Finite Group Databasebeta

← #14663151

Subgroups — #14663151

Order 2816.

598 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 81 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
1D11×#391C211yesmaximal, characteristic
2#13066944C212yesmaximal
3#13066550C211yesmaximal, characteristic, complemented
4#13066549C212yesmaximal, complemented
5C11×#1319C211yesmaximal, characteristic, complemented
6C22×Q8×D11C411yescharacteristic
7C2×C4⋊C4×D11C2211yescharacteristic
8C2×C42×D11C411yescharacteristic
9C11×#391C2211yescharacteristic
10#10622843C411yescharacteristic
11#10622587C2211yescharacteristic
12#10622542C411yescharacteristic
13#10622339—22no—
14D11×#95—22no—
15#10622259—22no—
16C11×#324C2212yes—
17#10622166C2212yes—
18#10622107—22no—
19C22×Q8×C11C2×C411yescharacteristic
20C2×Q8×D11—22no—
21C2×Q8×D11—22no—
22C2×Q8×D11—41no—
23C2×Q8×D11—41no—
24C2×Q8×D11—42no—
25C22×C4×D11—21no—
26C22×C4×D11—21no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D412yes—
29C22×Dic22—21no—
30C22×Dic22C2×C411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×Dic11⋊C4D412yes—
35C2×C4×Dic11—21no—
36C2×C4×Dic11C2×C411yescharacteristic
37C2×#4313—42no—
38C4⋊C4×D11—41no—
39C4⋊C4×D11—41no—
40C42×D11—42no—
41C11×C22⋊C8—22no—
42C11×#95—22no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C22⋊(C11⋊C8)—22no—
47(C2×D11)⋊C8—42no—
48#11506—111nomaximal, Sylow
49C23×D11C22⋊C411yescharacteristic
50C2×Q8×C11—21no—
51C2×Q8×C11—41no—
52C2×Q8×C11—41no—
53C2×Q8×C11M1612yescomplemented
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D412yes—
58C22×Dic11—21no—
59C22×Dic11—21no—
60C22×Dic11C22⋊C411yescharacteristic
61C22×Dic11C22⋊C412yes—
62Q8×D11—44no—
63Q8×D11—44no—
64Q8×D11—44no—
65Q8×D11—44no—
66C2×C4×D11—22no—
67C2×C4×D11—24no—
68C2×C4×D11—24no—
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—22no—
72C2×C4×D11—22no—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—42no—
76C2×C4×D11—42no—
77C2×C4×D11—42no—
78C2×C4×D11—44no—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C2×Dic22—24no—
82C2×Dic22—21no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×Dic22—42no—
86C2×Dic22—42no—
87C2×Dic22M1612yescomplemented
88C2×C8×C11—42no—
89C11×C4⋊C4—41no—
90C42×C11—41no—
91C4⋊Dic11—41no—
92Dic11⋊C4—42no—
93C4×Dic11—41no—
94C4×Dic11—42no—
95C2×C11⋊C8—42no—
96#4313—84no—
97C2×#391—111no—
98#1463—112no—
99#1319—111no—
100#1319—112no—
101#1319D1111yescharacteristic, complemented
102C23×C11C2×C22⋊C411yescharacteristic
103C22×D11—21no—
104C22×D11—21no—
105C22×D11—22no—
106C22×D11—22no—
107C22×D11#9911yescharacteristic
108C22×D11#9911yescharacteristic
109Q8×C11—42no—
110Q8×C11—42no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11C2×M1611yescharacteristic
122C2×C4×C11C2×M1611yescharacteristic
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—22no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—42no—
133C2×Dic11#10012yes—
134C4×D11—22no—
135C4×D11—22no—
136C4×D11—22no—
137C4×D11—22no—
138C4×D11—48no—
139C4×D11—44no—
140C4×D11—44no—
141C4×D11—44no—
142C4×D11—82no—
143Dic22—48no—
144Dic22—42no—
145Dic22—42no—
146C8×C11—82no—
147C11⋊C8—82no—
148C23×Q8—111no—
149C22×C4⋊C4—111no—
150C22×C42—111no—
151#407—222no—
152#391—111no—
153#391—111no—
154#391—111no—
155#391—222no—
156#391C2×D1111yescharacteristic
157C2×#95—222no—
158#324—112no—
159#324—222no—
160#324C2×D1112yes—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11#40711yescharacteristic
164C22×C11C2×#9911yescharacteristic
165C22×C11C2×#10011yescharacteristic
166C2×D11—24no—
167C2×D11—24no—
168C2×D11—21no—
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D11#35412yes—
173C2×D11#35612yes—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—42no—
178C4×C11—42no—
179Dic11—22no—
180Dic11—42no—
181Dic11—42no—
182Dic11—42no—
183C22×Q8—111no—
184C22×Q8—221no—
185C22×Q8—222no—
186C22×Q8—222no—
187C22×Q8—442no—
188C22×Q8—441no—
189C22×Q8—441no—
190C22×Q8C4×D1111yescharacteristic
191C23×C4—111no—
192C23×C4—112no—
193C23×C4—221no—
194C23×C4—221no—
195C2×M16—442no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—112no—
198C2×C4⋊C4—441no—
199C2×C4⋊C4—441no—
200C2×C4⋊C4C22×D1111yescharacteristic
201C2×C42—111no—
202C2×C42—221no—
203C2×C42—442no—
204C2×C42C4×D1111yescharacteristic
205C22⋊C8—22no—
206C22⋊C8—222no—
207C22⋊C8—442no—
208#95—22no—
209#95—222no—
210#95—222no—
211#95—222no—
212C2×C11—21no—
213C2×C11—21no—
214C2×C11#146211yescharacteristic
215C2×C11C2×#35411yescharacteristic
216C2×C11C2×#35611yescharacteristic
217D11—22no—
218D11—22no—
219C24—111no—
220C2×Q8—21no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—112no—
224C2×Q8—224no—
225C2×Q8—221no—
226C2×Q8—441no—
227C2×Q8—441no—
228C2×Q8—442no—
229C2×Q8—442no—
230C2×Q8—444no—
231C2×Q8—444no—
232C2×Q8—444no—
233C2×Q8—444no—
234C2×Q8#431312yescomplemented
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—111no—
238C22×C4—112no—
239C22×C4—222no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—222no—
243C22×C4—224no—
244C22×C4—224no—
245C22×C4—222no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—441no—
251C22×C4—441no—
252C22×C4—442no—
253C22×C4—442no—
254C22×C4—442no—
255C22×C4—444no—
256C22×C4C2×C4×D1111yescharacteristic
257C22×C4D4×D1112yes—
258M16—884no—
259C2×C8—42no—
260C2×C8—442no—
261C4⋊C4—41no—
262C4⋊C4—442no—
263C4⋊C4—441no—
264C42—41no—
265C42—441no—
266C42—442no—
267C11#1150611yescharacteristic, complemented, Sylow
268C23—111no—
269C23—111no—
270C23—222no—
271C23—222no—
272C23—221no—
273C23—221no—
274C23C22⋊C4×D1111yescharacteristic
275Q8—42no—
276Q8—42no—
277Q8—442no—
278Q8—442no—
279Q8—448no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—112no—
291C2×C4—222no—
292C2×C4—222no—
293C2×C4—222no—
294C2×C4—222no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—222no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—444no—
301C2×C4—444no—
302C2×C4—444no—
303C2×C4—448no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—442no—
309C2×C4—882no—
310C2×C4C2×#431311yescharacteristic
311C2×C4M16×D1111yescharacteristic
312C8—82no—
313C8—882no—
314C22—21no—
315C22—21no—
316C22—112no—
317C22—112no—
318C22—224no—
319C22—224no—
320C22—221no—
321C22—221no—
322C22—221no—
323C22—221no—
324C22#1062233911yescharacteristic
325C22D11×#9911yescharacteristic
326C22D11×#10011yescharacteristic
327C4—21no—
328C4—21no—
329C4—42no—
330C4—42no—
331C4—42no—
332C4—222no—
333C4—442no—
334C4—442no—
335C4—442no—
336C2—21no—
337C2—21no—
338C2—222no—
339C2—222no—
340C2#1306694111yescharacteristic
341C2D11×#35411yescharacteristic
342C2D11×#35611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1319C2
socleC22×C11C2×#99
prime radicalC23×D11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1319D11
hypocenterC11#11506
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
3. #13066550C2semidirect
4. #13066549C2semidirect
5. C11×#1319C2semidirect
53. C2×Q8×C11M16semidirect
87. C2×Dic22M16semidirect
101. #1319D11semidirect
234. C2×Q8#4313semidirect
267. C11#11506semidirect

Maximal subgroups

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

subgroupindex
D11×#3912
#130669442
#130665502
#130665492
C11×#13192
#1150611