Finite Group Databasebeta

← #14763701

Subgroups — #14763701

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622537C211yesmaximal, characteristic, complemented
2#13071023C211yesmaximal, characteristic, complemented
3#13069574C212yesmaximal, complemented
4#13069549C212yesmaximal, complemented
5#13069055C212yesmaximal
6#13069050C212yesmaximal, complemented
7#13068621C212yesmaximal, complemented
8#13068616C212yesmaximal, complemented
9C2×C11×#529C211yesmaximal, characteristic
10C11×#529—24no—
11C11×#529C418yescomplemented
12C2×C11×#126—21no—
13C2×C11×#125C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C22×C42×C11C2211yescharacteristic
23C2×#66979—21no—
24C22×#4318C2212yes—
25C2×#66899C2214yes—
26C2×#66896C2214yes—
27#10622825—21no—
28#10622825C2212yes—
29#10622549—21no—
30#10622548C2212yes—
31C4×C4⋊Dic11—21no—
32C4×C4⋊Dic11C2212yes—
33#10622537—24no—
34C2×C4⋊(C11⋊C8)C2212yes—
35C2×C4⋊(C11⋊C8)C2212yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11—21no—
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C11×#126—28no—
46C11×#125—22no—
47C11×#125C2×C414yes—
48C11×#124—22no—
49C11×#124C2×C414yes—
50C11×#123—28no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8C2×C414yes—
53C11×#121—22no—
54C11×#121C2×C414yes—
55C4×Q8×C11—22no—
56C4×Q8×C11C2×C414yes—
57C4×D4×C11—28no—
58C4×D4×C11—22no—
59C4×D4×C11C2×C414yes—
60C11×#117—28no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73C2×C42×C11C2×C414yes—
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D414yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—22no—
80#66979—44no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11C2314yes—
84C2×C4×Dic11—22no—
85C2×#4318—24no—
86C2×#4318—44no—
87C22×C11⋊C8C2314yes—
88#66899—44no—
89#66896—44no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C4⋊(C11⋊C8)—24no—
93C4⋊(C11⋊C8)—24no—
94#21890—111nomaximal, Sylow
95C24×C11—21no—
96C24×C11C2×D411yescharacteristic
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11C22×C412yes—
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—44no—
106C2×D4×C11C22×C412yes—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—24no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11C22⋊C414yes—
119C22×C4×C11C22⋊C414yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4C22×C412yes—
136C11×C4⋊C4C22×C412yes—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C42×C11—24no—
143C42×C11C22⋊C414yes—
144C42×C11C22⋊C414yes—
145C42×C11C22×C412yes—
146C42×C11C22×C412yes—
147C42×C11C2×D412yes—
148C42×C11C2×D412yes—
149C22⋊Dic11—44no—
150C4⋊Dic11—24no—
151C4⋊Dic11—24no—
152C4⋊Dic11—44no—
153C4⋊Dic11—44no—
154C4×Dic11—44no—
155#4318—48no—
156C2×C11⋊C8—24no—
157C2×C11⋊C8—24no—
158C2×C11⋊C8—24no—
159C2×#529D1111yescharacteristic
160C2×#423—111no—
161#2285—111no—
162#1989—112no—
163#1983—112no—
164#1895—112no—
165#1894—112no—
166#1803—112no—
167#1802—112no—
168C23×C11—22no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—42no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—42no—
177C23×C11C2×C22⋊C412yes—
178C23×C11C22×D411yescharacteristic
179Q8×C11—24no—
180Q8×C11—41no—
181Q8×C11—41no—
182D4×C11—24no—
183D4×C11—48no—
184D4×C11—41no—
185D4×C11—41no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—28no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—48no—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C2×C22⋊C412yes—
206C2×C4×C11C2×C22⋊C412yes—
207C2×C4×C11C2×C22⋊C412yes—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11AGL(1,ℤ/8)12yes—
210C2×C4×C11#13712yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11H(5,𝔽2)12yes—
214C2×C4×C112−1+412yes—
215C2×Dic11—44no—
216C2×Dic11—44no—
217C2×Dic11—44no—
218C11⋊C8—44no—
219C22×M16—112no—
220#529—24no—
221#529Dic1118yescomplemented
222C2×#126—21no—
223C2×#125C2×D1111yescharacteristic
224C2×#124C2×D1111yescharacteristic
225C2×#123—21no—
226C2×C22⋊Q8C2×D1111yescharacteristic
227C2×#121C2×D1111yescharacteristic
228C2×C4×Q8C2×D1111yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4C2×D1111yescharacteristic
231C2×#117—21no—
232C2×#117—221no—
233C22×C42C2×D1111yescharacteristic
234#423—224no—
235C2×C4⋊C8—112no—
236C2×C4⋊C8—112no—
237C2×#103—114no—
238C2×#102—114no—
239#384—112no—
240#382—221no—
241#380—112no—
242#380—221no—
243C4×C4⋊C4—112no—
244C4×C4⋊C4—221no—
245#340—114no—
246#340—114no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—82no—
256C22×C11—82no—
257C22×C11C22×C22⋊C411yescharacteristic
258C22×C11#53712yes—
259C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C11C2×#13711yescharacteristic
261C22×C11#57512yes—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11#41714yes—
270C4×C11#52012yes—
271C4×C11#53511yescharacteristic
272C4×C11#53611yescharacteristic
273Dic11—84no—
274C22×Q8C22×D1111yescharacteristic
275C22×D4—21no—
276C22×D4C22×D1111yescharacteristic
277C23×C4—21no—
278C23×C4C22⋊D1111yescharacteristic
279C23×C4C22⋊D1111yescharacteristic
280C23×C4C22×D1111yescharacteristic
281C2×M16—224no—
282C2×M16—444no—
283C22×C8—114no—
284#126—28no—
285#125—22no—
286#125C2×Dic1114yes—
287#124—22no—
288#124C2×Dic1114yes—
289#123—28no—
290C22⋊Q8—22no—
291C22⋊Q8C2×Dic1114yes—
292#121—22no—
293#121C2×Dic1114yes—
294C4×Q8—22no—
295C4×Q8C2×Dic1114yes—
296C4×D4—28no—
297C4×D4—22no—
298C4×D4C2×Dic1114yes—
299#117—28no—
300#117—444no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—114no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—222no—
316C2×C42—21no—
317C2×C42—222no—
318C2×C42C2×Dic1114yes—
319C2×C42C22⋊D1111yescharacteristic
320C2×C42C22⋊D1111yescharacteristic
321C2×C42C22⋊D1114yes—
322C2×C42C22×D1111yescharacteristic
323C2×C42C22×D1111yescharacteristic
324C4⋊C8—224no—
325C4⋊C8—224no—
326#103—444no—
327#102—444no—
328#95—222no—
329#95—222no—
330C2×C11—42no—
331C2×C11—82no—
332C2×C11#231111yescharacteristic
333C2×C11C2×#41711yescharacteristic
334C2×C11#289611yescharacteristic
335C2×C11#325112yes—
336C2×C11#325212yes—
337C24—21no—
338C24C2×C22⋊D1111yescharacteristic
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8C22×Dic1112yes—
343C2×D4—24no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4—44no—
348C2×D4C22×Dic1112yes—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—24no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—224no—
361C22×C4C22⋊Dic1114yes—
362C22×C4C22⋊Dic1114yes—
363C22×C4C22×Dic1112yes—
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1112yes—
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C23×D1111yescharacteristic
371M16—448no—
372C2×C8—224no—
373C2×C8—224no—
374C2×C8—224no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—224no—
382C4⋊C4—224no—
383C4⋊C4—444no—
384C4⋊C4—444no—
385C4⋊C4C22×Dic1112yes—
386C4⋊C4C22×Dic1112yes—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C22⋊C4—24no—
391C22⋊C4—24no—
392C22⋊C4—444no—
393C42—24no—
394C42—444no—
395C42C22⋊Dic1114yes—
396C42C22⋊Dic1114yes—
397C42C22×Dic1112yes—
398C42C22×Dic1112yes—
399C42C2×C22⋊D1112yes—
400C42C2×C22⋊D1112yes—
401C11#2189011yescharacteristic, complemented, Sylow
402C23—21no—
403C23—22no—
404C23—21no—
405C23—22no—
406C23—22no—
407C23—41no—
408C23—42no—
409C23—41no—
410C23—42no—
411C23C2×C22⋊Dic1112yes—
412C23C22×C22⋊D1111yescharacteristic
413Q8—24no—
414Q8—41no—
415Q8—41no—
416D4—24no—
417D4—48no—
418D4—41no—
419D4—41no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—28no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—44no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—48no—
438C2×C4—444no—
439C2×C4—444no—
440C2×C4—444no—
441C2×C4#6700212yes—
442C2×C4#6700412yes—
443C2×C4C2×C22⋊Dic1112yes—
444C2×C4C2×C22⋊Dic1112yes—
445C2×C4C2×C22⋊Dic1112yes—
446C2×C4C2×C22⋊Dic1112yes—
447C2×C4C2×C22⋊Dic1112yes—
448C2×C4#6704212yes—
449C2×C4#6704312yes—
450C2×C4C23×Dic1111yescharacteristic
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—444no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—82no—
462C22—82no—
463C22C2×#6700211yescharacteristic
464C22#1062335312yes—
465C22C2×#6700411yescharacteristic
466C22#1062336412yes—
467C22C22×C22⋊Dic1111yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—22no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—884no—
476C4#1062284514yes—
477C4#1062335611yescharacteristic
478C4#1062335812yes—
479C4#1062336111yescharacteristic
480C2—42no—
481C2—82no—
482C2#1307120811yescharacteristic
483C2C2×#1062284511yescharacteristic
484C2#1307713511yescharacteristic
485C2#1307997812yes—
486C2#1307998912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC2×#529D11
hypocenterC11#21890
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10622537C2semidirect
2. #13071023C2semidirect
3. #13069574C2semidirect
4. #13069549C2semidirect
6. #13069050C2semidirect
7. #13068621C2semidirect
8. #13068616C2semidirect
11. C11×#529C4semidirect
221. #529Dic11semidirect
401. C11#21890semidirect

Maximal subgroups

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

subgroupindex
C2×#106225372
#130710232
#130695742
#130695492
#130690552
#130690502
#130686212
#130686162
C2×C11×#5292
#2189011