Finite Group Databasebeta

← #14807066

Subgroups — #14807066

Order 2816.

1226 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622702C211yesmaximal, characteristic, complemented
2C2×#10622629C211yesmaximal, characteristic, complemented
3#13073555C211yesmaximal, characteristic, complemented
4#13069619C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069569C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068938C212yesmaximal, complemented
9#13068928C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×C11×#555C211yesmaximal, characteristic, complemented
12C11×#555—24no—
13C11×#555—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#124—22no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C11×#117—21no—
21C2×C11×#117C2212yes—
22C22×#4324C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66983C2212yes—
25C2×#66977C2212yes—
26C2×#66928C2211yescharacteristic
27#10622836—21no—
28C2×#66896C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622702—24no—
32#10622629—24no—
33#10622605—21no—
34C2×#66874C2211yescharacteristic
35C2×#66874C2212yes—
36C2×#66873C2211yescharacteristic
37C2×#66873C2212yes—
38#10622570—22no—
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11—22no—
47C22×D4×C11D411yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2312yes—
51C22×C22⋊D11—22no—
52C22×D44C2311yescharacteristic
53C22×Dic22C2311yescharacteristic
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8D414yescomplemented
56C11×#124—216no—
57C11×#121—28no—
58C11×#121—24no—
59C11×#121—24no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11D414yescomplemented
64C11×#117—28no—
65C11×#117—24no—
66C11×#117—24no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—22no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78C2×#4324—22no—
79C2×#4324—42no—
80C2×#4323—22no—
81C2×#4323—42no—
82#66983—24no—
83#66983—42no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—22no—
87C2×C4⋊Dic11C2312yes—
88#66977—24no—
89#66977—42no—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—21no—
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66928—22no—
96#66928—22no—
97#66896—24no—
98C11⋊#95—21no—
99C22⋊(C11⋊C8)—42no—
100C22⋊(C11⋊C8)—42no—
101#66874—22no—
102#66874—24no—
103#66873—22no—
104#66873—24no—
105C4⋊(C11⋊C8)—22no—
106#66867—22no—
107#25578—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11C2×D412yes—
110C23×D11—21no—
111C2×Q8×C11—24no—
112C2×Q8×C11—81no—
113C2×Q8×C11—81no—
114C2×D4×C11—28no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—42no—
120C2×D4×C11—82no—
121C2×D4×C11—82no—
122C2×D4×C11C2×D412yes—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—44no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—44no—
138C2×C22⋊D11—44no—
139C2×C22⋊D11—82no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—22no—
145C2×D44—22no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C2×D412yes—
155C11×C4⋊C4C2×D414yes—
156C11×C22⋊C4—28no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C42×C11—28no—
161C42×C11C2×D412yes—
162C42×C11C2×D412yes—
163C22⋊Dic11—44no—
164#4324—44no—
165#4323—44no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—42no—
169C4⋊Dic11—22no—
170C4⋊Dic11#4114yes—
171Dic11⋊C4—44no—
172C4×Dic11—81no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×#555D1111yescharacteristic, complemented
181C2×#489—111no—
182C2×#463—111no—
183#2540—111no—
184#2000—112no—
185#1999—112no—
186#1988—111no—
187#1955—111no—
188#1875—112no—
189#1873—112no—
190#1762—111no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11C22×D411yescharacteristic
204C22×D11—41no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—41no—
208C22×D11—41no—
209Q8×C11—84no—
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—44no—
213D4×C11—42no—
214D4×C11—88no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—48no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11#12012yes—
232C2×C4×C11#12012yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4112yes—
236C2×C4×C11H(5,𝔽2)12yes—
237C22⋊D11—88no—
238C2×Dic11—24no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243D44—41no—
244D44—41no—
245D44—42no—
246Dic22—41no—
247Dic22—41no—
248Dic22—42no—
249C11⋊C8—41no—
250C11⋊C8—41no—
251C11⋊C8—42no—
252C22×SD16—111no—
253C22×D8—111no—
254#555—24no—
255#555—24no—
256C2×C4⋊Q8C2×D1111yescharacteristic
257C2×#124—22no—
258C2×#124—111no—
259C2×C22⋊Q8—112no—
260C2×#121—21no—
261C2×#121—112no—
262C2×#121C2×D1112yes—
263C2×C4×D4C2×D1111yescharacteristic
264C2×C4×D4C2×D1111yescharacteristic
265C2×#117—21no—
266C2×#117C2×D1112yes—
267#489—224no—
268#463—224no—
269C2×C4⋊C8—111no—
270C2×#103—112no—
271C2×#103—111no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—111no—
275C2×C22⋊C8—112no—
276C2×C22⋊C8—112no—
277C2×#97—111no—
278#399—221no—
279#392—221no—
280#390—222no—
281C4×C4⋊C4—111no—
282#340—112no—
283#340—112no—
284#340—112no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11C2×#12011yescharacteristic
298C22×C11#54612yes—
299C22×C11#57512yes—
300C22×C11#57611yescharacteristic
301C22×C11#57711yescharacteristic
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—82no—
306C2×D11—82no—
307C4×C11—22no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—44no—
312C4×C11#53211yescharacteristic
313C4×C11#53511yescharacteristic
314C4×C11#55012yes—
315Dic11—44no—
316Dic11—81no—
317C22×Q8—21no—
318C22×Q8—111no—
319C22×D4—22no—
320C22×D4—111no—
321C22×D4—222no—
322C22×D4C22⋊D1111yescharacteristic
323C22×D4C22×D1111yescharacteristic
324C23×C4—21no—
325C23×C4C22×D1112yes—
326C2×SD16—222no—
327C2×SD16—442no—
328C2×D8—222no—
329C2×D8—442no—
330C22×C8—111no—
331C22×C8—111no—
332C22×C8—112no—
333C4⋊Q8—22no—
334C4⋊Q8C22⋊D1114yescomplemented
335#124—216no—
336#124—222no—
337#124—222no—
338C22⋊Q8—224no—
339C22⋊Q8—442no—
340#121—28no—
341#121—24no—
342#121—24no—
343#121—224no—
344#121—442no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4C22⋊D1114yescomplemented
349#117—28no—
350#117—24no—
351#117—24no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4C22⋊D1111yescharacteristic
356C2×C4⋊C4C22×D1111yescharacteristic
357C2×C4⋊C4C22×D1112yes—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4C22⋊D1112yes—
366C2×C42—22no—
367C2×C42—221no—
368C2×C42C22×D1111yescharacteristic
369C4⋊C8—222no—
370#103—222no—
371#103—224no—
372#102—224no—
373#102—222no—
374#102—224no—
375C22⋊C8—442no—
376C22⋊C8—442no—
377#97—222no—
378#95—221no—
379C2×C11—82no—
380C2×C11—82no—
381C2×C11#243111yescharacteristic
382C2×C11#300511yescharacteristic
383C2×C11#301211yescharacteristic
384C2×C11#331912yes—
385C2×C11#332112yes—
386D11—161no—
387C24—21no—
388C24—221no—
389C24C2×C22⋊D1112yes—
390C2×Q8—24no—
391C2×Q8—81no—
392C2×Q8—81no—
393C2×Q8—222no—
394C2×Q8—222no—
395C2×Q8—221no—
396C2×Q8—221no—
397C2×D4—28no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—42no—
403C2×D4—82no—
404C2×D4—82no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—221no—
408C2×D4—221no—
409C2×D4—444no—
410C2×D4—444no—
411C2×D4—882no—
412C2×D4C2×C22⋊D1112yes—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—44no—
423C22×C4—222no—
424C22×C4—221no—
425C22×C4C2×C22⋊D1112yes—
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429SD16—444no—
430D8—444no—
431C2×C8—222no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—221no—
437C2×C8—221no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—114no—
443C4⋊C4—222no—
444C4⋊C4—444no—
445C4⋊C4C2×C22⋊D1112yes—
446C4⋊C4C2×C22⋊D1114yes—
447C22⋊C4—28no—
448C22⋊C4—28no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—444no—
452C22⋊C4—444no—
453C22⋊C4—442no—
454C22⋊C4—442no—
455C42—28no—
456C42—881no—
457C42C2×C22⋊D1112yes—
458C42C2×C22⋊D1112yes—
459C11#2557811yescharacteristic, complemented, Sylow
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—42no—
469C23—42no—
470C23—41no—
471C23—41no—
472C23—442no—
473C23—442no—
474C23—441no—
475C23—441no—
476C23—441no—
477C23C22×C22⋊D1111yescharacteristic
478Q8—84no—
479Q8—441no—
480Q8—441no—
481Q8—442no—
482D4—22no—
483D4—22no—
484D4—44no—
485D4—42no—
486D4—88no—
487D4—441no—
488D4—441no—
489D4—442no—
490D4—888no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—48no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—224no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—441no—
512C2×C4#6700612yes—
513C2×C4#6700612yes—
514C2×C4#41×D1112yes—
515C2×C4#6704212yes—
516C2×C4C22×C22⋊D1111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—441no—
519C8—441no—
520C8—442no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—82no—
532C22—82no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—882no—
537C22—882no—
538C22#1062335312yes—
539C22#1062336012yes—
540C22#1062336611yescharacteristic
541C22#1062336711yescharacteristic
542C22C2×#6700611yescharacteristic
543C4—22no—
544C4—22no—
545C4—42no—
546C4—42no—
547C4—44no—
548C4—444no—
549C4—881no—
550C4#1062336111yescharacteristic
551C4#1062336311yescharacteristic
552C4#1062336512yes—
553C2—82no—
554C2—82no—
555C2—1761no—
556C2#1307223111yescharacteristic
557C2#1307785811yescharacteristic
558C2#1307792011yescharacteristic
559C2#1308076612yes—
560C2#1308079612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11#25578
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#10622702C2semidirect
2. C2×#10622629C2semidirect
3. #13073555C2semidirect
4. #13069619C2semidirect
5. #13069612C2semidirect
6. #13069569C2semidirect
7. #13069415C2semidirect
8. #13068938C2semidirect
9. #13068928C2semidirect
10. #13068441C2semidirect
11. C2×C11×#555C2semidirect
55. C11×C4⋊Q8D4semidirect
63. C4×D4×C11D4semidirect
180. C2×#555D11semidirect
334. C4⋊Q8C22⋊D11semidirect
348. C4×D4C22⋊D11semidirect
459. C11#25578semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
C2×#106226292
#130735552
#130696192
#130696122
#130695692
#130694152
#130689382
#130689282
#130684412
C2×C11×#5552
#2557811