Finite Group Databasebeta

← #14753595

Subgroups — #14753595

Order 2816.

1374 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623035C211yesmaximal, characteristic
2C2×#10622742C211yesmaximal, characteristic
3#13071204C211yesmaximal, characteristic
4#13068710C212yesmaximal, complemented
5#13068709C212yesmaximal, complemented
6#13068705C212yesmaximal, complemented
7#13068701C212yesmaximal, complemented
8#13068336C211yesmaximal, characteristic, complemented
9#13068332C211yesmaximal, characteristic, complemented
10C2×#10622167C211yesmaximal, characteristic, complemented
11C11×#1736C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×C4×C22⋊D11—22no—
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20#10623035—24no—
21#10623035C418yescomplemented
22C2×#66946—21no—
23C2×#66945C2212yes—
24C2×C4⋊C4×D11C2212yes—
25C2×#66940—21no—
26#10622742—24no—
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29#10622600C2212yes—
30#10622600C2212yes—
31#10622571—22no—
32#10622552—21no—
33#10622542—21no—
34C11×#340C2212yes—
35C11×#340C2212yes—
36#10622189C2212yes—
37#10622189C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11D412yes—
47C23×Dic11—21no—
48C2×#4339—22no—
49C2×#4339—22no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339C2×C414yes—
53C2×#4339D414yes—
54C22×D44D411yescharacteristic
55C22×C4×D11—22no—
56C22×C4×D11C2312yes—
57C22×Dic22D411yescharacteristic
58C2×C11×M16—22no—
59C2×C11×M16—22no—
60C2×C11×M16—22no—
61C22×C8×C11C2312yes—
62C11×#117—22no—
63C11×#117—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4C2×C414yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C22⋊Dic11—21no—
73C4×C22⋊D11—216no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77#66979—22no—
78#66979C2×C414yes—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2312yes—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—22no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8—22no—
90C22×C11⋊C8—22no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66946—28no—
94#66945—24no—
95#66945C2×C418yescomplemented
96C4⋊C4×D11—24no—
97C4⋊C4×D11C2×C418yescomplemented
98#66940—28no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101(C2×D11)⋊C8—24no—
102(C2×D11)⋊C8—24no—
103#20703—111nomaximal, Sylow
104C24×C11C2×D411yescharacteristic
105C23×D11C2×D412yes—
106C22×C4×C11—22no—
107C22×C4×C11—24no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—81no—
111C22×C4×C11—81no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11#4112yes—
116C22×C4×C11#4112yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11C2411yescharacteristic
120C2×C22⋊D11—24no—
121C2×C22⋊D11—24no—
122C2×C22⋊D11C22⋊C418yes—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11—42no—
127C22×Dic11—81no—
128C22×Dic11—81no—
129C22×Dic11C2×D412yes—
130#4339—28no—
131#4339—28no—
132#4339—28no—
133#4339—28no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44C22⋊C414yes—
137C2×C4×D11—28no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—82no—
143C2×C4×D11—82no—
144C2×C4×D11C22×C414yes—
145C2×C4×D11C2×D414yes—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22C22⋊C414yes—
149C11×M16—44no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4C22×C414yes—
160C11×C22⋊C4—42no—
161C42×C11—42no—
162C22⋊Dic11—24no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—82no—
165(C2×D11)⋊C4—82no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—42no—
171C4⋊Dic11C22×C412yes—
172C4⋊Dic11C22×C412yes—
173Dic11⋊C4—28no—
174C4×Dic11—28no—
175C4×Dic11—24no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—44no—
183C2×#520—111no—
184C2×#408—111no—
185#2311—111no—
186#1825—112no—
187#1825—112no—
188#1824—112no—
189#1823—112no—
190#1736—111no—
191#1736D1111yescharacteristic, complemented
192#1735—111no—
193C2×#340—111no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11C2×C22⋊C412yes—
199C23×C11#12312yes—
200C23×C11#12312yes—
201C23×C11C22×D411yescharacteristic
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11C2×C22⋊C414yes—
209C2×C4×C11—24no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—84no—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11#11714yes—
221C2×C4×C11#11714yes—
222C2×C4×C11#12314yes—
223C2×C4×C11#12312yes—
224C2×C4×C11#12314yes—
225C2×C4×C11#12312yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C22⋊D11—216no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—84no—
245C2×Dic11C2×C22⋊C414yes—
246D44—28no—
247C4×D11—24no—
248C4×D11—24no—
249C4×D11—24no—
250C4×D11—24no—
251C4×D11—88no—
252Dic22—28no—
253C8×C11—42no—
254C11⋊C8—41no—
255C11⋊C8—41no—
256C22×#41—111no—
257C22×M16C2×D1111yescharacteristic
258C23×C8—111no—
259#520—118no—
260#520—224no—
261C2×C4×Q8—221no—
262C2×C4×D4—221no—
263C2×C4×D4—222no—
264C2×#117—111no—
265C2×#117—112no—
266C2×#117C2×D1111yescharacteristic
267C22×C4⋊C4—112no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4C2×D1111yescharacteristic
270#408—224no—
271C2×C22⋊C8—112no—
272C2×C22⋊C8—112no—
273#391—221no—
274#390—221no—
275#386—222no—
276#380—112no—
277#380—112no—
278#340—112no—
279#340—112no—
280#340—111no—
281#340—112no—
282#340—111no—
283#340—112no—
284#340—111no—
285#340—111no—
286#340C2×D1112yes—
287#340C2×D1112yes—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11#38114yes—
295C22×C11C22×C22⋊C411yescharacteristic
296C22×C11C2×#12311yescharacteristic
297C22×C11C2×#12311yescharacteristic
298C22×C11#57611yescharacteristic
299C22×C11#57711yescharacteristic
300C22×C11#57711yescharacteristic
301C22×C11#57811yescharacteristic
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C4×C11—44no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11#38114yes—
313C4×C11C2×#11711yescharacteristic
314C4×C11C2×#11711yescharacteristic
315C4×C11C2×#12311yescharacteristic
316C4×C11C2×#12311yescharacteristic
317Dic11—24no—
318Dic11—42no—
319Dic11—42no—
320Dic11—82no—
321C2×#41—114no—
322C2×#41—114no—
323C2×#41—222no—
324C2×#41—222no—
325C2×#41—222no—
326C2×#41—222no—
327C22×Q8—111no—
328C22×D4—112no—
329C22×D4—111no—
330C23×C4—21no—
331C23×C4—112no—
332C23×C4—222no—
333C23×C4—221no—
334C23×C4C22×D1111yescharacteristic
335C2×M16—22no—
336C2×M16—22no—
337C2×M16—22no—
338C22×C8—111no—
339C22×C8—111no—
340C22×C8—222no—
341C22×C8—222no—
342C22×C8—222no—
343C22×C8C22×D1112yes—
344C4×Q8—228no—
345C4×D4—228no—
346C4×D4—2216no—
347#117—22no—
348#117—22no—
349#117—114no—
350#117—118no—
351#117—224no—
352#117—222no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C4×D1114yes—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C42—21no—
374C2×C42—222no—
375C2×C42—221no—
376C22⋊C8—224no—
377C22⋊C8—224no—
378#95—222no—
379#95—222no—
380C2×C11—24no—
381C2×C11C2×#38111yescharacteristic
382C2×C11#289711yescharacteristic
383C2×C11#289811yescharacteristic
384C2×C11#309611yescharacteristic
385C2×C11#309711yescharacteristic
386C2×C11#309811yescharacteristic
387C2×C11#309911yescharacteristic
388D11—44no—
389C24—112no—
390C24D4×D1111yescharacteristic
391#41—228no—
392#41—228no—
393#41—228no—
394#41—228no—
395C2×Q8—114no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×D4—118no—
399C2×D4—114no—
400C2×D4—224no—
401C2×D4—224no—
402C2×D4—222no—
403C2×D4—222no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—81no—
409C22×C4—81no—
410C22×C4—112no—
411C22×C4—114no—
412C22×C4—114no—
413C22×C4—228no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—442no—
422C22×C4—882no—
423C22×C4—882no—
424C22×C4—881no—
425C22×C4—881no—
426C22×C4C2×C4×D1112yes—
427C22×C4#433912yes—
428C22×C4#433912yes—
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1112yes—
431C22×C4#434112yes—
432C22×C4#434312yes—
433C22×C4C23×D1111yescharacteristic
434M16—44no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—444no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—112no—
452C4⋊C4—112no—
453C4⋊C4—228no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—442no—
459C4⋊C4C2×C4×D1114yes—
460C22⋊C4—42no—
461C22⋊C4—228no—
462C22⋊C4—224no—
463C22⋊C4—882no—
464C22⋊C4—882no—
465C42—42no—
466C42—228no—
467C42—224no—
468C11#2070311yescharacteristic, complemented, Sylow
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—114no—
474C23—222no—
475C23—222no—
476C23—222no—
477C23—222no—
478C23—222no—
479C23—222no—
480C23C22⋊C4×D1112yes—
481C23#6693612yes—
482C23#6694712yes—
483C23C2×D4×D1111yescharacteristic
484Q8—228no—
485D4—2216no—
486D4—228no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—84no—
497C2×C4—114no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—888no—
514C2×C4—884no—
515C2×C4#6692514yes—
516C2×C4C22⋊C4×D1112yes—
517C2×C4#6693614yes—
518C2×C4#6693612yes—
519C2×C4#6694514yes—
520C2×C4#6694714yes—
521C2×C4#6694712yes—
522C2×C4C22×C4×D1111yescharacteristic
523C2×C4C2×#433911yescharacteristic
524C2×C4C2×#433911yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4C2×#434111yescharacteristic
527C2×C4C2×#434311yescharacteristic
528C8—42no—
529C8—441no—
530C8—441no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—224no—
538C22—224no—
539C22—224no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—442no—
544C22#1062227714yes—
545C22C2×C22⋊C4×D1111yescharacteristic
546C22C2×#6693611yescharacteristic
547C22C2×#6694711yescharacteristic
548C22#1062330511yescharacteristic
549C22#1062330611yescharacteristic
550C22#1062330911yescharacteristic
551C22#1062331011yescharacteristic
552C4—44no—
553C4—81no—
554C4—81no—
555C4—224no—
556C4—442no—
557C4—442no—
558C4—882no—
559C4#1062227714yes—
560C4C2×#6692511yescharacteristic
561C4C2×#6693611yescharacteristic
562C4C2×#6694511yescharacteristic
563C4C2×#6694711yescharacteristic
564C2—24no—
565C2—444no—
566C2C2×#1062227711yescharacteristic
567C2#1307714111yescharacteristic
568C2#1307714811yescharacteristic
569C2#1307857611yescharacteristic
570C2#1307858711yescharacteristic
571C2#1307859311yescharacteristic
572C2#1307860411yescharacteristic
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#20703
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
4. #13068710C2semidirect
5. #13068709C2semidirect
6. #13068705C2semidirect
7. #13068701C2semidirect
8. #13068336C2semidirect
9. #13068332C2semidirect
10. C2×#10622167C2semidirect
11. C11×#1736C2semidirect
21. #10623035C4semidirect
95. #66945C2×C4semidirect
97. C4⋊C4×D11C2×C4semidirect
191. #1736D11semidirect
468. C11#20703semidirect

Maximal subgroups

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

subgroupindex
C2×#106230352
C2×#106227422
#130712042
#130687102
#130687092
#130687052
#130687012
#130683362
#130683322
C2×#106221672
C11×#17362
#2070311