Finite Group Databasebeta

← #14769413

Subgroups — #14769413

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623258C211yesmaximal, characteristic
2C2×#10622301C211yesmaximal, characteristic
3C2×#10622415C212yesmaximal, complemented
4#13071567C211yesmaximal, characteristic
5#13069540C211yesmaximal, characteristic, complemented
6#13069046C212yesmaximal, complemented
7#13068925C212yesmaximal, complemented
8#13068618C211yesmaximal, characteristic, complemented
9#13068549C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C11×#1956C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999C2212yes—
15C22×#4313C2212yes—
16#10623258—24no—
17#10623258C418yescomplemented
18C2×#66949—22no—
19C2×#66946—21no—
20C2×#66945C2212yes—
21C2×#66941—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#384C2211yescharacteristic
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33#10622603—22no—
34#10622601—21no—
35#10622600C2212yes—
36C4⋊C4×Dic11—21no—
37C2×#66874C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622415—28no—
41#10622301—24no—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44#10622167C2212yes—
45C22×Q8×C11C2312yes—
46C2×Q8×D11—24no—
47C2×Q8×D11—24no—
48C2×Q8×D11—24no—
49C2×Q8×D11—42no—
50C2×Q8×D11—42no—
51C2×Q8×D11C2×C418yes—
52C22×D44D411yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11C2312yes—
55C22×Dic22—22no—
56C22×Dic22C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8C2×C414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2312yes—
66C2×C42×C11C2311yescharacteristic
67#66999—24no—
68#66999C2×C418yes—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4D412yes—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—22no—
82C22×C11⋊C8C2312yes—
83C2×#4313—24no—
84C2×#4313—24no—
85C2×#4313—42no—
86#66949—216no—
87#66946—28no—
88#66945—24no—
89#66945—42no—
90#66941—28no—
91C4×D44C2×C414yes—
92C4×D44D414yes—
93C4×Dic22—22no—
94C4×Dic22C2×C414yes—
95C11×#103—24no—
96C11×#103—42no—
97C4×C8×C11—22no—
98#66899—24no—
99#66899—42no—
100C11⋊#95—21no—
101C11⋊#95—22no—
102(C2×D11)⋊C8—24no—
103#66880—22no—
104#66880D414yescomplemented
105#66874—24no—
106C4⋊(C11⋊C8)—22no—
107#22430—111nomaximal, Sylow
108C23×D11C2×D412yes—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C414yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11C2×D412yes—
125Q8×D11—216no—
126Q8×D11—48no—
127Q8×D11—48no—
128Q8×D11—48no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44C22⋊C414yes—
132C2×C4×D11—28no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—44no—
138C2×C4×D11—44no—
139C2×C4×D11C22×C414yes—
140C2×C4×D11C2×D414yes—
141C2×Dic22—28no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—44no—
146C2×Dic22—44no—
147C2×Dic22C22×C412yes—
148C2×Dic22C2×D412yes—
149C2×Dic22#4112yes—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C2×D412yes—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—81no—
162C42×C11C22×C412yes—
163C42×C11C2×D412yes—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—44no—
166(C2×D11)⋊C4—82no—
167(C2×D11)⋊C4C22⋊C418yes—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11C22⋊C414yes—
173C4⋊Dic11C22×C412yes—
174C4⋊Dic11C2×D412yes—
175Dic11⋊C4—28no—
176Dic11⋊C4—24no—
177C4×Dic11—24no—
178C4×Dic11—44no—
179C4×Dic11—42no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183#4313—48no—
184C2×D4×Q8—111no—
185C2×#436—111no—
186C2×#419—112no—
187#2354—111no—
188#1981—111no—
189#1956D1111yescharacteristic, complemented
190#1894—112no—
191#1873—112no—
192#1803—111no—
193#1787—112no—
194C4×#103—111no—
195C23×C11C22×D411yescharacteristic
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11C2×C22⋊C414yes—
203Q8×C11—24no—
204Q8×C11—24no—
205Q8×C11—42no—
206Q8×C11—42no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11#13712yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C23×C411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11C2×C22⋊C414yes—
240D44—28no—
241C4×D11—24no—
242C4×D11—24no—
243C4×D11—24no—
244C4×D11—24no—
245C4×D11—416no—
246Dic22—22no—
247Dic22—22no—
248Dic22—22no—
249Dic22—416no—
250Dic22C4×D414yes—
251C8×C11—22no—
252C8×C11—41no—
253C11⋊C8—42no—
254C23×Q8—112no—
255C22×M16—112no—
256D4×Q8—118no—
257D4×Q8—224no—
258C2×C4⋊Q8—221no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×C22⋊Q8—112no—
261C2×C22⋊Q8—222no—
262C2×C4×Q8—111no—
263C2×C4×D4—111no—
264C2×C4×D4—221no—
265C2×#117—112no—
266#436—224no—
267C2×C4⋊C8—111no—
268#419—228no—
269C2×#103—111no—
270C2×#103—112no—
271C2×#103—111no—
272C2×#103—112no—
273C2×#103—112no—
274C2×#103C2×D1112yes—
275C2×#103C2×D1112yes—
276C2×C22⋊C8—112no—
277C2×C4×C8C2×D1111yescharacteristic
278#390—221no—
279#388—222no—
280#384C2×D1111yescharacteristic
281#380—112no—
282C4×C4⋊C4—111no—
283C4×C4⋊C4—221no—
284#340—111no—
285#340—111no—
286#340—112no—
287C22×C11C22×C22⋊C411yescharacteristic
288C22×C11D4211yescharacteristic
289C22×C11#54611yescharacteristic
290C22×C11C2×#13711yescharacteristic
291C22×C11C2×#13711yescharacteristic
292C22×C11#57711yescharacteristic
293C22×C11#57811yescharacteristic
294C2×D11—24no—
295C2×D11—24no—
296C2×D11—24no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C4×C11—22no—
302C4×C11—44no—
303C4×C11—82no—
304C4×C11#41914yescomplemented
305C4×C11C2×C4×D411yescharacteristic
306C4×C11#51811yescharacteristic
307C4×C11D4211yescharacteristic
308C4×C11#54611yescharacteristic
309Dic11—24no—
310Dic11—24no—
311Dic11—42no—
312Dic11—42no—
313Dic11—81no—
314C22×Q8—118no—
315C22×Q8—111no—
316C22×Q8—222no—
317C22×Q8—224no—
318C22×Q8—224no—
319C22×Q8—224no—
320C22×Q8—442no—
321C22×Q8—442no—
322C22×Q8C22×D1112yes—
323C22×D4—111no—
324C23×C4—112no—
325C23×C4—222no—
326C2×M16—224no—
327C2×M16—224no—
328C2×M16—442no—
329C22×C8—112no—
330C22×C8C22×D1111yescharacteristic
331C22×C8C22×D1111yescharacteristic
332C4⋊Q8—22no—
333C4⋊Q8—228no—
334C4⋊Q8C4×D1114yes—
335C22⋊Q8—118no—
336C22⋊Q8—2216no—
337C22⋊Q8—224no—
338C4×Q8—114no—
339C4×Q8—222no—
340C4×D4—114no—
341C4×D4—114no—
342C4×D4—228no—
343#117—224no—
344#117—442no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4C22×D1112yes—
356C2×C22⋊C4—112no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—221no—
361C2×C42—222no—
362C2×C42—221no—
363C2×C42C22×D1111yescharacteristic
364C4⋊C8—222no—
365#103—24no—
366#103—42no—
367#103—114no—
368#103—224no—
369#103—224no—
370#103—222no—
371#103—442no—
372C22⋊C8—224no—
373C4×C8—22no—
374#95—222no—
375#95—221no—
376C2×C11D4×C22⋊C411yescharacteristic
377C2×C11C2×#41911yescharacteristic
378C2×C11#289811yescharacteristic
379C2×C11#327611yescharacteristic
380C2×C11#327811yescharacteristic
381C2×C11#332811yescharacteristic
382C2×C11#332911yescharacteristic
383D11—44no—
384C24—112no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—112no—
391C2×Q8—112no—
392C2×Q8—112no—
393C2×Q8—228no—
394C2×Q8—221no—
395C2×Q8—221no—
396C2×Q8—221no—
397C2×Q8—2216no—
398C2×Q8—444no—
399C2×Q8—444no—
400C2×Q8—448no—
401C2×Q8—448no—
402C2×Q8—448no—
403C2×Q8C2×C4×D1114yes—
404C2×D4—114no—
405C2×D4—222no—
406C2×D4—222no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—112no—
410C22×C4—114no—
411C22×C4—114no—
412C22×C4—228no—
413C22×C4—221no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—444no—
422C22×C4—444no—
423C22×C4D4×D1111yescharacteristic
424C22×C4D4×D1111yescharacteristic
425C22×C4C23×D1111yescharacteristic
426M16—448no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8D4×D1112yes—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—42no—
441C4⋊C4—81no—
442C4⋊C4—114no—
443C4⋊C4—112no—
444C4⋊C4—112no—
445C4⋊C4—228no—
446C4⋊C4—224no—
447C4⋊C4—221no—
448C4⋊C4—221no—
449C4⋊C4—221no—
450C4⋊C4—221no—
451C22⋊C4—118no—
452C22⋊C4—228no—
453C22⋊C4—444no—
454C22⋊C4—882no—
455C42—224no—
456C42—444no—
457C42—442no—
458C42C2×C4×D1112yes—
459C42D4×D1112yes—
460C11#2243011yescharacteristic, complemented, Sylow
461C23—114no—
462C23—222no—
463C23—222no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—222no—
468C23C2×D4×D1111yescharacteristic
469Q8—24no—
470Q8—24no—
471Q8—42no—
472Q8—42no—
473Q8—114no—
474Q8—222no—
475Q8—222no—
476Q8—222no—
477Q8—4416no—
478D4—228no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—114no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—4416no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4C22⋊C4×D1112yes—
508C2×C4C22⋊C4×D1112yes—
509C2×C4#6696812yes—
510C2×C4#6697112yes—
511C2×C4C22×C4×D1111yescharacteristic
512C2×C4C2×D4×D1111yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4#6703711yescharacteristic
515C2×C4#41×D1111yescharacteristic
516C2×C4#6704211yescharacteristic
517C8—22no—
518C8—41no—
519C8—442no—
520C22—224no—
521C22—224no—
522C22—224no—
523C22—442no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22C2×C22⋊C4×D1111yescharacteristic
528C22#1062320711yescharacteristic
529C22#1062324811yescharacteristic
530C22C2×#6696811yescharacteristic
531C22#1062329311yescharacteristic
532C22C2×#6697111yescharacteristic
533C22#1062329711yescharacteristic
534C4—22no—
535C4—44no—
536C4—82no—
537C4—224no—
538C4—224no—
539C4—442no—
540C4—442no—
541C4—881no—
542C4#1062241514yescomplemented
543C4C4×D4×D1111yescharacteristic
544C4#1062307611yescharacteristic
545C4#1062314011yescharacteristic
546C4#1062314311yescharacteristic
547C2—444no—
548C2#1307143711yescharacteristic
549C2C2×#1062241511yescharacteristic
550C2#1307714411yescharacteristic
551C2#1308026111yescharacteristic
552C2#1308028111yescharacteristic
553C2#1308089811yescharacteristic
554C2#1308090911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1956D11
hypocenterC11#22430
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
3. C2×#10622415C2semidirect
5. #13069540C2semidirect
6. #13069046C2semidirect
7. #13068925C2semidirect
8. #13068618C2semidirect
9. #13068549C2semidirect
10. C4×#66880C2semidirect
11. C11×#1956C2semidirect
17. #10623258C4semidirect
104. #66880D4semidirect
189. #1956D11semidirect
304. C4×C11#419semidirect
460. C11#22430semidirect
542. C4#10622415semidirect

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×#106223012
C2×#106224152
#130715672
#130695402
#130690462
#130689252
#130686182
#130685492
C4×#668802
C11×#19562
#2243011