Finite Group Databasebeta

← #14651663

Subgroups — #14651663

Order 2816.

458 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077254C211yesmaximal, characteristic
2#13067063C212yesmaximal, complemented
3#13066950C211yesmaximal, characteristic
4#13066480C212yesmaximal, complemented
5C11×#2599C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C11×#117C2211yescharacteristic
8C11×#398C411yescharacteristic
9C11×#397C411yescharacteristic
10C11×#395C411yescharacteristic
11C11×#393C411yescharacteristic
12C11×#388—21no—
13C11×#387—21no—
14C11×#387—21no—
15C11×#385—21no—
16C11×#383C2211yescharacteristic
17#10622820—21no—
18#10622613—24no—
19#10622539C2212yes—
20#10622537—21no—
21C4×#4318C2212yes—
22Q8⋊(C11⋊C8)—24no—
23#10622166—21no—
24#10622163—21no—
25C22×Q8×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C4×Q8×C11—22no—
28C4×Q8×C11—22no—
29C11×#117—22no—
30C11×#117—22no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11D411yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×#4318—22no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95C2×C411yescharacteristic
52C11×#95C2×C411yescharacteristic
53C22⋊(C11⋊C8)—24no—
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—24no—
56C4⋊(C11⋊C8)—22no—
57#66867—22no—
58#66867—22no—
59C4×C11⋊C8D414yes—
60#9493—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C2×Q8×C11—22no—
63C2×Q8×C11—42no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—42no—
88C11×C22⋊C4—42no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—42no—
92C42×C11C2×D412yes—
93C42×C11#4112yes—
94#4318—42no—
95#4318—42no—
96C2×C11⋊C8—24no—
97C2×C11⋊C8—42no—
98#2921—111no—
99#2599D1111yescharacteristic
100#1491—112no—
101#1464—111no—
102#1288—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11C2×C22⋊C411yescharacteristic
109Q8×C11—24no—
110Q8×C11—42no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11C4×D412yes—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12112yes—
139C2×C4×C11#12311yescharacteristic
140C11⋊C8—44no—
141C11⋊C8—82no—
142C2×C4×Q8C2×D1111yescharacteristic
143C2×#117C2×D1111yescharacteristic
144#433—224no—
145#432—112no—
146#423—221no—
147#407—221no—
148C4×M16—112no—
149#398Dic1111yescharacteristic
150#397Dic1111yescharacteristic
151#395Dic1111yescharacteristic
152#393Dic1111yescharacteristic
153#388—21no—
154#387—21no—
155#387—21no—
156#385—21no—
157#383C2×D1111yescharacteristic
158Q8⋊C8—224no—
159#324—221no—
160#323—221no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—42no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—81no—
168C22×C11#38611yescharacteristic
169C22×C11#42111yescharacteristic
170C22×C11#42111yescharacteristic
171C4×C11—22no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—22no—
175C4×C11—41no—
176C4×C11—42no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11—81no—
182C22×Q8C2×Dic1111yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C2×M16—222no—
185C4×Q8—22no—
186C4×Q8—22no—
187#117—22no—
188#117—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×Dic1111yescharacteristic
193C2×C4⋊C4C2×Dic1111yescharacteristic
194C2×C4⋊C4C22⋊D1111yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4C2×Dic1111yescharacteristic
198C2×C22⋊C4C22⋊D1111yescharacteristic
199C2×C42—21no—
200C2×C42C22⋊D1111yescharacteristic
201C2×C42C22×D1111yescharacteristic
202C4⋊C8—224no—
203C4⋊C8—222no—
204C22⋊C8—224no—
205C22⋊C8—222no—
206#97—222no—
207#97—222no—
208C4×C8—114no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95C2×Dic1111yescharacteristic
216#95C2×Dic1111yescharacteristic
217C2×C11—21no—
218C2×C11—21no—
219C2×C11—81no—
220C2×C11#189111yescharacteristic
221C2×C11#189711yescharacteristic
222C2×C11#190911yescharacteristic
223C24C22⋊Dic1111yescharacteristic
224C2×Q8—22no—
225C2×Q8—42no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4C22⋊Dic1111yescharacteristic
235C22×C4C22⋊Dic1111yescharacteristic
236C22×C4C22⋊Dic1111yescharacteristic
237C22×C4C22×Dic1111yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240M16—442no—
241M16—442no—
242C2×C8—224no—
243C2×C8—442no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C42—21no—
256C42—21no—
257C42—42no—
258C42D4×D1112yes—
259C42#434112yes—
260C11#949311yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23C2×C22⋊Dic1111yescharacteristic
267Q8—24no—
268Q8—42no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4D4×Dic1112yes—
295C2×C4#6698811yescharacteristic
296C2×C4#6699011yescharacteristic
297C2×C4#6699212yes—
298C8—444no—
299C8—882no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#1062283311yescharacteristic
308C22#1062284911yescharacteristic
309C22#1062284911yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—42no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C2—21no—
322C2—21no—
323C2—81no—
324C2#1306903511yescharacteristic
325C2#1306906511yescharacteristic
326C2#1306913911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2599C2
socleC22×C11#386
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2599D11
hypocenterC11#9493
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2599

Complements

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

NH ≅ G/Ntype
2. #13067063C2semidirect
4. #13066480C2semidirect
260. C11#9493semidirect

Maximal subgroups

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

subgroupindex
#130772542
#130670632
#130669502
#130664802
C11×#25992
#949311