Finite Group Databasebeta

← #14757477

Subgroups — #14757477

Order 2816.

1526 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2C2×#10622845C211yesmaximal, characteristic
3C2×#10622617C211yesmaximal, characteristic, complemented
4C22×#66880C211yesmaximal, characteristic, complemented
5C2×#10622714C211yesmaximal, characteristic, complemented
6#13071236C211yesmaximal, characteristic, complemented
7#13069434C212yesmaximal, complemented
8#13069431C212yesmaximal, complemented
9#13069426C212yesmaximal, complemented
10#13069416C212yesmaximal, complemented
11C2×C11×#416C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16#10623356—24no—
17#10623356C418yescomplemented
18C2×#66997C2212yes—
19C2×#66989C2212yes—
20C2×#66988—22no—
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×#66977—22no—
24C22×#4318C2211yescharacteristic
25C11×#416—24no—
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30#10622845—24no—
31C2×#66899C2212yes—
32C2×#66896C2212yes—
33C2×#66880—24no—
34C2×#66880C2212yes—
35C2×#66880C2212yes—
36#10622714—24no—
37C2×#66879C2212yes—
38C2×C8×Dic11C2212yes—
39#10622617—24no—
40#10622590C2212yes—
41#10622589C2212yes—
42C2×#66874C2212yes—
43C2×#66874C2212yes—
44#10622559—22no—
45#10622541—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41C2×C414yes—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11—21no—
58C23×Dic11—21no—
59C22×Dic22—22no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×Dic22C2×C414yes—
66C22×Dic22C2312yes—
67C22×C8×C11—22no—
68C22×C8×C11—22no—
69C22×C8×C11D414yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#117—22no—
73C11×#117—22no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11D412yes—
80#66997—24no—
81#66997C2×C418yescomplemented
82#66989—24no—
83#66989C2×C418yescomplemented
84#66988—216no—
85#66979C2×C414yes—
86#66979D414yes—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D412yes—
91C2×C4⋊Dic11C2312yes—
92#66977—216no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—24no—
95C2×C4×Dic11C2312yes—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318D414yes—
99C22×C11⋊C8C2312yes—
100C11×#103—22no—
101C11×#103—22no—
102C11×#102—22no—
103C11×#102—22no—
104#66899—24no—
105#66896—24no—
106C11⋊#95—24no—
107#66880—24no—
108#66880—24no—
109#66879—24no—
110C8×Dic11—24no—
111#66874—24no—
112#66874—24no—
113#21205—111nomaximal, Sylow
114C24×C11—21no—
115C24×C11C2×D411yescharacteristic
116C11×#41—28no—
117C11×#41—28no—
118C11×#41—44no—
119C11×#41—44no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11C22×C412yes—
126C2×D4×C11—24no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—42no—
133C2×D4×C11—42no—
134C2×D4×C11C22×C412yes—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11#4112yes—
147C22×C4×C11#4112yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—82no—
156C22×Dic11C2×D414yes—
157C2×Dic22—24no—
158C2×Dic22—28no—
159C2×Dic22—28no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—44no—
166C2×Dic22—44no—
167C2×Dic22—42no—
168C2×Dic22—42no—
169C2×Dic22C22×C414yes—
170C2×C8×C11—28no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D412yes—
176C2×C8×C11C2×D412yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C22⋊C4—42no—
182C42×C11—42no—
183C22⋊Dic11—216no—
184C22⋊Dic11C22⋊C418yes—
185C4⋊Dic11—22no—
186C4⋊Dic11—22no—
187C4⋊Dic11—42no—
188C4⋊Dic11C22⋊C418yes—
189Dic11⋊C4—216no—
190Dic11⋊C4—84no—
191C4×Dic11C22×C414yes—
192C4×Dic11C2×D414yes—
193#4318—28no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8C2×D414yes—
197C2×#536—111no—
198C2×#417—111no—
199C2×#419—111no—
200C2×#416D1111yescharacteristic
201C22×#103—111no—
202C2×#405—111no—
203#2317—111no—
204#1960—112no—
205#1959—112no—
206#1958—112no—
207#1956—112no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11C2×C22⋊C412yes—
216C23×C11#12412yes—
217C23×C11#12712yes—
218C23×C11C22×D411yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—48no—
226D4×C11—41no—
227D4×C11—41no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—48no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11C4×D414yes—
238C2×C4×C11C4×D414yes—
239C2×C4×C11#12114yes—
240C2×C4×C11#12114yes—
241C2×C4×C11#12412yes—
242C2×C4×C11#12712yes—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—48no—
255C2×Dic11—42no—
256C2×Dic11—44no—
257C2×Dic11—84no—
258C2×Dic11C2×C22⋊C418yes—
259Dic22—24no—
260Dic22—24no—
261Dic22—42no—
262Dic22—42no—
263Dic22—48no—
264C8×C11—22no—
265C8×C11—22no—
266C11⋊C8—24no—
267C22×#41C2×D1111yescharacteristic
268C23×Q8—111no—
269C22×M16—111no—
270C23×C8C2×D1111yescharacteristic
271#536—118no—
272#536—224no—
273C2×C4⋊Q8—112no—
274C2×#124—112no—
275C2×#123—222no—
276C2×C22⋊Q8—222no—
277C2×#117—111no—
278C2×#117C2×D1111yescharacteristic
279C22×C4⋊C4—111no—
280#419—224no—
281#417—224no—
282#416—24no—
283C2×#103—112no—
284C2×#103—112no—
285C2×#103—112no—
286C2×#103—112no—
287C2×#103—112no—
288C2×#103—224no—
289C2×#103C2×D1111yescharacteristic
290C2×#103C2×D1111yescharacteristic
291C2×#102—112no—
292C2×#102C2×D1111yescharacteristic
293C2×#102C2×D1111yescharacteristic
294#405—224no—
295C2×#97—112no—
296C2×C4×C8—112no—
297#389—222no—
298#385—222no—
299#384—112no—
300#382—112no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—44no—
306C22×C11—42no—
307C22×C11—82no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11#39014yes—
311C22×C11C22×C22⋊C411yescharacteristic
312C22×C11C2×#12411yescharacteristic
313C22×C11C2×#12711yescharacteristic
314C22×C11#57712yes—
315C22×C11#57812yes—
316C4×C11—42no—
317C4×C11—81no—
318C4×C11—81no—
319C4×C11#39014yes—
320C4×C11C2×C4×D411yescharacteristic
321C4×C11C2×C4×D411yescharacteristic
322C4×C11C2×#12111yescharacteristic
323C4×C11C2×#12111yescharacteristic
324Dic11—28no—
325Dic11—44no—
326Dic11—82no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41C4×D1114yes—
333C22×Q8—114no—
334C22×Q8—112no—
335C22×Q8—221no—
336C22×Q8—222no—
337C22×Q8—222no—
338C22×Q8—222no—
339C22×Q8—222no—
340C22×Q8—222no—
341C22×Q8C22×D1111yescharacteristic
342C22×D4—21no—
343C22×D4C22×D1111yescharacteristic
344C23×C4—21no—
345C23×C4—221no—
346C23×C4—221no—
347C23×C4C22×D1111yescharacteristic
348C2×M16—114no—
349C2×M16—222no—
350C2×M16—222no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—112no—
354C22×C8C22⋊D1114yes—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C4⋊Q8—118no—
358C4⋊Q8—224no—
359#124—118no—
360#124—224no—
361#123—2216no—
362C22⋊Q8—2216no—
363#117—22no—
364#117—22no—
365#117—114no—
366#117—114no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—112no—
378C2×C22⋊C4—224no—
379C2×C42—21no—
380C2×C42—112no—
381#103—22no—
382#103—22no—
383#103—224no—
384#103—224no—
385#103—224no—
386#103—224no—
387#103—224no—
388#102—22no—
389#102—22no—
390#102—224no—
391#97—224no—
392C4×C8—224no—
393#95—224no—
394C2×C11—24no—
395C2×C11—82no—
396C2×C11C2×#39011yescharacteristic
397C2×C11#289812yes—
398C2×C11#313712yes—
399C2×C11#315411yescharacteristic
400C2×C11#315611yescharacteristic
401C24—21no—
402C24D4×D1111yescharacteristic
403#41—28no—
404#41—28no—
405#41—44no—
406#41—44no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—114no—
413C2×Q8—224no—
414C2×Q8—222no—
415C2×Q8—228no—
416C2×Q8—228no—
417C2×Q8—222no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—222no—
421C2×Q8—444no—
422C2×Q8—442no—
423C2×Q8—444no—
424C2×Q8—442no—
425C2×Q8C2×C4×D1112yes—
426C2×D4—24no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4C2×C4×D1112yes—
435C22×C4—21no—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—114no—
442C22×C4—224no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4—882no—
449C22×C4C2×C4×D1112yes—
450C22×C4#433912yes—
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1112yes—
453C22×C4D4×D1112yes—
454C22×C4#434112yes—
455C22×C4C2×C22⋊D1112yes—
456C22×C4C23×D1111yescharacteristic
457M16—228no—
458C2×C8—28no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—114no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8C2×C22⋊D1112yes—
467C2×C8C2×C22⋊D1112yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—118no—
473C4⋊C4—2216no—
474C4⋊C4—222no—
475C4⋊C4—222no—
476C4⋊C4—442no—
477C4⋊C4—884no—
478C22⋊C4—42no—
479C22⋊C4—118no—
480C22⋊C4—2216no—
481C42—42no—
482C42—114no—
483C42—114no—
484C11#2120511yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23—22no—
488C23—41no—
489C23—42no—
490C23—42no—
491C23—41no—
492C23C22⋊C4×D1112yes—
493C23#6693812yes—
494C23#6699312yes—
495C23C2×D4×D1111yescharacteristic
496Q8—22no—
497Q8—22no—
498Q8—41no—
499Q8—41no—
500Q8—224no—
501Q8—224no—
502Q8—442no—
503Q8—442no—
504Q8—448no—
505D4—22no—
506D4—22no—
507D4—48no—
508D4—41no—
509D4—41no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—48no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—118no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—448no—
525C2×C4—444no—
526C2×C4—442no—
527C2×C4—884no—
528C2×C4C22⋊C4×D1112yes—
529C2×C4(C22⋊D11)⋊C414yes—
530C2×C4#6693714yes—
531C2×C4#6693812yes—
532C2×C4C4×C22⋊D1114yes—
533C2×C4#6699214yes—
534C2×C4#6699312yes—
535C2×C4C22×C4×D1111yescharacteristic
536C2×C4C2×#433911yescharacteristic
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—22no—
542C8—22no—
543C8—224no—
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—44no—
549C22—42no—
550C22—81no—
551C22—81no—
552C22—82no—
553C22#1062257014yes—
554C22C2×C22⋊C4×D1111yescharacteristic
555C22C2×#6693811yescharacteristic
556C22#1062330112yes—
557C22#1062330212yes—
558C22C2×#6699311yescharacteristic
559C4—42no—
560C4—81no—
561C4—81no—
562C4—228no—
563C4—444no—
564C4—882no—
565C4#1062257014yes—
566C4C2×(C22⋊D11)⋊C411yescharacteristic
567C4C2×#6693711yescharacteristic
568C4C2×C4×C22⋊D1111yescharacteristic
569C4C2×#6699211yescharacteristic
570C2—24no—
571C2—82no—
572C2C2×#1062257011yescharacteristic
573C2#1307714512yes—
574C2#1307898512yes—
575C2#1307909311yescharacteristic
576C2#1307911111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#416D11
hypocenterC11#21205
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
3. C2×#10622617C2semidirect
4. C22×#66880C2semidirect
5. C2×#10622714C2semidirect
6. #13071236C2semidirect
7. #13069434C2semidirect
8. #13069431C2semidirect
9. #13069426C2semidirect
10. #13069416C2semidirect
17. #10623356C4semidirect
81. #66997C2×C4semidirect
83. #66989C2×C4semidirect
484. C11#21205semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106228452
C2×#106226172
C22×#668802
C2×#106227142
#130712362
#130694342
#130694312
#130694262
#130694162
C2×C11×#4162
#2120511