Finite Group Databasebeta

← #14651259

Subgroups — #14651259

Order 2816.

442 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079350C211yesmaximal, characteristic
2#13077686C211yesmaximal, characteristic, complemented
3#13067251C211yesmaximal, characteristic, complemented
4#13067162C211yesmaximal, characteristic, complemented
5#13066489C211yesmaximal, characteristic, complemented
6#13066480C211yesmaximal, characteristic, complemented
7C11×#1514C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#383C2211yescharacteristic
12#10622701C411yescharacteristic, complemented
13#10622692C411yescharacteristic, complemented
14#10622686C411yescharacteristic, complemented
15#10622683C411yescharacteristic, complemented
16#10622652—22no—
17#10622627—22no—
18#10622539C2211yescharacteristic
19#10622539C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21#10622449—22no—
22#10622340—22no—
23#10622319—22no—
24C11×#327—22no—
25#10622178—22no—
26#10622089—22no—
27C2×C11×#41—21no—
28C2×#4339—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×#127C2×C411yescharacteristic
31C11×#124—21no—
32C11×#121—21no—
33C11×#121—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×#4323—22no—
38#66983—21no—
39#66983D412yes—
40C2×#4318—21no—
41C2×#4313—22no—
42C2×C8×D11—22no—
43#66928—21no—
44#66927C2×C411yescharacteristic
45C4×D44—21no—
46C4×D44D412yes—
47#66922C2×C411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C22⋊C8D412yes—
50C11×#97—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54#66896—22no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57(C2×D11)⋊C8—24no—
58#66873—22no—
59#66872—22no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62#66867—21no—
63#66867—21no—
64#66867D412yes—
65C4×C11⋊C8C2×C411yescharacteristic
66C4×C11⋊C8C2×C411yescharacteristic
67#9417—111nomaximal, Sylow
68C11×#41—82no—
69C2×Q8×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—22no—
80#4339—81no—
81#4339—81no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44C22⋊C412yes—
85C2×C4×D11—22no—
86C2×Dic22—21no—
87C2×C8×C11—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C42×C11C22×C411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96#4323—44no—
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—22no—
99C4⋊Dic11—21no—
100C4⋊Dic11C22⋊C412yes—
101#4318—42no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106#4313—82no—
107C8×D11—82no—
108#3184—111no—
109#2980—111no—
110#1536—111no—
111#1514—111no—
112#1514D1111yescharacteristic, complemented
113#1291—111no—
114#1288—111no—
115C23×C11—41no—
116C23×C11#12111yescharacteristic
117C22×D11—22no—
118Q8×C11—81no—
119D4×C11—42no—
120D4×C11—81no—
121D4×C11—81no—
122D4×C11—82no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—82no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11C2×C22⋊C411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C22⋊D11—82no—
138C2×Dic11—22no—
139D44—42no—
140D44—81no—
141D44—81no—
142C4×D11—42no—
143C4×D11—42no—
144Dic22—81no—
145C8×C11—42no—
146C11⋊C8—22no—
147C11⋊C8—42no—
148C11⋊C8—41no—
149C11⋊C8—81no—
150#532—111no—
151#532C2×D1111yescharacteristic
152#498—111no—
153#493—111no—
154#486—111no—
155#486—111no—
156#469—222no—
157#442—222no—
158#435—222no—
159#435—222no—
160#432—111no—
161#432—111no—
162#432C2×D1111yescharacteristic
163#408—222no—
164C4×M16—111no—
165#383C2×D1111yescharacteristic
166#329—222no—
167#327—22no—
168#327—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11#38611yescharacteristic
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—42no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11—161no—
187Dic11—42no—
188C2×#41—21no—
189C2×#41—221no—
190C2×D8—222no—
191C2×M16—222no—
192C2×M16—221no—
193C22×C8—222no—
194C4⋊Q8—111no—
195C4⋊Q8C4×D1111yescharacteristic
196#127—111no—
197#127C4×D1111yescharacteristic
198#124—21no—
199#124—221no—
200#121—21no—
201#121—21no—
202#121—112no—
203#121—221no—
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—112no—
207C4×D4—221no—
208C2×C42C22×D1111yescharacteristic
209#106—222no—
210C4⋊C8—21no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213#102—222no—
214#102—222no—
215C22⋊C8—224no—
216C22⋊C8—221no—
217C22⋊C8—221no—
218C22⋊C8C22⋊D1112yes—
219#97—21no—
220#97—112no—
221#97—221no—
222#97—221no—
223C4×C8—111no—
224C4×C8—111no—
225#95—21no—
226#95—21no—
227#95—21no—
228C2×C11—41no—
229C2×C11—161no—
230C2×C11#188411yescharacteristic
231C2×C11#190311yescharacteristic
232C2×C11#190411yescharacteristic
233D11—82no—
234#41—82no—
235#41—881no—
236#41—881no—
237C2×Q8—21no—
238C2×Q8—221no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—41no—
243C2×D4—112no—
244C2×D4—222no—
245C2×D4—221no—
246C2×D4—221no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—222no—
250C22×C4D4×D1111yescharacteristic
251C22×C4#434111yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253D8—444no—
254M16—442no—
255M16—882no—
256C2×C8—22no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—222no—
260C2×C8—441no—
261C2×C8—882no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—112no—
265C4⋊C4—221no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—222no—
269C22⋊C4—222no—
270C42C2×C4×D1111yescharacteristic
271C42#433911yescharacteristic
272C42D4×D1111yescharacteristic
273C42D4×D1111yescharacteristic
274C11#941711yescharacteristic, complemented, Sylow
275C23—41no—
276C23—222no—
277C23#6699111yescharacteristic
278Q8—81no—
279Q8—881no—
280D4—42no—
281D4—81no—
282D4—81no—
283D4—82no—
284D4—442no—
285D4—881no—
286D4—881no—
287D4—882no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—82no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—222no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4C22⋊C4×D1111yescharacteristic
300C2×C4(C22⋊D11)⋊C411yescharacteristic
301C2×C4#6693611yescharacteristic
302C2×C4#6693711yescharacteristic
303C2×C4C4×C22⋊D1111yescharacteristic
304C2×C4#6699011yescharacteristic
305C8—42no—
306C8—222no—
307C8—442no—
308C8—441no—
309C8—881no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—442no—
317C22—442no—
318C22—442no—
319C22#1062256911yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—81no—
327C4—161no—
328C4—442no—
329C2—41no—
330C2—161no—
331C2—882no—
332C2#1306899611yescharacteristic
333C2#1306909311yescharacteristic
334C2#1306910611yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1514C2
socleC22×C11#386
prime radical#13079350C2
cosocleC2×C42×C11C23
hypercenter#1514D11
hypocenterC11#9417
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1514

Complements

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

NH ≅ G/Ntype
2. #13077686C2semidirect
3. #13067251C2semidirect
4. #13067162C2semidirect
5. #13066489C2semidirect
6. #13066480C2semidirect
7. C11×#1514C2semidirect
12. #10622701C4semidirect
13. #10622692C4semidirect
14. #10622686C4semidirect
15. #10622683C4semidirect
112. #1514D11semidirect
274. C11#9417semidirect

Maximal subgroups

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

subgroupindex
#130793502
#130776862
#130672512
#130671622
#130664892
#130664802
C11×#15142
#941711