Finite Group Databasebeta

← #14770198

Subgroups — #14770198

Order 2816.

1370 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic
2C2×#10622301C211yesmaximal, characteristic, complemented
3#13071563C211yesmaximal, characteristic, complemented
4#13069577C211yesmaximal, characteristic, complemented
5#13069568C211yesmaximal, characteristic, complemented
6#13069051C212yesmaximal, complemented
7#13068935C212yesmaximal, complemented
8#13068705C212yesmaximal, complemented
9#13068616C211yesmaximal, characteristic, complemented
10#13068334C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66991C2212yes—
15C2×#66977—21no—
16C22×#4313C2212yes—
17#10623082—24no—
18#10623082C418yescomplemented
19C2×#66945C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×#66936—22no—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66896C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30#10622600C2212yes—
31#10622552—21no—
32#10622548C2211yescharacteristic
33C4×C4⋊Dic11—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622301—24no—
36#10622283—22no—
37C11×#340C2211yescharacteristic
38C11×#340C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×C22⋊D11—22no—
47C2×#4339—28no—
48C2×#4339—44no—
49C2×#4339—44no—
50C22×D44D411yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11C2312yes—
53C22×Dic22—21no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C4×D4×C11—22no—
57C4×D4×C11C2×C414yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—22no—
65#66991—24no—
66#66991C2×C418yes—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4D412yes—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2312yes—
76#66977—28no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—22no—
79C22×C11⋊C8C2312yes—
80C2×#4313—24no—
81C2×#4313—24no—
82C2×#4313—42no—
83#66945—24no—
84#66945—42no—
85C4⋊C4×D11—24no—
86C4⋊C4×D11C2×C418yes—
87#66936—216no—
88C4×D44C2×C414yes—
89C4×D44D414yes—
90#66922—22no—
91#66922C2×C414yes—
92C11×#102—22no—
93C11×#102—22no—
94C4×C8×C11—22no—
95C11×#95—21no—
96#66896—42no—
97C11⋊#95—22no—
98(C2×D11)⋊C8—24no—
99C4⋊(C11⋊C8)—22no—
100#22500—111nomaximal, Sylow
101C24×C11—21no—
102C23×D11C2×D412yes—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11C22×C412yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—21no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—28no—
119C2×C22⋊D11—44no—
120C2×C22⋊D11—44no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11C2×D412yes—
124#4339—432no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44C22⋊C414yes—
128C2×C4×D11—28no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—44no—
134C2×C4×D11—44no—
135C2×C4×D11C22×C414yes—
136C2×C4×D11C2×D414yes—
137C2×Dic22—24no—
138C2×Dic22—42no—
139C2×Dic22—42no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11#4112yescomplemented
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C22×C412yes—
151C11×C4⋊C4#4112yescomplemented
152C11×C22⋊C4—24no—
153C42×C11—42no—
154C42×C11C22×C412yes—
155C42×C11C2×D412yes—
156C22⋊Dic11—28no—
157(C2×D11)⋊C4—44no—
158(C2×D11)⋊C4—82no—
159(C2×D11)⋊C4C22⋊C418yes—
160C4⋊Dic11—24no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—42no—
165C4⋊Dic11—81no—
166C4⋊Dic11C22⋊C414yes—
167C4⋊Dic11C22×C414yes—
168Dic11⋊C4—28no—
169C4×Dic11—44no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173#4313—48no—
174C2×#547—111no—
175C2×#436—111no—
176#2354—111no—
177#1990—111no—
178#1988—111no—
179#1895—112no—
180#1875—112no—
181#1824—112no—
182#1802—111no—
183C4×#102D1111yescharacteristic, complemented
184#1736—112no—
185C23×C11—22no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11C22×D411yescharacteristic
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11C2×C22⋊C414yes—
200D4×C11—22no—
201D4×C11—22no—
202D4×C11—41no—
203D4×C11—41no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—48no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11AGL(1,ℤ/8)12yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C112−1+411yescharacteristic
226C22⋊D11—416no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11C2×C22⋊C414yes—
236D44—28no—
237C4×D11—24no—
238C4×D11—24no—
239C4×D11—24no—
240C4×D11—24no—
241C4×D11—416no—
242Dic22—48no—
243C8×C11—22no—
244C8×C11—41no—
245C11⋊C8—42no—
246C22×#41—221no—
247C22×M16—112no—
248#547—118no—
249#547—224no—
250C2×C4⋊Q8—111no—
251C2×#123—222no—
252C2×C22⋊Q8—221no—
253C2×#121—112no—
254C2×C4×D4—111no—
255C2×C4×D4C2×D1111yescharacteristic
256C2×#117—112no—
257C22×C4⋊C4—112no—
258#436—224no—
259C2×C4⋊C8—111no—
260C2×#102—112no—
261C2×#102C2×D1111yescharacteristic
262C2×#102C2×D1111yescharacteristic
263C2×C22⋊C8—112no—
264C2×C4×C8C2×D1111yescharacteristic
265#390—221no—
266#388—222no—
267#384—111no—
268#380—112no—
269C4×C4⋊C4—221no—
270C4×C4⋊C4C2×D1111yescharacteristic
271#340—112no—
272#340—112no—
273#340—112no—
274#340—112no—
275#340—112no—
276#340C2×D1111yescharacteristic
277#340C2×D1111yescharacteristic
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11C22×C22⋊C411yescharacteristic
286C22×C11#54611yescharacteristic
287C22×C11#54711yescharacteristic
288C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C11#57711yescharacteristic
291C22×C11#57811yescharacteristic
292C2×D11—24no—
293C2×D11—24no—
294C2×D11—24no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—81no—
303C4×C11#41814yes—
304C4×C11C4×#4111yescharacteristic
305C4×C11#52011yescharacteristic
306C4×C11#54611yescharacteristic
307C4×C11#54711yescharacteristic
308Dic11—24no—
309Dic11—44no—
310Dic11—82no—
311C2×#41—228no—
312C2×#41—444no—
313C2×#41—444no—
314C22×Q8—221no—
315C22×D4—111no—
316C22×D4—222no—
317C22×D4C22×D1111yescharacteristic
318C23×C4—21no—
319C23×C4—112no—
320C23×C4—222no—
321C2×M16—224no—
322C2×M16—224no—
323C2×M16—442no—
324C22×C8—112no—
325C22×C8C22×D1111yescharacteristic
326C22×C8C22×D1111yescharacteristic
327C4⋊Q8—114no—
328C4⋊Q8—222no—
329#123—2216no—
330C22⋊Q8—228no—
331#121—118no—
332#121—224no—
333C4×D4—22no—
334C4×D4—114no—
335C4×D4—114no—
336C4×D4C4×D1114yes—
337#117—224no—
338#117—442no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—118no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—224no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C4⋊C4C22×D1111yescharacteristic
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C22⋊C4—21no—
352C2×C22⋊C4—112no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C22⋊C4—222no—
356C2×C42—21no—
357C2×C42—222no—
358C2×C42C22×D1111yescharacteristic
359C4⋊C8—222no—
360#102—22no—
361#102—22no—
362#102—442no—
363C22⋊C8—224no—
364C4×C8—22no—
365#95—21no—
366#95—222no—
367C2×C11—82no—
368C2×C11#233911yescharacteristic
369C2×C11C2×#41811yescharacteristic
370C2×C11#289811yescharacteristic
371C2×C11#333011yescharacteristic
372C2×C11#333211yescharacteristic
373C2×C11#335311yescharacteristic
374C2×C11#335411yescharacteristic
375D11—44no—
376C24—21no—
377C24—112no—
378#41—4432no—
379C2×Q8—224no—
380C2×Q8—442no—
381C2×Q8—442no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—114no—
388C2×D4—228no—
389C2×D4—222no—
390C2×D4—222no—
391C2×D4—444no—
392C2×D4—444no—
393C2×D4C2×C4×D1112yes—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—24no—
397C22×C4—21no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—112no—
401C22×C4—114no—
402C22×C4—114no—
403C22×C4—228no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—444no—
411C22×C4—444no—
412C22×C4D4×D1111yescharacteristic
413C22×C4D4×D1111yescharacteristic
414C22×C4C23×D1111yescharacteristic
415M16—448no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8#433912yescomplemented
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—114no—
430C4⋊C4—114no—
431C4⋊C4—228no—
432C4⋊C4—224no—
433C4⋊C4—222no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—442no—
437C4⋊C4—881no—
438C4⋊C4C2×C4×D1112yes—
439C4⋊C4#433912yescomplemented
440C22⋊C4—24no—
441C22⋊C4—118no—
442C22⋊C4—228no—
443C22⋊C4—444no—
444C22⋊C4—882no—
445C42—42no—
446C42—444no—
447C42C2×C4×D1112yes—
448C42D4×D1112yes—
449C11#2250011yescharacteristic, complemented, Sylow
450C23—22no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—114no—
458C23—222no—
459C23—222no—
460C23—222no—
461C23—222no—
462C23—222no—
463C23—222no—
464C23C2×D4×D1111yescharacteristic
465Q8—448no—
466D4—22no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—228no—
471D4—4416no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—48no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—114no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—4416no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4C22⋊C4×D1112yes—
499C2×C4C22⋊C4×D1112yes—
500C2×C4#6696412yes—
501C2×C4#6696712yes—
502C2×C4C22×C4×D1111yescharacteristic
503C2×C4C2×#433911yescharacteristic
504C2×C4C2×#433911yescharacteristic
505C2×C4C2×D4×D1111yescharacteristic
506C2×C4#6704211yescharacteristic
507C2×C4#6704311yescharacteristic
508C8—22no—
509C8—41no—
510C8—442no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—224no—
519C22—224no—
520C22—224no—
521C22—442no—
522C22—442no—
523C22—442no—
524C22—442no—
525C22C2×C22⋊C4×D1111yescharacteristic
526C22#1062308111yescharacteristic
527C22#1062308211yescharacteristic
528C22C2×#6696411yescharacteristic
529C22C2×#6696711yescharacteristic
530C22#1062330111yescharacteristic
531C22#1062330211yescharacteristic
532C4—22no—
533C4—42no—
534C4—42no—
535C4—81no—
536C4—224no—
537C4—444no—
538C4—882no—
539C4#1062238314yes—
540C4C4×#433911yescharacteristic
541C4#1062305411yescharacteristic
542C4#1062308111yescharacteristic
543C4#1062308211yescharacteristic
544C2—82no—
545C2—444no—
546C2#1307144711yescharacteristic
547C2C2×#1062238311yescharacteristic
548C2#1307714511yescharacteristic
549C2#1308092311yescharacteristic
550C2#1308094511yescharacteristic
551C2#1308120211yescharacteristic
552C2#1308121311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#22500
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#10622301C2semidirect
3. #13071563C2semidirect
4. #13069577C2semidirect
5. #13069568C2semidirect
6. #13069051C2semidirect
7. #13068935C2semidirect
8. #13068705C2semidirect
9. #13068616C2semidirect
10. #13068334C2semidirect
11. C4×C11×#102C2semidirect
18. #10623082C4semidirect
145. C2×C8×C11#41semidirect
151. C11×C4⋊C4#41semidirect
183. C4×#102D11semidirect
424. C2×C8#4339semidirect
439. C4⋊C4#4339semidirect
449. C11#22500semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
C2×#106223012
#130715632
#130695772
#130695682
#130690512
#130689352
#130687052
#130686162
#130683342
C4×C11×#1022
#2250011