Finite Group Databasebeta

← #14760974

Subgroups — #14760974

Order 2816.

1048 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622390C211yesmaximal, characteristic
2C4×#66991C211yesmaximal, characteristic
3C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13069239C211yesmaximal, characteristic, complemented
5#13069238C211yesmaximal, characteristic, complemented
6#13069200C211yesmaximal, characteristic, complemented
7#13069199C211yesmaximal, characteristic, complemented
8#13068930C211yesmaximal, characteristic
9#13068805C211yesmaximal, characteristic, complemented
10#13068705C211yesmaximal, characteristic, complemented
11#13068514C211yesmaximal, characteristic, complemented
12#13068513C211yesmaximal, characteristic, complemented
13#13068441C211yesmaximal, characteristic, complemented
14#13068379C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C42×D11—21no—
22C2×C42×D11C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27#10622834C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C4×C22⋊Dic11—21no—
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35#10622600C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622569—21no—
42#10622557—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45C4×Dic11⋊C4—21no—
46C2×#66867C2211yescharacteristic
47#10622390C418yescomplemented
48D11×#95—21no—
49#10622262—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C22⋊D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81#66991—22no—
82#66991C2×C414yes—
83C4×C22⋊D11—44no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11D411yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C4⋊C4×D11—22no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11C2×C414yescomplemented
105C42×D11—22no—
106C42×D11—22no—
107C42×D11—44no—
108C11×#102—22no—
109C11×#102C2×C414yescomplemented
110C11×#97—22no—
111C11×#95—21no—
112#66896—22no—
113#66896C2×C414yescomplemented
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120(C2×D11)⋊C8—22no—
121(C2×D11)⋊C8C2×C414yescomplemented
122#66882—22no—
123#66881C2×C414yescomplemented
124#66872C2×C414yescomplemented
125#66871—22no—
126#66867—22no—
127#21580—111nomaximal, Sylow
128C24×C11—21no—
129C23×D11C2×D411yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11C22×C412yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—24no—
146C2×C22⋊D11—42no—
147C2×C22⋊D11—42no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×C4×D11—22no—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—41no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11C22×C412yes—
172C2×C4×D11#4112yes—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C22×C412yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C22×C412yes—
184C11×C4⋊C4#4112yes—
185C11×C22⋊C4—42no—
186C42×C11—42no—
187C42×C11#4112yes—
188C42×C11#4112yes—
189C22⋊Dic11—24no—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11C22×C412yes—
199C4⋊Dic11C22×C412yes—
200C4⋊Dic11#4112yes—
201Dic11⋊C4—24no—
202Dic11⋊C4—24no—
203Dic11⋊C4—42no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C22×C412yes—
218C2×#481—111no—
219C4×#121—111no—
220C2×C4×C4⋊C4—111no—
221#1925—111no—
222#1925—111no—
223#1920—111no—
224#1920—111no—
225#1874—111no—
226#1852—111no—
227#1824—111no—
228#1776—111no—
229#1776—111no—
230#1762—111no—
231#1762D1111yescharacteristic, complemented
232#1749—111no—
233C23×C11—22no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11C22×D411yescharacteristic
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11C4×D412yes—
246C22×D11AGL(1,ℤ/8)12yes—
247C22×D11#13712yes—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—41no—
251D4×C11—41no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—84no—
266C2×C4×C11#12312yes—
267C2×C4×C11#12312yes—
268C2×C4×C11C23×C411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C22⋊D11—48no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11C4×D412yes—
295C2×Dic11AGL(1,ℤ/8)12yes—
296C4×D11—28no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—44no—
302C4×D11—48no—
303C4×D11—48no—
304C8×C11—22no—
305C8×C11—41no—
306C11⋊C8—22no—
307C11⋊C8—41no—
308C2×#121—111no—
309C2×C4×D4—221no—
310C2×C4×D4C2×D1111yescharacteristic
311C22×C4⋊C4—111no—
312C22×C4⋊C4—111no—
313C22×C42—111no—
314C22×C42—221no—
315#481—118no—
316C2×#107—111no—
317C2×#107—111no—
318C2×#106—111no—
319C2×#106—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102C2×D1111yescharacteristic
323C2×#102C2×D1111yescharacteristic
324C2×C22⋊C8—111no—
325C2×C22⋊C8—111no—
326C2×#97—111no—
327C2×#97C2×D1111yescharacteristic
328#390—111no—
329#389—111no—
330#388—221no—
331#386—221no—
332#380—111no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—221no—
338C4×C4⋊C4—221no—
339C4×C4⋊C4C2×D1111yescharacteristic
340C4×C22⋊C4—221no—
341C2×#95—221no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350#336—111no—
351#336—111no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11C2×C4×D411yescharacteristic
360C22×C11C2×#12311yescharacteristic
361C22×C11#52511yescharacteristic
362C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C11C2×#13711yescharacteristic
365C22×C11#57511yescharacteristic
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—22no—
372C2×D11#44014yes—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11C4×#4111yescharacteristic
379C4×C11C4×#4111yescharacteristic
380C4×C11#52911yescharacteristic
381C4×C11#52911yescharacteristic
382Dic11—22no—
383Dic11—22no—
384Dic11—41no—
385Dic11—42no—
386Dic11—42no—
387Dic11—42no—
388Dic11—81no—
389C22×D4—221no—
390C22×D4C22×D1111yescharacteristic
391C23×C4—21no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—221no—
396C23×C4—221no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401#121—114no—
402#121—222no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—444no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—222no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C42—21no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—222no—
430C2×C42—222no—
431C2×C42—221no—
432C2×C42—221no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42—444no—
436C2×C42C22×D1111yescharacteristic
437#107—222no—
438#107—222no—
439#106—114no—
440#106—114no—
441#102—22no—
442#102—114no—
443#102—222no—
444#102C4×D1114yescomplemented
445C22⋊C8—114no—
446C22⋊C8—222no—
447#97—22no—
448#97—222no—
449#95—21no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—82no—
457C2×C11C4×#12311yescharacteristic
458C2×C11C2×#44011yescharacteristic
459C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
460C2×C11#309211yescharacteristic
461C2×C11#309411yescharacteristic
462C2×C11#310911yescharacteristic
463C2×C11#311711yescharacteristic
464D11—24no—
465C24—21no—
466C24—111no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—224no—
473C2×D4—442no—
474C2×D4—442no—
475C2×D4C2×C4×D1112yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—111no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—224no—
490C22×C4—222no—
491C22×C4—224no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—221no—
502C22×C4—441no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4D4×D1111yescharacteristic
508C22×C4D4×D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—112no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8C2×C4×D1112yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—112no—
527C4⋊C4—112no—
528C4⋊C4—112no—
529C4⋊C4—224no—
530C4⋊C4—224no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—442no—
537C4⋊C4C2×C4×D1112yes—
538C4⋊C4#433912yes—
539C22⋊C4—42no—
540C22⋊C4—224no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C42—42no—
545C42—222no—
546C42—222no—
547C42—221no—
548C42—221no—
549C42—442no—
550C42—442no—
551C42—442no—
552C42—442no—
553C42#433912yes—
554C42#434112yes—
555C11#2158011yescharacteristic, complemented, Sylow
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—112no—
564C23—112no—
565C23—112no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23C2×D4×D1111yescharacteristic
571D4—22no—
572D4—22no—
573D4—41no—
574D4—41no—
575D4—448no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—228no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—444no—
608C2×C4—448no—
609C2×C4—448no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4#6693612yes—
620C2×C4#6693612yes—
621C2×C4C22×C4×D1111yescharacteristic
622C2×C4C2×#433911yescharacteristic
623C2×C4C2×#433911yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C8—22no—
628C8—41no—
629C8—222no—
630C8—441no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—114no—
639C22—222no—
640C22—222no—
641C22—222no—
642C22—222no—
643C22—222no—
644C22—222no—
645C22C2×#6693611yescharacteristic
646C22C4×D4×D1111yescharacteristic
647C22#1062307811yescharacteristic
648C22D11×AGL(1,ℤ/8)11yescharacteristic
649C22D11×AGL(1,ℤ/8)11yescharacteristic
650C22#1062330411yescharacteristic
651C22D11×#13711yescharacteristic
652C4—22no—
653C4—22no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—222no—
658C4—222no—
659C4—441no—
660C4—442no—
661C4—442no—
662C4—442no—
663C4—881no—
664C4C4×#433911yescharacteristic
665C4#1062305911yescharacteristic
666C4C4×#434111yescharacteristic
667C4#1062308811yescharacteristic
668C2—82no—
669C2—224no—
670C2C4×#6693611yescharacteristic
671C2D11×#44011yescharacteristic
672C2#1307742711yescharacteristic
673C2#1307853711yescharacteristic
674C2#1307855411yescharacteristic
675C2#1307870511yescharacteristic
676C2#1307878511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1762C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1762D11
hypocenterC11#21580
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. C4×C4⋊C4×D11C2semidirect
4. #13069239C2semidirect
5. #13069238C2semidirect
6. #13069200C2semidirect
7. #13069199C2semidirect
9. #13068805C2semidirect
10. #13068705C2semidirect
11. #13068514C2semidirect
12. #13068513C2semidirect
13. #13068441C2semidirect
14. #13068379C2semidirect
15. C11×#1762C2semidirect
47. #10622390C4semidirect
104. C4⋊C4×D11C2×C4semidirect
109. C11×#102C2×C4semidirect
113. #66896C2×C4semidirect
121. (C2×D11)⋊C8C2×C4semidirect
123. #66881C2×C4semidirect
124. #66872C2×C4semidirect
231. #1762D11semidirect
444. #102C4×D11semidirect
555. C11#21580semidirect

Maximal subgroups

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

subgroupindex
C2×#106223902
C4×#669912
C4×C4⋊C4×D112
#130692392
#130692382
#130692002
#130691992
#130689302
#130688052
#130687052
#130685142
#130685132
#130684412
#130683792
C11×#17622
#2158011