Finite Group Databasebeta

← #14811908

Subgroups — #14811908

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073648C211yesmaximal, characteristic, complemented
2#13071561C211yesmaximal, characteristic
3#13070005C211yesmaximal, characteristic
4#13070003C211yesmaximal, characteristic
5#13069761C211yesmaximal, characteristic
6#13069759C211yesmaximal, characteristic
7#13069570C211yesmaximal, characteristic, complemented
8#13069373C211yesmaximal, characteristic, complemented
9#13069331C211yesmaximal, characteristic, complemented
10#13069208C211yesmaximal, characteristic, complemented
11#13069207C211yesmaximal, characteristic, complemented
12#13068742C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#1989C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66943C2211yescharacteristic
19C2×#66925—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×Dic11⋊C8C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622601C2211yescharacteristic
29#10622596—21no—
30#10622593—21no—
31#10622589—21no—
32#10622589C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622585—21no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622553—21no—
42#10622552C2211yescharacteristic
43C4×Dic11⋊C4C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622282—21no—
46#10622280—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#125—22no—
64C11×#125—41no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4D411yescharacteristic
90C2×Dic11⋊C4D411yescharacteristic
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66946—22no—
98#66946Q814yes—
99#66943—22no—
100#66943—41no—
101#66925—44no—
102C11×C4⋊C8—41no—
103C11×#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66885—22no—
111#66885—41no—
112#66882—22no—
113Dic11⋊C8—22no—
114Dic11⋊C8—41no—
115C8×Dic11—22no—
116#66873—22no—
117#66873—41no—
118#66871—22no—
119#26025—111nomaximal, Sylow
120C23×D11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C2×Q812yes—
141C2×C4×D11—24no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4C2×Q812yes—
159C11×C4⋊C4#4112yes—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—42no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—81no—
167(C2×D11)⋊C4—81no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—42no—
174C4⋊Dic11#4112yes—
175Dic11⋊C4—22no—
176Dic11⋊C4—22no—
177Dic11⋊C4—42no—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182Dic11⋊C4—81no—
183Dic11⋊C4—81no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—42no—
187C4×Dic11—42no—
188C4×Dic11C2×Q812yes—
189C4×Dic11#4112yes—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196#2552—111no—
197#2354—111no—
198#2067—111no—
199#2067—111no—
200#2025—111no—
201#2025—111no—
202#1989—111no—
203#1989D1111yescharacteristic, complemented
204#1947—111no—
205#1939—111no—
206#1921—111no—
207#1921—111no—
208#1834—111no—
209#1802—111no—
210C4×#102—111no—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11C22×Q811yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11C22⋊Q812yes—
261C2×Dic11C22⋊Q812yes—
262C2×Dic11#13512yes—
263C2×Dic11AGL(1,ℤ/8)12yes—
264D44—22no—
265D44—22no—
266D44—41no—
267D44—41no—
268C4×D11—48no—
269C8×C11—41no—
270C8×C11—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C2×#125—111no—
274C2×#125C2×D1111yescharacteristic
275C2×C4×D4—111no—
276C2×#117—221no—
277C2×#107—111no—
278C2×#107—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×C4⋊C8C2×D1111yescharacteristic
282C2×#102—111no—
283C2×#102—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×C4×C8—111no—
287#398—221no—
288#398—221no—
289#390—111no—
290#390—111no—
291#389—111no—
292#389—111no—
293#389—221no—
294#388—221no—
295#388—221no—
296#384—111no—
297#384—111no—
298#384—221no—
299#380—221no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C4⋊C4C2×D1111yescharacteristic
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340C2×D1111yescharacteristic
311#340C2×D1111yescharacteristic
312#340C2×D1111yescharacteristic
313#340C2×D1111yescharacteristic
314#336—111no—
315#336—111no—
316C22×C11C2×C22⋊Q811yescharacteristic
317C22×C11#54611yescharacteristic
318C22×C11#54811yescharacteristic
319C22×C11C2×#13511yescharacteristic
320C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C11#57611yescharacteristic
322C22×C11#57811yescharacteristic
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C4×C11—42no—
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11#53311yescharacteristic
337C4×C11#54411yescharacteristic
338C4×C11#55511yescharacteristic
339C4×C11#55611yescharacteristic
340Dic11—22no—
341Dic11—41no—
342Dic11—42no—
343Dic11—41no—
344Dic11—81no—
345Dic11—81no—
346Dic11#47814yes—
347C22×D4—111no—
348C23×C4—221no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353#125—22no—
354#125—41no—
355#125—222no—
356#125—441no—
357C4×D4—114no—
358C4×D4—222no—
359#117—444no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C42—21no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—221no—
388C2×C42—221no—
389C2×C42C22×D1111yescharacteristic
390#107—222no—
391#107—222no—
392C4⋊C8—41no—
393C4⋊C8—222no—
394C4⋊C8—441no—
395#102—222no—
396#102—222no—
397#102—441no—
398#102—441no—
399C4×C8—222no—
400#95—21no—
401#95—111no—
402#95—111no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407C2×C11#243911yescharacteristic
408C2×C11C2×#47811yescharacteristic
409C2×C11#308311yescharacteristic
410C2×C11#330511yescharacteristic
411C2×C11#333011yescharacteristic
412C2×C11#336411yescharacteristic
413C2×C11#336611yescharacteristic
414D11—82no—
415C24—221no—
416C2×D4—112no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—224no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—112no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—442no—
470C4⋊C4—442no—
471C4⋊C4—881no—
472C4⋊C4—881no—
473C4⋊C4—881no—
474C4⋊C4—881no—
475C4⋊C4#433912yes—
476C4⋊C4Q8×D1112yes—
477C22⋊C4—224no—
478C22⋊C4—442no—
479C22⋊C4—442no—
480C22⋊C4—881no—
481C22⋊C4—881no—
482C42—21no—
483C42—21no—
484C42—42no—
485C42—112no—
486C42—112no—
487C42—221no—
488C42—221no—
489C42—442no—
490C42—442no—
491C11#2602511yescharacteristic, complemented, Sylow
492C23—222no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23C2×D4×D1111yescharacteristic
500D4—222no—
501D4—222no—
502D4—441no—
503D4—441no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—112no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—222no—
535C2×C4—448no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4C2×#433911yescharacteristic
545C2×C4#6703711yescharacteristic
546C2×C4C2×Q8×D1111yescharacteristic
547C2×C4#6704011yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#41×D1111yescharacteristic
550C8—41no—
551C8—41no—
552C8—441no—
553C8—441no—
554C22—442no—
555C22—442no—
556C22—442no—
557C22—881no—
558C22—881no—
559C22—881no—
560C22—881no—
561C22#1062302111yescharacteristic
562C22D11×C22⋊Q811yescharacteristic
563C22#1062316411yescharacteristic
564C22D11×#13511yescharacteristic
565C22#1062330011yescharacteristic
566C22D11×AGL(1,ℤ/8)11yescharacteristic
567C22#1062331011yescharacteristic
568C4—41no—
569C4—42no—
570C4—42no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—114no—
575C4—222no—
576C4—441no—
577C4—442no—
578C4—441no—
579C4—881no—
580C4—881no—
581C4#1062309911yescharacteristic
582C4#1062310911yescharacteristic
583C4#1062320111yescharacteristic
584C4#1062326011yescharacteristic
585C2—882no—
586C2#1307230411yescharacteristic
587C2D11×#47811yescharacteristic
588C2#1307847011yescharacteristic
589C2#1308056211yescharacteristic
590C2#1308091711yescharacteristic
591C2#1308130411yescharacteristic
592C2#1308132611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1989D11
hypocenterC11#26025
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
1. #13073648C2semidirect
7. #13069570C2semidirect
8. #13069373C2semidirect
9. #13069331C2semidirect
10. #13069208C2semidirect
11. #13069207C2semidirect
12. #13068742C2semidirect
15. C11×#1989C2semidirect
203. #1989D11semidirect
491. C11#26025semidirect

Maximal subgroups

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

subgroupindex
#130736482
#130715612
#130700052
#130700032
#130697612
#130697592
#130695702
#130693732
#130693312
#130692082
#130692072
#130687422
#130686152
#130684302
C11×#19892
#2602511