Finite Group Databasebeta

← #14642936

Subgroups — #14642936

Order 2816.

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

normal subgroups only

This group has 366 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#13076569C211yesmaximal, characteristic
2#13070160C211yesmaximal, characteristic
3#13070093C211yesmaximal, characteristic
4#13066441C211yesmaximal, characteristic
5#13066439C211yesmaximal, characteristic
6#13066438C211yesmaximal, characteristic
7C11×#2083C211yesmaximal, characteristic
8C2×C11×#107—21no—
9C11×#389C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622599—21no—
12#10622599—21no—
13#10622598—21no—
14#10622594—21no—
15C2×#66874—21no—
16C2×#66872—21no—
17C2×#66872—21no—
18#10622542C2211yescharacteristic
19#10622541C2211yescharacteristic
20#10622269—21no—
21#10622268—21no—
22C11×#340—21no—
23C11×#336C2211yescharacteristic
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Dic22D411yescharacteristic
28C22×C8×C11—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44C22×C11⋊C8—21no—
45C11×#107—42no—
46C11×#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66874—42no—
56#66872—42no—
57#66872—42no—
58#7807—111nomaximal, Sylow
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C2×Dic22—21no—
70C2×Dic22—21no—
71C2×Dic22—41no—
72C2×Dic22—41no—
73C2×C8×C11—22no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4SD1612yes—
87C42×C11—41no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—81no—
93C4⋊Dic11—81no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96C4×Dic11—81no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103#2805—111no—
104#2096—111no—
105#2084—111no—
106#2083D1111yescharacteristic
107#1272—111no—
108#1271—111no—
109#1271—111no—
110C23×C11#12011yescharacteristic
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144Dic22—42no—
145Dic22—81no—
146C8×C11—42no—
147C11⋊C8—42no—
148C11⋊C8—42no—
149C2×#107—21no—
150C2×#106—221no—
151C2×#106—221no—
152C2×#103—221no—
153#400—221no—
154#400—221no—
155#395—221no—
156#391—111no—
157#389—111no—
158#389—221no—
159#389C2×D1111yescharacteristic
160#387—221no—
161#387—221no—
162#384C2×D1111yescharacteristic
163#340—21no—
164#340—221no—
165#336—111no—
166#336—111no—
167#336C2×D1111yescharacteristic
168C22×C11#44811yescharacteristic
169C22×C11#44911yescharacteristic
170C22×C11#45211yescharacteristic
171C22×C11#45311yescharacteristic
172C22×C11#45611yescharacteristic
173C22×C11#45611yescharacteristic
174C22×C11#45811yescharacteristic
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—81no—
183C4×C11—161no—
184Dic11—81no—
185Dic11—81no—
186Dic11—81no—
187Dic11—81no—
188C22×Q8—111no—
189C22×C8—21no—
190C22×C8—221no—
191C22×C8—221no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4C22⋊D1111yescharacteristic
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C42—221no—
205C2×C42C22×D1111yescharacteristic
206#107—42no—
207#106—442no—
208#106—442no—
209#103—442no—
210#95—21no—
211#95—221no—
212#95—221no—
213#95—221no—
214#95—221no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219C2×C11#160911yescharacteristic
220C2×C11#161111yescharacteristic
221C2×C11#161811yescharacteristic
222C2×C11#162211yescharacteristic
223C2×C11#165011yescharacteristic
224C2×C11#165311yescharacteristic
225C2×C11#166011yescharacteristic
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8—441no—
229C2×Q8—441no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4D4×D1111yescharacteristic
238C22×C4D4×D1111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—222no—
244C2×C8—222no—
245C2×C8—441no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—881no—
266C4⋊C4—881no—
267C4⋊C4#432412yes—
268C42—41no—
269C42—881no—
270C11#780711yescharacteristic, complemented, Sylow
271C23#6699011yescharacteristic
272Q8—442no—
273Q8—881no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4#6696411yescharacteristic
302C2×C4#6696511yescharacteristic
303C2×C4#6697111yescharacteristic
304C2×C4#6697211yescharacteristic
305C2×C4C2×#432411yescharacteristic
306C2×C4#6700411yescharacteristic
307C8—42no—
308C8—442no—
309C8—442no—
310C22#1062265311yescharacteristic
311C22#1062266611yescharacteristic
312C22#1062270811yescharacteristic
313C22#1062277111yescharacteristic
314C22#1062280011yescharacteristic
315C22#1062281111yescharacteristic
316C22#1062281811yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—81no—
325C4—161no—
326C4—881no—
327C4—881no—
328C4—881no—
329C4—881no—
330C2#1306761011yescharacteristic
331C2#1306762311yescharacteristic
332C2#1306766311yescharacteristic
333C2#1306768611yescharacteristic
334C2#1306786911yescharacteristic
335C2#1306789111yescharacteristic
336C2#1306792611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2083C2
socle, prime radicalC23×C11#120
hypercenter#2083D11
hypocenterC11#7807
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
270. C11#7807semidirect

Maximal subgroups

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

subgroupindex
#130765692
#130701602
#130700932
#130664412
#130664392
#130664382
C11×#20832
#780711