Finite Group Databasebeta

← #14770602

Subgroups — #14770602

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623073C211yesmaximal, characteristic
2C2×#10622444C211yesmaximal, characteristic, complemented
3#13071528C211yesmaximal, characteristic, complemented
4#13069547C212yesmaximal
5#13069538C211yesmaximal, characteristic, complemented
6#13069431C212yesmaximal
7#13069417C211yesmaximal, characteristic, complemented
8#13068620C212yesmaximal, complemented
9#13068445C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic
11C11×#1802C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66989C2212yes—
14C2×#66979—21no—
15C2×#66977—21no—
16#10623073—24no—
17#10623073C418yescomplemented
18C2×#66940—21no—
19C2×#66940C2212yes—
20C2×#66932—22no—
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2212yes—
25C11×#384C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66880C2212yes—
29C2×#66880C2212yes—
30C2×#66879C2212yes—
31C2×Dic11⋊C8C2212yes—
32#10622589C2212yes—
33C4⋊C4×Dic11C2212yes—
34#10622586—21no—
35#10622585—22no—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622444—24no—
41C11×#340C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×Dic22D411yescharacteristic
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C4×D4×C11—22no—
50C4×D4×C11C2×C414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59#66989—24no—
60#66989C2×C418yes—
61#66979—28no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67#66977—28no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4D412yes—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78#66940—24no—
79#66940—44no—
80#66940C2×C418yes—
81#66932—216no—
82#66922—22no—
83#66922C2×C414yes—
84C4×Dic22C2×C414yes—
85C4×Dic22D414yes—
86C11×C4⋊C8—22no—
87C11×#102—42no—
88#66896—22no—
89#66896—22no—
90C11⋊#95—21no—
91C11⋊#95—22no—
92#66880—24no—
93#66880—42no—
94#66879—24no—
95Dic11⋊C8—24no—
96#66874—24no—
97#66874—42no—
98C4×C11⋊C8—22no—
99#22544—111nomaximal, Sylow
100C24×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11C22×C412yes—
107C22×C4×C11—21no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—22no—
117C22×Dic11—21no—
118C22×Dic11C2×D412yes—
119C22×Dic11C2×D412yes—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22C22⋊C414yes—
128C2×Dic22C22×C414yes—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—81no—
137C11×C4⋊C4C22×C412yes—
138C11×C22⋊C4—24no—
139C42×C11C22×C412yes—
140C42×C11C2×D412yes—
141C22⋊Dic11—28no—
142C22⋊Dic11—28no—
143C4⋊Dic11—24no—
144C4⋊Dic11—24no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11C22⋊C414yes—
149C4⋊Dic11#4112yes—
150Dic11⋊C4—28no—
151Dic11⋊C4—44no—
152Dic11⋊C4—82no—
153Dic11⋊C4C22⋊C418yes—
154C4×Dic11—28no—
155C4×Dic11—44no—
156C4×Dic11—42no—
157C4×Dic11C22×C414yes—
158C4×Dic11C2×D414yes—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8#4112yes—
165C2×#556—111no—
166C2×#446—111no—
167Q8×C4⋊C4—111no—
168#1983—112no—
169#1981—111no—
170#1959—112no—
171#1956—111no—
172#1803—112no—
173#1802D1111yescharacteristic
174#1763—112no—
175C4×#102—111no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11C22×D411yescharacteristic
184D4×C11—22no—
185D4×C11—22no—
186D4×C11—41no—
187D4×C11—41no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—48no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11C2×C22⋊C412yes—
198C2×C4×C11C2×C22⋊C412yes—
199C2×C4×C11AGL(1,ℤ/8)12yes—
200C2×C4×C11#13712yes—
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—24no—
212C2×Dic11—22no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11C2×C22⋊C414yes—
221C2×Dic11C2×C22⋊C414yes—
222Dic22—28no—
223Dic22—24no—
224Dic22—24no—
225Dic22—42no—
226Dic22—42no—
227C8×C11—42no—
228C11⋊C8—22no—
229C11⋊C8—41no—
230#556—118no—
231#556—224no—
232C2×C4⋊Q8—111no—
233C2×#126—222no—
234C2×#124—112no—
235C2×C22⋊Q8—221no—
236C2×C4×Q8—111no—
237C2×C4×Q8—112no—
238C2×C4×Q8—221no—
239C2×C4×D4C2×D1111yescharacteristic
240C2×#117—221no—
241#446—224no—
242C2×C4⋊C8—112no—
243C2×C4⋊C8C2×D1111yescharacteristic
244C2×#103—112no—
245C2×#103—112no—
246C2×#103—112no—
247C2×#103—112no—
248C2×#102—111no—
249C2×#102—111no—
250C2×#102C2×D1112yes—
251C2×#97—112no—
252C2×C4×C8—111no—
253#389—222no—
254#389—221no—
255#384—112no—
256#384C2×D1111yescharacteristic
257C4×C4⋊C4—112no—
258C4×C4⋊C4—111no—
259#340—111no—
260#340—111no—
261#340C2×D1112yes—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11#54811yescharacteristic
271C22×C11#55011yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C4×C11—22no—
277C4×C11—42no—
278C4×C11—82no—
279C4×C11#41714yes—
280C4×C11C4×#4111yescharacteristic
281C4×C11#52011yescharacteristic
282C4×C11#54811yescharacteristic
283C4×C11#55011yescharacteristic
284Dic11—24no—
285Dic11—24no—
286Dic11—44no—
287Dic11—42no—
288Dic11—81no—
289C22×Q8—111no—
290C22×Q8—112no—
291C22×D4C22×D1111yescharacteristic
292C23×C4—21no—
293C22×C8—111no—
294C22×C8—111no—
295C22×C8C22×D1112yes—
296C4⋊Q8—114no—
297C4⋊Q8—222no—
298#126—2216no—
299#124—118no—
300#124—224no—
301C22⋊Q8—228no—
302C4×Q8—114no—
303C4×Q8—114no—
304C4×Q8—118no—
305C4×Q8—224no—
306C4×Q8—444no—
307C4×D4—22no—
308C4×D4C4×D1114yes—
309#117—228no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4C22×D1112yes—
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—222no—
326C2×C42—112no—
327C2×C42—222no—
328C2×C42—222no—
329C2×C42—221no—
330C2×C42C22×D1111yescharacteristic
331C4⋊C8—22no—
332C4⋊C8—224no—
333#103—224no—
334#103—224no—
335#103—442no—
336#103—442no—
337#102—42no—
338#102—222no—
339#102—222no—
340#97—224no—
341C4×C8—222no—
342#95—222no—
343#95—221no—
344C2×C11—82no—
345C2×C11#234111yescharacteristic
346C2×C11C2×#41711yescharacteristic
347C2×C11#289811yescharacteristic
348C2×C11#336711yescharacteristic
349C2×C11#336911yescharacteristic
350C2×C11#339711yescharacteristic
351C2×C11#339811yescharacteristic
352C24—21no—
353C2×Q8—114no—
354C2×Q8—114no—
355C2×Q8—222no—
356C2×Q8—222no—
357C2×Q8—222no—
358C2×Q8—222no—
359C2×Q8—222no—
360C2×Q8—222no—
361C2×Q8—222no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C2×C4×D1112yes—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—221no—
376C22×C4—222no—
377C22×C4—221no—
378C22×C4D4×D1111yescharacteristic
379C22×C4D4×D1111yescharacteristic
380C22×C4C23×D1111yescharacteristic
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—112no—
385C2×C8—221no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—221no—
389C2×C8—221no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—42no—
394C4⋊C4—81no—
395C4⋊C4—114no—
396C4⋊C4—118no—
397C4⋊C4—112no—
398C4⋊C4—228no—
399C4⋊C4—224no—
400C4⋊C4—224no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—444no—
405C4⋊C4—882no—
406C4⋊C4C2×C4×D1112yes—
407C22⋊C4—24no—
408C22⋊C4—228no—
409C22⋊C4—228no—
410C42—114no—
411C42—114no—
412C42—228no—
413C42—444no—
414C42—442no—
415C42C2×C4×D1112yes—
416C42D4×D1112yes—
417C11#2254411yescharacteristic, complemented, Sylow
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C2×D4×D1111yescharacteristic
426Q8—228no—
427Q8—224no—
428Q8—224no—
429Q8—442no—
430Q8—442no—
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—48no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—114no—
445C2×C4—114no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—224no—
451C2×C4—222no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4C22⋊C4×D1112yes—
460C2×C4C22⋊C4×D1112yes—
461C2×C4#6696412yes—
462C2×C4#6696812yes—
463C2×C4C22×C4×D1111yescharacteristic
464C2×C4C2×D4×D1111yescharacteristic
465C2×C4#6703711yescharacteristic
466C2×C4#6704011yescharacteristic
467C2×C4#41×D1111yescharacteristic
468C2×C4#41×D1111yescharacteristic
469C8—42no—
470C8—222no—
471C8—441no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22C2×C22⋊C4×D1111yescharacteristic
480C22#1062313011yescharacteristic
481C22#1062316411yescharacteristic
482C22C2×#6696411yescharacteristic
483C22C2×#6696811yescharacteristic
484C22#1062330611yescharacteristic
485C22#1062331011yescharacteristic
486C4—22no—
487C4—42no—
488C4—82no—
489C4—224no—
490C4—224no—
491C4—444no—
492C4—442no—
493C4—881no—
494C4#1062238414yes—
495C4#1062303511yescharacteristic
496C4#1062305311yescharacteristic
497C4#1062313011yescharacteristic
498C4#1062316411yescharacteristic
499C2—82no—
500C2#1307145311yescharacteristic
501C2C2×#1062238411yescharacteristic
502C2#1307714711yescharacteristic
503C2#1308133311yescharacteristic
504C2#1308135511yescharacteristic
505C2#1308164011yescharacteristic
506C2#1308165111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1802D11
hypocenterC11#22544
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#10622444C2semidirect
3. #13071528C2semidirect
5. #13069538C2semidirect
7. #13069417C2semidirect
8. #13068620C2semidirect
9. #13068445C2semidirect
17. #10623073C4semidirect
417. C11#22544semidirect

Maximal subgroups

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

subgroupindex
C2×#106230732
C2×#106224442
#130715282
#130695472
#130695382
#130694312
#130694172
#130686202
#130684452
C4×#668962
C11×#18022
#2254411