Finite Group Databasebeta

← #14764036

Subgroups — #14764036

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
2#13070999C211yesmaximal, characteristic
3#13068815C214yesmaximal, complemented
4#13068813C214yesmaximal, complemented
5#13068643C212yesmaximal, complemented
6#13068639C212yesmaximal, complemented
7C11×#2280C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C2×C11×#117C2212yes—
10C2×#66979C2212yes—
11C23×C11⋊C8C2211yescharacteristic
12C23×C11⋊C8C2211yescharacteristic
13C11×#381—21no—
14C11×#380C2212yes—
15C11×#380C2212yes—
16C11×#379—21no—
17C4×C11×C22⋊C4—21no—
18C4×C11×C22⋊C4—21no—
19#10622860—21no—
20#10622825C2212yes—
21#10622825C2212yes—
22#10622824—21no—
23C4×C22⋊Dic11—21no—
24C4×C22⋊Dic11—21no—
25C2×C22⋊(C11⋊C8)C418yescomplemented
26C2×C22⋊(C11⋊C8)C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×#66872C2214yescomplemented
29C2×#66871C2214yescomplemented
30#10622167C2214yescomplemented
31#10622167C2214yescomplemented
32C25×C11D411yescharacteristic
33C23×C4×C11—42no—
34C23×C4×C11—42no—
35C23×C4×C11C2×C414yes—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11Q814yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C11×#117—42no—
44C11×#117—42no—
45C2×C11×C4⋊C4C2314yes—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C42×C11—22no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—22no—
53#66979—42no—
54#66979—42no—
55C2×C4⋊Dic11C2314yes—
56C2×C4×Dic11—22no—
57C22×C11⋊C8—42no—
58C22×C11⋊C8—42no—
59C22×C11⋊C8C2×C414yes—
60C22×C11⋊C8C2×C414yes—
61C22×C11⋊C8C2312yes—
62C22×C11⋊C8C2312yes—
63C11×#95—22no—
64C11×#95—22no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C22⋊(C11⋊C8)C2×C418yes—
68C22⋊(C11⋊C8)C2×C418yes—
69#66872—44no—
70#66871—44no—
71#21939—111nomaximal, Sylow
72C24×C11—24no—
73C24×C11—42no—
74C24×C11—42no—
75C24×C11C4⋊C414yes—
76C24×C11C2×D411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C24×C11C2×D411yescharacteristic
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—24no—
86C22×C4×C11—44no—
87C22×C4×C11—44no—
88C22×C4×C11—48no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C4⋊C414yes—
93C22×C4×C11C4⋊C414yes—
94C22×C4×C11C4⋊C414yes—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—24no—
108C11×C22⋊C4—44no—
109C11×C22⋊C4—44no—
110C11×C22⋊C4—44no—
111C42×C11—44no—
112C22⋊Dic11—44no—
113C22⋊Dic11—44no—
114C22⋊Dic11—44no—
115C4⋊Dic11—24no—
116C4⋊Dic11—24no—
117C4×Dic11—44no—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—44no—
121C2×C11⋊C8—44no—
122C2×C11⋊C8C22×C414yes—
123C2×C11⋊C8C22×C414yes—
124C22×C22⋊C8—111no—
125#2280—111no—
126#2280D1111yescharacteristic
127#1854—114no—
128#1854—114no—
129#1808—112no—
130#1807—112no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—22no—
139C23×C11—28no—
140C23×C11—44no—
141C23×C11—44no—
142C23×C11—416no—
143C23×C11C2×C4⋊C412yes—
144C23×C11C2×C4⋊C412yes—
145C23×C11C2×C4⋊C412yes—
146C23×C11#13514yes—
147C23×C11C22×D411yescharacteristic
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11—44no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11C2×C4⋊C412yes—
167C2×C4×C11C2×C4⋊C412yes—
168C2×C4×C11C2×C4⋊C412yes—
169C2×C4×C11C23×C411yescharacteristic
170C2×C4×C11C22×Q811yescharacteristic
171C2×C4×C11H(5,𝔽2)12yes—
172C2×C4×C11H(5,𝔽2)12yes—
173C2×Dic11—44no—
174C2×Dic11—44no—
175C2×Dic11—44no—
176C11⋊C8—24no—
177C11⋊C8—24no—
178C24×C4C2×D1111yescharacteristic
179C23×C8—111no—
180C23×C8—111no—
181C2×#117—112no—
182C2×#117C2×D1112yes—
183C2×#107—114no—
184C2×#106—114no—
185C2×C22⋊C8—112no—
186C2×C22⋊C8—112no—
187C2×C22⋊C8—118no—
188#381—21no—
189#381—221no—
190#380—112no—
191#380—112no—
192#380C2×D1112yes—
193#380C2×D1112yes—
194#379—21no—
195#379—221no—
196C4×C22⋊C4—21no—
197C4×C22⋊C4—21no—
198C4×C22⋊C4—221no—
199C4×C22⋊C4—221no—
200#340—114no—
201#340—114no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—28no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—416no—
212C22×C11—44no—
213C22×C11—44no—
214C22×C11#42714yes—
215C22×C11C22×C4⋊C411yescharacteristic
216C22×C11#53412yes—
217C22×C11C2×#13512yes—
218C22×C11#57512yes—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—84no—
223C4×C11#51811yescharacteristic
224C4×C11#51811yescharacteristic
225C4×C11#54312yes—
226Dic11—84no—
227C25C22⋊D1111yescharacteristic
228C23×C4—42no—
229C23×C4—42no—
230C23×C4Dic2214yes—
231C23×C4C4×D1114yes—
232C23×C4C22⋊D1111yescharacteristic
233C23×C4C22⋊D1111yescharacteristic
234C23×C4C22⋊D1111yescharacteristic
235C23×C4C22×D1111yescharacteristic
236C23×C4C22×D1111yescharacteristic
237C23×C4C22×D1111yescharacteristic
238C22×C8—112no—
239C22×C8—112no—
240C22×C8—114no—
241C22×C8—114no—
242C22×C8—442no—
243C22×C8—442no—
244#117—42no—
245#117—42no—
246#117—442no—
247#117—442no—
248C2×C4⋊C4—114no—
249C2×C4⋊C4C22×D1114yes—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—222no—
254C2×C22⋊C4—222no—
255C2×C22⋊C4—222no—
256C2×C42—22no—
257C2×C42—222no—
258#107—444no—
259#106—444no—
260C22⋊C8—118no—
261C22⋊C8—118no—
262#95—22no—
263#95—22no—
264#95—222no—
265#95—222no—
266C2×C11—24no—
267C2×C11—42no—
268C2×C11—42no—
269C2×C11#231511yescharacteristic
270C2×C11C2×#42711yescharacteristic
271C2×C11#291111yescharacteristic
272C2×C11#319114yes—
273C24—24no—
274C24—42no—
275C24—42no—
276C24Dic11⋊C414yes—
277C24C2×C22⋊D1111yescharacteristic
278C24C2×C22⋊D1111yescharacteristic
279C24C2×C22⋊D1111yescharacteristic
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—48no—
288C22×C4—44no—
289C22×C4—44no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—224no—
294C22×C4Dic11⋊C414yes—
295C22×C4Dic11⋊C414yes—
296C22×C4Dic11⋊C414yes—
297C22×C4C2×Dic2212yes—
298C22×C4C2×Dic2212yes—
299C22×C4C2×Dic2212yes—
300C22×C4C2×C4×D1112yes—
301C22×C4C2×C4×D1112yes—
302C22×C4C2×C4×D1112yes—
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306C22×C4C23×D1111yescharacteristic
307C2×C8—114no—
308C2×C8—114no—
309C2×C8—224no—
310C2×C8—224no—
311C2×C8—444no—
312C2×C8—444no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—224no—
316C4⋊C4—224no—
317C22⋊C4—44no—
318C22⋊C4—44no—
319C22⋊C4—44no—
320C22⋊C4—444no—
321C22⋊C4—444no—
322C22⋊C4—444no—
323C42—44no—
324C42—444no—
325C11#2193911yescharacteristic, complemented, Sylow
326C23—22no—
327C23—22no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—22no—
333C23—22no—
334C23—28no—
335C23—44no—
336C23—44no—
337C23—416no—
338C23C2×Dic11⋊C412yes—
339C23C2×Dic11⋊C412yes—
340C23C2×Dic11⋊C412yes—
341C23#6700314yes—
342C23C22×C22⋊D1111yescharacteristic
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—444no—
362C2×C4—444no—
363C2×C4—444no—
364C2×C4C2×Dic11⋊C412yes—
365C2×C4C2×Dic11⋊C412yes—
366C2×C4C2×Dic11⋊C412yes—
367C2×C4C22×Dic2211yescharacteristic
368C2×C4C22×C4×D1111yescharacteristic
369C2×C4#6703712yes—
370C2×C4#6703712yes—
371C8—224no—
372C8—224no—
373C22—28no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—416no—
383C22—44no—
384C22—44no—
385C22#1062261114yes—
386C22C22×Dic11⋊C411yescharacteristic
387C22#1062333512yes—
388C22C2×#6700312yes—
389C22#1062335312yes—
390C4—22no—
391C4—22no—
392C4—22no—
393C4—84no—
394C4—884no—
395C4#1062301412yes—
396C4#1062301711yescharacteristic
397C4#1062301711yescharacteristic
398C2—24no—
399C2—42no—
400C2—42no—
401C2#1307122811yescharacteristic
402C2C2×#1062261111yescharacteristic
403C2#1307720511yescharacteristic
404C2#1307940414yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2280C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenter#2280D11
hypocenterC11#21939
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
3. #13068815C2semidirect
4. #13068813C2semidirect
5. #13068643C2semidirect
6. #13068639C2semidirect
25. C2×C22⋊(C11⋊C8)C4semidirect
28. C2×#66872C22semidirect
29. C2×#66871C22semidirect
30. #10622167C22semidirect
31. #10622167C22semidirect
325. C11#21939semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊(C11⋊C8)2
#130709992
#130688152
#130688132
#130686432
#130686392
C11×#22802
#2193911