Finite Group Databasebeta

← #14771068

Subgroups — #14771068

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622384C211yesmaximal, characteristic
2#13071484C211yesmaximal, characteristic, complemented
3#13071441C211yesmaximal, characteristic
4#13069307C211yesmaximal, characteristic, complemented
5#13069291C211yesmaximal, characteristic, complemented
6#13069256C211yesmaximal, characteristic, complemented
7#13069251C211yesmaximal, characteristic, complemented
8#13068879C211yesmaximal, characteristic, complemented
9#13068705C211yesmaximal, characteristic, complemented
10#13068650C211yesmaximal, characteristic, complemented
11#13068553C211yesmaximal, characteristic
12#13068443C211yesmaximal, characteristic, complemented
13C4×#66896C211yesmaximal, characteristic, complemented
14#13068396C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C2×#66945—21no—
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622826—21no—
29C2×C11⋊#95—21no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622591—21no—
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43#10622571—21no—
44#10622556—21no—
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622384C418yescomplemented
50#10622277—21no—
51#10622268—21no—
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C2×#4341—22no—
66C2×#4341—22no—
67C2×#4341—22no—
68C2×#4341—41no—
69C2×#4341—41no—
70C2×#4341C2×C414yes—
71C22×C4×D11—21no—
72C22×C4×D11C2311yescharacteristic
73C22×Dic22C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—41no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85D4×Dic11—22no—
86D4×Dic11—41no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×#4313—41no—
102C2×#4313—41no—
103C2×#4313C2×C414yescomplemented
104#66945—44no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11C2×C414yescomplemented
107C11×#107—41no—
108C11×#102—22no—
109C11×#102C2×C414yes—
110C11×#95—21no—
111#66896—22no—
112#66896C2×C414yes—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124(C2×D11)⋊C8—22no—
125#66881—41no—
126#66880—41no—
127#66880C2×C414yescomplemented
128#66879—41no—
129#66874—41no—
130#66874C2×C414yescomplemented
131C4×C11⋊C8—41no—
132#22582—111nomaximal, Sylow
133C24×C11—21no—
134C23×D11C2×D411yescharacteristic
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11C22×C412yes—
139C2×D4×C11#4112yes—
140C2×D4×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—24no—
151C2×C22⋊D11—42no—
152C2×C22⋊D11—42no—
153C22×Dic11—24no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—81no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166#4341—28no—
167#4341—44no—
168#4341—44no—
169#4341—44no—
170C2×C4×D11—24no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11C22×C412yes—
178C2×C4×D11#4112yes—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22C22×C412yes—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11C22×C412yes—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4C22×C412yes—
198C11×C22⋊C4—42no—
199C42×C11—21no—
200C42×C11—21no—
201C22⋊Dic11—42no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—41no—
204(C2×D11)⋊C4—42no—
205(C2×D11)⋊C4—81no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—42no—
212C4⋊Dic11C22×C412yes—
213Dic11⋊C4—24no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—42no—
217C4×Dic11—42no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8C22×C412yes—
224#4313—44no—
225C2×#417—111no—
226#2344—111no—
227#2339—111no—
228#1935—111no—
229#1933—111no—
230#1928—111no—
231#1927—111no—
232#1864—111no—
233#1862D1111yescharacteristic, complemented
234#1824—111no—
235#1809—111no—
236#1788—111no—
237#1762—111no—
238C4×#102—111no—
239#1753—111no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11C22×D411yescharacteristic
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11C4×D412yes—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11#11714yescomplemented
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—84no—
274C2×C4×C11AGL(1,ℤ/8)12yes—
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C22⋊D11—48no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—48no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—84no—
304C2×Dic11C4×D412yes—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—22no—
308C4×D11—22no—
309C4×D11—48no—
310Dic22—22no—
311Dic22—22no—
312Dic22—41no—
313Dic22—41no—
314C8×C11—22no—
315C8×C11—41no—
316C11⋊C8—22no—
317C11⋊C8—41no—
318C22×#41—111no—
319C22×M16—111no—
320C2×C4×D4—111no—
321C2×C4×D4C2×D1111yescharacteristic
322C2×#117—221no—
323C22×C4⋊C4—111no—
324C2×#107C2×D1111yescharacteristic
325C2×#106—111no—
326#417—118no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102C2×D1111yescharacteristic
334C2×#102C2×D1111yescharacteristic
335C2×C22⋊C8—111no—
336C2×#97—111no—
337C2×C4×C8—111no—
338#391—111no—
339#391—111no—
340#389—111no—
341#389C2×D1111yescharacteristic
342#387—221no—
343#387—221no—
344#386—221no—
345#386—221no—
346#381—221no—
347#381—221no—
348#380—111no—
349#380—111no—
350C4×C4⋊C4—111no—
351C4×C4⋊C4—111no—
352C4×C22⋊C4—111no—
353C2×#95—221no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340C2×D1111yescharacteristic
360#336—111no—
361#336C2×D1111yescharacteristic
362C22×C11—24no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11C2×C4×D411yescharacteristic
370C22×C11#54611yescharacteristic
371C22×C11#54611yescharacteristic
372C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57711yescharacteristic
375C22×C11#57811yescharacteristic
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—41no—
383C4×C11—22no—
384C4×C11—42no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11C2×#11711yescharacteristic
389C4×C11#51811yescharacteristic
390C4×C11#55111yescharacteristic
391C4×C11#55111yescharacteristic
392Dic11—22no—
393Dic11—41no—
394Dic11—42no—
395Dic11—42no—
396Dic11—41no—
397Dic11—81no—
398Dic11—81no—
399C2×#41—114no—
400C2×#41—222no—
401C2×#41—222no—
402C2×#41—222no—
403C2×#41—441no—
404C2×#41—441no—
405C22×Q8—111no—
406C22×D4—221no—
407C22×D4C22×D1111yescharacteristic
408C23×C4—21no—
409C23×C4—111no—
410C23×C4—221no—
411C23×C4—221no—
412C23×C4—221no—
413C2×M16—114no—
414C2×M16—441no—
415C2×M16—441no—
416C22×C8—111no—
417C22×C8—111no—
418C22×C8C22×D1111yescharacteristic
419C22×C8C22×D1111yescharacteristic
420C4×D4—22no—
421C4×D4—41no—
422C4×D4—222no—
423C4×D4—441no—
424#117—444no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—111no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C42—111no—
443C2×C42—221no—
444C2×C42—221no—
445C2×C42C22×D1111yescharacteristic
446#107—41no—
447#106—441no—
448#103—114no—
449#103—114no—
450#103—441no—
451#103—441no—
452#102—22no—
453#102—114no—
454#102—222no—
455#102C4×D1114yes—
456C22⋊C8—222no—
457#97—441no—
458C4×C8—441no—
459#95—21no—
460#95—111no—
461#95—111no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471C2×C11—44no—
472C2×C11#234211yescharacteristic
473C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
474C2×C11#294711yescharacteristic
475C2×C11#330611yescharacteristic
476C2×C11#331511yescharacteristic
477C2×C11#332311yescharacteristic
478C2×C11#333011yescharacteristic
479D11—42no—
480C24—21no—
481C24—111no—
482#41—228no—
483#41—444no—
484#41—444no—
485#41—444no—
486C2×Q8—112no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—224no—
496C2×D4—442no—
497C2×D4—442no—
498C2×D4C2×C4×D1112yes—
499C2×D4#434112yes—
500C2×D4#434312yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—111no—
508C22×C4—112no—
509C22×C4—112no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—224no—
513C22×C4—224no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—442no—
523C22×C4—442no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4—881no—
529C22×C4D4×D1111yescharacteristic
530C22×C4D4×D1111yescharacteristic
531C22×C4C23×D1111yescharacteristic
532M16—444no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—112no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8C2×C4×D1112yes—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—112no—
552C4⋊C4—224no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—442no—
559C4⋊C4C2×C4×D1112yes—
560C22⋊C4—42no—
561C22⋊C4—222no—
562C22⋊C4—441no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—881no—
566C42—21no—
567C42—21no—
568C42—221no—
569C42—221no—
570C42—442no—
571C42—442no—
572C11#2258211yescharacteristic, complemented, Sylow
573C23—22no—
574C23—22no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—112no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23C2×D4×D1111yescharacteristic
588Q8—222no—
589Q8—222no—
590Q8—441no—
591Q8—441no—
592D4—22no—
593D4—22no—
594D4—22no—
595D4—448no—
596D4#6694514yescomplemented
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—112no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—448no—
628C2×C4—448no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—884no—
640C2×C4#6696412yes—
641C2×C4C22×C4×D1111yescharacteristic
642C2×C4C2×#434111yescharacteristic
643C2×C4#6703711yescharacteristic
644C2×C4C2×#434311yescharacteristic
645C2×C4#41×D1111yescharacteristic
646C2×C4#6704211yescharacteristic
647C8—22no—
648C8—41no—
649C8—222no—
650C8—441no—
651C22—24no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—222no—
659C22—222no—
660C22—222no—
661C22—441no—
662C22—441no—
663C22—441no—
664C22—441no—
665C22C4×D4×D1111yescharacteristic
666C22#1062312211yescharacteristic
667C22#1062316111yescharacteristic
668C22C2×#6696411yescharacteristic
669C22#1062329911yescharacteristic
670C22#1062330611yescharacteristic
671C22#1062331011yescharacteristic
672C4—22no—
673C4—41no—
674C4—42no—
675C4—81no—
676C4—81no—
677C4—222no—
678C4—441no—
679C4—442no—
680C4—442no—
681C4—441no—
682C4—881no—
683C4—881no—
684C4C2×#6694511yescharacteristic
685C4#1062307611yescharacteristic
686C4#1062316811yescharacteristic
687C4#1062318911yescharacteristic
688C2—44no—
689C2—442no—
690C2#1307146311yescharacteristic
691C2C4×#6696411yescharacteristic
692C2#1307745611yescharacteristic
693C2#1308058111yescharacteristic
694C2#1308071611yescharacteristic
695C2#1308082911yescharacteristic
696C2#1308091811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
cosocleC22×C4×C11C24
hypercenter#1862D11
hypocenterC11#22582
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #13071484C2semidirect
4. #13069307C2semidirect
5. #13069291C2semidirect
6. #13069256C2semidirect
7. #13069251C2semidirect
8. #13068879C2semidirect
9. #13068705C2semidirect
10. #13068650C2semidirect
12. #13068443C2semidirect
13. C4×#66896C2semidirect
14. #13068396C2semidirect
15. C11×#1862C2semidirect
49. #10622384C4semidirect
103. C2×#4313C2×C4semidirect
106. C4⋊C4×D11C2×C4semidirect
127. #66880C2×C4semidirect
130. #66874C2×C4semidirect
233. #1862D11semidirect
258. D4×C11#117semidirect
572. C11#22582semidirect
596. D4#66945semidirect

Maximal subgroups

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

subgroupindex
C2×#106223842
#130714842
#130714412
#130693072
#130692912
#130692562
#130692512
#130688792
#130687052
#130686502
#130685532
#130684432
C4×#668962
#130683962
C11×#18622
#2258211