Finite Group Databasebeta

← #14663959

Subgroups — #14663959

Order 2816.

568 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 107 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#13074366C211yesmaximal, characteristic
2#13068349C211yesmaximal, characteristic, complemented
3#13066614C214yesmaximal, complemented
4C11×#1458C211yesmaximal, characteristic, complemented
5C2×C11×#117C2211yescharacteristic
6C2×#66983—21no—
7C2×#66979—21no—
8C2×#66927C411yescharacteristic, complemented
9C11×#431—21no—
10#10622604—21no—
11#10622604C412yescomplemented
12#10622573—21no—
13#10622573C2212yes—
14#10622552—21no—
15#10622549C411yescharacteristic, complemented
16C11×#324—21no—
17C11×#323C2212yes—
18#10622164—21no—
19#10622164C2212yes—
20C23×C4×C11D411yescharacteristic
21C22×C22⋊D11—22no—
22C22×D44—21no—
23C22×D44—21no—
24C22×D44C2×C412yes—
25C11×#117—41no—
26C11×#117—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C11×C22⋊C4C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—22no—
34#66983—42no—
35#66983—42no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39#66979—24no—
40#66979—42no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—41no—
43C2×C4×Dic11—41no—
44#66927—41no—
45#66927—41no—
46C11×C4⋊C8—41no—
47C11×C22⋊C8—22no—
48C4×C8×C11—41no—
49C11⋊#95—21no—
50C11⋊#95C2×C412yes—
51#11693—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C23×D11—22no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—22no—
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11D812yes—
62C22×C4×C11SD1612yes—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C2×C22⋊D11—42no—
66C2×C22⋊D11—42no—
67C2×C22⋊D11—82no—
68C2×C22⋊D11—82no—
69C22×Dic11—22no—
70C22×Dic11—42no—
71C2×D44—42no—
72C2×D44—42no—
73C2×D44—41no—
74C2×D44—41no—
75C2×D44—42no—
76C2×D44—42no—
77C2×D44—82no—
78C2×D44—82no—
79C2×C8×C11—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C22⋊Dic11—24no—
89C22⋊Dic11—42no—
90(C2×D11)⋊C4—44no—
91(C2×D11)⋊C4—82no—
92(C2×D11)⋊C4—82no—
93C4⋊Dic11—44no—
94C4⋊Dic11—42no—
95C4×Dic11—44no—
96#2619—111no—
97#1740—111no—
98#1458D1111yescharacteristic, complemented
99#1343—114no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11C2×C22⋊C411yescharacteristic
105C23×C11C2×D811yescharacteristic
106C23×C11C2×SD1611yescharacteristic
107C22×D11—42no—
108C22×D11—42no—
109C22×D11—42no—
110C22×D11—42no—
111C22×D11—42no—
112C22×D11—42no—
113C22×D11—42no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11#9911yescharacteristic
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#10212yes—
131C2×C4×C11#10212yes—
132C2×C4×C11#10412yes—
133C22⋊D11—84no—
134C22⋊D11—84no—
135C2×Dic11—44no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—82no—
140C2×Dic11—82no—
141D44—84no—
142D44—84no—
143D44—82no—
144D44—82no—
145C8×C11—82no—
146C2×#127—111no—
147C2×#121—221no—
148C2×#117—221no—
149C2×#117C2×D1111yescharacteristic
150#431—21no—
151#394—112no—
152#394—221no—
153#392—112no—
154#392—221no—
155#390—221no—
156#382—111no—
157#342—112no—
158#342—221no—
159#324—21no—
160#323C2×D1112yes—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—81no—
170C22×C11C2×#9911yescharacteristic
171C22×C11C2×#10211yescharacteristic
172C22×C11C2×#10411yescharacteristic
173C2×D11—82no—
174C2×D11—82no—
175C2×D11—82no—
176C2×D11—82no—
177C2×D11—82no—
178C2×D11—82no—
179C2×D11—82no—
180C4×C11—22no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11#32712yes—
186C4×C11#32712yes—
187Dic11—82no—
188Dic11—84no—
189C22×D4—112no—
190C22×D4—222no—
191C22×D4—221no—
192C22×D4—221no—
193C23×C4D4411yescharacteristic
194#127—441no—
195#127—441no—
196#121—442no—
197#121—442no—
198#117—41no—
199#117—41no—
200#117—224no—
201#117—442no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—441no—
204C2×C4⋊C4C4×D1111yescharacteristic
205C2×C4⋊C4C22⋊D1111yescharacteristic
206C2×C22⋊C4—222no—
207C2×C22⋊C4—222no—
208C2×C22⋊C4—222no—
209C2×C22⋊C4—222no—
210C2×C22⋊C4D4411yescharacteristic
211C2×C22⋊C4C22×D1111yescharacteristic
212C2×C42—441no—
213C2×C42C4×D1111yescharacteristic
214C2×C42C22⋊D1111yescharacteristic
215C4⋊C8—41no—
216C22⋊C8—22no—
217C4×C8—41no—
218#95—112no—
219#95—221no—
220C2×C11—21no—
221C2×C11—21no—
222C2×C11—41no—
223C2×C11—41no—
224C2×C11C2×#32711yescharacteristic
225C2×C11#212211yescharacteristic
226C2×C11#212811yescharacteristic
227D11—162no—
228C24—222no—
229C24C2×D4411yescharacteristic
230C2×D4—442no—
231C2×D4—442no—
232C2×D4—442no—
233C2×D4—442no—
234C2×D4—441no—
235C2×D4—441no—
236C2×D4—442no—
237C2×D4—442no—
238C2×D4—882no—
239C2×D4—882no—
240C2×D4—882no—
241C2×D4—882no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—222no—
246C22×C4—442no—
247C22×C4#431412yes—
248C22×C4D8812yes—
249C22×C4(C2×D11)⋊C411yescharacteristic
250C22×C4(C2×D11)⋊C411yescharacteristic
251C22×C4(C2×D11)⋊C411yescharacteristic
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4C2×C4×D1111yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255C2×C8—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—444no—
259C4⋊C4—442no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—224no—
263C22⋊C4—442no—
264C22⋊C4—444no—
265C22⋊C4—882no—
266C22⋊C4—882no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—444no—
272C11#1169311yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23—442no—
278C23—442no—
279C23—442no—
280C23—442no—
281C23—442no—
282C23—442no—
283C23—442no—
284C23C2×#431411yescharacteristic
285C23C2×D8811yescharacteristic
286C23C2×(C2×D11)⋊C411yescharacteristic
287D4—884no—
288D4—884no—
289D4—884no—
290D4—884no—
291D4—882no—
292D4—882no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—444no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—882no—
312C2×C4—882no—
313C2×C4#6687011yescharacteristic
314C2×C4#6687011yescharacteristic
315C2×C4#6688512yes—
316C2×C4#6688512yes—
317C2×C4#6688912yes—
318C8—82no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22—882no—
332C22—882no—
333C22—882no—
334C22—882no—
335C22C2×#6687011yescharacteristic
336C22C2×#6688511yescharacteristic
337C22C2×#6688911yescharacteristic
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—882no—
344C4—884no—
345C4#1062210812yes—
346C4#1062210812yes—
347C2—21no—
348C2—21no—
349C2—41no—
350C2—41no—
351C2—1762no—
352C2C2×#1062210811yescharacteristic
353C2#1307026711yescharacteristic
354C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1458C2
socleC22×C11C2×#99
prime radical#13074366C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1458D11
hypocenterC11#11693
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #13068349C2semidirect
3. #13066614C2semidirect
4. C11×#1458C2semidirect
8. C2×#66927C4semidirect
11. #10622604C4semidirect
15. #10622549C4semidirect
98. #1458D11semidirect
272. C11#11693semidirect

Maximal subgroups

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

subgroupindex
#130743662
#130683492
#130666142
C11×#14582
#1169311