Finite Group Databasebeta

← #14787814

Subgroups — #14787814

Order 2816.

1400 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3#13073513C211yesmaximal, characteristic, complemented
4#13069803C212yesmaximal, complemented
5#13069611C212yesmaximal, complemented
6#13069589C211yesmaximal, characteristic, complemented
7#13069414C211yesmaximal, characteristic, complemented
8#13068930C212yesmaximal, complemented
9#13068807C212yesmaximal, complemented
10#13068626C211yesmaximal, characteristic, complemented
11C2×C11×#442C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C22×C11×D8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66991C2212yes—
17C2×#66991C2212yes—
18C2×#66977—21no—
19#10623082—24no—
20#10623082—24no—
21C2×C4⋊C4×D11C2212yes—
22C2×#66936—22no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C11×#442—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×#66896C2212yes—
31C2×#66896C2212yes—
32#10622826—22no—
33C2×(C2×D11)⋊C8C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35#10622621—24no—
36#10622600C2212yes—
37C2×#66872C2212yes—
38#10622573—21no—
39#10622566—21no—
40#10622549C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45C22×D4×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C2×#4339—28no—
52C2×#4339—48no—
53C22×D44D411yescharacteristic
54C22×C4×D11—22no—
55C22×C4×D11C2312yes—
56C22×Dic22—21no—
57C2×C11×D8—22no—
58C2×C11×D8—22no—
59C2×C11×D8—22no—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C4×D4×C11D414yescomplemented
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73#66991—24no—
74#66991—24no—
75#66991—24no—
76#66991—42no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4D412yes—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2312yes—
82C2×C4⋊Dic11C2312yes—
83#66977—28no—
84C2×Dic11⋊C4—22no—
85C22×C11⋊C8C2312yes—
86C4⋊C4×D11—24no—
87C4⋊C4×D11—24no—
88#66936—216no—
89C4×D44—22no—
90C4×D44—22no—
91#66922—22no—
92#66922D414yescomplemented
93C11×#106—22no—
94C11×#102—22no—
95C11×#102—22no—
96C11×#97—22no—
97#66896—24no—
98#66896—42no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—22no—
102(C2×D11)⋊C8—24no—
103(C2×D11)⋊C8—42no—
104#66872—24no—
105C4⋊(C11⋊C8)—22no—
106#24128—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C23×D11C2×D412yes—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11C2×D412yes—
121C2×D4×C11#4112yescomplemented
122C22×C4×C11—21no—
123C22×C4×C11—24no—
124C22×C4×C11—21no—
125C22×C4×C11—44no—
126C22×C4×C11—42no—
127C22×C4×C11—82no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—28no—
132C2×C22⋊D11—44no—
133C2×C22⋊D11—44no—
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—82no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11C2×D412yes—
140#4339—432no—
141C2×D44—24no—
142C2×D44—22no—
143C2×C4×D11—28no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—44no—
151C2×C4×D11—44no—
152C2×Dic22—24no—
153C2×Dic22—44no—
154C11×D8—28no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11#4112yescomplemented
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—42no—
167C42×C11C2×D412yes—
168C42×C11C2×D412yes—
169C22⋊Dic11—28no—
170C22⋊Dic11—44no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—82no—
173C4⋊Dic11—24no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11C2×D414yes—
179Dic11⋊C4—28no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×#547—111no—
184C2×#476—111no—
185C2×#442D1111yescharacteristic, complemented
186#2535—111no—
187#2034—112no—
188#1999—112no—
189#1993—111no—
190#1955—111no—
191#1874—112no—
192#1853—112no—
193#1804—111no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11AGL(1,ℤ/8)14yes—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219D4×C11—41no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—48no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—84no—
228C2×C4×C11#12012yes—
229C2×C4×C11#12012yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C112−1+411yescharacteristic
236C22⋊D11—416no—
237C22⋊D11—88no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247D44—28no—
248C4×D11—416no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—42no—
253Dic22—48no—
254C8×C11—22no—
255C8×C11—41no—
256C11⋊C8—42no—
257C22×#41—221no—
258C22×D8C2×D1111yescharacteristic
259#547—224no—
260#547—224no—
261C2×C4⋊Q8—111no—
262C2×#123—222no—
263C2×C22⋊Q8—221no—
264C2×#121—112no—
265C2×#121—112no—
266C2×C4×D4—111no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×C4×D4C2×D1111yescharacteristic
269C22×C4⋊C4—112no—
270#476—224no—
271#442—24no—
272C2×#106—112no—
273C2×#106C2×D1111yescharacteristic
274C2×C4⋊C8—111no—
275C2×#102—112no—
276C2×#102—112no—
277C2×#102C2×D1111yescharacteristic
278C2×#102C2×D1111yescharacteristic
279C2×C22⋊C8—112no—
280C2×C22⋊C8—112no—
281C2×#97C2×D1111yescharacteristic
282#397—221no—
283#392—221no—
284#386—222no—
285#382—111no—
286#380—112no—
287#340—112no—
288#340—112no—
289#340—112no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—44no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—82no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#54611yescharacteristic
302C22×C11#54711yescharacteristic
303C22×C11C2×AGL(1,ℤ/8)12yes—
304C22×C11#57712yes—
305C2×D11—24no—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—81no—
316C4×C11#52511yescharacteristic
317C4×C11#53711yescharacteristic
318C4×C11#54811yescharacteristic
319C4×C11#55011yescharacteristic
320Dic11—42no—
321Dic11—44no—
322Dic11—82no—
323C2×#41—228no—
324C2×#41—448no—
325C22×Q8—221no—
326C22×D4—111no—
327C22×D4—222no—
328C22×D4—222no—
329C22×D4C22×D1111yescharacteristic
330C22×D4C22×D1111yescharacteristic
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—112no—
334C23×C4—222no—
335C2×D8—22no—
336C2×D8—22no—
337C2×D8—22no—
338C22×C8—112no—
339C22×C8C22×D1111yescharacteristic
340C22×C8C22×D1111yescharacteristic
341C4⋊Q8—114no—
342C4⋊Q8—222no—
343#123—2216no—
344C22⋊Q8—228no—
345#121—224no—
346#121—224no—
347#121—224no—
348#121—442no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—222no—
353C4×D4—222no—
354C4×D4C22⋊D1114yescomplemented
355C2×C4⋊C4—112no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—112no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C42C22×D1111yescharacteristic
371#106—22no—
372#106—224no—
373C4⋊C8—222no—
374#102—22no—
375#102—22no—
376#102—224no—
377#102—442no—
378C22⋊C8—224no—
379C22⋊C8—442no—
380#97—22no—
381#95—222no—
382#95—221no—
383#95—221no—
384C2×C11—82no—
385C2×C11—82no—
386C2×C11#240711yescharacteristic
387C2×C11#300311yescharacteristic
388C2×C11#301011yescharacteristic
389C2×C11#330612yes—
390C2×C11#334512yes—
391D11—44no—
392C24—21no—
393C24—21no—
394C24—112no—
395#41—4432no—
396C2×Q8—224no—
397C2×Q8—444no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—224no—
409C2×D4—228no—
410C2×D4—222no—
411C2×D4—444no—
412C2×D4—444no—
413C2×D4—444no—
414C2×D4—444no—
415C2×D4—882no—
416C2×D4#433912yescomplemented
417C2×D4C2×C22⋊D1112yes—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—44no—
422C22×C4—42no—
423C22×C4—82no—
424C22×C4—112no—
425C22×C4—228no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—444no—
435C22×C4—444no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439D8—28no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—222no—
446C2×C8—222no—
447C2×C8—222no—
448C2×C8#433912yescomplemented
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—114no—
453C4⋊C4—228no—
454C4⋊C4—222no—
455C4⋊C4—224no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4C2×C22⋊D1112yes—
460C22⋊C4—24no—
461C22⋊C4—42no—
462C22⋊C4—228no—
463C22⋊C4—224no—
464C22⋊C4—444no—
465C22⋊C4—882no—
466C42D4×D1112yes—
467C42C2×C22⋊D1112yes—
468C11#2412811yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—114no—
480C23—222no—
481C23—222no—
482C23—222no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23C2×D4×D1111yescharacteristic
487Q8—448no—
488D4—22no—
489D4—22no—
490D4—22no—
491D4—22no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—228no—
497D4—4416no—
498D4—888no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—48no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—84no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—4416no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4#6699012yes—
522C2×C4#6699012yes—
523C2×C4C2×#433911yescharacteristic
524C2×C4C2×#433911yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4#6704211yescharacteristic
527C2×C4#6704311yescharacteristic
528C2×C4C22×C22⋊D1111yescharacteristic
529C8—22no—
530C8—41no—
531C8—442no—
532C22—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—82no—
538C22—82no—
539C22—82no—
540C22—81no—
541C22—81no—
542C22—224no—
543C22—224no—
544C22—224no—
545C22—442no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22#1062308111yescharacteristic
550C22#1062308211yescharacteristic
551C22D11×AGL(1,ℤ/8)12yes—
552C22#1062330612yes—
553C22C2×#6699011yescharacteristic
554C4—22no—
555C4—22no—
556C4—42no—
557C4—81no—
558C4—444no—
559C4—442no—
560C4—882no—
561C4#1062308311yescharacteristic
562C4#1062308411yescharacteristic
563C4#1062332211yescharacteristic
564C4#1062336411yescharacteristic
565C2—82no—
566C2—82no—
567C2—444no—
568C2#1307196111yescharacteristic
569C2#1307784111yescharacteristic
570C2#1307790111yescharacteristic
571C2#1308058212yes—
572C2#1308109112yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
hypercenterC2×#442D11
hypocenterC11#24128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#10623082C2semidirect
2. C2×#10622621C2semidirect
3. #13073513C2semidirect
4. #13069803C2semidirect
5. #13069611C2semidirect
6. #13069589C2semidirect
7. #13069414C2semidirect
8. #13068930C2semidirect
9. #13068807C2semidirect
10. #13068626C2semidirect
11. C2×C11×#442C2semidirect
65. C4×D4×C11D4semidirect
92. #66922D4semidirect
121. C2×D4×C11#41semidirect
160. C2×C8×C11#41semidirect
185. C2×#442D11semidirect
354. C4×D4C22⋊D11semidirect
416. C2×D4#4339semidirect
448. C2×C8#4339semidirect
468. C11#24128semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
C2×#106226212
#130735132
#130698032
#130696112
#130695892
#130694142
#130689302
#130688072
#130686262
C2×C11×#4422
#2412811