Finite Group Databasebeta

← #14643001

Subgroups — #14643001

Order 2816.

410 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 87 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#13075647C211yesmaximal, characteristic
2#13070160C211yesmaximal, characteristic
3#13070093C211yesmaximal, characteristic
4#13066441C211yesmaximal, characteristic
5#13066439C211yesmaximal, characteristic
6#13066438C211yesmaximal, characteristic
7C11×#2084C211yesmaximal, characteristic
8C2×#66941—21no—
9C2×C11×#106—21no—
10C11×#389C2211yescharacteristic
11C11×#384C2211yescharacteristic
12#10622597—21no—
13#10622594—21no—
14#10622592—21no—
15C2×#66874—21no—
16C2×#66872—21no—
17C2×#66872—21no—
18#10622542C2211yescharacteristic
19#10622541C2211yescharacteristic
20#10622269—21no—
21#10622267—21no—
22C11×#340—21no—
23C11×#336C2211yescharacteristic
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Dic22—21no—
28C22×Dic22D411yescharacteristic
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47#66941—42no—
48#66941—42no—
49C11×#106—42no—
50C11×#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57#66874—42no—
58#66872—42no—
59#66872—42no—
60#7817—111nomaximal, Sylow
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×Dic22—21no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22—42no—
75C2×Dic22—81no—
76C2×Dic22—81no—
77C2×Dic22SD1612yes—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4SD1612yes—
92C42×C11—41no—
93C4⋊Dic11—21no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—42no—
97C4⋊Dic11SD1612yes—
98Dic11⋊C4—42no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—81no—
102C4×Dic11—42no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2734—111no—
110#2096—111no—
111#2084—111no—
112#2084D1111yescharacteristic
113#1272—111no—
114#1271—111no—
115#1271—111no—
116C23×C11#12011yescharacteristic
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11C2×SD1611yescharacteristic
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11C2×SD1611yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×Dic11—22no—
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150Dic22—42no—
151Dic22—81no—
152Dic22—84no—
153C8×C11—42no—
154C11⋊C8—42no—
155C11⋊C8—42no—
156C2×C4⋊Q8—221no—
157C2×#106—21no—
158C2×#106—221no—
159C2×#106—221no—
160C2×#103—221no—
161#398—221no—
162#395—221no—
163#395—221no—
164#391—111no—
165#389—111no—
166#389C2×D1111yescharacteristic
167#387—221no—
168#387—221no—
169#384C2×D1111yescharacteristic
170#340—21no—
171#340—221no—
172#336—111no—
173#336—111no—
174#336C2×D1111yescharacteristic
175C22×C11#44811yescharacteristic
176C22×C11#44811yescharacteristic
177C22×C11#45011yescharacteristic
178C22×C11#45311yescharacteristic
179C22×C11#45611yescharacteristic
180C22×C11#45611yescharacteristic
181C22×C11#45811yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—42no—
189C4×C11—81no—
190C4×C11—161no—
191Dic11—42no—
192Dic11—42no—
193Dic11—81no—
194Dic11—81no—
195C22×Q8—111no—
196C22×Q8—221no—
197C22×C8—21no—
198C22×C8—221no—
199C22×C8—221no—
200C4⋊Q8—442no—
201C4⋊Q8—442no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C42—221no—
216C2×C42C22×D1111yescharacteristic
217#106—42no—
218#106—442no—
219#106—442no—
220#103—442no—
221#95—21no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228C2×C11#161111yescharacteristic
229C2×C11#161111yescharacteristic
230C2×C11#161311yescharacteristic
231C2×C11#162311yescharacteristic
232C2×C11#165111yescharacteristic
233C2×C11#165111yescharacteristic
234C2×C11#166011yescharacteristic
235C2×Q8—112no—
236C2×Q8—221no—
237C2×Q8—441no—
238C2×Q8—441no—
239C2×Q8—442no—
240C2×Q8—881no—
241C2×Q8—881no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251C22×C4C2×C22⋊D1111yescharacteristic
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—222no—
256C2×C8—222no—
257C2×C8—441no—
258C2×C8—441no—
259C2×C8—441no—
260C2×C8—441no—
261C4⋊C4—21no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—112no—
272C4⋊C4—221no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—881no—
280C4⋊C4#432412yes—
281C42—41no—
282C42—442no—
283C11#781711yescharacteristic, complemented, Sylow
284C23#6699011yescharacteristic
285Q8—442no—
286Q8—881no—
287Q8—884no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4SD16×D1111yescharacteristic
316C2×C4SD16×D1111yescharacteristic
317C2×C4#6696711yescharacteristic
318C2×C4#6696811yescharacteristic
319C2×C4C2×#432411yescharacteristic
320C2×C4#6700411yescharacteristic
321C8—42no—
322C8—442no—
323C8—442no—
324C22#1062265311yescharacteristic
325C22#1062266611yescharacteristic
326C22#1062270811yescharacteristic
327C22#1062278211yescharacteristic
328C22#1062278311yescharacteristic
329C22#1062281111yescharacteristic
330C22#1062281811yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—161no—
340C4—442no—
341C4—442no—
342C4—881no—
343C4—881no—
344C2#1306762211yescharacteristic
345C2#1306762311yescharacteristic
346C2#1306763411yescharacteristic
347C2#1306769311yescharacteristic
348C2#1306787611yescharacteristic
349C2#1306787711yescharacteristic
350C2#1306792611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2084C2
socle, prime radicalC23×C11#120
hypercenter#2084D11
hypocenterC11#7817
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
283. C11#7817semidirect

Maximal subgroups

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

subgroupindex
#130756472
#130701602
#130700932
#130664412
#130664392
#130664382
C11×#20842
#781711