Finite Group Databasebeta

← #14770526

Subgroups — #14770526

Order 2816.

1172 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623096C211yesmaximal, characteristic
2#13071491C212yesmaximal, complemented
3#13069452C212yesmaximal, complemented
4#13069450C214yesmaximal, complemented
5#13068604C211yesmaximal, characteristic, complemented
6#13068603C212yesmaximal, complemented
7#13068403C212yesmaximal, complemented
8C4×C11×#99C211yesmaximal, characteristic, complemented
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66992C2212yes—
11C2×#66983C411yescharacteristic, complemented
12C2×#66983C2211yescharacteristic
13C2×#66979C411yescharacteristic, complemented
14C22×C4⋊Dic11C2211yescharacteristic
15#10623096—24no—
16#10623096—22no—
17#10623096—22no—
18C2×#66951C412yescomplemented
19C2×#66936C412yescomplemented
20C2×(C22⋊D11)⋊C4C2212yes—
21C2×C4×D44C411yescharacteristic, complemented
22C2×#66923C411yescharacteristic, complemented
23C2×C11×#99C2212yes—
24C4×C11×C22⋊C4C2212yes—
25C2×#66898C2212yes—
26#10622825C2212yes—
27C2×#66870C2214yes—
28C2×#66870C2214yes—
29#10622555C2214yes—
30C22⋊C4×Dic11C2214yes—
31C4×C4⋊Dic11—22no—
32#10622541—22no—
33#10622267—24no—
34C11×#342C2211yescharacteristic
35C11×#342C2211yescharacteristic
36#10622164C2212yes—
37C22×D4×C11C2311yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C412yes—
41C22×C22⋊D11C2312yes—
42C23×Dic11C2312yes—
43C22×D44C2×C411yescharacteristic
44C22×C4×D11C2×C412yes—
45C4×D4×C11—22no—
46C4×D4×C11—22no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4C2×C411yescharacteristic
49C2×C11×C22⋊C4C2312yes—
50C2×C11×C22⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4C2312yes—
52C2×C42×C11—22no—
53C2×C42×C11C2×C411yescharacteristic
54C2×C22⋊Dic11C2×C412yes—
55C2×C22⋊Dic11C2314yes—
56#66992—24no—
57#66992—24no—
58#66983—22no—
59#66983—22no—
60#66983—22no—
61#66983—22no—
62C2×(C2×D11)⋊C4C2×C412yes—
63C2×(C2×D11)⋊C4C2×C412yes—
64C2×(C2×D11)⋊C4C2×C412yes—
65#66979—22no—
66#66979—21no—
67#66979—21no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11C2×C411yescharacteristic
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C412yes—
73C2×C4⋊Dic11D414yes—
74C2×C4⋊Dic11D412yes—
75C2×C4⋊Dic11D412yes—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4C2×C412yes—
78C2×Dic11⋊C4C2×C412yes—
79C2×C4×Dic11—24no—
80C2×C4×Dic11C2×C412yes—
81#66951—24no—
82#66951—24no—
83#66936—24no—
84#66936—24no—
85(C22⋊D11)⋊C4—24no—
86(C22⋊D11)⋊C4—24no—
87C4×D44—22no—
88C4×D44—21no—
89C4×D44—21no—
90#66923—22no—
91#66923—22no—
92C11×#99—24no—
93C11×#95—22no—
94#66898—42no—
95C11⋊#95—22no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98#66870—28no—
99#66870—44no—
100#22535—111nomaximal, Sylow
101C24×C11C22×C411yescharacteristic
102C24×C11C2411yescharacteristic
103C23×D11C22×C412yes—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D412yes—
121C2×C22⋊D11—24no—
122C2×C22⋊D11—24no—
123C2×C22⋊D11—24no—
124C2×C22⋊D11—22no—
125C2×C22⋊D11—22no—
126C2×C22⋊D11—82no—
127C22×Dic11—24no—
128C22×Dic11—82no—
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C412yes—
131C22×Dic11C22×C412yes—
132C22×Dic11C2×D414yes—
133C22×Dic11C2×D414yes—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—42no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—82no—
140C11×C4⋊C4—22no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4#4114yes—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—44no—
150C22⋊Dic11—22no—
151C22⋊Dic11—22no—
152C22⋊Dic11—24no—
153C22⋊Dic11—24no—
154(C2×D11)⋊C4—22no—
155(C2×D11)⋊C4—22no—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—24no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—44no—
161C4⋊Dic11C22⋊C412yes—
162C4⋊Dic11C22⋊C412yes—
163C4⋊Dic11C22⋊C412yes—
164C4⋊Dic11C22⋊C411yescharacteristic
165C4⋊Dic11C22⋊C411yescharacteristic
166C4⋊Dic11C22⋊C414yes—
167C4⋊Dic11C22⋊C414yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—84no—
171C4×Dic11—22no—
172C4×Dic11—22no—
173C4×Dic11—84no—
174C2×#553—111no—
175#2345—112no—
176#1964—114no—
177#1964—112no—
178#1799—112no—
179#1799—111no—
180C4×#99—112no—
181C4×#99D1111yescharacteristic, complemented
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11C23×C411yescharacteristic
190C23×C11C22×D412yes—
191C23×C11C2×#4112yes—
192C23×C11H(5,𝔽2)11yescharacteristic
193C23×C112−1+411yescharacteristic
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—42no—
198C22×D11—42no—
199D4×C11—42no—
200D4×C11—42no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—24no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C22⋊D11—44no—
224C22⋊D11—44no—
225C22⋊D11—84no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—44no—
230C2×Dic11—44no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—44no—
234C2×Dic11—44no—
235C2×Dic11—44no—
236C2×Dic11C2×C22⋊C412yes—
237C2×Dic11C2×C22⋊C412yes—
238C2×Dic11C2×C22⋊C414yes—
239D44—42no—
240D44—42no—
241C4×D11—82no—
242C4×D11—82no—
243#553—222no—
244#553—224no—
245#553—222no—
246C2×#126—112no—
247C2×#125—111no—
248C2×#123—112no—
249C2×#121—112no—
250C2×#121—111no—
251C2×#121—111no—
252C2×C4×D4—112no—
253C2×C4×D4—111no—
254C2×C4×D4C2×D1111yescharacteristic
255C2×#117—111no—
256C22×C4⋊C4—111no—
257C2×#99—114no—
258C2×#99—112no—
259C2×#99—114no—
260C2×#99C2×D1112yes—
261#389—222no—
262#387—224no—
263#380—112no—
264#380—114no—
265C4×C4⋊C4—222no—
266C4×C22⋊C4—114no—
267C4×C22⋊C4C2×D1112yes—
268#342—112no—
269#342C2×D1111yescharacteristic
270#342C2×D1111yescharacteristic
271C22×C11—22no—
272C22×C11—21no—
273C22×C11—22no—
274C22×C11—21no—
275C22×C11—42no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11C22×C22⋊C411yescharacteristic
284C22×C11C4×#4111yescharacteristic
285C22×C11#52011yescharacteristic
286C22×C11#54812yes—
287C22×C11#55012yes—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—82no—
292C2×D11—82no—
293C4×C11—21no—
294C4×C11—22no—
295C4×C11—44no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—82no—
300C4×C11#41012yes—
301Dic11—22no—
302Dic11—22no—
303Dic11—24no—
304Dic11—42no—
305Dic11—84no—
306C22×D4—112no—
307C22×D4—112no—
308C22×D4—111no—
309C22×D4C22×D1111yescharacteristic
310C23×C4—112no—
311C23×C4—112no—
312C23×C4C4×D1111yescharacteristic
313C23×C4C22×D1111yescharacteristic
314#126—224no—
315#126—224no—
316#125—222no—
317#125—222no—
318#123—224no—
319#123—224no—
320#121—222no—
321#121—222no—
322#121—224no—
323#121—224no—
324#121—222no—
325#121—222no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—222no—
329C4×D4—221no—
330C4×D4—221no—
331C4×D4—224no—
332C4×D4—224no—
333#117—222no—
334#117—221no—
335#117—221no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—114no—
341C2×C4⋊C4—112no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4C4×D1111yescharacteristic
348C2×C22⋊C4—112no—
349C2×C22⋊C4—112no—
350C2×C22⋊C4—112no—
351C2×C22⋊C4—112no—
352C2×C22⋊C4—114no—
353C2×C22⋊C4C4×D1111yescharacteristic
354C2×C22⋊C4C22×D1112yes—
355C2×C22⋊C4C22×D1111yescharacteristic
356C2×C22⋊C4C22×D1112yes—
357C2×C42—22no—
358C2×C42—112no—
359C2×C42—224no—
360C2×C42C4×D1111yescharacteristic
361#99—24no—
362#99—228no—
363#99—444no—
364#99—442no—
365#95—22no—
366#95—224no—
367#95—224no—
368#95—222no—
369C2×C11—22no—
370C2×C11—22no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—81no—
374C2×C11#234111yescharacteristic
375C2×C11C2×#41011yescharacteristic
376C2×C11#288311yescharacteristic
377D11—82no—
378C24—112no—
379C24C2×C4×D1111yescharacteristic
380C24C23×D1111yescharacteristic
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—224no—
386C2×D4—224no—
387C2×D4—224no—
388C2×D4—222no—
389C2×D4—222no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—442no—
393C2×D4—882no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—114no—
403C22×C4—114no—
404C22×C4—112no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—224no—
408C22×C4—882no—
409C22×C4—882no—
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4C2×C4×D1111yescharacteristic
412C22×C4C2×C4×D1111yescharacteristic
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4C2×C4×D1111yescharacteristic
415C22×C4D4×D1112yes—
416C22×C4D4×D1112yes—
417C4⋊C4—22no—
418C4⋊C4—112no—
419C4⋊C4—111no—
420C4⋊C4—111no—
421C4⋊C4—112no—
422C4⋊C4—112no—
423C4⋊C4—114no—
424C4⋊C4—114no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—444no—
430C4⋊C4—884no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—222no—
437C22⋊C4—222no—
438C22⋊C4—224no—
439C22⋊C4—222no—
440C22⋊C4—222no—
441C22⋊C4—224no—
442C22⋊C4—224no—
443C22⋊C4—224no—
444C22⋊C4#433914yes—
445C42—21no—
446C42—21no—
447C42—44no—
448C42—222no—
449C42—222no—
450C42—884no—
451C11#2253511yescharacteristic, complemented, Sylow
452C23—21no—
453C23—21no—
454C23—21no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—222no—
460C23—222no—
461C23—222no—
462C23—442no—
463C23—442no—
464C23C22×C4×D1111yescharacteristic
465C23C2×#433912yes—
466C23C2×D4×D1112yes—
467C23#6704211yescharacteristic
468C23#6704311yescharacteristic
469D4—42no—
470D4—42no—
471D4—442no—
472D4—444no—
473D4—444no—
474D4—442no—
475D4—884no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—24no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—114no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—444no—
502C2×C4—444no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—444no—
506C2×C4—444no—
507C2×C4—444no—
508C2×C4—882no—
509C2×C4—882no—
510C2×C4C22⋊C4×D1111yescharacteristic
511C2×C4C22⋊C4×D1112yes—
512C2×C4C22⋊C4×D1111yescharacteristic
513C22—22no—
514C22—21no—
515C22—22no—
516C22—21no—
517C22—42no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—81no—
524C22—81no—
525C22—442no—
526C22—442no—
527C22—442no—
528C22—882no—
529C22—882no—
530C22C4×#433911yescharacteristic
531C22C2×C22⋊C4×D1111yescharacteristic
532C22#1062305411yescharacteristic
533C22#1062308312yes—
534C22#1062308412yes—
535C4—21no—
536C4—22no—
537C4—44no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—82no—
542C4—222no—
543C4—222no—
544C4—224no—
545C4—442no—
546C4—884no—
547C4#1062235312yes—
548C2—22no—
549C2—22no—
550C2—21no—
551C2—21no—
552C2—81no—
553C2—882no—
554C2#1307145611yescharacteristic
555C2C2×#1062235311yescharacteristic
556C2#1307707511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC4×C11×#99C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623096C2
cosocleC24×C11C24
hypercenterC4×#99D11
hypocenterC11#22535
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #13071491C2semidirect
3. #13069452C2semidirect
4. #13069450C2semidirect
5. #13068604C2semidirect
6. #13068603C2semidirect
7. #13068403C2semidirect
8. C4×C11×#99C2semidirect
11. C2×#66983C4semidirect
13. C2×#66979C4semidirect
18. C2×#66951C4semidirect
19. C2×#66936C4semidirect
21. C2×C4×D44C4semidirect
22. C2×#66923C4semidirect
181. C4×#99D11semidirect
451. C11#22535semidirect

Maximal subgroups

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

subgroupindex
C2×#106230962
#130714912
#130694522
#130694502
#130686042
#130686032
#130684032
C4×C11×#992
#2253511