Finite Group Databasebeta

← #14651527

Subgroups — #14651527

Order 2816.

726 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#13072270C211yesmaximal, characteristic
2#13068540C211yesmaximal, characteristic, complemented
3#13067144C212yesmaximal
4#13066468C212yesmaximal, complemented
5C11×#2310C211yesmaximal, characteristic, complemented
6C23×Q8×C11C2211yescharacteristic
7C2×C11×#117—21no—
8C2×#67000C412yescomplemented
9C2×#66983C2211yescharacteristic
10C11×#391—24no—
11C11×#381—21no—
12C11×#381C2212yes—
13#10622844—22no—
14#10622843C412yescomplemented
15C2×#66900—22no—
16#10622826—21no—
17#10622826—21no—
18C4×C22⋊Dic11C2211yescharacteristic
19#10622820C2212yes—
20#10622089—24no—
21C22×Q8×C11—22no—
22C22×Q8×C11—22no—
23C22×Q8×C11—44no—
24C22×Q8×C11C2×C412yes—
25C22×Q8×C11D412yes—
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—21no—
30C22×D44C2×C411yescharacteristic
31C11×#117—44no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C42×C11—22no—
35C2×C22⋊Dic11—21no—
36#67000—44no—
37#66983—22no—
38#66983—22no—
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4×Dic11C2×C412yes—
44C2×#4318—22no—
45C11×#95—24no—
46C11×#95—22no—
47C11×#95D414yes—
48#66900—44no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C11⋊#95—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54#9466—111nomaximal, Sylow
55C24×C11C2×D411yescharacteristic
56C23×D11—21no—
57C2×Q8×C11—24no—
58C2×Q8×C11—24no—
59C2×Q8×C11—24no—
60C2×Q8×C11—24no—
61C2×Q8×C11—42no—
62C2×Q8×C11—42no—
63C2×Q8×C11—44no—
64C2×Q8×C11—44no—
65C2×Q8×C11—48no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—24no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—24no—
72C22×C4×C11—42no—
73C22×C4×C11—42no—
74C22×C4×C11C22⋊C412yes—
75C22×C4×C11C22⋊C412yes—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C22×C4×C11#4112yes—
80C2×C22⋊D11—44no—
81C2×C22⋊D11—41no—
82C2×C22⋊D11—41no—
83C22×Dic11—21no—
84C22×Dic11—22no—
85C2×D44—22no—
86C2×D44—42no—
87C11×C4⋊C4—44no—
88C11×C22⋊C4—44no—
89C42×C11—44no—
90C22⋊Dic11—42no—
91(C2×D11)⋊C4—44no—
92(C2×D11)⋊C4—44no—
93(C2×D11)⋊C4—42no—
94C4⋊Dic11—22no—
95C4×Dic11—42no—
96#4318—44no—
97C2×C11⋊C8—42no—
98#2436—111no—
99#2310D1111yescharacteristic, complemented
100#1784—111no—
101#1510—112no—
102#1284—112no—
103C23×C11—22no—
104C23×C11—22no—
105C23×C11—41no—
106C23×C11C2×C22⋊C411yescharacteristic
107C23×C11#12011yescharacteristic
108C23×C11#12311yescharacteristic
109C22×D11—42no—
110C22×D11—42no—
111C22×D11—41no—
112C22×D11—42no—
113Q8×C11—48no—
114Q8×C11—48no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—24no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—44no—
132C2×C4×C11#9914yes—
133C2×C4×C11C4×D412yes—
134C2×C4×C11#12112yes—
135C22⋊D11—82no—
136C22⋊D11—82no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—41no—
141C2×Dic11—42no—
142D44—82no—
143C11⋊C8—82no—
144C23×Q8C2×D1111yescharacteristic
145C2×#124—112no—
146C2×#121—111no—
147C2×#117—21no—
148C2×#101—222no—
149#407—112no—
150#393—222no—
151#391—24no—
152#391—112no—
153#386—221no—
154#386—221no—
155#381—21no—
156#381C2×D1112yes—
157C4×C22⋊C4—111no—
158#327—224no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—44no—
167C22×C11#38611yescharacteristic
168C22×C11C2×#9912yes—
169C22×C11#45412yes—
170C2×D11—84no—
171C2×D11—81no—
172C2×D11—81no—
173C2×D11—81no—
174C4×C11—24no—
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—42no—
178C4×C11—84no—
179Dic11—82no—
180Dic11—81no—
181C22×Q8—22no—
182C22×Q8—22no—
183C22×Q8—44no—
184C22×Q8C4×D1112yes—
185C22×Q8D4412yes—
186C22×D4—111no—
187C22×D4—221no—
188C23×C4C22⋊D1111yescharacteristic
189C23×C4C22⋊D1111yescharacteristic
190C23×C4C22×D1111yescharacteristic
191C2×M16—222no—
192#124—444no—
193#121—222no—
194#121—222no—
195#117—44no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—111no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—221no—
200C2×C22⋊C4—222no—
201C2×C22⋊C4—222no—
202C2×C22⋊C4—221no—
203C2×C42—22no—
204C2×C42—112no—
205#101—444no—
206C22⋊C8—222no—
207C22⋊C8—222no—
208#95—24no—
209#95—22no—
210#95—222no—
211#95—222no—
212#95—221no—
213#95C22⋊D1114yes—
214C2×C11—22no—
215C2×C11—22no—
216C2×C11—41no—
217C2×C11#188811yescharacteristic
218C2×C11#189811yescharacteristic
219C2×C11#191211yescharacteristic
220D11—161no—
221C24—221no—
222C24C2×C22⋊D1111yescharacteristic
223C2×Q8—24no—
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8—44no—
230C2×Q8—44no—
231C2×Q8—48no—
232C2×D4—222no—
233C2×D4—442no—
234C2×D4—444no—
235C2×D4—441no—
236C2×D4—441no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—24no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—24no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—221no—
246C22×C4—222no—
247C22×C4(C2×D11)⋊C412yes—
248C22×C4(C2×D11)⋊C412yes—
249C22×C4C2×C4×D1111yescharacteristic
250C22×C4C2×D4411yescharacteristic
251C22×C4#433912yes—
252C22×C4C2×C22⋊D1112yes—
253M16—444no—
254C2×C8—442no—
255C4⋊C4—44no—
256C4⋊C4—222no—
257C22⋊C4—44no—
258C22⋊C4—444no—
259C22⋊C4—442no—
260C22⋊C4—444no—
261C22⋊C4—442no—
262C42—44no—
263C42—442no—
264C11#946611yescharacteristic, complemented, Sylow
265C23—22no—
266C23—22no—
267C23—41no—
268C23—442no—
269C23—442no—
270C23—442no—
271C23—441no—
272C23C2×(C2×D11)⋊C411yescharacteristic
273C23#6698211yescharacteristic
274C23#6700611yescharacteristic
275Q8—48no—
276Q8—48no—
277D4—882no—
278D4—882no—
279D4—882no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—441no—
302C2×C4#6687014yes—
303C2×C4C4×C22⋊D1112yes—
304C2×C4#6698312yes—
305C8—882no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—44no—
314C22—884no—
315C22—881no—
316C22—881no—
317C22—881no—
318C22C2×#6687012yes—
319C22#1062282611yescharacteristic
320C22#1062285812yes—
321C4—22no—
322C4—24no—
323C4—22no—
324C4—42no—
325C4—84no—
326C4—882no—
327C4—881no—
328C2—22no—
329C2—22no—
330C2—41no—
331C2—1761no—
332C2#1306901911yescharacteristic
333C2#1306906911yescharacteristic
334C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2310C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#2310D11
hypocenterC11#9466
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. #13068540C2semidirect
4. #13066468C2semidirect
5. C11×#2310C2semidirect
8. C2×#67000C4semidirect
14. #10622843C4semidirect
99. #2310D11semidirect
264. C11#9466semidirect

Maximal subgroups

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

subgroupindex
#130722702
#130685402
#130671442
#130664682
C11×#23102
#946611