Finite Group Databasebeta

← #14663232

Subgroups — #14663232

Order 2816.

530 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 83 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#13071270C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic, complemented
3#13066563C212yesmaximal, complemented
4#13066543C212yesmaximal, complemented
5C11×#1466C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66990C411yescharacteristic
8C22×(C2×D11)⋊C4C411yescharacteristic
9C11×#432—21no—
10#10622833C411yescharacteristic
11#10622826—21no—
12C4×C22⋊Dic11C411yescharacteristic
13#10622820—21no—
14#10622603—21no—
15#10622570—21no—
16#10622568C2211yescharacteristic
17#10622559C2211yescharacteristic
18#10622553—21no—
19C11×#323—21no—
20C11×#323C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C24×D11C2×C411yescharacteristic
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C22×C22⋊D11—21no—
28C23×Dic11C2×C411yescharacteristic
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11C2×C411yescharacteristic
37C2×C22⋊Dic11C2×C411yescharacteristic
38#66990—22no—
39#66990—22no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—41no—
46C2×(C2×D11)⋊C4—41no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C2×#4318—41no—
50C11×C4⋊C8—41no—
51C11×C22⋊C8—22no—
52C11×#97—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—22no—
57C22⋊(C11⋊C8)—41no—
58#11527—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C24×C11C22×C411yescharacteristic
61C23×D11—21no—
62C23×D11—21no—
63C23×D11—41no—
64C23×D11—41no—
65C23×D11—81no—
66C23×D11—81no—
67C23×D11M1612yescomplemented
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—81no—
77C22×C4×C11—81no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—24no—
84C2×C22⋊D11—81no—
85C2×C22⋊D11—81no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—41no—
90C22×Dic11—81no—
91C2×C8×C11—42no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—21no—
96C42×C11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—41no—
99C22⋊Dic11—81no—
100C22⋊Dic11M1612yescomplemented
101(C2×D11)⋊C4—24no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—81no—
106(C2×D11)⋊C4—81no—
107Dic11⋊C4—81no—
108C4×Dic11—81no—
109#4318—82no—
110C2×C11⋊C8—42no—
111#2321—111no—
112#1466D1111yescharacteristic, complemented
113#1465—111no—
114#1326—112no—
115#1316—112no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11C2×M1611yescharacteristic
127C23×C11C2×M1611yescharacteristic
128C22×D11—22no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—42no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—42no—
137C22×D11—82no—
138C22×D11—82no—
139C22×D11—84no—
140C22×D11—82no—
141C22×D11—82no—
142D4×C11—42no—
143D4×C11—42no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11—81no—
158C2×C4×C11#9911yescharacteristic
159C2×C4×C11#9911yescharacteristic
160C22⋊D11—84no—
161C2×Dic11—22no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—82no—
171C8×C11—82no—
172C11⋊C8—82no—
173C2×#120—111no—
174C2×C4×D4C2×D1111yescharacteristic
175C22×C22⋊C4—111no—
176#432—21no—
177#407—221no—
178#390—221no—
179#388—221no—
180#388—221no—
181#386—111no—
182#386—221no—
183#385—111no—
184#379—111no—
185C4×C22⋊C4—111no—
186#324—221no—
187#323—21no—
188#323—112no—
189#323C2×D1112yes—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—81no—
204C22×C11#40711yescharacteristic
205C22×C11C2×#9911yescharacteristic
206C22×C11#41311yescharacteristic
207C2×D11—42no—
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—84no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—84no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—41no—
222Dic11—42no—
223Dic11—81no—
224Dic11—81no—
225C25—111no—
226C22×D4—221no—
227C22×D4C4×D1111yescharacteristic
228C23×C4—111no—
229C23×C4C4×D1111yescharacteristic
230C23×C4D4411yescharacteristic
231C2×M16—441no—
232#120—222no—
233#120—222no—
234C4×D4—41no—
235C4×D4—41no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4D4411yescharacteristic
238C2×C22⋊C4—111no—
239C2×C22⋊C4—111no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4—221no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C22⋊C4—441no—
247C2×C22⋊C4—441no—
248C2×C22⋊C4C22⋊D1111yescharacteristic
249C2×C22⋊C4C22×D1111yescharacteristic
250C2×C42—221no—
251C2×C42C22⋊D1111yescharacteristic
252C4⋊C8—41no—
253C22⋊C8—22no—
254C22⋊C8—222no—
255C22⋊C8—441no—
256#97—41no—
257#95—221no—
258#95—221no—
259#95—221no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11—41no—
263C2×C11—41no—
264C2×C11—81no—
265C2×C11#146511yescharacteristic
266C2×C11#212111yescharacteristic
267C2×C11#212211yescharacteristic
268D11—82no—
269C24—112no—
270C24—221no—
271C24—221no—
272C24—441no—
273C24—441no—
274C24—881no—
275C24—881no—
276C24(C2×D11)⋊C411yescharacteristic
277C24C2×C4×D1111yescharacteristic
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—224no—
283C2×D4—881no—
284C2×D4—881no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—81no—
290C22×C4—81no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—441no—
295C22×C4—881no—
296C22×C4(C2×D11)⋊C411yescharacteristic
297C22×C4(C2×D11)⋊C411yescharacteristic
298C22×C4(C2×D11)⋊C411yescharacteristic
299C22×C4C2×D4411yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301M16—882no—
302C2×C8—42no—
303C2×C8—442no—
304C4⋊C4—41no—
305C4⋊C4—881no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—112no—
309C22⋊C4—224no—
310C22⋊C4—221no—
311C22⋊C4—442no—
312C22⋊C4—441no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—881no—
316C22⋊C4—881no—
317C22⋊C4—881no—
318C42—21no—
319C42—21no—
320C42—881no—
321C11#1152711yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—222no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23—442no—
337C23—442no—
338C23—441no—
339C23—441no—
340C23—882no—
341C23—882no—
342C23—882no—
343C23—882no—
344C23—884no—
345C23M16×D1111yescharacteristic
346C23M16×D1111yescharacteristic
347C23C2×(C2×D11)⋊C411yescharacteristic
348D4—42no—
349D4—42no—
350D4—884no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—222no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—882no—
375C2×C4#6687011yescharacteristic
376C2×C4#6687011yescharacteristic
377C8—82no—
378C8—882no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22—442no—
394C22—442no—
395C22—442no—
396C22—881no—
397C22—881no—
398C22—884no—
399C22—884no—
400C22—881no—
401C22—881no—
402C22C2×#6687011yescharacteristic
403C22#1062273911yescharacteristic
404C22#1062274511yescharacteristic
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—442no—
412C4—881no—
413C4—881no—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2—81no—
419C2—882no—
420C2#1306695211yescharacteristic
421C2#1307026311yescharacteristic
422C2#1307026511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1466C2
socleC22×C11C2×#99
prime radicalC2×#66990C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1466D11
hypocenterC11#11527
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #13066954C2semidirect
3. #13066563C2semidirect
4. #13066543C2semidirect
5. C11×#1466C2semidirect
67. C23×D11M16semidirect
100. C22⋊Dic11M16semidirect
112. #1466D11semidirect
321. C11#11527semidirect

Maximal subgroups

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

subgroupindex
#130712702
#130669542
#130665632
#130665432
C11×#14662
#1152711