Finite Group Databasebeta

← #14664841

Subgroups — #14664841

Order 2816.

422 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
2#13068641C211yesmaximal, characteristic, complemented
3#13066628C212yesmaximal, complemented
4#13066625C212yesmaximal, complemented
5C11×#3050C211yesmaximal, characteristic
6C2×C11×#135C411yescharacteristic, complemented
7C23×C8×C11C2211yescharacteristic
8C11×#525—21no—
9C11×#467C411yescharacteristic, complemented
10C11×#467C2211yescharacteristic
11C11×#466C411yescharacteristic, complemented
12C11×#466C2211yescharacteristic
13C11×#465—21no—
14C11×#465—21no—
15C11×#427C411yescharacteristic, complemented
16C11×#416—21no—
17#10622825—21no—
18C2×#66881—21no—
19C22×C11⋊C16—21no—
20#10622189C2212yes—
21C22⋊(C11⋊C16)—21no—
22C22⋊(C11⋊C16)C2212yes—
23C2×C11×#41—21no—
24C23×C4×C11D411yescharacteristic
25C11×#135—42no—
26C2×C11×Q16C2×C411yescharacteristic
27C2×C11×SD16—21no—
28C2×C11×D8C2×C411yescharacteristic
29C22×C8×C11—42no—
30C22×C8×C11C2×C411yescharacteristic
31C22×C8×C11C2×C411yescharacteristic
32C22×C8×C11D411yescharacteristic
33C22×C8×C11D411yescharacteristic
34C22×C8×C11D411yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C11×#123—41no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×#121—21no—
40C11×#121—21no—
41C11×#120—41no—
42C4×D4×C11—41no—
43C4×D4×C11—41no—
44C11×#117—21no—
45C2×C22⋊Dic11—41no—
46C2×C4⋊Dic11—22no—
47C11×#107C2×C411yescharacteristic
48C11×#107C2×C411yescharacteristic
49C11×#106—21no—
50C11×#103—21no—
51C11×#103—21no—
52C11×#102—21no—
53C11×#102—21no—
54C11⋊#95—41no—
55#66881—42no—
56C2×C11⋊C16—22no—
57C2×C11⋊C16—42no—
58#11885—111nomaximal, Sylow
59C24×C11D811yescharacteristic
60C11×#41—42no—
61C11×#41—42no—
62C2×Q8×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11D811yescharacteristic
73C22×C4×C11SD1611yescharacteristic
74C22×C4×C11SD1611yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—42no—
77C11×Q16—41no—
78C11×SD16—42no—
79C11×D8—41no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11C22⋊C411yescharacteristic
87C2×C8×C11C22⋊C411yescharacteristic
88C2×C8×C11C22×C411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11—41no—
100C22⋊Dic11—82no—
101C4⋊Dic11—42no—
102C4⋊Dic11—42no—
103C11⋊C16—42no—
104#3050D1111yescharacteristic
105C2×C22⋊C16—111no—
106#1807—111no—
107#1348—112no—
108#1347—112no—
109C23×C11—22no—
110C23×C11—22no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11#10211yescharacteristic
114C23×C11#10211yescharacteristic
115C23×C11C2×D811yescharacteristic
116Q8×C11—41no—
117Q8×C11—41no—
118D4×C11—41no—
119D4×C11—41no—
120D4×C11—82no—
121D4×C11—82no—
122D4×C11—82no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
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—82no—
136C2×C4×C11#10211yescharacteristic
137C2×C4×C11#10211yescharacteristic
138C2×C4×C11C2×C22⋊C411yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×Dic11—82no—
141C2×Dic11—82no—
142C2×Dic11—82no—
143C8×C11—21no—
144C8×C11—21no—
145C8×C11—21no—
146C8×C11#9912yes—
147C2×#135Dic1111yescharacteristic, complemented
148C23×C8C2×D1111yescharacteristic
149#525—21no—
150C22×C16—221no—
151#467Dic1111yescharacteristic, complemented
152#467C2×D1111yescharacteristic
153#466Dic1111yescharacteristic, complemented
154#466C2×D1111yescharacteristic
155#465—21no—
156#465—21no—
157#427Dic1111yescharacteristic, complemented
158C2×#106—221no—
159#416—21no—
160#380—221no—
161C22⋊C16—112no—
162C22⋊C16—221no—
163#340—112no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—44no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11#36012yes—
176C22×C11C2×#10211yescharacteristic
177C22×C11#50812yes—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—81no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11C2×#9911yescharacteristic
185C4×C11#42111yescharacteristic
186Dic11—162no—
187C2×#41—21no—
188C23×C4C22⋊D1111yescharacteristic
189#135—42no—
190C2×Q16C2×Dic1111yescharacteristic
191C2×SD16—21no—
192C2×D8C2×Dic1111yescharacteristic
193C22×C8—42no—
194C22×C8C2×Dic1111yescharacteristic
195C22×C8C2×Dic1111yescharacteristic
196C22×C8C22⋊D1111yescharacteristic
197C22×C8C22⋊D1111yescharacteristic
198C22×C8C22⋊D1111yescharacteristic
199C22×C8C22×D1111yescharacteristic
200#123—41no—
201C22⋊Q8—21no—
202C22⋊Q8—21no—
203#121—21no—
204#121—21no—
205#120—41no—
206C4×D4—41no—
207C4×D4—41no—
208#117—21no—
209C2×C4⋊C4—222no—
210C2×C22⋊C4—441no—
211C2×C16—222no—
212C2×C16—442no—
213#107C2×Dic1111yescharacteristic
214#107C2×Dic1111yescharacteristic
215#106—21no—
216#106—442no—
217#103—21no—
218#103—21no—
219#102—21no—
220#102—21no—
221#95—441no—
222C2×C11—22no—
223C2×C11—22no—
224C2×C11—41no—
225C2×C11—161no—
226C2×C11#151911yescharacteristic
227C2×C11#213811yescharacteristic
228C2×C11C2×#36011yescharacteristic
229C24#432311yescharacteristic
230#41—42no—
231#41—42no—
232C2×Q8—21no—
233C2×D4—21no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—442no—
241C22×C4#432311yescharacteristic
242C22×C4#432411yescharacteristic
243C22×C4#432411yescharacteristic
244C22×C4C22⋊Dic1111yescharacteristic
245C22×C4C22⋊Dic1111yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247Q16—41no—
248SD16—42no—
249D8—41no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8C22⋊Dic1111yescharacteristic
257C2×C8C22⋊Dic1111yescharacteristic
258C2×C8C22×Dic1111yescharacteristic
259C2×C8C2×C22⋊D1111yescharacteristic
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—882no—
272C42—41no—
273C16—442no—
274C11#1188511yescharacteristic, complemented, Sylow
275C23—22no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23#6689611yescharacteristic
280C23#6689611yescharacteristic
281C23C2×#432311yescharacteristic
282Q8—41no—
283Q8—41no—
284D4—41no—
285D4—41no—
286D4—82no—
287D4—82no—
288D4—82no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—882no—
303C2×C4—882no—
304C2×C4—882no—
305C2×C4#6689611yescharacteristic
306C2×C4#6689611yescharacteristic
307C2×C4C2×#432411yescharacteristic
308C2×C4C2×C22⋊Dic1111yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8#6689812yes—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—44no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#1062220412yes—
325C22#1062280712yes—
326C22C2×#6689611yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—1762no—
334C4C2×#6689811yescharacteristic
335C4#1062284911yescharacteristic
336C2—22no—
337C2—22no—
338C2—41no—
339C2—161no—
340C2#1306718411yescharacteristic
341C2#1307032311yescharacteristic
342C2C2×#1062220411yescharacteristic
subgroupG/H
centerC22C2×#66896
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
Fitting, prime radicalC11×#3050C2
socleC22×C11C2×#102
cosocleC22×C8×C11C23
hypercenter#3050D11
hypocenterC11#11885
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊(C11⋊C16)C2semidirect
2. #13068641C2semidirect
3. #13066628C2semidirect
4. #13066625C2semidirect
6. C2×C11×#135C4semidirect
9. C11×#467C4semidirect
11. C11×#466C4semidirect
15. C11×#427C4semidirect
147. C2×#135Dic11semidirect
151. #467Dic11semidirect
153. #466Dic11semidirect
157. #427Dic11semidirect
274. C11#11885semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊(C11⋊C16)2
#130686412
#130666282
#130666252
C11×#30502
#1188511