Finite Group Databasebeta

← #14666146

Subgroups — #14666146

Order 2816.

354 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 59 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#13069845C211yesmaximal, characteristic
2#13067652C211yesmaximal, characteristic
3#13067618C211yesmaximal, characteristic
4#13066643C211yesmaximal, characteristic, complemented
5#13066622C211yesmaximal, characteristic, complemented
6#13066560C211yesmaximal, characteristic, complemented
7C11×#2769C211yesmaximal, characteristic, complemented
8#10623041C2211yescharacteristic
9C11×#400—21no—
10C11×#400C2211yescharacteristic
11C11×#398—21no—
12C11×#398C2211yescharacteristic
13C11×#389—21no—
14C11×#387—21no—
15C11×#387—21no—
16C11×#383—21no—
17C11×#382C2211yescharacteristic
18#10622581—21no—
19#10622580—21no—
20#10622579—21no—
21C2×#66869—21no—
22#10622168C2211yescharacteristic
23#10622166C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622089—21no—
26#10622089—21no—
27C2×#4339—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11D411yescharacteristic
38#66983—21no—
39#66983—21no—
40C2×#4318—21no—
41#66950—41no—
42#66948—41no—
43C11×#95—21no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95D411yescharacteristic
53C11×#95D411yescharacteristic
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)—21no—
56#66874—41no—
57#66873—41no—
58#66873—41no—
59#66873—41no—
60#66872—41no—
61#66871—41no—
62#66869—42no—
63#12147—111nomaximal, Sylow
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—41no—
74#4339—41no—
75#4339—41no—
76#4339—41no—
77#4339—41no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×C4×D11—41no—
82C2×Dic22—21no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—81no—
92C42×C11—21no—
93C42×C11—21no—
94C42×C11—42no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99#4318—41no—
100#4318—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2769D1111yescharacteristic, complemented
105#2040—111no—
106#1616—111no—
107#1610—111no—
108#1353—111no—
109#1346—111no—
110#1324—111no—
111C23×C11#12011yescharacteristic
112C22×D11—41no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C22⋊D11—81no—
140C22⋊D11—81no—
141C2×Dic11—41no—
142D44—41no—
143D44—41no—
144D44—81no—
145D44—81no—
146C4×D11—81no—
147C4×D11—81no—
148Dic22—41no—
149Dic22—41no—
150C11⋊C8—81no—
151C11⋊C8—81no—
152C11⋊C8—81no—
153#537—111no—
154#481—221no—
155#480—221no—
156C2×#104—221no—
157#417—221no—
158#400—21no—
159#400C2×D1111yescharacteristic
160#398—21no—
161#398C2×D1111yescharacteristic
162#389—21no—
163#387—21no—
164#387—21no—
165#383—21no—
166#382C2×D1111yescharacteristic
167#343—111no—
168#327—221no—
169#327—221no—
170#324—111no—
171#324—111no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#44911yescharacteristic
175C22×C11#45411yescharacteristic
176C22×C11B(4,𝔽2)11yescharacteristic
177C2×D11—81no—
178C2×D11—81no—
179C2×D11—81no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—81no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11—81no—
190Dic11—81no—
191C2×#41—221no—
192C2×M16—221no—
193C22⋊Q8—441no—
194#121—221no—
195#121—221no—
196#121—441no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C22⋊D1111yescharacteristic
202C2×C4⋊C4C22⋊D1111yescharacteristic
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C4⋊C4C22×D1111yescharacteristic
205C2×C42—21no—
206C2×C42C22⋊D1111yescharacteristic
207#107—441no—
208#106—441no—
209#104—442no—
210#103—441no—
211#102—441no—
212#102—441no—
213#102—441no—
214C22⋊C8—221no—
215C22⋊C8—221no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C22⋊D1111yescharacteristic
226#95C22⋊D1111yescharacteristic
227C2×C11—21no—
228C2×C11—21no—
229C2×C11#159711yescharacteristic
230C2×C11#220111yescharacteristic
231C2×C11#220411yescharacteristic
232D11—161no—
233#41—441no—
234#41—441no—
235#41—441no—
236#41—441no—
237C2×Q8—221no—
238C2×D4—221no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—441no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—441no—
249C22×C4C2×C22⋊D1111yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251C22×C4C2×C22⋊D1111yescharacteristic
252M16—441no—
253M16—441no—
254C2×C8—441no—
255C2×C8—441no—
256C2×C8—441no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C22⋊C4—441no—
269C22⋊C4—441no—
270C42—21no—
271C42—21no—
272C42—42no—
273C11#1214711yescharacteristic, complemented, Sylow
274C23—441no—
275C23#6700611yescharacteristic
276Q8—441no—
277Q8—441no—
278D4—441no—
279D4—441no—
280D4—881no—
281D4—881no—
282D4—881no—
283D4—881no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—441no—
309C2×C4—881no—
310C2×C4—881no—
311C2×C4#6700211yescharacteristic
312C2×C4#6700311yescharacteristic
313C8—881no—
314C8—881no—
315C8—881no—
316C22—21no—
317C22—21no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22#1062285111yescharacteristic
322C22#1062285711yescharacteristic
323C22#1062285811yescharacteristic
324C4—21no—
325C4—21no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—81no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—881no—
335C2—21no—
336C2—21no—
337C2—1761no—
338C2#1306754511yescharacteristic
339C2#1307062911yescharacteristic
340C2#1307064211yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2769C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#2769D11
hypocenterC11#12147
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2769

Complements

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

NH ≅ G/Ntype
4. #13066643C2semidirect
5. #13066622C2semidirect
6. #13066560C2semidirect
7. C11×#2769C2semidirect
104. #2769D11semidirect
273. C11#12147semidirect

Maximal subgroups

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

subgroupindex
#130698452
#130676522
#130676182
#130666432
#130666222
#130665602
C11×#27692
#1214711