Finite Group Databasebeta

← #14810731

Subgroups — #14810731

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic, complemented
3#13074105C211yesmaximal, characteristic, complemented
4#13069765C212yesmaximal, complemented
5#13069760C212yesmaximal, complemented
6#13069567C211yesmaximal, characteristic, complemented
7#13069555C211yesmaximal, characteristic, complemented
8#13068966C212yesmaximal
9#13068952C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×C11×#463C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×D4×Dic11C2212yes—
17C22×C4⋊Dic11—21no—
18C2×#66977—21no—
19#10623074—24no—
20#10623074—24no—
21C2×#66943C2212yes—
22C2×#66931—22no—
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#463—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29#10622843C2212yes—
30C2×#66899C2212yes—
31#10622834C2212yes—
32C2×#66896C2212yes—
33C2×#66896C2212yes—
34#10622668—24no—
35#10622566—21no—
36#10622560—21no—
37#10622558—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×Dic11—22no—
50C22×Dic22—21no—
51C22×Dic22D411yescharacteristic
52C2×C11×SD16—22no—
53C2×C11×SD16—24no—
54C2×C11×D8—22no—
55C2×C11×D8—24no—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×#124—22no—
59C11×#124—22no—
60C4×D4×C11—22no—
61C4×D4×C11D414yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70D4×Dic11—24no—
71D4×Dic11—24no—
72C2×C4⋊Dic11—28no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×C4⋊Dic11C2312yes—
78#66977—28no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4D412yes—
81C2×C4×Dic11—21no—
82C2×C4×Dic11C2312yes—
83C22×C11⋊C8C2312yes—
84#66943—24no—
85#66943—24no—
86#66931—216no—
87#66922—22no—
88#66922D414yes—
89C4×Dic22—22no—
90C4×Dic22—22no—
91C11×C4⋊C8—22no—
92C11×#103—22no—
93C11×#102—22no—
94#66899—24no—
95#66896—24no—
96#66896—24no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100#66867—22no—
101#25940—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11C2×D412yes—
115C2×D4×C11#4114yes—
116C22×C4×C11—21no—
117C22×C4×C11—24no—
118C22×C4×C11—21no—
119C22×C4×C11—44no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—28no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—82no—
127C22×Dic11—82no—
128C22×Dic11C2×D412yes—
129C22×Dic11C2×D412yes—
130C2×Dic22—22no—
131C2×Dic22—24no—
132C2×Dic22—42no—
133C2×Dic22—81no—
134C2×Dic22—81no—
135C11×SD16—44no—
136C11×D8—44no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4C2×D412yes—
143C11×C22⋊C4—24no—
144C11×C22⋊C4—42no—
145C11×C22⋊C4—42no—
146C42×C11C2×D412yes—
147C42×C11C2×D412yes—
148C22⋊Dic11—28no—
149C22⋊Dic11—44no—
150C22⋊Dic11—82no—
151C4⋊Dic11—28no—
152C4⋊Dic11—22no—
153C4⋊Dic11—24no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C2×D414yes—
158Dic11⋊C4—28no—
159Dic11⋊C4—24no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C4×Dic11—81no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×#554—111no—
167C2×#489—111no—
168C2×#463D1111yescharacteristic
169#2592—111no—
170#2026—112no—
171#2025—112no—
172#1988—111no—
173#1985—111no—
174#1879—112no—
175#1877—112no—
176#1762—111no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11C22×D411yescharacteristic
188Q8×C11—41no—
189Q8×C11—41no—
190Q8×C11—42no—
191D4×C11—22no—
192D4×C11—24no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—42no—
196D4×C11#12414yes—
197C2×C4×C11—22no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—48no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11#12012yes—
206C2×C4×C11#12012yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C2×#4112yes—
210C2×C4×C112−1+412yes—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—24no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—88no—
224Dic22—44no—
225Dic22—84no—
226C8×C11—41no—
227C8×C11—41no—
228C11⋊C8—42no—
229C22×SD16C2×D1111yescharacteristic
230C22×D8C2×D1111yescharacteristic
231#554—224no—
232#554—224no—
233C2×C4⋊Q8—111no—
234C2×#125—112no—
235C2×#124C2×D1111yescharacteristic
236C2×C22⋊Q8—222no—
237C2×C22⋊Q8—221no—
238C2×C4×Q8—111no—
239C2×C4×D4—112no—
240C2×C4×D4C2×D1111yescharacteristic
241C22×C4⋊C4—221no—
242#489—224no—
243#463—24no—
244C2×C4⋊C8C2×D1111yescharacteristic
245C2×#103—112no—
246C2×#103C2×D1111yescharacteristic
247C2×#102—112no—
248C2×#102—112no—
249C2×#102C2×D1111yescharacteristic
250C2×#97—111no—
251#397—221no—
252#393—221no—
253#391—112no—
254#390—112no—
255#388—222no—
256C4×C4⋊C4—111no—
257#340—112no—
258#340—112no—
259#340—112no—
260#336—112no—
261#336—112no—
262C22×C11—24no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11C2×#12011yescharacteristic
273C22×C11#54812yes—
274C22×C11#57512yes—
275C22×C11#57611yescharacteristic
276C22×C11#57711yescharacteristic
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—42no—
280C4×C11—81no—
281C4×C11C2×#12411yescharacteristic
282C4×C11#53611yescharacteristic
283C4×C11#54812yes—
284Dic11—42no—
285Dic11—44no—
286Dic11—42no—
287Dic11—82no—
288C22×Q8—111no—
289C22×Q8—221no—
290C22×Q8C22×D1111yescharacteristic
291C22×D4C22×D1111yescharacteristic
292C22×D4C22×D1111yescharacteristic
293C23×C4—21no—
294C23×C4—222no—
295C2×SD16—24no—
296C2×SD16—22no—
297C2×D8—24no—
298C2×D8—22no—
299C22×C8—112no—
300C22×C8C22×D1111yescharacteristic
301C22×C8C22×D1111yescharacteristic
302C4⋊Q8—114no—
303C4⋊Q8—222no—
304#125—224no—
305#125—224no—
306#124—22no—
307#124—22no—
308C22⋊Q8—2216no—
309C22⋊Q8—228no—
310C4×Q8—222no—
311C4×Q8—222no—
312C4×D4—22no—
313C4×D4—224no—
314C4×D4—224no—
315C4×D4C22⋊D1114yes—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—112no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—228no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4C22×D1111yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—222no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C42—112no—
332C2×C42—221no—
333C2×C42C22×D1111yescharacteristic
334C4⋊C8—22no—
335#103—22no—
336#103—224no—
337#102—22no—
338#102—224no—
339#102—224no—
340#97—222no—
341#95—222no—
342#95—222no—
343#95—221no—
344C2×C11—44no—
345C2×C11—161no—
346C2×C11#243611yescharacteristic
347C2×C11#300511yescharacteristic
348C2×C11#301211yescharacteristic
349C2×C11#337012yes—
350C2×C11#337612yes—
351C24—21no—
352C24—21no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8—222no—
358C2×Q8—224no—
359C2×Q8—442no—
360C2×Q8—881no—
361C2×Q8—881no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4#434114yes—
369C2×D4C2×C22⋊D1112yes—
370C22×C4—21no—
371C22×C4—24no—
372C22×C4—21no—
373C22×C4—44no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—222no—
377C22×C4—228no—
378C22×C4—222no—
379C22×C4—882no—
380C22×C4—882no—
381C22×C4D4×D1111yescharacteristic
382C22×C4D4×D1111yescharacteristic
383C22×C4C23×D1111yescharacteristic
384SD16—44no—
385D8—44no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C4⋊C4—21no—
394C4⋊C4—114no—
395C4⋊C4—228no—
396C4⋊C4—228no—
397C4⋊C4—222no—
398C4⋊C4—224no—
399C4⋊C4—224no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4C2×C22⋊D1112yes—
404C22⋊C4—24no—
405C22⋊C4—42no—
406C22⋊C4—42no—
407C22⋊C4—228no—
408C22⋊C4—444no—
409C22⋊C4—882no—
410C42—222no—
411C42—222no—
412C42—881no—
413C42D4×D1112yes—
414C42C2×C22⋊D1112yes—
415C11#2594011yescharacteristic, complemented, Sylow
416C23—22no—
417C23—24no—
418C23—41no—
419C23—41no—
420C23—42no—
421C23—41no—
422C23—41no—
423C23—42no—
424C23—41no—
425C23—42no—
426C23C2×D4×D1111yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—42no—
430Q8—444no—
431Q8—884no—
432D4—22no—
433D4—24no—
434D4—41no—
435D4—41no—
436D4—42no—
437D4#6698914yes—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—48no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—224no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—888no—
459C2×C4#6699012yes—
460C2×C4#6699012yes—
461C2×C4C2×D4×D1111yescharacteristic
462C2×C4C2×#434112yes—
463C2×C4#6704312yes—
464C2×C4C22×C22⋊D1111yescharacteristic
465C8—41no—
466C8—41no—
467C8—442no—
468C22—24no—
469C22—44no—
470C22—42no—
471C22—44no—
472C22—42no—
473C22—82no—
474C22—81no—
475C22—82no—
476C22—81no—
477C22—81no—
478C22#1062312912yes—
479C22#1062330011yescharacteristic
480C22#1062330111yescharacteristic
481C22#1062330412yes—
482C22C2×#6699011yescharacteristic
483C4—22no—
484C4—22no—
485C4—42no—
486C4—81no—
487C4—442no—
488C4—442no—
489C4—444no—
490C4—882no—
491C4#1062312912yes—
492C4C2×#6698911yescharacteristic
493C4#1062335611yescharacteristic
494C2—44no—
495C2—161no—
496C2#1307227511yescharacteristic
497C2#1307785511yescharacteristic
498C2#1307791611yescharacteristic
499C2#1308136612yes—
500C2#1308144012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×#463D11
hypocenterC11#25940
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. C2×#10622668C2semidirect
3. #13074105C2semidirect
4. #13069765C2semidirect
5. #13069760C2semidirect
6. #13069567C2semidirect
7. #13069555C2semidirect
9. #13068952C2semidirect
10. #13068441C2semidirect
415. C11#25940semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106226682
#130741052
#130697652
#130697602
#130695672
#130695552
#130689662
#130689522
#130684412
C2×C11×#4632
#2594011