Finite Group Databasebeta

← #14754359

Subgroups — #14754359

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66867C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic
3#13068782C212yesmaximal, complemented
4#13068751C212yesmaximal, complemented
5#13068643C212yesmaximal
6#13068639C212yesmaximal
7#13068514C214yesmaximal, complemented
8C11×#2285C211yesmaximal, characteristic
9C2×C11×#117—21no—
10C22×C42×C11C2211yescharacteristic
11C23×C11⋊C8C2212yes—
12C11×#384C2212yes—
13C11×#382—21no—
14C11×#380—21no—
15C11×#380C2212yes—
16C4×C11×C4⋊C4—21no—
17C4×C11×C4⋊C4C2212yes—
18#10622825C2211yescharacteristic
19#10622825C2211yescharacteristic
20#10622824—21no—
21C4×C22⋊Dic11—21no—
22C2×#66872C2214yes—
23C2×#66871C2214yes—
24#10622550—21no—
25#10622549C2212yes—
26C4×C4⋊Dic11C2212yes—
27#10622545—21no—
28C2×#66867C418yescomplemented
29C2×#66867C2211yescharacteristic
30C2×#66867C2212yes—
31C2×#66867C2211yescharacteristic
32#10622167C2214yes—
33#10622167C2214yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C11×#117—44no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4C2314yes—
41C2×C11×C22⋊C4—22no—
42C2×C42×C11—22no—
43C2×C42×C11C2×C414yes—
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11Q814yes—
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51C2×C4⋊Dic11C2312yes—
52C2×C4⋊Dic11C2312yes—
53C2×C4×Dic11—22no—
54C22×C11⋊C8—28no—
55C22×C11⋊C8C2×C418yes—
56C22×C11⋊C8C2312yes—
57C22×C11⋊C8C2312yes—
58C11×#95—22no—
59C11×#95—22no—
60C11⋊#95—22no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65#66872—28no—
66#66871—28no—
67#66867C2×C414yes—
68#66867C2×C418yes—
69#66867C2×C414yes—
70#20823—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—42no—
77C22×C4×C11C4⋊C414yes—
78C22×C4×C11C4⋊C414yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×Q812yes—
86C22×C4×C11C2411yescharacteristic
87C22×Dic11—22no—
88C22×Dic11—22no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—44no—
92C11×C4⋊C4—44no—
93C11×C22⋊C4—44no—
94C42×C11—44no—
95C42×C11C4⋊C414yes—
96C42×C11C4⋊C414yes—
97C42×C11C22×C412yes—
98C42×C11C22×C412yes—
99C42×C11C2×Q812yes—
100C42×C11C2×Q812yes—
101C22⋊Dic11—42no—
102C22⋊Dic11—42no—
103C4⋊Dic11—24no—
104C4⋊Dic11—24no—
105C4×Dic11—44no—
106C2×C11⋊C8—216no—
107C2×C11⋊C8—24no—
108C2×C11⋊C8C22×C414yes—
109C2×C11⋊C8C22×C414yes—
110C2×C11⋊C8#4118yes—
111C22×#97—111no—
112#2285D1111yescharacteristic
113#2283—111no—
114#1847—112no—
115#1836—112no—
116#1808—112no—
117#1807—112no—
118#1776—114no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11C2×C4⋊C412yes—
122C23×C11AGL(1,ℤ/8)12yes—
123C23×C11#13712yes—
124C23×C11C22×D411yescharacteristic
125C2×C4×C11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—28no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—44no—
136C2×C4×C11—44no—
137C2×C4×C11—44no—
138C2×C4×C11—44no—
139C2×C4×C11C2×C4⋊C412yes—
140C2×C4×C11C2×C4⋊C412yes—
141C2×C4×C11C2×C4⋊C412yes—
142C2×C4×C11C2×C4⋊C412yes—
143C2×C4×C11C2×C4⋊C412yes—
144C2×C4×C11C23×C411yescharacteristic
145C2×C4×C11C22×Q811yescharacteristic
146C2×C4×C11C2×#4114yes—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C11⋊C8—24no—
154C11⋊C8#11718yescomplemented
155C23×C8—112no—
156C2×#117—21no—
157C22×C42C2×D1111yescharacteristic
158C2×#107—114no—
159C2×#106—114no—
160C2×#97—111no—
161C2×#97—111no—
162C2×#97—112no—
163C2×#97—118no—
164#384C2×D1112yes—
165#383—221no—
166#382—21no—
167#382—112no—
168#381—221no—
169#380—21no—
170#380—111no—
171#380—111no—
172#380C2×D1112yes—
173C4×C4⋊C4—21no—
174C4×C4⋊C4—112no—
175C4×C4⋊C4C2×D1112yes—
176C4×C22⋊C4—221no—
177#376—221no—
178#340—114no—
179#340—114no—
180C22×C11—22no—
181C22×C11—24no—
182C22×C11—24no—
183C22×C11—22no—
184C22×C11#42814yes—
185C22×C11C22×C4⋊C411yescharacteristic
186C22×C11#53212yes—
187C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
188C22×C11C2×#13711yescharacteristic
189C22×C11#57512yes—
190C4×C11—22no—
191C4×C11—22no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—22no—
195C4×C11—84no—
196C4×C11C2×#11712yes—
197C4×C11#53312yes—
198Dic11—82no—
199Dic11—82no—
200C23×C4C22⋊D1111yescharacteristic
201C23×C4C22⋊D1111yescharacteristic
202C23×C4C22×D1111yescharacteristic
203C22×C8—112no—
204C22×C8—118no—
205C22×C8—112no—
206C22×C8—228no—
207#117—44no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—112no—
211C2×C4⋊C4—112no—
212C2×C4⋊C4C22×D1114yes—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C42—22no—
217C2×C42—222no—
218C2×C42Dic2214yes—
219C2×C42C4×D1114yes—
220C2×C42C22⋊D1111yescharacteristic
221C2×C42C22⋊D1111yescharacteristic
222C2×C42C22×D1111yescharacteristic
223C2×C42C22×D1111yescharacteristic
224#107—228no—
225#106—228no—
226#97—114no—
227#97—118no—
228#97—114no—
229#95—22no—
230#95—22no—
231#95—221no—
232#95—221no—
233#95—222no—
234#95—222no—
235#95—222no—
236C2×C11—24no—
237C2×C11#228511yescharacteristic
238C2×C11C2×#42811yescharacteristic
239C2×C11#291111yescharacteristic
240C2×C11#318012yes—
241C2×C11#318112yes—
242C24C2×C22⋊D1111yescharacteristic
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—42no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4Dic11⋊C414yes—
251C22×C4Dic11⋊C414yes—
252C22×C4C2×Dic2212yes—
253C22×C4C2×C4×D1112yes—
254C22×C4C2×C22⋊D1111yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256C22×C4C2×C22⋊D1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259C22×C4C23×D1111yescharacteristic
260C2×C8—114no—
261C2×C8—118no—
262C2×C8—114no—
263C2×C8—2216no—
264C2×C8—224no—
265C4⋊C4—24no—
266C4⋊C4—24no—
267C4⋊C4—44no—
268C4⋊C4—44no—
269C4⋊C4—224no—
270C4⋊C4—224no—
271C22⋊C4—44no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C42—44no—
275C42—444no—
276C42Dic11⋊C414yes—
277C42Dic11⋊C414yes—
278C42C2×Dic2212yes—
279C42C2×Dic2212yes—
280C42C2×C4×D1112yes—
281C42C2×C4×D1112yes—
282C11#2082311yescharacteristic, complemented, Sylow
283C23—22no—
284C23—22no—
285C23C2×Dic11⋊C412yes—
286C23#6698512yes—
287C23#6699512yes—
288C23C22×C22⋊D1111yescharacteristic
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—28no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—44no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4C2×Dic11⋊C412yes—
310C2×C4C2×Dic11⋊C412yes—
311C2×C4C2×Dic11⋊C412yes—
312C2×C4C2×Dic11⋊C412yes—
313C2×C4C2×Dic11⋊C412yes—
314C2×C4C22×Dic2211yescharacteristic
315C2×C4C22×C4×D1111yescharacteristic
316C2×C4#41×D1114yes—
317C8—118no—
318C8—224no—
319C22—24no—
320C22—24no—
321C22—22no—
322C22—22no—
323C22#1062257714yes—
324C22C22×Dic11⋊C411yescharacteristic
325C22C2×#6698511yescharacteristic
326C22C2×#6699511yescharacteristic
327C22#1062335312yes—
328C22#1062336312yes—
329C4—22no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—22no—
334C4—84no—
335C4—882no—
336C4—882no—
337C4#1062304812yes—
338C4D11×#11712yes—
339C2—24no—
340C2#1307101911yescharacteristic
341C2C2×#1062257711yescharacteristic
342C2#1307720511yescharacteristic
343C2#1307930812yes—
344C2#1307931912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2285C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2285D11
hypocenterC11#20823
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2285

Complements

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

NH ≅ G/Ntype
3. #13068782C2semidirect
4. #13068751C2semidirect
7. #13068514C2semidirect
28. C2×#66867C4semidirect
154. C11⋊C8#117semidirect
282. C11#20823semidirect

Maximal subgroups

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

subgroupindex
C22×#668672
#130710142
#130687822
#130687512
#130686432
#130686392
#130685142
C11×#22852
#2082311