Finite Group Databasebeta

← #14783651

Subgroups — #14783651

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622734C211yesmaximal, characteristic, complemented
2C22×#66872C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic
4#13071240C211yesmaximal, characteristic, complemented
5#13071208C211yesmaximal, characteristic
6#13070162C212yesmaximal, complemented
7#13070157C212yesmaximal, complemented
8#13070147C212yesmaximal, complemented
9#13070135C212yesmaximal, complemented
10#13068314C211yesmaximal, characteristic, complemented
11C2×C11×#417C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C11×#417—24no—
20C2×C11×#103C2212yes—
21C2×C11×#102C2212yes—
22#10622846—24no—
23#10622843C2212yes—
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26#10622834C2212yes—
27#10622833—22no—
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622825—22no—
31#10622823—22no—
32#10622734—24no—
33C2×#66882C2212yes—
34C2×#66881C2212yes—
35#10622590C2212yes—
36#10622589C2212yes—
37#10622586—22no—
38C2×#66872—24no—
39C2×#66872C2212yes—
40C2×#66872C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41Q814yes—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C23×Dic11—21no—
56C2×C11×M16—22no—
57C2×C11×M16—22no—
58C2×C11×M16D414yes—
59C22×C8×C11C2312yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2312yes—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11D412yes—
67#66979—22no—
68#66979—22no—
69#66979—22no—
70#66979—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11D412yes—
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—24no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8—22no—
82C22×C11⋊C8—22no—
83C22×C11⋊C8D414yes—
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C11×#103—24no—
87C11×#102—24no—
88#66899—22no—
89#66899—22no—
90#66896—22no—
91#66896—22no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94#66882—24no—
95#66881—24no—
96#66872—24no—
97#66872—24no—
98#23738—111nomaximal, Sylow
99C24×C11—21no—
100C24×C11C2×D411yescharacteristic
101C11×#41—28no—
102C11×#41—28no—
103C11×#41—44no—
104C11×#41—44no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11C2×Q812yes—
111C2×D4×C11—24no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11C2×Q812yes—
120C22×C4×C11—21no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—82no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×Q812yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—42no—
139C22×Dic11—82no—
140C22×Dic11C2×D414yes—
141C11×M16—28no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11C2×D414yes—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—42no—
148C22⋊Dic11—24no—
149C22⋊Dic11—42no—
150C22⋊Dic11—84no—
151C4⋊Dic11—24no—
152C4⋊Dic11—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—22no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—42no—
159Dic11⋊C4—84no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C4×Dic11—42no—
163C2×C11⋊C8—28no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8C2×D412yes—
169C2×C11⋊C8C2×D412yes—
170C2×#428—111no—
171C22×#106—111no—
172C2×#417D1111yescharacteristic
173C2×#416—111no—
174#2317—111no—
175#2311—111no—
176#2097—112no—
177#2096—112no—
178#2094—112no—
179#2092—112no—
180#1729—111no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11C22⋊Q812yes—
189C23×C11#12312yes—
190C23×C11#12712yes—
191C23×C11C22×D411yescharacteristic
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—41no—
195Q8×C11—41no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—48no—
199D4×C11—41no—
200D4×C11—41no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—48no—
205C2×C4×C11—42no—
206C2×C4×C11—44no—
207C2×C4×C11—84no—
208C2×C4×C11C22⋊Q814yes—
209C2×C4×C11C22⋊Q812yes—
210C2×C4×C11C22⋊Q814yes—
211C2×C4×C11#12314yes—
212C2×C4×C11#12312yes—
213C2×C4×C11#12314yes—
214C2×C4×C11#12712yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×Q811yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—44no—
229C2×Dic11—42no—
230C2×Dic11—84no—
231C8×C11—24no—
232C11⋊C8—22no—
233C11⋊C8—22no—
234C22×#41C2×D1111yescharacteristic
235C22×M16C2×D1111yescharacteristic
236C23×C8—111no—
237C2×#117—111no—
238C2×#117—111no—
239C22×C4⋊C4—111no—
240C22×C4⋊C4C2×D1111yescharacteristic
241#428—224no—
242C2×#107—112no—
243C2×#106—112no—
244C2×#106—112no—
245C2×#106—112no—
246C2×#106—224no—
247#417—24no—
248#416—224no—
249C2×#103—111no—
250C2×#103—111no—
251C2×#103C2×D1112yes—
252C2×#102—111no—
253C2×#102—111no—
254C2×#102C2×D1112yes—
255#391—112no—
256#390—112no—
257#389—222no—
258#386—222no—
259#385—222no—
260#384—112no—
261#382—112no—
262#380—222no—
263#336—112no—
264#336—112no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—44no—
270C22×C11—42no—
271C22×C11—82no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11#39914yes—
275C22×C11C2×C22⋊Q811yescharacteristic
276C22×C11C2×#12311yescharacteristic
277C22×C11C2×#12711yescharacteristic
278C22×C11#57712yes—
279C22×C11#57712yes—
280C4×C11—42no—
281C4×C11—82no—
282C4×C11#39914yes—
283C4×C11C2×C22⋊Q811yescharacteristic
284C4×C11C2×C22⋊Q811yescharacteristic
285C4×C11C2×#12311yescharacteristic
286C4×C11C2×#12311yescharacteristic
287Dic11—44no—
288Dic11—81no—
289Dic11—81no—
290Dic11—82no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41Dic2214yes—
297C22×Q8C22×D1111yescharacteristic
298C22×D4—21no—
299C22×D4C22×D1111yescharacteristic
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—221no—
303C23×C4C22×D1111yescharacteristic
304C2×M16—22no—
305C2×M16—22no—
306C2×M16C22⋊D1114yes—
307C22×C8—114no—
308C22×C8—111no—
309C22×C8—111no—
310C22×C8—222no—
311C22×C8—222no—
312C22×C8C22×D1112yes—
313#117—222no—
314#117—222no—
315#117—222no—
316#117—222no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—224no—
328C2×C4⋊C4C22×D1112yes—
329C2×C22⋊C4—112no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—224no—
332C2×C42—112no—
333C2×C42—221no—
334#107—224no—
335#106—224no—
336#106—224no—
337#106—224no—
338#103—24no—
339#103—222no—
340#103—222no—
341#102—24no—
342#102—222no—
343#102—222no—
344#95—224no—
345#95—224no—
346C2×C11—24no—
347C2×C11—82no—
348C2×C11C2×#39911yescharacteristic
349C2×C11#308412yes—
350C2×C11#309912yes—
351C2×C11#315411yescharacteristic
352C2×C11#315411yescharacteristic
353C24—21no—
354C24D4×D1111yescharacteristic
355#41—28no—
356#41—28no—
357#41—44no—
358#41—44no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8C2×Dic2212yes—
365C2×D4—24no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4C2×Dic2212yes—
374C22×C4—21no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—82no—
381C22×C4—114no—
382C22×C4—221no—
383C22×C4—222no—
384C22×C4—221no—
385C22×C4—442no—
386C22×C4—882no—
387C22×C4C2×Dic2212yes—
388C22×C4#433912yes—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1112yes—
391C22×C4#434112yes—
392C22×C4#434112yes—
393C22×C4C2×C22⋊D1112yes—
394C22×C4C23×D1111yescharacteristic
395M16—28no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—112no—
399C2×C8—112no—
400C2×C8—228no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8C2×C22⋊D1114yes—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—42no—
409C4⋊C4—224no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—221no—
416C4⋊C4—442no—
417C4⋊C4—884no—
418C22⋊C4—224no—
419C22⋊C4—442no—
420C22⋊C4—884no—
421C42—222no—
422C42—222no—
423C42—442no—
424C11#2373811yescharacteristic, complemented, Sylow
425C23—22no—
426C23—22no—
427C23—22no—
428C23—41no—
429C23—42no—
430C23—42no—
431C23—41no—
432C23#6693112yes—
433C23#6693612yes—
434C23#6699312yes—
435C23C2×D4×D1111yescharacteristic
436Q8—22no—
437Q8—22no—
438Q8—41no—
439Q8—41no—
440D4—22no—
441D4—22no—
442D4—48no—
443D4—41no—
444D4—41no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—48no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—84no—
452C2×C4—224no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—442no—
456C2×C4—444no—
457C2×C4—442no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—442no—
461C2×C4—884no—
462C2×C4#6693114yes—
463C2×C4#6693112yes—
464C2×C4#6693614yes—
465C2×C4#6693612yes—
466C2×C4#6697714yes—
467C2×C4#6698814yes—
468C2×C4#6699312yes—
469C2×C4C22×Dic2211yescharacteristic
470C2×C4C2×#433911yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4C2×#434111yescharacteristic
473C2×C4C2×#434111yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C8—24no—
476C8—222no—
477C8—222no—
478C22—22no—
479C22—22no—
480C22—24no—
481C22—24no—
482C22—44no—
483C22—42no—
484C22—81no—
485C22—81no—
486C22—82no—
487C22#1062256214yes—
488C22C2×#6693111yescharacteristic
489C22C2×#6693611yescharacteristic
490C22#1062330612yes—
491C22#1062330912yes—
492C22C2×#6699311yescharacteristic
493C4—42no—
494C4—82no—
495C4—444no—
496C4—881no—
497C4—882no—
498C4—881no—
499C4#1062256214yes—
500C4C2×#6693111yescharacteristic
501C4C2×#6693611yescharacteristic
502C4C2×#6697711yescharacteristic
503C4C2×#6698811yescharacteristic
504C2—24no—
505C2—82no—
506C2C2×#1062256211yescharacteristic
507C2#1307848212yes—
508C2#1307860412yes—
509C2#1307909011yescharacteristic
510C2#1307909511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#417D11
hypocenterC11#23738
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#10622734C2semidirect
2. C22×#66872C2semidirect
4. #13071240C2semidirect
6. #13070162C2semidirect
7. #13070157C2semidirect
8. #13070147C2semidirect
9. #13070135C2semidirect
10. #13068314C2semidirect
424. C11#23738semidirect

Maximal subgroups

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

subgroupindex
C2×#106227342
C22×#668722
C2×#106228462
#130712402
#130712082
#130701622
#130701572
#130701472
#130701352
#130683142
C2×C11×#4172
#2373811