Finite Group Databasebeta

← #14760307

Subgroups — #14760307

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622714C211yesmaximal, characteristic, complemented
3#13071311C212yesmaximal, complemented
4#13069483C211yesmaximal, characteristic, complemented
5#13069350C211yesmaximal, characteristic, complemented
6#13069315C212yesmaximal, complemented
7#13069055C212yesmaximal, complemented
8#13068645C211yesmaximal, characteristic, complemented
9#107×Dic11C211yesmaximal, characteristic, complemented
10#13068443C212yesmaximal, complemented
11C2×C11×#466C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#121C2212yes—
15C2×D4×Dic11C2212yes—
16C2×#66979C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C11×#466C418yescomplemented
19C2×C11×#107C2211yescharacteristic
20C2×C11×#102C2212yes—
21#10622834—22no—
22#10622834C2212yes—
23#10622833—22no—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26#10622825C2212yes—
27D8×Dic11—24no—
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30#10622714—24no—
31C2×#66879C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622598C2212yes—
36C4⋊C4×Dic11C2212yes—
37#10622564—22no—
38#10622563—22no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11—22no—
43C22×D4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—22no—
46C2×C11×D8—22no—
47C2×C11×D8—22no—
48C2×C11×D8C2×C414yes—
49C22×C8×C11—22no—
50C22×C8×C11—22no—
51C22×C8×C11C2×C414yescomplemented
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×#121—24no—
55C11×#121C2×C418yescomplemented
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—22no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11D411yescharacteristic
63C2×C22⋊Dic11D411yescharacteristic
64D4×Dic11—24no—
65D4×Dic11—24no—
66#66979—22no—
67#66979—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2312yes—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2311yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C2×#4318—22no—
77C2×#4318—22no—
78C2×#4318—22no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C11×#107C2×C414yescomplemented
82C11×#102C2×C418yescomplemented
83#66896—24no—
84#66896—24no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66882—22no—
89#66882—22no—
90#66879—22no—
91#66879—22no—
92C8×Dic11—22no—
93C8×Dic11D414yescomplemented
94#21524—111nomaximal, Sylow
95C24×C11—22no—
96C24×C11C2×D411yescharacteristic
97C2×D4×C11—28no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—82no—
104C2×D4×C11—82no—
105C2×D4×C11C22×C414yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4112yes—
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—44no—
118C22×Dic11—82no—
119C22×Dic11—82no—
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C22×Dic11C2×D411yescharacteristic
124C11×D8—28no—
125C2×C8×C11—28no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C2×D412yes—
131C2×C8×C11#4112yes—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C22×C414yes—
134C11×C22⋊C4—28no—
135C22⋊Dic11—22no—
136C22⋊Dic11—22no—
137C22⋊Dic11—44no—
138C22⋊Dic11—82no—
139C22⋊Dic11—82no—
140C22⋊Dic11—82no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—82no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150C4×Dic11—82no—
151C4×Dic11C2×D412yes—
152C4×Dic11#4112yes—
153#4318—28no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8C2×D412yes—
159C2×C11⋊C8#4112yes—
160C2×#466D1111yescharacteristic
161C2×C4×D8—111no—
162C2×#405—111no—
163#2324—112no—
164#1970—111no—
165#1942—111no—
166#1936—112no—
167#1895—112no—
168#1808—111no—
169C4×#107—111no—
170#1762—112no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—24no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11C4×D412yes—
185C23×C11C22×D411yescharacteristic
186D4×C11—24no—
187D4×C11—24no—
188D4×C11—42no—
189D4×C11—42no—
190D4×C11—88no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11C4×D412yes—
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—88no—
224C2×Dic11#12112yes—
225C2×Dic11#12112yes—
226C8×C11—22no—
227C8×C11C4×D414yes—
228C11⋊C8—22no—
229C11⋊C8—22no—
230C22×D8C2×D1111yescharacteristic
231C22×M16—111no—
232C23×C8C2×D1111yescharacteristic
233C2×#121C2×D1112yes—
234C2×C4×D4—112no—
235C2×#117—111no—
236#466Dic1118yescomplemented
237C4×D8—224no—
238C2×#107—111no—
239C2×#107—111no—
240C2×#107C2×D1111yescharacteristic
241C2×#102—112no—
242C2×#102—112no—
243C2×#102C2×D1112yes—
244#405—224no—
245C2×#97—111no—
246C2×#97—111no—
247C2×C4×C8—111no—
248C2×C4×C8—111no—
249#390—112no—
250#390—222no—
251#389—112no—
252#388—222no—
253#386—222no—
254#385—222no—
255#380—112no—
256C4×C4⋊C4—112no—
257#340—112no—
258#340—112no—
259#340—112no—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11C2×C4×D411yescharacteristic
275C22×C11C2×#12111yescharacteristic
276C22×C11#53211yescharacteristic
277C22×C11#57611yescharacteristic
278C22×C11#57611yescharacteristic
279C22×C11#57611yescharacteristic
280C22×C11#57811yescharacteristic
281C4×C11—22no—
282C4×C11—44no—
283C4×C11C2×C4×D411yescharacteristic
284C4×C11C4×#4111yescharacteristic
285C4×C11#52511yescharacteristic
286C4×C11#52911yescharacteristic
287Dic11—22no—
288Dic11—22no—
289Dic11—41no—
290Dic11—41no—
291Dic11—82no—
292Dic11—82no—
293C22×D4—22no—
294C22×D4C22×D1112yes—
295C23×C4—222no—
296C23×C4C22×D1111yescharacteristic
297C2×D8—22no—
298C2×D8—22no—
299C2×D8C2×Dic1114yes—
300C2×M16—222no—
301C2×M16—222no—
302C2×M16—222no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—111no—
306C22×C8—111no—
307C22×C8C2×Dic1114yescomplemented
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310#121—24no—
311#121C2×Dic1118yescomplemented
312C4×D4—224no—
313C4×D4—224no—
314#117—222no—
315#117—222no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—112no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4C22×D1112yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—111no—
324C2×C22⋊C4—111no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C42—111no—
330C2×C42—111no—
331C2×C42—222no—
332#107—222no—
333#107—222no—
334#107C2×Dic1114yescomplemented
335#102—224no—
336#102—224no—
337#102C2×Dic1118yescomplemented
338#97—222no—
339#97—222no—
340C4×C8—114no—
341C4×C8—222no—
342#95—222no—
343#95—222no—
344#95—222no—
345C2×C11—42no—
346C2×C11—84no—
347C2×C11C4×#12111yescharacteristic
348C2×C11#294811yescharacteristic
349C2×C11#295111yescharacteristic
350C2×C11#305811yescharacteristic
351C2×C11#306111yescharacteristic
352C2×C11#317511yescharacteristic
353C2×C11#317611yescharacteristic
354C24—22no—
355C24D4×D1111yescharacteristic
356C2×D4—28no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—82no—
363C2×D4—82no—
364C2×D4C22×Dic1114yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—444no—
377C22×C4—882no—
378C22×C4—882no—
379C22×C4D4×D1111yescharacteristic
380C22×C4#434112yes—
381C22×C4C22×Dic1112yes—
382C22×C4C23×D1111yescharacteristic
383D8—28no—
384M16—228no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—28no—
388C2×C8—112no—
389C2×C8—112no—
390C2×C8—221no—
391C2×C8—221no—
392C2×C8—221no—
393C2×C8—221no—
394C2×C8D4×D1112yes—
395C2×C8#434112yes—
396C2×C8C22×Dic1112yes—
397C2×C8C22×Dic1112yes—
398C4⋊C4—22no—
399C4⋊C4—222no—
400C4⋊C4—222no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—222no—
405C4⋊C4—882no—
406C4⋊C4C22×Dic1114yes—
407C22⋊C4—28no—
408C22⋊C4—222no—
409C22⋊C4—222no—
410C22⋊C4—444no—
411C22⋊C4—882no—
412C22⋊C4—882no—
413C22⋊C4—882no—
414C42—112no—
415C42—112no—
416C42—221no—
417C42—221no—
418C42—882no—
419C11#2152411yescharacteristic, complemented, Sylow
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—24no—
427C23—42no—
428C23—42no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23D4×Dic1112yes—
434C23C2×D4×D1111yescharacteristic
435D4—24no—
436D4—24no—
437D4—42no—
438D4—42no—
439D4—88no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—888no—
468C2×C4D4×Dic1112yes—
469C2×C4C2×D4×D1111yescharacteristic
470C2×C4C2×#434111yescharacteristic
471C2×C4C2×#434111yescharacteristic
472C2×C4#41×D1111yescharacteristic
473C2×C4#41×D1111yescharacteristic
474C2×C4C23×Dic1111yescharacteristic
475C8—22no—
476C8—222no—
477C8—222no—
478C8D4×Dic1114yes—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—44no—
487C22—44no—
488C22—44no—
489C22—82no—
490C22—82no—
491C22—82no—
492C22—82no—
493C22#1062312711yescharacteristic
494C22D11×#12111yescharacteristic
495C22#1062328811yescharacteristic
496C22#1062328811yescharacteristic
497C22#1062330011yescharacteristic
498C22#1062330211yescharacteristic
499C22C2×D4×Dic1111yescharacteristic
500C4—22no—
501C4—44no—
502C4—222no—
503C4—222no—
504C4—441no—
505C4—441no—
506C4—882no—
507C4—882no—
508C4#1062313111yescharacteristic
509C4#1062313711yescharacteristic
510C4C2×D4×Dic1111yescharacteristic
511C4#41×Dic1111yescharacteristic
512C2—42no—
513C2—84no—
514C2#121×Dic1111yescharacteristic
515C2#1307746811yescharacteristic
516C2#1307749211yescharacteristic
517C2#1307825911yescharacteristic
518C2#1307828111yescharacteristic
519C2#1307924811yescharacteristic
520C2#1307925911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#466C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#466D11
hypocenterC11#21524
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×D8×Dic11C2semidirect
2. C2×#10622714C2semidirect
3. #13071311C2semidirect
4. #13069483C2semidirect
5. #13069350C2semidirect
6. #13069315C2semidirect
7. #13069055C2semidirect
8. #13068645C2semidirect
9. #107×Dic11C2semidirect
10. #13068443C2semidirect
18. C11×#466C4semidirect
51. C22×C8×C11C2×C4semidirect
55. C11×#121C2×C4semidirect
81. C11×#107C2×C4semidirect
82. C11×#102C2×C4semidirect
93. C8×Dic11D4semidirect
236. #466Dic11semidirect
307. C22×C8C2×Dic11semidirect
311. #121C2×Dic11semidirect
334. #107C2×Dic11semidirect
337. #102C2×Dic11semidirect
419. C11#21524semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic112
C2×#106227142
#130713112
#130694832
#130693502
#130693152
#130690552
#130686452
#107×Dic112
#130684432
C2×C11×#4662
#2152411