no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—224no—
333C2×C4—224no—
334C2×C4—222no—
335C2×C4—224no—
336C2×C4—222no—
337C2×C4—222no—
338C2×C4—448no—
339C2×C4—4416no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4#6693514yes—
346C2×C4C22×D4411yescharacteristic
347C2×C4C2×D4×D1111yescharacteristic
348C2×C4#6704012yes—
349C2×C4#41×D1112yes—
350C8—42no—
351C8—442no—
352C22—114no—
353C22—224no—
354C22—224no—
355C22—222no—
356C22—222no—
357C22C2×#6693511yescharacteristic
358C22D11×#12411yescharacteristic
359C22#1062325511yescharacteristic
360C22#1062330412yes—
361C22D11×#13712yes—
362C4—24no—
363C4—44no—
364C4—82no—
365C4—222no—
366C4—442no—
367C4—444no—
368C4—882no—
369C4#1062310712yes—
370C4#1062316412yes—
371C2—224no—
372C2#1307227311yescharacteristic
373C2#1307787712yes—
374C2D11×#49111yescharacteristic
375C2#1307901511yescharacteristic
376C2#1307982312yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1992C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1992D11
hypocenterC11#25912
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
2. C2×#10622682C2semidirect
3. C2×#10622316C2semidirect
5. #13069766C2semidirect
6. #13069584C2semidirect
9. C11×#1992C2semidirect
132. #1992D11semidirect
207. C2×D11#491semidirect
313. C11#25912semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×#106226822
C2×#106223162
#130769692
#130697662
#130695842
#130689222
#130683792
C11×#19922
#2591211