Finite Group Databasebeta

← #14651123

Subgroups — #14651123

Order 2816.

446 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 99 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#13074314C211yesmaximal, characteristic
2#13067217C212yesmaximal, complemented
3#13066950C211yesmaximal, characteristic
4#13066510C212yesmaximal, complemented
5C11×#2921C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66923C2211yescharacteristic
8C11×#433—24no—
9C11×#423—21no—
10C11×#407—21no—
11C4×C11×M16C2212yes—
12#10622823—21no—
13#10622599C411yescharacteristic
14#10622596C411yescharacteristic
15#10622585—21no—
16#10622566C411yescharacteristic
17#10622562C411yescharacteristic
18#10622558—21no—
19#10622546—21no—
20#10622545C2211yescharacteristic
21#10622539C2212yes—
22#10622166—21no—
23#10622163—21no—
24#10622103—24no—
25C23×C4×C11D411yescharacteristic
26C2×C11×M16—22no—
27C11×#117—22no—
28C11×#117—22no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44#66923—22no—
45#66923—22no—
46C11×C4⋊C8—24no—
47C11×C22⋊C8—24no—
48C11×#97D414yes—
49C4×C8×C11—22no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95C2×C411yescharacteristic
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59#66867—22no—
60#9390—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C11×M16—42no—
77C11×M16—42no—
78C2×C8×C11—24no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C22⋊C4—22no—
82C11×C22⋊C4—22no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11C2×D412yes—
86C42×C11#4112yes—
87C22⋊Dic11—42no—
88C22⋊Dic11—42no—
89C4⋊Dic11—22no—
90C4⋊Dic11—22no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—41no—
94Dic11⋊C4—42no—
95Dic11⋊C4—41no—
96C4×Dic11—42no—
97C2×C11⋊C8—42no—
98#2921D1111yescharacteristic
99#2611—111no—
100#1528—112no—
101#1464—111no—
102#1300—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11C2×C22⋊C411yescharacteristic
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11C4×D412yes—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12112yes—
125C2×C4×C11#12311yescharacteristic
126C2×Dic11—22no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C8×C11—44no—
139C11⋊C8—82no—
140C2×#125—111no—
141C2×#117C2×D1111yescharacteristic
142#433—24no—
143#432—112no—
144#423—21no—
145#407—21no—
146C4×M16C2×D1112yes—
147#400—111no—
148#399—111no—
149#398—111no—
150#397—111no—
151#389—221no—
152#388—221no—
153#387—221no—
154#385—221no—
155#376—111no—
156#330—224no—
157#324—221no—
158#323—221no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—42no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—81no—
166C22×C11#38611yescharacteristic
167C22×C11#42111yescharacteristic
168C22×C11#42111yescharacteristic
169C4×C11—22no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176Dic11—42no—
177Dic11—81no—
178Dic11—81no—
179Dic11—81no—
180C23×C4C22⋊D1111yescharacteristic
181C2×M16—22no—
182#125—222no—
183#125—222no—
184#117—22no—
185#117—22no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4C4×D1111yescharacteristic
193C2×C4⋊C4D4411yescharacteristic
194C2×C22⋊C4—221no—
195C2×C22⋊C4—221no—
196C2×C22⋊C4C4×D1111yescharacteristic
197C2×C22⋊C4D4411yescharacteristic
198C2×C42—221no—
199C2×C42C22⋊D1111yescharacteristic
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—24no—
202C4⋊C8—222no—
203C22⋊C8—24no—
204C22⋊C8—222no—
205#97—222no—
206#97C22⋊D1114yes—
207C4×C8—22no—
208#95—111no—
209#95—111no—
210#95—221no—
211#95—221no—
212#95—221no—
213#95—221no—
214#95—221no—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11—81no—
218C2×C11#188411yescharacteristic
219C2×C11#189711yescharacteristic
220C2×C11#191511yescharacteristic
221C24(C2×D11)⋊C411yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—221no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4C2×C4×D1111yescharacteristic
234C22×C4C2×D4411yescharacteristic
235C22×C4C2×C22⋊D1111yescharacteristic
236M16—42no—
237M16—42no—
238C2×C8—24no—
239C2×C8—442no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—222no—
243C4⋊C4—222no—
244C4⋊C4—442no—
245C4⋊C4—442no—
246C4⋊C4—441no—
247C4⋊C4—442no—
248C4⋊C4—441no—
249C22⋊C4—22no—
250C22⋊C4—22no—
251C22⋊C4—442no—
252C22⋊C4—442no—
253C42—21no—
254C42—21no—
255C42—442no—
256C42#433912yes—
257C42C2×C22⋊D1112yes—
258C11#939011yescharacteristic, complemented, Sylow
259C23—21no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23C2×(C2×D11)⋊C411yescharacteristic
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—222no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4C4×C22⋊D1112yes—
291C2×C4#6698211yescharacteristic
292C2×C4#6698312yes—
293C2×C4#6700611yescharacteristic
294C8—44no—
295C8—882no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22#1062261811yescharacteristic
304C22#1062261811yescharacteristic
305C22#1062282611yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—22no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—442no—
314C4—881no—
315C4—881no—
316C4—881no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1306899911yescharacteristic
321C2#1306906411yescharacteristic
322C2#1306916811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2921C2
socleC22×C11#386
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2921D11
hypocenterC11#9390
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #13067217C2semidirect
4. #13066510C2semidirect
258. C11#9390semidirect

Maximal subgroups

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

subgroupindex
#130743142
#130672172
#130669502
#130665102
C11×#29212
#939011