Finite Group Databasebeta

← #14770357

Subgroups — #14770357

Order 2816.

1314 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×D4×Dic22C211yesmaximal, characteristic
2C2×#10622443C211yesmaximal, characteristic, complemented
3#13071528C211yesmaximal, characteristic, complemented
4#13069576C211yesmaximal, characteristic, complemented
5#13069575C212yesmaximal, complemented
6#13069567C211yesmaximal, characteristic, complemented
7#13069566C212yesmaximal, complemented
8#13068614C212yesmaximal
9#102×Dic11C212yesmaximal
10C4×#66896C211yesmaximal, characteristic
11C11×#1802C211yesmaximal, characteristic
12C23×Dic22—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×D4×Dic11C2212yes—
15C2×#66977—21no—
16D4×Dic22—24no—
17D4×Dic22C418yescomplemented
18C2×#66941C2212yes—
19C2×#66940—21no—
20C2×#66931—22no—
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#102C2212yes—
25C11×#384C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×Dic11⋊C8C2212yes—
29C2×C8×Dic11C2212yes—
30#10622589C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622586—21no—
33#10622585—22no—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622443—24no—
37C11×#340C2212yes—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622167C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×Dic11—22no—
47C22×Dic22—21no—
48C22×Dic22—22no—
49C22×Dic22—28no—
50C22×Dic22—44no—
51C22×Dic22—44no—
52C22×Dic22D411yescharacteristic
53C22×C8×C11C2312yes—
54C4×D4×C11—22no—
55C4×D4×C11C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63D4×Dic11—24no—
64D4×Dic11C2×C418yes—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70#66977—28no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4D412yes—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2312yes—
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80#66941—24no—
81#66941C2×C418yes—
82#66940—44no—
83#66931—216no—
84#66922—22no—
85#66922C2×C414yes—
86C4×Dic22C2×C414yes—
87C4×Dic22D414yes—
88C11×C4⋊C8—22no—
89C11×#102—24no—
90#66896—22no—
91#66896Q814yescomplemented
92C11⋊#95—21no—
93C11⋊#95—22no—
94Dic11⋊C8—24no—
95C8×Dic11—24no—
96C4×C11⋊C8—22no—
97Q8×#102—111nomaximal, Sylow
98C24×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11C22×C412yes—
103C2×D4×C11C2×Q812yes—
104C2×D4×C11#4112yes—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—28no—
114C22×Dic11—21no—
115C22×Dic11—22no—
116C22×Dic11—21no—
117C22×Dic11—44no—
118C22×Dic11—44no—
119C22×Dic11C2×D412yes—
120C22×Dic11C2×D412yes—
121C2×Dic22—28no—
122C2×Dic22—24no—
123C2×Dic22—44no—
124C2×Dic22—44no—
125C2×Dic22—432no—
126C2×Dic22—42no—
127C2×Dic22—42no—
128C2×Dic22C22⋊C414yes—
129C2×Dic22D814yes—
130C2×Dic22SD1614yes—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—81no—
139C11×C4⋊C4C22×C412yes—
140C11×C22⋊C4—24no—
141C42×C11C22×C412yes—
142C42×C11C2×D412yes—
143C22⋊Dic11—28no—
144C4⋊Dic11—24no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11C22⋊C414yes—
150C4⋊Dic11C22×C414yes—
151C4⋊Dic11C2×Q812yescomplemented
152Dic11⋊C4—28no—
153Dic11⋊C4—44no—
154Dic11⋊C4—82no—
155Dic11⋊C4C22⋊C418yes—
156C4×Dic11—44no—
157C4×Dic11—42no—
158C4×Dic11C22×C414yes—
159C4×Dic11C2×D414yes—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8C2×Q812yescomplemented
166C2×D4×Q8—111no—
167C2×C8×Q8—111no—
168Q8×C4⋊C4—111no—
169#1990—111no—
170#1990—112no—
171#1988—111no—
172#1988—112no—
173#1802—112no—
174#1802D1111yescharacteristic
175C4×#102—112no—
176C4×#102—111no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11C22×D411yescharacteristic
185D4×C11—22no—
186D4×C11—22no—
187D4×C11—22no—
188D4×C11C4×Q814yescomplemented
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—48no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11C2×C22⋊C412yes—
199C2×C4×C11C2×C22⋊C412yes—
200C2×C4×C11C2×D812yes—
201C2×C4×C11C2×SD1612yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×Q811yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—24no—
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—416no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11C2×C22⋊C414yes—
221C2×Dic11C2×C22⋊C414yes—
222C2×Dic11C2×D814yes—
223C2×Dic11C2×SD1614yes—
224Dic22—48no—
225Dic22—416no—
226Dic22#102116yescomplemented
227C8×C11—42no—
228C11⋊C8—22no—
229C11⋊C8—41no—
230C23×Q8—221no—
231D4×Q8—118no—
232D4×Q8—224no—
233C2×C4⋊Q8—112no—
234C2×C4⋊Q8—111no—
235C2×C22⋊Q8—222no—
236C2×C22⋊Q8—221no—
237C2×C4×Q8—111no—
238C2×C4×Q8—221no—
239C2×C4×D4—112no—
240C2×C4×D4C2×D1111yescharacteristic
241C8×Q8—224no—
242C2×C4⋊C8—112no—
243C2×C4⋊C8C2×D1111yescharacteristic
244C2×#102—111no—
245C2×#102—111no—
246C2×#102C2×D1112yes—
247C2×C4×C8—112no—
248C2×C4×C8—111no—
249#389—222no—
250#389—221no—
251#384—112no—
252#384C2×D1111yescharacteristic
253C4×C4⋊C4—112no—
254C4×C4⋊C4—111no—
255#340—112no—
256#340—112no—
257#340—112no—
258#340—111no—
259#340—112no—
260#340—111no—
261#340C2×D1112yes—
262C22×C11—24no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11C22×C22⋊C411yescharacteristic
270C22×C11#54811yescharacteristic
271C22×C11D4×Q811yescharacteristic
272C22×C11C22×D811yescharacteristic
273C22×C11C22×SD1611yescharacteristic
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C4×C11—22no—
277C4×C11—42no—
278C4×C11—82no—
279C4×C11C2×#10214yes—
280C4×C11C2×C4×Q811yescharacteristic
281C4×C11#51911yescharacteristic
282C4×C11#54811yescharacteristic
283C4×C11D4×Q811yescharacteristic
284Dic11—24no—
285Dic11—42no—
286Dic11—44no—
287Dic11—81no—
288Dic11C2×#10218yes—
289C22×Q8—111no—
290C22×Q8—222no—
291C22×Q8—228no—
292C22×Q8—221no—
293C22×Q8—444no—
294C22×Q8—444no—
295C22×D4C22×D1111yescharacteristic
296C23×C4—21no—
297C23×C4—222no—
298C22×C8—111no—
299C22×C8—111no—
300C22×C8C22×D1112yes—
301C4⋊Q8—118no—
302C4⋊Q8—114no—
303C4⋊Q8—224no—
304C4⋊Q8—222no—
305C22⋊Q8—2216no—
306C22⋊Q8—228no—
307C4×Q8—114no—
308C4×Q8—114no—
309C4×Q8—444no—
310C4×D4—22no—
311C4×D4—118no—
312C4×D4—224no—
313C4×D4C4×D1114yes—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4C22×D1112yes—
326C2×C4⋊C4C22×D1111yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—222no—
329C2×C42—112no—
330C2×C42—222no—
331C2×C42—221no—
332C2×C42C22×D1111yescharacteristic
333C4⋊C8—22no—
334C4⋊C8—224no—
335#102—24no—
336#102—114no—
337#102—222no—
338C4×C8—224no—
339C4×C8—222no—
340#95—222no—
341#95—221no—
342C2×C11—44no—
343C2×C11Q8×C22⋊C411yescharacteristic
344C2×C11C22×#10211yescharacteristic
345C2×C11#289811yescharacteristic
346C2×C11#335811yescharacteristic
347C2×C11#335911yescharacteristic
348C2×C11Q8×D811yescharacteristic
349C2×C11Q8×SD1611yescharacteristic
350C24—21no—
351C2×Q8—114no—
352C2×Q8—114no—
353C2×Q8—114no—
354C2×Q8—228no—
355C2×Q8—224no—
356C2×Q8—444no—
357C2×Q8—444no—
358C2×Q8—4432no—
359C2×Q8—442no—
360C2×Q8—442no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4C2×C4×D1112yes—
365C2×D4#434112yes—
366C2×D4Q8×D1112yes—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—112no—
373C22×C4—112no—
374C22×C4—228no—
375C22×C4—221no—
376C22×C4—222no—
377C22×C4—221no—
378C22×C4—444no—
379C22×C4—444no—
380C22×C4D4×D1111yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—112no—
387C2×C8—221no—
388C2×C8—221no—
389C2×C8—221no—
390C2×C8—221no—
391C2×C8—221no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—42no—
396C4⋊C4—81no—
397C4⋊C4—118no—
398C4⋊C4—114no—
399C4⋊C4—114no—
400C4⋊C4—112no—
401C4⋊C4—228no—
402C4⋊C4—224no—
403C4⋊C4—222no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—444no—
408C4⋊C4—882no—
409C4⋊C4C2×C4×D1112yes—
410C22⋊C4—24no—
411C22⋊C4—228no—
412C42—114no—
413C42—114no—
414C42—444no—
415C42—442no—
416C42C2×C4×D1112yes—
417C42D4×D1112yes—
418C11Q8×#10211yescharacteristic, complemented, Sylow
419C23—22no—
420C23—22no—
421C23—22no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23C2×D4×D1111yescharacteristic
427Q8—1116no—
428Q8—4416no—
429Q8—448no—
430D4—22no—
431D4—22no—
432D4—22no—
433D4#6694014yescomplemented
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—48no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—114no—
444C2×C4—114no—
445C2×C4—114no—
446C2×C4—114no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—224no—
450C2×C4—222no—
451C2×C4—4416no—
452C2×C4—441no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4C22⋊C4×D1112yes—
460C2×C4C22⋊C4×D1112yes—
461C2×C4D8×D1112yes—
462C2×C4SD16×D1112yes—
463C2×C4C22×C4×D1111yescharacteristic
464C2×C4C2×D4×D1111yescharacteristic
465C2×C4C2×#434111yescharacteristic
466C2×C4C2×Q8×D1111yescharacteristic
467C2×C4#6704311yescharacteristic
468C2×C4#6704311yescharacteristic
469C8—42no—
470C8—222no—
471C8—441no—
472C22—24no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—42no—
478C22—42no—
479C22C2×C22⋊C4×D1111yescharacteristic
480C22#1062312911yescharacteristic
481C22#1062316311yescharacteristic
482C22C2×D8×D1111yescharacteristic
483C22C2×SD16×D1111yescharacteristic
484C22#1062330611yescharacteristic
485C22#1062331011yescharacteristic
486C4—22no—
487C4—42no—
488C4—82no—
489C4—118no—
490C4—224no—
491C4—444no—
492C4—442no—
493C4—881no—
494C4D11×#10214yes—
495C4C2×#6694011yescharacteristic
496C4#1062304711yescharacteristic
497C4#1062312911yescharacteristic
498C4#1062316311yescharacteristic
499C2—44no—
500C2#1307144811yescharacteristic
501C2C2×D11×#10211yescharacteristic
502C2#1307714711yescharacteristic
503C2#1308124611yescharacteristic
504C2#1308125311yescharacteristic
505C2#1308146611yescharacteristic
506C2#1308147111yescharacteristic
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
hypocenterC11Q8×#102
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×#10622443C2semidirect
3. #13071528C2semidirect
4. #13069576C2semidirect
5. #13069575C2semidirect
6. #13069567C2semidirect
7. #13069566C2semidirect
17. D4×Dic22C4semidirect
91. #66896Q8semidirect
151. C4⋊Dic11C2×Q8semidirect
165. C2×C11⋊C8C2×Q8semidirect
188. D4×C11C4×Q8semidirect
226. Dic22#102semidirect
418. C11Q8×#102semidirect
433. D4#66940semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×#106224432
#130715282
#130695762
#130695752
#130695672
#130695662
#130686142
#102×Dic112
C4×#668962
C11×#18022
Q8×#10211