Finite Group Databasebeta

← #14737796

Subgroups — #14737796

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079198C211yesmaximal, characteristic, complemented
2#13078415C211yesmaximal, characteristic
3#13078409C211yesmaximal, characteristic
4C2×#10622451C211yesmaximal, characteristic
5#13068194C212yesmaximal, complemented
6#13068190C212yesmaximal, complemented
7#13068138C212yesmaximal, complemented
8#13068104C212yesmaximal, complemented
9#13067371C211yesmaximal, characteristic, complemented
10#13067304C211yesmaximal, characteristic, complemented
11C11×#1550C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C22×#4313—21no—
14C2×C4×D44C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18#10622744—21no—
19#10622734—21no—
20C2×(C2×D11)⋊C8—21no—
21#10622706C2211yescharacteristic, complemented
22#10622705C2211yescharacteristic, complemented
23#10622700C2212yes—
24#10622697C2212yes—
25#10622694C2211yescharacteristic, complemented
26#10622691C2211yescharacteristic, complemented
27#10622679—22no—
28#10622664—21no—
29#10622664—21no—
30C4×#4326—21no—
31C4×#4326—21no—
32#10622614—21no—
33#10622608—21no—
34#10622537C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622460—22no—
37#10622459C2212yes—
38#10622455C2212yes—
39#10622451—21no—
40#10622451—21no—
41#10622451C2212yes—
42#10622451C2212yes—
43C11×#333C2212yescomplemented
44C11×#332C2212yescomplemented
45#10622120C2212yescomplemented
46#10622119C2212yescomplemented
47#10622118C2212yescomplemented
48#10622118C2212yescomplemented
49C22×D44D411yescharacteristic
50C22×C4×D11—21no—
51C2×C11×M16—21no—
52C22×C8×C11—21no—
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—
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—21no—
63C2×#4326—21no—
64C2×(C2×D11)⋊C4—21no—
65#66979—21no—
66C2×C4⋊Dic11D411yescharacteristic
67#66977—21no—
68#66977—21no—
69C2×#4318—21no—
70C22×C11⋊C8D411yescharacteristic
71C22×C11⋊C8D411yescharacteristic
72C2×#4313—22no—
73C2×#4313—22no—
74C2×#4313—44no—
75C4×D44—21no—
76C4×D44—21no—
77C4×D44D412yes—
78C4×D44C2312yes—
79#66923—21no—
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8C2312yes—
87C11×C4⋊C8C2312yes—
88#66899—21no—
89#66899—21no—
90#66885—22no—
91#66885—22no—
92(C2×D11)⋊C8—22no—
93(C2×D11)⋊C8—22no—
94#66882—22no—
95#66881—22no—
96#66874—21no—
97#66874—21no—
98#66873—22no—
99#66873—22no—
100#66872—22no—
101#66871—22no—
102#66871—21no—
103#66871—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19281—111nomaximal, Sylow
111C23×D11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×Dic11—21no—
118C2×D44—21no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44C2×D412yes—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C11×M16—42no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—42no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C22⋊C4—41no—
139C42×C11—41no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144C22⋊Dic11—41no—
145#4326—42no—
146#4326—42no—
147(C2×D11)⋊C4—22no—
148(C2×D11)⋊C4—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11C2×D412yes—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157C4×Dic11—41no—
158#4318—42no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—41no—
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166#4313—44no—
167#4313—44no—
168#3170—111no—
169#3077—111no—
170#3077—111no—
171C2×#436—111no—
172#1703—112no—
173#1703—112no—
174#1695—112no—
175#1689—112no—
176#1566—111no—
177#1550—111no—
178#1550D1111yescharacteristic, complemented
179C23×C11#12111yescharacteristic
180C22×D11—22no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—81no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#13712yes—
196C2×C4×C11#13712yes—
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×Dic11—22no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204D44—22no—
205D44—22no—
206D44—42no—
207C4×D11—44no—
208C4×D11—42no—
209C4×D11—42no—
210Dic22—41no—
211Dic22—41no—
212Dic22—81no—
213C8×C11—42no—
214C8×C11—42no—
215C11⋊C8—21no—
216C11⋊C8—21no—
217C11⋊C8—21no—
218C11⋊C8—42no—
219C11⋊C8AGL(1,ℤ/8)12yes—
220C22×M16—221no—
221#533—111no—
222#533C2×D1111yescharacteristic
223C2×C4×D4—111no—
224#500—111no—
225#494—111no—
226#487—111no—
227#487—111no—
228#478—222no—
229#478—222no—
230#476—112no—
231#476—112no—
232#474—112no—
233#474—112no—
234#467—221no—
235#467—221no—
236C4×Q16—221no—
237C4×Q16—221no—
238#436—112no—
239#436—112no—
240#436—221no—
241#436—221no—
242#428—221no—
243#428—221no—
244#423—111no—
245#423C2×D1111yescharacteristic
246C2×C4⋊C8C2×D1111yescharacteristic
247#418—221no—
248#418—221no—
249C2×C22⋊C8—221no—
250C2×C4×C8—111no—
251#334—112no—
252#334—112no—
253#333—112no—
254#333C2×D1112yescomplemented
255#332—112no—
256#332C2×D1112yescomplemented
257C22×C11—21no—
258C22×C11—21no—
259C22×C11#47012yes—
260C22×C11C2×#12111yescharacteristic
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—84no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11#47012yes—
271C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C4×C11C2×#13711yescharacteristic
273C4×C11C2×#13711yescharacteristic
274C4×C11#57511yescharacteristic
275Dic11—42no—
276Dic11—81no—
277Dic11—81no—
278C22×D4—111no—
279C23×C4—221no—
280C2×Q16—221no—
281C2×Q16—221no—
282C2×M16—21no—
283C2×M16—222no—
284C2×M16—222no—
285C2×M16—221no—
286C2×M16—444no—
287C22×C8—21no—
288C22×C8—111no—
289C22×C8—111no—
290C4⋊Q8—111no—
291C4⋊Q8—111no—
292C4⋊Q8C22×D1111yescharacteristic
293C4⋊Q8C22×D1111yescharacteristic
294#125—21no—
295#125—221no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—221no—
299C22⋊Q8—221no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—221no—
303C4×Q8—221no—
304C4×D4—112no—
305C4×D4—112no—
306C4×D4—221no—
307C4×D4—221no—
308#117—21no—
309#117—221no—
310C2×C4⋊C4—111no—
311C2×C22⋊C4—221no—
312C2×C42C22×D1111yescharacteristic
313#107—222no—
314#107—221no—
315#107—221no—
316#107—222no—
317#106—222no—
318#106—222no—
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—112no—
322C4⋊C8—221no—
323C4⋊C8C22×D1112yes—
324C4⋊C8C22×D1112yes—
325#103—221no—
326#103—221no—
327#103—221no—
328#103—221no—
329#102—222no—
330#102—222no—
331#102—222no—
332#102—222no—
333C22⋊C8—222no—
334C22⋊C8—222no—
335C4×C8—111no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8—111no—
339C2×C11—22no—
340C2×C11#303611yescharacteristic
341C2×C11C2×#47011yescharacteristic
342C2×C11#306711yescharacteristic
343D11—82no—
344C24—221no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×D4—112no—
350C2×D4—221no—
351C2×D4—222no—
352C2×D4—222no—
353C22×C4—221no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—442no—
357C22×C4—442no—
358C22×C4#433911yescharacteristic
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361Q16—442no—
362Q16—442no—
363M16—42no—
364M16—444no—
365M16—444no—
366M16—442no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—111no—
371C2×C8—111no—
372C2×C8—111no—
373C2×C8—111no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—441no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—112no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C22⋊C4—41no—
392C22⋊C4—222no—
393C22⋊C4—222no—
394C22⋊C4—441no—
395C42—41no—
396C42—441no—
397C42#433911yescharacteristic
398C42D4×D1111yescharacteristic
399C42D4×D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1928111yescharacteristic, complemented, Sylow
402C23—222no—
403C23—442no—
404C23—442no—
405C23—442no—
406C23#6693711yescharacteristic
407Q8—41no—
408Q8—41no—
409Q8—81no—
410Q8—441no—
411Q8—441no—
412Q8—881no—
413D4—222no—
414D4—222no—
415D4—442no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—222no—
422C2×C4—444no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4#6693711yescharacteristic
429C2×C4#6693711yescharacteristic
430C2×C4#6693711yescharacteristic
431C2×C4#6696812yes—
432C2×C4#6697112yes—
433C2×C4C2×#433911yescharacteristic
434C2×C4C2×D4×D1111yescharacteristic
435C2×C4C2×D4×D1111yescharacteristic
436C8—42no—
437C8—42no—
438C8—112no—
439C8—221no—
440C8—221no—
441C8—221no—
442C8—442no—
443C22—21no—
444C22—21no—
445C22—442no—
446C22—442no—
447C22—442no—
448C22—884no—
449C22#1062242912yes—
450C22C2×#6693711yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—81no—
455C4—81no—
456C4—442no—
457C4—881no—
458C4—881no—
459C4#1062242912yes—
460C4C2×#6696811yescharacteristic
461C4C2×#6697111yescharacteristic
462C4D11×AGL(1,ℤ/8)11yescharacteristic
463C4#1062330811yescharacteristic
464C2—22no—
465C2—882no—
466C2#1307807911yescharacteristic
467C2C2×#1062242911yescharacteristic
468C2#1307833511yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1550C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#1550D11
hypocenterC11#19281
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
1. #13079198C2semidirect
5. #13068194C2semidirect
6. #13068190C2semidirect
7. #13068138C2semidirect
8. #13068104C2semidirect
9. #13067371C2semidirect
10. #13067304C2semidirect
11. C11×#1550C2semidirect
21. #10622706C22semidirect
22. #10622705C22semidirect
25. #10622694C22semidirect
26. #10622691C22semidirect
43. C11×#333C22semidirect
44. C11×#332C22semidirect
45. #10622120C22semidirect
46. #10622119C22semidirect
47. #10622118C22semidirect
48. #10622118C22semidirect
178. #1550D11semidirect
254. #333C2×D11semidirect
256. #332C2×D11semidirect
401. C11#19281semidirect

Maximal subgroups

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

subgroupindex
#130791982
#130784152
#130784092
C2×#106224512
#130681942
#130681902
#130681382
#130681042
#130673712
#130673042
C11×#15502
#1928111