Finite Group Databasebeta

← #14737801

Subgroups — #14737801

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#13078711C211yesmaximal, characteristic, complemented
2#13078703C211yesmaximal, characteristic
3C2×#10622301C211yesmaximal, characteristic, complemented
4#13068188C212yesmaximal, complemented
5#13068174C212yesmaximal, complemented
6#13068112C212yesmaximal, complemented
7#13068078C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067316C211yesmaximal, characteristic, complemented
10#13067311C211yesmaximal, characteristic, complemented
11C11×#3167C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C22×#4313—21no—
15C2×C4×D44C2211yescharacteristic
16C11×#498C2211yescharacteristic, complemented
17C11×#492C2211yescharacteristic, complemented
18C11×#487C2211yescharacteristic, complemented
19C11×#486C2211yescharacteristic, complemented
20C11×#465—21no—
21C11×#465—21no—
22C4×C11×SD16—21no—
23C4×C11×SD16—21no—
24C2×C4×C8×C11C2211yescharacteristic
25C2×(C2×D11)⋊C8—21no—
26#10622700C2212yes—
27#10622697C2212yes—
28#10622696C2212yes—
29#10622685C2212yes—
30#10622659—21no—
31#10622657—21no—
32#10622649—21no—
33#10622647—21no—
34#10622639—22no—
35#10622627—22no—
36#10622539C2211yescharacteristic
37#10622539C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622301—21no—
40#10622301—21no—
41#10622301C2212yes—
42#10622301C2212yes—
43#10622185C2212yescomplemented
44#10622185C2212yescomplemented
45#10622184C2212yescomplemented
46#10622182C2212yescomplemented
47#10622096C2212yescomplemented
48#10622095C2212yescomplemented
49C2×C11×#41—21no—
50C22×D44D411yescharacteristic
51C22×C4×D11—21no—
52C2×C11×SD16—21no—
53C2×C11×SD16—21no—
54C22×C8×C11D411yescharacteristic
55C22×C8×C11D411yescharacteristic
56C11×C4⋊Q8C2311yescharacteristic
57C11×C4⋊Q8C2311yescharacteristic
58C11×C4⋊Q8C2311yescharacteristic
59C11×#127C2311yescharacteristic
60C11×#125—21no—
61C11×#124—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×#121—21no—
65C11×#121—21no—
66C4×Q8×C11—21no—
67C4×Q8×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C11×#117—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4325—22no—
73C2×#4323—22no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11D411yescharacteristic
76C22×C11⋊C8—21no—
77C2×#4313—22no—
78C2×#4313—22no—
79C2×#4313—44no—
80C4×D44—21no—
81C4×D44—21no—
82C4×D44D412yes—
83C4×D44C2312yes—
84C11×#106—21no—
85C11×#106—21no—
86C11×#103—21no—
87C11×#103—21no—
88C11×#102—21no—
89C11×#102—21no—
90C4×C8×C11D411yescharacteristic
91C4×C8×C11D411yescharacteristic
92C4×C8×C11C2311yescharacteristic
93C4×C8×C11C2311yescharacteristic
94#66899—22no—
95#66896—22no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98(C2×D11)⋊C8—22no—
99(C2×D11)⋊C8—22no—
100#66873—22no—
101#66873—22no—
102#66872—22no—
103#66871—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108#66867—21no—
109#66867—21no—
110#19282—111nomaximal, Sylow
111C23×D11—21no—
112C11×#41—82no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×Dic11—21no—
125C2×D44—21no—
126C2×D44—42no—
127C2×D44C2×D412yes—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C11×SD16—42no—
133C11×SD16—42no—
134C2×C8×C11—22no—
135C2×C8×C11—41no—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11—41no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11#4111yescharacteristic
155C42×C11C2411yescharacteristic
156#4325—44no—
157#4323—44no—
158(C2×D11)⋊C4—22no—
159(C2×D11)⋊C4—22no—
160C4⋊Dic11—21no—
161C4⋊Dic11C2×D412yes—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—42no—
166#4313—44no—
167#4313—44no—
168#3167D1111yescharacteristic, complemented
169#3110—111no—
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—41no—
180C23×C11#12111yescharacteristic
181C22×D11—22no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185Q8×C11—41no—
186Q8×C11—42no—
187Q8×C11—41no—
188Q8×C11—81no—
189D4×C11—41no—
190D4×C11—42no—
191D4×C11—41no—
192D4×C11—81no—
193D4×C11—82no—
194C2×C4×C11—22no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—82no—
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—42no—
210D44—22no—
211D44—22no—
212D44—42no—
213C4×D11—44no—
214C4×D11—42no—
215C4×D11—42no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11AGL(1,ℤ/8)12yes—
220C11⋊C8—42no—
221C11⋊C8—42no—
222C11⋊C8—42no—
223C22×M16—221no—
224#533C2×D1111yescharacteristic
225#532C2×D1111yescharacteristic
226C2×C4×D4—111no—
227#498C2×D1111yescharacteristic, complemented
228#492C2×D1111yescharacteristic, complemented
229#487C2×D1111yescharacteristic, complemented
230#486C2×D1111yescharacteristic, complemented
231#484—221no—
232#481—221no—
233#476—112no—
234#474—112no—
235#465—21no—
236#465—21no—
237#461—112no—
238#459—112no—
239#450—221no—
240#447—221no—
241#442—222no—
242#440—222no—
243C4×SD16—21no—
244C4×SD16—21no—
245#436—112no—
246#436—112no—
247#436—221no—
248#436—221no—
249#432—111no—
250#432—111no—
251C2×C4⋊C8—111no—
252C2×C22⋊C8—221no—
253C2×C4×C8C2×D1111yescharacteristic
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—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11#47112yes—
266C22×C11C2×#12111yescharacteristic
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—84no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C4×C11#57512yes—
280C4×C11#57511yescharacteristic
281Dic11—42no—
282C2×#41—21no—
283C22×D4—111no—
284C23×C4—221no—
285C2×SD16—21no—
286C2×SD16—21no—
287C2×SD16—222no—
288C2×D8—222no—
289C2×M16—222no—
290C2×M16—222no—
291C2×M16—444no—
292C22×C8—221no—
293C22×C8C22⋊D1111yescharacteristic
294C22×C8C22⋊D1111yescharacteristic
295C4⋊Q8C22×D1111yescharacteristic
296C4⋊Q8C22×D1111yescharacteristic
297C4⋊Q8C22×D1111yescharacteristic
298#127C22×D1111yescharacteristic
299#125—21no—
300#124—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303#121—21no—
304#121—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—112no—
310C4×D4—112no—
311C4×D4—221no—
312C4×D4—221no—
313#117—21no—
314C2×C4⋊C4—111no—
315C2×C22⋊C4—221no—
316C2×C42C22×D1111yescharacteristic
317#107—222no—
318#106—21no—
319#106—21no—
320#106—222no—
321C4⋊C8—112no—
322C4⋊C8—112no—
323C4⋊C8—112no—
324C4⋊C8—221no—
325#103—21no—
326#103—21no—
327#103—222no—
328#102—21no—
329#102—21no—
330#102—222no—
331#102—222no—
332#102—222no—
333C22⋊C8—221no—
334C22⋊C8—221no—
335C22⋊C8—222no—
336C22⋊C8—222no—
337#97—221no—
338#97—221no—
339C4×C8C22⋊D1111yescharacteristic
340C4×C8C22⋊D1111yescharacteristic
341C4×C8C22×D1111yescharacteristic
342C4×C8C22×D1111yescharacteristic
343C2×C11—22no—
344C2×C11—161no—
345C2×C11#303611yescharacteristic
346C2×C11#305411yescharacteristic
347C2×C11C2×#47111yescharacteristic
348D11—82no—
349C24—221no—
350#41—82no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4—112no—
359C2×D4—221no—
360C2×D4—442no—
361C22×C4—41no—
362C22×C4—221no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—442no—
366C22×C4—442no—
367C22×C4D4×D1111yescharacteristic
368C22×C4#434111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370SD16—42no—
371SD16—42no—
372SD16—444no—
373D8—444no—
374M16—444no—
375M16—444no—
376C2×C8—22no—
377C2×C8—41no—
378C2×C8—222no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—442no—
382C2×C8C2×C22⋊D1111yescharacteristic
383C2×C8C2×C22⋊D1111yescharacteristic
384C2×C8C2×C22⋊D1111yescharacteristic
385C2×C8C2×C22⋊D1111yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—112no—
395C4⋊C4—221no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—222no—
400C22⋊C4—222no—
401C42—41no—
402C42D4×D1111yescharacteristic
403C42#434111yescharacteristic
404C42C2×C22⋊D1111yescharacteristic
405C42C23×D1111yescharacteristic
406C11#1928211yescharacteristic, complemented, Sylow
407C23—41no—
408C23—222no—
409C23—442no—
410C23—442no—
411C23—442no—
412C23#6699111yescharacteristic
413Q8—42no—
414Q8—41no—
415Q8—41no—
416Q8—81no—
417D4—42no—
418D4—41no—
419D4—41no—
420D4—81no—
421D4—82no—
422D4—222no—
423D4—222no—
424D4—442no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—82no—
433C2×C4—222no—
434C2×C4—444no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4#6699111yescharacteristic
439C2×C4#6699111yescharacteristic
440C2×C4#6699111yescharacteristic
441C2×C4C2×D4×D1111yescharacteristic
442C2×C4C2×#434111yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C8—21no—
445C8—21no—
446C8—21no—
447C8—442no—
448C8—442no—
449C8—442no—
450C8#6700212yes—
451C22—21no—
452C22—21no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—442no—
457C22—442no—
458C22—442no—
459C22—884no—
460C22#1062279012yes—
461C22C2×#6699111yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—442no—
470C4#1062329912yes—
471C4C2×#6700211yescharacteristic
472C4#1062335311yescharacteristic
473C2—22no—
474C2—161no—
475C2—882no—
476C2#1307807611yescharacteristic
477C2#1307822111yescharacteristic
478C2C2×#1062279011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3167C2
socleC22×C11C2×#121
prime radical#13078703C2
hypercenter#3167D11
hypocenterC11#19282
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #13078711C2semidirect
3. C2×#10622301C2semidirect
4. #13068188C2semidirect
5. #13068174C2semidirect
6. #13068112C2semidirect
7. #13068078C2semidirect
8. #13067379C2semidirect
9. #13067316C2semidirect
10. #13067311C2semidirect
11. C11×#3167C2semidirect
16. C11×#498C22semidirect
17. C11×#492C22semidirect
18. C11×#487C22semidirect
19. C11×#486C22semidirect
43. #10622185C22semidirect
44. #10622185C22semidirect
45. #10622184C22semidirect
46. #10622182C22semidirect
47. #10622096C22semidirect
48. #10622095C22semidirect
168. #3167D11semidirect
227. #498C2×D11semidirect
228. #492C2×D11semidirect
229. #487C2×D11semidirect
230. #486C2×D11semidirect
406. C11#19282semidirect

Maximal subgroups

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

subgroupindex
#130787112
#130787032
C2×#106223012
#130681882
#130681742
#130681122
#130680782
#130673792
#130673162
#130673112
C11×#31672
#1928211