Finite Group Databasebeta

← #14788680

Subgroups — #14788680

Order 2816.

1180 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3#13073970C211yesmaximal, characteristic, complemented
4#13069853C212yesmaximal, complemented
5#13069690C212yesmaximal, complemented
6#13069556C211yesmaximal, characteristic, complemented
7#13069440C211yesmaximal, characteristic, complemented
8#13068961C212yesmaximal, complemented
9#13068860C212yesmaximal, complemented
10#13068631C211yesmaximal, characteristic, complemented
11C2×C11×#440C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#67000C2212yes—
16C22×#4323C2212yes—
17#10623116—24no—
18#10623116—24no—
19C2×#66947—22no—
20C2×#66946C2212yes—
21C2×#66928—21no—
22C2×#66927C2211yescharacteristic
23C2×C4×D44—21no—
24C2×C4×Dic22C2211yescharacteristic
25C11×#440—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×#66899C2212yes—
31#10622834C2212yes—
32#10622823—22no—
33C2×#66885C2212yes—
34C2×#66885C2212yes—
35#10622628—24no—
36#10622586C2212yes—
37C2×#66873C2212yes—
38#10622562—21no—
39#10622560—21no—
40#10622549C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44C2312yes—
51C22×C4×D11—22no—
52C22×Dic22D411yescharacteristic
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C2×C11×SD16—22no—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C4×Q8×C11—22no—
59C4×Q8×C11D414yes—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70#67000—24no—
71#67000—24no—
72C2×#4323—24no—
73C2×#4323—24no—
74C2×#4323—42no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4D412yes—
82C2×C4×Dic11C2312yes—
83C22×C11⋊C8C2312yes—
84#66947—216no—
85#66946—24no—
86#66946—24no—
87#66928—28no—
88#66927—22no—
89#66927D414yes—
90C4×D44—28no—
91C4×Dic22—22no—
92C4×Dic22—22no—
93C11×#107—22no—
94C11×#103—22no—
95C11×#102—22no—
96C11×#97—22no—
97#66899—42no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—22no—
101#66885—24no—
102#66885—42no—
103#66873—24no—
104C4⋊(C11⋊C8)—22no—
105#24198—111nomaximal, Sylow
106C24×C11—21no—
107C23×D11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11C2×D412yes—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11#4112yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—42no—
124C22×C4×C11—82no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—22no—
129C22×Dic11C2×D412yes—
130C22×Dic11C2×D412yes—
131C2×D44—24no—
132C2×D44—24no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—44no—
139C2×D44—82no—
140C2×D44C2×D414yes—
141C2×C4×D11—28no—
142C2×C4×D11—82no—
143C2×C4×D11—82no—
144C2×Dic22—22no—
145C2×Dic22—42no—
146C11×SD16—28no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11#4112yes—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—42no—
159C42×C11—24no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—44no—
163C22⋊Dic11—82no—
164#4323—48no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—28no—
167(C2×D11)⋊C4—28no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171Dic11⋊C4—24no—
172Dic11⋊C4—82no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×#559—111no—
179C2×#459—111no—
180C2×#440D1111yescharacteristic, complemented
181#2580—111no—
182#2042—112no—
183#2012—112no—
184#1985—111no—
185#1961—111no—
186#1879—112no—
187#1862—112no—
188#1805—111no—
189C23×C11—22no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11C22×D411yescharacteristic
195C22×D11—24no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202Q8×C11—22no—
203Q8×C11—22no—
204Q8×C11—41no—
205Q8×C11—41no—
206D4×C11—22no—
207D4×C11—22no—
208D4×C11—41no—
209D4×C11—41no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—84no—
220C2×C4×C11#12012yes—
221C2×C4×C11#12012yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11H(5,𝔽2)11yescharacteristic
227C2×C4×C112−1+411yescharacteristic
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237D44—24no—
238D44—24no—
239D44—48no—
240D44—42no—
241D44—42no—
242D44—84no—
243C4×D11—88no—
244Dic22—44no—
245C8×C11—22no—
246C8×C11—41no—
247C11⋊C8—42no—
248C22×SD16C2×D1111yescharacteristic
249C22×D8—112no—
250#559—224no—
251#559—224no—
252C2×#127—111no—
253C2×#124—112no—
254C2×#124—221no—
255C2×#123—222no—
256C2×C4×Q8—111no—
257C2×C4×Q8C2×D1111yescharacteristic
258C2×C4×D4—112no—
259C2×C4×D4—221no—
260C2×C4×D4C2×D1111yescharacteristic
261#459—224no—
262#440—24no—
263C2×#107C2×D1111yescharacteristic
264C2×C4⋊C8—111no—
265C2×#103—112no—
266C2×#103C2×D1111yescharacteristic
267C2×#102—112no—
268C2×#102—112no—
269C2×#102—112no—
270C2×#102C2×D1111yescharacteristic
271C2×#97C2×D1111yescharacteristic
272#399—221no—
273#393—221no—
274#390—112no—
275#389—112no—
276#385—222no—
277#382—111no—
278#340—112no—
279#336—112no—
280#336—112no—
281C22×C11—44no—
282C22×C11—42no—
283C22×C11—82no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11C2×#12011yescharacteristic
287C22×C11#54811yescharacteristic
288C22×C11#55011yescharacteristic
289C22×C11#57512yes—
290C22×C11#57612yes—
291C2×D11—44no—
292C2×D11—44no—
293C2×D11—44no—
294C2×D11—82no—
295C2×D11—82no—
296C2×D11—82no—
297C2×D11—82no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—81no—
303C4×C11#52511yescharacteristic
304C4×C11#53711yescharacteristic
305C4×C11#54611yescharacteristic
306C4×C11#54711yescharacteristic
307Dic11—42no—
308Dic11—42no—
309Dic11—82no—
310C22×Q8—111no—
311C22×Q8C22×D1111yescharacteristic
312C22×D4—112no—
313C22×D4—221no—
314C22×D4—221no—
315C22×D4C22×D1111yescharacteristic
316C23×C4—21no—
317C23×C4—222no—
318C2×SD16—22no—
319C2×SD16—22no—
320C2×SD16—22no—
321C2×D8—224no—
322C2×D8—224no—
323C2×D8—442no—
324C22×C8—112no—
325C22×C8C22×D1111yescharacteristic
326C22×C8C22×D1111yescharacteristic
327#127—114no—
328#127—222no—
329#124—228no—
330#124—224no—
331#124—224no—
332#123—2216no—
333C4×Q8—22no—
334C4×Q8—222no—
335C4×Q8—222no—
336C4×Q8C22⋊D1114yes—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—228no—
340C4×D4—224no—
341C4×D4—224no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—222no—
351C2×C22⋊C4—222no—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C42—21no—
356C2×C42—112no—
357C2×C42C22×D1111yescharacteristic
358#107—22no—
359C4⋊C8—222no—
360#103—22no—
361#103—442no—
362#102—22no—
363#102—224no—
364#102—224no—
365#102—442no—
366#97—22no—
367#95—222no—
368#95—221no—
369#95—221no—
370C2×C11—82no—
371C2×C11#240711yescharacteristic
372C2×C11#300511yescharacteristic
373C2×C11#300811yescharacteristic
374C2×C11#337012yes—
375C2×C11#340312yes—
376D11—84no—
377C24—21no—
378C24—222no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—222no—
385C2×Q8—442no—
386C2×Q8C2×C22⋊D1112yes—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—114no—
393C2×D4—224no—
394C2×D4—224no—
395C2×D4—222no—
396C2×D4—222no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—444no—
401C2×D4—882no—
402C2×D4#433912yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—42no—
407C22×C4—82no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—228no—
411C22×C4—222no—
412C22×C4—882no—
413C22×C4—882no—
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417SD16—28no—
418D8—448no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8#433912yes—
428C4⋊C4—24no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—222no—
433C4⋊C4—224no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—882no—
437C4⋊C4C2×C22⋊D1112yes—
438C22⋊C4—42no—
439C22⋊C4—228no—
440C22⋊C4—228no—
441C22⋊C4—228no—
442C22⋊C4—444no—
443C22⋊C4—882no—
444C42—24no—
445C42—222no—
446C42—222no—
447C42D4×D1112yes—
448C42C2×C22⋊D1112yes—
449C11#2419811yescharacteristic, complemented, Sylow
450C23—22no—
451C23—42no—
452C23—42no—
453C23—41no—
454C23—41no—
455C23—224no—
456C23—442no—
457C23—442no—
458C23—442no—
459C23—442no—
460C23—442no—
461C23—442no—
462C23C2×D4×D1111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—41no—
466Q8—41no—
467Q8—444no—
468D4—22no—
469D4—22no—
470D4—41no—
471D4—41no—
472D4—224no—
473D4—224no—
474D4—448no—
475D4—442no—
476D4—442no—
477D4—884no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—84no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—888no—
498C2×C4#6699012yes—
499C2×C4#6699012yes—
500C2×C4C2×#433911yescharacteristic
501C2×C4C2×#433911yescharacteristic
502C2×C4C2×D4×D1111yescharacteristic
503C2×C4#6704211yescharacteristic
504C2×C4#6704311yescharacteristic
505C2×C4C22×C22⋊D1111yescharacteristic
506C8—22no—
507C8—41no—
508C8—442no—
509C22—44no—
510C22—42no—
511C22—81no—
512C22—82no—
513C22—81no—
514C22—444no—
515C22—444no—
516C22—444no—
517C22—882no—
518C22—882no—
519C22—882no—
520C22—882no—
521C22#1062308311yescharacteristic
522C22#1062308411yescharacteristic
523C22#1062330512yes—
524C22#1062330812yes—
525C22C2×#6699011yescharacteristic
526C4—22no—
527C4—22no—
528C4—42no—
529C4—42no—
530C4—81no—
531C4—442no—
532C4—442no—
533C4—882no—
534C4#1062308111yescharacteristic
535C4#1062308211yescharacteristic
536C4#1062332211yescharacteristic
537C4#1062336411yescharacteristic
538C2—82no—
539C2—884no—
540C2#1307196111yescharacteristic
541C2#1307785711yescharacteristic
542C2#1307788311yescharacteristic
543C2#1308137012yes—
544C2#1308170512yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC2×#440D11
hypocenterC11#24198
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
3. #13073970C2semidirect
4. #13069853C2semidirect
5. #13069690C2semidirect
6. #13069556C2semidirect
7. #13069440C2semidirect
8. #13068961C2semidirect
9. #13068860C2semidirect
10. #13068631C2semidirect
11. C2×C11×#440C2semidirect
180. C2×#440D11semidirect
449. C11#24198semidirect

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106226282
#130739702
#130698532
#130696902
#130695562
#130694402
#130689612
#130688602
#130686312
C2×C11×#4402
#2419811