Finite Group Databasebeta

← #14736314

Subgroups — #14736314

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079126C211yesmaximal, characteristic, complemented
2#13078625C211yesmaximal, characteristic
3#13078620C211yesmaximal, characteristic
4C2×#10622451C211yesmaximal, characteristic
5#13068138C212yesmaximal, complemented
6#13068128C212yesmaximal, complemented
7#13068118C212yesmaximal, complemented
8#13068114C212yesmaximal, complemented
9#13067362C211yesmaximal, characteristic, complemented
10#13067274C211yesmaximal, characteristic, complemented
11C11×#1542C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C22×#4313—21no—
14C2×C4×D44C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×(C2×D11)⋊C8—21no—
19#10622697C2212yes—
20#10622696C2212yes—
21#10622692C2211yescharacteristic, complemented
22#10622692C2211yescharacteristic, complemented
23#10622691C2211yescharacteristic, complemented
24#10622691C2211yescharacteristic, complemented
25#10622677—21no—
26#10622677—21no—
27#10622659—21no—
28#10622656—21no—
29C4×#4325—22no—
30#10622611—21no—
31#10622611—21no—
32#10622538C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622455C2212yes—
35#10622454C2212yes—
36#10622451—21no—
37#10622451—21no—
38#10622451C2212yes—
39#10622451C2212yes—
40#10622344—21no—
41#10622334—21no—
42C4×#4314—22no—
43C11×#333C2212yescomplemented
44C11×#332C2212yescomplemented
45#10622124C2212yescomplemented
46#10622119C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×D44D411yescharacteristic
50C22×C4×D11—21no—
51C22×C8×C11—21no—
52C11×C4⋊Q8C2311yescharacteristic
53C11×C4⋊Q8C2311yescharacteristic
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C11×#117—21no—
60C2×C42×C11C2311yescharacteristic
61C2×#4325—22no—
62C2×(C2×D11)⋊C4—21no—
63#66979—21no—
64C2×C4⋊Dic11D411yescharacteristic
65#66977—21no—
66#66977—21no—
67C22×C11⋊C8D411yescharacteristic
68C22×C11⋊C8D411yescharacteristic
69C2×#4314—22no—
70C2×#4313—22no—
71C2×#4313—22no—
72C2×#4313—44no—
73C4×D44—21no—
74C4×D44—21no—
75C4×D44D412yes—
76C4×D44C2312yes—
77#66923—21no—
78#66922C2311yescharacteristic
79#66922C2311yescharacteristic
80C4×Dic22—21no—
81C4×Dic22—21no—
82C11×C4⋊C8—21no—
83C11×C4⋊C8C2312yes—
84C11×C4⋊C8C2312yes—
85C11×C22⋊C8—21no—
86C4×C8×C11—21no—
87#66899—22no—
88C22⋊(C11⋊C8)—21no—
89#66885—22no—
90(C2×D11)⋊C8—22no—
91(C2×D11)⋊C8—22no—
92#66881—22no—
93#66880—22no—
94#66873—22no—
95#66872—22no—
96#66872—21no—
97#66872—21no—
98#66872—21no—
99#66872—21no—
100#66871—21no—
101#66871—21no—
102#66871—21no—
103#66871—21no—
104C4⋊(C11⋊C8)C2312yes—
105C4×C11⋊C8—21no—
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8D411yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109C4×C11⋊C8C2311yescharacteristic
110#19137—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—42no—
120C2×D44C2×D412yes—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—42no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11—41no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11#4111yescharacteristic
141C42×C11C2411yescharacteristic
142C22⋊Dic11—41no—
143#4325—44no—
144(C2×D11)⋊C4—22no—
145(C2×D11)⋊C4—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11C2×D412yes—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154C4×Dic11—41no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8SD1614yescomplemented
158C2×C11⋊C8C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162#4314—44no—
163#4313—44no—
164#4313—44no—
165#3160—111no—
166#3101—111no—
167#3101—111no—
168C2×#436—111no—
169#1695—112no—
170#1693—112no—
171#1691—112no—
172#1691—112no—
173#1564—111no—
174#1542—111no—
175#1542D1111yescharacteristic, complemented
176C23×C11#12111yescharacteristic
177C22×D11—22no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181Q8×C11—42no—
182Q8×C11—81no—
183C2×C4×C11—22no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11C2×SD1612yes—
191C2×C4×C11#13712yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×Dic11—22no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199D44—22no—
200D44—22no—
201D44—42no—
202C4×D11—42no—
203C4×D11—42no—
204C4×D11—44no—
205Dic22—42no—
206Dic22—81no—
207C8×C11—42no—
208C8×C11—42no—
209C11⋊C8—21no—
210C11⋊C8—21no—
211C11⋊C8—42no—
212C11⋊C8C2×SD1612yes—
213C11⋊C8C2×SD1612yes—
214C22×M16—221no—
215#533—111no—
216#533C2×D1111yescharacteristic
217C2×C4×D4—111no—
218#500—111no—
219#500—111no—
220#499—221no—
221#499—221no—
222#498—111no—
223#498—111no—
224#483—221no—
225#483—221no—
226#476—112no—
227#476—112no—
228#461—112no—
229#461—112no—
230#450—221no—
231#450—221no—
232C4×SD16—222no—
233C4×SD16—222no—
234#436—112no—
235#436—112no—
236#436—221no—
237#436—221no—
238#431—111no—
239#431C2×D1111yescharacteristic
240#427—221no—
241#427—221no—
242C2×C4⋊C8C2×D1111yescharacteristic
243C2×C22⋊C8—221no—
244C2×C4×C8—111no—
245#335—112no—
246#334—112no—
247#333—112no—
248#333C2×D1112yescomplemented
249#332—112no—
250#332C2×D1112yescomplemented
251C22×C11—21no—
252C22×C11—21no—
253C22×C11#46112yes—
254C22×C11C2×#12111yescharacteristic
255C2×D11—42no—
256C2×D11—42no—
257C2×D11—42no—
258C2×D11—84no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—81no—
263C4×C11—81no—
264C4×C11#46112yes—
265C4×C11C22×SD1611yescharacteristic
266C4×C11C2×#13711yescharacteristic
267C4×C11#57512yes—
268Dic11—42no—
269Dic11—81no—
270Dic11—81no—
271C22×D4—111no—
272C23×C4—221no—
273C2×SD16—222no—
274C2×SD16—222no—
275C2×M16—222no—
276C2×M16—222no—
277C2×M16—444no—
278C22×C8—21no—
279C22×C8—111no—
280C22×C8—111no—
281C4⋊Q8—111no—
282C4⋊Q8—111no—
283C4⋊Q8C22×D1111yescharacteristic
284C4⋊Q8C22×D1111yescharacteristic
285#125—21no—
286#125—221no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—221no—
290C22⋊Q8—221no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—221no—
294C4×Q8—221no—
295C4×D4—112no—
296C4×D4—112no—
297C4×D4—221no—
298C4×D4—221no—
299#117—21no—
300#117—221no—
301C2×C4⋊C4—111no—
302C2×C22⋊C4—221no—
303C2×C42C22×D1111yescharacteristic
304#107—221no—
305#107—221no—
306#107—221no—
307#107—221no—
308#106—222no—
309#106—221no—
310#106—221no—
311#106—221no—
312#106—221no—
313#106—222no—
314C4⋊C8—21no—
315C4⋊C8—112no—
316C4⋊C8C22×D1112yes—
317C4⋊C8C22×D1112yes—
318#103—222no—
319#103—222no—
320#102—222no—
321#102—222no—
322C22⋊C8—21no—
323C22⋊C8—222no—
324C22⋊C8—222no—
325C22⋊C8—221no—
326C4×C8—21no—
327C4×C8—111no—
328C4×C8—111no—
329C4×C8—111no—
330C4×C8—111no—
331C4×C8—221no—
332C2×C11—22no—
333C2×C11C2×#46111yescharacteristic
334C2×C11#305411yescharacteristic
335C2×C11#306711yescharacteristic
336D11—82no—
337C24—221no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—221no—
341C2×Q8—221no—
342C2×D4—112no—
343C2×D4—221no—
344C2×D4—442no—
345C22×C4—221no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—442no—
349C22×C4—442no—
350C22×C4#433911yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4D4×D1111yescharacteristic
353SD16—444no—
354SD16—444no—
355M16—444no—
356M16—444no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—42no—
360C2×C8—114no—
361C2×C8—111no—
362C2×C8—111no—
363C2×C8—111no—
364C2×C8—111no—
365C2×C8—222no—
366C2×C8—222no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—112no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C22⋊C4—41no—
382C22⋊C4—222no—
383C22⋊C4—222no—
384C22⋊C4—441no—
385C42—41no—
386C42—441no—
387C42#433911yescharacteristic
388C42D4×D1111yescharacteristic
389C42D4×D1111yescharacteristic
390C42C23×D1111yescharacteristic
391C11#1913711yescharacteristic, complemented, Sylow
392C23—222no—
393C23—442no—
394C23—442no—
395C23—442no—
396C23#6693711yescharacteristic
397Q8—42no—
398Q8—81no—
399Q8—442no—
400Q8—881no—
401D4—222no—
402D4—222no—
403D4—442no—
404C2×C4—22no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—222no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—444no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4#6693711yescharacteristic
416C2×C4#6693711yescharacteristic
417C2×C4#6693711yescharacteristic
418C2×C4SD16×D1112yes—
419C2×C4#6697112yes—
420C2×C4C2×#433911yescharacteristic
421C2×C4C2×D4×D1111yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C8—42no—
424C8—42no—
425C8—112no—
426C8—112no—
427C8—221no—
428C8—221no—
429C8—442no—
430C22—21no—
431C22—21no—
432C22—442no—
433C22—442no—
434C22—442no—
435C22—884no—
436C22#1062243112yes—
437C22C2×#6693711yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—442no—
444C4—881no—
445C4—881no—
446C4#1062243112yes—
447C4C2×SD16×D1111yescharacteristic
448C4C2×#6697111yescharacteristic
449C4#1062329912yes—
450C2—22no—
451C2—882no—
452C2C2×#1062243111yescharacteristic
453C2#1307822411yescharacteristic
454C2#1307833511yescharacteristic
subgroupG/H
centerC2×C4#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#1542D11
hypocenterC11#19137
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #13079126C2semidirect
5. #13068138C2semidirect
6. #13068128C2semidirect
7. #13068118C2semidirect
8. #13068114C2semidirect
9. #13067362C2semidirect
10. #13067274C2semidirect
11. C11×#1542C2semidirect
21. #10622692C22semidirect
22. #10622692C22semidirect
23. #10622691C22semidirect
24. #10622691C22semidirect
43. C11×#333C22semidirect
44. C11×#332C22semidirect
45. #10622124C22semidirect
46. #10622119C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
157. C2×C11⋊C8SD16semidirect
175. #1542D11semidirect
248. #333C2×D11semidirect
250. #332C2×D11semidirect
391. C11#19137semidirect

Maximal subgroups

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

subgroupindex
#130791262
#130786252
#130786202
C2×#106224512
#130681382
#130681282
#130681182
#130681142
#130673622
#130672742
C11×#15422
#1913711