Finite Group Databasebeta

← #14680425

Subgroups — #14680425

Order 2816.

1934 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic, complemented
3C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
4#13066886C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066859C212yesmaximal, complemented
7#13066855C212yesmaximal
8#13066854C211yesmaximal, characteristic, complemented
9#13066853C211yesmaximal, characteristic, complemented
10#13066852C211yesmaximal, characteristic, complemented
11C11×#1437C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×#66938—24no—
27C2×#66938—24no—
28C2×#66938C418yescomplemented
29C2×C11×#95C2211yescharacteristic
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#10622264—24no—
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—22no—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—42no—
49C22×C22⋊D11—42no—
50C22×C22⋊D11C2×C414yes—
51C23×Dic11C2312yes—
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—42no—
59C22×Dic22—42no—
60C22×Dic22C2×C414yes—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—42no—
65C2×C11×C22⋊C4—42no—
66C2×C11×C22⋊C4C2×C414yes—
67C2×C42×C11—22no—
68C2×C42×C11—42no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11C2×C414yes—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4C2×C414yes—
86C2×(C2×D11)⋊C4C2×C414yes—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—42no—
92C2×C4×Dic11C2×C414yes—
93C2×C4×Dic11D414yes—
94C2×C4×Dic11D414yes—
95#66938—232no—
96C11×#95—22no—
97C11×#95—42no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14288—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11C22×C412yes—
115C24×C11C2411yescharacteristic
116C23×D11—21no—
117C23×D11—21no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11C22×C412yes—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4114yes—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—44no—
152C2×C22⋊D11—48no—
153C2×C22⋊D11—44no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11C22×C412yes—
176C22×Dic11C22×C412yes—
177C22×Dic11C22×C412yes—
178C22×Dic11C2×D412yes—
179C22×Dic11C2×D412yes—
180C22×Dic11C2×D412yes—
181C22×Dic11C2×D412yes—
182C22×Dic11#4114yes—
183C2×Dic22—28no—
184C2×Dic22—48no—
185C2×Dic22—44no—
186C2×Dic22—48no—
187C2×Dic22—44no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—48no—
190C42×C11—44no—
191C22⋊Dic11—28no—
192C22⋊Dic11—48no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—48no—
196(C2×D11)⋊C4—48no—
197Dic11⋊C4—216no—
198C4×Dic11—44no—
199C4×Dic11C22⋊C4116yescomplemented
200C22×#124—111no—
201C2×#383—111no—
202C2×C4×C4⋊C4—111no—
203#1446—112no—
204#1439—112no—
205#1439—112no—
206#1438—112no—
207#1437—111no—
208#1437—111no—
209#1437—111no—
210#1437D1111yescharacteristic, complemented
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—41no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11C23×C411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C22×D411yescharacteristic
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11H(5,𝔽2)12yes—
238C23×C11H(5,𝔽2)12yes—
239C23×C11H(5,𝔽2)12yes—
240C23×C112−1+412yes—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—41no—
249C22×D11—42no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—42no—
259C22×D11—42no—
260C22×D11—42no—
261C22×D11—42no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—41no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11C2×C22⋊C414yes—
286C22⋊D11—416no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—22no—
293C2×Dic11—24no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—24no—
297C2×Dic11—24no—
298C2×Dic11—24no—
299C2×Dic11—24no—
300C2×Dic11—42no—
301C2×Dic11—41no—
302C2×Dic11—42no—
303C2×Dic11—41no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C2×Dic11—42no—
314C2×Dic11C2×C22⋊C414yes—
315C2×Dic11C2×C22⋊C414yes—
316Dic22—416no—
317C23×Q8—111no—
318C23×D4—111no—
319C2×#124—118no—
320C2×#124—224no—
321C2×#124—224no—
322C22×C4⋊C4—112no—
323C22×C22⋊C4—111no—
324C22×C22⋊C4—111no—
325C22×C22⋊C4—111no—
326C22×C22⋊C4—112no—
327C22×C22⋊C4—112no—
328C22×C22⋊C4—112no—
329C22×C22⋊C4C2×D1111yescharacteristic
330C22×C22⋊C4C2×D1112yes—
331C22×C42—111no—
332C22×C42—111no—
333C22×C42C2×D1111yescharacteristic
334#383—224no—
335C4×C4⋊C4—224no—
336C2×#95—111no—
337C2×#95—112no—
338C2×#95—112no—
339C2×#95—112no—
340C2×#95—112no—
341C2×#95—112no—
342C2×#95—112no—
343C2×#95C2×D1111yescharacteristic
344C2×#95C2×D1112yes—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—44no—
348C22×C11—44no—
349C22×C11—42no—
350C22×C11—82no—
351C22×C11—82no—
352C22×C11—82no—
353C22×C11—82no—
354C22×C11C22×C22⋊C411yescharacteristic
355C22×C11C4×#4111yescharacteristic
356C22×C11C4×#4111yescharacteristic
357C22×C11#51812yes—
358C22×C11#52012yes—
359C22×C11#52512yes—
360C22×C11#53212yes—
361C22×C11#53511yescharacteristic
362C22×C11#53511yescharacteristic
363C22×C11#53512yes—
364C22×C11#53511yescharacteristic
365C22×C11#53611yescharacteristic
366C22×C11#53712yes—
367C22×C11#53812yes—
368C22×C11#53812yes—
369C22×C11#53812yes—
370C22×C11#53812yes—
371C22×C11#54212yes—
372C22×C11#54212yes—
373C22×C11#54212yes—
374C22×C11#54212yes—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—44no—
378C2×D11—44no—
379C2×D11—42no—
380C2×D11—82no—
381C2×D11—82no—
382C2×D11—82no—
383C2×D11—82no—
384C4×C11—24no—
385C4×C11—42no—
386C4×C11—44no—
387C4×C11—82no—
388Dic11—24no—
389Dic11—24no—
390Dic11—42no—
391Dic11—44no—
392Dic11—82no—
393C25—111no—
394C25C22×D1111yescharacteristic
395C22×Q8—114no—
396C22×Q8—222no—
397C22×Q8—222no—
398C22×Q8—442no—
399C22×Q8—442no—
400C22×D4—114no—
401C22×D4—222no—
402C22×D4—222no—
403C22×D4—442no—
404C22×D4—442no—
405C23×C4—111no—
406C23×C4—111no—
407C23×C4—112no—
408C23×C4—111no—
409C23×C4—112no—
410C23×C4C22×D1112yes—
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414#124—2232no—
415C2×C4⋊C4—224no—
416C2×C4⋊C4—224no—
417C2×C4⋊C4—224no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—114no—
424C2×C22⋊C4—114no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—222no—
427C2×C22⋊C4—222no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—222no—
430C2×C22⋊C4—222no—
431C2×C22⋊C4—222no—
432C2×C22⋊C4—224no—
433C2×C22⋊C4—224no—
434C2×C22⋊C4—224no—
435C2×C22⋊C4—442no—
436C2×C22⋊C4—442no—
437C2×C22⋊C4—442no—
438C2×C22⋊C4—442no—
439C2×C22⋊C4—442no—
440C2×C22⋊C4—442no—
441C2×C22⋊C4C4×D1114yes—
442C2×C42—22no—
443C2×C42—42no—
444C2×C42—114no—
445C2×C42—114no—
446C2×C42—114no—
447C2×C42—222no—
448C2×C42—442no—
449#95—22no—
450#95—42no—
451#95—224no—
452#95—224no—
453#95—224no—
454#95—222no—
455#95—442no—
456#95—442no—
457#95—442no—
458C2×C11—82no—
459C2×C11#229711yescharacteristic
460C2×C11#230911yescharacteristic
461C2×C11#231111yescharacteristic
462C2×C11#233712yes—
463C2×C11#233712yes—
464C2×C11#263112yes—
465C2×C11#263212yes—
466C2×C11#266212yes—
467C2×C11#266212yes—
468D11—82no—
469C24—22no—
470C24—21no—
471C24—21no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—112no—
478C24—222no—
479C24—221no—
480C24—221no—
481C24—222no—
482C24—222no—
483C24—222no—
484C24—222no—
485C24—222no—
486C24C2×C4×D1112yes—
487C24C23×D1111yescharacteristic
488C2×Q8—228no—
489C2×Q8—448no—
490C2×Q8—444no—
491C2×Q8—448no—
492C2×Q8—444no—
493C2×D4—228no—
494C2×D4—448no—
495C2×D4—444no—
496C2×D4—448no—
497C2×D4—444no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—112no—
518C22×C4—112no—
519C22×C4—112no—
520C22×C4—112no—
521C22×C4—112no—
522C22×C4—112no—
523C22×C4—112no—
524C22×C4—114no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—222no—
542C22×C4—222no—
543C22×C4—222no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4C2×C4×D1112yes—
547C22×C4C2×C4×D1112yes—
548C22×C4#433914yes—
549C22×C4D4×D1112yes—
550C22×C4D4×D1112yes—
551C4⋊C4—2216no—
552C22⋊C4—28no—
553C22⋊C4—48no—
554C22⋊C4—228no—
555C22⋊C4—228no—
556C22⋊C4—228no—
557C22⋊C4—448no—
558C22⋊C4—448no—
559C22⋊C4—448no—
560C42—44no—
561C42—1116no—
562C42—444no—
563C11#1428811yescharacteristic, complemented, Sylow
564C23—22no—
565C23—22no—
566C23—22no—
567C23—24no—
568C23—24no—
569C23—42no—
570C23—41no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—41no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—41no—
582C23—42no—
583C23—42no—
584C23—41no—
585C23—222no—
586C23—222no—
587C23—222no—
588C23—224no—
589C23—224no—
590C23—442no—
591C23—441no—
592C23—442no—
593C23—442no—
594C23—442no—
595C23—442no—
596C23—442no—
597C23—442no—
598C23—441no—
599C23—442no—
600C23—442no—
601C23—442no—
602C23—441no—
603C23—442no—
604C23—442no—
605C23—441no—
606C23C22×C4×D1111yescharacteristic
607C23C2×#433912yes—
608C23C2×D4×D1111yescharacteristic
609C23C2×D4×D1111yescharacteristic
610C23#6703712yes—
611C23#6703712yes—
612C23#41×D1112yes—
613C23#6704212yes—
614C23#6704312yes—
615Q8—4416no—
616D4—4416no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—114no—
641C2×C4—114no—
642C2×C4—222no—
643C2×C4—222no—
644C2×C4—222no—
645C2×C4—224no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—224no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—224no—
652C2×C4—224no—
653C2×C4—224no—
654C2×C4—224no—
655C2×C4—441no—
656C2×C4—442no—
657C2×C4—442no—
658C2×C4—442no—
659C2×C4—442no—
660C2×C4—442no—
661C2×C4—441no—
662C2×C4—442no—
663C2×C4—442no—
664C2×C4—442no—
665C2×C4—442no—
666C2×C4—442no—
667C2×C4—442no—
668C2×C4—442no—
669C2×C4C22⋊C4×D1114yes—
670C22—44no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—82no—
676C22—82no—
677C22—82no—
678C22—82no—
679C22—444no—
680C22—444no—
681C22—442no—
682C22—442no—
683C22—442no—
684C22—882no—
685C22—882no—
686C22—882no—
687C22—882no—
688C22C4×#433911yescharacteristic
689C22C2×C22⋊C4×D1111yescharacteristic
690C22#1062302512yes—
691C22#1062305311yescharacteristic
692C22#1062306512yes—
693C22#1062307612yes—
694C22#1062307712yes—
695C22#1062307812yes—
696C22#1062307912yes—
697C22#1062309112yes—
698C22#1062309212yes—
699C22#1062312311yescharacteristic
700C22#1062312812yes—
701C22#1062313812yes—
702C22#1062314412yes—
703C22#1062317911yescharacteristic
704C22#1062318812yes—
705C22#1062320012yes—
706C22#1062320511yescharacteristic
707C22#1062324112yes—
708C22#1062324611yescharacteristic
709C4—24no—
710C4—44no—
711C4—42no—
712C4—82no—
713C4—224no—
714C4—224no—
715C4—444no—
716C4—442no—
717C4—882no—
718C2—82no—
719C2—882no—
720C2#1307110211yescharacteristic
721C2#1307119511yescharacteristic
722C2#1307120311yescharacteristic
723C2#1307142412yes—
724C2#1307142712yes—
725C2#1307447212yes—
726C2#1307448012yes—
727C2#1307475712yes—
728C2#1307475912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1437D11
hypocenterC11#14288
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#10622264C2semidirect
3. C2×C4×Dic11⋊C4C2semidirect
4. #13066886C2semidirect
5. #13066860C2semidirect
6. #13066859C2semidirect
8. #13066854C2semidirect
9. #13066853C2semidirect
10. #13066852C2semidirect
11. C11×#1437C2semidirect
28. C2×#66938C4semidirect
199. C4×Dic11C22⋊C4semidirect
210. #1437D11semidirect
563. C11#14288semidirect

Maximal subgroups

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

subgroupindex
C22×#669382
C2×#106222642
C2×C4×Dic11⋊C42
#130668862
#130668602
#130668592
#130668552
#130668542
#130668532
#130668522
C11×#14372
#1428811