Finite Group Databasebeta

← #14769637

Subgroups — #14769637

Order 2816.

1450 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
1C22×#67003C211yesmaximal, characteristic
2C2×#10622403C212yesmaximal, complemented
3#13071457C211yesmaximal, characteristic, complemented
4#13071453C211yesmaximal, characteristic, complemented
5#13069479C212yesmaximal, complemented
6#13068969C212yesmaximal, complemented
7#13068968C212yesmaximal, complemented
8#13068643C211yesmaximal, characteristic, complemented
9#13068557C211yesmaximal, characteristic, complemented
10#13068390C211yesmaximal, characteristic, complemented
11C11×#1788C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C2×#67003—28no—
15C2×#67003C418yescomplemented
16C2×Q8×Dic11C2212yes—
17C22×#4326C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×#66940C2212yes—
23C2×C11×#103C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622834—22no—
28#10622834C2212yes—
29#10622825—21no—
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11—21no—
32C4×C22⋊Dic11C2211yescharacteristic
33C2×#66885C2212yes—
34C2×#66880C2212yes—
35C2×C8×Dic11C2212yes—
36#10622601C2212yes—
37C2×#66871C2212yes—
38#10622570—22no—
39#10622403—28no—
40#10622280—21no—
41#10622279—21no—
42#10622188C2212yes—
43#10622167C2212yes—
44C2×C11×#41—22no—
45C2×C11×#41—24no—
46C2×C11×#41—42no—
47C2×C11×#41C2×C414yes—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—21no—
54C2×#4339—22no—
55C2×#4339—24no—
56C2×#4339—42no—
57C2×#4339C2×C414yes—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—21no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11D412yes—
68#67003—232no—
69Q8×Dic11—24no—
70Q8×Dic11—42no—
71C2×#4326C2×C414yes—
72C2×#4326D418yes—
73C2×#4325—24no—
74C2×#4325C2×C414yes—
75C2×#4324—24no—
76C2×#4324C2×C414yes—
77C2×#4323—24no—
78C2×#4323C2×C414yes—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11C2312yes—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11C2312yes—
87C22×C11⋊C8—24no—
88C22×C11⋊C8C2×C414yes—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66940—24no—
92#66940—42no—
93C11×#103—24no—
94C11×#102—42no—
95C11×C22⋊C8—22no—
96C11×#95—21no—
97C11⋊#95—21no—
98C11⋊#95D411yescharacteristic
99C11⋊#95D411yescharacteristic
100#66885—42no—
101#66880—24no—
102C8×Dic11—24no—
103#66871—24no—
104#22451—111nomaximal, Sylow
105C24×C11—21no—
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C11×#41—28no—
109C11×#41—44no—
110C11×#41—48no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11C22×C412yes—
114C2×Q8×C11C2×D414yes—
115C2×D4×C11—24no—
116C2×D4×C11—22no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—44no—
120C2×D4×C11C22×C412yes—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—44no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—24no—
132C2×C22⋊D11—44no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11C2×D412yes—
136C22×Dic11C2×D412yes—
137#4339—28no—
138#4339—44no—
139#4339—48no—
140C2×D44—22no—
141C2×D44—21no—
142C2×D44—22no—
143C2×D44C22×C412yes—
144C2×C4×D11—24no—
145C2×C4×D11—44no—
146C2×Dic22—21no—
147C2×Dic22—22no—
148C2×Dic22C22×C412yes—
149C2×Dic22C2×D414yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C22⋊C4—81no—
156C22⋊Dic11—24no—
157C22⋊Dic11—44no—
158C22⋊Dic11—81no—
159C22⋊Dic11—82no—
160#4326C22⋊C4116yescomplemented
161#4325—28no—
162#4324—28no—
163#4323—28no—
164(C2×D11)⋊C4—44no—
165(C2×D11)⋊C4—82no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—44no—
169Dic11⋊C4—44no—
170C4×Dic11—22no—
171C4×Dic11—22no—
172C4×Dic11—44no—
173C4×Dic11—44no—
174C2×C11⋊C8—28no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8C22×C412yes—
177C2×C11⋊C8C22×C412yes—
178C2×C11⋊C8C2×D414yes—
179C22×#135—111no—
180C2×C4×Q16—112no—
181#2341—111no—
182#2341—111no—
183#1970—112no—
184#1880—112no—
185#1880—112no—
186#1808—111no—
187#1788—111no—
188#1788D1111yescharacteristic, complemented
189C8×C22⋊C4—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11C4×D412yes—
200C23×C11C22×D411yescharacteristic
201C22×D11—22no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—41no—
205C22×D11—41no—
206Q8×C11—22no—
207Q8×C11—24no—
208Q8×C11C2×C22⋊C414yes—
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—48no—
212D4×C11—42no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—48no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11C4×D412yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)12yes—
228C22⋊D11—48no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11#13514yescomplemented
240D44—22no—
241D44—22no—
242D44—42no—
243C4×D11—48no—
244Dic22—22no—
245Dic22—24no—
246Dic22C2×C22⋊C414yes—
247C8×C11—42no—
248C11⋊C8—22no—
249C11⋊C8C2×C22⋊C414yes—
250C22×#41—111no—
251C22×#41C2×D1111yescharacteristic
252C2×#135—118no—
253C2×#135—228no—
254C22×Q16—111no—
255C22×SD16—111no—
256C22×SD16—111no—
257C22×D8—111no—
258C23×C8—111no—
259C2×C4×Q8—112no—
260C2×C4×Q8—112no—
261C4×Q16—228no—
262C2×#107—112no—
263C2×#103—112no—
264C2×#103C2×D1112yes—
265C2×#102—112no—
266C2×#102C2×D1112yes—
267C2×C22⋊C8C2×D1111yescharacteristic
268C2×C4×C8—112no—
269#390—112no—
270#390—112no—
271#390—222no—
272#390—222no—
273#380—111no—
274#380—221no—
275#380—221no—
276#380C2×D1111yescharacteristic
277C4×C22⋊C4—111no—
278C4×C22⋊C4—221no—
279C4×C22⋊C4—221no—
280#340—112no—
281#336—112no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—82no—
291C22×C11—82no—
292C22×C11C2×C4×D411yescharacteristic
293C22×C11D4212yes—
294C22×C11C2×#13512yes—
295C22×C11#57611yescharacteristic
296C22×C11#57811yescharacteristic
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—82no—
301C2×D11—82no—
302C4×C11—22no—
303C4×C11—24no—
304C4×C11—82no—
305C4×C11C22×C22⋊C411yescharacteristic
306C4×C11#51811yescharacteristic
307C4×C11#54612yes—
308Dic11—24no—
309Dic11—24no—
310Dic11—42no—
311Dic11—82no—
312C2×#41—22no—
313C2×#41—24no—
314C2×#41—42no—
315C2×#41—114no—
316C2×#41—224no—
317C2×#41—222no—
318C2×#41—442no—
319C2×#41C4×D1114yes—
320C22×Q8—111no—
321C22×Q8C22×D1111yescharacteristic
322C22×D4—21no—
323C22×D4—111no—
324C22×D4—221no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—221no—
328C23×C4C22×D1111yescharacteristic
329#135—2232no—
330C2×Q16—114no—
331C2×Q16—118no—
332C2×SD16—114no—
333C2×SD16—114no—
334C2×SD16—224no—
335C2×SD16—224no—
336C2×D8—114no—
337C2×D8—224no—
338C22×C8—111no—
339C22×C8—114no—
340C22×C8—111no—
341C22×C8—224no—
342C22×C8C22×D1112yes—
343C4×Q8—224no—
344C4×Q8—224no—
345C4×Q8—442no—
346C4×Q8—442no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4C22×D1112yes—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—112no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—221no—
358C2×C42—112no—
359C2×C42—222no—
360C2×C42—222no—
361#107—224no—
362#103—24no—
363#103—224no—
364#102—42no—
365#102—442no—
366C22⋊C8—22no—
367C4×C8—224no—
368#95—21no—
369#95—111no—
370#95—111no—
371#95—221no—
372C2×C11—42no—
373C2×C11—82no—
374C2×C11D4×C22⋊C411yescharacteristic
375C2×C11C4×#13511yescharacteristic
376C2×C11#295111yescharacteristic
377C2×C11#328512yes—
378C2×C11#328712yes—
379D11—82no—
380C24—21no—
381C24—221no—
382C24D4×D1111yescharacteristic
383#41—28no—
384#41—44no—
385#41—48no—
386#41—228no—
387#41—444no—
388#41—448no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—112no—
392C2×Q8—114no—
393C2×Q8—221no—
394C2×Q8—222no—
395C2×Q8C2×C4×D1112yes—
396C2×Q8D4×D1114yes—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—44no—
402C2×D4—112no—
403C2×D4—224no—
404C2×D4—222no—
405C2×D4—221no—
406C2×D4—222no—
407C2×D4—444no—
408C2×D4C2×C4×D1112yes—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—44no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—221no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—444no—
421C22×C4C2×C4×D1112yes—
422C22×C4D4×D1111yescharacteristic
423C22×C4#434112yes—
424C22×C4C23×D1111yescharacteristic
425Q16—1116no—
426SD16—228no—
427SD16—228no—
428D8—228no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—112no—
433C2×C8—114no—
434C2×C8—112no—
435C2×C8—228no—
436C2×C8—222no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—222no—
440C4⋊C4—222no—
441C4⋊C4—444no—
442C4⋊C4—444no—
443C22⋊C4—81no—
444C22⋊C4—224no—
445C22⋊C4—444no—
446C22⋊C4—444no—
447C22⋊C4—882no—
448C22⋊C4—882no—
449C22⋊C4—881no—
450C42—222no—
451C42—222no—
452C42—444no—
453C42—444no—
454C11#2245111yescharacteristic, complemented, Sylow
455C23—22no—
456C23—21no—
457C23—21no—
458C23—22no—
459C23—22no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—222no—
465C23—442no—
466C23—441no—
467C23—441no—
468C23—442no—
469C23(C22⋊D11)⋊C412yes—
470C23C2×D4×D1111yescharacteristic
471Q8—22no—
472Q8—24no—
473Q8—114no—
474Q8—222no—
475Q8—224no—
476Q8C22⋊C4×D1114yes—
477D4—22no—
478D4—22no—
479D4—48no—
480D4—42no—
481D4—222no—
482D4—222no—
483D4—448no—
484D4—442no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—114no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—448no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4(C22⋊D11)⋊C412yes—
508C2×C4C22×C4×D1111yescharacteristic
509C2×C4C2×D4×D1112yes—
510C2×C4C2×#434111yescharacteristic
511C2×C4#6703712yes—
512C8—42no—
513C8—114no—
514C8—222no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—82no—
524C22—82no—
525C22—442no—
526C22—442no—
527C22—442no—
528C22—882no—
529C22—882no—
530C22C2×(C22⋊D11)⋊C411yescharacteristic
531C22#1062312112yes—
532C22D11×#13512yes—
533C22#1062330511yescharacteristic
534C22#1062331011yescharacteristic
535C4—22no—
536C4—24no—
537C4—82no—
538C4—224no—
539C4—224no—
540C4—442no—
541C4—882no—
542C4C2×C22⋊C4×D1111yescharacteristic
543C4#1062301711yescharacteristic
544C4#1062312212yes—
545C2—42no—
546C2—82no—
547C2—882no—
548C2#1307143211yescharacteristic
549C2#1307738411yescharacteristic
550C2#1307748711yescharacteristic
551C2#1308035512yes—
552C2#1308036912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC22×#67003C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#22451
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622403C2semidirect
3. #13071457C2semidirect
4. #13071453C2semidirect
5. #13069479C2semidirect
6. #13068969C2semidirect
7. #13068968C2semidirect
8. #13068643C2semidirect
9. #13068557C2semidirect
10. #13068390C2semidirect
11. C11×#1788C2semidirect
15. C2×#67003C4semidirect
160. #4326C22⋊C4semidirect
188. #1788D11semidirect
239. C2×Dic11#135semidirect
454. C11#22451semidirect

Maximal subgroups

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

subgroupindex
C22×#670032
C2×#106224032
#130714572
#130714532
#130694792
#130689692
#130689682
#130686432
#130685572
#130683902
C11×#17882
#2245111