Finite Group Databasebeta

← #14960987

Subgroups — #14960987

Order 2816.

2130 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076898C212yesmaximal, complemented
2#13075755C214yesmaximal, complemented
3#13075716C214yesmaximal, complemented
4#13075203C214yesmaximal, complemented
5#13075052C214yesmaximal, complemented
6#13074718C211yesmaximal, characteristic, complemented
7#13074586C211yesmaximal, characteristic, complemented
8#13072366C214yesmaximal, complemented
9#13072152C214yesmaximal, complemented
10#13071319C212yesmaximal, complemented
11C2×C11×#381C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C2×#67006C2214yes—
15C2×#66983C2212yes—
16C2×#66983C2212yes—
17C2×#66983C2214yes—
18C2×#66983C2212yes—
19C2×C4×C22⋊D11C2214yes—
20C2×#66937C2214yes—
21C11×#381C2214yes—
22C11×#381C2214yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26#10622826C2214yes—
27#10622826C2214yes—
28#10622826C2214yes—
29#10622826C2214yes—
30#10622825C2212yes—
31#10622825C2212yes—
32#10622825C2212yes—
33#10622823C2214yes—
34#10622573C2214yes—
35#10622572C2214yes—
36#10622572C2214yes—
37#10622570C2214yes—
38#10622569C2214yes—
39#10622564C2214yes—
40#10622561C2214yes—
41#10622290C2214yescomplemented
42#10622288C2214yescomplemented
43#10622288C2214yescomplemented
44#10622285C2214yescomplemented
45#10622284C2214yescomplemented
46#10622283C2214yescomplemented
47#10622282C2214yescomplemented
48#10622281C2214yescomplemented
49#10622278C2214yescomplemented
50#10622278C2214yescomplemented
51#10622277C2214yescomplemented
52#10622273C2214yescomplemented
53#10622273C2214yescomplemented
54#10622270C2214yescomplemented
55#10622268C2214yescomplemented
56#10622266C2214yescomplemented
57C25×C11C2311yescharacteristic
58C23×C4×C11—24no—
59C23×C4×C11—44no—
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2314yes—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2314yes—
69C22×D44C2312yes—
70C22×D44C2314yes—
71C22×C4×D11C2314yes—
72C2×C11×C22⋊C4—44no—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C2314yes—
75#67006—48no—
76C2×C22⋊Dic11C2314yes—
77C2×C22⋊Dic11C2314yes—
78C2×C22⋊Dic11C2314yes—
79#66983—28no—
80#66983—48no—
81#66983—44no—
82#66983—44no—
83C4×C22⋊D11—48no—
84C2×(C2×D11)⋊C4C2314yes—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2312yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×C4×Dic11C2314yes—
100#66937—48no—
101C11×#95C2314yes—
102C11×#95C2314yes—
103C11×#95C2314yes—
104C11×#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112#36731—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—41no—
117C24×C11—41no—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C23×D11C2414yes—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—416no—
137C22×C4×C11#4114yes—
138C22×C4×C11C2411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×C4×C11C2414yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C2×C22⋊D11—28no—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—28no—
146C2×C22⋊D11—28no—
147C2×C22⋊D11—28no—
148C2×C22⋊D11—44no—
149C2×C22⋊D11—44no—
150C2×C22⋊D11—44no—
151C2×C22⋊D11—44no—
152C22×Dic11C2414yes—
153C22×Dic11C2414yes—
154C22×Dic11C2414yes—
155C2×D44—24no—
156C2×D44—44no—
157C2×D44—42no—
158C2×D44—42no—
159C2×D44—44no—
160C2×D44—44no—
161C2×C4×D11—44no—
162C2×C4×D11—44no—
163C2×C4×D11—44no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—44no—
166C22⋊Dic11—28no—
167C22⋊Dic11—44no—
168C22⋊Dic11—44no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—44no—
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4—44no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—44no—
175(C2×D11)⋊C4—44no—
176(C2×D11)⋊C4—44no—
177C4⋊Dic11—24no—
178C4⋊Dic11—42no—
179C4⋊Dic11—42no—
180C4⋊Dic11—44no—
181Dic11⋊C4—44no—
182Dic11⋊C4—44no—
183Dic11⋊C4—44no—
184C4×Dic11—44no—
185#2847—112no—
186#2743—114no—
187#2740—114no—
188#2699—114no—
189#2688—114no—
190#2656—111no—
191#2646—111no—
192#2444—114no—
193#2424—114no—
194#2325—112no—
195C2×#381D1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—28no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—44no—
209C23×C11—44no—
210C23×C11C2×#4112yes—
211C23×C11H(5,𝔽2)14yes—
212C23×C11H(5,𝔽2)14yes—
213C23×C11C2511yescharacteristic
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—44no—
234C2×C4×C11—48no—
235C2×C4×C11—48no—
236C2×C4×C11—44no—
237C2×C4×C11—84no—
238C2×C4×C11—84no—
239C2×C4×C11C2×#4114yes—
240C22⋊D11—416no—
241C22⋊D11—88no—
242C22⋊D11—88no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252D44—84no—
253D44—88no—
254C4×D11—88no—
255C24×C4C2×D1111yescharacteristic
256C2×#121—112no—
257C2×#121—112no—
258C2×#121—112no—
259C2×#121—114no—
260C2×#121—114no—
261C2×#120—114no—
262C2×C4×D4—114no—
263C22×C22⋊C4C2×D1112yes—
264#400—114no—
265#400—114no—
266#399—114no—
267#398—114no—
268#397—114no—
269#397—114no—
270#396—114no—
271#394—114no—
272#394—114no—
273#394—114no—
274#392—114no—
275#392—114no—
276#390—114no—
277#388—114no—
278#388—114no—
279#388—114no—
280#387—114no—
281#387—114no—
282#386—114no—
283#386—114no—
284#386—114no—
285#386—114no—
286#386—114no—
287#386—114no—
288#386—114no—
289#385—114no—
290#385—114no—
291#381—114no—
292#381C2×D1114yes—
293#381C2×D1114yes—
294#380—112no—
295#380—112no—
296#380—112no—
297C2×#95C2×D1111yescharacteristic
298C2×#95C2×D1111yescharacteristic
299C2×#95C2×D1112yes—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—416no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11#54014yes—
313C22×C11C22×#4111yescharacteristic
314C22×C11C2×H(5,𝔽2)12yes—
315C22×C11C2×H(5,𝔽2)12yes—
316C22×C11#58511yescharacteristic
317C22×C11#58511yescharacteristic
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—44no—
325C4×C11—24no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—44no—
329C4×C11—44no—
330Dic11—44no—
331Dic11—44no—
332Dic11—44no—
333C25C22×D1111yescharacteristic
334C22×D4—114no—
335C22×D4—114no—
336C22×D4—114no—
337C22×D4—112no—
338C22×D4—114no—
339C23×C4—24no—
340C23×C4—44no—
341C23×C4—114no—
342C23×C4C22×D1112yes—
343C23×C4C22×D1112yes—
344C23×C4C22×D1112yes—
345C23×C4C22×D1112yes—
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348#121—228no—
349#121—448no—
350#121—444no—
351#121—444no—
352#121—448no—
353#120—448no—
354C4×D4—448no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—114no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—114no—
364C2×C22⋊C4—114no—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—114no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—114no—
374C2×C22⋊C4C22×D1114yes—
375C2×C22⋊C4C22×D1114yes—
376C2×C42—114no—
377#95—114no—
378#95—114no—
379#95—114no—
380#95—114no—
381#95—114no—
382#95—114no—
383#95—114no—
384#95C22×D1114yes—
385#95C22×D1114yes—
386#95C22×D1114yes—
387#95C22×D1114yes—
388C2×C11—24no—
389C2×C11—44no—
390C2×C11C2×#54011yescharacteristic
391C2×C11#349011yescharacteristic
392C2×C11#349311yescharacteristic
393C2×C11#353412yes—
394C2×C11#353412yes—
395D11—84no—
396C24—22no—
397C24—24no—
398C24—24no—
399C24—41no—
400C24—41no—
401C24—114no—
402C24C23×D1112yes—
403C24C23×D1111yescharacteristic
404C2×D4—228no—
405C2×D4—228no—
406C2×D4—228no—
407C2×D4—228no—
408C2×D4—228no—
409C2×D4—224no—
410C2×D4—442no—
411C2×D4—442no—
412C2×D4—444no—
413C2×D4—444no—
414C2×D4—444no—
415C2×D4—444no—
416C2×D4—444no—
417C2×D4—444no—
418C2×D4—444no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—416no—
435C22×C4—114no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—444no—
439C22×C4—444no—
440C22×C4—444no—
441C22×C4#433914yes—
442C22×C4C23×D1111yescharacteristic
443C22×C4C23×D1111yescharacteristic
444C22×C4C23×D1114yes—
445C22×C4C23×D1114yes—
446C22×C4C23×D1112yes—
447C4⋊C4—224no—
448C4⋊C4—444no—
449C4⋊C4—444no—
450C4⋊C4—442no—
451C4⋊C4—442no—
452C4⋊C4—444no—
453C4⋊C4—444no—
454C22⋊C4—28no—
455C22⋊C4—44no—
456C22⋊C4—228no—
457C22⋊C4—228no—
458C22⋊C4—444no—
459C22⋊C4—444no—
460C22⋊C4—444no—
461C22⋊C4—444no—
462C22⋊C4—444no—
463C22⋊C4—444no—
464C22⋊C4—444no—
465C22⋊C4—444no—
466C22⋊C4—444no—
467C42—444no—
468C11#3673111yescharacteristic, complemented, Sylow
469C23—22no—
470C23—21no—
471C23—21no—
472C23—28no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—48no—
480C23—48no—
481C23—44no—
482C23—44no—
483C23—224no—
484C23—224no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23—224no—
489C23—224no—
490C23C2×#433912yes—
491C23#6703714yes—
492C23#6704214yes—
493C23C24×D1111yescharacteristic
494D4—4416no—
495D4—884no—
496D4—888no—
497D4—888no—
498D4—888no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—48no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—84no—
516C2×C4—84no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—888no—
527C2×C4C2×#433914yes—
528C22—24no—
529C22—24no—
530C22—22no—
531C22—22no—
532C22—24no—
533C22—24no—
534C22—24no—
535C22—416no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—444no—
541C22—444no—
542C22—444no—
543C22—444no—
544C22—444no—
545C22—444no—
546C22—444no—
547C22#1062306614yes—
548C22C22×#433911yescharacteristic
549C22C2×#6703712yes—
550C22C2×#6704212yes—
551C22#1062345311yescharacteristic
552C22#1062345311yescharacteristic
553C4—24no—
554C4—44no—
555C4—44no—
556C4—41no—
557C4—41no—
558C4—444no—
559C4—444no—
560C4—444no—
561C2—24no—
562C2—44no—
563C2—884no—
564C2C2×#1062306611yescharacteristic
565C2#1308230511yescharacteristic
566C2#1308233611yescharacteristic
567C2#1308281012yes—
568C2#1308281012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#381C2
hypercenterC2×#381D11
hypocenterC11#36731
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
1. #13076898C2semidirect
2. #13075755C2semidirect
3. #13075716C2semidirect
4. #13075203C2semidirect
5. #13075052C2semidirect
6. #13074718C2semidirect
7. #13074586C2semidirect
8. #13072366C2semidirect
9. #13072152C2semidirect
10. #13071319C2semidirect
11. C2×C11×#381C2semidirect
41. #10622290C22semidirect
42. #10622288C22semidirect
43. #10622288C22semidirect
44. #10622285C22semidirect
45. #10622284C22semidirect
46. #10622283C22semidirect
47. #10622282C22semidirect
48. #10622281C22semidirect
49. #10622278C22semidirect
50. #10622278C22semidirect
51. #10622277C22semidirect
52. #10622273C22semidirect
53. #10622273C22semidirect
54. #10622270C22semidirect
55. #10622268C22semidirect
56. #10622266C22semidirect
195. C2×#381D11semidirect
468. C11#36731semidirect

Maximal subgroups

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

subgroupindex
#130768982
#130757552
#130757162
#130752032
#130750522
#130747182
#130745862
#130723662
#130721522
#130713192
C2×C11×#3812
#3673111