Finite Group Databasebeta

← #14656860

Subgroups — #14656860

Order 2816.

454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 93 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#13076992C211yesmaximal, characteristic, complemented
2#13069443C211yesmaximal, characteristic
3#13067177C211yesmaximal, characteristic
4#13067175C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic, complemented
6#13066448C211yesmaximal, characteristic, complemented
7C11×#1286C211yesmaximal, characteristic, complemented
8C2×#66941—21no—
9#10623008C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×#66889—21no—
14C2×#66889—21no—
15#10622590—21no—
16#10622549C2211yescharacteristic
17C42×Dic11C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622259—22no—
20#10622259—22no—
21#10622108—22no—
22#10622089—22no—
23C2×#4339—21no—
24C22×Dic22—22no—
25C2×C11×M16—21no—
26C2×C11×C4⋊C4—21no—
27C2×C42×C11C2311yescharacteristic
28#66983—21no—
29#66983—21no—
30C2×C4⋊Dic11—21no—
31C2×Dic11⋊C4—22no—
32C2×C4×Dic11—21no—
33C2×C4×Dic11—21no—
34C2×C4×Dic11D411yescharacteristic
35C2×C4×Dic11D411yescharacteristic
36#66941—42no—
37#66941—42no—
38#66928—21no—
39#66927Q811yescharacteristic, complemented
40C4×D44—21no—
41C4×D44—21no—
42#66922Q811yescharacteristic, complemented
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C22⋊C8—21no—
47C4×C8×C11—21no—
48C11×#95—21no—
49C11×#95D412yes—
50C11⋊#95—24no—
51C11⋊#95—21no—
52C11⋊#95D412yes—
53C22⋊(C11⋊C8)—21no—
54#66889—42no—
55#66889—42no—
56C4⋊(C11⋊C8)—21no—
57C4×C11⋊C8—21no—
58#10362—111nomaximal, Sylow
59C22×C4×C11—22no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C2×C22⋊D11—41no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—22no—
67#4339—41no—
68#4339—41no—
69#4339—41no—
70#4339—41no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×C4×D11—41no—
75C2×Dic22—21no—
76C2×Dic22—44no—
77C2×Dic22—44no—
78C2×Dic22—44no—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C42×C11C2×Q811yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C42×C11#4111yescharacteristic
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—44no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—42no—
99C4×Dic11—42no—
100C4×Dic11D812yes—
101C4×Dic11SD1612yes—
102C2×C11⋊C8—41no—
103#2862—111no—
104#1962—111no—
105#1517—111no—
106#1517—111no—
107#1286—111no—
108#1286D1111yescharacteristic, complemented
109#1276—111no—
110C23×C11#12011yescharacteristic
111C22×D11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11C22⋊Q811yescharacteristic
118C2×C4×C11C22⋊Q811yescharacteristic
119C2×C4×C11C22⋊Q811yescharacteristic
120C2×C4×C11#12411yescharacteristic
121C2×C4×C11#12411yescharacteristic
122C2×C4×C11#12411yescharacteristic
123C2×C4×C11C2×D811yescharacteristic
124C2×C4×C11C2×SD1611yescharacteristic
125C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C22⋊D11—81no—
128C22⋊D11—81no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—41no—
138C2×Dic11—42no—
139D44—41no—
140D44—41no—
141D44—81no—
142D44—81no—
143C4×D11—81no—
144C4×D11—81no—
145Dic22—41no—
146Dic22—41no—
147Dic22—88no—
148C8×C11—81no—
149C8×C11—81no—
150C11⋊C8—81no—
151#532—111no—
152C2×C4⋊Q8—221no—
153#431—111no—
154#431C2×D1111yescharacteristic
155#423C2×D1111yescharacteristic
156C2×#104—221no—
157C2×#104—221no—
158#391—222no—
159#391—222no—
160#382—111no—
161#382—221no—
162#382C2×D1111yescharacteristic
163C43—111no—
164#327—222no—
165#327—222no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39311yescharacteristic
169C22×C11#44711yescharacteristic
170C22×C11#44811yescharacteristic
171C2×D11—81no—
172C2×D11—81no—
173C2×D11—81no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—82no—
179C4×C11#47411yescharacteristic
180C4×C11#47611yescharacteristic
181C4×C11#48611yescharacteristic
182C4×C11#48911yescharacteristic
183Dic11—24no—
184Dic11—42no—
185Dic11—82no—
186Dic11—81no—
187C2×#41—221no—
188C22×Q8—222no—
189C2×M16—21no—
190C4⋊Q8—111no—
191C4⋊Q8—442no—
192C4⋊Q8—442no—
193#127—111no—
194#124—221no—
195#121—221no—
196#121—221no—
197C4×D4—221no—
198C4×D4—221no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4—221no—
202C2×C42—111no—
203C2×C42—111no—
204C2×C42—221no—
205C2×C42—221no—
206C2×C42C22×D1111yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—221no—
211#104—442no—
212#104—442no—
213C22⋊C8—21no—
214C22⋊C8—221no—
215C4×C8—21no—
216C4×C8—221no—
217#95—21no—
218#95—112no—
219#95—224no—
220#95—221no—
221#95D4412yes—
222C2×C11—21no—
223C2×C11—21no—
224C2×C11#202311yescharacteristic
225C2×C11#203111yescharacteristic
226C2×C11#203111yescharacteristic
227D11—161no—
228#41—441no—
229#41—441no—
230#41—441no—
231#41—441no—
232C2×Q8—221no—
233C2×Q8—444no—
234C2×Q8—444no—
235C2×Q8—444no—
236C2×D4—221no—
237C2×D4—221no—
238C2×D4—221no—
239C2×D4—441no—
240C22×C4—22no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4—222no—
244C22×C4—441no—
245C22×C4C2×D4411yescharacteristic
246C22×C4D4×D1111yescharacteristic
247C22×C4D4×D1111yescharacteristic
248M16—41no—
249M16—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—441no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—444no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—441no—
261C22⋊C4—441no—
262C42—112no—
263C42—112no—
264C42—221no—
265C42—221no—
266C42—442no—
267C42—442no—
268C42#433911yescharacteristic
269C42#433911yescharacteristic
270C42#434111yescharacteristic
271C42Q8×D1111yescharacteristic
272C11#1036211yescharacteristic, complemented, Sylow
273C23—441no—
274C23#6693511yescharacteristic
275Q8—441no—
276Q8—441no—
277Q8—888no—
278D4—441no—
279D4—441no—
280D4—881no—
281D4—881no—
282D4—881no—
283D4—881no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—222no—
290C2×C4—222no—
291C2×C4—222no—
292C2×C4—222no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4—441no—
298C2×C4—442no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4#6692811yescharacteristic
302C2×C4#6693811yescharacteristic
303C2×C4#6693811yescharacteristic
304C2×C4#6694911yescharacteristic
305C2×C4#6694911yescharacteristic
306C2×C4#6695011yescharacteristic
307C2×C4D8×D1111yescharacteristic
308C2×C4SD16×D1111yescharacteristic
309C2×C4#6696711yescharacteristic
310C2×C4#6697111yescharacteristic
311C8—81no—
312C8—81no—
313C8—881no—
314C22—21no—
315C22—21no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22#1062228611yescharacteristic
320C22#1062238611yescharacteristic
321C22#1062241911yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—224no—
328C4—442no—
329C4—882no—
330C4—881no—
331C4#1062237311yescharacteristic
332C4#1062240811yescharacteristic
333C4#1062248311yescharacteristic
334C4#1062250311yescharacteristic
335C2—21no—
336C2—21no—
337C2—1761no—
338C2#1306975111yescharacteristic
339C2#1306978711yescharacteristic
340C2#1306979111yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#1286D11
hypocenterC11#10362
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
1. #13076992C2semidirect
5. #13066476C2semidirect
6. #13066448C2semidirect
7. C11×#1286C2semidirect
39. #66927Q8semidirect
42. #66922Q8semidirect
108. #1286D11semidirect
272. C11#10362semidirect

Maximal subgroups

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

subgroupindex
#130769922
#130694432
#130671772
#130671752
#130664762
#130664482
C11×#12862
#1036211