Finite Group Databasebeta

← #14729920

Subgroups — #14729920

Order 2816.

1168 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079012C211yesmaximal, characteristic, complemented
2#13078738C211yesmaximal, characteristic, complemented
3#13078707C211yesmaximal, characteristic
4#13067781C214yesmaximal, complemented
5#13067719C214yesmaximal, complemented
6#13067333C211yesmaximal, characteristic, complemented
7#13067063C211yesmaximal, characteristic, complemented
8#13067059C211yesmaximal, characteristic, complemented
9C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
10C23×Q8×C11—21no—
11D4×Q8×C11—22no—
12D4×Q8×C11—22no—
13D4×Q8×C11—22no—
14D4×Q8×C11C2214yes—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22#10623008C2211yescharacteristic
23#10622840—21no—
24#10622830—21no—
25#10622706C2212yescomplemented
26#10622702—22no—
27#10622701C2212yescomplemented
28#10622640C2212yescomplemented
29#10622639—22no—
30#10622634C2212yescomplemented
31#10622628C2212yes—
32#10622627—22no—
33#10622621C2212yes—
34#10622581—21no—
35#10622580—21no—
36#10622579—22no—
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40#10622185C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yes—
43C22×Q8×C11—22no—
44C22×Q8×C11—24no—
45C22×Q8×C11—24no—
46C22×Q8×C11—21no—
47C22×Q8×C11—48no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—22no—
51C23×C4×C11—21no—
52C2×#4339—21no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—24no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8D412yes—
58C11×C4⋊Q8C2312yes—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—28no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—28no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11D412yes—
66C4×Q8×C11C2312yes—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11D412yes—
72C4×D4×C11C2312yes—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4325—22no—
84C2×#4323—22no—
85#66983—21no—
86#66983—21no—
87C2×#4318—21no—
88#66928—21no—
89#66927C2311yescharacteristic
90C4×D44—21no—
91C4×D44—21no—
92#66922C2311yescharacteristic
93#66899—22no—
94#66896—22no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97#66874—24no—
98#66873—24no—
99#66873—22no—
100#66873—22no—
101#66872—22no—
102#66871—22no—
103C4⋊(C11⋊C8)C2312yes—
104C4⋊(C11⋊C8)C2312yes—
105#66867—21no—
106#66867—21no—
107#66867—21no—
108C4×C11⋊C8C2312yes—
109#18534—111nomaximal, Sylow
110C24×C11—21no—
111C2×Q8×C11—24no—
112C2×Q8×C11—28no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—48no—
117C2×Q8×C11—44no—
118C2×Q8×C11—416no—
119C2×Q8×C11—48no—
120C2×Q8×C11—48no—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—24no—
123C2×D4×C11—21no—
124C2×D4×C11C2×D412yes—
125C22×C4×C11—21no—
126C22×C4×C11—28no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—48no—
133C22×C4×C11—44no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C2×C22⋊D11—41no—
138#4339—44no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×C4×D11—41no—
143C2×Dic22—21no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4C2×D412yes—
153C11×C4⋊C4C2×D412yes—
154C11×C4⋊C4C2×D414yes—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2411yescharacteristic
164#4325—44no—
165#4323—44no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170#4318—42no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×D4×Q8D1111yescharacteristic, complemented
175#3141—111no—
176#3112—111no—
177#3109—111no—
178#1637—114no—
179#1627—114no—
180#1556—111no—
181#1491—111no—
182#1490—111no—
183C23×C11—24no—
184C23×C11—22no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11#12011yescharacteristic
188C22×D11—41no—
189Q8×C11—24no—
190Q8×C11—22no—
191Q8×C11—416no—
192Q8×C11—44no—
193Q8×C11—44no—
194Q8×C11AGL(1,ℤ/8)14yes—
195D4×C11—24no—
196D4×C11—22no—
197D4×C11#13714yes—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—416no—
207C2×C4×C11—44no—
208C2×C4×C11—44no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—44no—
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C22⋊D11—82no—
219C2×Dic11—41no—
220D44—42no—
221D44—42no—
222D44—42no—
223C4×D11—82no—
224Dic22—42no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C11⋊C8—42no—
228C23×Q8—21no—
229D4×Q8—22no—
230D4×Q8—22no—
231D4×Q8—22no—
232D4×Q8C2×D1114yes—
233#532—111no—
234C2×C4⋊Q8—21no—
235C2×C4⋊Q8C2×D1111yescharacteristic
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—22no—
238C2×C4×Q8C2×D1111yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4C2×D1111yescharacteristic
241#489—222no—
242#487—112no—
243#486—112no—
244#481—221no—
245#480—221no—
246#477—112no—
247#476—112no—
248#460—112no—
249#459—112no—
250#448—221no—
251#447—221no—
252#442—222no—
253#440—222no—
254#432—111no—
255#432—111no—
256#417—222no—
257C4×M16—111no—
258#332—114no—
259Q8⋊C8—114no—
260D4⋊C8—114no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—24no—
264C22×C11—48no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11#45412yes—
268C22×C11C2×#12011yescharacteristic
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C4×C11—24no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—44no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11C2×AGL(1,ℤ/8)12yes—
281C4×C11C2×#13712yes—
282Dic11—81no—
283C2×#41—221no—
284C22×Q8—22no—
285C22×Q8—24no—
286C22×Q8—24no—
287C22×Q8—21no—
288C22×Q8—48no—
289C22×Q8C22⋊D1111yescharacteristic
290C22×D4C22⋊D1111yescharacteristic
291C23×C4—22no—
292C23×C4—21no—
293C2×SD16—222no—
294C2×D8—222no—
295C2×M16—221no—
296C4⋊Q8—24no—
297C4⋊Q8—24no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—111no—
301C4⋊Q8C22⋊D1112yes—
302C4⋊Q8C22×D1112yes—
303#127—111no—
304#124—221no—
305C22⋊Q8—24no—
306C22⋊Q8—28no—
307C22⋊Q8—24no—
308C22⋊Q8—28no—
309#121—221no—
310#121—221no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8C22⋊D1112yes—
314C4×Q8C22×D1112yes—
315C4×D4—24no—
316C4×D4—24no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—221no—
320C4×D4—221no—
321C4×D4C22⋊D1112yes—
322C4×D4C22×D1112yes—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C4⋊C4C22⋊D1111yescharacteristic
328C2×C4⋊C4C22⋊D1112yes—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C42—21no—
332C2×C42C22×D1111yescharacteristic
333#107—222no—
334#106—222no—
335C4⋊C8—112no—
336C4⋊C8—112no—
337#103—222no—
338#103—224no—
339#102—222no—
340#102—224no—
341#102—222no—
342#102—222no—
343C22⋊C8—221no—
344C22⋊C8—221no—
345#97—221no—
346#97—221no—
347#97—221no—
348C4×C8—112no—
349C2×C11—22no—
350C2×C11—44no—
351C2×C11#300311yescharacteristic
352C2×C11#300411yescharacteristic
353C2×C11C2×#45411yescharacteristic
354D11—161no—
355C24—21no—
356#41—444no—
357C2×Q8—24no—
358C2×Q8—28no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—48no—
363C2×Q8—44no—
364C2×Q8—416no—
365C2×Q8—48no—
366C2×Q8—48no—
367C2×Q8—221no—
368C2×Q8C2×C22⋊D1112yes—
369C2×D4—24no—
370C2×D4—21no—
371C2×D4—221no—
372C2×D4—221no—
373C2×D4—221no—
374C2×D4—441no—
375C2×D4C2×C22⋊D1112yes—
376C22×C4—21no—
377C22×C4—28no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—48no—
384C22×C4—44no—
385C22×C4—441no—
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389SD16—444no—
390D8—444no—
391M16—442no—
392C2×C8—222no—
393C2×C8—222no—
394C2×C8—222no—
395C4⋊C4—28no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4C2×C22⋊D1114yes—
406C4⋊C4C2×C22⋊D1112yes—
407C4⋊C4C2×C22⋊D1112yes—
408C22⋊C4—28no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C42—22no—
414C42—22no—
415C42C2×C22⋊D1111yescharacteristic
416C42C2×C22⋊D1111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C42C23×D1111yescharacteristic
419C11#1853411yescharacteristic, complemented, Sylow
420C23—24no—
421C23—22no—
422C23—42no—
423C23—42no—
424C23—441no—
425C23#6700611yescharacteristic
426Q8—24no—
427Q8—22no—
428Q8—416no—
429Q8—44no—
430Q8—44no—
431Q8—442no—
432Q8#6698514yes—
433D4—24no—
434D4—22no—
435D4—442no—
436D4—442no—
437D4—442no—
438D4—882no—
439D4#6699514yes—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—416no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—441no—
455C2×C4—882no—
456C2×C4#6700611yescharacteristic
457C2×C4#6700611yescharacteristic
458C2×C4#6700611yescharacteristic
459C2×C4C22×C22⋊D1111yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—442no—
463C8—442no—
464C8—442no—
465C22—21no—
466C22—21no—
467C22—24no—
468C22—48no—
469C22—42no—
470C22—42no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22#1062285812yes—
475C22C2×#6700611yescharacteristic
476C4—24no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—42no—
483C4—42no—
484C4—881no—
485C4C2×#6698512yes—
486C4C2×#6699512yes—
487C2—22no—
488C2—44no—
489C2—1761no—
490C2#1307784311yescharacteristic
491C2#1307785011yescharacteristic
492C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D4×Q8×C11C2
socleC22×C11C2×#120
prime radical#13078707C2
hypercenterC2×D4×Q8D11
hypocenterC11#18534
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #13079012C2semidirect
2. #13078738C2semidirect
4. #13067781C2semidirect
5. #13067719C2semidirect
6. #13067333C2semidirect
7. #13067063C2semidirect
8. #13067059C2semidirect
9. C2×D4×Q8×C11C2semidirect
25. #10622706C22semidirect
27. #10622701C22semidirect
28. #10622640C22semidirect
30. #10622634C22semidirect
40. #10622185C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
174. C2×D4×Q8D11semidirect
419. C11#18534semidirect

Maximal subgroups

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

subgroupindex
#130790122
#130787382
#130787072
#130677812
#130677192
#130673332
#130670632
#130670592
C2×D4×Q8×C112
#1853411