Finite Group Databasebeta

← #14663426

Subgroups — #14663426

Order 2816.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#13073806C211yesmaximal, characteristic
2#13066958C211yesmaximal, characteristic
3#13066938C211yesmaximal, characteristic
4#13066561C211yesmaximal, characteristic
5#13066561C211yesmaximal, characteristic
6#13066560C211yesmaximal, characteristic
7C11×#1324C211yesmaximal, characteristic
8C2×#66943C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C11×#382C2211yescharacteristic
11#10622589C2211yescharacteristic
12#10622587C411yescharacteristic
13C4×Dic11⋊C4C411yescharacteristic
14#10622542C411yescharacteristic
15#10622332—21no—
16#10622331—21no—
17#10622270—21no—
18#10622270—21no—
19#10622265—21no—
20#10622265—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C22×Dic22C2×C411yescharacteristic
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11C2×C411yescharacteristic
33C2×Dic11⋊C4—21no—
34C2×Dic11⋊C4—21no—
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4D411yescharacteristic
38C2×Dic11⋊C4D411yescharacteristic
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43#66943—41no—
44#66943—41no—
45#66940—41no—
46#66940—41no—
47C11×C22⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66879—41no—
59Dic11⋊C8—41no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11571—111nomaximal, Sylow
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11C22⋊C411yescharacteristic
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C2×Dic22—22no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C42×C11—21no—
83C42×C11—21no—
84C4⋊Dic11—41no—
85C4⋊Dic11—42no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—42no—
89Dic11⋊C4—42no—
90Dic11⋊C4—42no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103#2565—111no—
104#1467—111no—
105#1461—111no—
106#1325—111no—
107#1325—111no—
108#1324—111no—
109#1324D1111yescharacteristic
110C23×C11C2×C22⋊C411yescharacteristic
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11#13111yescharacteristic
123C2×C4×C11#13111yescharacteristic
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—22no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11#9911yescharacteristic
139C2×Dic11#9911yescharacteristic
140C2×Dic11#10112yes—
141Dic22—42no—
142Dic22—42no—
143C8×C11—81no—
144C8×C11—81no—
145C11⋊C8—81no—
146C11⋊C8—81no—
147C2×#125—111no—
148C2×C4×Q8—111no—
149#432—221no—
150#431—221no—
151#398—221no—
152#398—221no—
153#391—111no—
154#391—111no—
155#387—221no—
156#387—221no—
157#384—111no—
158#382C2×D1111yescharacteristic
159C4×C4⋊C4—111no—
160#324—111no—
161#324—111no—
162#324—221no—
163#324—221no—
164#324C2×D1111yescharacteristic
165#324C2×D1111yescharacteristic
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#40811yescharacteristic
169C22×C11C2×#9911yescharacteristic
170C22×C11C2×#10111yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—81no—
176C4×C11—81no—
177Dic11—21no—
178Dic11—21no—
179Dic11—22no—
180Dic11—42no—
181Dic11—41no—
182Dic11—41no—
183Dic11—81no—
184C22×Q8—111no—
185#125—441no—
186#125—441no—
187C4×Q8—441no—
188C4×Q8—441no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4—221no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4C4×D1111yescharacteristic
198C2×C4⋊C4C22×D1111yescharacteristic
199C2×C42—111no—
200C2×C42—111no—
201C2×C42—111no—
202C2×C42—111no—
203C2×C42C4×D1111yescharacteristic
204C4⋊C8—441no—
205C4⋊C8—441no—
206C22⋊C8—21no—
207C22⋊C8—21no—
208C22⋊C8—221no—
209C22⋊C8—221no—
210#97—441no—
211C4×C8—441no—
212#95—21no—
213#95—21no—
214#95—221no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219C2×C11—21no—
220C2×C11—21no—
221C2×C11#147211yescharacteristic
222C2×C11#212611yescharacteristic
223C2×C11#213311yescharacteristic
224C2×Q8—222no—
225C2×Q8—221no—
226C2×Q8—221no—
227C2×Q8—441no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4C2×C4×D1111yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C22×C4D4×D1111yescharacteristic
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—441no—
242C2×C8—441no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4—441no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C4⋊C4—442no—
253C4⋊C4—442no—
254C42—21no—
255C42—21no—
256C42—221no—
257C42—221no—
258C42—221no—
259C42—221no—
260C42—221no—
261C42—221no—
262C42—221no—
263C42—221no—
264C11#1157111yescharacteristic, complemented, Sylow
265C23C22⋊C4×D1111yescharacteristic
266Q8—442no—
267Q8—442no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—111no—
280C2×C4—111no—
281C2×C4—112no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—222no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4#6695411yescharacteristic
297C2×C4#6696011yescharacteristic
298C8—81no—
299C8—81no—
300C8—881no—
301C8—881no—
302C22—21no—
303C22—21no—
304C22#1062234011yescharacteristic
305C22D11×#9911yescharacteristic
306C22D11×#10111yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—221no—
314C4—221no—
315C4—222no—
316C4—442no—
317C4—441no—
318C4—441no—
319C4—881no—
320C2—21no—
321C2—21no—
322C2#1306697811yescharacteristic
323C2#1307028011yescharacteristic
324C2#1307030211yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1324D11
hypocenterC11#11571
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
264. C11#11571semidirect

Maximal subgroups

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

subgroupindex
#130738062
#130669582
#130669382
#130665612
#130665602
C11×#13242
#1157111