Finite Group Databasebeta

← #14651264

Subgroups — #14651264

Order 2816.

442 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 99 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#13077687C211yesmaximal, characteristic, complemented
2#13067251C211yesmaximal, characteristic, complemented
3#13067163C211yesmaximal, characteristic, complemented
4#13067163C211yesmaximal, characteristic, complemented
5#13066488C211yesmaximal, characteristic, complemented
6#13066481C211yesmaximal, characteristic, complemented
7C11×#3184C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C11×#498C411yescharacteristic, complemented
11C11×#493C411yescharacteristic, complemented
12C11×#486C411yescharacteristic, complemented
13C11×#486C411yescharacteristic, complemented
14C11×#469—22no—
15C11×#442—22no—
16C4×C11×M16C2211yescharacteristic
17#10622847—22no—
18#10622624—22no—
19#10622624—22no—
20#10622550C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23#10622539C2211yescharacteristic
24#10622178—22no—
25#10622175—22no—
26#10622175—22no—
27C2×C11×#41—21no—
28C2×C11×#41—21no—
29C2×C11×D8—22no—
30C2×C11×M16—21no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#127C2×C411yescharacteristic
34C11×#127C2×C411yescharacteristic
35C11×#124—21no—
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—21no—
40C11×#121D412yes—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×#4318—22no—
47C22×C11⋊C8—22no—
48C11×#106—22no—
49C11×#102—22no—
50C11×#102—22no—
51C11×#97—21no—
52C4×C8×C11C2×C411yescharacteristic
53C4×C8×C11C2×C411yescharacteristic
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C22⋊(C11⋊C8)—24no—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)D412yes—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64#66867—21no—
65#66867—21no—
66#66867D412yes—
67#9417—111nomaximal, Sylow
68C11×#41—81no—
69C11×#41—81no—
70C11×#41—82no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×D4×C11—22no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C2×D4×C11C22⋊C412yes—
81C22×C4×C11—22no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—41no—
87C11×D8—44no—
88C11×M16—42no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4C22⋊C412yes—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11C22×C411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103#4318—82no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—82no—
108#3184D1111yescharacteristic
109#2980—111no—
110#1536—111no—
111#1514—111no—
112#1514—111no—
113#1291—111no—
114#1288—111no—
115C23×C11—22no—
116C23×C11—41no—
117C23×C11#12111yescharacteristic
118Q8×C11—81no—
119Q8×C11—81no—
120D4×C11—42no—
121D4×C11—42no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11—81no—
125D4×C11—81no—
126D4×C11—82no—
127D4×C11—82no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—41no—
135C2×C4×C11—82no—
136C2×C4×C11C2×C22⋊C411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×Dic11—81no—
143C2×Dic11—81no—
144C2×Dic11—81no—
145C8×C11—22no—
146C8×C11—41no—
147C11⋊C8—42no—
148C11⋊C8—42no—
149C11⋊C8—81no—
150#532C2×D1111yescharacteristic
151#532C2×D1111yescharacteristic
152#498Dic1111yescharacteristic, complemented
153#493Dic1111yescharacteristic, complemented
154#486Dic1111yescharacteristic, complemented
155#486Dic1111yescharacteristic, complemented
156#469—22no—
157#442—22no—
158#435—222no—
159#435—222no—
160#432—111no—
161#432—111no—
162#432—111no—
163#408—222no—
164C4×M16C2×D1111yescharacteristic
165#383—111no—
166#329—222no—
167#327—222no—
168#327—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—42no—
175C22×C11—81no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11#38611yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—81no—
187Dic11—161no—
188C2×#41—21no—
189C2×#41—21no—
190C2×D8—22no—
191C2×M16—21no—
192C2×M16—222no—
193C22×C8—222no—
194C4⋊Q8C2×Dic1111yescharacteristic
195C4⋊Q8C2×Dic1111yescharacteristic
196#127C2×Dic1111yescharacteristic
197#127C2×Dic1111yescharacteristic
198#124—21no—
199#124—21no—
200#121—21no—
201#121—21no—
202#121—21no—
203#121C22⋊D1112yes—
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—21no—
207C4×D4C22⋊D1112yes—
208C2×C42C22×D1111yescharacteristic
209#106—22no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213#102—22no—
214#102—22no—
215C22⋊C8—112no—
216C22⋊C8—224no—
217C22⋊C8—221no—
218C22⋊C8—221no—
219#97—21no—
220#97—112no—
221#97—221no—
222#97—221no—
223C4×C8C2×Dic1111yescharacteristic
224C4×C8C2×Dic1111yescharacteristic
225#95—221no—
226#95—221no—
227#95—221no—
228C2×C11—41no—
229C2×C11—82no—
230C2×C11—161no—
231C2×C11#188411yescharacteristic
232C2×C11#190311yescharacteristic
233C2×C11#190411yescharacteristic
234#41—81no—
235#41—81no—
236#41—82no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—41no—
246C2×D4C22⋊Dic1112yes—
247C22×C4—22no—
248C22×C4—41no—
249C22×C4—441no—
250C22×C4D4×D1111yescharacteristic
251C22×C4#434111yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253D8—44no—
254M16—42no—
255M16—882no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—222no—
259C2×C8—222no—
260C2×C8—441no—
261C2×C8—882no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4C22⋊Dic1112yes—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C42D4×D1111yescharacteristic
271C42#434111yescharacteristic
272C42C22×Dic1111yescharacteristic
273C42C2×C22⋊D1111yescharacteristic
274C11#941711yescharacteristic, complemented, Sylow
275C23—22no—
276C23—41no—
277C23#6699211yescharacteristic
278Q8—81no—
279Q8—81no—
280D4—42no—
281D4—42no—
282D4—81no—
283D4—81no—
284D4—81no—
285D4—81no—
286D4—82no—
287D4—82no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—82no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4D4×Dic1111yescharacteristic
300C2×C4D4×Dic1111yescharacteristic
301C2×C4#6698811yescharacteristic
302C2×C4#6699011yescharacteristic
303C2×C4#6699211yescharacteristic
304C2×C4C2×C22⋊Dic1111yescharacteristic
305C8—22no—
306C8—41no—
307C8—442no—
308C8—442no—
309C8—881no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1062283311yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—81no—
328C4—1761no—
329C2—41no—
330C2—82no—
331C2—161no—
332C2#1306900011yescharacteristic
333C2#1306909811yescharacteristic
334C2#1306910511yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3184C2
socleC22×C11#386
cosocleC2×C42×C11C23
hypercenter#3184D11
hypocenterC11#9417
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3184

Complements

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

NH ≅ G/Ntype
1. #13077687C2semidirect
2. #13067251C2semidirect
3. #13067163C2semidirect
4. #13067163C2semidirect
5. #13066488C2semidirect
6. #13066481C2semidirect
10. C11×#498C4semidirect
11. C11×#493C4semidirect
12. C11×#486C4semidirect
13. C11×#486C4semidirect
152. #498Dic11semidirect
153. #493Dic11semidirect
154. #486Dic11semidirect
155. #486Dic11semidirect
274. C11#9417semidirect

Maximal subgroups

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

subgroupindex
#130776872
#130672512
#130671632
#130664882
#130664812
C11×#31842
#941711