Finite Group Databasebeta

← #14726626

Subgroups — #14726626

Order 2816.

934 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 167 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#13082426C211yesmaximal, characteristic, complemented
2#13078715C212yesmaximal
3#13067657C214yesmaximal, complemented
4#13067555C214yesmaximal
5#13067127C212yesmaximal, complemented
6#13066960C211yesmaximal, characteristic, complemented
7C11×#2398C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623343—21no—
11#10623101—22no—
12#10623100—24no—
13Q8×Dic22—22no—
14#10623031—21no—
15#10623031C2214yes—
16#10623001—22no—
17#10623001C2212yes—
18C11×#400C2212yes—
19C11×#397—21no—
20C11×#394C2212yes—
21C11×#393—21no—
22C4×C11×C22⋊C4—22no—
23C11×#376C2211yescharacteristic
24#10622831C2214yes—
25#10622632—22no—
26#10622631—24no—
27#10622620—22no—
28#10622583C2214yes—
29#10622539C2212yes—
30#10622166C2214yes—
31#10622090C2218yes—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11—21no—
35C4×Q8×C11—22no—
36C4×Q8×C11—22no—
37C4×D4×C11—22no—
38C4×D4×C11—22no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4C2311yescharacteristic
41C2×C11×C4⋊C4C2312yes—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—21no—
45C2×C42×C11—21no—
46C2×C42×C11D412yes—
47C2×C42×C11C2311yescharacteristic
48Q8×Dic11—24no—
49Q8×Dic11—24no—
50C2×#4324—24no—
51#66979—24no—
52#66979—22no—
53#66977—22no—
54#66977—24no—
55#66977C2314yes—
56#66943—24no—
57#66943—28no—
58#66941—24no—
59#66941—28no—
60#66923—24no—
61#66923—22no—
62#66922—22no—
63#66922—22no—
64#66922D412yes—
65#66922D412yes—
66C4×Dic22—24no—
67C4×Dic22—24no—
68C4×Dic22—22no—
69C4×Dic22D414yes—
70C11×#95—21no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95C2312yes—
74#66896—24no—
75C22⋊(C11⋊C8)C2314yes—
76#66874—24no—
77#66871—24no—
78C4⋊(C11⋊C8)—22no—
79#66867—22no—
80#18188—111nomaximal, Sylow
81C24×C11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—24no—
84C2×D4×C11—22no—
85C2×D4×C11—42no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—44no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2411yescharacteristic
96C2×Dic22—24no—
97C2×Dic22—22no—
98C2×Dic22C2×D414yes—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—22no—
102C11×C22⋊C4—44no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—44no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—42no—
108C42×C11C2×D412yes—
109C42×C11C2×D412yes—
110C22⋊Dic11—24no—
111#4324—48no—
112C4⋊Dic11—24no—
113C4⋊Dic11—24no—
114C4⋊Dic11—24no—
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11C2×D414yes—
119Dic11⋊C4—28no—
120Dic11⋊C4—24no—
121Dic11⋊C4—24no—
122C4×Dic11—28no—
123C4×Dic11—24no—
124C2×C11⋊C8—24no—
125#3502—111no—
126#3110—112no—
127#2398D1111yescharacteristic
128#1617—114no—
129#1599—114no—
130#1506—112no—
131#1467—111no—
132C23×C11—22no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—42no—
137C23×C11C22×D411yescharacteristic
138Q8×C11—28no—
139D4×C11—24no—
140D4×C11—42no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11#12012yes—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#13714yes—
159C2×C4×C11C22×D412yes—
160C2×Dic11—24no—
161C2×Dic11—24no—
162Dic22—44no—
163Dic22—44no—
164Dic22—84no—
165C11⋊C8—44no—
166Q82—222no—
167#557—224no—
168#557—222no—
169#544—114no—
170#544—221no—
171#533—112no—
172#533—222no—
173#519—221no—
174C2×C4×Q8C2×D1111yescharacteristic
175C2×C4×D4C2×D1111yescharacteristic
176#484—114no—
177#474—222no—
178#461—222no—
179#450—114no—
180#440—224no—
181#432—112no—
182#400C2×D1112yes—
183#397—21no—
184#394C2×D1112yes—
185#393—21no—
186C4×C22⋊C4—22no—
187#376C2×D1111yescharacteristic
188#328—118no—
189#324—114no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—44no—
193C22×C11—42no—
194C22×C11—82no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11C2×#12011yescharacteristic
198C22×C11C2×#13712yes—
199C4×C11—22no—
200C4×C11—24no—
201C4×C11—21no—
202C4×C11—22no—
203C4×C11—42no—
204C4×C11—82no—
205C4×C11—81no—
206C4×C11#45412yes—
207Dic11—44no—
208Dic11—44no—
209C22×Q8C22⋊D1111yescharacteristic
210C22×D4C22×D1111yescharacteristic
211C23×C4—21no—
212C2×SD16—224no—
213C4⋊Q8—112no—
214C4⋊Q8—112no—
215C4⋊Q8—222no—
216C4⋊Q8—222no—
217C4⋊Q8—228no—
218C4⋊Q8—224no—
219#125—224no—
220#125—228no—
221#125—224no—
222#125—222no—
223C22⋊Q8—114no—
224C22⋊Q8—222no—
225C22⋊Q8—224no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×Q8—114no—
229C4×Q8—224no—
230C4×Q8—224no—
231C4×Q8—224no—
232C4×Q8—224no—
233C4×Q8—222no—
234C4×D4—22no—
235C4×D4—22no—
236#117—222no—
237#117—224no—
238C2×C4⋊C4C22⋊D1111yescharacteristic
239C2×C4⋊C4C22×D1111yescharacteristic
240C2×C4⋊C4C22×D1112yes—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C42—21no—
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—21no—
254#95—22no—
255#95—22no—
256#95C22×D1112yes—
257C2×C11—22no—
258C2×C11—82no—
259C2×C11#300411yescharacteristic
260C2×C11C2×#45411yescharacteristic
261C2×C11#302511yescharacteristic
262C24—21no—
263C2×Q8—22no—
264C2×Q8—24no—
265C2×Q8—114no—
266C2×Q8—224no—
267C2×Q8—222no—
268C2×D4—22no—
269C2×D4—42no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—44no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4C2×C22⋊D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277C22×C4C2×C22⋊D1112yes—
278C22×C4C2×C22⋊D1112yes—
279C22×C4C23×D1111yescharacteristic
280SD16—448no—
281C2×C8—224no—
282C4⋊C4—22no—
283C4⋊C4—24no—
284C4⋊C4—22no—
285C4⋊C4—114no—
286C4⋊C4—224no—
287C4⋊C4—224no—
288C4⋊C4—224no—
289C4⋊C4—228no—
290C4⋊C4—222no—
291C4⋊C4—222no—
292C4⋊C4—224no—
293C4⋊C4—222no—
294C4⋊C4—224no—
295C22⋊C4—44no—
296C22⋊C4—42no—
297C22⋊C4—44no—
298C22⋊C4—224no—
299C42—22no—
300C42—22no—
301C42—42no—
302C42—228no—
303C42—224no—
304C42D4×D1112yes—
305C42D4×D1112yes—
306C11#1818811yescharacteristic, complemented, Sylow
307C23—22no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23C22×C22⋊D1111yescharacteristic
313Q8—28no—
314Q8—444no—
315Q8—444no—
316Q8—884no—
317D4—24no—
318D4—42no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—224no—
334C2×C4—224no—
335C2×C4#6699011yescharacteristic
336C2×C4#6699012yes—
337C2×C4#6699011yescharacteristic
338C2×C4#6700414yes—
339C2×C4C2×D4×D1112yes—
340C8—444no—
341C22—21no—
342C22—21no—
343C22—44no—
344C22—42no—
345C22—82no—
346C22—81no—
347C22—81no—
348C22C2×#6699011yescharacteristic
349C22C2×#6700412yes—
350C4—22no—
351C4—24no—
352C4—21no—
353C4—22no—
354C4—42no—
355C4—82no—
356C4—81no—
357C4—444no—
358C4—444no—
359C4#1062267512yes—
360C2—22no—
361C2—82no—
362C2#1307784911yescharacteristic
363C2C2×#1062267511yescharacteristic
364C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2398C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenter#2398D11
hypocenterC11#18188
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. #13082426C2semidirect
3. #13067657C2semidirect
5. #13067127C2semidirect
6. #13066960C2semidirect
306. C11#18188semidirect

Maximal subgroups

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

subgroupindex
#130824262
#130787152
#130676572
#130675552
#130671272
#130669602
C11×#23982
#1818811