Finite Group Databasebeta

← #14754222

Subgroups — #14754222

Order 2816.

1070 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×#10622494C211yesmaximal, characteristic
2C2×#10622474C211yesmaximal, characteristic
3C2×#10622473C211yesmaximal, characteristic
4C2×D11×#107C211yesmaximal, characteristic
5C2×#10622321C211yesmaximal, characteristic
6#13071241C211yesmaximal, characteristic
7#13071237C211yesmaximal, characteristic
8#13068784C211yesmaximal, characteristic, complemented
9#13068783C211yesmaximal, characteristic, complemented
10#13068781C211yesmaximal, characteristic, complemented
11#13068778C211yesmaximal, characteristic, complemented
12#13068777C211yesmaximal, characteristic, complemented
13#13068775C211yesmaximal, characteristic, complemented
14#13068774C211yesmaximal, characteristic, complemented
15C11×#1847C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C11×#382C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622602—22no—
37#10622590C2211yescharacteristic
38#10622590C2211yescharacteristic
39#10622589C2211yescharacteristic
40#10622589C2211yescharacteristic
41#10622585—22no—
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622549C2211yescharacteristic
51#10622548C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622494—24no—
54D11×#107—24no—
55#10622474—24no—
56#10622473—24no—
57#10622321C418yescomplemented
58#10622281—22no—
59#10622260—22no—
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4D412yes—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4D412yes—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C2×#4313C2×C414yes—
90C2×#4313D414yes—
91C2×#4313Q814yes—
92C2×C8×D11C2×C414yes—
93C2×C8×D11D414yes—
94C2×C8×D11Q814yes—
95#66945—22no—
96#66945—22no—
97#66945—22no—
98#66945—22no—
99C4⋊C4×D11—22no—
100C4⋊C4×D11—22no—
101C4⋊C4×D11—22no—
102C4⋊C4×D11—22no—
103#66925C2×C414yes—
104#66925Q814yes—
105C11×#107—22no—
106C11×#107—22no—
107C11×#106—22no—
108C11×#106—22no—
109C11×#97C2×C414yescomplemented
110C11×#95—22no—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114#66882—22no—
115#66882—22no—
116#66881—22no—
117#66881—22no—
118#66879C2×C414yescomplemented
119C8×Dic11C2×C414yescomplemented
120#66872—22no—
121#66872—22no—
122#66871—22no—
123#66871—22no—
124#66871—22no—
125#66871—22no—
126#66871—22no—
127#66871—22no—
128C4×C11⋊C8C2×C414yescomplemented
129#20803—111nomaximal, Sylow
130C23×D11C2×D411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D412yes—
142C22×Dic11C2×D411yescharacteristic
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—82no—
146C2×C4×D11—82no—
147C2×C4×D11C22×C412yes—
148C2×C4×D11C2×D412yes—
149C2×C4×D11C2×D412yes—
150C2×C4×D11C2×Q812yes—
151C2×C4×D11C2×Q812yes—
152C2×C4×D11C2×Q812yes—
153C2×C8×C11C22×C412yes—
154C2×C8×C11C22×C412yes—
155C2×C8×C11C2×D412yes—
156C2×C8×C11C2×D412yes—
157C2×C8×C11C2×Q812yes—
158C2×C8×C11C2×Q812yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—82no—
168C42×C11C22×C412yes—
169C42×C11C2×Q812yes—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4C4⋊C418yes—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—82no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—82no—
185Dic11⋊C4—82no—
186Dic11⋊C4C4⋊C418yes—
187C4×Dic11—42no—
188C4×Dic11—42no—
189C4×Dic11C22×C412yes—
190C4×Dic11C2×Q812yes—
191C2×C11⋊C8C22×C412yes—
192C2×C11⋊C8C22×C412yes—
193C2×C11⋊C8C2×D412yes—
194C2×C11⋊C8C2×D412yes—
195C2×C11⋊C8C2×Q812yes—
196C2×C11⋊C8C2×Q812yes—
197#4313C4⋊C4116yescomplemented
198C8×D11C4⋊C4116yescomplemented
199C2×#428—111no—
200C2×#428—111no—
201C2×#427—111no—
202C22×#107—111no—
203C2×#405—111no—
204#2317—111no—
205#2317—111no—
206#1847—111no—
207#1847—111no—
208#1847—111no—
209#1847D1111yescharacteristic, complemented
210#1846—111no—
211#1846—111no—
212#1845—111no—
213#1845—111no—
214C23×C11C22×D411yescharacteristic
215C22×D11—22no—
216C22×D11—22no—
217C22×D11C2×C4⋊C412yes—
218C22×D11#12712yes—
219C22×D11C4⋊Q812yes—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11C2×C4⋊C414yes—
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×Q811yescharacteristic
235C2×C4×C11C22×Q811yescharacteristic
236C2×C4×C11C22×Q811yescharacteristic
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11C2×C4⋊C414yes—
248C2×Dic11C2×C4⋊C412yes—
249C2×Dic11#12712yes—
250C2×Dic11C4⋊Q812yes—
251C4×D11—84no—
252C4×D11—84no—
253C4×D11C2×C4⋊C414yes—
254C4×D11C2×C4⋊C414yes—
255C4×D11C4⋊Q814yes—
256C4×D11C4⋊Q814yes—
257C8×C11C2×C4⋊C414yes—
258C8×C11C2×C4⋊C414yes—
259C11⋊C8C2×C4⋊C414yes—
260C11⋊C8C2×C4⋊C414yes—
261C22×M16—111no—
262C23×C8—111no—
263C2×#117—111no—
264C2×#117—111no—
265C2×#117—111no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—111no—
268#428—224no—
269#428—224no—
270#427—224no—
271C2×#107—111no—
272C2×#107—111no—
273C2×#107—111no—
274C2×#107—111no—
275C2×#107—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#107—111no—
279C2×#107—224no—
280C2×#107C2×D1111yescharacteristic
281C2×#107C2×D1111yescharacteristic
282C2×#106—111no—
283C2×#106—111no—
284C2×#106—111no—
285C2×#106—111no—
286C2×#106C2×D1111yescharacteristic
287C2×#106C2×D1111yescharacteristic
288#405—118no—
289C2×#97—111no—
290C2×#97C2×D1111yescharacteristic
291C2×C4×C8—111no—
292C2×C4×C8—111no—
293#389—222no—
294#389—222no—
295#385—222no—
296#385—222no—
297#384—111no—
298#384—111no—
299#384—111no—
300#384C2×D1111yescharacteristic
301#382—111no—
302#382—111no—
303#382—111no—
304#382C2×D1111yescharacteristic
305C22×C11C22×C4⋊C411yescharacteristic
306C22×C11C2×#12711yescharacteristic
307C22×C11C2×C4⋊Q811yescharacteristic
308C22×C11#57612yes—
309C22×C11#57812yes—
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—24no—
313C2×D11—24no—
314C2×D11#38414yes—
315C4×C11—24no—
316C4×C11—81no—
317C4×C11—81no—
318C4×C11—81no—
319C4×C11—81no—
320C4×C11C22×C4⋊C411yescharacteristic
321C4×C11C22×C4⋊C411yescharacteristic
322C4×C11C2×C4⋊Q811yescharacteristic
323C4×C11C2×C4⋊Q811yescharacteristic
324Dic11—24no—
325Dic11—81no—
326Dic11—81no—
327Dic11—81no—
328Dic11—81no—
329Dic11#38414yes—
330C23×C4—111no—
331C23×C4—221no—
332C23×C4—221no—
333C2×M16—114no—
334C2×M16—114no—
335C2×M16—114no—
336C22×C8—111no—
337C22×C8—111no—
338C22×C8—114no—
339C22×C8—114no—
340C22×C8—114no—
341C22×C8C22×D1111yescharacteristic
342C22×C8C22×D1111yescharacteristic
343#117—114no—
344#117—114no—
345#117—222no—
346#117—222no—
347#117—222no—
348#117—222no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4—112no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C42—111no—
372C2×C42—221no—
373C2×C42—221no—
374C2×C42C22×D1111yescharacteristic
375#107—22no—
376#107—22no—
377#107—222no—
378#107—222no—
379#107—222no—
380#107—222no—
381#107—222no—
382#107—222no—
383#107—222no—
384#107—222no—
385#106—22no—
386#106—22no—
387#106—222no—
388#106—222no—
389#106—222no—
390#106—222no—
391#97—114no—
392#97C4×D1114yescomplemented
393C4×C8—114no—
394C4×C8—114no—
395#95—22no—
396#95—222no—
397#95—222no—
398#95—222no—
399C2×C11C2×#38411yescharacteristic
400C2×C11#291312yes—
401C2×C11#315511yescharacteristic
402C2×C11#315611yescharacteristic
403C2×C11#316412yes—
404D11—24no—
405C24—111no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—111no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—882no—
425C22×C4—882no—
426C22×C4D4×D1112yes—
427C22×C4C23×D1111yescharacteristic
428M16—1116no—
429C2×C8—112no—
430C2×C8—112no—
431C2×C8—112no—
432C2×C8—112no—
433C2×C8—112no—
434C2×C8—112no—
435C2×C8—1116no—
436C2×C8C2×C4×D1112yes—
437C2×C8C2×C4×D1112yes—
438C2×C8D4×D1112yes—
439C2×C8D4×D1112yes—
440C2×C8Q8×D1112yes—
441C2×C8Q8×D1112yes—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—82no—
451C4⋊C4—118no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—442no—
461C4⋊C4—442no—
462C4⋊C4—882no—
463C4⋊C4—882no—
464C4⋊C4—882no—
465C22⋊C4—118no—
466C22⋊C4—442no—
467C22⋊C4—442no—
468C42—112no—
469C42—112no—
470C42—442no—
471C42—442no—
472C42C2×C4×D1112yes—
473C42Q8×D1112yes—
474C11#2080311yescharacteristic, complemented, Sylow
475C23—112no—
476C23—112no—
477C23—112no—
478C23—222no—
479C23—222no—
480C23C2×D4×D1111yescharacteristic
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—112no—
492C2×C4—112no—
493C2×C4—112no—
494C2×C4—114no—
495C2×C4—114no—
496C2×C4—114no—
497C2×C4—114no—
498C2×C4—114no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—441no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—884no—
510C2×C4—884no—
511C2×C4C4⋊C4×D1114yes—
512C2×C4C22×C4×D1111yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×Q8×D1111yescharacteristic
516C2×C4C2×Q8×D1111yescharacteristic
517C2×C4C2×Q8×D1111yescharacteristic
518C8—114no—
519C8—114no—
520C8C4⋊C4×D1114yes—
521C8C4⋊C4×D1114yes—
522C22—114no—
523C22—222no—
524C22—222no—
525C22—224no—
526C22—224no—
527C22C2×C4⋊C4×D1111yescharacteristic
528C22D11×#12711yescharacteristic
529C22D11×C4⋊Q811yescharacteristic
530C22#1062330512yes—
531C22#1062331012yes—
532C4—24no—
533C4—81no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—114no—
538C4—224no—
539C4—881no—
540C4—881no—
541C4—881no—
542C4—881no—
543C4C2×C4⋊C4×D1111yescharacteristic
544C4C2×C4⋊C4×D1111yescharacteristic
545C4D11×C4⋊Q811yescharacteristic
546C4D11×C4⋊Q811yescharacteristic
547C2—224no—
548C2D11×#38411yescharacteristic
549C2#1307721512yes—
550C2#1307910011yescharacteristic
551C2#1307910811yescharacteristic
552C2#1307915112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1847C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1847D11
hypocenterC11#20803
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
8. #13068784C2semidirect
9. #13068783C2semidirect
10. #13068781C2semidirect
11. #13068778C2semidirect
12. #13068777C2semidirect
13. #13068775C2semidirect
14. #13068774C2semidirect
15. C11×#1847C2semidirect
57. #10622321C4semidirect
109. C11×#97C2×C4semidirect
118. #66879C2×C4semidirect
119. C8×Dic11C2×C4semidirect
128. C4×C11⋊C8C2×C4semidirect
197. #4313C4⋊C4semidirect
198. C8×D11C4⋊C4semidirect
209. #1847D11semidirect
392. #97C4×D11semidirect
474. C11#20803semidirect

Maximal subgroups

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

subgroupindex
C2×#106224942
C2×#106224742
C2×#106224732
C2×D11×#1072
C2×#106223212
#130712412
#130712372
#130687842
#130687832
#130687812
#130687782
#130687772
#130687752
#130687742
C11×#18472
#2080311