Finite Group Databasebeta

← #14755030

Subgroups — #14755030

Order 2816.

1778 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×#10623057C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic
3C2×#10622733C211yesmaximal, characteristic, complemented
4C22×#66874C211yesmaximal, characteristic, complemented
5C2×#10622742C211yesmaximal, characteristic
6#13068927C214yesmaximal, complemented
7#13068922C214yesmaximal, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×C4×C22⋊D11—22no—
16C2×#66979C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18#10623057—24no—
19#10623057C418yescomplemented
20C2×#66950C2214yes—
21#10623035—24no—
22#10623035—24no—
23C2×#66946—21no—
24C2×#66945C2212yes—
25C2×C4⋊C4×D11C2212yes—
26C2×#66940—21no—
27C2×#66939—22no—
28C2×#66928—21no—
29C2×#66922—21no—
30#10622742—24no—
31#10622733—24no—
32C2×(C2×D11)⋊C8C2214yes—
33C2×#66880C2212yes—
34C2×#66880C2212yes—
35C2×#66874—24no—
36C2×#66874C2214yes—
37C11×#340C2214yes—
38#10622167C2212yes—
39#10622167C2212yes—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11D412yes—
43C23×Dic11—21no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—22no—
48C2×#4339C2×C414yes—
49C2×#4339D414yes—
50C22×D44D411yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11C2312yes—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22—21no—
58C22×Dic22—22no—
59C22×Dic22C2×C414yescomplemented
60C22×Dic22D411yescharacteristic
61C22×Dic22C2312yes—
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C22×C8×C11C2312yes—
66C11×#117—22no—
67C11×#117C2×C414yescomplemented
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4D414yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C22⋊Dic11—21no—
76C4×C22⋊D11—216no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—22no—
79#66979—22no—
80#66979D414yes—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8—22no—
90C22×C11⋊C8C2312yes—
91#66950—28no—
92#66950C2×C4116yescomplemented
93#66946—28no—
94#66945—24no—
95#66945—24no—
96C4⋊C4×D11—24no—
97C4⋊C4×D11—24no—
98#66940—28no—
99#66939—216no—
100#66928—28no—
101#66922—28no—
102(C2×D11)⋊C8—28no—
103#66880—24no—
104#66880—24no—
105#66874—28no—
106#20913—111nomaximal, Sylow
107C24×C11C2×D411yescharacteristic
108C23×D11C2×D412yes—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—82no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—24no—
122C2×C22⋊D11—24no—
123C2×C22⋊D11C22⋊C418yes—
124C22×Dic11—24no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—42no—
129C22×Dic11—42no—
130C22×Dic11C2×D412yes—
131#4339—28no—
132#4339—28no—
133#4339—28no—
134#4339—28no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44C22⋊C414yes—
138C2×C4×D11—28no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—84no—
144C2×C4×D11C22×C414yes—
145C2×C4×D11C2×D414yes—
146C2×Dic22—24no—
147C2×Dic22—28no—
148C2×Dic22—28no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—42no—
157C2×Dic22—44no—
158C2×Dic22—44no—
159C2×Dic22—42no—
160C2×Dic22C22⋊C414yes—
161C2×Dic22C22×C414yes—
162C11×M16—44no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C22×C414yes—
170C11×C4⋊C4C2×D414yes—
171C11×C22⋊C4—24no—
172C42×C11—24no—
173C22⋊Dic11—24no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—216no—
176C4⋊Dic11—216no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C2×D412yes—
180C4⋊Dic11C2×D412yes—
181Dic11⋊C4—28no—
182C4×Dic11—28no—
183C4×Dic11—24no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—44no—
188C2×#536—111no—
189C2×#520—111no—
190C2×#419—111no—
191C22×#103—111no—
192C2×#408—111no—
193#1873—114no—
194#1872—114no—
195#1736D1111yescharacteristic, complemented
196#1735—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11C2×C22⋊C412yes—
200C23×C11#12012yes—
201C23×C11#12312yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11C2×C22⋊C414yes—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—84no—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C4×D414yes—
216C2×C4×C11C4×D414yes—
217C2×C4×C11#12012yes—
218C2×C4×C11#12114yes—
219C2×C4×C11#12114yes—
220C2×C4×C11#12312yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C22⋊D11—216no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—48no—
238C2×Dic11C2×C22⋊C414yes—
239D44—28no—
240C4×D11—24no—
241C4×D11—24no—
242C4×D11—24no—
243C4×D11—24no—
244C4×D11—88no—
245Dic22—28no—
246Dic22—24no—
247Dic22—24no—
248Dic22—42no—
249Dic22—42no—
250Dic22—48no—
251C8×C11—42no—
252C11⋊C8—42no—
253C22×#41—111no—
254C23×Q8—111no—
255C22×M16C2×D1111yescharacteristic
256C23×C8—111no—
257#536—118no—
258#536—224no—
259C2×C4⋊Q8—221no—
260C2×#124—221no—
261C2×#123—222no—
262C2×C22⋊Q8—114no—
263#520—224no—
264#520—224no—
265C2×C4×Q8—221no—
266C2×C4×D4—221no—
267C2×C4×D4—222no—
268C2×#117—111no—
269C2×#117—112no—
270C2×#117C2×D1111yescharacteristic
271C22×C4⋊C4—112no—
272C22×C4⋊C4C2×D1111yescharacteristic
273#419—224no—
274C2×#103—112no—
275C2×#103—112no—
276C2×#103—114no—
277C2×#103—224no—
278#408—224no—
279C2×C22⋊C8—114no—
280#340—112no—
281#340—112no—
282#340C2×D1114yes—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11#38614yes—
288C22×C11C22×C22⋊C411yescharacteristic
289C22×C11C2×#12011yescharacteristic
290C22×C11C2×#12311yescharacteristic
291C22×C11#57712yes—
292C22×C11#57812yes—
293C2×D11—28no—
294C2×D11—24no—
295C2×D11—44no—
296C2×D11—42no—
297C2×D11—42no—
298C4×C11—44no—
299C4×C11—44no—
300C4×C11#38614yes—
301C4×C11C2×C4×D411yescharacteristic
302C4×C11C2×C4×D411yescharacteristic
303C4×C11C2×#12111yescharacteristic
304C4×C11C2×#12111yescharacteristic
305Dic11—24no—
306Dic11—42no—
307Dic11—42no—
308Dic11—44no—
309C2×#41—114no—
310C2×#41—114no—
311C2×#41—222no—
312C2×#41—222no—
313C2×#41—222no—
314C2×#41—222no—
315C22×Q8—111no—
316C22×Q8—114no—
317C22×Q8—112no—
318C22×Q8—221no—
319C22×Q8—222no—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×Q8—222no—
324C22×D4—112no—
325C22×D4—111no—
326C23×C4—21no—
327C23×C4—112no—
328C23×C4—222no—
329C23×C4—221no—
330C23×C4C22×D1111yescharacteristic
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C22×C8—112no—
335C22×C8—222no—
336C22×C8—222no—
337C22×C8—222no—
338C22×C8C22×D1112yes—
339C4⋊Q8—228no—
340#124—228no—
341#123—2216no—
342C22⋊Q8—1116no—
343C22⋊Q8—228no—
344C4×Q8—228no—
345C4×D4—228no—
346C4×D4—2216no—
347#117—22no—
348#117—114no—
349#117—224no—
350#117—222no—
351#117—224no—
352#117C4×D1114yescomplemented
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4D4414yes—
362C2×C4⋊C4C22×D1112yes—
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—221no—
368C2×C42—21no—
369C2×C42—222no—
370C2×C42—221no—
371#103—224no—
372#103—224no—
373#103—228no—
374C22⋊C8—228no—
375C2×C11—24no—
376C2×C11C2×#38611yescharacteristic
377C2×C11#289812yes—
378C2×C11#300911yescharacteristic
379C2×C11#301111yescharacteristic
380C2×C11#309712yes—
381D11—44no—
382C24—112no—
383C24D4×D1111yescharacteristic
384#41—228no—
385#41—228no—
386#41—228no—
387#41—228no—
388C2×Q8—114no—
389C2×Q8—114no—
390C2×Q8—224no—
391C2×Q8—222no—
392C2×Q8—222no—
393C2×Q8—222no—
394C2×Q8—228no—
395C2×Q8—228no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—222no—
400C2×Q8—442no—
401C2×Q8—444no—
402C2×Q8—442no—
403C2×Q8—444no—
404C2×D4—118no—
405C2×D4—114no—
406C2×D4—224no—
407C2×D4—224no—
408C2×D4—222no—
409C2×D4—222no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—82no—
414C22×C4—112no—
415C22×C4—114no—
416C22×C4—114no—
417C22×C4—228no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—224no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—222no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—884no—
429C22×C4C2×C4×D1112yes—
430C22×C4C2×D4412yes—
431C22×C4#433912yes—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1112yes—
434C22×C4D4×D1112yes—
435C22×C4#434312yes—
436C22×C4C23×D1111yescharacteristic
437M16—44no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—444no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—112no—
449C4⋊C4—112no—
450C4⋊C4—2216no—
451C4⋊C4—228no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4C2×C4×D1114yes—
455C4⋊C4C2×D4414yes—
456C22⋊C4—24no—
457C22⋊C4—2216no—
458C22⋊C4—228no—
459C22⋊C4—224no—
460C42—24no—
461C42—228no—
462C42—224no—
463C11#2091311yescharacteristic, complemented, Sylow
464C23—22no—
465C23—22no—
466C23—114no—
467C23—222no—
468C23—222no—
469C23—224no—
470C23—224no—
471C23C22⋊C4×D1112yes—
472C23#6693512yes—
473C23#6694712yes—
474C23C2×D4×D1111yescharacteristic
475Q8—228no—
476Q8—224no—
477Q8—224no—
478Q8—442no—
479Q8—442no—
480Q8—448no—
481D4—2216no—
482D4—228no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—42no—
488C2×C4—84no—
489C2×C4—114no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—448no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—888no—
505C2×C4C4×D4414yes—
506C2×C4C22⋊C4×D1112yes—
507C2×C4#6693512yes—
508C2×C4#6693714yes—
509C2×C4#6694614yes—
510C2×C4#6694712yes—
511C2×C4#6694814yes—
512C2×C4C22×C4×D1111yescharacteristic
513C2×C4C22×D4411yescharacteristic
514C2×C4C2×#433911yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4C2×#434311yescharacteristic
518C8—42no—
519C8—442no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—228no—
525C22—224no—
526C22—444no—
527C22—442no—
528C22—442no—
529C22#1062227814yes—
530C22C2×C22⋊C4×D1111yescharacteristic
531C22C2×#6693511yescharacteristic
532C22C2×#6694711yescharacteristic
533C22#1062330612yes—
534C22#1062331012yes—
535C4—44no—
536C4—44no—
537C4—224no—
538C4—442no—
539C4—442no—
540C4—444no—
541C4#1062227814yes—
542C4C2×C4×D4411yescharacteristic
543C4C2×#6693711yescharacteristic
544C4C2×#6694611yescharacteristic
545C4C2×#6694811yescharacteristic
546C2—24no—
547C2—444no—
548C2C2×#1062227811yescharacteristic
549C2#1307714712yes—
550C2#1307789411yescharacteristic
551C2#1307791211yescharacteristic
552C2#1307858712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#20913
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. C2×#10622733C2semidirect
4. C22×#66874C2semidirect
6. #13068927C2semidirect
7. #13068922C2semidirect
8. #13068332C2semidirect
9. C11×#1736C2semidirect
19. #10623057C4semidirect
59. C22×Dic22C2×C4semidirect
67. C11×#117C2×C4semidirect
92. #66950C2×C4semidirect
195. #1736D11semidirect
352. #117C4×D11semidirect
463. C11#20913semidirect

Maximal subgroups

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

subgroupindex
C2×#106230572
C2×#106230352
C2×#106227332
C22×#668742
C2×#106227422
#130689272
#130689222
#130683322
C11×#17362
#2091311