Finite Group Databasebeta

← #14737808

Subgroups — #14737808

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic, complemented
2#13078707C211yesmaximal, characteristic
3C2×#10622625C211yesmaximal, characteristic, complemented
4#13068189C212yesmaximal, complemented
5#13068179C212yesmaximal, complemented
6#13068113C212yesmaximal, complemented
7#13068083C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067316C211yesmaximal, characteristic, complemented
10#13067312C211yesmaximal, characteristic, complemented
11C11×#3110C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4318—21no—
15#10623008C2211yescharacteristic
16C11×#484—21no—
17C11×#474C2212yes—
18C11×#461C2212yes—
19C11×#450—21no—
20C11×#440—22no—
21C11×#432C2211yescharacteristic
22#10622830—21no—
23C2×C22⋊(C11⋊C8)—21no—
24#10622701C2211yescharacteristic, complemented
25#10622698C2211yescharacteristic, complemented
26#10622694C2211yescharacteristic, complemented
27#10622692C2211yescharacteristic, complemented
28#10622661—21no—
29#10622661—21no—
30C4×#4325—21no—
31C4×#4325—21no—
32#10622628C2212yes—
33#10622627—22no—
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#10622185C2212yescomplemented
44#10622185C2212yescomplemented
45#10622123C2212yescomplemented
46#10622119C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C2×#4339—21no—
52C2×C11×SD16—22no—
53C11×C4⋊Q8C2311yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×#125—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11D412yes—
63C4×D4×C11C2312yes—
64C11×#117—21no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4325—21no—
69C2×#4325—21no—
70C2×#4323—22no—
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×#107—22no—
85C11×C4⋊C8C2312yes—
86C11×#103—22no—
87C11×#102—22no—
88C11×C22⋊C8—21no—
89C11×#97—21no—
90#66899—21no—
91#66899—21no—
92#66896—22no—
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#66872—21no—
101#66872—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#19282—111nomaximal, Sylow
111C24×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—42no—
116C2×D4×C11C2×D412yes—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×C22⋊D11—41no—
126#4339—82no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×C4×D11—41no—
131C2×Dic22—21no—
132C11×SD16—44no—
133C2×C8×C11—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4C2×D412yes—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—41no—
145C42×C11—41no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11#4111yescharacteristic
149C42×C11C2411yescharacteristic
150#4325—42no—
151#4325—42no—
152#4323—44no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157#4318—44no—
158#4318—44no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—41no—
163C2×C11⋊C8—42no—
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168#3167—111no—
169#3110D1111yescharacteristic, complemented
170#3109—111no—
171C2×#436—111no—
172#1703—112no—
173#1701—112no—
174#1691—112no—
175#1685—112no—
176#1568—111no—
177#1552—111no—
178#1551—111no—
179C23×C11—22no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11#12111yescharacteristic
184C22×D11—41no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11—42no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—42no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—44no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C22⋊D11—82no—
209C2×Dic11—41no—
210D44—41no—
211D44—42no—
212D44—41no—
213D44—81no—
214C4×D11—82no—
215Dic22—81no—
216C8×C11—42no—
217C11⋊C8—21no—
218C11⋊C8—21no—
219C11⋊C8—21no—
220C11⋊C8—42no—
221C11⋊C8—42no—
222C11⋊C8AGL(1,ℤ/8)12yes—
223C22×M16—221no—
224#533C2×D1111yescharacteristic
225#532—111no—
226C2×C4×D4C2×D1111yescharacteristic
227#498—111no—
228#492—111no—
229#487—111no—
230#486—111no—
231#484—21no—
232#481—221no—
233#476—112no—
234#474C2×D1112yes—
235#465—221no—
236#465—221no—
237#461C2×D1112yes—
238#459—112no—
239#450—21no—
240#447—221no—
241#442—222no—
242#440—22no—
243C4×SD16—221no—
244C4×SD16—221no—
245#436—112no—
246#436—112no—
247#436—221no—
248#436—221no—
249#432—111no—
250#432C2×D1111yescharacteristic
251C2×C4⋊C8—111no—
252C2×C22⋊C8—221no—
253C2×C4×C8—111no—
254#335—112no—
255#334—112no—
256#333—112no—
257#332—112no—
258#332—112no—
259#331—112no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—84no—
266C22×C11#47112yes—
267C22×C11C2×#12111yescharacteristic
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—42no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C4×C11#57511yescharacteristic
280C4×C11#57512yes—
281Dic11—81no—
282C2×#41—221no—
283C22×D4C22⋊D1111yescharacteristic
284C23×C4—21no—
285C2×SD16—22no—
286C2×SD16—221no—
287C2×SD16—221no—
288C2×D8—222no—
289C2×M16—222no—
290C2×M16—222no—
291C2×M16—444no—
292C22×C8—111no—
293C22×C8—111no—
294C22×C8—221no—
295C4⋊Q8—111no—
296C4⋊Q8C22×D1111yescharacteristic
297C4⋊Q8C22×D1111yescharacteristic
298#127—111no—
299#125—21no—
300#124—221no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303#121—221no—
304#121—221no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—221no—
310C4×D4—221no—
311C4×D4C22⋊D1112yes—
312C4×D4C22×D1112yes—
313#117—21no—
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C22⋊C4—21no—
316C2×C42C22×D1111yescharacteristic
317#107—22no—
318#106—221no—
319#106—221no—
320#106—222no—
321C4⋊C8—112no—
322C4⋊C8—112no—
323C4⋊C8—221no—
324C4⋊C8C22×D1112yes—
325#103—22no—
326#103—221no—
327#103—221no—
328#102—22no—
329#102—221no—
330#102—221no—
331#102—222no—
332#102—222no—
333C22⋊C8—21no—
334C22⋊C8—222no—
335C22⋊C8—222no—
336C22⋊C8—221no—
337#97—21no—
338#97—221no—
339C4×C8—111no—
340C4×C8—111no—
341C4×C8—111no—
342C4×C8—111no—
343C2×C11—22no—
344C2×C11—82no—
345C2×C11#303611yescharacteristic
346C2×C11#305411yescharacteristic
347C2×C11C2×#47111yescharacteristic
348D11—161no—
349C24—21no—
350#41—882no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—221no—
354C2×D4—21no—
355C2×D4—42no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—441no—
360C2×D4C2×C22⋊D1112yes—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—441no—
367C22×C4D4×D1111yescharacteristic
368C22×C4#434111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370SD16—44no—
371SD16—442no—
372SD16—442no—
373D8—444no—
374M16—444no—
375M16—444no—
376C2×C8—22no—
377C2×C8—111no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—441no—
385C2×C8—442no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4C2×C22⋊D1112yes—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—41no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C42—41no—
402C42D4×D1111yescharacteristic
403C42#434111yescharacteristic
404C42C2×C22⋊D1111yescharacteristic
405C42C23×D1111yescharacteristic
406C11#1928211yescharacteristic, complemented, Sylow
407C23—22no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—441no—
412C23#6699211yescharacteristic
413Q8—41no—
414Q8—41no—
415Q8—42no—
416Q8—881no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—441no—
421D4—441no—
422D4—442no—
423D4—881no—
424D4—882no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—441no—
437C2×C4—882no—
438C2×C4#6699211yescharacteristic
439C2×C4#6699211yescharacteristic
440C2×C4#6699211yescharacteristic
441C2×C4C2×D4×D1111yescharacteristic
442C2×C4C2×#434111yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C8—42no—
445C8—112no—
446C8—221no—
447C8—221no—
448C8—221no—
449C8—442no—
450C8—442no—
451C22—21no—
452C22—21no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—84no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22#1062281612yes—
461C22C2×#6699211yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—881no—
470C4D11×AGL(1,ℤ/8)11yescharacteristic
471C4#1062330411yescharacteristic
472C4#1062335312yes—
473C2—22no—
474C2—82no—
475C2—1761no—
476C2#1307807711yescharacteristic
477C2#1307822211yescharacteristic
478C2C2×#1062281611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3110C2
socleC22×C11C2×#121
prime radical#13078707C2
hypercenter#3110D11
hypocenterC11#19282
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3110

Complements

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

NH ≅ G/Ntype
1. #13079176C2semidirect
3. C2×#10622625C2semidirect
4. #13068189C2semidirect
5. #13068179C2semidirect
6. #13068113C2semidirect
7. #13068083C2semidirect
8. #13067377C2semidirect
9. #13067316C2semidirect
10. #13067312C2semidirect
11. C11×#3110C2semidirect
24. #10622701C22semidirect
25. #10622698C22semidirect
26. #10622694C22semidirect
27. #10622692C22semidirect
43. #10622185C22semidirect
44. #10622185C22semidirect
45. #10622123C22semidirect
46. #10622119C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
169. #3110D11semidirect
406. C11#19282semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130787072
C2×#106226252
#130681892
#130681792
#130681132
#130680832
#130673772
#130673162
#130673122
C11×#31102
#1928211