Finite Group Databasebeta

← #14738521

Subgroups — #14738521

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079631C211yesmaximal, characteristic
2C2×#10622698C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068090C212yesmaximal, complemented
5#13068083C212yesmaximal, complemented
6#13067966C212yesmaximal, complemented
7#13067959C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067333C211yesmaximal, characteristic, complemented
10#13067329C211yesmaximal, characteristic, complemented
11C11×#3239C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C11×#529C2211yescharacteristic
14C22×#4325—21no—
15C22×#4325—21no—
16C2×#66927C2211yescharacteristic
17C11×#501—21no—
18C11×#489—21no—
19C11×#484—21no—
20C11×#481—21no—
21C11×#475C2212yescomplemented
22C11×#474C2212yescomplemented
23C11×#432C2211yescharacteristic
24#10622698—21no—
25#10622698—21no—
26#10622698C2212yes—
27#10622698C2212yes—
28#10622680—21no—
29#10622671—21no—
30#10622659—21no—
31#10622649—21no—
32#10622640C2212yes—
33#10622637C2211yescharacteristic, complemented
34Q8×C11⋊C8C2211yescharacteristic, complemented
35#10622628C2212yes—
36#10622625C2211yescharacteristic, complemented
37#10622624—21no—
38D4×C11⋊C8—21no—
39D4×C11⋊C8C2211yescharacteristic, complemented
40#10622613—21no—
41#10622610—21no—
42#10622539C2211yescharacteristic
43#10622539C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yescomplemented
46#10622185C2212yescomplemented
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×#4325—22no—
74C2×#4325—22no—
75C2×#4325—22no—
76C2×#4325—22no—
77C2×#4325—44no—
78C2×#4325—44no—
79C2×#4323—22no—
80C2×#4318—21no—
81C22×C11⋊C8—21no—
82C22×C11⋊C8D411yescharacteristic
83C22×C11⋊C8D411yescharacteristic
84#66927—21no—
85#66927—21no—
86#66927—21no—
87#66927C2312yes—
88C11×#107—22no—
89C11×#106—22no—
90C11×C4⋊C8C2312yes—
91C11×#103—22no—
92C11×#102—22no—
93C11×C22⋊C8—21no—
94C11×#97—21no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99#66873—22no—
100#66873—22no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4⋊(C11⋊C8)C2311yescharacteristic
105C4⋊(C11⋊C8)C2312yes—
106#66867—21no—
107#66867—21no—
108#66867—21no—
109C4×C11⋊C8—21no—
110C4×C11⋊C8D411yescharacteristic
111C4×C11⋊C8D411yescharacteristic
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2311yescharacteristic
114#19352—111nomaximal, Sylow
115C23×D11—41no—
116C2×Q8×C11—22no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11—41no—
120C2×Q8×C11C2×D411yescharacteristic
121C2×D4×C11—21no—
122C2×D4×C11C2×D411yescharacteristic
123C22×C4×C11—21no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—42no—
132C2×D44—42no—
133C2×D44—41no—
134C2×D44—41no—
135C2×D44—41no—
136C2×D44—82no—
137C2×D44—82no—
138C2×C8×C11—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4C2×D411yescharacteristic
148C11×C4⋊C4C2×D411yescharacteristic
149C11×C22⋊C4—21no—
150C11×C22⋊C4—21no—
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C42×C11—21no—
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11#4111yescharacteristic
158C42×C11C2411yescharacteristic
159#4325—44no—
160#4325—44no—
161#4325—44no—
162#4325—44no—
163#4325—82no—
164#4323—82no—
165#4318—42no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176#3239D1111yescharacteristic, complemented
177#3217—111no—
178C2×#492—111no—
179#2966—111no—
180#1686—112no—
181#1685—112no—
182#1666—112no—
183#1665—112no—
184#1568—111no—
185#1556—111no—
186#1555—111no—
187C23×C11—21no—
188C23×C11#12111yescharacteristic
189C22×D11—42no—
190C22×D11—82no—
191C22×D11—82no—
192C22×D11—82no—
193Q8×C11—22no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—82no—
197D4×C11—22no—
198D4×C11—42no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—82no—
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216D44—42no—
217D44—42no—
218D44—42no—
219D44—42no—
220D44—82no—
221D44—82no—
222D44—82no—
223D44—82no—
224C8×C11—42no—
225C11⋊C8—21no—
226C11⋊C8—21no—
227C11⋊C8—41no—
228C11⋊C8—41no—
229C11⋊C8—42no—
230C11⋊C8AGL(1,ℤ/8)12yes—
231C11⋊C8AGL(1,ℤ/8)12yes—
232C22×SD16—221no—
233C22×SD16—221no—
234C2×C4⋊Q8C2×D1111yescharacteristic
235C2×#127—111no—
236#529C2×D1111yescharacteristic
237#501—21no—
238#496—221no—
239#492—112no—
240#492—112no—
241#492—221no—
242#492—221no—
243#490—221no—
244#489—21no—
245#484—21no—
246#481—21no—
247#475C2×D1112yescomplemented
248#474C2×D1112yescomplemented
249#460—112no—
250#459—112no—
251#450—221no—
252#447—221no—
253#446—111no—
254C8×Q8—111no—
255#436—111no—
256#435—221no—
257C8×D4—111no—
258C8×D4—221no—
259#433—221no—
260#432—111no—
261#432—111no—
262#432C2×D1111yescharacteristic
263#405—221no—
264C2×C4×C8—111no—
265#335—112no—
266#334—112no—
267#332—112no—
268#332—112no—
269#331—112no—
270#331—112no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11#47112yes—
277C22×C11C2×#12111yescharacteristic
278C2×D11—82no—
279C2×D11—82no—
280C2×D11—82no—
281C2×D11—164no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11—41no—
289C4×C11—82no—
290C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C11#57712yes—
293C22×Q8—21no—
294C22×D4—221no—
295C22×D4—221no—
296C22×D4—221no—
297C2×SD16—222no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×SD16—222no—
301C2×SD16—222no—
302C2×SD16—444no—
303C2×SD16—444no—
304C2×D8—222no—
305C2×M16—221no—
306C22×C8—111no—
307C22×C8—111no—
308C22×C8—221no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8C22×D1112yes—
313#127—112no—
314#127—221no—
315#127—221no—
316#127—221no—
317#126—21no—
318#125C22⋊D1111yescharacteristic
319#124C22⋊D1111yescharacteristic
320#123—21no—
321C22⋊Q8C22⋊D1111yescharacteristic
322#121C22⋊D1111yescharacteristic
323C4×Q8C22×D1111yescharacteristic
324C4×D4—21no—
325C4×D4C22×D1111yescharacteristic
326#117—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C42C22×D1111yescharacteristic
330#107—22no—
331#106—22no—
332C4⋊C8—111no—
333C4⋊C8—111no—
334C4⋊C8—112no—
335C4⋊C8—221no—
336C4⋊C8—221no—
337C4⋊C8C22×D1112yes—
338#103—22no—
339#102—22no—
340#102—222no—
341#102—222no—
342C22⋊C8—21no—
343C22⋊C8—221no—
344C22⋊C8—221no—
345C22⋊C8—221no—
346C22⋊C8—221no—
347#97—21no—
348#97—221no—
349#97—221no—
350#97—221no—
351C4×C8—111no—
352C4×C8—111no—
353C4×C8—111no—
354C4×C8—111no—
355C4×C8—221no—
356C2×C11—22no—
357C2×C11—81no—
358C2×C11#303811yescharacteristic
359C2×C11#305711yescharacteristic
360C2×C11C2×#47111yescharacteristic
361D11—162no—
362C24—441no—
363C2×Q8—22no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8—41no—
367C2×Q8C2×C22⋊D1111yescharacteristic
368C2×D4—21no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—442no—
373C2×D4—442no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—441no—
377C2×D4—882no—
378C2×D4—882no—
379C2×D4C2×C22⋊D1111yescharacteristic
380C22×C4—21no—
381C22×C4—41no—
382C22×C4D4×D1111yescharacteristic
383C22×C4#434111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385SD16—444no—
386SD16—444no—
387SD16—444no—
388SD16—444no—
389SD16—882no—
390D8—882no—
391M16—442no—
392C2×C8—22no—
393C2×C8—111no—
394C2×C8—111no—
395C2×C8—111no—
396C2×C8—111no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—222no—
402C2×C8—442no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4C2×C22⋊D1111yescharacteristic
412C4⋊C4C2×C22⋊D1111yescharacteristic
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C42—21no—
419C42D4×D1111yescharacteristic
420C42#434111yescharacteristic
421C42C2×C22⋊D1111yescharacteristic
422C42C23×D1111yescharacteristic
423C11#1935211yescharacteristic, complemented, Sylow
424C23—21no—
425C23—442no—
426C23—882no—
427C23—882no—
428C23—882no—
429C23#6699211yescharacteristic
430Q8—22no—
431Q8—42no—
432Q8—42no—
433Q8—82no—
434D4—22no—
435D4—42no—
436D4—442no—
437D4—442no—
438D4—442no—
439D4—442no—
440D4—882no—
441D4—882no—
442D4—882no—
443D4—882no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—82no—
455C2×C4#6699211yescharacteristic
456C2×C4#6699211yescharacteristic
457C2×C4#6699211yescharacteristic
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4C2×#434111yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—42no—
462C8—112no—
463C8—112no—
464C8—221no—
465C8—221no—
466C8—441no—
467C8—441no—
468C8—442no—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—882no—
475C22—882no—
476C22—882no—
477C22—1764no—
478C22#1062281612yes—
479C22C2×#6699211yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—82no—
488C4D11×AGL(1,ℤ/8)11yescharacteristic
489C4D11×AGL(1,ℤ/8)11yescharacteristic
490C4#1062336812yes—
491C2—22no—
492C2—81no—
493C2—1762no—
494C2#1307809411yescharacteristic
495C2#1307825711yescharacteristic
496C2C2×#1062281611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3239C2
socleC22×C11C2×#121
prime radical#13079631C2
hypercenter#3239D11
hypocenterC11#19352
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3239

Complements

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

NH ≅ G/Ntype
2. C2×#10622698C2semidirect
3. #13077592C2semidirect
4. #13068090C2semidirect
5. #13068083C2semidirect
6. #13067966C2semidirect
7. #13067959C2semidirect
8. #13067377C2semidirect
9. #13067333C2semidirect
10. #13067329C2semidirect
11. C11×#3239C2semidirect
21. C11×#475C22semidirect
22. C11×#474C22semidirect
33. #10622637C22semidirect
34. Q8×C11⋊C8C22semidirect
36. #10622625C22semidirect
39. D4×C11⋊C8C22semidirect
45. #10622185C22semidirect
46. #10622185C22semidirect
49. #10622118C22semidirect
50. #10622117C22semidirect
176. #3239D11semidirect
247. #475C2×D11semidirect
248. #474C2×D11semidirect
423. C11#19352semidirect

Maximal subgroups

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

subgroupindex
#130796312
C2×#106226982
#130775922
#130680902
#130680832
#130679662
#130679592
#130673772
#130673332
#130673292
C11×#32392
#1935211