Finite Group Databasebeta

← #14764367

Subgroups — #14764367

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622613C211yesmaximal, characteristic
2#13071239C211yesmaximal, characteristic
3#13069384C212yesmaximal, complemented
4#13069374C212yesmaximal, complemented
5#13068813C212yesmaximal
6#13068803C212yesmaximal
7#13068782C211yesmaximal, characteristic, complemented
8#13068775C211yesmaximal, characteristic, complemented
9#13068749C211yesmaximal, characteristic, complemented
10#13068746C211yesmaximal, characteristic, complemented
11C11×#2314C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C11×#388—22no—
16C11×#387—22no—
17C11×#384C2211yescharacteristic
18C11×#382C2211yescharacteristic
19C11×#380C2212yes—
20C4×C11×C4⋊C4C2212yes—
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622613C418yescomplemented
23#10622598—22no—
24C2×#66872C2212yes—
25C2×#66871C2212yes—
26C2×#66871C2212yes—
27C2×#66871C2212yes—
28#10622563—22no—
29#10622549C2211yescharacteristic
30#10622549C2211yescharacteristic
31#10622548C2211yescharacteristic
32#10622548C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34C2×#66867C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—21no—
42C11×#117C2×C414yes—
43C11×#117Q814yes—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4D412yes—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4D412yes—
50C2×C42×C11—22no—
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—21no—
54#66979—42no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—42no—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4×Dic11—21no—
64C22×C11⋊C8C2312yes—
65C22×C11⋊C8C2312yes—
66C11×#95—22no—
67C11×#95—22no—
68C11×#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C22⋊(C11⋊C8)C2×C418yes—
72#66872—42no—
73#66871—42no—
74#66871—42no—
75#66871—42no—
76C4⋊(C11⋊C8)C2×C418yescomplemented
77#66867C2×C414yescomplemented
78C4×C11⋊C8C2×C414yescomplemented
79#21991—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×Q812yes—
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—42no—
96C22×Dic11—82no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—24no—
100C11×C4⋊C4—82no—
101C11×C4⋊C4C4⋊C418yes—
102C11×C22⋊C4—82no—
103C11×C22⋊C4C4⋊C418yes—
104C42×C11—82no—
105C42×C11C22×C412yes—
106C42×C11C22×C412yes—
107C42×C11C2×Q812yes—
108C42×C11C2×Q812yes—
109C22⋊Dic11—42no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—42no—
115C4⋊Dic11—82no—
116C4⋊Dic11—82no—
117C4×Dic11—42no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8C22×C414yes—
123C2×C11⋊C8C22×C414yes—
124C2×#433—111no—
125#2317—111no—
126#2314D1111yescharacteristic
127#1949—112no—
128#1947—112no—
129#1854—112no—
130#1852—112no—
131#1847—111no—
132#1845—111no—
133#1836—111no—
134#1835—111no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—22no—
138C23×C11—22no—
139C23×C11C2×C4⋊C412yes—
140C23×C11C22×D411yescharacteristic
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—24no—
148C2×C4×C11—24no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11C2×C4⋊C414yes—
156C2×C4×C11C2×C4⋊C414yes—
157C2×C4×C11C2×C4⋊C412yes—
158C2×C4×C11C23×C411yescharacteristic
159C2×C4×C11C22×Q811yescharacteristic
160C2×C4×C11H(5,𝔽2)12yes—
161C2×C4×C112−1+412yes—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—84no—
171C11⋊C8—24no—
172C11⋊C8—24no—
173C2×#117—111no—
174C2×#117C2×D1111yescharacteristic
175C22×C4⋊C4—111no—
176#433—118no—
177C2×#107—112no—
178C2×#107—112no—
179C2×#107—112no—
180C2×#106—112no—
181C2×C4⋊C8—112no—
182C2×C22⋊C8—112no—
183C2×#97—111no—
184C2×C4×C8—111no—
185#389—222no—
186#388—22no—
187#387—22no—
188#385—222no—
189#384—111no—
190#384—111no—
191#384C2×D1111yescharacteristic
192#382—111no—
193#382—111no—
194#382C2×D1111yescharacteristic
195#380C2×D1112yes—
196C4×C4⋊C4C2×D1112yes—
197#340—112no—
198#340—112no—
199#340—112no—
200#340—112no—
201C22×C11—22no—
202C22×C11—24no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—42no—
206C22×C11C22×C4⋊C411yescharacteristic
207C22×C11#53511yescharacteristic
208C22×C11#53611yescharacteristic
209C22×C11#57612yes—
210C22×C11#57812yes—
211C4×C11—22no—
212C4×C11—24no—
213C4×C11—24no—
214C4×C11—82no—
215C4×C11—82no—
216C4×C11#52012yes—
217C4×C11#54412yes—
218Dic11—81no—
219Dic11—81no—
220Dic11—81no—
221Dic11—81no—
222C23×C4—221no—
223C23×C4C22×D1111yescharacteristic
224C22×C8—112no—
225C22×C8—112no—
226#117—442no—
227#117Dic2214yes—
228#117C4×D1114yes—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—222no—
236C2×C4⋊C4—222no—
237C2×C4⋊C4—442no—
238C2×C4⋊C4C22⋊D1112yes—
239C2×C4⋊C4C22×D1112yes—
240C2×C4⋊C4C22×D1112yes—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4C22⋊D1112yes—
244C2×C42—22no—
245C2×C42—221no—
246C2×C42C22×D1111yescharacteristic
247C2×C42C22×D1111yescharacteristic
248#107—442no—
249#107—442no—
250#107—442no—
251#106—442no—
252C4⋊C8—118no—
253C22⋊C8—118no—
254#97—114no—
255C4×C8—114no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—222no—
260#95—222no—
261C2×C11—42no—
262C2×C11#231711yescharacteristic
263C2×C11#291312yes—
264C2×C11#322011yescharacteristic
265C2×C11#322311yescharacteristic
266C2×C11#324312yes—
267C24C2×C22⋊D1111yescharacteristic
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—442no—
277C22×C4—882no—
278C22×C4C2×Dic2212yes—
279C22×C4C2×C4×D1112yes—
280C22×C4C2×C22⋊D1111yescharacteristic
281C22×C4C2×C22⋊D1112yes—
282C22×C4C2×C22⋊D1112yes—
283C22×C4C23×D1111yescharacteristic
284C2×C8—114no—
285C2×C8—114no—
286C2×C8—222no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—222no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—24no—
293C4⋊C4—82no—
294C4⋊C4—222no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—442no—
299C4⋊C4—882no—
300C4⋊C4—882no—
301C4⋊C4Dic11⋊C418yes—
302C22⋊C4—82no—
303C22⋊C4—442no—
304C22⋊C4Dic11⋊C418yes—
305C42—82no—
306C42—442no—
307C42C2×Dic2212yes—
308C42C2×Dic2212yes—
309C42C2×C4×D1112yes—
310C42C2×C4×D1112yes—
311C11#2199111yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—22no—
315C23—22no—
316C23C2×Dic11⋊C412yes—
317C23C22×C22⋊D1111yescharacteristic
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—884no—
341C2×C4C2×Dic11⋊C414yes—
342C2×C4C2×Dic11⋊C414yes—
343C2×C4C2×Dic11⋊C412yes—
344C2×C4C22×Dic2211yescharacteristic
345C2×C4C22×C4×D1111yescharacteristic
346C2×C4#6704212yes—
347C2×C4#6704312yes—
348C8—224no—
349C8—224no—
350C22—22no—
351C22—24no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22C22×Dic11⋊C411yescharacteristic
356C22#1062335611yescharacteristic
357C22#1062336111yescharacteristic
358C22#1062336612yes—
359C22#1062336912yes—
360C4—22no—
361C4—24no—
362C4—24no—
363C4—82no—
364C4—82no—
365C4—881no—
366C4—881no—
367C4—881no—
368C4—881no—
369C4#1062305012yes—
370C4#1062305412yes—
371C2—42no—
372C2#1307123611yescharacteristic
373C2#1307721412yes—
374C2#1307966011yescharacteristic
375C2#1307969311yescharacteristic
376C2#1307989312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2314C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2314D11
hypocenterC11#21991
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #13069384C2semidirect
4. #13069374C2semidirect
7. #13068782C2semidirect
8. #13068775C2semidirect
9. #13068749C2semidirect
10. #13068746C2semidirect
22. #10622613C4semidirect
76. C4⋊(C11⋊C8)C2×C4semidirect
77. #66867C2×C4semidirect
78. C4×C11⋊C8C2×C4semidirect
311. C11#21991semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
#130712392
#130693842
#130693742
#130688132
#130688032
#130687822
#130687752
#130687492
#130687462
C11×#23142
#2199111