Finite Group Databasebeta

← #14651581

Subgroups — #14651581

Order 2816.

734 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 97 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#13072892C211yesmaximal, characteristic
2#13070968C211yesmaximal, characteristic
3#13068716C211yesmaximal, characteristic, complemented
4#13068713C211yesmaximal, characteristic, complemented
5#13066942C211yesmaximal, characteristic
6#13066468C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C22×(C2×D11)⋊C4C2211yescharacteristic
9C2×#66979C2211yescharacteristic
10C2×C22⋊C4×D11—21no—
11C11×#407C2211yescharacteristic
12C11×#381C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622568—21no—
17#10622563—21no—
18C22⋊C4×Dic11—21no—
19C4×(C2×D11)⋊C4—22no—
20#10622290C412yescomplemented
21#10622287C412yescomplemented
22#10622283—22no—
23#10622279—22no—
24#10622193—22no—
25#10622161—22no—
26#10622106—22no—
27C24×D11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×C4×D11—22no—
31C2×C11×M16—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C42×C11D412yes—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4C2×C412yes—
45C2×(C2×D11)⋊C4D412yes—
46#66979—21no—
47#66979—21no—
48#66979—21no—
49#66979—21no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11C2×C411yescharacteristic, complemented
52C2×C4⋊Dic11C2×C411yescharacteristic, complemented
53C2×C4×Dic11—21no—
54C2×C4×Dic11—22no—
55C2×C4×Dic11D412yes—
56C2×#4318—21no—
57C22⋊C4×D11—28no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95C2×C412yescomplemented
63C11⋊#95—22no—
64C11⋊#95—21no—
65C11⋊#95—22no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68#9477—111nomaximal, Sylow
69C24×C11C2×D411yescharacteristic
70C23×D11—21no—
71C23×D11—21no—
72C23×D11—24no—
73C23×D11—42no—
74C23×D11—81no—
75C23×D11C22⋊C412yes—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—42no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—22no—
89C22×Dic11—21no—
90C22×Dic11—81no—
91C22×Dic11C22⋊C412yes—
92C2×C4×D11—28no—
93C2×C4×D11—82no—
94C2×C4×D11—82no—
95C11×M16—42no—
96C2×C8×C11—41no—
97C11×C22⋊C4—24no—
98C11×C22⋊C4—42no—
99C42×C11—42no—
100C22⋊Dic11—24no—
101C22⋊Dic11—41no—
102C22⋊Dic11—41no—
103(C2×D11)⋊C4—28no—
104(C2×D11)⋊C4—22no—
105(C2×D11)⋊C4—22no—
106(C2×D11)⋊C4—22no—
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—44no—
109(C2×D11)⋊C4—82no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—82no—
115C4×Dic11—42no—
116C4×Dic11—41no—
117C4×Dic11—41no—
118C4×Dic11—82no—
119#4318—42no—
120C2×C11⋊C8—41no—
121#2482—111no—
122#2273—111no—
123#1826—111no—
124#1826—111no—
125#1462—111no—
126#1284—111no—
127#1284D1111yescharacteristic, complemented
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—41no—
131C23×C11C2×C22⋊C411yescharacteristic
132C23×C11#12011yescharacteristic
133C23×C11#12311yescharacteristic
134C22×D11—22no—
135C22×D11—22no—
136C22×D11—22no—
137C22×D11—24no—
138C22×D11—22no—
139C22×D11—42no—
140C22×D11—42no—
141C22×D11—42no—
142C22×D11—42no—
143C22×D11—88no—
144C22×D11—81no—
145C22×D11—81no—
146C22×D11#10414yes—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11C4×D411yescharacteristic
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×Dic11—24no—
164C2×Dic11—22no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173C2×Dic11—81no—
174C4×D11—88no—
175C8×C11—81no—
176C11⋊C8—81no—
177C2×#117—111no—
178C22×C22⋊C4—111no—
179C22×C22⋊C4—221no—
180#407—111no—
181#407C2×D1111yescharacteristic
182#399—112no—
183#397—112no—
184#388—222no—
185#385—221no—
186#381C2×D1111yescharacteristic
187#379—221no—
188C4×C22⋊C4—111no—
189C4×C22⋊C4—222no—
190C4×C22⋊C4—221no—
191C4×C22⋊C4—222no—
192C4×C22⋊C4C2×D1111yescharacteristic
193#339—222no—
194#339—222no—
195#323—222no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—44no—
204C22×C11#38611yescharacteristic
205C22×C11C2×#10412yes—
206C22×C11#45812yes—
207C2×D11—24no—
208C2×D11—44no—
209C2×D11—44no—
210C2×D11—42no—
211C2×D11—42no—
212C2×D11—44no—
213C2×D11—82no—
214C2×D11—84no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—44no—
220C4×C11—82no—
221Dic11—44no—
222Dic11—42no—
223Dic11—81no—
224Dic11—81no—
225C25—111no—
226C23×C4—111no—
227C23×C4—222no—
228C23×C4C22×D1111yescharacteristic
229C2×M16—21no—
230C2×M16—221no—
231#117—221no—
232#117—221no—
233#117—221no—
234#117—221no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—111no—
237C2×C4⋊C4—222no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—112no—
241C2×C22⋊C4—112no—
242C2×C22⋊C4—228no—
243C2×C22⋊C4—222no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—222no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—222no—
252C2×C42—112no—
253C2×C42—221no—
254C2×C42—222no—
255C2×C42D4412yes—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—221no—
259C22⋊C8—221no—
260#95—21no—
261#95—21no—
262#95—222no—
263#95—222no—
264#95—221no—
265#95C4×D1112yescomplemented
266C2×C11—22no—
267C2×C11—22no—
268C2×C11—41no—
269C2×C11#189011yescharacteristic
270C2×C11#189611yescharacteristic
271C2×C11#191111yescharacteristic
272D11—44no—
273C24—112no—
274C24—224no—
275C24—221no—
276C24—221no—
277C24—442no—
278C24—881no—
279C24D4×D1111yescharacteristic
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—112no—
284C22×C4—228no—
285C22×C4—222no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—882no—
291C22×C4—882no—
292C22×C4—881no—
293C22×C4C2×C4×D1111yescharacteristic
294C22×C4C2×D4411yescharacteristic
295C22×C4#433911yescharacteristic
296C22×C4D4×D1111yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4#434311yescharacteristic
299M16—42no—
300M16—442no—
301C2×C8—41no—
302C2×C8—441no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4—882no—
308C22⋊C4—24no—
309C22⋊C4—42no—
310C22⋊C4—228no—
311C22⋊C4—224no—
312C22⋊C4—222no—
313C22⋊C4—222no—
314C22⋊C4—222no—
315C22⋊C4—222no—
316C22⋊C4—444no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—882no—
320C42—42no—
321C42—442no—
322C42—441no—
323C42—441no—
324C42—882no—
325C11#947711yescharacteristic, complemented, Sylow
326C23—22no—
327C23—22no—
328C23—41no—
329C23—114no—
330C23—222no—
331C23—222no—
332C23—224no—
333C23—222no—
334C23—222no—
335C23—442no—
336C23—442no—
337C23—442no—
338C23—442no—
339C23—881no—
340C23—881no—
341C23—888no—
342C23C22⋊C4×D1111yescharacteristic
343C23#6693511yescharacteristic
344C23#6694711yescharacteristic
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—224no—
358C2×C4—222no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—442no—
367C2×C4—888no—
368C2×C4—881no—
369C2×C4C4×D4411yescharacteristic
370C2×C4#6693711yescharacteristic
371C2×C4#6694611yescharacteristic
372C2×C4#6694811yescharacteristic
373C8—81no—
374C8—881no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—44no—
383C22—224no—
384C22—444no—
385C22—444no—
386C22—444no—
387C22—442no—
388C22—442no—
389C22—882no—
390C22—884no—
391C22#1062227811yescharacteristic
392C22#1062235512yes—
393C22D11×#10412yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—44no—
399C4—82no—
400C4—444no—
401C4—442no—
402C4—881no—
403C4—881no—
404C2—22no—
405C2—22no—
406C2—41no—
407C2—444no—
408C2#1306902811yescharacteristic
409C2#1306905811yescharacteristic
410C2#1306914711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#386
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#9477
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
3. #13068716C2semidirect
4. #13068713C2semidirect
6. #13066468C2semidirect
7. C11×#1284C2semidirect
20. #10622290C4semidirect
21. #10622287C4semidirect
51. C2×C4⋊Dic11C2×C4semidirect
52. C2×C4⋊Dic11C2×C4semidirect
62. C11×#95C2×C4semidirect
127. #1284D11semidirect
265. #95C4×D11semidirect
325. C11#9477semidirect

Maximal subgroups

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

subgroupindex
#130728922
#130709682
#130687162
#130687132
#130669422
#130664682
C11×#12842
#947711