Finite Group Databasebeta

← #14770598

Subgroups — #14770598

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×#10622637C211yesmaximal, characteristic, complemented
2Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069549C212yesmaximal
4#13069540C211yesmaximal, characteristic, complemented
5#13069433C212yesmaximal
6#13069419C211yesmaximal, characteristic, complemented
7#13068621C212yesmaximal, complemented
8#13068616C211yesmaximal, characteristic
9#13068446C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#556C211yesmaximal, characteristic
12C11×#556—24no—
13C11×#556C418yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C2×Q8×Dic11—21no—
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26C2×#66899C2212yes—
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2212yes—
30#10622637—24no—
31#10622598—21no—
32#10622598—22no—
33#10622548C2211yescharacteristic
34#10622548C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×#66867C2212yes—
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11D411yescharacteristic
45C22×Q8×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8C2×C414yes—
50C11×#126—216no—
51C11×#124—24no—
52C11×#124C2×C418yes—
53C11×C22⋊Q8—28no—
54C4×Q8×C11—24no—
55C4×Q8×C11C2×C418yes—
56C4×Q8×C11C2×C414yes—
57C4×Q8×C11D414yes—
58C4×D4×C11—22no—
59C4×D4×C11C2×C414yes—
60C11×#117—28no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11—22no—
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2312yes—
73Q8×Dic11—44no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4×Dic11—22no—
82C2×C4×Dic11—21no—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2311yescharacteristic
86#66899—24no—
87#66899—24no—
88#66899—42no—
89#66899—42no—
90#66896—22no—
91#66896—22no—
92#66896—42no—
93C11⋊#95—22no—
94C11⋊#95—21no—
95C4⋊(C11⋊C8)—24no—
96C4⋊(C11⋊C8)—22no—
97#66867—24no—
98C4×C11⋊C8—22no—
99#22544—111nomaximal, Sylow
100C24×C11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11C22⋊C414yes—
109C2×Q8×C11C22×C414yes—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11C22×C412yes—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—28no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4C22⋊C414yes—
134C11×C4⋊C4C22⋊C418yes—
135C11×C4⋊C4C22×C412yes—
136C11×C22⋊C4—28no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—28no—
139C42×C11—28no—
140C42×C11C22×C412yes—
141C42×C11C22×C414yes—
142C42×C11C2×D412yes—
143C42×C11C2×D414yes—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—44no—
150C4⋊Dic11—42no—
151C4⋊Dic11—82no—
152C4⋊Dic11—81no—
153C4⋊Dic11#4112yes—
154C4×Dic11—44no—
155C4×Dic11—42no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8#4112yes—
165C2×#556D1111yescharacteristic
166C2×#446—111no—
167Q8×C4⋊C4—111no—
168#1983—112no—
169#1981—111no—
170#1959—112no—
171#1956—111no—
172#1803—112no—
173#1802—111no—
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
184Q8×C11—28no—
185Q8×C11—24no—
186Q8×C11—24no—
187Q8×C11—42no—
188Q8×C11—42no—
189D4×C11—22no—
190D4×C11—22no—
191D4×C11—41no—
192D4×C11—41no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—48no—
206C2×C4×C11C2×C22⋊C414yes—
207C2×C4×C11C2×C22⋊C412yes—
208C2×C4×C11C2×C22⋊C414yes—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11#13712yes—
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C2×Dic11—22no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C11⋊C8—22no—
228C11⋊C8—41no—
229C11⋊C8—42no—
230#556—24no—
231#556Dic1118yescomplemented
232C2×C4⋊Q8C2×D1111yescharacteristic
233C2×#126—22no—
234C2×#124C2×D1112yes—
235C2×C22⋊Q8—21no—
236C2×C4×Q8—221no—
237C2×C4×Q8C2×D1112yes—
238C2×C4×Q8C2×D1111yescharacteristic
239C2×C4×D4C2×D1111yescharacteristic
240C2×#117—21no—
241#446—224no—
242C2×C4⋊C8—111no—
243C2×C4⋊C8—112no—
244C2×#103—112no—
245C2×#103—112no—
246C2×#103—112no—
247C2×#103—112no—
248C2×#102—111no—
249C2×#102—111no—
250C2×#102—112no—
251C2×#97—112no—
252C2×C4×C8—111no—
253#389—221no—
254#389—222no—
255#384—111no—
256#384—112no—
257C4×C4⋊C4—111no—
258C4×C4⋊C4—112no—
259#340—112no—
260#340—111no—
261#340—111no—
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—24no—
277C4×C11—24no—
278C4×C11—22no—
279C4×C11—44no—
280C4×C11—42no—
281C4×C11#41714yes—
282C4×C11C4×#4111yescharacteristic
283C4×C11#52011yescharacteristic
284C4×C11#54811yescharacteristic
285C4×C11#55011yescharacteristic
286Dic11—42no—
287Dic11—81no—
288Dic11—82no—
289C22×Q8C22⋊D1111yescharacteristic
290C22×Q8C22×D1112yes—
291C22×D4C22×D1111yescharacteristic
292C23×C4—21no—
293C22×C8—111no—
294C22×C8—111no—
295C22×C8—112no—
296C4⋊Q8—22no—
297C4⋊Q8C2×Dic1114yes—
298#126—216no—
299#124—24no—
300#124C2×Dic1118yes—
301C22⋊Q8—28no—
302C4×Q8—24no—
303C4×Q8—444no—
304C4×Q8C2×Dic1118yes—
305C4×Q8C2×Dic1114yes—
306C4×Q8C22⋊D1114yes—
307C4×D4—22no—
308C4×D4C2×Dic1114yes—
309#117—28no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C4⋊C4C22⋊D1112yes—
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C22⋊C4—22no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—22no—
326C2×C42—22no—
327C2×C42—222no—
328C2×C42—221no—
329C2×C42C22×D1111yescharacteristic
330C2×C42C22×D1112yes—
331C4⋊C8—222no—
332C4⋊C8—224no—
333#103—224no—
334#103—224no—
335#103—442no—
336#103—442no—
337#102—222no—
338#102—222no—
339#102—442no—
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—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8C22⋊Dic1114yes—
361C2×Q8C22×Dic1114yes—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C22×Dic1112yes—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—221no—
374C22×C4—222no—
375C22×C4—221no—
376C22×C4C2×C22⋊D1112yes—
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C2×C22⋊D1112yes—
379C22×C4C2×C22⋊D1111yescharacteristic
380C22×C4C23×D1111yescharacteristic
381C2×C8—112no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8—221no—
388C2×C8—221no—
389C2×C8—222no—
390C4⋊C4—24no—
391C4⋊C4—28no—
392C4⋊C4—24no—
393C4⋊C4—21no—
394C4⋊C4—112no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—221no—
400C4⋊C4—444no—
401C4⋊C4—442no—
402C4⋊C4—882no—
403C4⋊C4—881no—
404C4⋊C4C22⋊Dic1114yes—
405C4⋊C4C22⋊Dic1118yes—
406C4⋊C4C22×Dic1112yes—
407C22⋊C4—28no—
408C22⋊C4—24no—
409C22⋊C4—28no—
410C42—28no—
411C42—444no—
412C42—442no—
413C42C22×Dic1112yes—
414C42C22×Dic1114yes—
415C42C2×C22⋊D1112yes—
416C42C2×C22⋊D1114yes—
417C11#2254411yescharacteristic, complemented, Sylow
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23C22×C22⋊D1111yescharacteristic
426Q8—28no—
427Q8—24no—
428Q8—24no—
429Q8—42no—
430Q8—42no—
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—48no—
448C2×C4—222no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—442no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—441no—
457C2×C4#6700212yes—
458C2×C4#6700412yes—
459C2×C4C2×C22⋊Dic1114yes—
460C2×C4C2×C22⋊Dic1112yes—
461C2×C4C2×C22⋊Dic1114yes—
462C2×C4C2×C22⋊Dic1112yes—
463C2×C4#41×D1111yescharacteristic
464C2×C4#41×D1111yescharacteristic
465C2×C4#6704211yescharacteristic
466C2×C4#6704311yescharacteristic
467C2×C4C23×Dic1111yescharacteristic
468C2×C4C22×C22⋊D1111yescharacteristic
469C8—222no—
470C8—441no—
471C8—442no—
472C22—42no—
473C22—42no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22C2×#6700211yescharacteristic
480C22C2×#6700411yescharacteristic
481C22#1062336211yescharacteristic
482C22#1062336511yescharacteristic
483C22#1062336811yescharacteristic
484C22#1062336911yescharacteristic
485C22C22×C22⋊Dic1111yescharacteristic
486C4—24no—
487C4—24no—
488C4—22no—
489C4—44no—
490C4—42no—
491C4—442no—
492C4—882no—
493C4—881no—
494C4#1062284514yes—
495C4#41×Dic1111yescharacteristic
496C4#1062335811yescharacteristic
497C4#1062336211yescharacteristic
498C4#1062336511yescharacteristic
499C2—82no—
500C2#1307145711yescharacteristic
501C2C2×#1062284511yescharacteristic
502C2#1307714911yescharacteristic
503C2#1308133011yescharacteristic
504C2#1308135211yescharacteristic
505C2#1308163611yescharacteristic
506C2#1308164711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#556D11
hypocenterC11#22544
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10622637C2semidirect
2. Q8×C4⋊Dic11C2semidirect
4. #13069540C2semidirect
6. #13069419C2semidirect
7. #13068621C2semidirect
9. #13068446C2semidirect
13. C11×#556C4semidirect
231. #556Dic11semidirect
417. C11#22544semidirect

Maximal subgroups

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

subgroupindex
C2×#106226372
Q8×C4⋊Dic112
#130695492
#130695402
#130694332
#130694192
#130686212
#130686162
#130684462
C4×#668962
C2×C11×#5562
#2254411