Finite Group Databasebeta

← #14770830

Subgroups — #14770830

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66874C211yesmaximal, characteristic
2#13071485C211yesmaximal, characteristic
3#13071448C211yesmaximal, characteristic
4#13069307C212yesmaximal, complemented
5#13069255C212yesmaximal, complemented
6#13068871C212yesmaximal, complemented
7#13068643C211yesmaximal, characteristic
8#13068552C211yesmaximal, characteristic
9#13068445C212yesmaximal, complemented
10#13068395C211yesmaximal, characteristic
11C11×#1823C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66979—21no—
15C23×C11⋊C8C2211yescharacteristic
16C2×#66940C2212yes—
17C2×C11×C22⋊C8C2211yescharacteristic
18C11×#380C2211yescharacteristic
19#10622825C2211yescharacteristic
20#10622824—21no—
21C4×C22⋊Dic11C2211yescharacteristic
22C2×#66880C2212yes—
23C2×#66880C2212yes—
24C2×#66879C2212yes—
25#10622598C2212yes—
26#10622594—22no—
27C4⋊C4×Dic11C2212yes—
28#10622587C2212yes—
29C2×#66874C418yescomplemented
30C2×#66874C2211yescharacteristic
31C2×#66874C2211yescharacteristic
32C2×#66874C2211yescharacteristic
33C2×#66874C2211yescharacteristic
34C2×#66871C2212yes—
35#10622555—21no—
36C22⋊C4×Dic11—21no—
37#10622259—22no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C22×Dic22—24no—
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×Dic22—42no—
49C22×Dic22C2×C414yes—
50C22×Dic22C2311yescharacteristic
51C22×Dic22C2311yescharacteristic
52C22×C8×C11C2312yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11D411yescharacteristic
62C2×C22⋊Dic11D411yescharacteristic
63#66979—44no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8—42no—
71C22×C11⋊C8C2×C414yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74#66940—24no—
75#66940—42no—
76C11×C22⋊C8—22no—
77C11×#95—21no—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95D412yes—
84#66880—24no—
85#66880—42no—
86#66879—42no—
87#66874C2×C414yes—
88#66874C2×C414yes—
89#66874C2×C414yes—
90#66874C2×C414yes—
91#66871—42no—
92#22563—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4112yes—
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—24no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11—44no—
111C22×Dic11C2×D412yes—
112C22×Dic11C2×D412yes—
113C2×Dic22—28no—
114C2×Dic22—24no—
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—44no—
121C2×Dic22—48no—
122C2×Dic22—44no—
123C2×Dic22C22×C412yes—
124C2×Dic22C22×C412yes—
125C2×Dic22#4114yes—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4C22×C412yes—
135C11×C4⋊C4C22×C412yes—
136C11×C22⋊C4—42no—
137C22⋊Dic11—22no—
138C22⋊Dic11—22no—
139C22⋊Dic11—42no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—44no—
143Dic11⋊C4—44no—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C4×Dic11—44no—
147C4×Dic11—44no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—44no—
151C2×C11⋊C8C22×C412yes—
152C2×C11⋊C8C22×C412yes—
153C22×#103—111no—
154#2344—111no—
155Q8×C22⋊C4—111no—
156#1935—112no—
157#1928—112no—
158#1863—112no—
159#1823D1111yescharacteristic
160#1808—111no—
161#1787—111no—
162#1763—112no—
163#1752—111no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11C4×D412yes—
167C23×C11AGL(1,ℤ/8)12yes—
168C23×C11#13712yes—
169C23×C11C22×D411yescharacteristic
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—48no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11C4×D412yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4112yes—
188C2×C4×C11H(5,𝔽2)12yes—
189C2×Dic11—22no—
190C2×Dic11—24no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—48no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203Dic22—22no—
204Dic22—24no—
205Dic22—22no—
206Dic22—22no—
207Dic22—48no—
208Dic22—42no—
209Dic22#11714yescomplemented
210C8×C11—42no—
211C11⋊C8—22no—
212C11⋊C8—22no—
213C23×Q8—111no—
214C23×C8—111no—
215C2×C4×Q8—112no—
216C2×#117—221no—
217C22×C4⋊C4C2×D1111yescharacteristic
218C2×#107—112no—
219C2×#103—111no—
220C2×#103—111no—
221C2×#103—111no—
222C2×#103—111no—
223C2×#103—118no—
224C2×#103—112no—
225C2×#103—112no—
226C2×C22⋊C8C2×D1111yescharacteristic
227C2×#97—112no—
228#391—112no—
229#391—222no—
230#389—112no—
231#387—222no—
232#381—221no—
233#380—111no—
234#380—221no—
235#380C2×D1111yescharacteristic
236C4×C4⋊C4—112no—
237C4×C22⋊C4—111no—
238C4×C22⋊C4—221no—
239#340—112no—
240#340C2×D1112yes—
241#340C2×D1112yes—
242#336—112no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—24no—
246C22×C11—24no—
247C22×C11#44014yes—
248C22×C11C2×C4×D411yescharacteristic
249C22×C11#54612yes—
250C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C11C2×#13711yescharacteristic
252C22×C11#57812yes—
253C4×C11—22no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—82no—
257C4×C11C2×#11711yescharacteristic
258C4×C11#51811yescharacteristic
259C4×C11#55112yes—
260Dic11—24no—
261Dic11—42no—
262Dic11—42no—
263Dic11—42no—
264Dic11—82no—
265C22×Q8—114no—
266C22×Q8—111no—
267C22×Q8—111no—
268C22×Q8—224no—
269C22×Q8—221no—
270C22×Q8—222no—
271C22×Q8—442no—
272C23×C4—21no—
273C23×C4—221no—
274C23×C4C22×D1111yescharacteristic
275C22×C8—111no—
276C22×C8—111no—
277C22×C8—114no—
278C22×C8—442no—
279C22×C8C22×D1112yes—
280C4×Q8—224no—
281C4×Q8—442no—
282#117—444no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4C4×D1114yes—
289C2×C4⋊C4C22×D1112yes—
290C2×C4⋊C4C22×D1111yescharacteristic
291C2×C4⋊C4C22×D1111yescharacteristic
292C2×C22⋊C4—21no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—221no—
296C2×C42—112no—
297C2×C42—222no—
298C2×C42—222no—
299#107—442no—
300#103—114no—
301#103—114no—
302#103—114no—
303#103—114no—
304#103—224no—
305#103—442no—
306C22⋊C8—22no—
307#97—442no—
308#95—21no—
309#95—112no—
310#95—222no—
311#95—222no—
312#95—222no—
313#95—222no—
314#95—221no—
315C2×C11—24no—
316C2×C11#234211yescharacteristic
317C2×C11C2×#44011yescharacteristic
318C2×C11#295011yescharacteristic
319C2×C11#330812yes—
320C2×C11#331212yes—
321C24D4×D1111yescharacteristic
322C2×Q8—112no—
323C2×Q8—112no—
324C2×Q8—114no—
325C2×Q8—228no—
326C2×Q8—224no—
327C2×Q8—221no—
328C2×Q8—221no—
329C2×Q8—222no—
330C2×Q8—222no—
331C2×Q8—222no—
332C2×Q8—444no—
333C2×Q8—444no—
334C2×Q8—448no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—24no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—221no—
346C22×C4—224no—
347C22×C4—221no—
348C22×C4—222no—
349C22×C4—444no—
350C22×C4C2×C4×D1112yes—
351C22×C4D4×D1111yescharacteristic
352C22×C4#434112yes—
353C22×C4C23×D1111yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—112no—
358C2×C8—112no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—444no—
362C4⋊C4—24no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—444no—
370C4⋊C4—444no—
371C4⋊C4C2×C4×D1112yes—
372C4⋊C4C2×C4×D1112yes—
373C22⋊C4—42no—
374C22⋊C4—222no—
375C22⋊C4—222no—
376C22⋊C4—442no—
377C42—222no—
378C42—222no—
379C42—444no—
380C42—444no—
381C11#2256311yescharacteristic, complemented, Sylow
382C23—22no—
383C23—22no—
384C23(C22⋊D11)⋊C412yes—
385C23#6696412yes—
386C23#6696812yes—
387C23C2×D4×D1111yescharacteristic
388Q8—114no—
389Q8—222no—
390Q8—224no—
391Q8—222no—
392Q8—222no—
393Q8—448no—
394Q8—442no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—48no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—222no—
410C2×C4—224no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—448no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4(C22⋊D11)⋊C412yes—
424C2×C4C22×C4×D1111yescharacteristic
425C2×C4C2×#434111yescharacteristic
426C2×C4#41×D1112yes—
427C2×C4#6704212yes—
428C8—42no—
429C8—222no—
430C8—222no—
431C22—24no—
432C22—24no—
433C22—22no—
434C22—22no—
435C22#1062237014yes—
436C22C2×(C22⋊D11)⋊C411yescharacteristic
437C22#1062318512yes—
438C22C2×#6696411yescharacteristic
439C22C2×#6696811yescharacteristic
440C22#1062331012yes—
441C4—22no—
442C4—42no—
443C4—42no—
444C4—82no—
445C4—224no—
446C4—442no—
447C4—442no—
448C4—442no—
449C4—882no—
450C4D11×#11711yescharacteristic
451C4#1062305211yescharacteristic
452C4#1062318912yes—
453C2—24no—
454C2#1307145811yescharacteristic
455C2C2×#1062237011yescharacteristic
456C2#1307748011yescharacteristic
457C2#1308060512yes—
458C2#1308066512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1823D11
hypocenterC11#22563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #13069307C2semidirect
5. #13069255C2semidirect
6. #13068871C2semidirect
9. #13068445C2semidirect
29. C2×#66874C4semidirect
209. Dic22#117semidirect
381. C11#22563semidirect

Maximal subgroups

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

subgroupindex
C22×#668742
#130714852
#130714482
#130693072
#130692552
#130688712
#130686432
#130685522
#130684452
#130683952
C11×#18232
#2256311