Finite Group Databasebeta

← #14663440

Subgroups — #14663440

Order 2816.

374 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 73 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#13073822C211yesmaximal, characteristic
2#13066958C211yesmaximal, characteristic
3#13066938C211yesmaximal, characteristic
4#13066562C211yesmaximal, characteristic
5#13066561C211yesmaximal, characteristic
6#13066561C211yesmaximal, characteristic
7C11×#1325C211yesmaximal, characteristic
8C2×#66941C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622592—21no—
12#10622592—21no—
13#10622589C2211yescharacteristic
14#10622587C411yescharacteristic
15#10622585—21no—
16#10622585—21no—
17C4×Dic11⋊C4C411yescharacteristic
18#10622542C411yescharacteristic
19#10622332—21no—
20#10622331—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622107—21no—
26#10622107—21no—
27C22×Dic22—21no—
28C22×Dic22C2×C411yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4D411yescharacteristic
40C2×Dic11⋊C4D411yescharacteristic
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45#66941—41no—
46#66941—41no—
47#66940—41no—
48#66940—41no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—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#11574—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×Dic22—42no—
79C2×Dic22—81no—
80C2×Dic22—81no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—81no—
86C11×C4⋊C4—81no—
87C42×C11—21no—
88C42×C11—21no—
89C4⋊Dic11—41no—
90Dic11⋊C4—24no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—81no—
96Dic11⋊C4—81no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2567—111no—
108#1467—111no—
109#1461—111no—
110#1325—111no—
111#1325—111no—
112#1325—111no—
113#1325D1111yescharacteristic
114C23×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11#13111yescharacteristic
128C2×C4×C11#13111yescharacteristic
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11#9911yescharacteristic
144C2×Dic11#9911yescharacteristic
145C2×Dic11#10112yes—
146Dic22—42no—
147Dic22—42no—
148Dic22—84no—
149C8×C11—81no—
150C8×C11—81no—
151C11⋊C8—81no—
152C11⋊C8—81no—
153C2×C4⋊Q8—111no—
154C2×C4×Q8—111no—
155#432—221no—
156#431—221no—
157#395—221no—
158#395—221no—
159#391—111no—
160#391—111no—
161#389—221no—
162#389—221no—
163#384—111no—
164#384C2×D1111yescharacteristic
165C4×C4⋊C4—111no—
166#324—111no—
167#324—111no—
168#324—221no—
169#324—221no—
170#324C2×D1111yescharacteristic
171#324C2×D1111yescharacteristic
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#40811yescharacteristic
175C22×C11C2×#9911yescharacteristic
176C22×C11C2×#10111yescharacteristic
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—42no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—81no—
183Dic11—21no—
184Dic11—22no—
185Dic11—42no—
186Dic11—41no—
187Dic11—41no—
188Dic11—81no—
189Dic11#35612yes—
190C22×Q8—111no—
191C22×Q8—221no—
192C4⋊Q8—441no—
193C4⋊Q8—441no—
194C4×Q8—441no—
195C4×Q8—441no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4C4×D1111yescharacteristic
206C2×C4⋊C4C22×D1111yescharacteristic
207C2×C42—111no—
208C2×C42—111no—
209C2×C42—111no—
210C2×C42—111no—
211C2×C42C4×D1111yescharacteristic
212C4⋊C8—441no—
213C4⋊C8—441no—
214C22⋊C8—21no—
215C22⋊C8—21no—
216C22⋊C8—221no—
217C22⋊C8—221no—
218#97—441no—
219C4×C8—441no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11#147211yescharacteristic
228C2×C11#212811yescharacteristic
229C2×C11C2×#35611yescharacteristic
230C2×Q8—222no—
231C2×Q8—221no—
232C2×Q8—221no—
233C2×Q8—441no—
234C2×Q8—442no—
235C2×Q8—881no—
236C2×Q8—881no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—111no—
242C22×C4—111no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4C2×C4×D1111yescharacteristic
246C22×C4D4×D1111yescharacteristic
247C22×C4D4×D1111yescharacteristic
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—441no—
251C2×C8—441no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4—224no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—881no—
263C4⋊C4—881no—
264C42—21no—
265C42—21no—
266C42—221no—
267C42—221no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42—221no—
272C42—221no—
273C42—221no—
274C11#1157411yescharacteristic, complemented, Sylow
275C23C22⋊C4×D1111yescharacteristic
276Q8—442no—
277Q8—442no—
278Q8—884no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—111no—
292C2×C4—111no—
293C2×C4—112no—
294C2×C4—222no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—222no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4#6695411yescharacteristic
309C2×C4#6696011yescharacteristic
310C8—81no—
311C8—81no—
312C8—881no—
313C8—881no—
314C22—21no—
315C22—21no—
316C22#1062234011yescharacteristic
317C22D11×#9911yescharacteristic
318C22D11×#10111yescharacteristic
319C4—21no—
320C4—21no—
321C4—42no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—112no—
326C4—221no—
327C4—222no—
328C4—442no—
329C4—441no—
330C4—441no—
331C4—881no—
332C2—21no—
333C2—21no—
334C2#1306697811yescharacteristic
335C2#1307028611yescharacteristic
336C2D11×#35611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1325D11
hypocenterC11#11574
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
274. C11#11574semidirect

Maximal subgroups

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

subgroupindex
#130738222
#130669582
#130669382
#130665622
#130665612
C11×#13252
#1157411