Finite Group Databasebeta

← #14853511

Subgroups — #14853511

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076975C211yesmaximal, characteristic, complemented
2#13071155C211yesmaximal, characteristic
3#13070183C211yesmaximal, characteristic, complemented
4#13069858C211yesmaximal, characteristic
5#13069857C211yesmaximal, characteristic
6#13069314C211yesmaximal, characteristic
7#13069311C211yesmaximal, characteristic
8#13069307C211yesmaximal, characteristic, complemented
9#13069304C211yesmaximal, characteristic, complemented
10#13068620C211yesmaximal, characteristic, complemented
11#13068620C211yesmaximal, characteristic, complemented
12#13068615C211yesmaximal, characteristic
13#13068615C211yesmaximal, characteristic
14#13068468C211yesmaximal, characteristic, complemented
15C11×#2101C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66942—21no—
18C2×#66940C2211yescharacteristic
19C2×#66928C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C11×#382C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66880C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30#10622601C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622589C2211yescharacteristic
33#10622589C2211yescharacteristic
34#10622587C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622585—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C42×Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622282—21no—
44#10622282—21no—
45#10622279—21no—
46#10622279—21no—
47#10622263—21no—
48#10622260—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66946—22no—
95#66946—22no—
96#66942—44no—
97#66940—22no—
98#66940—22no—
99#66928—22no—
100#66928—22no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109#66885—22no—
110#66885—41no—
111#66880—22no—
112#66880—41no—
113#66879—41no—
114#66879—41no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117#66874—22no—
118#66874—41no—
119#66873—22no—
120#66873—41no—
121#29131—111nomaximal, Sylow
122C23×D11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44#4112yes—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22#4112yes—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—42no—
167C42×C11—21no—
168C42×C11—21no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—42no—
173(C2×D11)⋊C4—42no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—41no—
191C4×Dic11—41no—
192C4×Dic11—42no—
193C4×Dic11#4112yes—
194C4×Dic11#4112yes—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201#2859—111no—
202C4×#124—111no—
203#2101—111no—
204#2101D1111yescharacteristic, complemented
205#2042—111no—
206#2042—111no—
207#1936—111no—
208#1936—111no—
209#1935—111no—
210#1935—111no—
211#1803—111no—
212#1803—111no—
213#1802—111no—
214#1802—111no—
215#1767—111no—
216C23×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
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×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—22no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11#12412yes—
266C2×Dic11#12412yes—
267C2×Dic11AGL(1,ℤ/8)12yes—
268C2×Dic11#13712yes—
269D44—22no—
270D44—22no—
271D44—41no—
272D44—41no—
273C4×D11—84no—
274Dic22—22no—
275Dic22—22no—
276Dic22—41no—
277Dic22—41no—
278C8×C11—41no—
279C8×C11—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C2×#125—221no—
283C2×#124—111no—
284C2×C4×Q8—111no—
285C2×C4×D4—111no—
286C2×C4⋊C8—111no—
287C2×C4⋊C8—111no—
288C2×#103—111no—
289C2×#103—111no—
290C2×#103—111no—
291C2×#103—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102—111no—
296C2×#97—111no—
297C2×#97—111no—
298#391—111no—
299#390—111no—
300#389—111no—
301#389—111no—
302#389—111no—
303#389—221no—
304#389—221no—
305#389C2×D1111yescharacteristic
306#388—221no—
307#388—221no—
308#384—111no—
309#384—111no—
310#382—221no—
311#382C2×D1111yescharacteristic
312C4×C22⋊C4—221no—
313C4×C22⋊C4—221no—
314C43—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340C2×D1111yescharacteristic
320#340C2×D1111yescharacteristic
321#340C2×D1111yescharacteristic
322#340C2×D1111yescharacteristic
323#336—111no—
324#336C2×D1111yescharacteristic
325C22×C11#52511yescharacteristic
326C22×C11C2×#12411yescharacteristic
327C22×C11#53711yescharacteristic
328C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C11C2×#13711yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57511yescharacteristic
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11#55211yescharacteristic
346C4×C11#55211yescharacteristic
347C4×C11#55311yescharacteristic
348C4×C11#55311yescharacteristic
349Dic11—22no—
350Dic11—42no—
351Dic11—41no—
352Dic11—41no—
353Dic11—81no—
354Dic11—81no—
355Dic11#48914yes—
356C22×Q8—111no—
357C22×D4—111no—
358C23×C4—221no—
359C22×C8—111no—
360C22×C8—111no—
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1111yescharacteristic
363#125—444no—
364#124—222no—
365#124—222no—
366C4×Q8—222no—
367C4×Q8—222no—
368C4×D4—222no—
369C4×D4—222no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—221no—
397C2×C42C22×D1111yescharacteristic
398C4⋊C8—222no—
399C4⋊C8—222no—
400#103—222no—
401#103—222no—
402#103—441no—
403#103—441no—
404#102—222no—
405#102—222no—
406#102—441no—
407#102—441no—
408#97—441no—
409#97—441no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418C2×C11#256211yescharacteristic
419C2×C11#311511yescharacteristic
420C2×C11#311611yescharacteristic
421C2×C11C2×#48911yescharacteristic
422C2×C11#314211yescharacteristic
423C2×C11#325111yescharacteristic
424C2×C11#325211yescharacteristic
425D11—82no—
426C24—221no—
427C2×Q8—112no—
428C2×Q8—221no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×D4—112no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—221no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—42no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C22⋊C4—224no—
490C22⋊C4—224no—
491C22⋊C4—442no—
492C22⋊C4—442no—
493C22⋊C4—442no—
494C42—21no—
495C42—21no—
496C42—112no—
497C42—112no—
498C42—222no—
499C42—222no—
500C42—221no—
501C42—221no—
502C42—441no—
503C42—441no—
504C42—442no—
505C11#2913111yescharacteristic, complemented, Sylow
506C23—222no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23C2×D4×D1111yescharacteristic
514Q8—222no—
515Q8—222no—
516Q8—441no—
517Q8—441no—
518D4—222no—
519D4—222no—
520D4—441no—
521D4—441no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—112no—
541C2×C4—112no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—222no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—884no—
562C2×C4#6704011yescharacteristic
563C2×C4#41×D1111yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#41×D1111yescharacteristic
566C2×C4#41×D1111yescharacteristic
567C2×C4#6704211yescharacteristic
568C8—41no—
569C8—41no—
570C8—441no—
571C8—441no—
572C22—442no—
573C22—442no—
574C22—442no—
575C22—881no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22#1062316011yescharacteristic
580C22#1062318711yescharacteristic
581C22D11×#12411yescharacteristic
582C22#1062329911yescharacteristic
583C22#1062329911yescharacteristic
584C22D11×AGL(1,ℤ/8)11yescharacteristic
585C22D11×#13711yescharacteristic
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—114no—
593C4—222no—
594C4—442no—
595C4—441no—
596C4—441no—
597C4—881no—
598C4—881no—
599C4#1062322411yescharacteristic
600C4#1062322411yescharacteristic
601C4#1062324011yescharacteristic
602C4#1062324011yescharacteristic
603C2—882no—
604C2#1307377811yescharacteristic
605C2#1307876211yescharacteristic
606C2#1307877311yescharacteristic
607C2D11×#48911yescharacteristic
608C2#1307901311yescharacteristic
609C2#1307997711yescharacteristic
610C2#1307998811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2101C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2101D11
hypocenterC11#29131
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
1. #13076975C2semidirect
3. #13070183C2semidirect
8. #13069307C2semidirect
9. #13069304C2semidirect
10. #13068620C2semidirect
11. #13068620C2semidirect
14. #13068468C2semidirect
15. C11×#2101C2semidirect
204. #2101D11semidirect
505. C11#29131semidirect

Maximal subgroups

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

subgroupindex
#130769752
#130711552
#130701832
#130698582
#130698572
#130693142
#130693112
#130693072
#130693042
#130686202
#130686152
#130684682
C11×#21012
#2913111