Finite Group Databasebeta

← #14684446

Subgroups — #14684446

Order 2816.

1586 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622834C211yesmaximal, characteristic
2C2×#10622594C211yesmaximal, characteristic, complemented
3#13066881C211yesmaximal, characteristic, complemented
4#13066869C211yesmaximal, characteristic, complemented
5#13066865C212yesmaximal, complemented
6#13066861C212yesmaximal, complemented
7#13066861C212yesmaximal, complemented
8#13066861C212yesmaximal, complemented
9#13066857C211yesmaximal, characteristic
10#13066841C211yesmaximal, characteristic, complemented
11C2×C11×#394C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C11×#394C418yescomplemented
25C2×C11×#95C2211yescharacteristic
26#10622834—24no—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622594—24no—
38C25×C11C2312yes—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—42no—
42C22×D4×C11—42no—
43C22×D4×C11C2×C414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2311yescharacteristic
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—42no—
59C2×C11×C22⋊C4—42no—
60C2×C11×C22⋊C4—42no—
61C2×C11×C22⋊C4C2×C418yes—
62C2×C11×C22⋊C4C2×C418yes—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—42no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11—42no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11—42no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—42no—
78C2×C4⋊Dic11—42no—
79C2×C4⋊Dic11—42no—
80C2×C4⋊Dic11—42no—
81C2×C4⋊Dic11—42no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11D414yes—
84C11×#95C2×C414yes—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93C11⋊#95—42no—
94C11⋊#95—42no—
95#14624—111nomaximal, Sylow
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C22×C414yes—
111C24×C11C2411yescharacteristic
112C2×D4×C11—28no—
113C2×D4×C11—48no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—48no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
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—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—21no—
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×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11C2×D412yes—
174C22×Dic11C2×D412yes—
175C11×C4⋊C4—28no—
176C11×C22⋊C4—48no—
177C11×C22⋊C4—48no—
178C22⋊Dic11—48no—
179C22⋊Dic11—48no—
180C22⋊Dic11—48no—
181C22⋊Dic11—48no—
182C4⋊Dic11—44no—
183C4⋊Dic11—44no—
184C4⋊Dic11—48no—
185C4×Dic11—44no—
186C2×#394D1111yescharacteristic
187C2×#390—111no—
188C2×#387—111no—
189#1444—111no—
190#1441—111no—
191#1440—112no—
192#1439—112no—
193#1439—112no—
194#1439—112no—
195#1438—111no—
196#1434—111no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
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×C11C2×#4111yescharacteristic
235C23×C11H(5,𝔽2)12yes—
236C23×C11H(5,𝔽2)12yes—
237C23×C11H(5,𝔽2)11yescharacteristic
238C23×C11H(5,𝔽2)11yescharacteristic
239C23×C11H(5,𝔽2)11yescharacteristic
240C23×C11H(5,𝔽2)12yes—
241C23×C112−1+412yes—
242C23×C112−1+411yescharacteristic
243D4×C11—416no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11C4×D414yes—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—41no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302C23×D4C2×D1111yescharacteristic
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—112no—
306C22×C4⋊C4C2×D1111yescharacteristic
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4C2×D1112yes—
312C22×C22⋊C4C2×D1112yes—
313C22×C42—111no—
314#394Dic1118yescomplemented
315#390—224no—
316#387—224no—
317C2×#95—111no—
318C2×#95—111no—
319C2×#95—111no—
320C2×#95—111no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95C2×D1111yescharacteristic
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—82no—
336C22×C11—82no—
337C22×C11—82no—
338C22×C11—82no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11—82no—
343C22×C11C2×C4×D411yescharacteristic
344C22×C11#51812yes—
345C22×C11#51811yescharacteristic
346C22×C11#52011yescharacteristic
347C22×C11#52012yes—
348C22×C11#53411yescharacteristic
349C22×C11#53511yescharacteristic
350C22×C11#53511yescharacteristic
351C22×C11#53511yescharacteristic
352C22×C11#53611yescharacteristic
353C22×C11#53711yescharacteristic
354C22×C11#53812yes—
355C22×C11#54011yescharacteristic
356C22×C11#54211yescharacteristic
357C22×C11#54212yes—
358C22×C11#56012yes—
359C22×C11#56012yes—
360C22×C11#56012yes—
361C22×C11#56212yes—
362C22×C11#56212yes—
363C22×C11#56212yes—
364C22×C11#56212yes—
365C22×C11#56312yes—
366C4×C11—24no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—44no—
370Dic11—42no—
371Dic11—42no—
372Dic11—82no—
373Dic11—81no—
374Dic11—82no—
375Dic11—81no—
376C25C22×D1112yes—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4C2×Dic1114yes—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—112no—
386C23×C4—111no—
387C23×C4—112no—
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1112yes—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—442no—
397C2×C4⋊C4—442no—
398C2×C4⋊C4—442no—
399C2×C4⋊C4—442no—
400C2×C4⋊C4—442no—
401C2×C4⋊C4C2×Dic1114yes—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4—442no—
409C2×C22⋊C4—442no—
410C2×C22⋊C4—442no—
411C2×C22⋊C4—442no—
412C2×C22⋊C4—442no—
413C2×C22⋊C4—442no—
414C2×C22⋊C4—442no—
415C2×C22⋊C4—442no—
416C2×C22⋊C4—442no—
417C2×C22⋊C4—442no—
418C2×C22⋊C4C2×Dic1118yes—
419C2×C22⋊C4C2×Dic1118yes—
420C2×C42—114no—
421C2×C42—442no—
422#95—222no—
423#95—222no—
424#95—222no—
425#95—222no—
426#95—222no—
427#95—442no—
428#95—442no—
429#95—442no—
430#95—442no—
431#95—442no—
432#95C2×Dic1114yes—
433C2×C11—84no—
434C2×C11#232111yescharacteristic
435C2×C11#232411yescharacteristic
436C2×C11#232611yescharacteristic
437C2×C11#237612yes—
438C2×C11#237712yes—
439C2×C11#281311yescharacteristic
440C2×C11#281611yescharacteristic
441C2×C11#281811yescharacteristic
442C2×C11#282011yescharacteristic
443C2×C11#282912yes—
444C2×C11#283012yes—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C22×Dic1114yes—
460C24C23×D1111yescharacteristic
461C2×D4—28no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—48no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—221no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—221no—
493C22×C4—222no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—221no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—221no—
517C22×C4—222no—
518C22×C4D4×D1112yes—
519C22×C4#434112yes—
520C22×C4C22×Dic1114yes—
521C22×C4C22×Dic1112yes—
522C22×C4C22×Dic1112yes—
523C22×C4C22×Dic1112yes—
524C4⋊C4—28no—
525C4⋊C4—444no—
526C4⋊C4—444no—
527C4⋊C4—448no—
528C22⋊C4—48no—
529C22⋊C4—48no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C22⋊C4—448no—
534C42—444no—
535C11#1462411yescharacteristic, complemented, Sylow
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23C2×D4×D1111yescharacteristic
572C23C2×#434111yescharacteristic
573C23#6703712yes—
574C23#6703712yes—
575C23#6703711yescharacteristic
576C23#6703711yescharacteristic
577C23#6704211yescharacteristic
578C23#6704212yes—
579C23#6704311yescharacteristic
580C23#6704312yes—
581C23C23×Dic1111yescharacteristic
582D4—416no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—441no—
617C2×C4—442no—
618C2×C4—441no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—442no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—442no—
640C2×C4D4×Dic1114yes—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22—44no—
648C22—82no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—82no—
653C22—82no—
654C22—82no—
655C22—82no—
656C22#1062312011yescharacteristic
657C22#1062312311yescharacteristic
658C22#1062312412yes—
659C22#1062313411yescharacteristic
660C22#1062313811yescharacteristic
661C22#1062313911yescharacteristic
662C22#1062315011yescharacteristic
663C22#1062315112yes—
664C22#1062315112yes—
665C22#1062315212yes—
666C22#1062315212yes—
667C22#1062318212yes—
668C22#1062319712yes—
669C22#1062319812yes—
670C22#1062319812yes—
671C22#1062320511yescharacteristic
672C22#1062320611yescharacteristic
673C22#1062321312yes—
674C22C2×D4×Dic1111yescharacteristic
675C22#1062332912yes—
676C22#1062332911yescharacteristic
677C22#1062335811yescharacteristic
678C22#1062335812yes—
679C4—24no—
680C4—44no—
681C4—42no—
682C4—42no—
683C4—442no—
684C4—442no—
685C4—882no—
686C4—881no—
687C4—882no—
688C4—881no—
689C2—84no—
690C2#1307127711yescharacteristic
691C2#1307131111yescharacteristic
692C2#1307132911yescharacteristic
693C2#1307176412yes—
694C2#1307177312yes—
695C2#1307661711yescharacteristic
696C2#1307664711yescharacteristic
697C2#1307665811yescharacteristic
698C2#1307666911yescharacteristic
699C2#1307675212yes—
700C2#1307676212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#394C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11#14624
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×#10622594C2semidirect
3. #13066881C2semidirect
4. #13066869C2semidirect
5. #13066865C2semidirect
6. #13066861C2semidirect
7. #13066861C2semidirect
8. #13066861C2semidirect
10. #13066841C2semidirect
24. C11×#394C4semidirect
314. #394Dic11semidirect
535. C11#14624semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225942
#130668812
#130668692
#130668652
#130668612
#130668572
#130668412
C2×C11×#3942
#1462411