Finite Group Databasebeta

← #14787035

Subgroups — #14787035

Order 2816.

1424 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623247C211yesmaximal, characteristic
2C2×#10622387C212yesmaximal, complemented
3D11×#389C211yesmaximal, characteristic, complemented
4#13069945C211yesmaximal, characteristic, complemented
5#13069944C211yesmaximal, characteristic, complemented
6#13069847C211yesmaximal, characteristic, complemented
7#13068930C212yesmaximal, complemented
8#13068865C212yesmaximal, complemented
9#13068861C212yesmaximal, complemented
10#13068683C211yesmaximal, characteristic, complemented
11C11×#2041C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C2×C11×#127C2211yescharacteristic
14C2×#66991—21no—
15C2×#66991C2212yes—
16C2×#66989—21no—
17C2×D4×Dic11—21no—
18C2×D4×Dic11C2212yes—
19#10623247—28no—
20C2×C4⋊C4×D11—21no—
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C11×#102C2212yes—
26C2×C11×#102C2212yes—
27C11×#389C2211yescharacteristic
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66882C2212yes—
32#10622598C2211yescharacteristic
33#10622586C2211yescharacteristic
34#10622585—21no—
35C2×#66871C2212yes—
36#10622541C2211yescharacteristic
37#10622387—28no—
38D11×#95—21no—
39#10622260—21no—
40C11×#336C2211yescharacteristic
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622162C2211yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×C22⋊D11—22no—
49C23×Dic11—22no—
50C2×#4341—28no—
51C2×#4341—44no—
52C2×#4341—44no—
53C22×C4×D11—21no—
54C22×C4×D11—21no—
55C22×C4×D11D411yescharacteristic
56C22×C4×D11D411yescharacteristic
57C22×C4×D11C2311yescharacteristic
58C22×Dic22—21no—
59C22×C8×C11C2312yes—
60C11×#127—24no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67#66991—28no—
68#66991—24no—
69#66991D418yes—
70#66989—28no—
71D4×Dic11—28no—
72D4×Dic11—24no—
73D4×Dic11—24no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87C4⋊C4×D11—22no—
88C4⋊C4×D11—22no—
89C4⋊C4×D11—24no—
90C4⋊C4×D11—44no—
91C42×D11—24no—
92#66922—24no—
93C11×#102—24no—
94C11×#102—24no—
95C11×#95—21no—
96#66896—24no—
97#66896—24no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101(C2×D11)⋊C8—24no—
102#66882—24no—
103#66871—24no—
104#24060—111nomaximal, Sylow
105C24×C11—22no—
106C23×D11C2×D411yescharacteristic
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—42no—
118C2×D4×C11C2×D414yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—28no—
125C2×C22⋊D11—44no—
126C2×C22⋊D11—44no—
127C22×Dic11—28no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—21no—
131C22×Dic11—44no—
132C22×Dic11—44no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136#4341—432no—
137C2×C4×D11—24no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—22no—
145C2×C4×D11—41no—
146C2×C4×D11—42no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11D814yes—
152C2×C4×D11C2×D414yes—
153C2×Dic22—24no—
154C2×Dic22—42no—
155C2×Dic22—42no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4#4112yescomplemented
163C42×C11—22no—
164C22⋊Dic11—28no—
165C22⋊Dic11—28no—
166C4⋊Dic11—24no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—21no—
170C4⋊Dic11—42no—
171C4⋊Dic11C2×D414yes—
172C4⋊Dic11#4112yescomplemented
173Dic11⋊C4—24no—
174Dic11⋊C4—42no—
175Dic11⋊C4—42no—
176Dic11⋊C4—42no—
177C4×Dic11—22no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×#532—111no—
184C2×#480—112no—
185C2×#389—111no—
186#2057—111no—
187#2057—111no—
188#2041—111no—
189#2041D1111yescharacteristic, complemented
190#1874—112no—
191#1862—112no—
192#1862—112no—
193#1817—111no—
194C23×C11—24no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11C22×D411yescharacteristic
202C22×D11—21no—
203C22×D11—21no—
204C22×D11—21no—
205C22×D11—21no—
206C22×D11#12012yes—
207C22×D11C2×D812yes—
208C22×D11AGL(1,ℤ/8)12yes—
209D4×C11—24no—
210D4×C11—24no—
211D4×C11—48no—
212D4×C11—48no—
213D4×C11—42no—
214D4×C11—42no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11C2×D812yes—
226C2×C4×C11#13712yes—
227C2×C4×C11C22×D412yes—
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C112−1+412yes—
231C22⋊D11—416no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—416no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11#12012yes—
250C2×Dic11C2×D812yes—
251C4×D11—28no—
252C4×D11—24no—
253C4×D11—24no—
254C4×D11—44no—
255C4×D11—48no—
256C4×D11—84no—
257Dic22—48no—
258C8×C11—42no—
259C11⋊C8—42no—
260C22×#41—221no—
261#532—228no—
262C2×C4⋊Q8—111no—
263C2×#127C2×D1111yescharacteristic
264C2×#124—221no—
265C2×#121—112no—
266C2×#121—221no—
267C2×C4×D4—112no—
268C2×C4×D4—221no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4—221no—
272C22×C42—111no—
273#480—228no—
274C2×#107—112no—
275C2×#107—112no—
276C2×#102—112no—
277C2×#102—112no—
278C2×#102C2×D1112yes—
279C2×#102C2×D1112yes—
280C2×C22⋊C8—112no—
281#389—111no—
282#389—111no—
283#389—111no—
284#389—221no—
285#389—221no—
286#389C2×D1111yescharacteristic
287C2×#95—221no—
288#340—112no—
289#340—112no—
290#336—112no—
291#336—111no—
292#336C2×D1111yescharacteristic
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#52511yescharacteristic
302C22×C11#53611yescharacteristic
303C22×C11C22×D811yescharacteristic
304C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C11C2×#13711yescharacteristic
306C22×C11#57511yescharacteristic
307C2×D11—22no—
308C2×D11—22no—
309C2×D11—22no—
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—22no—
313C2×D11#44714yes—
314C4×C11—22no—
315C4×C11—22no—
316C4×C11—42no—
317C4×C11—81no—
318C4×C11#54712yes—
319C4×C11#54712yes—
320Dic11—22no—
321Dic11—22no—
322Dic11—42no—
323Dic11—44no—
324Dic11—41no—
325Dic11—81no—
326C2×#41—228no—
327C2×#41—444no—
328C2×#41—444no—
329C22×Q8—221no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—222no—
333C22×D4C22×D1112yes—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—221no—
338C23×C4—221no—
339C23×C4—222no—
340C22×C8—112no—
341C22×C8C22×D1112yes—
342C4⋊Q8—224no—
343#127—24no—
344#124—228no—
345#121—118no—
346#121—224no—
347#121—228no—
348C4×D4—224no—
349C4×D4—228no—
350C4×D4—224no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—444no—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—224no—
373C2×C42C22×D1111yescharacteristic
374#107—224no—
375#107—224no—
376#102—24no—
377#102—24no—
378#102—224no—
379#102—224no—
380C22⋊C8—224no—
381#95—21no—
382#95—221no—
383#95—221no—
384#95—221no—
385C2×C11—84no—
386C2×C11#240611yescharacteristic
387C2×C11C2×#44711yescharacteristic
388C2×C11#300711yescharacteristic
389C2×C11#310011yescharacteristic
390C2×C11#311211yescharacteristic
391C2×C11#322611yescharacteristic
392C2×C11#323411yescharacteristic
393D11—24no—
394C24—22no—
395C24—111no—
396#41—4432no—
397C2×Q8—224no—
398C2×Q8—442no—
399C2×Q8—442no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—228no—
412C2×D4—444no—
413C2×D4—444no—
414C2×D4D4×D1114yes—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—111no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—228no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—221no—
434C22×C4—441no—
435C22×C4—442no—
436C22×C4—442no—
437C22×C4—442no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4—444no—
441C22×C4—444no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—222no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—42no—
454C4⋊C4—114no—
455C4⋊C4—112no—
456C4⋊C4—224no—
457C4⋊C4—224no—
458C4⋊C4—222no—
459C4⋊C4—221no—
460C4⋊C4—222no—
461C4⋊C4—442no—
462C4⋊C4—442no—
463C4⋊C4—442no—
464C4⋊C4—442no—
465C4⋊C4#434112yescomplemented
466C22⋊C4—228no—
467C22⋊C4—228no—
468C42—22no—
469C42—222no—
470C42—222no—
471C42—222no—
472C11#2406011yescharacteristic, complemented, Sylow
473C23—24no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—112no—
481C23—112no—
482C23—112no—
483C23—221no—
484C23—221no—
485C23—221no—
486C23—221no—
487C23C2×D4×D1111yescharacteristic
488Q8—448no—
489D4—24no—
490D4—24no—
491D4—48no—
492D4—48no—
493D4—42no—
494D4—42no—
495D4—4416no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—228no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—444no—
521C2×C4—448no—
522C2×C4—4416no—
523C2×C4—441no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—884no—
531C2×C4D8×D1112yes—
532C2×C4#6696812yes—
533C2×C4C2×D4×D1112yes—
534C2×C4C2×#434111yescharacteristic
535C2×C4#41×D1111yescharacteristic
536C2×C4#6704312yes—
537C8—42no—
538C8—442no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22—82no—
546C22—114no—
547C22—222no—
548C22—222no—
549C22—222no—
550C22—222no—
551C22—222no—
552C22—222no—
553C22D11×#12011yescharacteristic
554C22#1062313711yescharacteristic
555C22#1062320611yescharacteristic
556C22C2×D8×D1111yescharacteristic
557C22C2×#6696811yescharacteristic
558C22D11×AGL(1,ℤ/8)11yescharacteristic
559C22#1062330411yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—81no—
564C4—222no—
565C4—222no—
566C4—444no—
567C4—442no—
568C4—441no—
569C4—881no—
570C4#1062314212yes—
571C4#1062318612yes—
572C2—84no—
573C2—224no—
574C2#1307194611yescharacteristic
575C2D11×#44711yescharacteristic
576C2#1307787111yescharacteristic
577C2#1307861511yescharacteristic
578C2#1307873711yescharacteristic
579C2#1307973311yescharacteristic
580C2#1307980111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2041C2
socleC23×C11C22×D4
prime radicalC2×#10623247C2
hypercenter#2041D11
hypocenterC11#24060
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
2. C2×#10622387C2semidirect
3. D11×#389C2semidirect
4. #13069945C2semidirect
5. #13069944C2semidirect
6. #13069847C2semidirect
7. #13068930C2semidirect
8. #13068865C2semidirect
9. #13068861C2semidirect
10. #13068683C2semidirect
11. C11×#2041C2semidirect
162. C11×C4⋊C4#41semidirect
172. C4⋊Dic11#41semidirect
189. #2041D11semidirect
465. C4⋊C4#4341semidirect
472. C11#24060semidirect

Maximal subgroups

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

subgroupindex
C2×#106232472
C2×#106223872
D11×#3892
#130699452
#130699442
#130698472
#130689302
#130688652
#130688612
#130686832
C11×#20412
#2406011