Finite Group Databasebeta

← #14755031

Subgroups — #14755031

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×#10623358C211yesmaximal, characteristic
2C2×#10622838C211yesmaximal, characteristic, complemented
3C22×#66899C211yesmaximal, characteristic, complemented
4C2×#10622847C211yesmaximal, characteristic
5#13068929C214yesmaximal, complemented
6#13068924C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C2×C11×#536C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C11×#536—24no—
13C11×#536C418yescomplemented
14C2×C11×C4⋊Q8—21no—
15C2×C11×#124—21no—
16C2×C11×#123—22no—
17C2×C11×C22⋊Q8C2214yes—
18C2×C11×#117C2211yescharacteristic
19#10623358—24no—
20#10623358—24no—
21C2×Q8×Dic11—21no—
22C2×D4×Dic11—22no—
23C2×D4×Dic11—21no—
24C2×#66979C2212yes—
25C2×#66979C2211yescharacteristic
26C22×C4⋊Dic11C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×#4318C2211yescharacteristic
29C23×C11⋊C8C2211yescharacteristic
30#10622847—24no—
31#10622838—24no—
32C2×#66899—24no—
33C2×#66899C2214yes—
34C2×#66899C2212yes—
35C2×#66899C2212yes—
36C2×C22⋊(C11⋊C8)C2214yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2214yes—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yes—
45C2×C11×#41D414yes—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11C2×C414yescomplemented
53C22×Q8×C11D411yescharacteristic
54C22×Q8×C11C2312yes—
55C22×D4×C11D412yes—
56C22×D4×C11D411yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×Dic11—22no—
61C23×Dic11—21no—
62C11×C4⋊Q8—28no—
63C11×#124—28no—
64C11×#123—216no—
65C11×C22⋊Q8—28no—
66C11×C22⋊Q8C2×C4116yescomplemented
67C11×#117—22no—
68C11×#117C2×C414yescomplemented
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—24no—
73C2×C42×C11—21no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—21no—
76Q8×Dic11—28no—
77D4×Dic11—216no—
78D4×Dic11—28no—
79#66979—22no—
80#66979—24no—
81#66979—24no—
82#66979D414yes—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11—24no—
88C2×C4⋊Dic11D414yes—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2312yes—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4×Dic11—22no—
93C2×C4×Dic11—21no—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8C2312yes—
101C22×C11⋊C8C2312yes—
102#66899—28no—
103#66899—24no—
104#66899—24no—
105C22⋊(C11⋊C8)—28no—
106#20913—111nomaximal, Sylow
107C24×C11C2×D412yes—
108C24×C11C2×D411yescharacteristic
109C11×#41—28no—
110C11×#41—28no—
111C11×#41—28no—
112C11×#41—28no—
113C2×Q8×C11—24no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—28no—
118C2×Q8×C11—28no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—42no—
124C2×Q8×C11—44no—
125C2×Q8×C11—44no—
126C2×Q8×C11—42no—
127C2×Q8×C11C22⋊C414yes—
128C2×Q8×C11C22×C414yes—
129C2×D4×C11—24no—
130C2×D4×C11—24no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11C22⋊C418yes—
134C2×D4×C11C22⋊C414yes—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—28no—
156C22×Dic11—24no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—82no—
161C22×Dic11—84no—
162C11×C4⋊C4—216no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4C22×C414yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—216no—
167C42×C11—24no—
168C22⋊Dic11—28no—
169C22⋊Dic11—24no—
170C4⋊Dic11—28no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11C2×D412yes—
176C4⋊Dic11C2×D414yes—
177C4⋊Dic11C2×D412yes—
178C4×Dic11—28no—
179C4×Dic11—24no—
180#4318—44no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—44no—
188C2×#536D1111yescharacteristic
189C2×#520—111no—
190C2×#419—111no—
191C22×#103—111no—
192C2×#408—111no—
193#1873—114no—
194#1872—114no—
195#1736—111no—
196#1735—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11C2×C22⋊C414yes—
204C23×C11C2×C22⋊C412yes—
205C23×C11#12012yes—
206C23×C11#12312yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—28no—
209Q8×C11—24no—
210Q8×C11—24no—
211Q8×C11—42no—
212Q8×C11—42no—
213Q8×C11—48no—
214D4×C11—216no—
215D4×C11—28no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—48no—
229C2×C4×C11C2×C22⋊C414yes—
230C2×C4×C11C2×C22⋊C412yes—
231C2×C4×C11C4×D414yes—
232C2×C4×C11C4×D414yes—
233C2×C4×C11#12012yes—
234C2×C4×C11#12114yes—
235C2×C4×C11#12114yes—
236C2×C4×C11#12312yes—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—44no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—84no—
250C2×Dic11—88no—
251C11⋊C8—42no—
252C11⋊C8—42no—
253C22×#41C2×D1111yescharacteristic
254C23×Q8C2×D1111yescharacteristic
255C22×M16—111no—
256C23×C8—111no—
257#536—24no—
258#536Dic1118yescomplemented
259C2×C4⋊Q8—21no—
260C2×#124—21no—
261C2×#123—22no—
262C2×C22⋊Q8C2×D1114yes—
263#520—224no—
264#520—224no—
265C2×C4×Q8—221no—
266C2×C4×D4—222no—
267C2×C4×D4—221no—
268C2×#117—111no—
269C2×#117—112no—
270C2×#117C2×D1111yescharacteristic
271C22×C4⋊C4—111no—
272C22×C4⋊C4—112no—
273#419—224no—
274C2×#103—114no—
275C2×#103—112no—
276C2×#103—112no—
277C2×#103—224no—
278#408—224no—
279C2×C22⋊C8—114no—
280#340—112no—
281#340—114no—
282#340—112no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—28no—
288C22×C11—24no—
289C22×C11—44no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11#38614yes—
293C22×C11C22×C22⋊C411yescharacteristic
294C22×C11C2×#12011yescharacteristic
295C22×C11C2×#12311yescharacteristic
296C22×C11#57712yes—
297C22×C11#57812yes—
298C4×C11—24no—
299C4×C11—44no—
300C4×C11—44no—
301C4×C11#38614yes—
302C4×C11C2×C4×D411yescharacteristic
303C4×C11C2×C4×D411yescharacteristic
304C4×C11C2×#12111yescharacteristic
305C4×C11C2×#12111yescharacteristic
306Dic11—44no—
307Dic11—42no—
308Dic11—42no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41C2×Dic1114yes—
314C2×#41C22⋊D1114yes—
315C22×Q8—21no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8C2×Dic1114yescomplemented
322C22×Q8C22⋊D1111yescharacteristic
323C22×Q8C22×D1112yes—
324C22×D4C22⋊D1112yes—
325C22×D4C22⋊D1111yescharacteristic
326C23×C4—21no—
327C23×C4—222no—
328C23×C4—221no—
329C23×C4C22×D1112yes—
330C23×C4C22×D1111yescharacteristic
331C2×M16—222no—
332C2×M16—222no—
333C2×M16—222no—
334C22×C8—112no—
335C22×C8—112no—
336C22×C8—222no—
337C22×C8—222no—
338C22×C8—222no—
339C4⋊Q8—28no—
340#124—28no—
341#123—216no—
342C22⋊Q8—28no—
343C22⋊Q8C2×Dic11116yescomplemented
344C4×Q8—228no—
345C4×D4—2216no—
346C4×D4—228no—
347#117—22no—
348#117—114no—
349#117—224no—
350#117—224no—
351#117—222no—
352#117C2×Dic1114yescomplemented
353C2×C4⋊C4—24no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—221no—
368C2×C42—21no—
369C2×C42—222no—
370C2×C42—221no—
371#103—228no—
372#103—224no—
373#103—224no—
374C22⋊C8—228no—
375C2×C11—24no—
376C2×C11—44no—
377C2×C11C2×#38611yescharacteristic
378C2×C11#289812yes—
379C2×C11#300911yescharacteristic
380C2×C11#301111yescharacteristic
381C2×C11#309712yes—
382C24C2×C22⋊D1112yes—
383C24C2×C22⋊D1111yescharacteristic
384#41—28no—
385#41—28no—
386#41—28no—
387#41—28no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—24no—
391C2×Q8—22no—
392C2×Q8—28no—
393C2×Q8—28no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—42no—
399C2×Q8—42no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8C22⋊Dic1114yes—
403C2×Q8C22×Dic1114yes—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4C22⋊Dic1118yes—
409C2×D4C22⋊Dic1114yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—221no—
422C22×C4—228no—
423C22×C4—224no—
424C22×C4—882no—
425C22×C4—884no—
426C22×C4D4×D1112yes—
427C22×C4D4×D1112yes—
428C22×C4#434112yes—
429C22×C4#434112yes—
430C22×C4C22×Dic1114yes—
431C22×C4C22×Dic1112yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1114yes—
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1112yes—
436C22×C4C23×D1111yescharacteristic
437M16—444no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—444no—
445C4⋊C4—216no—
446C4⋊C4—22no—
447C4⋊C4—114no—
448C4⋊C4—112no—
449C4⋊C4—112no—
450C4⋊C4—228no—
451C4⋊C4—224no—
452C4⋊C4—221no—
453C4⋊C4—222no—
454C4⋊C4—221no—
455C4⋊C4C22×Dic1114yes—
456C22⋊C4—24no—
457C22⋊C4—216no—
458C22⋊C4—228no—
459C22⋊C4—224no—
460C42—24no—
461C42—228no—
462C42—224no—
463C11#2091311yescharacteristic, complemented, Sylow
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—24no—
469C23—24no—
470C23#6698812yes—
471C23#6699012yes—
472C23C2×C22⋊Dic1114yes—
473C23C2×C22⋊Dic1112yes—
474C23C22×C22⋊D1111yescharacteristic
475Q8—28no—
476Q8—24no—
477Q8—24no—
478Q8—42no—
479Q8—42no—
480Q8—48no—
481D4—216no—
482D4—28no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—48no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—444no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—884no—
503C2×C4—888no—
504C2×C4D4×Dic1114yes—
505C2×C4D4×Dic1114yes—
506C2×C4#6698812yes—
507C2×C4#6699012yes—
508C2×C4#6699214yes—
509C2×C4#6699214yes—
510C2×C4C2×C22⋊Dic1114yes—
511C2×C4C2×C22⋊Dic1112yes—
512C2×C4C2×D4×D1111yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4C2×#434111yescharacteristic
515C2×C4C2×#434111yescharacteristic
516C2×C4C23×Dic1111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—442no—
519C8—442no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—28no—
525C22—24no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22#1062283314yes—
530C22C2×#6698811yescharacteristic
531C22C2×#6699011yescharacteristic
532C22#1062336812yes—
533C22#1062336912yes—
534C22C22×C22⋊Dic1111yescharacteristic
535C4—24no—
536C4—44no—
537C4—44no—
538C4—444no—
539C4—442no—
540C4—442no—
541C4#1062283314yes—
542C4C2×D4×Dic1111yescharacteristic
543C4C2×D4×Dic1111yescharacteristic
544C4C2×#6699211yescharacteristic
545C4C2×#6699211yescharacteristic
546C2—24no—
547C2—44no—
548C2C2×#1062283311yescharacteristic
549C2#1307714912yes—
550C2#1307789111yescharacteristic
551C2#1307790911yescharacteristic
552C2#1307857912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#536D11
hypocenterC11#20913
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. C2×#10622838C2semidirect
3. C22×#66899C2semidirect
5. #13068929C2semidirect
6. #13068924C2semidirect
7. #13068337C2semidirect
8. #13068332C2semidirect
13. C11×#536C4semidirect
52. C22×Q8×C11C2×C4semidirect
66. C11×C22⋊Q8C2×C4semidirect
68. C11×#117C2×C4semidirect
258. #536Dic11semidirect
321. C22×Q8C2×Dic11semidirect
343. C22⋊Q8C2×Dic11semidirect
352. #117C2×Dic11semidirect
463. C11#20913semidirect

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#106228382
C22×#668992
C2×#106228472
#130689292
#130689242
#130683372
#130683322
C2×C11×#5362
#2091311