Finite Group Databasebeta

← #14763066

Subgroups — #14763066

Order 2816.

1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623361C211yesmaximal, characteristic
2#13077251C212yesmaximal, complemented
3#13069464C214yesmaximal, complemented
4#13069454C214yesmaximal, complemented
5#13068544C211yesmaximal, characteristic, complemented
6#13068536C212yesmaximal, complemented
7C11×#1785C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C23×D44C2211yescharacteristic
10#10623361—28no—
11C2×#67000C2212yes—
12C2×#66993C2212yes—
13C2×#66990C414yes—
14C2×#66983C414yes—
15C2×#66979C2211yescharacteristic
16C2×C11×#101C2212yescomplemented
17C2×C11×#100C2212yescomplemented
18C11×#407C2212yes—
19C2×#66900C2212yescomplemented
20C2×#66897C2212yescomplemented
21#10622820C2212yes—
22C2×#66887C2214yes—
23C2×#66887C2214yes—
24#10622731C2214yescomplemented
25M16×Dic11C2214yescomplemented
26#10622333—28no—
27C24×D11C2×C412yes—
28C2×C11×#41—24no—
29C2×C11×#41—42no—
30C2×C11×#41—42no—
31C22×Q8×C11C2311yescharacteristic
32C22×D4×C11C2×C412yes—
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11C2×C412yes—
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11C2×C418yes—
37C22×D44—24no—
38C22×D44—42no—
39C22×D44—42no—
40C22×D44C2×C412yes—
41C22×D44C2312yes—
42C2×C11×M16C2314yes—
43C2×C22⋊Dic11C2×C412yes—
44#67000—24no—
45#67000—24no—
46#66993—24no—
47#66993—24no—
48#66990—216no—
49#66983—216no—
50C2×(C2×D11)⋊C4C2×C418yes—
51#66979D418yes—
52C2×C4⋊Dic11C2×C412yes—
53C2×C4×Dic11C2312yes—
54C2×#4318C2314yes—
55C11×#101—42no—
56C11×#100—42no—
57C11×C22⋊C8—24no—
58#66900—42no—
59#66897—42no—
60C22⋊(C11⋊C8)—24no—
61#66887—44no—
62#66887—44no—
63#66879—24no—
64Dic11⋊C8—28no—
65C8×Dic11—24no—
66#21801—111nomaximal, Sylow
67C24×C11C22×C412yes—
68C24×C11C22×C411yescharacteristic
69C23×D11—24no—
70C23×D11—42no—
71C23×D11—42no—
72C23×D11—84no—
73C23×D11C22×C414yes—
74C11×#41—416no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×D4×C11—24no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—24no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11C22×C412yes—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D414yes—
92C22×C4×C11C2411yescharacteristic
93C2×C22⋊D11—216no—
94C2×C22⋊D11—88no—
95C22×Dic11C22×C414yes—
96C2×D44—24no—
97C2×D44—22no—
98C2×D44—22no—
99C2×D44—24no—
100C2×D44—24no—
101C2×D44—42no—
102C2×D44—42no—
103C2×D44—416no—
104C11×M16—24no—
105C11×M16—24no—
106C2×C8×C11—24no—
107C22⋊Dic11C22⋊C418yes—
108(C2×D11)⋊C4—216no—
109C4⋊Dic11C22⋊C418yes—
110C4×Dic11C2×D414yes—
111C4×Dic11C2×D414yes—
112#4318—24no—
113#4318—24no—
114C2×C11⋊C8—24no—
115C2×#535—111no—
116#2921—112no—
117#1967—114no—
118#1965—114no—
119#1785—111no—
120#1785D1111yescharacteristic, complemented
121#1783—112no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—42no—
128C23×C11—44no—
129C23×C11C2×C22⋊C412yes—
130C23×C11C23×C411yescharacteristic
131C22×D11—24no—
132C22×D11—24no—
133C22×D11—24no—
134C22×D11—48no—
135C22×D11—48no—
136C22×D11—88no—
137C22×D11—88no—
138C22×D11—88no—
139Q8×C11—44no—
140D4×C11—48no—
141D4×C11—44no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—28no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—48no—
149C2×C4×C11C2×C22⋊C412yes—
150C2×C4×C11C22×D412yes—
151C2×C4×C11H(5,𝔽2)12yes—
152C2×C4×C11H(5,𝔽2)12yes—
153C22⋊D11—816no—
154C2×Dic11—44no—
155C2×Dic11C2×C22⋊C418yes—
156D44—48no—
157D44—44no—
158D44—44no—
159C8×C11—44no—
160C11⋊C8—44no—
161C22×#41C2×D1111yescharacteristic
162C23×D4—111no—
163#535—228no—
164C2×#127—112no—
165C2×#124—112no—
166C2×#121—114no—
167C2×#120—114no—
168C2×#117—111no—
169#433—228no—
170#423—114no—
171C2×#101—112no—
172C2×#101C2×D1112yescomplemented
173C2×#100—112no—
174C2×#100—114no—
175C2×#100—114no—
176C2×#100C2×D1112yescomplemented
177#407—112no—
178#407C2×D1112yes—
179C4×M16—114no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—24no—
183C22×C11—42no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—44no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11C22×C22⋊C411yescharacteristic
190C22×C11#51811yescharacteristic
191C22×C11#51811yescharacteristic
192C2×D11—44no—
193C2×D11—48no—
194C2×D11—816no—
195C2×D11—84no—
196C2×D11—84no—
197C4×C11—22no—
198C4×C11—42no—
199C4×C11#53514yes—
200Dic11—28no—
201C25—112no—
202C2×#41—24no—
203C2×#41—42no—
204C2×#41—42no—
205C22×Q8C22×D1111yescharacteristic
206C22×D4—118no—
207C22×D4—112no—
208C22×D4—112no—
209C22×D4—224no—
210C22×D4—442no—
211C22×D4—442no—
212C22×D4C4×D1112yes—
213C22×D4C22×D1111yescharacteristic
214C23×C4C4×D1112yes—
215C23×C4C22×D1111yescharacteristic
216C2×M16—114no—
217C2×M16C22×D1114yes—
218#127—224no—
219#127—224no—
220#124—224no—
221#124—224no—
222#121—2216no—
223#120—2216no—
224#117—118no—
225C2×C4⋊C4—112no—
226C2×C22⋊C4—112no—
227C2×C22⋊C4—118no—
228C2×C42—112no—
229C4⋊C8—228no—
230#101—42no—
231#101—442no—
232#100—42no—
233#100—444no—
234#100—444no—
235#100—442no—
236C22⋊C8—24no—
237C22⋊C8—224no—
238#97—224no—
239C4×C8—224no—
240C2×C11—21no—
241C2×C11—21no—
242C2×C11—42no—
243C2×C11—82no—
244C2×C11#230911yescharacteristic
245C2×C11#288812yes—
246D11—84no—
247C24—114no—
248C24—224no—
249C24—442no—
250C24—442no—
251C24—884no—
252C24C2×C4×D1112yes—
253C24C2×C4×D1111yescharacteristic
254#41—416no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×D4—24no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—2216no—
265C2×D4—224no—
266C2×D4—222no—
267C2×D4—222no—
268C2×D4—224no—
269C2×D4—224no—
270C2×D4—442no—
271C2×D4—442no—
272C2×D4—4416no—
273C2×D4—888no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—114no—
280C22×C4C2×C4×D1112yes—
281C22×C4C2×C4×D1111yescharacteristic
282C22×C4D4×D1114yes—
283C22×C4C23×D1111yescharacteristic
284M16—24no—
285M16—24no—
286M16—224no—
287M16—224no—
288C2×C8—24no—
289C2×C8—224no—
290C4⋊C4—118no—
291C22⋊C4—118no—
292C22⋊C4—2216no—
293C42—114no—
294C42—114no—
295C11#2180111yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—42no—
302C23—44no—
303C23—224no—
304C23—224no—
305C23—224no—
306C23—448no—
307C23—448no—
308C23—888no—
309C23—888no—
310C23—888no—
311C23C22⋊C4×D1112yes—
312C23C22×C4×D1111yescharacteristic
313Q8—44no—
314D4—48no—
315D4—44no—
316D4—448no—
317D4—444no—
318D4—444no—
319D4—8816no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—28no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—48no—
327C2×C4—118no—
328C2×C4—444no—
329C2×C4C22⋊C4×D1112yes—
330C2×C4C2×D4×D1112yes—
331C2×C4#6703712yes—
332C2×C4#6703712yes—
333C8—44no—
334C8—444no—
335C22—22no—
336C22—22no—
337C22—24no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—44no—
342C22—82no—
343C22—82no—
344C22—444no—
345C22—448no—
346C22—884no—
347C22—884no—
348C22—8816no—
349C22C2×C22⋊C4×D1111yescharacteristic
350C22#1062301711yescharacteristic
351C22#1062301711yescharacteristic
352C4—22no—
353C4—42no—
354C4—228no—
355C4#1062312314yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—82no—
360C2—884no—
361C2#1307119711yescharacteristic
362C2#1307709312yes—
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1785C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623361C2
cosocleC22×C4×C11C24
hypercenter#1785D11
hypocenterC11#21801
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1785

Complements

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

NH ≅ G/Ntype
2. #13077251C2semidirect
3. #13069464C2semidirect
4. #13069454C2semidirect
5. #13068544C2semidirect
6. #13068536C2semidirect
7. C11×#1785C2semidirect
16. C2×C11×#101C22semidirect
17. C2×C11×#100C22semidirect
19. C2×#66900C22semidirect
20. C2×#66897C22semidirect
24. #10622731C22semidirect
25. M16×Dic11C22semidirect
120. #1785D11semidirect
172. C2×#101C2×D11semidirect
176. C2×#100C2×D11semidirect
295. C11#21801semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
#130772512
#130694642
#130694542
#130685442
#130685362
C11×#17852
#2180111