Finite Group Databasebeta

← #14758694

Subgroups — #14758694

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622613C211yesmaximal, characteristic
2#13071225C211yesmaximal, characteristic
3#13069384C212yesmaximal, complemented
4#13069374C212yesmaximal, complemented
5#13068815C212yesmaximal
6#13068804C212yesmaximal
7#13068514C212yesmaximal, complemented
8C4×#66871C212yesmaximal, complemented
9C11×#2274C211yesmaximal, characteristic
10C2×C11×#117C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C4×C11×C4⋊C4—22no—
14C4×C11×C4⋊C4C2212yes—
15C4×C11×C4⋊C4C2212yes—
16C4×C11×C22⋊C4—22no—
17#10622825C2212yes—
18C2×C22⋊(C11⋊C8)C2212yes—
19#10622613C418yescomplemented
20#10622594—22no—
21C2×#66872C2212yes—
22C2×#66871C2212yes—
23C2×#66871C2212yes—
24C2×#66871C2212yes—
25#10622564—22no—
26#10622549C2211yescharacteristic
27#10622548C2211yescharacteristic
28C4×C4⋊Dic11C2212yes—
29C2×C4⋊(C11⋊C8)C2212yes—
30C2×#66867C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32#10622167C2212yes—
33#10622167C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36C23×C4×C11—21no—
37C23×C4×C11C2311yescharacteristic
38C11×#117—24no—
39C11×#117C2×C414yes—
40C11×#117Q814yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—24no—
43C2×C11×C4⋊C4D412yes—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4D412yes—
48C2×C42×C11—21no—
49C2×C42×C11—22no—
50C2×C42×C11—22no—
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11C2312yes—
56C2×C4⋊Dic11C2312yes—
57C2×C4×Dic11—22no—
58C22×C11⋊C8C2312yes—
59C22×C11⋊C8C2312yes—
60C11×#95—22no—
61C11×#95—22no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C22⋊(C11⋊C8)C2×C418yes—
66#66872—24no—
67#66871—24no—
68#66871—24no—
69#66871—24no—
70C4⋊(C11⋊C8)C2×C418yescomplemented
71#66867C2×C414yescomplemented
72C4×C11⋊C8C2×C414yescomplemented
73#21368—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—82no—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×Q812yes—
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—22no—
88C22×Dic11—22no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4C4⋊C418yes—
93C11×C4⋊C4#4114yes—
94C11×C4⋊C4#4114yes—
95C11×C22⋊C4—24no—
96C11×C22⋊C4C4⋊C418yes—
97C42×C11—24no—
98C42×C11—82no—
99C42×C11—82no—
100C42×C11C22×C412yes—
101C42×C11C22×C412yes—
102C42×C11C2×Q812yes—
103C42×C11C2×Q812yes—
104C22⋊Dic11—82no—
105C4⋊Dic11—22no—
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—82no—
110C4×Dic11—82no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8C22×C414yes—
116C2×C11⋊C8C22×C414yes—
117C2×#433—111no—
118#2314—111no—
119#2274D1111yescharacteristic
120#1949—112no—
121#1947—112no—
122#1854—112no—
123#1852—112no—
124#1776—112no—
125C4×#107—112no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11C2×C4⋊C412yes—
131C23×C11C22×D411yescharacteristic
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—24no—
139C2×C4×C11—24no—
140C2×C4×C11—24no—
141C2×C4×C11—24no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—84no—
147C2×C4×C11C2×C4⋊C414yes—
148C2×C4×C11C2×C4⋊C414yes—
149C2×C4×C11C2×C4⋊C412yes—
150C2×C4×C11C23×C411yescharacteristic
151C2×C4×C11C22×Q811yescharacteristic
152C2×C4×C11C2×#4112yes—
153C2×C4×C11C2×#4112yes—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C11⋊C8—24no—
161C11⋊C8—24no—
162C2×#117C2×D1111yescharacteristic
163C2×#117C2×D1111yescharacteristic
164C22×C4⋊C4C2×D1111yescharacteristic
165#433—118no—
166C2×#107—112no—
167C2×#107—112no—
168C2×#107—112no—
169C2×#106—112no—
170C2×C4⋊C8—112no—
171C2×C22⋊C8—112no—
172C2×#97—111no—
173C2×C4×C8—111no—
174#388—222no—
175#387—222no—
176#384—111no—
177#382—111no—
178#380—112no—
179C4×C4⋊C4—22no—
180C4×C4⋊C4—112no—
181C4×C4⋊C4C2×D1112yes—
182C4×C4⋊C4C2×D1112yes—
183C4×C22⋊C4—22no—
184#340—112no—
185#340—112no—
186#340—112no—
187#340—112no—
188C22×C11—24no—
189C22×C11—22no—
190C22×C11—41no—
191C22×C11—42no—
192C22×C11—41no—
193C22×C11C22×C4⋊C411yescharacteristic
194C22×C11#52511yescharacteristic
195C22×C11#52511yescharacteristic
196C22×C11#57612yes—
197C22×C11#57812yes—
198C4×C11—24no—
199C4×C11—24no—
200C4×C11—22no—
201C4×C11—44no—
202C4×C11—44no—
203C4×C11C4×#4112yes—
204C4×C11#53312yes—
205Dic11—82no—
206Dic11—82no—
207C23×C4—21no—
208C23×C4C22×D1111yescharacteristic
209C22×C8—112no—
210C22×C8—112no—
211#117—24no—
212#117Dic2214yes—
213#117C4×D1114yes—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—112no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4C22⋊D1112yes—
220C2×C4⋊C4C22×D1112yes—
221C2×C4⋊C4C22×D1112yes—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—222no—
224C2×C22⋊C4C22⋊D1112yes—
225C2×C42—21no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—222no—
229C2×C42C22×D1111yescharacteristic
230C2×C42C22×D1111yescharacteristic
231#107—224no—
232#107—224no—
233#107—224no—
234#106—224no—
235C4⋊C8—118no—
236C22⋊C8—118no—
237#97—114no—
238C4×C8—114no—
239#95—22no—
240#95—22no—
241#95—222no—
242#95—222no—
243#95—222no—
244C2×C11—42no—
245C2×C11#229611yescharacteristic
246C2×C11#291312yes—
247C2×C11#312211yescharacteristic
248C2×C11#312412yes—
249C2×C11#312711yescharacteristic
250C24C2×C22⋊D1111yescharacteristic
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—24no—
256C22×C4—82no—
257C22×C4—222no—
258C22×C4—222no—
259C22×C4C2×Dic2212yes—
260C22×C4C2×C4×D1112yes—
261C22×C4C2×C22⋊D1112yes—
262C22×C4C2×C22⋊D1112yes—
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C23×D1111yescharacteristic
265C2×C8—114no—
266C2×C8—114no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—222no—
270C2×C8—222no—
271C4⋊C4—24no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—222no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—222no—
278C4⋊C4—882no—
279C4⋊C4Dic11⋊C418yes—
280C4⋊C4#433914yes—
281C4⋊C4#433914yes—
282C22⋊C4—24no—
283C22⋊C4—882no—
284C22⋊C4Dic11⋊C418yes—
285C42—24no—
286C42—82no—
287C42—82no—
288C42—882no—
289C42C2×Dic2212yes—
290C42C2×Dic2212yes—
291C42C2×C4×D1112yes—
292C42C2×C4×D1112yes—
293C11#2136811yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—22no—
297C23—22no—
298C23C2×Dic11⋊C412yes—
299C23C22×C22⋊D1111yescharacteristic
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—84no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—442no—
321C2×C4C2×Dic11⋊C414yes—
322C2×C4C2×Dic11⋊C414yes—
323C2×C4C2×Dic11⋊C412yes—
324C2×C4C22×Dic2211yescharacteristic
325C2×C4C22×C4×D1111yescharacteristic
326C2×C4C2×#433912yes—
327C2×C4C2×#433912yes—
328C8—224no—
329C8—224no—
330C22—24no—
331C22—22no—
332C22—41no—
333C22—42no—
334C22—41no—
335C22C22×Dic11⋊C411yescharacteristic
336C22#1062332211yescharacteristic
337C22#1062332211yescharacteristic
338C22#1062336612yes—
339C22#1062336912yes—
340C4—24no—
341C4—24no—
342C4—22no—
343C4—44no—
344C4—44no—
345C4—882no—
346C4—882no—
347C4#1062300112yes—
348C4C4×#433912yes—
349C2—42no—
350C2#1307109911yescharacteristic
351C2#1307721412yes—
352C2#1307885911yescharacteristic
353C2#1307887812yes—
354C2#1307891611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2274C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2274D11
hypocenterC11#21368
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2274

Complements

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

NH ≅ G/Ntype
3. #13069384C2semidirect
4. #13069374C2semidirect
7. #13068514C2semidirect
8. C4×#66871C2semidirect
19. #10622613C4semidirect
70. C4⋊(C11⋊C8)C2×C4semidirect
71. #66867C2×C4semidirect
72. C4×C11⋊C8C2×C4semidirect
293. C11#21368semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
#130712252
#130693842
#130693742
#130688152
#130688042
#130685142
C4×#668712
C11×#22742
#2136811