Finite Group Databasebeta

← #14770917

Subgroups — #14770917

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66885C211yesmaximal, characteristic
2#13071483C211yesmaximal, characteristic, complemented
3C22⋊C4×D44C211yesmaximal, characteristic
4#13069299C212yesmaximal, complemented
5#13069237C212yesmaximal, complemented
6#13068866C212yesmaximal, complemented
7#13068703C211yesmaximal, characteristic, complemented
8#13068645C211yesmaximal, characteristic, complemented
9#13068548C211yesmaximal, characteristic
10C4×#66885C212yesmaximal, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C2×C22⋊C4×D11—21no—
16C2×#66930—21no—
17C2×C4×D44C2212yes—
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C4×C8×C11C2212yescomplemented
20C4×C11×C22⋊C4C2211yescharacteristic
21#10622825C2211yescharacteristic
22#10622825C2211yescharacteristic
23C2×#66885C418yescomplemented
24C2×#66885C2212yes—
25C2×#66885C2212yes—
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66882C2212yescomplemented
31#10622568—21no—
32#10622556—21no—
33#10622552C2212yes—
34C4×C4⋊Dic11C2212yescomplemented
35#10622541C2212yescomplemented
36#10622278—22no—
37#10622266—22no—
38C11×#336C2212yescomplemented
39#10622189C2212yescomplemented
40#10622189C2212yescomplemented
41#10622189C2212yescomplemented
42C24×D11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C22×D44—24no—
46C22×D44—21no—
47C22×D44—22no—
48C22×D44—42no—
49C22×D44C2×C414yes—
50C22×D44C2311yescharacteristic
51C22×D44C2311yescharacteristic
52C22×C4×D11—22no—
53C22×C8×C11—42no—
54C22×C8×C11C2×C414yescomplemented
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C2×C11×C22⋊C4D411yescharacteristic
59C2×C11×C22⋊C4D411yescharacteristic
60C2×C42×C11C2312yes—
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11C2×C414yescomplemented
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—22no—
75C22⋊C4×D11—44no—
76#66930—44no—
77C4×D44—24no—
78C4×D44—42no—
79C11×C22⋊C8—22no—
80C4×C8×C11—42no—
81C11×#95D412yes—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—21no—
86#66885—24no—
87#66885—42no—
88#66885C2×C414yes—
89#66885C2×C414yes—
90#66885C2×C414yescomplemented
91#66885C2×C414yescomplemented
92#66882—42no—
93#22570—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C23×D11—21no—
96C23×D11—21no—
97C23×D11—24no—
98C23×D11—44no—
99C23×D11—42no—
100C23×D11—42no—
101C23×D11—82no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11#4112yes—
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—24no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—42no—
116C22×Dic11—42no—
117C2×D44—28no—
118C2×D44—24no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—44no—
125C2×D44—44no—
126C2×D44—48no—
127C2×D44C22×C412yes—
128C2×D44C22×C412yes—
129C2×D44#4114yes—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×C4×D11—82no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—44no—
139C2×C8×C11C22×C412yes—
140C2×C8×C11C22×C412yes—
141C11×C22⋊C4—22no—
142C11×C22⋊C4D814yes—
143C42×C11—22no—
144C42×C11—22no—
145C22⋊Dic11—42no—
146C22⋊Dic11—42no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—82no—
150C4⋊Dic11—24no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C22×C412yes—
158C4⋊Dic11C22×C412yes—
159Dic11⋊C4—44no—
160C4×Dic11—44no—
161C22×#102—111no—
162#2344—111no—
163D4×C22⋊C4—111no—
164#1934—112no—
165#1925—112no—
166#1862—112no—
167#1823—111no—
168#1808—111no—
169#1786—111no—
170C4×#102—112no—
171C8×C22⋊C4D1111yescharacteristic, complemented
172C23×C11—22no—
173C23×C11—22no—
174C23×C11C4×D412yes—
175C23×C11C2×D812yes—
176C23×C11#13512yes—
177C23×C11C22×D411yescharacteristic
178C22×D11—22no—
179C22×D11—24no—
180C22×D11—22no—
181C22×D11—48no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—42no—
189C22×D11—48no—
190C22×D11—84no—
191C22×D11—88no—
192C22×D11—88no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11C4×D412yes—
203C2×C4×C11C2×D814yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4112yes—
207C2×C4×C11H(5,𝔽2)12yes—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—48no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221D44—22no—
222D44—22no—
223D44—22no—
224D44—24no—
225D44—48no—
226D44—42no—
227D44#11714yescomplemented
228C4×D11—88no—
229C8×C11—22no—
230C8×C11—22no—
231C8×C11—42no—
232C23×D4—111no—
233C23×C8C2×D1111yescharacteristic
234C2×C4×D4—112no—
235C2×#117—221no—
236C22×C4⋊C4—111no—
237C22×C22⋊C4—221no—
238C2×#107—112no—
239C2×#102—111no—
240C2×#102—111no—
241C2×#102—111no—
242C2×#102—111no—
243C2×#102—118no—
244C2×#102—112no—
245C2×#102—112no—
246C2×C22⋊C8C2×D1111yescharacteristic
247C2×C4×C8C2×D1112yescomplemented
248#390—112no—
249#389—112no—
250#387—222no—
251#386—222no—
252#381—221no—
253#380—111no—
254#380—111no—
255#379—221no—
256C4×C4⋊C4—112no—
257C4×C22⋊C4C2×D1111yescharacteristic
258#340—112no—
259#340—112no—
260#340—112no—
261#336C2×D1112yescomplemented
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—24no—
265C22×C11—24no—
266C22×C11C4×D814yes—
267C22×C11C2×C4×D411yescharacteristic
268C22×C11#54612yes—
269C22×C11C22×D811yescharacteristic
270C22×C11C2×#13511yescharacteristic
271C22×C11#57712yes—
272C2×D11—24no—
273C2×D11—42no—
274C2×D11—42no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—816no—
281C2×D11—82no—
282C2×D11—82no—
283C4×C11—22no—
284C4×C11—24no—
285C4×C11—42no—
286C4×C11C2×#11711yescharacteristic
287C4×C11#51811yescharacteristic
288C4×C11#55112yes—
289Dic11—42no—
290Dic11—42no—
291Dic11—82no—
292Dic11—82no—
293C25—221no—
294C22×D4—114no—
295C22×D4—111no—
296C22×D4—111no—
297C22×D4—224no—
298C22×D4—221no—
299C22×D4—222no—
300C22×D4—442no—
301C23×C4—221no—
302C23×C4—222no—
303C23×C4C22×D1111yescharacteristic
304C22×C8—42no—
305C22×C8C4×D1114yescomplemented
306C22×C8C22×D1112yes—
307C22×C8C22×D1111yescharacteristic
308C22×C8C22×D1111yescharacteristic
309C4×D4—224no—
310C4×D4—442no—
311#117—444no—
312C2×C4⋊C4—114no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—222no—
320C2×C22⋊C4—221no—
321C2×C22⋊C4—221no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—444no—
326C2×C22⋊C4D4411yescharacteristic
327C2×C22⋊C4D4411yescharacteristic
328C2×C42—222no—
329C2×C42C22×D1112yes—
330#107—442no—
331#102—114no—
332#102—114no—
333#102—114no—
334#102—114no—
335#102—224no—
336#102—442no—
337C22⋊C8—22no—
338C4×C8—42no—
339#95—222no—
340#95—221no—
341#95—221no—
342#95—222no—
343#95D4412yes—
344C2×C11—24no—
345C2×C11#234211yescharacteristic
346C2×C11C2×C4×D811yescharacteristic
347C2×C11#294911yescharacteristic
348C2×C11#329412yes—
349C2×C11#329612yes—
350D11—44no—
351D11—82no—
352C24—221no—
353C24—221no—
354C24—224no—
355C24—444no—
356C24—442no—
357C24—442no—
358C24—882no—
359C24C2×D4411yescharacteristic
360C2×D4—112no—
361C2×D4—112no—
362C2×D4—114no—
363C2×D4—228no—
364C2×D4—224no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—222no—
370C2×D4—444no—
371C2×D4—448no—
372C2×D4—444no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—224no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—444no—
381C22×C4—442no—
382C22×C4—442no—
383C22×C4—444no—
384C22×C4—882no—
385C22×C4C2×C4×D1112yes—
386C22×C4C2×D4412yes—
387C22×C4C2×D4411yescharacteristic
388C22×C4C2×D4412yes—
389C22×C4#433912yes—
390C22×C4C23×D1111yescharacteristic
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—44no—
397C2×C8C2×C4×D1112yes—
398C2×C8C2×C4×D1112yes—
399C4⋊C4—112no—
400C4⋊C4—112no—
401C4⋊C4—224no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—444no—
409C22⋊C4—22no—
410C22⋊C4—444no—
411C22⋊C4—442no—
412C22⋊C4—442no—
413C22⋊C4—444no—
414C22⋊C4—882no—
415C22⋊C4D8814yes—
416C42—22no—
417C42—22no—
418C42—444no—
419C11#2257011yescharacteristic, complemented, Sylow
420C23—22no—
421C23—22no—
422C23—222no—
423C23—224no—
424C23—222no—
425C23—448no—
426C23—441no—
427C23—441no—
428C23—442no—
429C23—441no—
430C23—441no—
431C23—442no—
432C23—448no—
433C23—442no—
434C23—884no—
435C23—888no—
436C23—888no—
437C23C4×D4412yes—
438C23C2×D8812yes—
439C23#6695712yes—
440C23C22×D4411yescharacteristic
441D4—114no—
442D4—222no—
443D4—222no—
444D4—222no—
445D4—224no—
446D4—448no—
447D4—442no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—448no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—888no—
471C2×C4C4×D4412yes—
472C2×C4C2×D8814yes—
473C2×C4C22×C4×D1111yescharacteristic
474C2×C4C2×#433911yescharacteristic
475C2×C4#6703712yes—
476C2×C4#41×D1112yes—
477C8—22no—
478C8—22no—
479C8—42no—
480C22—22no—
481C22—24no—
482C22—24no—
483C22—22no—
484C22—224no—
485C22—444no—
486C22—442no—
487C22—444no—
488C22—442no—
489C22—442no—
490C22—442no—
491C22—442no—
492C22—8816no—
493C22—882no—
494C22—882no—
495C22C4×D8814yes—
496C22C2×C4×D4411yescharacteristic
497C22#1062308512yes—
498C22C22×D8811yescharacteristic
499C22C2×#6695711yescharacteristic
500C22#1062328212yes—
501C4—22no—
502C4—24no—
503C4—42no—
504C4—442no—
505C4—442no—
506C4—882no—
507C4—882no—
508C4#1062301711yescharacteristic
509C4D11×#11711yescharacteristic
510C4#1062308712yes—
511C2—24no—
512C2—444no—
513C2—882no—
514C2#1307146811yescharacteristic
515C2C2×C4×D8811yescharacteristic
516C2#1307747711yescharacteristic
517C2#1308043012yes—
518C2#1308045312yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterC8×C22⋊C4D11
hypocenterC11#22570
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071483C2semidirect
4. #13069299C2semidirect
5. #13069237C2semidirect
6. #13068866C2semidirect
7. #13068703C2semidirect
8. #13068645C2semidirect
10. C4×#66885C2semidirect
11. C8×C11×C22⋊C4C2semidirect
19. C2×C4×C8×C11C22semidirect
23. C2×#66885C4semidirect
30. C2×#66882C22semidirect
34. C4×C4⋊Dic11C22semidirect
35. #10622541C22semidirect
38. C11×#336C22semidirect
39. #10622189C22semidirect
40. #10622189C22semidirect
41. #10622189C22semidirect
54. C22×C8×C11C2×C4semidirect
68. C2×C4⋊Dic11C2×C4semidirect
90. #66885C2×C4semidirect
91. #66885C2×C4semidirect
171. C8×C22⋊C4D11semidirect
227. D44#117semidirect
247. C2×C4×C8C2×D11semidirect
261. #336C2×D11semidirect
305. C22×C8C4×D11semidirect
419. C11#22570semidirect

Maximal subgroups

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

subgroupindex
C22×#668852
#130714832
C22⋊C4×D442
#130692992
#130692372
#130688662
#130687032
#130686452
#130685482
C4×#668852
C8×C11×C22⋊C42
#2257011