Finite Group Databasebeta

← #14755025

Subgroups — #14755025

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×#10623347C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×#10622723C211yesmaximal, characteristic
5#13068925C214yesmaximal, complemented
6#13068920C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068333C211yesmaximal, characteristic, complemented
9C22×C11×#103C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14#10623347—24no—
15#10623347C418yescomplemented
16C2×#67000—21no—
17C2×#66999C2214yes—
18C2×#66997—21no—
19C2×#66982—22no—
20C2×C4×C22⋊D11—22no—
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24#10623035—24no—
25#10623035—24no—
26C2×#66946—21no—
27C2×#66945C2212yes—
28C2×C4⋊C4×D11C2212yes—
29C2×#66940—21no—
30C2×C11×#103—24no—
31C2×C11×#103C2214yes—
32#10622838—24no—
33C2×#66899C2212yes—
34C2×#66899C2212yes—
35#10622723—24no—
36C2×(C2×D11)⋊C8C2214yes—
37#10622189C2212yes—
38#10622189C2212yes—
39#10622167C2214yes—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11C2×C414yescomplemented
47C22×Q8×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11D412yes—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339C2×C414yes—
57C2×#4339D414yes—
58C22×D44D411yescharacteristic
59C22×C4×D11—22no—
60C22×C4×D11C2312yes—
61C22×Dic22D411yescharacteristic
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11C2312yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4D414yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72#67000—28no—
73#66999—28no—
74#66999C2×C4116yescomplemented
75#66997—28no—
76#66982—216no—
77C4×C22⋊D11—216no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—24no—
80#66979—22no—
81#66979—22no—
82#66979C2×C414yescomplemented
83#66979D414yes—
84C2×C4⋊Dic11C2312yes—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—24no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—22no—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318—22no—
95C22×C11⋊C8C2312yes—
96#66946—28no—
97#66945—24no—
98#66945—24no—
99C4⋊C4×D11—24no—
100C4⋊C4×D11—24no—
101#66940—28no—
102C11×#103—28no—
103#66899—24no—
104#66899—24no—
105(C2×D11)⋊C8—28no—
106#20913—111nomaximal, Sylow
107C24×C11C2×D411yescharacteristic
108C23×D11C2×D412yes—
109C2×Q8×C11—24no—
110C2×Q8×C11—22no—
111C2×Q8×C11—28no—
112C2×Q8×C11—28no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—42no—
118C2×Q8×C11—44no—
119C2×Q8×C11—44no—
120C2×Q8×C11—42no—
121C2×Q8×C11C22×C414yes—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—82no—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—24no—
138C2×C22⋊D11—24no—
139C2×C22⋊D11C22⋊C418yes—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11C2×D412yes—
144#4339—28no—
145#4339—28no—
146#4339—28no—
147#4339—28no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44C22⋊C414yes—
151C2×C4×D11—28no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—84no—
157C2×C4×D11C22×C414yes—
158C2×C4×D11C2×D414yes—
159C2×Dic22—22no—
160C2×Dic22—22no—
161C2×Dic22C22⋊C414yes—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—44no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D414yes—
169C22⋊Dic11—24no—
170C22⋊Dic11—24no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—216no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—22no—
176C4⋊Dic11C22×C414yes—
177C4⋊Dic11C2×D412yes—
178C4⋊Dic11C2×D412yes—
179Dic11⋊C4—28no—
180Dic11⋊C4—216no—
181C4×Dic11—28no—
182C4×Dic11—24no—
183C4×Dic11—24no—
184#4318—44no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×#536—111no—
189C2×#520—111no—
190C2×#419—111no—
191C22×#103D1111yescharacteristic, complemented
192C2×#408—111no—
193#1873—114no—
194#1872—114no—
195#1736—111no—
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—
208Q8×C11—24no—
209Q8×C11—24no—
210Q8×C11—42no—
211Q8×C11—42no—
212Q8×C11—48no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—44no—
218C2×C4×C11—48no—
219C2×C4×C11—84no—
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11C4×D414yes—
222C2×C4×C11C4×D414yes—
223C2×C4×C11#12012yes—
224C2×C4×C11#12114yes—
225C2×C4×C11#12114yes—
226C2×C4×C11#12312yes—
227C2×C4×C11C23×C411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C22⋊D11—216no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11C2×C22⋊C414yes—
244D44—28no—
245C4×D11—24no—
246C4×D11—24no—
247C4×D11—24no—
248C4×D11—24no—
249C4×D11—88no—
250Dic22—28no—
251C8×C11—42no—
252C11⋊C8—42no—
253C22×#41—111no—
254C23×Q8C2×D1111yescharacteristic
255C22×M16—111no—
256C23×C8C2×D1111yescharacteristic
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—111no—
270C2×#117—112no—
271C22×C4⋊C4—112no—
272C22×C4⋊C4C2×D1111yescharacteristic
273#419—224no—
274C2×#103—24no—
275C2×#103—112no—
276C2×#103—112no—
277C2×#103C2×D1114yes—
278#408—224no—
279C2×C22⋊C8—114no—
280#340—112no—
281#340—112no—
282#340—114no—
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—44no—
307Dic11—42no—
308Dic11—42no—
309C2×#41—114no—
310C2×#41—114no—
311C2×#41—222no—
312C2×#41—222no—
313C2×#41—222no—
314C2×#41—222no—
315C22×Q8—21no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—111no—
322C22×Q8C4×D1114yescomplemented
323C22×Q8C22×D1112yes—
324C22×D4—112no—
325C22×D4—111no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—112no—
329C23×C4—222no—
330C23×C4C22×D1111yescharacteristic
331C2×M16—222no—
332C2×M16—222no—
333C2×M16—222no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—22no—
337C22×C8—112no—
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—114no—
348#117—114no—
349#117—224no—
350#117—222no—
351#117—222no—
352#117—224no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4C22⋊D1114yes—
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C42—222no—
369C2×C42—221no—
370C2×C42—221no—
371#103—28no—
372#103—224no—
373#103—224no—
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—24no—
389C2×Q8—22no—
390C2×Q8—28no—
391C2×Q8—28no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—42no—
397C2×Q8—44no—
398C2×Q8—42no—
399C2×Q8—44no—
400C2×Q8—114no—
401C2×Q8—222no—
402C2×Q8—222no—
403C2×Q8C2×C4×D1114yes—
404C2×D4—118no—
405C2×D4—114no—
406C2×D4—224no—
407C2×D4—224no—
408C2×D4—222no—
409C2×D4—222no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—82no—
417C22×C4—112no—
418C22×C4—114no—
419C22×C4—114no—
420C22×C4—228no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—221no—
426C22×C4—222no—
427C22×C4—221no—
428C22×C4—884no—
429C22×C4C2×C4×D1112yes—
430C22×C4#433912yes—
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1112yes—
433C22×C4D4×D1112yes—
434C22×C4#434112yes—
435C22×C4C2×C22⋊D1112yes—
436C22×C4C23×D1111yescharacteristic
437M16—444no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—44no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—114no—
448C4⋊C4—112no—
449C4⋊C4—112no—
450C4⋊C4—2216no—
451C4⋊C4—228no—
452C4⋊C4—222no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4C2×C22⋊D1114yes—
456C22⋊C4—2216no—
457C22⋊C4—228no—
458C22⋊C4—224no—
459C22⋊C4—224no—
460C42—228no—
461C42—224no—
462C42—224no—
463C11#2091311yescharacteristic, complemented, Sylow
464C23—22no—
465C23—22no—
466C23—114no—
467C23—222no—
468C23—224no—
469C23—224no—
470C23—222no—
471C23C22⋊C4×D1112yes—
472C23#6693612yes—
473C23#6699012yes—
474C23C2×D4×D1111yescharacteristic
475Q8—24no—
476Q8—24no—
477Q8—42no—
478Q8—42no—
479Q8—48no—
480Q8—228no—
481D4—2216no—
482D4—228no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—42no—
488C2×C4—48no—
489C2×C4—84no—
490C2×C4—114no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—888no—
505C2×C4C22⋊C4×D1112yes—
506C2×C4(C22⋊D11)⋊C414yes—
507C2×C4#6693612yes—
508C2×C4#6693714yes—
509C2×C4C4×C22⋊D1114yes—
510C2×C4#6699012yes—
511C2×C4#6699114yes—
512C2×C4C22×C4×D1111yescharacteristic
513C2×C4C2×#433911yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×#434111yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—42no—
519C8—442no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—228no—
525C22—224no—
526C22—444no—
527C22—442no—
528C22—442no—
529C22#1062256914yes—
530C22C2×C22⋊C4×D1111yescharacteristic
531C22C2×#6693611yescharacteristic
532C22#1062329312yes—
533C22#1062329712yes—
534C22C2×#6699011yescharacteristic
535C4—44no—
536C4—44no—
537C4—224no—
538C4—442no—
539C4—442no—
540C4—444no—
541C4#1062256914yes—
542C4C2×(C22⋊D11)⋊C411yescharacteristic
543C4C2×#6693711yescharacteristic
544C4C2×C4×C22⋊D1111yescharacteristic
545C4C2×#6699111yescharacteristic
546C2—24no—
547C2—444no—
548C2C2×#1062256911yescharacteristic
549C2#1307714412yes—
550C2#1307788911yescharacteristic
551C2#1307790711yescharacteristic
552C2#1307858112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC22×#103D11
hypocenterC11#20913
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C2×#10622838C2semidirect
5. #13068925C2semidirect
6. #13068920C2semidirect
7. #13068335C2semidirect
8. #13068333C2semidirect
9. C22×C11×#103C2semidirect
15. #10623347C4semidirect
46. C22×Q8×C11C2×C4semidirect
74. #66999C2×C4semidirect
82. #66979C2×C4semidirect
191. C22×#103D11semidirect
322. C22×Q8C4×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×#106233472
C2×#106230352
C2×#106228382
C2×#106227232
#130689252
#130689202
#130683352
#130683332
C22×C11×#1032
#2091311