Finite Group Databasebeta

← #14738623

Subgroups — #14738623

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079631C211yesmaximal, characteristic
2C2×#10622701C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068158C212yesmaximal, complemented
5#13068151C212yesmaximal, complemented
6#13068034C212yesmaximal, complemented
7#13068027C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067342C211yesmaximal, characteristic, complemented
10#13067329C211yesmaximal, characteristic, complemented
11C11×#3238C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C11×#529C2211yescharacteristic
14C2×#66927C2211yescharacteristic
15C11×#501—21no—
16C11×#489—21no—
17C11×#483—21no—
18C11×#480—21no—
19C11×#477C2212yescomplemented
20C11×#476C2212yescomplemented
21C11×#432C2211yescharacteristic
22#10622701—21no—
23#10622701—21no—
24#10622701C2212yes—
25#10622701C2212yes—
26#10622680—21no—
27#10622671—21no—
28#10622659—21no—
29#10622649—21no—
30#10622640C2212yes—
31#10622637C2211yescharacteristic, complemented
32Q8×C11⋊C8C2211yescharacteristic, complemented
33#10622628C2212yes—
34#10622625C2211yescharacteristic, complemented
35#10622624—21no—
36D4×C11⋊C8—21no—
37D4×C11⋊C8C2211yescharacteristic, complemented
38#10622613—21no—
39#10622610—21no—
40C2×#66873—21no—
41C2×#66873—21no—
42#10622539C2211yescharacteristic
43#10622539C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622184C2212yescomplemented
46#10622184C2212yescomplemented
47#10622123C2212yes—
48#10622123C2212yes—
49#10622118C2212yescomplemented
50#10622117C2212yescomplemented
51C22×Q8×C11—21no—
52C22×D44—21no—
53C22×D44—21no—
54C22×D44—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8C2312yes—
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×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4325—22no—
73C2×#4323—22no—
74C2×#4318—21no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8D411yescharacteristic
77C22×C11⋊C8D411yescharacteristic
78#66927—21no—
79#66927—21no—
80#66927—21no—
81#66927C2312yes—
82C11×#107—22no—
83C11×#106—22no—
84C11×C4⋊C8C2312yes—
85C11×#103—22no—
86C11×#102—22no—
87C11×C22⋊C8—21no—
88C11×#97—21no—
89C22⋊(C11⋊C8)—21no—
90C22⋊(C11⋊C8)—21no—
91C22⋊(C11⋊C8)—21no—
92C22⋊(C11⋊C8)—21no—
93#66873—22no—
94#66873—22no—
95#66873—22no—
96#66873—22no—
97#66873—22no—
98#66873—22no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4⋊(C11⋊C8)C2312yes—
104#66867—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8—21no—
108C4×C11⋊C8D411yescharacteristic
109C4×C11⋊C8D411yescharacteristic
110C4×C11⋊C8C2311yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112#19362—111nomaximal, Sylow
113C23×D11—41no—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—82no—
117C2×Q8×C11C2×D411yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—42no—
129C2×D44—42no—
130C2×D44—41no—
131C2×D44—41no—
132C2×D44—41no—
133C2×D44—82no—
134C2×D44—82no—
135C2×C8×C11—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4C2×D411yescharacteristic
145C11×C4⋊C4C2×D411yescharacteristic
146C11×C22⋊C4—21no—
147C11×C22⋊C4—21no—
148C11×C22⋊C4—21no—
149C11×C22⋊C4—21no—
150C11×C22⋊C4—21no—
151C42×C11—21no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11#4111yescharacteristic
155C42×C11C2411yescharacteristic
156#4325—82no—
157#4323—82no—
158#4318—42no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—41no—
163C2×C11⋊C8—41no—
164C2×C11⋊C8—42no—
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169#3238D1111yescharacteristic, complemented
170#3217—111no—
171C2×#486—111no—
172#2966—111no—
173#1698—112no—
174#1697—112no—
175#1678—112no—
176#1677—112no—
177#1568—111no—
178#1558—111no—
179#1555—111no—
180C23×C11—21no—
181C23×C11#12111yescharacteristic
182C22×D11—42no—
183C22×D11—82no—
184C22×D11—82no—
185C22×D11—82no—
186Q8×C11—22no—
187Q8×C11—82no—
188Q8×C11—82no—
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—42no—
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
208D44—42no—
209D44—42no—
210D44—42no—
211D44—42no—
212D44—82no—
213D44—82no—
214D44—82no—
215D44—82no—
216C8×C11—42no—
217C11⋊C8—21no—
218C11⋊C8—21no—
219C11⋊C8—21no—
220C11⋊C8—21no—
221C11⋊C8—41no—
222C11⋊C8—41no—
223C11⋊C8—42no—
224C2×C4⋊Q8C2×D1111yescharacteristic
225C2×#127—111no—
226#529C2×D1111yescharacteristic
227#501—21no—
228#496—221no—
229#490—221no—
230#489—21no—
231#486—112no—
232#486—112no—
233#486—221no—
234#486—221no—
235#483—21no—
236#480—21no—
237#477C2×D1112yescomplemented
238#476C2×D1112yescomplemented
239#460—112no—
240#459—112no—
241#450—221no—
242#447—221no—
243#446—111no—
244C8×Q8—111no—
245#436—111no—
246#435—221no—
247C8×D4—111no—
248C8×D4—221no—
249#433—221no—
250#432—111no—
251#432—111no—
252#432C2×D1111yescharacteristic
253C2×#102—221no—
254C2×#102—221no—
255#405—221no—
256C2×C4×C8—111no—
257#335—112no—
258#334—112no—
259#333—112no—
260#333—112no—
261#331—112no—
262#331—112no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11#47212yes—
269C22×C11C2×#12111yescharacteristic
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—82no—
273C2×D11—164no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11—82no—
282C4×C11#57511yescharacteristic
283C4×C11#57511yescharacteristic
284C4×C11#57712yes—
285C22×Q8—21no—
286C22×D4—221no—
287C22×D4—221no—
288C22×D4—221no—
289C2×SD16—222no—
290C2×D8—222no—
291C2×M16—221no—
292C22×C8—111no—
293C22×C8—111no—
294C22×C8—221no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8C22×D1112yes—
299#127—112no—
300#127—221no—
301#127—221no—
302#127—221no—
303#126—21no—
304#125C22⋊D1111yescharacteristic
305#124C22⋊D1111yescharacteristic
306#123—21no—
307C22⋊Q8C22⋊D1111yescharacteristic
308#121C22⋊D1111yescharacteristic
309C4×Q8C22×D1111yescharacteristic
310C4×D4—21no—
311C4×D4C22×D1111yescharacteristic
312#117—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C42C22×D1111yescharacteristic
316#107—22no—
317#106—22no—
318C4⋊C8—111no—
319C4⋊C8—111no—
320C4⋊C8—112no—
321C4⋊C8—221no—
322C4⋊C8—221no—
323C4⋊C8C22×D1112yes—
324#103—22no—
325#102—22no—
326#102—222no—
327#102—222no—
328#102—222no—
329#102—222no—
330#102—222no—
331#102—222no—
332C22⋊C8—21no—
333C22⋊C8—221no—
334C22⋊C8—221no—
335C22⋊C8—221no—
336C22⋊C8—221no—
337#97—21no—
338#97—221no—
339#97—221no—
340#97—221no—
341C4×C8—111no—
342C4×C8—111no—
343C4×C8—111no—
344C4×C8—111no—
345C4×C8—221no—
346C2×C11—22no—
347C2×C11—81no—
348C2×C11#304011yescharacteristic
349C2×C11#305711yescharacteristic
350C2×C11C2×#47211yescharacteristic
351D11—162no—
352C24—441no—
353C2×Q8—22no—
354C2×Q8—41no—
355C2×Q8—82no—
356C2×Q8C2×C22⋊D1111yescharacteristic
357C2×D4—21no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—442no—
362C2×D4—442no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—882no—
367C2×D4—882no—
368C2×D4C2×C22⋊D1111yescharacteristic
369C22×C4—21no—
370C22×C4—41no—
371C22×C4D4×D1111yescharacteristic
372C22×C4#434111yescharacteristic
373C22×C4C2×C22⋊D1111yescharacteristic
374SD16—882no—
375D8—882no—
376M16—442no—
377C2×C8—22no—
378C2×C8—111no—
379C2×C8—111no—
380C2×C8—111no—
381C2×C8—111no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—222no—
385C2×C8—441no—
386C2×C8—441no—
387C2×C8—442no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×C22⋊D1111yescharacteristic
397C4⋊C4C2×C22⋊D1111yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C42—21no—
404C42D4×D1111yescharacteristic
405C42#434111yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C42C23×D1111yescharacteristic
408C11#1936211yescharacteristic, complemented, Sylow
409C23—21no—
410C23—442no—
411C23—882no—
412C23—882no—
413C23—882no—
414C23#6699211yescharacteristic
415Q8—22no—
416Q8—82no—
417Q8—82no—
418D4—22no—
419D4—42no—
420D4—442no—
421D4—442no—
422D4—442no—
423D4—442no—
424D4—882no—
425D4—882no—
426D4—882no—
427D4—882no—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—82no—
439C2×C4#6699211yescharacteristic
440C2×C4#6699211yescharacteristic
441C2×C4#6699211yescharacteristic
442C2×C4C2×D4×D1111yescharacteristic
443C2×C4C2×#434111yescharacteristic
444C2×C4C22×C22⋊D1111yescharacteristic
445C8—42no—
446C8—221no—
447C8—221no—
448C8—221no—
449C8—221no—
450C8—441no—
451C8—441no—
452C8—442no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—882no—
459C22—882no—
460C22—882no—
461C22—1764no—
462C22#1062281212yes—
463C22C2×#6699211yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—82no—
472C4#1062330811yescharacteristic
473C4#1062330811yescharacteristic
474C4#1062336812yes—
475C2—22no—
476C2—81no—
477C2—1762no—
478C2#1307811211yescharacteristic
479C2#1307825711yescharacteristic
480C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3238C2
socleC22×C11C2×#121
prime radical#13079631C2
hypercenter#3238D11
hypocenterC11#19362
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
2. C2×#10622701C2semidirect
3. #13077592C2semidirect
4. #13068158C2semidirect
5. #13068151C2semidirect
6. #13068034C2semidirect
7. #13068027C2semidirect
8. #13067377C2semidirect
9. #13067342C2semidirect
10. #13067329C2semidirect
11. C11×#3238C2semidirect
19. C11×#477C22semidirect
20. C11×#476C22semidirect
31. #10622637C22semidirect
32. Q8×C11⋊C8C22semidirect
34. #10622625C22semidirect
37. D4×C11⋊C8C22semidirect
45. #10622184C22semidirect
46. #10622184C22semidirect
49. #10622118C22semidirect
50. #10622117C22semidirect
169. #3238D11semidirect
237. #477C2×D11semidirect
238. #476C2×D11semidirect
408. C11#19362semidirect

Maximal subgroups

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

subgroupindex
#130796312
C2×#106227012
#130775922
#130681582
#130681512
#130680342
#130680272
#130673772
#130673422
#130673292
C11×#32382
#1936211