Finite Group Databasebeta

← #14739554

Subgroups — #14739554

Order 2816.

682 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#13079554C211yesmaximal, characteristic, complemented
2#13078096C211yesmaximal, characteristic
3#13077733C211yesmaximal, characteristic, complemented
4#13068158C212yesmaximal, complemented
5#13068151C212yesmaximal, complemented
6#13068090C212yesmaximal, complemented
7#13068083C212yesmaximal, complemented
8#13067390C211yesmaximal, characteristic, complemented
9#13067306C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#3076C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C4×C11×#41C2211yescharacteristic
14C2×#67002—21no—
15C2×#66927C2211yescharacteristic
16C11×#479—21no—
17C11×#478—21no—
18C11×#477C2211yescharacteristic, complemented
19C11×#476C2211yescharacteristic, complemented
20C11×#475C2211yescharacteristic, complemented
21C11×#474C2211yescharacteristic, complemented
22C11×#427—21no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C11×#416—21no—
25#10622701C2212yes—
26#10622698C2212yes—
27#10622659—22no—
28#10622640—21no—
29#10622640—21no—
30#10622640—21no—
31#10622640C2212yes—
32#10622637C2212yescomplemented
33#10622628—21no—
34#10622628C2212yes—
35#10622625C2212yescomplemented
36#10622624—22no—
37#10622614—21no—
38#10622539—21no—
39#10622538C2211yescharacteristic
40#10622537—21no—
41#10622537C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622184C2212yescomplemented
45#10622123C2212yes—
46#10622123C2212yes—
47#10622117C2212yescomplemented
48#10622117C2212yescomplemented
49C2×C11×#41D411yescharacteristic
50C22×D44—21no—
51C22×D44—21no—
52C22×D44—21no—
53C22×C8×C11—21no—
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#125—21no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×Q8×C11D411yescharacteristic
62C4×Q8×C11C2311yescharacteristic
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11D411yescharacteristic
66C4×D4×C11C2311yescharacteristic
67C11×#117—21no—
68C11×#117—21no—
69C11×#117D411yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72#67002—44no—
73C2×#4325—22no—
74C2×#4325—22no—
75C2×#4325—22no—
76C2×#4323—22no—
77C2×#4318—21no—
78C2×#4318—22no—
79C22×C11⋊C8—21no—
80#66927—21no—
81#66927—21no—
82#66927—21no—
83#66927C2312yes—
84C11×#107—21no—
85C11×#107—21no—
86C11×#106—21no—
87C11×#106—21no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8C2311yescharacteristic
90C11×C4⋊C8C2311yescharacteristic
91C11×#103—21no—
92C11×#103—21no—
93C11×#102—21no—
94C11×#102—21no—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)D412yes—
97#66873—22no—
98#66873—22no—
99#66873—22no—
100#66873—22no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)D411yescharacteristic
105C4⋊(C11⋊C8)D411yescharacteristic
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108#66867—22no—
109C4×C11⋊C8C2312yes—
110#19445—111nomaximal, Sylow
111C23×D11—41no—
112C11×#41—22no—
113C11×#41—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11C2×D411yescharacteristic
117C2×D4×C11—21no—
118C2×D4×C11C2×D411yescharacteristic
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—41no—
129C2×D44—41no—
130C2×D44—41no—
131C2×D44—42no—
132C2×D44—42no—
133C2×D44—81no—
134C2×D44—81no—
135C2×D44—82no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—42no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4C2×D411yescharacteristic
148C11×C4⋊C4C2×D411yescharacteristic
149C11×C22⋊C4—21no—
150C11×C22⋊C4—21no—
151C11×C22⋊C4—21no—
152C11×C22⋊C4—41no—
153C42×C11—21no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11—41no—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11#4111yescharacteristic
160C42×C11C2411yescharacteristic
161#4325—44no—
162#4325—82no—
163#4325—82no—
164#4323—44no—
165#4318—42no—
166#4318—82no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—81no—
170C2×C11⋊C8C2×D412yes—
171C2×C11⋊C8C2×D412yes—
172#3208—111no—
173#3076D1111yescharacteristic, complemented
174#3038—111no—
175#2989—111no—
176#1698—112no—
177#1697—112no—
178#1686—112no—
179#1685—112no—
180#1571—111no—
181#1550—111no—
182C2×#331—111no—
183C23×C11—21no—
184C23×C11#12111yescharacteristic
185C22×D11—42no—
186C22×D11—82no—
187C22×D11—82no—
188C22×D11—82no—
189Q8×C11—21no—
190Q8×C11—21no—
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11—81no—
194D4×C11—21no—
195D4×C11—21no—
196D4×C11—42no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—81no—
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11AGL(1,ℤ/8)12yes—
213C2×C4×C11#13712yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217D44—42no—
218D44—42no—
219D44—42no—
220D44—42no—
221D44—82no—
222D44—82no—
223D44—82no—
224D44—82no—
225C8×C11—41no—
226C8×C11—41no—
227C11⋊C8—22no—
228C11⋊C8—22no—
229C11⋊C8—42no—
230C11⋊C8—42no—
231C2×AGL(1,ℤ/8)—221no—
232#533C2×D1111yescharacteristic
233C2×#127—111no—
234C4×#41C2×D1111yescharacteristic
235#492—112no—
236#486—112no—
237#479—21no—
238#478—21no—
239#477C2×D1111yescharacteristic, complemented
240#476C2×D1111yescharacteristic, complemented
241#475C2×D1111yescharacteristic, complemented
242#474C2×D1111yescharacteristic, complemented
243#460—112no—
244#460—221no—
245#460—221no—
246#460—221no—
247#459—112no—
248#459—221no—
249#450—222no—
250#446—112no—
251#436—112no—
252#435—222no—
253#432—221no—
254#431—111no—
255#427—21no—
256#423—111no—
257#423—221no—
258C2×C4⋊C8—111no—
259C2×C4⋊C8C2×D1111yescharacteristic
260#418—221no—
261#416—21no—
262#335—112no—
263#335—112no—
264#333—112no—
265#332—112no—
266#331—112no—
267#331—112no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11#46812yes—
274C22×C11C2×#12111yescharacteristic
275C2×D11—82no—
276C2×D11—82no—
277C2×D11—82no—
278C2×D11—164no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11—41no—
285C4×C11—81no—
286C4×C11—81no—
287C4×C11#46812yes—
288C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C11C2×#13711yescharacteristic
290C4×C11#57611yescharacteristic
291C4×C11#57711yescharacteristic
292C2×#41C22⋊D1111yescharacteristic
293C22×D4—221no—
294C22×D4—221no—
295C22×D4—221no—
296AGL(1,ℤ/8)—444no—
297C2×SD16—222no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×D8—222no—
301C2×M16—222no—
302C2×M16—221no—
303C22×C8—21no—
304C22×C8—221no—
305C4⋊Q8C22×D1111yescharacteristic
306C4⋊Q8C22×D1111yescharacteristic
307#127—112no—
308#127—221no—
309#127—221no—
310#127—221no—
311#125—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8C22⋊D1111yescharacteristic
317C4×Q8C22×D1111yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4C22⋊D1111yescharacteristic
321C4×D4C22×D1111yescharacteristic
322#117—21no—
323#117—21no—
324#117C22⋊D1111yescharacteristic
325C2×C42—21no—
326C2×C42C22×D1111yescharacteristic
327#107—21no—
328#107—21no—
329#106—21no—
330#106—21no—
331C4⋊C8—21no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—112no—
335C4⋊C8—112no—
336C4⋊C8—222no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339C4⋊C8C22×D1111yescharacteristic
340C4⋊C8C22×D1111yescharacteristic
341#103—21no—
342#103—21no—
343#102—21no—
344#102—21no—
345#102—222no—
346#102—222no—
347#102—222no—
348#102—222no—
349C22⋊C8—112no—
350C22⋊C8—222no—
351#97—222no—
352C4×C8—112no—
353C2×C11—22no—
354C2×C11—81no—
355C2×C11#304511yescharacteristic
356C2×C11C2×#46811yescharacteristic
357C2×C11#306811yescharacteristic
358D11—162no—
359C24—441no—
360#41—22no—
361#41—22no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8C2×C22⋊D1111yescharacteristic
365C2×D4—21no—
366C2×D4—222no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C2×D4—442no—
373C2×D4—442no—
374C2×D4—881no—
375C2×D4—881no—
376C2×D4—882no—
377C2×D4C2×C22⋊D1111yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4D4×D1111yescharacteristic
382C22×C4#434111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384SD16—444no—
385SD16—882no—
386SD16—882no—
387D8—444no—
388M16—442no—
389M16—882no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—42no—
393C2×C8—112no—
394C2×C8—112no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—881no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4C2×C22⋊D1111yescharacteristic
407C4⋊C4C2×C22⋊D1111yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—41no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—41no—
416C42D4×D1111yescharacteristic
417C42#434111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1944511yescharacteristic, complemented, Sylow
421C23—21no—
422C23—442no—
423C23—882no—
424C23—882no—
425C23—882no—
426C23#6699211yescharacteristic
427Q8—21no—
428Q8—21no—
429Q8—41no—
430Q8—41no—
431Q8—81no—
432D4—21no—
433D4—21no—
434D4—42no—
435D4—442no—
436D4—442no—
437D4—442no—
438D4—442no—
439D4—882no—
440D4—882no—
441D4—882no—
442D4—882no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—81no—
455C2×C4#6699211yescharacteristic
456C2×C4#6699211yescharacteristic
457C2×C4#6699211yescharacteristic
458C2×C4#6699512yes—
459C2×C4#6700212yes—
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4C22×C22⋊D1111yescharacteristic
463C8—41no—
464C8—41no—
465C8—222no—
466C8—222no—
467C8—442no—
468C8—442no—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—882no—
475C22—882no—
476C22—882no—
477C22—1764no—
478C22#1062266212yes—
479C22C2×#6699211yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—81no—
487C4—81no—
488C4#1062266212yes—
489C4#1062330011yescharacteristic
490C4#1062330111yescharacteristic
491C4C2×#6699511yescharacteristic
492C4C2×#6700211yescharacteristic
493C2—22no—
494C2—81no—
495C2—1762no—
496C2#1307815311yescharacteristic
497C2C2×#1062266211yescharacteristic
498C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3076C2
socleC22×C11C2×#121
prime radical#13078096C2
hypercenter#3076D11
hypocenterC11#19445
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #13079554C2semidirect
3. #13077733C2semidirect
4. #13068158C2semidirect
5. #13068151C2semidirect
6. #13068090C2semidirect
7. #13068083C2semidirect
8. #13067390C2semidirect
9. #13067306C2semidirect
10. C2×#10622123C2semidirect
11. C11×#3076C2semidirect
18. C11×#477C22semidirect
19. C11×#476C22semidirect
20. C11×#475C22semidirect
21. C11×#474C22semidirect
32. #10622637C22semidirect
35. #10622625C22semidirect
43. #10622185C22semidirect
44. #10622184C22semidirect
47. #10622117C22semidirect
48. #10622117C22semidirect
173. #3076D11semidirect
239. #477C2×D11semidirect
240. #476C2×D11semidirect
241. #475C2×D11semidirect
242. #474C2×D11semidirect
420. C11#19445semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130780962
#130777332
#130681582
#130681512
#130680902
#130680832
#130673902
#130673062
C2×#106221232
C11×#30762
#1944511