Finite Group Databasebeta

← #14680449

Subgroups — #14680449

Order 2816.

1610 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
1C22×#66951C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic, complemented
3C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
4#13066868C212yesmaximal, complemented
5#13066867C212yesmaximal, complemented
6#13066860C212yesmaximal
7#13066860C212yesmaximal
8#13066854C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic
10#13066848C211yesmaximal, characteristic, complemented
11C11×#1436C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C2×#66951—24no—
26C2×#66951—24no—
27C2×#66951C418yescomplemented
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4×Dic11⋊C4—24no—
39#10622263—24no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C42×C11—22no—
55C2×C42×C11—42no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4C2×C414yes—
69C2×(C2×D11)⋊C4C2×C414yes—
70C2×(C2×D11)⋊C4C2×C414yes—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11C2×C414yes—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—24no—
80C2×Dic11⋊C4—42no—
81C2×Dic11⋊C4—42no—
82C2×Dic11⋊C4C2×C414yes—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—42no—
85C2×C4×Dic11C2×C414yes—
86C2×C4×Dic11D414yes—
87C2×C4×Dic11D414yes—
88#66951—232no—
89C11×#95—22no—
90C11×#95—24no—
91C11×#95—42no—
92C11⋊#95—22no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99#14291—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C23×D11—21no—
102C23×D11—21no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11C22×C412yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11#4114yes—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11C22×C412yes—
161C22×Dic11C22×C412yes—
162C22×Dic11C22×C412yes—
163C22×Dic11C2×D412yes—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×D412yes—
166C22×Dic11C2×D412yes—
167C22×Dic11#4114yes—
168C11×C4⋊C4—28no—
169C42×C11—44no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—48no—
174(C2×D11)⋊C4—48no—
175C4⋊Dic11—28no—
176Dic11⋊C4—216no—
177Dic11⋊C4—28no—
178Dic11⋊C4—48no—
179C4×Dic11—44no—
180C4×Dic11C22⋊C4116yescomplemented
181C22×#126—111no—
182C2×#382—111no—
183C2×C4×C4⋊C4—111no—
184#1441—112no—
185#1441—112no—
186#1439—112no—
187#1439—112no—
188#1437—111no—
189#1437—111no—
190#1436—111no—
191#1436D1111yescharacteristic, complemented
192C23×C11C23×C411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C22×D411yescharacteristic
195C23×C11C2×#4112yes—
196C23×C11C2×#4112yes—
197C23×C11H(5,𝔽2)12yes—
198C23×C11H(5,𝔽2)12yes—
199C23×C112−1+412yes—
200C23×C112−1+412yes—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11C2×C22⋊C414yes—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—42no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11C2×C22⋊C414yes—
279C2×Dic11C2×C22⋊C414yes—
280C2×#126—118no—
281C2×#126—224no—
282C2×#126—224no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—112no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4C2×D1111yescharacteristic
288C22×C22⋊C4—111no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C42—111no—
294C22×C42—111no—
295C22×C42C2×D1111yescharacteristic
296#382—224no—
297C4×C4⋊C4—224no—
298C2×#95—111no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95C2×D1111yescharacteristic
306C2×#95C2×D1112yes—
307C2×#95C2×D1112yes—
308C22×C11C22×C22⋊C411yescharacteristic
309C22×C11C4×#4111yescharacteristic
310C22×C11C4×#4111yescharacteristic
311C22×C11#52012yes—
312C22×C11#52012yes—
313C22×C11#52512yes—
314C22×C11#53212yes—
315C22×C11#53511yescharacteristic
316C22×C11#53511yescharacteristic
317C22×C11#53611yescharacteristic
318C22×C11#53611yescharacteristic
319C22×C11#53712yes—
320C22×C11#53712yes—
321C22×C11#53812yes—
322C22×C11#53812yes—
323C22×C11#53912yes—
324C22×C11#53912yes—
325C22×C11#54112yes—
326C22×C11#54112yes—
327C22×C11#54212yes—
328C22×C11#54212yes—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—42no—
334C2×D11—82no—
335C2×D11—82no—
336C2×D11—82no—
337C2×D11—82no—
338C4×C11—24no—
339C4×C11—42no—
340C4×C11—44no—
341C4×C11—42no—
342C4×C11—82no—
343Dic11—24no—
344Dic11—24no—
345Dic11—42no—
346Dic11—44no—
347Dic11—82no—
348C25—111no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—112no—
353C23×C4—112no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1112yes—
358C23×C4C22×D1111yescharacteristic
359#126—2232no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—224no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4—442no—
373C2×C4⋊C4—442no—
374C2×C4⋊C4C4×D1114yes—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—114no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—442no—
387C2×C22⋊C4—442no—
388C2×C22⋊C4—442no—
389C2×C22⋊C4—442no—
390C2×C42—22no—
391C2×C42—42no—
392C2×C42—114no—
393C2×C42—114no—
394C2×C42—114no—
395C2×C42—222no—
396C2×C42—442no—
397#95—24no—
398#95—22no—
399#95—42no—
400#95—224no—
401#95—224no—
402#95—224no—
403#95—222no—
404#95—442no—
405#95—442no—
406#95—442no—
407C2×C11#229711yescharacteristic
408C2×C11#231111yescharacteristic
409C2×C11#231111yescharacteristic
410C2×C11#233412yes—
411C2×C11#233412yes—
412C2×C11#263612yes—
413C2×C11#263712yes—
414C2×C11#266212yes—
415C2×C11#266412yes—
416D11—82no—
417C24—112no—
418C24—222no—
419C24—221no—
420C24—221no—
421C24—222no—
422C24—222no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24C23×D1111yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—112no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4C2×C4×D1112yes—
480C22×C4C2×C4×D1112yes—
481C22×C4C2×C4×D1112yes—
482C22×C4#433914yes—
483C22×C4D4×D1112yes—
484C22×C4D4×D1112yes—
485C4⋊C4—28no—
486C4⋊C4—228no—
487C4⋊C4—228no—
488C4⋊C4—2216no—
489C4⋊C4—448no—
490C22⋊C4—228no—
491C22⋊C4—228no—
492C22⋊C4—228no—
493C22⋊C4—448no—
494C22⋊C4—448no—
495C42—44no—
496C42—1116no—
497C42—444no—
498C11#1429111yescharacteristic, complemented, Sylow
499C23—222no—
500C23—222no—
501C23—222no—
502C23—224no—
503C23—224no—
504C23—442no—
505C23—441no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—441no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—441no—
517C23—442no—
518C23—441no—
519C23—442no—
520C23C22×C4×D1111yescharacteristic
521C23C2×#433912yes—
522C23C2×D4×D1111yescharacteristic
523C23C2×D4×D1111yescharacteristic
524C23#6703712yes—
525C23#6704012yes—
526C23#41×D1112yes—
527C23#6704212yes—
528C23#6704312yes—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—114no—
558C2×C4—114no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—441no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—441no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4C22⋊C4×D1114yes—
587C22—444no—
588C22—444no—
589C22—442no—
590C22—442no—
591C22—442no—
592C22—882no—
593C22—882no—
594C22—882no—
595C22—882no—
596C22C4×#433911yescharacteristic
597C22C2×C22⋊C4×D1111yescharacteristic
598C22#1062304612yes—
599C22#1062305311yescharacteristic
600C22#1062306512yes—
601C22#1062307712yes—
602C22#1062307812yes—
603C22#1062307912yes—
604C22#1062309112yes—
605C22#1062310512yes—
606C22#1062311412yes—
607C22#1062312311yescharacteristic
608C22#1062312812yes—
609C22#1062316012yes—
610C22#1062316912yes—
611C22#1062317911yescharacteristic
612C22#1062318812yes—
613C22#1062320511yescharacteristic
614C22#1062322712yes—
615C22#1062324112yes—
616C22#1062325511yescharacteristic
617C4—24no—
618C4—44no—
619C4—42no—
620C4—42no—
621C4—82no—
622C4—224no—
623C4—224no—
624C4—444no—
625C4—442no—
626C4—882no—
627C2—882no—
628C2#1307110211yescharacteristic
629C2#1307120311yescharacteristic
630C2#1307120711yescharacteristic
631C2#1307138512yes—
632C2#1307139712yes—
633C2#1307451912yes—
634C2#1307453012yes—
635C2#1307475912yes—
636C2#1307477912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14291
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622263C2semidirect
3. C2×C4×Dic11⋊C4C2semidirect
4. #13066868C2semidirect
5. #13066867C2semidirect
10. #13066848C2semidirect
11. C11×#1436C2semidirect
27. C2×#66951C4semidirect
180. C4×Dic11C22⋊C4semidirect
191. #1436D11semidirect
498. C11#14291semidirect

Maximal subgroups

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

subgroupindex
C22×#669512
C2×#106222632
C2×C4×Dic11⋊C42
#130668682
#130668672
#130668602
#130668542
#130668522
#130668482
C11×#14362
#1429111