Finite Group Databasebeta

← #14726565

Subgroups — #14726565

Order 2816.

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

normal subgroups only

This group has 970 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#13082419C211yesmaximal, characteristic
2#13078746C212yesmaximal, complemented
3#13067606C214yesmaximal, complemented
4#13067572C214yesmaximal, complemented
5#13067127C212yesmaximal, complemented
6#13066957C211yesmaximal, characteristic
7C11×#2398C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623329—21no—
11C2×#66977—22no—
12#10623074—22no—
13#10623070—24no—
14D4×Dic22—22no—
15#10623031—21no—
16#10623014C2214yes—
17#10623001C2212yes—
18C11×#400—21no—
19C11×#397C2212yes—
20C11×#394—21no—
21C11×#393C2212yes—
22C4×C11×C22⋊C4—22no—
23C11×#376C2211yescharacteristic
24#10622841C2214yes—
25#10622644—22no—
26#10622643—24no—
27#10622633—22no—
28#10622584C2214yes—
29#10622539C2212yes—
30#10622163C2214yes—
31#10622090C2218yes—
32C22×Q8×C11C2311yescharacteristic
33C22×D4×C11D411yescharacteristic
34C23×C4×C11D412yes—
35C22×Dic22—22no—
36C4×Q8×C11—22no—
37C4×Q8×C11—22no—
38C4×D4×C11—22no—
39C4×D4×C11—22no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4C2311yescharacteristic
43C2×C11×C22⋊C4—22no—
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4C2312yes—
46C2×C42×C11—21no—
47C2×C42×C11—21no—
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11—24no—
50C2×#4326—24no—
51D4×Dic11—24no—
52D4×Dic11—24no—
53#66979—22no—
54C2×C4⋊Dic11—22no—
55#66977—24no—
56#66977—24no—
57#66977—22no—
58#66977—24no—
59#66977C2314yes—
60C2×Dic11⋊C4—24no—
61#66943—24no—
62#66941—24no—
63#66931—28no—
64#66931—28no—
65#66923—22no—
66#66922D412yes—
67#66922D412yes—
68C4×Dic22—22no—
69C4×Dic22D414yes—
70C11×#95—21no—
71C11×#95—22no—
72C11×#95—22no—
73C11×#95C2312yes—
74#66899—24no—
75C22⋊(C11⋊C8)C2314yes—
76#66874—24no—
77#66872—24no—
78C4⋊(C11⋊C8)—22no—
79#66867—22no—
80#18181—111nomaximal, Sylow
81C24×C11C2×D412yes—
82C2×Q8×C11—22no—
83C2×Q8×C11—42no—
84C2×D4×C11—24no—
85C2×D4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—44no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—24no—
97C22×Dic11—24no—
98C2×Dic22—24no—
99C2×Dic22—22no—
100C2×Dic22—84no—
101C2×Dic22C2×D414yes—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—42no—
105C11×C22⋊C4—24no—
106C11×C22⋊C4—44no—
107C11×C22⋊C4—44no—
108C42×C11—42no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11C2×D412yes—
112C42×C11C2×D412yes—
113C22⋊Dic11—28no—
114C22⋊Dic11—24no—
115#4326—48no—
116C4⋊Dic11—24no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11C2×D414yes—
121Dic11⋊C4—28no—
122Dic11⋊C4—24no—
123Dic11⋊C4—24no—
124C4×Dic11—24no—
125C2×C11⋊C8—24no—
126#3501—111no—
127#3113—112no—
128#2398D1111yescharacteristic
129#1608—114no—
130#1602—114no—
131#1506—112no—
132#1466—111no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11#13714yes—
138C23×C11C22×D411yescharacteristic
139Q8×C11—24no—
140Q8×C11—42no—
141D4×C11—28no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—44no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—82no—
157C2×C4×C11#12012yes—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11C22×D412yes—
161C2×Dic11—24no—
162C2×Dic11—24no—
163C2×Dic11—84no—
164C2×Dic11—84no—
165Dic22—44no—
166Dic22—44no—
167Dic22—84no—
168C11⋊C8—44no—
169#554—224no—
170#554—222no—
171D4×Q8—222no—
172#544—221no—
173#543—114no—
174#533—112no—
175C2×C22⋊Q8—222no—
176#518—221no—
177C2×C4×Q8C2×D1111yescharacteristic
178C2×C4×D4C2×D1111yescharacteristic
179#483—114no—
180#475—222no—
181#462—222no—
182#451—114no—
183#441—224no—
184#432—112no—
185#400—21no—
186#397C2×D1112yes—
187#394—21no—
188#393C2×D1112yes—
189C4×C22⋊C4—22no—
190#376C2×D1111yescharacteristic
191#328—118no—
192#323—114no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—24no—
196C22×C11—44no—
197C22×C11—42no—
198C22×C11—42no—
199C22×C11—82no—
200C22×C11C2×#12011yescharacteristic
201C22×C11C2×#13712yes—
202C4×C11—22no—
203C4×C11—21no—
204C4×C11—22no—
205C4×C11—42no—
206C4×C11—42no—
207C4×C11—82no—
208C4×C11—81no—
209C4×C11#45512yes—
210Dic11—44no—
211Dic11—44no—
212C22×Q8—222no—
213C22×Q8C22×D1111yescharacteristic
214C22×D4C22⋊D1111yescharacteristic
215C23×C4C22⋊D1112yes—
216C2×Q16—224no—
217C4⋊Q8—112no—
218C4⋊Q8—112no—
219C4⋊Q8—224no—
220#125—224no—
221#125—222no—
222C22⋊Q8—114no—
223C22⋊Q8—228no—
224C22⋊Q8—228no—
225C22⋊Q8—224no—
226C22⋊Q8—224no—
227C22⋊Q8—222no—
228C22⋊Q8—224no—
229C4×Q8—22no—
230C4×Q8—22no—
231C4×Q8—114no—
232C4×Q8—222no—
233C4×D4—22no—
234C4×D4—22no—
235C4×D4—224no—
236C4×D4—224no—
237#117—222no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—224no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4C22⋊D1111yescharacteristic
242C2×C4⋊C4C22×D1111yescharacteristic
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—224no—
246C2×C22⋊C4C22×D1112yes—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42C22×D1111yescharacteristic
250#106—224no—
251C4⋊C8—222no—
252#103—224no—
253#103—224no—
254C22⋊C8—114no—
255#97—222no—
256#95—21no—
257#95—22no—
258#95—22no—
259#95C22×D1112yes—
260C2×C11—22no—
261C2×C11—44no—
262C2×C11#300411yescharacteristic
263C2×C11C2×#45511yescharacteristic
264C2×C11#302511yescharacteristic
265C24C2×C22⋊D1112yes—
266C2×Q8—22no—
267C2×Q8—42no—
268C2×Q8—114no—
269C2×Q8—224no—
270C2×Q8—222no—
271C2×Q8—884no—
272C2×D4—24no—
273C2×D4—22no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—44no—
280C22×C4—224no—
281C22×C4—224no—
282C22×C4C2×C22⋊D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C22×C4C2×C22⋊D1112yes—
285C22×C4C23×D1111yescharacteristic
286Q16—448no—
287C2×C8—224no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—42no—
291C4⋊C4—114no—
292C4⋊C4—224no—
293C4⋊C4—228no—
294C4⋊C4—224no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—224no—
299C22⋊C4—24no—
300C22⋊C4—44no—
301C22⋊C4—44no—
302C22⋊C4—228no—
303C22⋊C4—224no—
304C42—42no—
305C42—41no—
306C42—41no—
307C42—224no—
308C42D4×D1112yes—
309C42D4×D1112yes—
310C11#1818111yescharacteristic, complemented, Sylow
311C23—22no—
312C23—22no—
313C23—42no—
314C23—42no—
315C23#6700414yes—
316C23C22×C22⋊D1111yescharacteristic
317Q8—24no—
318Q8—42no—
319Q8—444no—
320Q8—444no—
321Q8—884no—
322D4—28no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—44no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—224no—
339C2×C4—224no—
340C2×C4—884no—
341C2×C4—884no—
342C2×C4#6699011yescharacteristic
343C2×C4#6699012yes—
344C2×C4#6699011yescharacteristic
345C2×C4C2×D4×D1112yes—
346C8—444no—
347C22—21no—
348C22—21no—
349C22—24no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22C2×#6699011yescharacteristic
355C22C2×#6700412yes—
356C4—22no—
357C4—21no—
358C4—22no—
359C4—42no—
360C4—42no—
361C4—82no—
362C4—81no—
363C4—444no—
364C4—444no—
365C4#1062267412yes—
366C2—22no—
367C2—44no—
368C2#1307784911yescharacteristic
369C2C2×#1062267411yescharacteristic
370C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2398C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenter#2398D11
hypocenterC11#18181
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
2. #13078746C2semidirect
3. #13067606C2semidirect
4. #13067572C2semidirect
5. #13067127C2semidirect
310. C11#18181semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130787462
#130676062
#130675722
#130671272
#130669572
C11×#23982
#1818111