Finite Group Databasebeta

← #14651417

Subgroups — #14651417

Order 2816.

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

normal subgroups only

This group has 474 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#13073065C211yesmaximal, characteristic
2#13068693C211yesmaximal, characteristic
3#13067150C212yesmaximal
4#13066470C212yesmaximal
5C11×#2921C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C11×#433—24no—
9C11×#423—21no—
10C11×#407C2212yes—
11C4×C11×M16—21no—
12#10622824C2212yes—
13C4×C22⋊Dic11C2211yescharacteristic
14#10622590C411yescharacteristic, complemented
15#10622589C411yescharacteristic, complemented
16#10622587C411yescharacteristic, complemented
17#10622587C411yescharacteristic, complemented
18#10622565—21no—
19#10622565—21no—
20#10622546—21no—
21#10622546—21no—
22#10622164—21no—
23#10622164—21no—
24#10622105—24no—
25C23×C4×C11C2311yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C2×C11×M16—22no—
28C11×#117—22no—
29C11×#117—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—22no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40#66977—22no—
41#66977—22no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C11×C4⋊C8—24no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8D414yes—
50C11×#97—22no—
51C4×C8×C11—22no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61#9444—111nomaximal, Sylow
62C24×C11C2×D411yescharacteristic
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D412yes—
72C22×C4×C11#4112yes—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—42no—
78C2×Dic22—22no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C11×M16—42no—
82C11×M16—42no—
83C2×C8×C11—24no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C22⋊Dic11—42no—
93C22⋊Dic11—42no—
94C22⋊Dic11—42no—
95C22⋊Dic11—42no—
96C4⋊Dic11—22no—
97Dic11⋊C4—42no—
98Dic11⋊C4—42no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—41no—
102C4×Dic11—41no—
103#2921D1111yescharacteristic
104#2499—111no—
105#1820—111no—
106#1511—112no—
107#1284—112no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11#12112yes—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11C4×D412yes—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12311yescharacteristic
131C2×Dic11—22no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—82no—
144C2×Dic11—82no—
145C2×Dic11—82no—
146Dic22—82no—
147C8×C11—44no—
148C2×C22⋊Q8—111no—
149C2×#117C2×D1111yescharacteristic
150#433—24no—
151#423—21no—
152#407C2×D1112yes—
153C4×M16—21no—
154#397—221no—
155#397—221no—
156#391—111no—
157#391—111no—
158#387—221no—
159#387—221no—
160#384—111no—
161#382—111no—
162#381—112no—
163C4×C22⋊C4—111no—
164#342—221no—
165#342—221no—
166#328—224no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—22no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11#38611yescharacteristic
175C22×C11#41011yescharacteristic
176C22×C11#41011yescharacteristic
177C4×C11—22no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184Dic11—42no—
185Dic11—81no—
186Dic11—81no—
187Dic11—81no—
188Dic11—162no—
189C22×Q8—111no—
190C23×C4C22×D1111yescharacteristic
191C2×M16—22no—
192C22⋊Q8—222no—
193C22⋊Q8—222no—
194#117—22no—
195#117—22no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4C4×D1111yescharacteristic
201C2×C4⋊C4C4×D1111yescharacteristic
202C2×C22⋊C4—221no—
203C2×C22⋊C4—221no—
204C2×C22⋊C4—222no—
205C2×C22⋊C4D4411yescharacteristic
206C2×C22⋊C4D4411yescharacteristic
207C2×C42—111no—
208C2×C42—111no—
209C2×C42C22⋊D1111yescharacteristic
210C2×C42C22⋊D1111yescharacteristic
211C4⋊C8—24no—
212C22⋊C8—22no—
213C22⋊C8C22⋊D1114yes—
214#97—22no—
215C4×C8—22no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—222no—
224#95—222no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—42no—
228C2×C11#188411yescharacteristic
229C2×C11#189911yescharacteristic
230C2×C11#190911yescharacteristic
231C24C2×D4411yescharacteristic
232C2×Q8—222no—
233C2×Q8—441no—
234C2×Q8—441no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—442no—
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4C2×C4×D1111yescharacteristic
247C22×C4#433912yes—
248C22×C4C2×C22⋊D1111yescharacteristic
249C22×C4C2×C22⋊D1112yes—
250M16—42no—
251M16—42no—
252C2×C8—24no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—222no—
256C4⋊C4—442no—
257C4⋊C4—442no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—442no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C22⋊C4—442no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—441no—
271C42—441no—
272C11#944411yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23C2×(C2×D11)⋊C411yescharacteristic
278C23#6698312yes—
279Q8—882no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—222no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—882no—
307C2×C4—882no—
308C2×C4—882no—
309C2×C4C4×C22⋊D1112yes—
310C2×C4#6698211yescharacteristic
311C2×C4#6700611yescharacteristic
312C8—44no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—81no—
319C22—81no—
320C22#1062261911yescharacteristic
321C22#1062261911yescharacteristic
322C22#1062282611yescharacteristic
323C4—21no—
324C4—22no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—442no—
331C4—881no—
332C4—881no—
333C4—881no—
334C4—1762no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1306899911yescharacteristic
339C2#1306907411yescharacteristic
340C2#1306913811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2921C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2921D11
hypocenterC11#9444
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2921

Complements

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

NH ≅ G/Ntype
14. #10622590C4semidirect
15. #10622589C4semidirect
16. #10622587C4semidirect
17. #10622587C4semidirect
272. C11#9444semidirect

Maximal subgroups

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

subgroupindex
#130730652
#130686932
#130671502
#130664702
C11×#29212
#944411