Finite Group Databasebeta

← #14760437

Subgroups — #14760437

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622393C211yesmaximal, characteristic
2C2×C4×#4324C211yesmaximal, characteristic, complemented
3C2×#10622321C211yesmaximal, characteristic, complemented
4#13071303C211yesmaximal, characteristic
5#13071299C211yesmaximal, characteristic, complemented
6#13069498C211yesmaximal, characteristic, complemented
7#13069353C211yesmaximal, characteristic, complemented
8#13069301C211yesmaximal, characteristic, complemented
9#13069290C211yesmaximal, characteristic, complemented
10#13069041C211yesmaximal, characteristic
11#13069038C211yesmaximal, characteristic, complemented
12#13068648C211yesmaximal, characteristic, complemented
13C4×#66871C211yesmaximal, characteristic, complemented
14#13068447C211yesmaximal, characteristic, complemented
15C11×#1762C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C22×#4324C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×#66950C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622826—21no—
31#10622823—21no—
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C4×#4324—24no—
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622570—21no—
47#10622558—21no—
48#10622553—21no—
49C4×C4⋊Dic11C2211yescharacteristic
50#10622541—21no—
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622393C418yescomplemented
53#10622321—24no—
54#10622283—21no—
55#10622266—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×C22⋊D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80#66991—22no—
81#66991C2×C414yes—
82C2×#4324—22no—
83C2×#4324—22no—
84C2×#4324C2×C414yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4D411yescharacteristic
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C2×#4313—22no—
105C2×#4313—22no—
106C2×#4313C2×C414yescomplemented
107C2×C8×D11—22no—
108C2×C8×D11—22no—
109C2×C8×D11—22no—
110#66950—22no—
111#66950C2×C414yescomplemented
112#66925—22no—
113#66925—22no—
114C4×Dic22—22no—
115C4×Dic22—22no—
116C11×#102—22no—
117C11×#102C2×C414yes—
118C11×#97—22no—
119C11×#95—21no—
120#66896—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66880—22no—
129#66880C2×C414yescomplemented
130#66879—22no—
131C8×Dic11—22no—
132#66874—22no—
133#66872—22no—
134#66871—22no—
135#66871C2×C414yescomplemented
136C4×C11⋊C8D414yescomplemented
137#21535—111nomaximal, Sylow
138C24×C11—21no—
139C23×D11C2×D411yescharacteristic
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11C22×C412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—81no—
157C2×C22⋊D11—81no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11C22×C412yes—
170C2×C4×D11#4112yes—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22C22×C412yes—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11C22×C412yes—
182C2×C8×C11#4112yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C22×C412yes—
189C11×C22⋊C4—42no—
190C42×C11—81no—
191C42×C11C2×D412yes—
192C42×C11#4112yes—
193C22⋊Dic11—24no—
194C22⋊Dic11—81no—
195C22⋊Dic11—81no—
196#4324—28no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—81no—
201(C2×D11)⋊C4—81no—
202C4⋊Dic11—24no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—81no—
209C4⋊Dic11C22×C412yes—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—42no—
213Dic11⋊C4—81no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—42no—
217C4×Dic11—81no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C2×C11⋊C8C2×D412yes—
222C2×C11⋊C8C2×D412yes—
223C2×C11⋊C8#4112yes—
224#4313—28no—
225C8×D11—28no—
226C2×#468—111no—
227C2×C4×SD16—111no—
228C2×#405—111no—
229#2324—111no—
230#2323—111no—
231#1973—111no—
232#1943—111no—
233#1934—111no—
234#1933—111no—
235#1893—111no—
236#1892—111no—
237#1809—111no—
238C4×#107—111no—
239#1763—111no—
240#1762D1111yescharacteristic, complemented
241C23×C11—22no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C22×D411yescharacteristic
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11C4×D412yes—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—41no—
259D4×C11—41no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
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×C11#12112yes—
275C2×C4×C11#12112yes—
276C2×C4×C11C23×C411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C22⋊D11—84no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
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×Dic11C4×D412yes—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—22no—
308Dic22—22no—
309Dic22—22no—
310Dic22—41no—
311Dic22—41no—
312C8×C11—22no—
313C8×C11—22no—
314C11⋊C8—22no—
315C11⋊C8C4×D414yes—
316C22×SD16—111no—
317C22×M16—111no—
318C23×C8—111no—
319C2×C22⋊Q8—111no—
320C2×#121—111no—
321C2×C4×Q8—111no—
322C2×C4×D4C2×D1111yescharacteristic
323C2×#117—111no—
324#468—118no—
325C4×SD16—224no—
326C2×#107—111no—
327C2×#107—111no—
328C2×#106—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#102—111no—
333C2×#102C2×D1111yescharacteristic
334C2×#102C2×D1111yescharacteristic
335#405—224no—
336C2×#97—111no—
337C2×#97C2×D1111yescharacteristic
338C2×C4×C8—111no—
339C2×C4×C8—111no—
340#391—111no—
341#390—111no—
342#390—221no—
343#389—111no—
344#389—111no—
345#389—221no—
346#388—221no—
347#388—221no—
348#388—221no—
349#387—221no—
350#386—221no—
351#385—221no—
352#380—111no—
353#380—111no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4C2×D1111yescharacteristic
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340C2×D1111yescharacteristic
361#340C2×D1111yescharacteristic
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11C2×C4×D411yescharacteristic
370C22×C11C2×#12111yescharacteristic
371C22×C11#53211yescharacteristic
372C22×C11#57611yescharacteristic
373C22×C11#57711yescharacteristic
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—22no—
385C4×C11—42no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11C2×C4×D411yescharacteristic
389C4×C11C4×#4111yescharacteristic
390C4×C11#52511yescharacteristic
391C4×C11#52911yescharacteristic
392Dic11—22no—
393Dic11—42no—
394Dic11—41no—
395Dic11—41no—
396Dic11—42no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8—111no—
400C22×D4—221no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—21no—
403C23×C4—111no—
404C2×SD16—114no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×M16—114no—
408C2×M16—222no—
409C2×M16—222no—
410C22×C8—111no—
411C22×C8—111no—
412C22×C8—222no—
413C22×C8—222no—
414C22×C8—222no—
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417C22⋊Q8—114no—
418C22⋊Q8—222no—
419#121—114no—
420#121—222no—
421C4×Q8—222no—
422C4×Q8—222no—
423C4×D4—22no—
424C4×D4—22no—
425#117—222no—
426#117—222no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—111no—
441C2×C22⋊C4—111no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C42—21no—
449C2×C42—111no—
450C2×C42—221no—
451C2×C42—221no—
452C2×C42C22×D1111yescharacteristic
453#107—114no—
454#107—222no—
455#106—222no—
456#103—114no—
457#103—222no—
458#103—222no—
459#102—22no—
460#102—222no—
461#102C4×D1114yes—
462#97—22no—
463#97—222no—
464C4×C8—114no—
465C4×C8—222no—
466#95—21no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474C2×C11—82no—
475C2×C11C4×#12111yescharacteristic
476C2×C11#294611yescharacteristic
477C2×C11#294711yescharacteristic
478C2×C11#305711yescharacteristic
479C2×C11#306111yescharacteristic
480C2×C11#317811yescharacteristic
481C2×C11#317911yescharacteristic
482D11—42no—
483C24—21no—
484C24—111no—
485C2×Q8—112no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—224no—
497C2×D4—881no—
498C2×D4—881no—
499C2×D4C2×C4×D1112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—111no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4D4×D1111yescharacteristic
520C22×C4D4×D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522SD16—228no—
523M16—228no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—112no—
529C2×C8—112no—
530C2×C8—112no—
531C2×C8—112no—
532C2×C8—228no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8C2×C4×D1112yes—
536C2×C8#433912yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—112no—
543C4⋊C4—224no—
544C4⋊C4—222no—
545C4⋊C4—222no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—442no—
552C4⋊C4—881no—
553C4⋊C4—881no—
554C4⋊C4C2×C4×D1112yes—
555C22⋊C4—42no—
556C22⋊C4—224no—
557C22⋊C4—224no—
558C22⋊C4—222no—
559C22⋊C4—222no—
560C22⋊C4—881no—
561C22⋊C4—881no—
562C22⋊C4—881no—
563C22⋊C4—881no—
564C42—81no—
565C42—221no—
566C42—221no—
567C42—442no—
568C42—881no—
569C42#433912yes—
570C42D4×D1112yes—
571C11#2153511yescharacteristic, complemented, Sylow
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—112no—
580C23—221no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23C2×D4×D1111yescharacteristic
587Q8—222no—
588Q8—222no—
589Q8—441no—
590Q8—441no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—884no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—112no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4#6693712yes—
636C2×C4#6693712yes—
637C2×C4C22×C4×D1111yescharacteristic
638C2×C4C2×#433911yescharacteristic
639C2×C4C2×#433911yescharacteristic
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C8—22no—
644C8—22no—
645C8—114no—
646C8—222no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—222no—
655C22—222no—
656C22—222no—
657C22—441no—
658C22—441no—
659C22—441no—
660C22—441no—
661C22C2×#6693711yescharacteristic
662C22C4×D4×D1111yescharacteristic
663C22#1062307911yescharacteristic
664C22#1062330511yescharacteristic
665C22#1062330611yescharacteristic
666C22#1062330611yescharacteristic
667C22#1062331011yescharacteristic
668C4—22no—
669C4—22no—
670C4—42no—
671C4—81no—
672C4—81no—
673C4—222no—
674C4—441no—
675C4—442no—
676C4—442no—
677C4—441no—
678C4—881no—
679C4—881no—
680C4C4×#433911yescharacteristic
681C4#1062305911yescharacteristic
682C4C4×D4×D1111yescharacteristic
683C4#1062307811yescharacteristic
684C2—82no—
685C2—442no—
686C2C4×#6693711yescharacteristic
687C2#1307744511yescharacteristic
688C2#1307745611yescharacteristic
689C2#1307825411yescharacteristic
690C2#1307828511yescharacteristic
691C2#1307928211yescharacteristic
692C2#1307930511yescharacteristic
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#21535
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
2. C2×C4×#4324C2semidirect
3. C2×#10622321C2semidirect
5. #13071299C2semidirect
6. #13069498C2semidirect
7. #13069353C2semidirect
8. #13069301C2semidirect
9. #13069290C2semidirect
11. #13069038C2semidirect
12. #13068648C2semidirect
13. C4×#66871C2semidirect
14. #13068447C2semidirect
15. C11×#1762C2semidirect
52. #10622393C4semidirect
106. C2×#4313C2×C4semidirect
111. #66950C2×C4semidirect
129. #66880C2×C4semidirect
135. #66871C2×C4semidirect
136. C4×C11⋊C8D4semidirect
240. #1762D11semidirect
571. C11#21535semidirect

Maximal subgroups

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

subgroupindex
C2×#106223932
C2×C4×#43242
C2×#106223212
#130713032
#130712992
#130694982
#130693532
#130693012
#130692902
#130690412
#130690382
#130686482
C4×#668712
#130684472
C11×#17622
#2153511