Finite Group Databasebeta

← #14737813

Subgroups — #14737813

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079191C211yesmaximal, characteristic, complemented
2#13078707C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068151C212yesmaximal, complemented
5#13068147C212yesmaximal, complemented
6#13068137C212yesmaximal, complemented
7#13068093C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067312C211yesmaximal, characteristic, complemented
10#13067311C211yesmaximal, characteristic, complemented
11C11×#3109C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4318—21no—
15#10623008C2211yescharacteristic
16C11×#481—21no—
17C11×#476C2212yes—
18C11×#459C2212yes—
19C11×#447—21no—
20C11×#442—22no—
21C11×#432C2211yescharacteristic
22#10622830—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622701C2211yescharacteristic, complemented
25#10622691C2211yescharacteristic, complemented
26#10622686C2211yescharacteristic, complemented
27#10622683C2211yescharacteristic, complemented
28#10622651—21no—
29#10622651—21no—
30#10622628C2212yes—
31#10622627—22no—
32C4×#4323—21no—
33C4×#4323—21no—
34#10622625—21no—
35#10622625—21no—
36#10622625C2212yes—
37#10622625C2212yes—
38#10622621C2212yes—
39#10622581—21no—
40#10622539C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622184C2212yescomplemented
44#10622182C2212yescomplemented
45#10622123C2212yescomplemented
46#10622119C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C2×C11×#41—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C2×#4339—21no—
53C2×C11×D8—22no—
54C11×C4⋊Q8C2311yescharacteristic
55C11×#127C2311yescharacteristic
56C11×#124—21no—
57C11×#121—21no—
58C11×#121—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11D412yes—
64C4×D4×C11C2312yes—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4323—22no—
69C2×#4323—21no—
70C2×#4323—21no—
71#66983—21no—
72#66983—21no—
73C2×#4318—22no—
74C2×#4318—22no—
75C2×#4318—44no—
76C22×C11⋊C8—21no—
77C22×C11⋊C8D411yescharacteristic
78C22×C11⋊C8D411yescharacteristic
79#66928—21no—
80#66927C2311yescharacteristic
81C4×D44—21no—
82C4×D44—21no—
83#66922C2311yescharacteristic
84C11×#106—22no—
85C11×C4⋊C8C2312yes—
86C11×#102—22no—
87C11×#102—22no—
88C11×C22⋊C8—21no—
89C11×#97—21no—
90#66896—22no—
91#66896—21no—
92#66896—21no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)—22no—
96#66873—22no—
97#66873—21no—
98#66873—21no—
99#66872—22no—
100#66871—21no—
101#66871—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2312yes—
105#66867—21no—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19283—111nomaximal, Sylow
111C24×C11—21no—
112C11×#41—82no—
113C2×Q8×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—42no—
119C2×D4×C11—41no—
120C2×D4×C11C2×D412yes—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11#4111yescharacteristic
130C2×C22⋊D11—41no—
131#4339—82no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C2×Dic22—21no—
137C11×D8—44no—
138C2×C8×C11—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4C2×D412yes—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11#4111yescharacteristic
150C42×C11C2411yescharacteristic
151#4323—44no—
152#4323—42no—
153#4323—42no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158#4318—44no—
159#4318—44no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—41no—
164C2×C11⋊C8—42no—
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169#3169—111no—
170#3109—111no—
171#3109D1111yescharacteristic, complemented
172C2×#436—111no—
173#1697—112no—
174#1697—112no—
175#1695—112no—
176#1687—112no—
177#1568—111no—
178#1551—111no—
179#1551—111no—
180C23×C11—22no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—41no—
185C23×C11#12111yescharacteristic
186C22×D11—41no—
187Q8×C11—81no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—42no—
191D4×C11—41no—
192D4×C11—41no—
193D4×C11—42no—
194D4×C11—81no—
195D4×C11—82no—
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—44no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—82no—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C22⋊D11—82no—
214C2×Dic11—41no—
215D44—41no—
216D44—41no—
217D44—42no—
218D44—81no—
219C4×D11—82no—
220Dic22—81no—
221C8×C11—42no—
222C11⋊C8—21no—
223C11⋊C8—21no—
224C11⋊C8—21no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C11⋊C8AGL(1,ℤ/8)12yes—
228C22×M16—221no—
229#532—111no—
230#532C2×D1111yescharacteristic
231C2×C4×D4C2×D1111yescharacteristic
232#500—111no—
233#493—111no—
234#486—111no—
235#486—111no—
236#481—21no—
237#481—221no—
238#476—112no—
239#476C2×D1112yes—
240#466—221no—
241#466—221no—
242#459—112no—
243#459C2×D1112yes—
244#447—21no—
245#447—221no—
246#442—22no—
247#442—222no—
248C4×D8—221no—
249C4×D8—221no—
250#436—112no—
251#436—112no—
252#436—221no—
253#436—221no—
254#432—111no—
255#432C2×D1111yescharacteristic
256C2×C4⋊C8—111no—
257C2×C22⋊C8—221no—
258C2×C4×C8—111no—
259#335—112no—
260#334—112no—
261#333—112no—
262#333—112no—
263#331—112no—
264#331—112no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—84no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11#47212yes—
275C22×C11C2×#12111yescharacteristic
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—42no—
284C4×C11—81no—
285C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C11#57511yescharacteristic
287C4×C11#57512yes—
288Dic11—81no—
289C2×#41—21no—
290C2×#41—221no—
291C22×D4C22⋊D1111yescharacteristic
292C23×C4—21no—
293C2×D8—22no—
294C2×D8—221no—
295C2×D8—221no—
296C2×D8—222no—
297C2×M16—222no—
298C2×M16—222no—
299C2×M16—444no—
300C22×C8—111no—
301C22×C8—111no—
302C22×C8—221no—
303C4⋊Q8—111no—
304C4⋊Q8C22×D1111yescharacteristic
305#127—111no—
306#127C22×D1111yescharacteristic
307#124—21no—
308#124—221no—
309#121—21no—
310#121—21no—
311#121—221no—
312#121—221no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—221no—
318C4×D4—221no—
319C4×D4C22⋊D1112yes—
320C4×D4C22×D1112yes—
321C2×C4⋊C4C22⋊D1111yescharacteristic
322C2×C22⋊C4—21no—
323C2×C42C22×D1111yescharacteristic
324#107—221no—
325#107—221no—
326#106—22no—
327#106—222no—
328C4⋊C8—112no—
329C4⋊C8—112no—
330C4⋊C8—221no—
331C4⋊C8C22×D1112yes—
332#102—22no—
333#102—22no—
334#102—221no—
335#102—221no—
336#102—221no—
337#102—221no—
338#102—222no—
339#102—222no—
340C22⋊C8—21no—
341C22⋊C8—222no—
342C22⋊C8—222no—
343C22⋊C8—221no—
344#97—21no—
345#97—221no—
346C4×C8—111no—
347C4×C8—111no—
348C4×C8—111no—
349C4×C8—111no—
350C2×C11—22no—
351C2×C11—82no—
352C2×C11—161no—
353C2×C11#303611yescharacteristic
354C2×C11#305411yescharacteristic
355C2×C11C2×#47211yescharacteristic
356D11—161no—
357C24—21no—
358#41—82no—
359#41—882no—
360C2×Q8—21no—
361C2×Q8—221no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—42no—
367C2×D4—41no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—441no—
372C2×D4C2×C22⋊D1112yes—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—41no—
379C22×C4—441no—
380C22×C4D4×D1111yescharacteristic
381C22×C4#434111yescharacteristic
382C22×C4C2×C22⋊D1111yescharacteristic
383D8—44no—
384D8—442no—
385D8—442no—
386D8—444no—
387M16—444no—
388M16—444no—
389C2×C8—22no—
390C2×C8—111no—
391C2×C8—111no—
392C2×C8—111no—
393C2×C8—111no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—441no—
398C2×C8—442no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4C2×C22⋊D1112yes—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C42D4×D1111yescharacteristic
412C42#434111yescharacteristic
413C42C2×C22⋊D1111yescharacteristic
414C42C23×D1111yescharacteristic
415C11#1928311yescharacteristic, complemented, Sylow
416C23—22no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—41no—
421C23—441no—
422C23#6699211yescharacteristic
423Q8—81no—
424Q8—881no—
425D4—22no—
426D4—22no—
427D4—42no—
428D4—41no—
429D4—41no—
430D4—42no—
431D4—81no—
432D4—82no—
433D4—441no—
434D4—441no—
435D4—442no—
436D4—881no—
437D4—882no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4—441no—
450C2×C4—882no—
451C2×C4#6699211yescharacteristic
452C2×C4#6699211yescharacteristic
453C2×C4#6699211yescharacteristic
454C2×C4C2×D4×D1111yescharacteristic
455C2×C4C2×#434111yescharacteristic
456C2×C4C22×C22⋊D1111yescharacteristic
457C8—42no—
458C8—112no—
459C8—221no—
460C8—221no—
461C8—221no—
462C8—442no—
463C8—442no—
464C22—21no—
465C22—21no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—84no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—881no—
474C22—881no—
475C22—881no—
476C22#1062281212yes—
477C22C2×#6699211yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—881no—
485C4D11×AGL(1,ℤ/8)11yescharacteristic
486C4#1062330411yescharacteristic
487C4#1062335312yes—
488C2—22no—
489C2—82no—
490C2—161no—
491C2—1761no—
492C2#1307807711yescharacteristic
493C2#1307822211yescharacteristic
494C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3109C2
socleC22×C11C2×#121
hypercenter#3109D11
hypocenterC11#19283
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. #13079191C2semidirect
2. #13078707C2semidirect
3. C2×#10622625C2semidirect
4. #13068151C2semidirect
5. #13068147C2semidirect
6. #13068137C2semidirect
7. #13068093C2semidirect
8. #13067377C2semidirect
9. #13067312C2semidirect
10. #13067311C2semidirect
11. C11×#3109C2semidirect
24. #10622701C22semidirect
25. #10622691C22semidirect
26. #10622686C22semidirect
27. #10622683C22semidirect
43. #10622184C22semidirect
44. #10622182C22semidirect
45. #10622123C22semidirect
46. #10622119C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
171. #3109D11semidirect
415. C11#19283semidirect

Maximal subgroups

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

subgroupindex
#130791912
#130787072
C2×#106226252
#130681512
#130681472
#130681372
#130680932
#130673772
#130673122
#130673112
C11×#31092
#1928311