Finite Group Databasebeta

← #14739172

Subgroups — #14739172

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078398C211yesmaximal, characteristic, complemented
2#13078092C211yesmaximal, characteristic
3#13077724C211yesmaximal, characteristic, complemented
4#13068029C212yesmaximal, complemented
5#13068022C212yesmaximal, complemented
6#13067961C212yesmaximal, complemented
7#13067954C212yesmaximal, complemented
8#13067387C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3208C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×#66985—21no—
15C4×#4339C2211yescharacteristic
16C11×#492C2212yes—
17C11×#486C2212yes—
18C11×#460—21no—
19C11×#460—21no—
20C11×#450—22no—
21C11×#431C2211yescharacteristic
22#10622828—21no—
23#10622707C2211yescharacteristic, complemented
24#10622704C2211yescharacteristic, complemented
25#10622700C2211yescharacteristic, complemented
26#10622697C2211yescharacteristic, complemented
27#10622688—21no—
28#10622688C2212yes—
29#10622685—21no—
30#10622685C2212yes—
31#10622679—21no—
32#10622676—21no—
33#10622615—21no—
34#10622611—21no—
35#10622537C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622446—21no—
39D11×C4⋊C8—21no—
40(C22⋊D11)⋊C8—22no—
41C8×D44C2212yescomplemented
42C8×Dic22C2212yescomplemented
43#10622185C2212yescomplemented
44#10622184C2212yescomplemented
45#10622182C2212yes—
46#10622182C2212yes—
47#10622095C2212yescomplemented
48#10622095C2212yescomplemented
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C2×#4339D411yescharacteristic
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2312yes—
61C11×#125—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66C11×#117—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4324—22no—
69#66985—44no—
70C2×#4323—22no—
71C4×C22⋊D11—21no—
72C4×C22⋊D11—21no—
73#66979D411yescharacteristic
74C2×#4318—21no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77C2×C8×D11—22no—
78C4×D44D411yescharacteristic
79C4×D44C2311yescharacteristic
80#66925—21no—
81C42×D11—21no—
82C4×Dic22D411yescharacteristic
83C4×Dic22C2311yescharacteristic
84C11×C4⋊C8D411yescharacteristic
85C11×C4⋊C8D411yescharacteristic
86C11×#102—22no—
87C11×#102—22no—
88C11×C22⋊C8D412yes—
89C4×C8×C11C2312yes—
90#66896—22no—
91#66896—22no—
92(C2×D11)⋊C8—22no—
93Dic11⋊C8—22no—
94C8×Dic11—22no—
95#66874—21no—
96#66874—21no—
97#66873—21no—
98#66873—21no—
99#66872—21no—
100#66872—21no—
101#66871—21no—
102#66871—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2312yes—
110#19409—111nomaximal, Sylow
111C24×C11—41no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—81no—
123C2×D4×C11—81no—
124C2×D4×C11—82no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C2×C22⋊D11—21no—
129#4339—22no—
130#4339SD1614yescomplemented
131C2×D44C2×D411yescharacteristic
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×Dic22C2×D411yescharacteristic
136C11×SD16—82no—
137C11×SD16—82no—
138C2×C8×C11C2×D412yes—
139C2×C8×C11C2×D412yes—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11—41no—
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11#4111yescharacteristic
151C42×C11C2411yescharacteristic
152C22⋊Dic11—21no—
153#4324—44no—
154#4323—44no—
155(C2×D11)⋊C4—21no—
156(C2×D11)⋊C4—21no—
157C4⋊Dic11C2×D411yescharacteristic
158C4⋊Dic11C2×D411yescharacteristic
159Dic11⋊C4—21no—
160Dic11⋊C4—21no—
161C4×Dic11—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164#4318—42no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170C2×C11⋊C8—81no—
171C8×D11—82no—
172#3208D1111yescharacteristic, complemented
173#3076—111no—
174#3038—111no—
175#2988—111no—
176#1678—112no—
177#1677—112no—
178#1666—112no—
179#1665—112no—
180#1570—111no—
181#1550—111no—
182C2×#331—111no—
183C23×C11—42no—
184C23×C11—82no—
185C23×C11—82no—
186C23×C11—82no—
187C23×C11#12111yescharacteristic
188C22×D11—21no—
189Q8×C11—41no—
190Q8×C11—41no—
191Q8×C11—81no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—42no—
196D4×C11—82no—
197D4×C11—82no—
198D4×C11—82no—
199D4×C11—82no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11C2×SD1612yes—
209C2×C4×C11#13512yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C22⋊D11—24no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217D44—21no—
218D44C2×SD1612yes—
219C4×D11—24no—
220C4×D11—41no—
221C4×D11—41no—
222C4×D11—81no—
223Dic22—21no—
224Dic22C2×SD1612yes—
225C8×C11—22no—
226C8×C11—22no—
227C11⋊C8—42no—
228C11⋊C8—41no—
229C11⋊C8—41no—
230C11⋊C8—42no—
231C2×AGL(1,ℤ/8)—221no—
232#533C2×D1111yescharacteristic
233C2×#127C2×D1111yescharacteristic
234C4×#41—111no—
235#492C2×D1112yes—
236#486C2×D1112yes—
237#479—221no—
238#478—221no—
239#477—111no—
240#476—111no—
241#475—111no—
242#474—111no—
243#460—21no—
244#460—21no—
245#460—112no—
246#460—221no—
247#459—112no—
248#459—221no—
249#450—22no—
250C8×Q8—112no—
251C8×D4—112no—
252C8×D4—222no—
253#431—221no—
254#431C2×D1111yescharacteristic
255#427—221no—
256#423—111no—
257C2×C4⋊C8—111no—
258C2×C4⋊C8—111no—
259C2×C4⋊C8—221no—
260#418—221no—
261#416—221no—
262#334—112no—
263#334—112no—
264#333—112no—
265#332—112no—
266#331—112no—
267#331—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—164no—
274C22×C11#46512yes—
275C22×C11C2×#12111yescharacteristic
276C2×D11—22no—
277C2×D11—41no—
278C2×D11—41no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11#46512yes—
285C4×C11C22×SD1611yescharacteristic
286C4×C11C2×#13511yescharacteristic
287C4×C11#57611yescharacteristic
288C4×C11#57711yescharacteristic
289Dic11—22no—
290Dic11—41no—
291Dic11—41no—
292C2×#41—111no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296AGL(1,ℤ/8)—444no—
297C2×SD16—22no—
298C2×SD16—22no—
299C2×SD16—222no—
300C2×D8—222no—
301C2×M16—221no—
302C22×C8—221no—
303C22×C8—221no—
304C22×C8—222no—
305C4⋊Q8C22×D1111yescharacteristic
306C4⋊Q8C22×D1111yescharacteristic
307#127—21no—
308#127—21no—
309#127—21no—
310#127C22×D1112yes—
311#125—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—111no—
317C4×Q8—111no—
318C4×D4—111no—
319C4×D4—111no—
320C4×D4—221no—
321C4×D4—221no—
322#117—21no—
323#117—111no—
324#117—221no—
325C2×C42—221no—
326C2×C42C22×D1111yescharacteristic
327#107—221no—
328#107—221no—
329#106—221no—
330#106—221no—
331C4⋊C8—112no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—112no—
335C4⋊C8—222no—
336C4⋊C8—221no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339C4⋊C8C22⋊D1111yescharacteristic
340C4⋊C8C22⋊D1111yescharacteristic
341#103—221no—
342#103—221no—
343#102—22no—
344#102—22no—
345#102—221no—
346#102—221no—
347#102—222no—
348#102—222no—
349C22⋊C8—222no—
350C22⋊C8C22⋊D1112yes—
351C4×C8—222no—
352C4×C8C22×D1112yes—
353C2×C11—22no—
354C2×C11—162no—
355C2×C11#304511yescharacteristic
356C2×C11C2×#46511yescharacteristic
357C2×C11#306811yescharacteristic
358D11—42no—
359C24—41no—
360#41—114no—
361#41—222no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—111no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—81no—
374C2×D4—81no—
375C2×D4—82no—
376C2×D4—111no—
377C2×D4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4D4×D1111yescharacteristic
382C22×C4#434111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384SD16—82no—
385SD16—82no—
386SD16—444no—
387D8—444no—
388M16—442no—
389C2×C8—222no—
390C2×C8—221no—
391C2×C8—221no—
392C2×C8—222no—
393C2×C8—442no—
394C2×C8—882no—
395C2×C8—881no—
396C2×C8C2×C22⋊D1112yes—
397C2×C8C2×C22⋊D1112yes—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—111no—
405C4⋊C4—111no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C22⋊C4—41no—
409C22⋊C4—221no—
410C22⋊C4—221no—
411C22⋊C4—221no—
412C42—41no—
413C42—221no—
414C42—221no—
415C42—221no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1940911yescharacteristic, complemented, Sylow
421C23—42no—
422C23—82no—
423C23—82no—
424C23—82no—
425C23—221no—
426C23#6699111yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—81no—
430Q8—112no—
431Q8—221no—
432D4—42no—
433D4—42no—
434D4—42no—
435D4—42no—
436D4—82no—
437D4—82no—
438D4—82no—
439D4—82no—
440D4—112no—
441D4—224no—
442D4—221no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—221no—
449C2×C4—224no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—881no—
455C2×C4SD16×D1112yes—
456C2×C4#6696912yes—
457C2×C4#6699111yescharacteristic
458C2×C4#6699111yescharacteristic
459C2×C4#6699111yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4C22×C22⋊D1111yescharacteristic
463C8—22no—
464C8—22no—
465C8—442no—
466C8—441no—
467C8—441no—
468C8—442no—
469C22—21no—
470C22—21no—
471C22—82no—
472C22—82no—
473C22—82no—
474C22—164no—
475C22—222no—
476C22—441no—
477C22—441no—
478C22#1062278412yes—
479C22C2×#6699111yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—81no—
484C4—81no—
485C4—222no—
486C4—441no—
487C4—441no—
488C4#1062278412yes—
489C4C2×SD16×D1111yescharacteristic
490C4C2×#6696911yescharacteristic
491C4#1062336611yescharacteristic
492C4#1062336711yescharacteristic
493C2—22no—
494C2—162no—
495C2—442no—
496C2#1307815111yescharacteristic
497C2C2×#1062278411yescharacteristic
498C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3208C2
socleC22×C11C2×#121
prime radical#13078092C2
hypercenter#3208D11
hypocenterC11#19409
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #13078398C2semidirect
3. #13077724C2semidirect
4. #13068029C2semidirect
5. #13068022C2semidirect
6. #13067961C2semidirect
7. #13067954C2semidirect
8. #13067387C2semidirect
9. #13067306C2semidirect
10. C2×#10622182C2semidirect
11. C11×#3208C2semidirect
23. #10622707C22semidirect
24. #10622704C22semidirect
25. #10622700C22semidirect
26. #10622697C22semidirect
41. C8×D44C22semidirect
42. C8×Dic22C22semidirect
43. #10622185C22semidirect
44. #10622184C22semidirect
47. #10622095C22semidirect
48. #10622095C22semidirect
130. #4339SD16semidirect
172. #3208D11semidirect
420. C11#19409semidirect

Maximal subgroups

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

subgroupindex
#130783982
#130780922
#130777242
#130680292
#130680222
#130679612
#130679542
#130673872
#130673062
C2×#106221822
C11×#32082
#1940911