Finite Group Databasebeta

← #14650673

Subgroups — #14650673

Order 2816.

536 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 107 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#13078746C211yesmaximal, characteristic
2#13070981C211yesmaximal, characteristic
3#13069560C211yesmaximal, characteristic
4#13067129C211yesmaximal, characteristic
5#13066510C211yesmaximal, characteristic
6#13066471C211yesmaximal, characteristic
7C11×#1491C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×Q8×Dic11—21no—
10#10623001C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622841—21no—
14#10622644C412yescomplemented
15#10622643—22no—
16#10622633C412yescomplemented
17C4⋊C4×Dic11—21no—
18C4⋊C4×Dic11—22no—
19#10622584—21no—
20C4×C4⋊Dic11—21no—
21C4×C4⋊Dic11C2211yescharacteristic
22#10622545—21no—
23#10622545C2211yescharacteristic
24#10622539C2211yescharacteristic
25C11×Q8⋊C8—22no—
26#10622193—22no—
27#10622105—21no—
28#10622105—21no—
29C22×Q8×C11D411yescharacteristic
30C2×C11×M16—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11C2×C412yes—
34C4×Q8×C11D412yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39Q8×Dic11—28no—
40C2×#4326—22no—
41#66979—21no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11—21no—
44#66977—21no—
45#66977—21no—
46C2×C4×Dic11—22no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11—22no—
49C2×C4×Dic11D412yes—
50#66923—21no—
51#66922C2×C411yescharacteristic
52#66922C2×C411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C11×#97—21no—
59C4×C8×C11—21no—
60#66899—22no—
61C11⋊#95—22no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95D411yescharacteristic
65C11⋊#95D411yescharacteristic
66C22⋊(C11⋊C8)—21no—
67#66874—22no—
68#66872—22no—
69C4⋊(C11⋊C8)C2×C412yes—
70#66867—21no—
71#9324—111nomaximal, Sylow
72C2×Q8×C11—24no—
73C2×Q8×C11—21no—
74C2×Q8×C11C22⋊C412yes—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—22no—
82C22×Dic11—21no—
83C2×Dic22—21no—
84C2×Dic22—21no—
85C11×M16—22no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4C22⋊C412yes—
93C42×C11—22no—
94C42×C11—22no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99C22⋊Dic11—41no—
100#4326—44no—
101C4⋊Dic11—28no—
102C4⋊Dic11—24no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—28no—
110C4×Dic11—24no—
111C4×Dic11—42no—
112C4×Dic11—41no—
113C4×Dic11—82no—
114C2×C11⋊C8—22no—
115#3113—111no—
116#2276—111no—
117#1986—111no—
118#1506—111no—
119#1491D1111yescharacteristic
120#1300—111no—
121#1285—111no—
122C23×C11#12011yescharacteristic
123Q8×C11—24no—
124Q8×C11—22no—
125Q8×C11#10414yes—
126C2×C4×C11—24no—
127C2×C4×C11—22no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12311yescharacteristic
141C2×Dic11—22no—
142C2×Dic11—24no—
143C2×Dic11—22no—
144C2×Dic11—41no—
145C2×Dic11—42no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152Dic22—42no—
153Dic22—81no—
154C8×C11—42no—
155C8×C11—81no—
156C11⋊C8—42no—
157#533—111no—
158C2×C4×Q8—221no—
159C2×C4×Q8C2×D1111yescharacteristic
160#483—221no—
161#475—112no—
162#462—112no—
163#451—221no—
164#441—222no—
165#432—111no—
166#432C2×D1111yescharacteristic
167C4×M16C2×D1111yescharacteristic
168C4×C4⋊C4—111no—
169C4×C4⋊C4—221no—
170C4×C4⋊C4—222no—
171C4×C4⋊C4—221no—
172#376—111no—
173#376—221no—
174#339—222no—
175#328—221no—
176#328—221no—
177Q8⋊C8—22no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#38611yescharacteristic
181C22×C11#45511yescharacteristic
182C22×C11#45611yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—24no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11C2×#10412yes—
191Dic11—44no—
192Dic11—42no—
193Dic11—42no—
194Dic11—81no—
195Dic11—81no—
196C22×Q8D4411yescharacteristic
197C2×Q16—222no—
198C2×M16—21no—
199C4⋊Q8—111no—
200C4⋊Q8—111no—
201#125—221no—
202C22⋊Q8—221no—
203C22⋊Q8—221no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8—228no—
207C4×Q8—221no—
208C4×Q8—221no—
209C4×Q8C4×D1112yes—
210C4×Q8C22⋊D1112yes—
211#117—221no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—222no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4D4411yescharacteristic
216C2×C42—21no—
217C2×C42—112no—
218C2×C42—222no—
219C2×C42—221no—
220C2×C42—222no—
221C2×C42C22×D1111yescharacteristic
222#106—222no—
223C4⋊C8—21no—
224C4⋊C8—112no—
225#103—222no—
226#103—222no—
227C22⋊C8—21no—
228C22⋊C8—221no—
229#97—21no—
230#97—21no—
231#97—221no—
232C4×C8—21no—
233#95—111no—
234#95—111no—
235#95—222no—
236#95—221no—
237#95—221no—
238C2×C11—21no—
239C2×C11—21no—
240C2×C11#188211yescharacteristic
241C2×C11#189611yescharacteristic
242C2×C11#190511yescharacteristic
243C2×Q8—24no—
244C2×Q8—21no—
245C2×Q8—221no—
246C2×Q8—221no—
247C2×Q8(C2×D11)⋊C412yes—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—222no—
253C22×C4C2×D4411yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C22×C4D4×D1111yescharacteristic
256Q16—444no—
257M16—22no—
258M16—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—222no—
262C4⋊C4—22no—
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—228no—
266C4⋊C4—224no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4(C2×D11)⋊C412yes—
274C22⋊C4—441no—
275C42—22no—
276C42—22no—
277C42—228no—
278C42—224no—
279C42—442no—
280C42—441no—
281C42—882no—
282C42C2×C4×D1111yescharacteristic
283C42#434111yescharacteristic
284C42#434111yescharacteristic
285C42C2×C22⋊D1111yescharacteristic
286C11#932411yescharacteristic, complemented, Sylow
287C23#6693511yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—442no—
291Q8—881no—
292Q8#6688914yes—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—222no—
303C2×C4—222no—
304C2×C4—224no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4(C22⋊D11)⋊C411yescharacteristic
314C2×C4(C22⋊D11)⋊C411yescharacteristic
315C2×C4#6693911yescharacteristic
316C2×C4C2×(C2×D11)⋊C411yescharacteristic
317C2×C4#6699211yescharacteristic
318C2×C4#6699211yescharacteristic
319C8—42no—
320C8—81no—
321C8—442no—
322C22—21no—
323C22—21no—
324C22#1062243811yescharacteristic
325C22#1062243911yescharacteristic
326C22#1062257111yescharacteristic
327C4—24no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—42no—
334C4—444no—
335C4—442no—
336C4—442no—
337C4—881no—
338C4—881no—
339C4C2×#6688912yes—
340C2—21no—
341C2—21no—
342C2#1306898311yescharacteristic
343C2#1306905711yescharacteristic
344C2#1306910811yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1491C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1491D11
hypocenterC11#9324
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
14. #10622644C4semidirect
16. #10622633C4semidirect
286. C11#9324semidirect

Maximal subgroups

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

subgroupindex
#130787462
#130709812
#130695602
#130671292
#130665102
#130664712
C11×#14912
#932411