Finite Group Databasebeta

← #14821803

Subgroups — #14821803

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072981C211yesmaximal, characteristic, complemented
2#13071632C211yesmaximal, characteristic, complemented
3#13069925C211yesmaximal, characteristic, complemented
4#13069799C211yesmaximal, characteristic, complemented
5#13069751C211yesmaximal, characteristic, complemented
6#13069612C211yesmaximal, characteristic
7#13069566C211yesmaximal, characteristic, complemented
8#13069296C211yesmaximal, characteristic, complemented
9#13069238C211yesmaximal, characteristic, complemented
10#13069225C211yesmaximal, characteristic, complemented
11#13069186C211yesmaximal, characteristic, complemented
12#13068961C211yesmaximal, characteristic, complemented
13#13068702C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1874C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66989—21no—
19C22×#4323C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×C4×C22⋊D11—21no—
22C2×#66946C2211yescharacteristic
23C2×#66941C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622835—21no—
28#10622834C2211yescharacteristic
29#10622834C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31#10622826—21no—
32#10622825C2211yescharacteristic
33C4×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40#10622603—21no—
41#10622602—21no—
42#10622601C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C4⋊C4×Dic11C2211yescharacteristic
45#10622586C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47#10622560—21no—
48#10622558—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#121—22no—
70C11×#121—41no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85#66989—44no—
86C2×#4323—22no—
87C2×#4323—41no—
88C2×#4323—41no—
89#66983—22no—
90#66983—22no—
91C4×C22⋊D11—44no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66946—22no—
108#66946—41no—
109#66941—22no—
110#66941—41no—
111C11×#102—22no—
112C11×#102—41no—
113C11×C22⋊C8—41no—
114#66896—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121C22⋊(C11⋊C8)—41no—
122#66885—22no—
123#66885—41no—
124#66882—22no—
125Dic11⋊C8—41no—
126C8×Dic11—41no—
127#66873—22no—
128#26720—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11C2×D411yescharacteristic
131C23×D11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—81no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—81no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44#4112yes—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—81no—
174C2×Dic22—42no—
175C2×Dic22—42no—
176C2×Dic22—81no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4#4112yes—
189C11×C4⋊C4#4112yes—
190C11×C22⋊C4—42no—
191C22⋊Dic11—41no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195C22⋊Dic11—42no—
196C22⋊Dic11—81no—
197C22⋊Dic11D814yescomplemented
198#4323—44no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—81no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11#4112yes—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223#2491—111no—
224#2361—111no—
225#2054—111no—
226#2033—111no—
227#2023—111no—
228#1999—111no—
229#1988—111no—
230#1934—111no—
231#1925—111no—
232#1923—111no—
233#1918—111no—
234#1879—111no—
235#1874D1111yescharacteristic, complemented
236#1823—111no—
237C4×#102—111no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11C2×D812yes—
252C23×C11C22×D411yescharacteristic
253C22×D11—22no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—84no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—84no—
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C22⋊D11—48no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—22no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11C2×D812yes—
309C2×Dic11C2×D812yes—
310D44—22no—
311D44—22no—
312D44—41no—
313D44—41no—
314C4×D11—84no—
315Dic22—84no—
316C8×C11—41no—
317C8×C11—41no—
318C11⋊C8—41no—
319C11⋊C8—41no—
320C22×D8—111no—
321C2×C4⋊Q8—111no—
322C2×#124—221no—
323C2×#121—111no—
324C2×#121C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×C4×D4—221no—
327C22×C4⋊C4C2×D1111yescharacteristic
328C2×#107—111no—
329C2×C4⋊C8—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102C2×D1111yescharacteristic
335C2×#102C2×D1111yescharacteristic
336C2×C22⋊C8—111no—
337C2×C22⋊C8C2×D1111yescharacteristic
338C2×C4×C8—111no—
339#394—221no—
340#393—221no—
341#390—111no—
342#390—111no—
343#390—111no—
344#389—111no—
345#388—221no—
346#388—221no—
347#386—221no—
348#385—221no—
349#380—111no—
350C4×C4⋊C4—111no—
351C4×C4⋊C4—111no—
352C4×C22⋊C4—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340C2×D1111yescharacteristic
360#340C2×D1111yescharacteristic
361#336—111no—
362#336—111no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11#52511yescharacteristic
378C22×C11#54611yescharacteristic
379C22×C11#54611yescharacteristic
380C22×C11C22×D811yescharacteristic
381C22×C11#57511yescharacteristic
382C22×C11#57711yescharacteristic
383C22×C11#57711yescharacteristic
384C2×D11—42no—
385C2×D11—42no—
386C2×D11—42no—
387C2×D11—81no—
388C2×D11—81no—
389C2×D11—81no—
390C2×D11—81no—
391C4×C11—41no—
392C4×C11—42no—
393C4×C11—42no—
394C4×C11—81no—
395C4×C11#52911yescharacteristic
396C4×C11#53811yescharacteristic
397C4×C11#55511yescharacteristic
398C4×C11#55911yescharacteristic
399Dic11—22no—
400Dic11—22no—
401Dic11—42no—
402Dic11—41no—
403Dic11—41no—
404Dic11—81no—
405Dic11—81no—
406C22×Q8—221no—
407C22×D4—21no—
408C22×D4—111no—
409C22×D4—221no—
410C22×D4C22×D1111yescharacteristic
411C23×C4—21no—
412C23×C4—221no—
413C23×C4C22×D1111yescharacteristic
414C2×D8—222no—
415C2×D8—441no—
416C2×D8—441no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421C4⋊Q8—222no—
422C4⋊Q8—441no—
423#124—444no—
424#121—22no—
425#121—41no—
426#121—222no—
427#121—222no—
428C4×D4—222no—
429C4×D4—441no—
430C4×D4—444no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C42—111no—
455C2×C42—111no—
456C2×C42—221no—
457C2×C42—221no—
458#107—222no—
459C4⋊C8—441no—
460#102—22no—
461#102—41no—
462#102—222no—
463#102—222no—
464#102—222no—
465#102—441no—
466C22⋊C8—41no—
467C22⋊C8—441no—
468C4×C8—441no—
469#95—111no—
470#95—111no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475C2×C11—42no—
476C2×C11—161no—
477C2×C11#245911yescharacteristic
478C2×C11#310011yescharacteristic
479C2×C11#312511yescharacteristic
480C2×C11#329411yescharacteristic
481C2×C11#329411yescharacteristic
482C2×C11#332111yescharacteristic
483C2×C11#332611yescharacteristic
484D11—82no—
485C24—21no—
486C24—221no—
487C24D4×D1111yescharacteristic
488C2×Q8—442no—
489C2×Q8—442no—
490C2×Q8—881no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—81no—
500C2×D4—112no—
501C2×D4—224no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4—221no—
506C2×D4—221no—
507C2×D4—442no—
508C2×D4—442no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—81no—
521C22×C4—111no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—111no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—442no—
529C22×C4—442no—
530C22×C4—881no—
531C22×C4D4×D1111yescharacteristic
532C22×C4C23×D1111yescharacteristic
533D8—444no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8—221no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—112no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4#433912yes—
560C4⋊C4#434112yes—
561C22⋊C4—42no—
562C22⋊C4—114no—
563C22⋊C4—224no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—441no—
569C22⋊C4—442no—
570C22⋊C4—442no—
571C22⋊C4—881no—
572C22⋊C4—881no—
573C42—221no—
574C42—221no—
575C42—221no—
576C42—221no—
577C42—442no—
578C42—442no—
579C11#2672011yescharacteristic, complemented, Sylow
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—222no—
594C23—441no—
595C23—441no—
596C23—441no—
597C23—441no—
598C23—441no—
599C23—441no—
600C23D8×D1112yes—
601C23C2×D4×D1111yescharacteristic
602Q8—884no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—84no—
608D4—222no—
609D4—222no—
610D4—448no—
611D4—441no—
612D4—441no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—84no—
630C2×C4—112no—
631C2×C4—112no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—221no—
638C2×C4—221no—
639C2×C4—221no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—222no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4—441no—
651C2×C4—884no—
652C2×C4C2×#433911yescharacteristic
653C2×C4C2×#434111yescharacteristic
654C2×C4#6703711yescharacteristic
655C2×C4#6703711yescharacteristic
656C2×C4#41×D1111yescharacteristic
657C2×C4#41×D1111yescharacteristic
658C8—41no—
659C8—41no—
660C8—441no—
661C8—441no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—442no—
677C22—442no—
678C22—442no—
679C22—881no—
680C22—881no—
681C22—881no—
682C22—881no—
683C22#1062302111yescharacteristic
684C22#1062312211yescharacteristic
685C22#1062318711yescharacteristic
686C22C2×D8×D1111yescharacteristic
687C22#1062329311yescharacteristic
688C22#1062330611yescharacteristic
689C22#1062330811yescharacteristic
690C4—42no—
691C4—42no—
692C4—41no—
693C4—81no—
694C4—222no—
695C4—222no—
696C4—441no—
697C4—442no—
698C4—441no—
699C4—881no—
700C4—881no—
701C4#1062308811yescharacteristic
702C4#1062309011yescharacteristic
703C4#1062314411yescharacteristic
704C4#1062314711yescharacteristic
705C2—42no—
706C2—161no—
707C2—882no—
708C2#1307255211yescharacteristic
709C2#1307861311yescharacteristic
710C2#1307889611yescharacteristic
711C2#1308042211yescharacteristic
712C2#1308042511yescharacteristic
713C2#1308079511yescharacteristic
714C2#1308087011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radical#13069612C2
hypercenter#1874D11
hypocenterC11#26720
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. #13072981C2semidirect
2. #13071632C2semidirect
3. #13069925C2semidirect
4. #13069799C2semidirect
5. #13069751C2semidirect
7. #13069566C2semidirect
8. #13069296C2semidirect
9. #13069238C2semidirect
10. #13069225C2semidirect
11. #13069186C2semidirect
12. #13068961C2semidirect
13. #13068702C2semidirect
14. #13068430C2semidirect
15. C11×#1874C2semidirect
197. C22⋊Dic11D8semidirect
235. #1874D11semidirect
579. C11#26720semidirect

Maximal subgroups

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

subgroupindex
#130729812
#130716322
#130699252
#130697992
#130697512
#130696122
#130695662
#130692962
#130692382
#130692252
#130691862
#130689612
#130687022
#130684302
C11×#18742
#2672011