Finite Group Databasebeta

← #14651659

Subgroups — #14651659

Order 2816.

458 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 89 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#13077252C211yesmaximal, characteristic
2#13074187C211yesmaximal, characteristic
3#13067063C211yesmaximal, characteristic, complemented
4#13066948C211yesmaximal, characteristic
5#13066482C211yesmaximal, characteristic, complemented
6#13066481C211yesmaximal, characteristic, complemented
7C11×#1491C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66925C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12#10622844C411yescharacteristic
13#10622842C411yescharacteristic
14#10622739—21no—
15#10622731—21no—
16#10622606C411yescharacteristic
17#10622602—21no—
18#10622593C411yescharacteristic
19#10622591—21no—
20#10622553—21no—
21#10622550C2211yescharacteristic
22#10622546—21no—
23#10622539C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622322—22no—
26#10622303—22no—
27C11×Q8⋊C8—22no—
28Q8⋊(C11⋊C8)—22no—
29#10622107—21no—
30#10622106—21no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C2×C11×M16—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4C2×C411yescharacteristic
45C2×(C2×D11)⋊C4D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4C2×C411yescharacteristic
49C2×Dic11⋊C4D411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C2×#4318—21no—
52#66925—21no—
53#66925—21no—
54#66925—21no—
55#66925—21no—
56C11×C4⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#97—21no—
59C11×#97—21no—
60C4×C8×C11D412yes—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95C2×C411yescharacteristic
68C11⋊#95C2×C411yescharacteristic
69C22⋊(C11⋊C8)—21no—
70(C2×D11)⋊C8—24no—
71Dic11⋊C8—24no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74#66867—21no—
75C4×C11⋊C8D412yes—
76#9493—111nomaximal, Sylow
77C23×D11C22⋊C411yescharacteristic
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—42no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C11×M16—41no—
96C11×M16—41no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C42×C11—41no—
104C42×C11—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11#4111yescharacteristic
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—21no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117Dic11⋊C4—21no—
118Dic11⋊C4—21no—
119Dic11⋊C4—42no—
120Dic11⋊C4—42no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123#4318—41no—
124#4318—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127#2921—111no—
128#2599—111no—
129#1491—111no—
130#1491D1111yescharacteristic, complemented
131#1464—111no—
132#1288—111no—
133#1288—111no—
134C23×C11C2×C22⋊C411yescharacteristic
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—41no—
139C22×D11—41no—
140Q8×C11—22no—
141Q8×C11—22no—
142Q8×C11—41no—
143Q8×C11—41no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12311yescharacteristic
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C4×D11—42no—
174C4×D11—42no—
175C8×C11—42no—
176C8×C11—81no—
177C11⋊C8—42no—
178C11⋊C8—81no—
179C2×C4×Q8C2×D1111yescharacteristic
180C2×#117—111no—
181#433—222no—
182#433—222no—
183#432—111no—
184#432C2×D1111yescharacteristic
185#423—221no—
186#407—221no—
187C4×M16—111no—
188C4×M16C2×D1111yescharacteristic
189#398—111no—
190#397—111no—
191#395—111no—
192#393—111no—
193#388—221no—
194#387—221no—
195#387—221no—
196#385—221no—
197#383—111no—
198Q8⋊C8—22no—
199Q8⋊C8—222no—
200#324—221no—
201#323—221no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11#38611yescharacteristic
205C22×C11#42111yescharacteristic
206C22×C11#42111yescharacteristic
207C2×D11—42no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—81no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—81no—
220Dic11—41no—
221Dic11—41no—
222Dic11—41no—
223Dic11—81no—
224Dic11—81no—
225C22×Q8C4×D1111yescharacteristic
226C23×C4—111no—
227C2×M16—21no—
228C2×M16—221no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233#117—221no—
234#117—221no—
235#117—221no—
236#117—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4C4×D1111yescharacteristic
243C2×C22⋊C4—111no—
244C2×C22⋊C4—111no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C42—21no—
248C2×C42—111no—
249C2×C42C22×D1111yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—224no—
252C4⋊C8—221no—
253C22⋊C8—21no—
254C22⋊C8—224no—
255C22⋊C8—221no—
256#97—21no—
257#97—21no—
258#97—221no—
259#97—221no—
260C4×C8—112no—
261C4×C8C22⋊D1112yes—
262#95—111no—
263#95—111no—
264#95—221no—
265#95—221no—
266#95—221no—
267#95—221no—
268#95—221no—
269#95—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11#189111yescharacteristic
273C2×C11#189711yescharacteristic
274C2×C11#190911yescharacteristic
275D11—81no—
276C24—111no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—42no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—111no—
283C22×C4—111no—
284C22×C4—111no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—441no—
290C22×C4—441no—
291C22×C4C2×C4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294M16—41no—
295M16—41no—
296M16—441no—
297M16—441no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—222no—
301C2×C8—441no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—442no—
311C4⋊C4—442no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4—442no—
317C22⋊C4—442no—
318C42—41no—
319C42—41no—
320C42—221no—
321C42—221no—
322C42#433911yescharacteristic
323C42D4×D1111yescharacteristic
324C42#434111yescharacteristic
325C42C2×C22⋊D1111yescharacteristic
326C11#949311yescharacteristic, complemented, Sylow
327C23—221no—
328C23—221no—
329C23—221no—
330C23—441no—
331C23—441no—
332C23C22⋊C4×D1111yescharacteristic
333Q8—22no—
334Q8—22no—
335Q8—41no—
336Q8—41no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4(C22⋊D11)⋊C411yescharacteristic
363C2×C4#6693611yescharacteristic
364C2×C4#6693711yescharacteristic
365C2×C4C4×C22⋊D1111yescharacteristic
366C2×C4#6699011yescharacteristic
367C2×C4#6699111yescharacteristic
368C8—42no—
369C8—81no—
370C8—442no—
371C8—881no—
372C22—21no—
373C22—21no—
374C22—442no—
375C22—441no—
376C22—441no—
377C22—441no—
378C22—881no—
379C22#1062243411yescharacteristic
380C22#1062243411yescharacteristic
381C22#1062256911yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—81no—
390C4—441no—
391C4—441no—
392C4—441no—
393C4—881no—
394C4—881no—
395C2—21no—
396C2—21no—
397C2—881no—
398C2#1306903111yescharacteristic
399C2#1306906111yescharacteristic
400C2#1306913511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1491C2
socleC22×C11#386
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1491D11
hypocenterC11#9493
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
3. #13067063C2semidirect
5. #13066482C2semidirect
6. #13066481C2semidirect
7. C11×#1491C2semidirect
130. #1491D11semidirect
326. C11#9493semidirect

Maximal subgroups

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

subgroupindex
#130772522
#130741872
#130670632
#130669482
#130664822
#130664812
C11×#14912
#949311