Finite Group Databasebeta

← #14781066

Subgroups — #14781066

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic
3#13071107C211yesmaximal, characteristic
4#13069765C212yesmaximal, complemented
5#13069760C212yesmaximal, complemented
6#13069755C212yesmaximal, complemented
7#13069750C212yesmaximal, complemented
8#13068333C211yesmaximal, characteristic, complemented
9#13068332C211yesmaximal, characteristic, complemented
10C2×#10622188C211yesmaximal, characteristic, complemented
11C2×C11×#416C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19#10623048—24no—
20#10623048—24no—
21C2×#66943C2212yes—
22C2×#66941C2212yes—
23C2×#66931—22no—
24C2×C4×Dic22—22no—
25C11×#416—24no—
26C2×C11×#103C2212yes—
27C2×C11×#102C2212yes—
28#10622846—24no—
29#10622843C2211yescharacteristic
30#10622843C2211yescharacteristic
31C2×#66899C2212yes—
32#10622834C2211yescharacteristic
33#10622834C2211yescharacteristic
34#10622833—22no—
35C2×#66896C2212yes—
36C4×C22⋊Dic11—22no—
37#10622189C2212yes—
38#10622189C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41Q814yescomplemented
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11D412yes—
55C22×Dic22—22no—
56C22×C8×C11—22no—
57C22×C8×C11—22no—
58C22×C8×C11—22no—
59C22×C8×C11C2312yes—
60C11×#117—22no—
61C11×#117D414yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69#66979—22no—
70#66979—22no—
71#66979—22no—
72#66979D414yes—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11D412yes—
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8C2312yes—
90#66943—24no—
91#66943—24no—
92#66941—24no—
93#66941—24no—
94#66931—216no—
95C4×Dic22—216no—
96C11×#103—24no—
97C11×#102—24no—
98#66899—24no—
99#66896—24no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102#23451—111nomaximal, Sylow
103C24×C11—21no—
104C24×C11C2×D411yescharacteristic
105C11×#41—28no—
106C11×#41—28no—
107C11×#41—44no—
108C11×#41—44no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11C2×Q812yes—
115C2×D4×C11—24no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11C2×Q812yes—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×Q812yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—42no—
143C22×Dic11C2×D412yes—
144C22×Dic11C2×D412yes—
145C2×Dic22—28no—
146C2×Dic22—44no—
147C2×Dic22—44no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—44no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C2×D414yes—
154C11×C22⋊C4—24no—
155C42×C11—24no—
156C22⋊Dic11—24no—
157C22⋊Dic11—44no—
158C22⋊Dic11—44no—
159C22⋊Dic11—42no—
160C4⋊Dic11—28no—
161C4⋊Dic11—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11C2×D414yes—
167Dic11⋊C4—28no—
168Dic11⋊C4—28no—
169C4×Dic11—24no—
170C4×Dic11—24no—
171C4×Dic11—21no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174C4×Dic11—21no—
175C4×Dic11—42no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—44no—
180C2×#533—111no—
181C2×#416—111no—
182C2×#416D1111yescharacteristic
183#2297—111no—
184#2026—112no—
185#2025—112no—
186#2024—112no—
187#2023—112no—
188#1735—111no—
189#1735—111no—
190C2×#336—111no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11#12012yes—
199C23×C11C22⋊Q812yes—
200C23×C11#12412yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—22no—
203Q8×C11—22no—
204Q8×C11—41no—
205Q8×C11—41no—
206D4×C11—22no—
207D4×C11—22no—
208D4×C11—48no—
209D4×C11—41no—
210D4×C11—41no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—48no—
218C2×C4×C11#12012yes—
219C2×C4×C11C22⋊Q814yes—
220C2×C4×C11C22⋊Q812yes—
221C2×C4×C11C22⋊Q814yes—
222C2×C4×C11#12414yes—
223C2×C4×C11#12412yes—
224C2×C4×C11#12414yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×Q811yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—48no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11#13514yes—
245Dic22—416no—
246C8×C11—42no—
247C11⋊C8—42no—
248C22×#41C2×D1111yescharacteristic
249C23×C8—111no—
250C23×C8C2×D1111yescharacteristic
251#533—224no—
252#533—224no—
253C2×C4⋊Q8—112no—
254C2×#125—112no—
255C2×C22⋊Q8—222no—
256C2×C4×Q8—222no—
257C2×#117—111no—
258C2×#117—111no—
259C2×#117C2×D1111yescharacteristic
260C22×C42—111no—
261#416—24no—
262#416—224no—
263C2×#103—112no—
264C2×#103C2×D1112yes—
265C2×#102—112no—
266C2×#102C2×D1112yes—
267#391—111no—
268#391—111no—
269#390—111no—
270#390—111no—
271#386—222no—
272C4×C22⋊C4—222no—
273#340—112no—
274#340—112no—
275#340—112no—
276#340—112no—
277#336—112no—
278#336—112no—
279C22×C11—24no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—24no—
283C22×C11—44no—
284C22×C11—42no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—82no—
288C22×C11#39314yes—
289C22×C11C2×#12011yescharacteristic
290C22×C11C2×C22⋊Q811yescharacteristic
291C22×C11C2×#12411yescharacteristic
292C22×C11C2×#13512yes—
293C22×C11#57512yes—
294C4×C11—42no—
295C4×C11—44no—
296C4×C11#39314yes—
297C4×C11C2×C22⋊Q811yescharacteristic
298C4×C11C2×C22⋊Q811yescharacteristic
299C4×C11C2×#12411yescharacteristic
300C4×C11C2×#12411yescharacteristic
301Dic11—24no—
302Dic11—44no—
303Dic11—42no—
304Dic11—81no—
305Dic11—81no—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41Dic2214yescomplemented
312C22×Q8—222no—
313C22×Q8C22×D1111yescharacteristic
314C22×D4—21no—
315C22×D4C22×D1111yescharacteristic
316C23×C4—21no—
317C23×C4—112no—
318C23×C4C22×D1111yescharacteristic
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—112no—
323C22×C8—222no—
324C22×C8—222no—
325C22×C8—222no—
326C22×C8C22×D1112yes—
327C4⋊Q8—224no—
328C4⋊Q8—224no—
329#125—224no—
330#125—224no—
331C22⋊Q8—2216no—
332C4×Q8—2216no—
333#117—22no—
334#117—114no—
335#117—222no—
336#117—222no—
337#117—222no—
338#117C22⋊D1114yes—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—111no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4C22×D1112yes—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—221no—
351C2×C42—21no—
352C2×C42—112no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—222no—
356C2×C42—221no—
357C2×C42—222no—
358C2×C42—221no—
359#103—24no—
360#103—224no—
361#102—24no—
362#102—224no—
363#95—222no—
364#95—222no—
365C2×C11—24no—
366C2×C11—82no—
367C2×C11C2×#39311yescharacteristic
368C2×C11#300212yes—
369C2×C11#307612yes—
370C2×C11#313111yescharacteristic
371C2×C11#313511yescharacteristic
372C24—21no—
373C24D4×D1111yescharacteristic
374#41—28no—
375#41—28no—
376#41—44no—
377#41—44no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—228no—
384C2×Q8—444no—
385C2×Q8—444no—
386C2×Q8C2×Dic2212yes—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4C2×Dic2212yes—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—222no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—442no—
409C22×C4C2×Dic2212yes—
410C22×C4#433912yes—
411C22×C4D4×D1112yes—
412C22×C4D4×D1111yescharacteristic
413C22×C4#434112yes—
414C22×C4#434112yes—
415C22×C4C2×C22⋊D1112yes—
416C22×C4C23×D1111yescharacteristic
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—44no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—444no—
425C4⋊C4—22no—
426C4⋊C4—114no—
427C4⋊C4—228no—
428C4⋊C4—228no—
429C4⋊C4—228no—
430C4⋊C4—222no—
431C4⋊C4—221no—
432C4⋊C4—221no—
433C4⋊C4—221no—
434C4⋊C4—221no—
435C4⋊C4C2×C22⋊D1114yes—
436C22⋊C4—24no—
437C22⋊C4—224no—
438C22⋊C4—444no—
439C22⋊C4—444no—
440C22⋊C4—442no—
441C42—24no—
442C42—224no—
443C42—224no—
444C42—221no—
445C42—221no—
446C42—221no—
447C42—221no—
448C42—442no—
449C11#2345111yescharacteristic, complemented, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—41no—
454C23—42no—
455C23—42no—
456C23—41no—
457C23#6693112yes—
458C23#6693812yes—
459C23#6699012yes—
460C23C2×D4×D1111yescharacteristic
461Q8—22no—
462Q8—22no—
463Q8—41no—
464Q8—41no—
465Q8—4416no—
466D4—22no—
467D4—22no—
468D4—48no—
469D4—41no—
470D4—41no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—48no—
478C2×C4—114no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—224no—
485C2×C4—448no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4#6693114yes—
493C2×C4#6693112yes—
494C2×C4#6693814yes—
495C2×C4#6693812yes—
496C2×C4#6697714yes—
497C2×C4#6698914yes—
498C2×C4#6699012yes—
499C2×C4C22×Dic2211yescharacteristic
500C2×C4C2×#433911yescharacteristic
501C2×C4C2×D4×D1111yescharacteristic
502C2×C4C2×#434111yescharacteristic
503C2×C4C2×#434111yescharacteristic
504C2×C4C22×C22⋊D1111yescharacteristic
505C8—42no—
506C8—442no—
507C22—24no—
508C22—24no—
509C22—22no—
510C22—22no—
511C22—44no—
512C22—42no—
513C22—82no—
514C22—81no—
515C22—81no—
516C22#1062256014yes—
517C22C2×#6693111yescharacteristic
518C22C2×#6693811yescharacteristic
519C22D11×#13512yes—
520C22#1062329912yes—
521C22C2×#6699011yescharacteristic
522C4—44no—
523C4—42no—
524C4—224no—
525C4—442no—
526C4—444no—
527C4—881no—
528C4—881no—
529C4#1062256014yes—
530C4C2×#6693111yescharacteristic
531C4C2×#6693811yescharacteristic
532C4C2×#6697711yescharacteristic
533C4C2×#6698911yescharacteristic
534C2—24no—
535C2—82no—
536C2C2×#1062256011yescharacteristic
537C2#1307783012yes—
538C2#1307840012yes—
539C2#1307893611yescharacteristic
540C2#1307895911yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#416D11
hypocenterC11#23451
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
4. #13069765C2semidirect
5. #13069760C2semidirect
6. #13069755C2semidirect
7. #13069750C2semidirect
8. #13068333C2semidirect
9. #13068332C2semidirect
10. C2×#10622188C2semidirect
48. C2×C11×#41Q8semidirect
311. C2×#41Dic22semidirect
449. C11#23451semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106228462
#130711072
#130697652
#130697602
#130697552
#130697502
#130683332
#130683322
C2×#106221882
C2×C11×#4162
#2345111