Finite Group Databasebeta

← #14738519

Subgroups — #14738519

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#13079843C211yesmaximal, characteristic, complemented
2#13079631C211yesmaximal, characteristic
3C2×#10622306C211yesmaximal, characteristic, complemented
4#13068088C212yesmaximal, complemented
5#13068081C212yesmaximal, complemented
6#13067964C212yesmaximal, complemented
7#13067957C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067334C211yesmaximal, characteristic, complemented
10#13067329C211yesmaximal, characteristic, complemented
11C11×#2966C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13C22×#4314—21no—
14C22×#4314—21no—
15C2×#66927C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C11×#446C2211yescharacteristic, complemented
18C8×Q8×C11C2211yescharacteristic, complemented
19C11×#436C2211yescharacteristic, complemented
20C11×#435—21no—
21C8×D4×C11—21no—
22C8×D4×C11C2211yescharacteristic, complemented
23C11×#433—21no—
24C11×#432C2211yescharacteristic
25C11×#405—21no—
26C2×C4×C8×C11C2211yescharacteristic
27#10622680—21no—
28#10622678—21no—
29#10622671—21no—
30#10622668—21no—
31#10622659—21no—
32#10622657—21no—
33#10622649—21no—
34#10622647—21no—
35#10622640C2212yes—
36#10622633C2212yescomplemented
37#10622628C2212yes—
38#10622620C2212yescomplemented
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41#10622306—21no—
42#10622306—21no—
43#10622306C2212yes—
44#10622306C2212yes—
45#10622123C2212yes—
46#10622123C2212yes—
47#10622120C2212yescomplemented
48#10622120C2212yescomplemented
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×#4325—22no—
71C2×#4323—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×#4314—22no—
75C2×#4314—22no—
76C2×#4314—22no—
77C2×#4314—22no—
78C2×#4314—44no—
79C2×#4314—44no—
80#66927—21no—
81#66927—21no—
82#66927—21no—
83#66927C2312yes—
84#66922—21no—
85#66922—21no—
86#66922—21no—
87#66922C2312yes—
88C11×C4⋊C8—21no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2311yescharacteristic
91C11×C4⋊C8C2311yescharacteristic
92C11×C22⋊C8—21no—
93C11×C22⋊C8—21no—
94C11×C22⋊C8—21no—
95C11×#97—21no—
96C11×#97—21no—
97C4×C8×C11—21no—
98C4×C8×C11D411yescharacteristic
99C4×C8×C11D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101C4×C8×C11C2311yescharacteristic
102#66899—22no—
103#66896—22no—
104C22⋊(C11⋊C8)—21no—
105C22⋊(C11⋊C8)—21no—
106#66873—22no—
107#66873—22no—
108#66872—22no—
109#66871—22no—
110C4⋊(C11⋊C8)C2312yes—
111C4⋊(C11⋊C8)C2312yes—
112#66867—21no—
113#66867—21no—
114#19352—111nomaximal, Sylow
115C23×D11—41no—
116C2×Q8×C11C2×D411yescharacteristic
117C2×D4×C11—21no—
118C2×D4×C11C2×D411yescharacteristic
119C22×C4×C11—21no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×Dic11—41no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—42no—
128C2×D44—42no—
129C2×D44—41no—
130C2×D44—41no—
131C2×D44—41no—
132C2×D44—82no—
133C2×D44—82no—
134C2×Dic22—22no—
135C2×Dic22—42no—
136C2×Dic22—42no—
137C2×Dic22—41no—
138C11×M16—42no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—42no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4C2×D411yescharacteristic
153C11×C4⋊C4C2×D411yescharacteristic
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C11×C22⋊C4—21no—
158C11×C22⋊C4—21no—
159C42×C11—21no—
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11#4111yescharacteristic
163C42×C11C2411yescharacteristic
164#4325—82no—
165#4323—82no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—41no—
169C4⋊Dic11—41no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172#4314—44no—
173#4314—44no—
174#4314—44no—
175#4314—44no—
176#3239—111no—
177#3217—111no—
178C2×#492—111no—
179#2966D1111yescharacteristic, complemented
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—
194D4×C11—22no—
195D4×C11—42no—
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×Dic11—42no—
212C2×Dic11—82no—
213D44—42no—
214D44—42no—
215D44—42no—
216D44—42no—
217D44—82no—
218D44—82no—
219D44—82no—
220D44—82no—
221Dic22—42no—
222Dic22—42no—
223Dic22—82no—
224C8×C11—21no—
225C8×C11—21no—
226C8×C11—41no—
227C8×C11—41no—
228C8×C11AGL(1,ℤ/8)12yes—
229C8×C11AGL(1,ℤ/8)12yes—
230C11⋊C8—42no—
231C11⋊C8—42no—
232C22×SD16—221no—
233C22×SD16—221no—
234C2×C4⋊Q8—111no—
235C2×#127—111no—
236#529C2×D1111yescharacteristic
237#501—221no—
238#496—221no—
239#492—112no—
240#492—112no—
241#492—221no—
242#492—221no—
243#490—221no—
244#489—221no—
245#484—221no—
246#481—221no—
247#475—112no—
248#474—112no—
249#460—112no—
250#459—112no—
251#450—221no—
252#447—221no—
253#446C2×D1111yescharacteristic, complemented
254C8×Q8C2×D1111yescharacteristic, complemented
255#436C2×D1111yescharacteristic, complemented
256#435—21no—
257C8×D4—21no—
258C8×D4C2×D1111yescharacteristic, complemented
259#433—21no—
260#432—111no—
261#432—111no—
262#432C2×D1111yescharacteristic
263#405—21no—
264C2×C4×C8C2×D1111yescharacteristic
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×C11C2×AGL(1,ℤ/8)11yescharacteristic
290C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
291C4×C11#57712yes—
292Dic11—82no—
293C22×Q8—221no—
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—21no—
306C22×C8—21no—
307C22×C8C22⋊D1111yescharacteristic
308C22×C8C22⋊D1111yescharacteristic
309C4⋊Q8—112no—
310C4⋊Q8—221no—
311C4⋊Q8—221no—
312C4⋊Q8—221no—
313#127—112no—
314#127—221no—
315#127—221no—
316#127—221no—
317#126—21no—
318#125D4411yescharacteristic
319#124D4411yescharacteristic
320#123—21no—
321C22⋊Q8D4411yescharacteristic
322#121D4411yescharacteristic
323C4×Q8C22×D1111yescharacteristic
324C4×D4—21no—
325C4×D4C22×D1111yescharacteristic
326#117—21no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C42C22×D1111yescharacteristic
330#107—222no—
331#106—222no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8—112no—
335C4⋊C8—112no—
336C4⋊C8C22×D1111yescharacteristic
337C4⋊C8C22×D1111yescharacteristic
338#103—222no—
339#102—222no—
340#102—222no—
341#102—222no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—221no—
346C22⋊C8—221no—
347#97—21no—
348#97—21no—
349#97—221no—
350#97—221no—
351C4×C8—21no—
352C4×C8C22⋊D1111yescharacteristic
353C4×C8C22⋊D1111yescharacteristic
354C4×C8C22×D1111yescharacteristic
355C4×C8C22×D1111yescharacteristic
356C2×C11—22no—
357C2×C11—81no—
358C2×C11#303811yescharacteristic
359C2×C11#305711yescharacteristic
360C2×C11C2×#47111yescharacteristic
361D11—162no—
362C24—441no—
363C2×Q8—222no—
364C2×Q8—442no—
365C2×Q8—442no—
366C2×Q8—441no—
367C2×Q8C2×D4411yescharacteristic
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×D4411yescharacteristic
380C22×C4—21no—
381C22×C4—441no—
382C22×C4C2×D4411yescharacteristic
383C22×C4#433911yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385SD16—444no—
386SD16—444no—
387SD16—444no—
388SD16—444no—
389SD16—882no—
390D8—882no—
391M16—42no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—42no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8C2×C22⋊D1111yescharacteristic
400C2×C8C2×C22⋊D1111yescharacteristic
401C2×C8C2×C22⋊D1111yescharacteristic
402C2×C8C2×C22⋊D1111yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4C2×D4411yescharacteristic
412C4⋊C4C2×D4411yescharacteristic
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C42—21no—
419C42C2×D4411yescharacteristic
420C42#433911yescharacteristic
421C42C2×C22⋊D1111yescharacteristic
422C42C23×D1111yescharacteristic
423C11#1935211yescharacteristic, complemented, Sylow
424C23—21no—
425C23—442no—
426C23—882no—
427C23—882no—
428C23—882no—
429C23#6698311yescharacteristic
430Q8—22no—
431Q8—442no—
432Q8—442no—
433Q8—882no—
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—22no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—442no—
454C2×C4—882no—
455C2×C4#6698311yescharacteristic
456C2×C4#6698311yescharacteristic
457C2×C4#6698311yescharacteristic
458C2×C4C22×D4411yescharacteristic
459C2×C4C2×#433911yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—21no—
462C8—21no—
463C8—41no—
464C8—41no—
465C8—442no—
466C8—442no—
467C8#6700212yes—
468C8#6700212yes—
469C22—21no—
470C22—21no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—882no—
475C22—882no—
476C22—882no—
477C22—1764no—
478C22#1062275412yes—
479C22C2×#6698311yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—882no—
488C4#1062328212yes—
489C4C2×#6700211yescharacteristic
490C4C2×#6700211yescharacteristic
491C2—22no—
492C2—81no—
493C2—1762no—
494C2#1307809611yescharacteristic
495C2#1307825511yescharacteristic
496C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radical#13079631C2
hypercenter#2966D11
hypocenterC11#19352
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. #13079843C2semidirect
3. C2×#10622306C2semidirect
4. #13068088C2semidirect
5. #13068081C2semidirect
6. #13067964C2semidirect
7. #13067957C2semidirect
8. #13067379C2semidirect
9. #13067334C2semidirect
10. #13067329C2semidirect
11. C11×#2966C2semidirect
17. C11×#446C22semidirect
18. C8×Q8×C11C22semidirect
19. C11×#436C22semidirect
22. C8×D4×C11C22semidirect
36. #10622633C22semidirect
38. #10622620C22semidirect
47. #10622120C22semidirect
48. #10622120C22semidirect
49. #10622096C22semidirect
50. #10622095C22semidirect
179. #2966D11semidirect
253. #446C2×D11semidirect
254. C8×Q8C2×D11semidirect
255. #436C2×D11semidirect
258. C8×D4C2×D11semidirect
423. C11#19352semidirect

Maximal subgroups

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

subgroupindex
#130798432
#130796312
C2×#106223062
#130680882
#130680812
#130679642
#130679572
#130673792
#130673342
#130673292
C11×#29662
#1935211