Finite Group Databasebeta

← #14656408

Subgroups — #14656408

Order 2816.

690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079541C211yesmaximal, characteristic, complemented
2#13079534C211yesmaximal, characteristic
3#13069444C211yesmaximal, characteristic, complemented
4#13067297C211yesmaximal, characteristic, complemented
5#13067284C211yesmaximal, characteristic, complemented
6#13066449C211yesmaximal, characteristic, complemented
7C11×#2858C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×C11×#124—22no—
11#10623008C2211yescharacteristic
12C11×#390—22no—
13C11×#390—22no—
14C43×C11C2211yescharacteristic
15#10622840—22no—
16#10622830—22no—
17#10622698—21no—
18#10622696—22no—
19#10622694—21no—
20#10622686—21no—
21#10622685—22no—
22#10622683—21no—
23C2×#66869—22no—
24#10622538C2211yescharacteristic
25#10622538C2211yescharacteristic
26#10622537C2211yescharacteristic
27#10622184—22no—
28#10622182—22no—
29C22×Q8×C11D412yes—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×#4339—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#124—48no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C22⋊C4—28no—
46C2×C42×C11—21no—
47C2×C42×C11—21no—
48C2×C42×C11D412yes—
49C2×C42×C11C2311yescharacteristic
50C2×#4325—24no—
51C2×#4323—24no—
52#66983—21no—
53#66983—21no—
54C2×#4318—21no—
55#66928—21no—
56#66927D411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922D411yescharacteristic
60#66899—24no—
61#66896—24no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64#66869—44no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10281—111nomaximal, Sylow
72C24×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—44no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—44no—
79C2×D4×C11—44no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—42no—
85C2×D4×C11—42no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—41no—
92#4339—42no—
93#4339—42no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×C4×D11—41no—
98C2×Dic22—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—416no—
104C42×C11—24no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—42no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112#4325—84no—
113#4323—84no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118#4318—42no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#3206—111no—
123#3205—111no—
124#2858D1111yescharacteristic, complemented
125#1962—111no—
126#1548—111no—
127#1545—111no—
128#1276—111no—
129C23×C11—44no—
130C23×C11—44no—
131C23×C11—42no—
132C23×C11—44no—
133C23×C11#12011yescharacteristic
134C22×D11—41no—
135Q8×C11—44no—
136Q8×C11—82no—
137D4×C11—44no—
138D4×C11—82no—
139D4×C11—82no—
140D4×C11—82no—
141D4×C11—82no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—24no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—44no—
150C2×C4×C11—42no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×C4×C11#13512yes—
158C2×C4×C11AGL(1,ℤ/8)12yes—
159C22⋊D11—82no—
160C2×Dic11—41no—
161D44—42no—
162D44—42no—
163D44—42no—
164C4×D11—81no—
165C4×D11—81no—
166Dic22—42no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170#532—111no—
171C2×C4⋊Q8C2×D1111yescharacteristic
172C2×#127C2×D1111yescharacteristic
173C2×#124—22no—
174#493—221no—
175#492—221no—
176#487—221no—
177#486—221no—
178#461—222no—
179#459—222no—
180#448—222no—
181#447—222no—
182#431—111no—
183#431—111no—
184#423—111no—
185C2×#104—222no—
186#390—22no—
187#390—22no—
188C43C2×D1111yescharacteristic
189#333—222no—
190#331—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—88no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11#39211yescharacteristic
198C22×C11#44912yes—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—44no—
205C4×C11—82no—
206C4×C11#45312yes—
207C4×C11#45512yes—
208C4×C11#46312yes—
209C4×C11#49511yescharacteristic
210C4×C11#49611yescharacteristic
211Dic11—81no—
212C2×#41—221no—
213C22×Q8C22⋊D1112yes—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4C22⋊D1112yes—
217C2×SD16—224no—
218C2×D8—224no—
219C2×M16—221no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—111no—
225#127—21no—
226#127—21no—
227#127—21no—
228#127—21no—
229#127—111no—
230#124—48no—
231#124—221no—
232#121—221no—
233#121—221no—
234C4×D4—221no—
235C4×D4—221no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C22⋊C4—28no—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42C22⋊D1112yes—
242C2×C42C22×D1111yescharacteristic
243C4⋊C8—112no—
244C4⋊C8—112no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247#104—444no—
248#103—224no—
249#102—224no—
250C22⋊C8—221no—
251C22⋊C8—221no—
252C4×C8—221no—
253C4×C8—221no—
254C2×C11—22no—
255C2×C11—162no—
256C2×C11#200211yescharacteristic
257C2×C11#200411yescharacteristic
258C2×C11#201211yescharacteristic
259D11—161no—
260C24—22no—
261#41—442no—
262#41—442no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—44no—
266C2×Q8—221no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—441no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—441no—
284C22×C4C2×C22⋊D1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286C22×C4C2×C22⋊D1111yescharacteristic
287SD16—884no—
288D8—884no—
289M16—442no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—441no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C22⋊C4—416no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C42—24no—
303C42—22no—
304C42—22no—
305C42—42no—
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42D4×D1111yescharacteristic
309C42#434111yescharacteristic
310C11#1028111yescharacteristic, complemented, Sylow
311C23—44no—
312C23—44no—
313C23—42no—
314C23—44no—
315C23—441no—
316C23#6700611yescharacteristic
317Q8—44no—
318Q8—82no—
319Q8—442no—
320D4—44no—
321D4—82no—
322D4—82no—
323D4—82no—
324D4—81no—
325D4—81no—
326D4—82no—
327D4—442no—
328D4—442no—
329D4—442no—
330D4—882no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—441no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4#6699011yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699111yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4#6699211yescharacteristic
346C2×C4#6699311yescharacteristic
347C2×C4#6700212yes—
348C2×C4#6700312yes—
349C8—442no—
350C8—442no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—88no—
355C22—82no—
356C22—82no—
357C22—82no—
358C22—881no—
359C22—881no—
360C22—881no—
361C22#1062283611yescharacteristic
362C22#1062285112yes—
363C4—21no—
364C4—21no—
365C4—44no—
366C4—82no—
367C4—881no—
368C4#1062267012yes—
369C4#1062267111yescharacteristic
370C4#1062267211yescharacteristic
371C4#1062267412yes—
372C4#1062269012yes—
373C2—22no—
374C2—162no—
375C2—1761no—
376C2#1306963111yescharacteristic
377C2#1306964511yescharacteristic
378C2#1306969311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2858C2
socleC22×C11#392
prime radical#13079534C2
hypercenter#2858D11
hypocenterC11#10281
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2858

Complements

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

NH ≅ G/Ntype
1. #13079541C2semidirect
3. #13069444C2semidirect
4. #13067297C2semidirect
5. #13067284C2semidirect
6. #13066449C2semidirect
7. C11×#2858C2semidirect
124. #2858D11semidirect
310. C11#10281semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130795342
#130694442
#130672972
#130672842
#130664492
C11×#28582
#1028111