Finite Group Databasebeta

← #14738643

Subgroups — #14738643

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079640C211yesmaximal, characteristic, complemented
2#13079631C211yesmaximal, characteristic
3C2×#10622307C211yesmaximal, characteristic, complemented
4#13068184C212yesmaximal, complemented
5#13068177C212yesmaximal, complemented
6#13068060C212yesmaximal, complemented
7#13068053C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067332C211yesmaximal, characteristic, complemented
10#13067329C211yesmaximal, characteristic, complemented
11C11×#2966C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13C2×#66927C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#446C2211yescharacteristic, complemented
16C8×Q8×C11C2211yescharacteristic, complemented
17C11×#436C2211yescharacteristic, complemented
18C11×#435—21no—
19C8×D4×C11—21no—
20C8×D4×C11C2211yescharacteristic, complemented
21C11×#433—21no—
22C11×#432C2211yescharacteristic
23C11×#405—21no—
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66885—21no—
26C2×#66885—21no—
27#10622682—21no—
28#10622680—21no—
29#10622673—21no—
30#10622671—21no—
31#10622663—21no—
32#10622659—21no—
33#10622653—21no—
34#10622649—21no—
35#10622644C2212yescomplemented
36#10622640C2212yes—
37#10622632C2212yescomplemented
38#10622628C2212yes—
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41#10622307—21no—
42#10622307—21no—
43#10622307C2212yes—
44#10622307C2212yes—
45#10622124C2212yescomplemented
46#10622124C2212yescomplemented
47#10622123C2212yes—
48#10622123C2212yes—
49#10622096C2212yescomplemented
50#10622095C2212yescomplemented
51C22×D44—21no—
52C22×D44—21no—
53C22×D44—21no—
54C22×Dic22—21no—
55C2×C11×M16—21no—
56C22×C8×C11—21no—
57C22×C8×C11D411yescharacteristic
58C22×C8×C11D411yescharacteristic
59C11×#126—21no—
60C11×#125D411yescharacteristic
61C11×#124D411yescharacteristic
62C11×#123—21no—
63C11×C22⋊Q8D411yescharacteristic
64C11×#121D411yescharacteristic
65C4×Q8×C11C2311yescharacteristic
66C4×D4×C11—21no—
67C4×D4×C11C2311yescharacteristic
68C11×#117—21no—
69C2×C42×C11C2311yescharacteristic
70C2×#4326—22no—
71C2×#4325—22no—
72C2×#4324—22no—
73C2×#4323—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76#66927—21no—
77#66927—21no—
78#66927—21no—
79#66927C2312yes—
80#66922—21no—
81#66922—21no—
82#66922—21no—
83#66922C2312yes—
84C11×C4⋊C8—21no—
85C11×C4⋊C8—21no—
86C11×C4⋊C8C2311yescharacteristic
87C11×C4⋊C8C2311yescharacteristic
88C11×C22⋊C8—21no—
89C11×C22⋊C8—21no—
90C11×C22⋊C8—21no—
91C11×#97—21no—
92C11×#97—21no—
93C4×C8×C11—21no—
94C4×C8×C11D411yescharacteristic
95C4×C8×C11D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97C4×C8×C11C2311yescharacteristic
98C22⋊(C11⋊C8)—21no—
99C22⋊(C11⋊C8)—21no—
100#66885—22no—
101#66885—22no—
102#66885—22no—
103#66885—22no—
104#66874—22no—
105#66874—22no—
106#66873—22no—
107#66873—22no—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2312yes—
110#66867—21no—
111#66867—21no—
112#19364—111nomaximal, Sylow
113C23×D11—41no—
114C2×Q8×C11C2×D411yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11C2×D411yescharacteristic
117C22×C4×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×Dic11—41no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—42no—
126C2×D44—42no—
127C2×D44—41no—
128C2×D44—41no—
129C2×D44—41no—
130C2×D44—82no—
131C2×D44—82no—
132C2×Dic22—22no—
133C2×Dic22—41no—
134C2×Dic22—82no—
135C11×M16—42no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—41no—
139C2×C8×C11—41no—
140C2×C8×C11—42no—
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4C2×D411yescharacteristic
150C11×C4⋊C4C2×D411yescharacteristic
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C42×C11—21no—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11#4111yescharacteristic
160C42×C11C2411yescharacteristic
161#4326—82no—
162#4325—82no—
163#4324—82no—
164#4323—82no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—41no—
168C4⋊Dic11—41no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171#3218—111no—
172#3217—111no—
173C2×#486—111no—
174#2966D1111yescharacteristic, complemented
175#1702—112no—
176#1701—112no—
177#1682—112no—
178#1681—112no—
179#1568—111no—
180#1556—111no—
181#1555—111no—
182C23×C11—21no—
183C23×C11#12111yescharacteristic
184C22×D11—42no—
185C22×D11—82no—
186C22×D11—82no—
187C22×D11—82no—
188Q8×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—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×Dic11—42no—
207C2×Dic11—82no—
208D44—42no—
209D44—42no—
210D44—42no—
211D44—42no—
212D44—82no—
213D44—82no—
214D44—82no—
215D44—82no—
216Dic22—42no—
217Dic22—42no—
218Dic22—82no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11—21no—
222C8×C11—21no—
223C8×C11—41no—
224C8×C11—41no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C2×C4⋊Q8—111no—
228C2×#127—111no—
229#529C2×D1111yescharacteristic
230#497—221no—
231#496—221no—
232#491—221no—
233#490—221no—
234#486—112no—
235#486—112no—
236#486—221no—
237#486—221no—
238#462—112no—
239#461—112no—
240#460—112no—
241#459—112no—
242#451—221no—
243#450—221no—
244#448—221no—
245#447—221no—
246#446C2×D1111yescharacteristic, complemented
247C8×Q8C2×D1111yescharacteristic, complemented
248#436C2×D1111yescharacteristic, complemented
249#435—21no—
250C8×D4—21no—
251C8×D4C2×D1111yescharacteristic, complemented
252#433—21no—
253#432—111no—
254#432—111no—
255#432C2×D1111yescharacteristic
256C2×#102—221no—
257C2×#102—221no—
258#405—21no—
259C2×C4×C8C2×D1111yescharacteristic
260#335—112no—
261#334—112no—
262#332—112no—
263#332—112no—
264#331—112no—
265#331—112no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—41no—
269C22×C11—41no—
270C22×C11—41no—
271C22×C11#47112yes—
272C22×C11C2×#12111yescharacteristic
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—82no—
276C2×D11—164no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—41no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11#57511yescharacteristic
285C4×C11#57511yescharacteristic
286C4×C11#57612yes—
287Dic11—82no—
288C22×Q8—221no—
289C22×D4—221no—
290C22×D4—221no—
291C22×D4—221no—
292C2×Q16—222no—
293C2×SD16—222no—
294C2×SD16—222no—
295C2×D8—222no—
296C2×M16—21no—
297C22×C8—21no—
298C22×C8C22⋊D1111yescharacteristic
299C22×C8C22⋊D1111yescharacteristic
300C4⋊Q8—112no—
301C4⋊Q8—221no—
302C4⋊Q8—221no—
303C4⋊Q8—221no—
304#127—112no—
305#127—221no—
306#127—221no—
307#127—221no—
308#126—21no—
309#125D4411yescharacteristic
310#124D4411yescharacteristic
311#123—21no—
312C22⋊Q8D4411yescharacteristic
313#121D4411yescharacteristic
314C4×Q8C22×D1111yescharacteristic
315C4×D4—21no—
316C4×D4C22×D1111yescharacteristic
317#117—21no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—221no—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8—112no—
324C4⋊C8—112no—
325C4⋊C8C22×D1111yescharacteristic
326C4⋊C8C22×D1111yescharacteristic
327#103—222no—
328#103—222no—
329#102—222no—
330#102—222no—
331#102—222no—
332#102—222no—
333#102—222no—
334#102—222no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8—221no—
339C22⋊C8—221no—
340#97—21no—
341#97—21no—
342#97—221no—
343#97—221no—
344C4×C8—21no—
345C4×C8C22⋊D1111yescharacteristic
346C4×C8C22⋊D1111yescharacteristic
347C4×C8C22×D1111yescharacteristic
348C4×C8C22×D1111yescharacteristic
349C2×C11—22no—
350C2×C11—81no—
351C2×C11#304011yescharacteristic
352C2×C11#305811yescharacteristic
353C2×C11C2×#47111yescharacteristic
354D11—162no—
355C24—441no—
356C2×Q8—222no—
357C2×Q8—441no—
358C2×Q8—882no—
359C2×Q8C2×D4411yescharacteristic
360C2×D4—21no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—222no—
364C2×D4—442no—
365C2×D4—442no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—882no—
370C2×D4—882no—
371C2×D4C2×D4411yescharacteristic
372C22×C4—21no—
373C22×C4—441no—
374C22×C4C2×D4411yescharacteristic
375C22×C4#433911yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—882no—
378SD16—882no—
379SD16—882no—
380D8—882no—
381M16—42no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—42no—
387C2×C8—222no—
388C2×C8—222no—
389C2×C8C2×C22⋊D1111yescharacteristic
390C2×C8C2×C22⋊D1111yescharacteristic
391C2×C8C2×C22⋊D1111yescharacteristic
392C2×C8C2×C22⋊D1111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4C2×D4411yescharacteristic
402C4⋊C4C2×D4411yescharacteristic
403C22⋊C4—21no—
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C42—21no—
409C42C2×D4411yescharacteristic
410C42#433911yescharacteristic
411C42C2×C22⋊D1111yescharacteristic
412C42C23×D1111yescharacteristic
413C11#1936411yescharacteristic, complemented, Sylow
414C23—21no—
415C23—442no—
416C23—882no—
417C23—882no—
418C23—882no—
419C23#6698311yescharacteristic
420Q8—22no—
421Q8—442no—
422Q8—442no—
423Q8—882no—
424D4—22no—
425D4—42no—
426D4—442no—
427D4—442no—
428D4—442no—
429D4—442no—
430D4—882no—
431D4—882no—
432D4—882no—
433D4—882no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—442no—
444C2×C4—882no—
445C2×C4#6698311yescharacteristic
446C2×C4#6698311yescharacteristic
447C2×C4#6698311yescharacteristic
448C2×C4C22×D4411yescharacteristic
449C2×C4C2×#433911yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—21no—
452C8—21no—
453C8—21no—
454C8—21no—
455C8—41no—
456C8—41no—
457C8—442no—
458C8—442no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—882no—
465C22—882no—
466C22—882no—
467C22—1764no—
468C22#1062275412yes—
469C22C2×#6698311yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—882no—
478C4#1062328312yes—
479C4#1062335311yescharacteristic
480C4#1062335311yescharacteristic
481C2—22no—
482C2—81no—
483C2—1762no—
484C2#1307811011yescharacteristic
485C2#1307826411yescharacteristic
486C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radical#13079631C2
hypercenter#2966D11
hypocenterC11#19364
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #13079640C2semidirect
3. C2×#10622307C2semidirect
4. #13068184C2semidirect
5. #13068177C2semidirect
6. #13068060C2semidirect
7. #13068053C2semidirect
8. #13067379C2semidirect
9. #13067332C2semidirect
10. #13067329C2semidirect
11. C11×#2966C2semidirect
15. C11×#446C22semidirect
16. C8×Q8×C11C22semidirect
17. C11×#436C22semidirect
20. C8×D4×C11C22semidirect
35. #10622644C22semidirect
37. #10622632C22semidirect
45. #10622124C22semidirect
46. #10622124C22semidirect
49. #10622096C22semidirect
50. #10622095C22semidirect
174. #2966D11semidirect
246. #446C2×D11semidirect
247. C8×Q8C2×D11semidirect
248. #436C2×D11semidirect
251. C8×D4C2×D11semidirect
413. C11#19364semidirect

Maximal subgroups

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

subgroupindex
#130796402
#130796312
C2×#106223072
#130681842
#130681772
#130680602
#130680532
#130673792
#130673322
#130673292
C11×#29662
#1936411