Finite Group Databasebeta

← #14724522

Subgroups — #14724522

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic
2#13077325C211yesmaximal, characteristic, complemented
3#13077323C211yesmaximal, characteristic, complemented
4#13067483C211yesmaximal, characteristic, complemented
5#13067482C211yesmaximal, characteristic, complemented
6#13067481C211yesmaximal, characteristic, complemented
7#13067480C211yesmaximal, characteristic, complemented
8#13067479C211yesmaximal, characteristic, complemented
9#13067478C211yesmaximal, characteristic, complemented
10#13067477C211yesmaximal, characteristic, complemented
11#13067370C211yesmaximal, characteristic, complemented
12#13067065C211yesmaximal, characteristic, complemented
13#13067065C211yesmaximal, characteristic, complemented
14D11×#322C211yesmaximal, characteristic, complemented
15C11×#1586C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17C2×#66954—21no—
18#10623079C2211yescharacteristic
19#10623079C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C11×#436C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622770C411yescharacteristic
24#10622764C411yescharacteristic
25#10622741—21no—
26C8×C22⋊D11—21no—
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622496C411yescharacteristic
32#10622487C411yescharacteristic
33#10622451C2211yescharacteristic
34#10622450C2211yescharacteristic
35#10622450C2211yescharacteristic
36#10622447C2211yescharacteristic
37#10622388C411yescharacteristic
38#10622388C411yescharacteristic
39#10622373C411yescharacteristic
40#10622373C411yescharacteristic
41#10622342—21no—
42#10622340—21no—
43#10622340—21no—
44(C22⋊D11)⋊C8—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic
47C8×D44C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4339—21no—
68C2×#4339—21no—
69C2×C11×D8C2×C411yescharacteristic
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66993C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77#66991C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C2×#4323C2×C411yescharacteristic
80C4×C22⋊D11—21no—
81C4×C22⋊D11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84#66960—44no—
85C2×D88C2×C411yescharacteristic
86#66954—44no—
87C2×#4313—21no—
88C2×#4313—21no—
89C2×#4313—21no—
90C2×#4313—21no—
91C2×C8×D11—21no—
92C2×C8×D11—21no—
93C2×C8×D11—21no—
94C2×C8×D11C2×C411yescharacteristic
95C2×C8×D11C2×C411yescharacteristic
96C2×C8×D11D411yescharacteristic
97C2×C8×D11D411yescharacteristic
98#66948C2×C411yescharacteristic
99#66948C2×C411yescharacteristic
100#66941C2×C411yescharacteristic
101#66941C2×C411yescharacteristic
102#66938—21no—
103#66938—21no—
104#66937—21no—
105#66937—21no—
106C4×D44C2311yescharacteristic
107C4×D44C2311yescharacteristic
108C42×D11C2311yescharacteristic
109C11×#107C2×C411yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×#102C2×C411yescharacteristic
114C11×C22⋊C8—21no—
115C11×C22⋊C8—21no—
116C4×C8×C11C2311yescharacteristic
117C4×C8×C11C2311yescharacteristic
118C4×C8×C11C2311yescharacteristic
119#66896C2×C411yescharacteristic
120#66896C2×C411yescharacteristic
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123#66885C2×C411yescharacteristic
124#66885C2×C411yescharacteristic
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8—21no—
129#66882C2×C411yescharacteristic
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132C8×Dic11—21no—
133C8×Dic11C2×C411yescharacteristic
134C8×Dic11C2×C411yescharacteristic
135C8×Dic11D411yescharacteristic
136C8×Dic11D411yescharacteristic
137#66873C2×C411yescharacteristic
138#66873C2×C411yescharacteristic
139#66871C2×C411yescharacteristic
140#66871C2×C411yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#17981—111nomaximal, Sylow
147C2×D4×C11C22×C411yescharacteristic
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C2×C22⋊D11—21no—
155C2×C22⋊D11—21no—
156C2×C22⋊D11—21no—
157#4339—42no—
158#4339—42no—
159#4339—42no—
160#4339—42no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C22×C411yescharacteristic
164C2×D44C22×C411yescharacteristic
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11C22×C411yescharacteristic
168C2×C4×D11C2×D411yescharacteristic
169C2×C4×D11#4111yescharacteristic
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×D8—41no—
173C11×M16—42no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—42no—
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C22×C411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11C2411yescharacteristic
187C22⋊Dic11—21no—
188C22⋊Dic11—21no—
189#4323—41no—
190#4323—41no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199C4×Dic11C22×C411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201C4×Dic11#4111yescharacteristic
202#4318—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211D88—41no—
212#4313—42no—
213#4313—42no—
214#4313—42no—
215#4313—42no—
216C8×D11—24no—
217C8×D11—22no—
218C8×D11—22no—
219C8×D11—41no—
220C8×D11—41no—
221C8×D11—42no—
222C8×D11—42no—
223#3169—111no—
224#2931—111no—
225#2931—111no—
226#1586—111no—
227#1586—111no—
228#1586—111no—
229#1586—111no—
230#1586—111no—
231#1586—111no—
232#1586—111no—
233#1586D1111yescharacteristic, complemented
234#1566—111no—
235#1492—111no—
236#1492—111no—
237C2×#322—111no—
238C23×C11—21no—
239C23×C11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11C4×D411yescharacteristic
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C22⋊D11—42no—
257C22⋊D11—42no—
258C22⋊D11—42no—
259C22⋊D11—42no—
260C22⋊D11—42no—
261C22⋊D11—42no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11C4×D411yescharacteristic
265C2×Dic11C4×D411yescharacteristic
266C2×Dic11C4×D411yescharacteristic
267D44—21no—
268D44—21no—
269D44—21no—
270D44—21no—
271D44—42no—
272D44—42no—
273C4×D11—21no—
274C4×D11—21no—
275C4×D11—22no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11AGL(1,ℤ/8)12yes—
281C4×D11AGL(1,ℤ/8)12yes—
282Dic22—42no—
283Dic22—42no—
284C8×C11—22no—
285C8×C11—21no—
286C8×C11—21no—
287C8×C11—21no—
288C8×C11—21no—
289C8×C11—41no—
290C8×C11—41no—
291C11⋊C8—22no—
292C11⋊C8—21no—
293C11⋊C8—21no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C2×#131—221no—
299C2×#131—221no—
300#532—111no—
301#532—111no—
302#500—111no—
303#493—111no—
304#486—111no—
305#486—111no—
306#466—111no—
307#466—111no—
308#466—111no—
309#466—111no—
310C4×D8—111no—
311C4×D8—111no—
312C4×D8—111no—
313C4×D8C2×D1111yescharacteristic
314#436—111no—
315#436—111no—
316#436—111no—
317#436—221no—
318#436—221no—
319#436C2×D1111yescharacteristic
320C8×D4—111no—
321C8×D4—111no—
322C8×D4—111no—
323C8×D4—221no—
324C8×D4—221no—
325C8×D4C2×D1111yescharacteristic
326#423—111no—
327#423—111no—
328#408—221no—
329#408—221no—
330C2×C4×C8—111no—
331C2×C4×C8—111no—
332C2×C4×C8—111no—
333#334—111no—
334#334—111no—
335#334—111no—
336#334C2×D1111yescharacteristic
337D4⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341D4⋊C8—111no—
342D4⋊C8—111no—
343D4⋊C8C2×D1111yescharacteristic
344D4⋊C8C2×D1111yescharacteristic
345#322—111no—
346#322—111no—
347#322—111no—
348#322C2×D1111yescharacteristic
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11C2×C4×D411yescharacteristic
356C2×D11—21no—
357C2×D11—21no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11#44212yes—
365C4×C11—21no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11#56811yescharacteristic
369C4×C11#56811yescharacteristic
370C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
371C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
372Dic11—21no—
373Dic11—41no—
374Dic11—41no—
375Dic11#44212yes—
376Dic11#44312yes—
377C2×#41—221no—
378C2×#41—221no—
379C2×D8—111no—
380C2×D8—111no—
381C2×D8—111no—
382C2×D8C4×D1111yescharacteristic
383#131—444no—
384#131—444no—
385C2×M16—21no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—221no—
390C2×M16—221no—
391C22×C8—21no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—221no—
397C22×C8—221no—
398C22×C8—221no—
399C22×C8—221no—
400C4⋊Q8—111no—
401C4⋊Q8—111no—
402#127—111no—
403#127—111no—
404#124—221no—
405#124—221no—
406#121—111no—
407#121—111no—
408#121—111no—
409#121—111no—
410#121—221no—
411#121—221no—
412C4×D4—111no—
413C4×D4—111no—
414C4×D4—221no—
415C4×D4—221no—
416C4×D4C22×D1111yescharacteristic
417C4×D4C22×D1111yescharacteristic
418C2×C42—111no—
419#107—111no—
420#107—111no—
421#107—111no—
422#107C4×D1111yescharacteristic
423C4⋊C8—111no—
424C4⋊C8—111no—
425C4⋊C8—221no—
426C4⋊C8—221no—
427C4⋊C8C22×D1111yescharacteristic
428C4⋊C8C22×D1111yescharacteristic
429#102—111no—
430#102—111no—
431#102—111no—
432#102—111no—
433#102—111no—
434#102—111no—
435#102C4×D1111yescharacteristic
436#102C4×D1111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—221no—
440C22⋊C8—221no—
441C22⋊C8—221no—
442C22⋊C8—221no—
443C22⋊C8—221no—
444C22⋊C8—221no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8—111no—
448C4×C8—111no—
449C4×C8—111no—
450C4×C8—111no—
451C4×C8—111no—
452C4×C8—221no—
453C4×C8C22×D1111yescharacteristic
454C4×C8C22×D1111yescharacteristic
455C4×C8C22×D1111yescharacteristic
456C2×C11—81no—
457C2×C11—81no—
458C2×C11#293211yescharacteristic
459C2×C11C2×#44211yescharacteristic
460C2×C11C2×#44311yescharacteristic
461D11—22no—
462D11—81no—
463D11—81no—
464#41—442no—
465#41—442no—
466#41—442no—
467#41—442no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×D4—111no—
471C2×D4—111no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4C2×C4×D1111yescharacteristic
481C2×D4C2×C4×D1111yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—221no—
488C22×C4—221no—
489D8—41no—
490D8—441no—
491D8—441no—
492D8—441no—
493M16—42no—
494M16—442no—
495M16—442no—
496M16—442no—
497M16—442no—
498M16—442no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—42no—
503C2×C8—111no—
504C2×C8—111no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—224no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—441no—
514C2×C8—441no—
515C2×C8—442no—
516C2×C8—442no—
517C2×C8—442no—
518C2×C8C2×C4×D1111yescharacteristic
519C2×C8C2×C4×D1111yescharacteristic
520C2×C8D4×D1111yescharacteristic
521C2×C8D4×D1111yescharacteristic
522C4⋊C4—111no—
523C4⋊C4—111no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4C2×C4×D1111yescharacteristic
527C4⋊C4C2×C4×D1111yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—221no—
531C22⋊C4—221no—
532C22⋊C4—221no—
533C22⋊C4—221no—
534C22⋊C4—221no—
535C22⋊C4—221no—
536C42—111no—
537C42—111no—
538C42—111no—
539C42C23×D1111yescharacteristic
540C11#1798111yescharacteristic, complemented, Sylow
541C23—21no—
542C23—21no—
543C23—111no—
544C23—221no—
545C23—221no—
546Q8—442no—
547Q8—442no—
548D4—21no—
549D4—21no—
550D4—21no—
551D4—21no—
552D4—221no—
553D4—221no—
554D4—221no—
555D4—221no—
556D4—442no—
557D4—442no—
558D4—442no—
559D4—442no—
560D4—442no—
561D4—442no—
562D4—442no—
563D4—442no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—111no—
571C2×C4—111no—
572C2×C4—112no—
573C2×C4—112no—
574C2×C4—111no—
575C2×C4—222no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4C22×C4×D1111yescharacteristic
585C2×C4C2×D4×D1111yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C8—22no—
588C8—21no—
589C8—21no—
590C8—21no—
591C8—21no—
592C8—41no—
593C8—41no—
594C8—222no—
595C8—221no—
596C8—221no—
597C8—221no—
598C8—221no—
599C8—441no—
600C8—441no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—112no—
608C22—221no—
609C22—221no—
610C22—441no—
611C22—441no—
612C22—441no—
613C22—441no—
614C22—441no—
615C22—441no—
616C22C4×D4×D1111yescharacteristic
617C4—21no—
618C4—41no—
619C4—41no—
620C4—112no—
621C4—112no—
622C4—221no—
623C4—441no—
624C4—441no—
625C4#1062327611yescharacteristic
626C4#1062328111yescharacteristic
627C4D11×AGL(1,ℤ/8)11yescharacteristic
628C4D11×AGL(1,ℤ/8)11yescharacteristic
629C2—81no—
630C2—81no—
631C2—222no—
632C2—881no—
633C2—881no—
634C2#1307733011yescharacteristic
635C2D11×#44211yescharacteristic
636C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1586C2
socleC22×C11C2×C4×D4
prime radical#13079192C2
cosocleC42×C11C24
hypercenter#1586D11
hypocenterC11#17981
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #13077325C2semidirect
3. #13077323C2semidirect
4. #13067483C2semidirect
5. #13067482C2semidirect
6. #13067481C2semidirect
7. #13067480C2semidirect
8. #13067479C2semidirect
9. #13067478C2semidirect
10. #13067477C2semidirect
11. #13067370C2semidirect
12. #13067065C2semidirect
13. #13067065C2semidirect
14. D11×#322C2semidirect
15. C11×#1586C2semidirect
233. #1586D11semidirect
540. C11#17981semidirect

Maximal subgroups

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

subgroupindex
#130791922
#130773252
#130773232
#130674832
#130674822
#130674812
#130674802
#130674792
#130674782
#130674772
#130673702
#130670652
D11×#3222
C11×#15862
#1798111