Finite Group Databasebeta

← #14726627

Subgroups — #14726627

Order 2816.

934 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 183 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#13078711C212yesmaximal
2#13071899C211yesmaximal, characteristic
3#13067658C214yesmaximal, complemented
4#13067556C214yesmaximal
5#13067128C212yesmaximal, complemented
6#13066960C211yesmaximal, characteristic, complemented
7C11×#3502C211yesmaximal, characteristic, complemented
8Q82×C11—22no—
9C11×#557—22no—
10C11×#557—24no—
11C11×#544—21no—
12C11×#544C2214yes—
13C11×#533—22no—
14C11×#533C2212yes—
15C11×#519—21no—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18#10622844—21no—
19#10622700—22no—
20#10622696—22no—
21#10622659C2214yes—
22#10622657C2214yes—
23#10622639—24no—
24#10622606—21no—
25#10622604C2212yes—
26#10622599C2212yes—
27C4×(C2×D11)⋊C4—22no—
28#10622545C2211yescharacteristic
29#10622539C2212yes—
30#10622176C2218yes—
31#10622166C2214yes—
32C22×Q8×C11D411yescharacteristic
33C22×D44C2311yescharacteristic
34C22×C4×D11—21no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8—28no—
39C11×C4⋊Q8D412yes—
40C11×C4⋊Q8D412yes—
41C11×#125—24no—
42C11×#125—24no—
43C11×#125—28no—
44C11×#125—22no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8C2314yes—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C4×Q8×C11—24no—
51C4×Q8×C11—24no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11D414yes—
56C11×#117—24no—
57C11×#117—22no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11D412yes—
61C2×C42×C11C2311yescharacteristic
62C2×#4325—24no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4×Dic11—21no—
68C4×D44—22no—
69C4×D44—22no—
70#66899—24no—
71C11⋊#95—21no—
72C11⋊#95—22no—
73C11⋊#95—22no—
74C11⋊#95C2312yes—
75C22⋊(C11⋊C8)C2314yes—
76#66873—24no—
77#66871—24no—
78C4⋊(C11⋊C8)—22no—
79#66867—22no—
80#18188—111nomaximal, Sylow
81C23×D11—21no—
82C2×Q8×C11—24no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—24no—
86C2×Q8×C11C2×D414yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D412yes—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—21no—
93C22×Dic11—22no—
94C2×D44—22no—
95C2×D44—42no—
96C2×C4×D11—44no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4—28no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—24no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4C2×D414yes—
111C11×C22⋊C4—24no—
112C42×C11—28no—
113C42×C11—22no—
114C42×C11—22no—
115C42×C11—24no—
116C42×C11C2×D412yes—
117C42×C11C2×D412yes—
118#4325—48no—
119(C2×D11)⋊C4—44no—
120(C2×D11)⋊C4—42no—
121(C2×D11)⋊C4—44no—
122C4⋊Dic11—22no—
123C4×Dic11—42no—
124C2×C11⋊C8—24no—
125#3502D1111yescharacteristic, complemented
126#3110—112no—
127#2398—111no—
128#1617—114no—
129#1599—114no—
130#1506—112no—
131#1467—111no—
132C23×C11C22×D411yescharacteristic
133C22×D11—22no—
134C22×D11—42no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—42no—
138Q8×C11—28no—
139Q8×C11—44no—
140Q8×C11—44no—
141Q8×C11—84no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—24no—
147C2×C4×C11—24no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11#12012yes—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#13714yes—
155C2×C4×C11C22×D412yes—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161D44—24no—
162D44—42no—
163C4×D11—82no—
164C4×D11—82no—
165C11⋊C8—44no—
166Q82—22no—
167#557—22no—
168#557—24no—
169#544—21no—
170#544C2×D1114yes—
171#533—22no—
172#533C2×D1112yes—
173#519—21no—
174C2×C4×Q8C2×D1111yescharacteristic
175C2×C4×D4—111no—
176#484—114no—
177#474—222no—
178#461—222no—
179#450—114no—
180#440—224no—
181#432—112no—
182#400—112no—
183#397—221no—
184#394—112no—
185#393—221no—
186C4×C22⋊C4—222no—
187#376—111no—
188#328—118no—
189#324—114no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11C2×#12011yescharacteristic
193C22×C11C2×#13712yes—
194C2×D11—44no—
195C2×D11—42no—
196C2×D11—82no—
197C2×D11—81no—
198C2×D11—81no—
199C4×C11—22no—
200C4×C11—24no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—44no—
204C4×C11—42no—
205C4×C11—44no—
206C4×C11#45412yes—
207Dic11—82no—
208Dic11—81no—
209C22×Q8C22⋊D1111yescharacteristic
210C22×D4—111no—
211C23×C4—221no—
212C2×SD16—224no—
213C4⋊Q8—22no—
214C4⋊Q8—22no—
215C4⋊Q8—24no—
216C4⋊Q8—28no—
217C4⋊Q8C22⋊D1112yes—
218C4⋊Q8C22⋊D1112yes—
219#125—24no—
220#125—24no—
221#125—28no—
222#125—22no—
223C22⋊Q8—22no—
224C22⋊Q8—24no—
225C22⋊Q8C22×D1114yes—
226C4×Q8—24no—
227C4×Q8—24no—
228C4×Q8—24no—
229C4×Q8—24no—
230C4×Q8—22no—
231C4×Q8—22no—
232C4×Q8—22no—
233C4×Q8C22⋊D1114yes—
234C4×D4—222no—
235C4×D4—222no—
236#117—24no—
237#117—22no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4C22⋊D1111yescharacteristic
240C2×C4⋊C4C22×D1112yes—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—222no—
243C2×C22⋊C4—222no—
244C2×C42—221no—
245C2×C42C22⋊D1112yes—
246C2×C42C22×D1111yescharacteristic
247#107—224no—
248C4⋊C8—222no—
249#103—224no—
250#102—224no—
251C22⋊C8—114no—
252#97—222no—
253#95—112no—
254#95—221no—
255#95—222no—
256#95—222no—
257C2×C11—22no—
258C2×C11#300411yescharacteristic
259C2×C11C2×#45411yescharacteristic
260C2×C11#302511yescharacteristic
261D11—82no—
262C24—221no—
263C2×Q8—24no—
264C2×Q8—24no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8C2×C22⋊D1114yes—
268C2×D4—222no—
269C2×D4—442no—
270C22×C4—222no—
271C22×C4—221no—
272C22×C4—444no—
273C22×C4—441no—
274C22×C4—441no—
275C22×C4C2×C22⋊D1112yes—
276C22×C4C2×C22⋊D1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278C22×C4C2×C22⋊D1112yes—
279C22×C4C23×D1111yescharacteristic
280SD16—448no—
281C2×C8—224no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—28no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—222no—
294C4⋊C4C2×C22⋊D1114yes—
295C22⋊C4—24no—
296C22⋊C4—444no—
297C22⋊C4—444no—
298C22⋊C4—442no—
299C42—28no—
300C42—22no—
301C42—22no—
302C42—24no—
303C42—442no—
304C42C2×C22⋊D1112yes—
305C42C2×C22⋊D1112yes—
306C11#1818811yescharacteristic, complemented, Sylow
307C23—222no—
308C23—442no—
309C23—441no—
310C23—442no—
311C23—441no—
312C23C22×C22⋊D1111yescharacteristic
313Q8—28no—
314Q8—44no—
315Q8—44no—
316Q8—84no—
317D4—224no—
318D4—442no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—441no—
333C2×C4—882no—
334C2×C4—882no—
335C2×C4#6699514yes—
336C2×C4#6700612yes—
337C2×C4#6700611yescharacteristic
338C2×C4#6700611yescharacteristic
339C2×C4C22×C22⋊D1112yes—
340C8—444no—
341C22—21no—
342C22—21no—
343C22—444no—
344C22—442no—
345C22—882no—
346C22—881no—
347C22—881no—
348C22C2×#6699512yes—
349C22C2×#6700611yescharacteristic
350C4—24no—
351C4—22no—
352C4—21no—
353C4—22no—
354C4—44no—
355C4—42no—
356C4—44no—
357C4—882no—
358C4—881no—
359C4#1062285812yes—
360C2—22no—
361C2—882no—
362C2#1307785011yescharacteristic
363C2C2×#1062285811yescharacteristic
364C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3502C2
socleC22×C11C2×#120
prime radicalC22×D44C23
hypercenter#3502D11
hypocenterC11#18188
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
3. #13067658C2semidirect
5. #13067128C2semidirect
6. #13066960C2semidirect
7. C11×#3502C2semidirect
125. #3502D11semidirect
306. C11#18188semidirect

Maximal subgroups

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

subgroupindex
#130787112
#130718992
#130676582
#130675562
#130671282
#130669602
C11×#35022
#1818811