Finite Group Databasebeta

← #14770873

Subgroups — #14770873

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66885C211yesmaximal, characteristic
2#13071491C211yesmaximal, characteristic, complemented
3C22⋊C4×D44C211yesmaximal, characteristic
4#13069313C212yesmaximal, complemented
5#13069237C212yesmaximal, complemented
6#13068866C212yesmaximal, complemented
7#13068707C211yesmaximal, characteristic, complemented
8#13068645C211yesmaximal, characteristic, complemented
9#13068548C211yesmaximal, characteristic
10#13068442C212yesmaximal, complemented
11C11×#1752C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C2×C22⋊C4×D11—21no—
16C2×C4×D44C2212yes—
17C2×C11×C22⋊C8C2211yescharacteristic
18C2×C11×#97C2212yescomplemented
19C4×C11×C22⋊C4C2211yescharacteristic
20#10622825C2211yescharacteristic
21#10622825C2211yescharacteristic
22C2×#66885C418yescomplemented
23C2×#66885C2212yes—
24C2×#66885C2212yes—
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66882C2212yescomplemented
30#10622568—21no—
31#10622555—21no—
32C22⋊C4×Dic11—21no—
33#10622552C2212yes—
34C4×C4⋊Dic11C2212yescomplemented
35#10622541C2212yescomplemented
36#10622278—22no—
37#10622267—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—
76C4×D44—24no—
77C4×D44—42no—
78C11×C22⋊C8—22no—
79C11×#97—42no—
80C11×#95D412yes—
81C11⋊#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—21no—
85#66885—24no—
86#66885—42no—
87#66885C2×C414yes—
88#66885C2×C414yes—
89#66885C2×C414yescomplemented
90#66885C2×C414yescomplemented
91#66882—42no—
92#22566—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C23×D11—21no—
95C23×D11—21no—
96C23×D11—24no—
97C23×D11—44no—
98C23×D11—42no—
99C23×D11—42no—
100C23×D11—82no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4112yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—24no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—82no—
115C2×D44—28no—
116C2×D44—24no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—44no—
123C2×D44—44no—
124C2×D44—48no—
125C2×D44C22×C412yes—
126C2×D44C22×C412yes—
127C2×D44#4114yes—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11—82no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—44no—
137C2×C8×C11C22×C412yes—
138C2×C8×C11C22×C412yes—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C42×C11—22no—
142C42×C11—22no—
143C22⋊Dic11—42no—
144C22⋊Dic11—42no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—44no—
147(C2×D11)⋊C4—82no—
148C4⋊Dic11—24no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11C22×C412yes—
156C4⋊Dic11C22×C412yes—
157Dic11⋊C4—82no—
158C4×Dic11—82no—
159C22×#102—111no—
160#2345—111no—
161D4×C22⋊C4—111no—
162#1936—112no—
163#1925—112no—
164#1862—112no—
165#1824—111no—
166#1808—111no—
167#1786—111no—
168#1762—112no—
169#1752D1111yescharacteristic, complemented
170C23×C11—22no—
171C23×C11—22no—
172C23×C11C4×D412yes—
173C23×C11AGL(1,ℤ/8)12yes—
174C23×C11#13712yes—
175C23×C11C22×D411yescharacteristic
176C22×D11—22no—
177C22×D11—24no—
178C22×D11—22no—
179C22×D11—48no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—42no—
187C22×D11—48no—
188C22×D11—84no—
189C22×D11—88no—
190C22×D11—88no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4112yes—
205C2×C4×C11H(5,𝔽2)12yes—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—84no—
217D44—22no—
218D44—22no—
219D44—22no—
220D44—24no—
221D44—48no—
222D44—42no—
223D44#11714yes—
224C4×D11—88no—
225C8×C11—22no—
226C8×C11—22no—
227C8×C11—42no—
228C23×D4—111no—
229C23×C8C2×D1111yescharacteristic
230C2×C4×D4—112no—
231C22×C4⋊C4—111no—
232C22×C22⋊C4—221no—
233C2×#107—112no—
234C2×#102—111no—
235C2×#102—111no—
236C2×#102—111no—
237C2×#102—111no—
238C2×#102—118no—
239C2×#102—112no—
240C2×#102—112no—
241C2×C22⋊C8C2×D1111yescharacteristic
242C2×#97C2×D1112yescomplemented
243#390—112no—
244#389—112no—
245#387—222no—
246#386—222no—
247#380—111no—
248#380—111no—
249#380—221no—
250#379—221no—
251C4×C4⋊C4—112no—
252C4×C22⋊C4—221no—
253C4×C22⋊C4C2×D1111yescharacteristic
254#340—112no—
255#340—112no—
256#340—112no—
257#336C2×D1112yescomplemented
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—24no—
261C22×C11—24no—
262C22×C11#44014yes—
263C22×C11C2×C4×D411yescharacteristic
264C22×C11#54612yes—
265C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C22×C11#57612yes—
268C2×D11—24no—
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—44no—
272C2×D11—44no—
273C2×D11—42no—
274C2×D11—42no—
275C2×D11—42no—
276C2×D11—816no—
277C2×D11—82no—
278C2×D11—82no—
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11C2×#11711yescharacteristic
283C4×C11#51811yescharacteristic
284C4×C11#55112yes—
285Dic11—42no—
286Dic11—42no—
287Dic11—82no—
288Dic11—82no—
289C25—221no—
290C22×D4—114no—
291C22×D4—111no—
292C22×D4—111no—
293C22×D4—224no—
294C22×D4—221no—
295C22×D4—222no—
296C22×D4—442no—
297C23×C4—221no—
298C23×C4—222no—
299C23×C4C22×D1111yescharacteristic
300C22×C8—42no—
301C22×C8C4×D1114yescomplemented
302C22×C8C22×D1112yes—
303C22×C8C22×D1111yescharacteristic
304C22×C8C22×D1111yescharacteristic
305C4×D4—224no—
306C4×D4—442no—
307C2×C4⋊C4—114no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C22⋊C4—221no—
316C2×C22⋊C4—221no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—444no—
321C2×C22⋊C4D4411yescharacteristic
322C2×C22⋊C4D4411yescharacteristic
323C2×C42—222no—
324C2×C42C22×D1112yes—
325#107—442no—
326#102—114no—
327#102—114no—
328#102—114no—
329#102—114no—
330#102—224no—
331#102—442no—
332C22⋊C8—22no—
333#97—42no—
334#95—222no—
335#95—222no—
336#95—221no—
337#95—221no—
338#95D4412yes—
339C2×C11—24no—
340C2×C11#234211yescharacteristic
341C2×C11C2×#44011yescharacteristic
342C2×C11#294811yescharacteristic
343C2×C11#331412yes—
344C2×C11#331812yes—
345D11—44no—
346D11—82no—
347C24—221no—
348C24—221no—
349C24—224no—
350C24—444no—
351C24—442no—
352C24—442no—
353C24—882no—
354C24C2×D4411yescharacteristic
355C2×D4—112no—
356C2×D4—112no—
357C2×D4—114no—
358C2×D4—228no—
359C2×D4—224no—
360C2×D4—221no—
361C2×D4—221no—
362C2×D4—222no—
363C2×D4—222no—
364C2×D4—222no—
365C2×D4—444no—
366C2×D4—448no—
367C2×D4—444no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—224no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—444no—
376C22×C4—444no—
377C22×C4—882no—
378C22×C4—882no—
379C22×C4C2×C4×D1112yes—
380C22×C4C2×D4412yes—
381C22×C4C2×D4412yes—
382C22×C4C2×D4411yescharacteristic
383C22×C4#433912yes—
384C22×C4C23×D1111yescharacteristic
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—44no—
391C2×C8C2×C4×D1112yes—
392C2×C8C2×C4×D1112yes—
393C4⋊C4—112no—
394C4⋊C4—112no—
395C4⋊C4—224no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4—882no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—444no—
406C22⋊C4—444no—
407C22⋊C4—442no—
408C22⋊C4—442no—
409C22⋊C4—882no—
410C42—22no—
411C42—22no—
412C42—882no—
413C11#2256611yescharacteristic, complemented, Sylow
414C23—22no—
415C23—22no—
416C23—222no—
417C23—224no—
418C23—222no—
419C23—448no—
420C23—441no—
421C23—441no—
422C23—442no—
423C23—441no—
424C23—441no—
425C23—442no—
426C23—442no—
427C23—448no—
428C23—884no—
429C23—888no—
430C23—888no—
431C23C4×D4412yes—
432C23#6696112yes—
433C23#6696212yes—
434C23C22×D4411yescharacteristic
435D4—114no—
436D4—222no—
437D4—222no—
438D4—222no—
439D4—224no—
440D4—448no—
441D4—442no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—888no—
463C2×C4—884no—
464C2×C4C4×D4412yes—
465C2×C4C22×C4×D1111yescharacteristic
466C2×C4C2×#433911yescharacteristic
467C2×C4#6703712yes—
468C2×C4#41×D1112yes—
469C8—22no—
470C8—22no—
471C8—42no—
472C22—22no—
473C22—24no—
474C22—24no—
475C22—22no—
476C22—224no—
477C22—444no—
478C22—442no—
479C22—444no—
480C22—442no—
481C22—442no—
482C22—442no—
483C22—442no—
484C22—8816no—
485C22—882no—
486C22—882no—
487C22#1062232314yes—
488C22C2×C4×D4411yescharacteristic
489C22#1062308512yes—
490C22C2×#6696111yescharacteristic
491C22C2×#6696211yescharacteristic
492C22#1062328312yes—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—442no—
497C4—442no—
498C4—882no—
499C4—882no—
500C4#1062301711yescharacteristic
501C4D11×#11711yescharacteristic
502C4#1062308712yes—
503C2—24no—
504C2—444no—
505C2—882no—
506C2#1307146811yescharacteristic
507C2C2×#1062232311yescharacteristic
508C2#1307746911yescharacteristic
509C2#1308069912yes—
510C2#1308075912yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22566
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. #13071491C2semidirect
4. #13069313C2semidirect
5. #13069237C2semidirect
6. #13068866C2semidirect
7. #13068707C2semidirect
8. #13068645C2semidirect
10. #13068442C2semidirect
11. C11×#1752C2semidirect
18. C2×C11×#97C22semidirect
22. C2×#66885C4semidirect
29. 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
89. #66885C2×C4semidirect
90. #66885C2×C4semidirect
169. #1752D11semidirect
242. C2×#97C2×D11semidirect
257. #336C2×D11semidirect
301. C22×C8C4×D11semidirect
413. C11#22566semidirect

Maximal subgroups

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

subgroupindex
C22×#668852
#130714912
C22⋊C4×D442
#130693132
#130692372
#130688662
#130687072
#130686452
#130685482
#130684422
C11×#17522
#2256611