Finite Group Databasebeta

← #14663352

Subgroups — #14663352

Order 2816.

408 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 79 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#13073074C211yesmaximal, characteristic
2#13066950C211yesmaximal, characteristic, complemented
3#13066561C212yesmaximal, complemented
4#13066547C212yesmaximal, complemented
5C11×#1458C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C11×#431—21no—
9C4×C22⋊Dic11C411yescharacteristic
10#10622601C411yescharacteristic
11#10622601C2211yescharacteristic
12#10622590C411yescharacteristic
13#10622589C2211yescharacteristic
14#10622572—21no—
15#10622572—21no—
16#10622553—21no—
17#10622553—21no—
18#10622539—21no—
19C11×#324C2212yes—
20C11×#323—21no—
21#10622166C2212yes—
22#10622163—21no—
23C23×C4×C11C2×C411yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C11×#117—41no—
27C11×#117—41no—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—21no—
35#66983—41no—
36#66983—41no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C11×C4⋊C8—41no—
48C11×C22⋊C8—22no—
49C4×C8×C11—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55#66867—41no—
56#11554—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C23×D11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—41no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C2×C22⋊D11—42no—
70C2×C22⋊D11—81no—
71C2×C22⋊D11—81no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×D44—22no—
76C2×D44—41no—
77C2×D44—41no—
78C2×C8×C11—42no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C22⋊Dic11—42no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—42no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—81no—
93(C2×D11)⋊C4—81no—
94C4⋊Dic11—41no—
95Dic11⋊C4—81no—
96Dic11⋊C4—81no—
97C4×Dic11—22no—
98C4×Dic11—41no—
99C2×C11⋊C8—42no—
100#2500—111no—
101#1464—111no—
102#1458D1111yescharacteristic, complemented
103#1325—112no—
104#1318—112no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11C2×C22⋊C411yescharacteristic
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#13112yes—
135C22⋊D11—84no—
136C2×Dic11—22no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145D44—82no—
146C8×C11—82no—
147C11⋊C8—82no—
148C2×#121—111no—
149C2×#117C2×D1111yescharacteristic
150#432—221no—
151#431—21no—
152#394—221no—
153#394—221no—
154#390—111no—
155#390—111no—
156#388—221no—
157#388—221no—
158#384—111no—
159#382—111no—
160C4×C22⋊C4—111no—
161#324—112no—
162#324C2×D1112yes—
163#323—21no—
164#323—221no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—81no—
171C22×C11—81no—
172C22×C11#40811yescharacteristic
173C22×C11C2×#9911yescharacteristic
174C22×C11#41311yescharacteristic
175C2×D11—81no—
176C2×D11—81no—
177C2×D11—81no—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—81no—
181C2×D11—81no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—41no—
189Dic11—42no—
190Dic11—81no—
191Dic11—81no—
192C22×D4—111no—
193C22×D4—221no—
194C23×C4C4×D1111yescharacteristic
195#121—441no—
196#121—441no—
197#117—41no—
198#117—41no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4C4×D1111yescharacteristic
203C2×C4⋊C4C22×D1111yescharacteristic
204C2×C22⋊C4—221no—
205C2×C22⋊C4—221no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4D4411yescharacteristic
211C2×C22⋊C4C22⋊D1111yescharacteristic
212C2×C42—111no—
213C2×C42—111no—
214C2×C42D4411yescharacteristic
215C2×C42C22⋊D1111yescharacteristic
216C4⋊C8—41no—
217C4⋊C8—441no—
218C22⋊C8—22no—
219C22⋊C8—222no—
220#97—441no—
221C4×C8—41no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—81no—
228C2×C11#146811yescharacteristic
229C2×C11#212811yescharacteristic
230C2×C11#213211yescharacteristic
231D11—161no—
232C24—221no—
233C24(C2×D11)⋊C411yescharacteristic
234C2×D4—222no—
235C2×D4—441no—
236C2×D4—441no—
237C2×D4—442no—
238C2×D4—881no—
239C2×D4—881no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4(C2×D11)⋊C411yescharacteristic
249C22×C4(C2×D11)⋊C411yescharacteristic
250C22×C4C2×C4×D1111yescharacteristic
251C22×C4C2×D4411yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253C2×C8—42no—
254C2×C8—442no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—441no—
258C4⋊C4—881no—
259C4⋊C4—881no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—442no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C22⋊C4—441no—
266C22⋊C4—441no—
267C22⋊C4—881no—
268C22⋊C4—881no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—222no—
274C42—441no—
275C11#1155411yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—441no—
282C23—441no—
283C23—441no—
284C23—441no—
285C23—441no—
286C23—441no—
287C23—441no—
288C23C2×(C2×D11)⋊C411yescharacteristic
289D4—882no—
290D4—884no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—222no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4#6687011yescharacteristic
315C2×C4#6687011yescharacteristic
316C2×C4#6695412yes—
317C8—82no—
318C8—882no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—881no—
327C22—881no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22—881no—
332C22—881no—
333C22C2×#6687011yescharacteristic
334C22#1062272311yescharacteristic
335C22#1062274511yescharacteristic
336C4—21no—
337C4—21no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—442no—
344C4—881no—
345C4—881no—
346C2—21no—
347C2—21no—
348C2—81no—
349C2—1761no—
350C2#1306696211yescharacteristic
351C2#1307028711yescharacteristic
352C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1458C2
socleC22×C11C2×#99
prime radicalC2×#66983C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1458D11
hypocenterC11#11554
LCSG ▷ C22×C4×C11 ▷ C22×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. #13066950C2semidirect
3. #13066561C2semidirect
4. #13066547C2semidirect
5. C11×#1458C2semidirect
102. #1458D11semidirect
275. C11#11554semidirect

Maximal subgroups

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

subgroupindex
#130730742
#130669502
#130665612
#130665472
C11×#14582
#1155411