Finite Group Databasebeta

← #14675643

Subgroups — #14675643

Order 2816.

7150 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Dic11C211yesmaximal, characteristic, complemented
2C2×#10622833C214yesmaximal, complemented
3C2×#10622860C211yesmaximal, characteristic, complemented
4C2×#10622860C212yesmaximal, complemented
5#13066857C214yesmaximal, complemented
6#13066839C212yesmaximal, complemented
7C24×D4×C11C211yesmaximal, characteristic
8C26×C11C2211yescharacteristic
9C26×C11C2211yescharacteristic
10C23×D4×C11—24no—
11C23×D4×C11—24no—
12C23×D4×C11—216no—
13C23×D4×C11C418yescomplemented
14C23×D4×C11C2212yes—
15C23×D4×C11C2212yes—
16C24×C4×C11C2211yescharacteristic
17C24×Dic11C2212yescomplemented
18C22×C22⋊Dic11—24no—
19C22×C22⋊Dic11—28no—
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yescomplemented
23C22×C22⋊Dic11C2212yescomplemented
24C22×C22⋊Dic11C2218yescomplemented
25C22×C22⋊Dic11C2212yescomplemented
26#10622860—24no—
27#10622860—28no—
28#10622833—216no—
29C2×C11⋊#95C2218yescomplemented
30C25×C11—24no—
31C25×C11—28no—
32C25×C11—28no—
33C25×C11—22no—
34C25×C11—22no—
35C25×C11—24no—
36C25×C11—24no—
37C25×C11—24no—
38C25×C11—44no—
39C25×C11—44no—
40C25×C11C2×C414yes—
41C25×C11C2×C414yescomplemented
42C25×C11D414yes—
43C25×C11D414yes—
44C25×C11C2311yescharacteristic
45C25×C11C2312yes—
46C25×C11C2311yescharacteristic
47C25×C11C2311yescharacteristic
48C22×D4×C11—264no—
49C22×D4×C11—264no—
50C22×D4×C11—232no—
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11—28no—
54C22×D4×C11—24no—
55C22×D4×C11—28no—
56C22×D4×C11—24no—
57C22×D4×C11—264no—
58C22×D4×C11—28no—
59C22×D4×C11C2×C418yes—
60C22×D4×C11C2×C418yescomplemented
61C22×D4×C11D4116yes—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—28no—
65C23×C4×C11C2×C414yescomplemented
66C23×C4×C11C2312yes—
67C23×Dic11—24no—
68C23×Dic11—28no—
69C23×Dic11—28no—
70C23×Dic11—44no—
71C23×Dic11C2314yes—
72C23×Dic11C2314yes—
73C2×C22⋊Dic11—232no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11—216no—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—216no—
86C2×C22⋊Dic11—48no—
87C2×C22⋊Dic11—44no—
88C2×C22⋊Dic11D418yescomplemented
89C11⋊#95—216no—
90#13867—111nomaximal, Sylow
91C24×C11—22no—
92C24×C11—24no—
93C24×C11—22no—
94C24×C11—24no—
95C24×C11—24no—
96C24×C11—216no—
97C24×C11—216no—
98C24×C11—216no—
99C24×C11—28no—
100C24×C11—216no—
101C24×C11—216no—
102C24×C11—28no—
103C24×C11—216no—
104C24×C11—216no—
105C24×C11—216no—
106C24×C11—28no—
107C24×C11—22no—
108C24×C11—24no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—22no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—28no—
117C24×C11—216no—
118C24×C11—48no—
119C24×C11—48no—
120C24×C11—48no—
121C24×C11—48no—
122C24×C11—432no—
123C24×C11—432no—
124C24×C11—432no—
125C24×C11—432no—
126C24×C11—48no—
127C24×C11—48no—
128C24×C11—44no—
129C24×C11—48no—
130C24×C11—44no—
131C24×C11C22⋊C4116yescomplemented
132C24×C11C22×C412yes—
133C24×C11C22×C414yes—
134C24×C11C22×C412yes—
135C24×C11C22×C412yes—
136C24×C11C2×D412yes—
137C24×C11C2×D412yes—
138C24×C11C2×D418yes—
139C24×C11C2×D412yes—
140C24×C11C2×D418yes—
141C24×C11C2×D412yes—
142C24×C11C2×D412yes—
143C24×C11C2×D412yes—
144C24×C11C2×D414yes—
145C24×C11#4114yes—
146C24×C11C2411yescharacteristic
147C2×D4×C11—2256no—
148C2×D4×C11—232no—
149C2×D4×C11—232no—
150C2×D4×C11—216no—
151C2×D4×C11—216no—
152C2×D4×C11—216no—
153C2×D4×C11—216no—
154C2×D4×C11—232no—
155C2×D4×C11—232no—
156C2×D4×C11—216no—
157C2×D4×C11C22⋊C4132yescomplemented
158C22×C4×C11—216no—
159C22×C4×C11—216no—
160C22×C4×C11—28no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—24no—
164C22×C4×C11—216no—
165C22×C4×C11C22×C414yes—
166C22×C4×C11C2×D418yes—
167C22×Dic11—216no—
168C22×Dic11—28no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—28no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—28no—
176C22×Dic11—28no—
177C22×Dic11—432no—
178C22×Dic11—48no—
179C22×Dic11—48no—
180C22×Dic11C2×D418yescomplemented
181C22⋊Dic11—216no—
182C22⋊Dic11—216no—
183C22⋊Dic11—432no—
184C22⋊Dic11—48no—
185C22⋊Dic11—48no—
186C22⋊Dic11—48no—
187C24×D4D1111yescharacteristic
188C23×C22⋊C4—111no—
189C2×#386—114no—
190C2×#379—112no—
191C2×#379—111no—
192#1438—114no—
193C22⋊#95—112no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—22no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—216no—
208C23×C11—216no—
209C23×C11—216no—
210C23×C11—216no—
211C23×C11—232no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—28no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—28no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—28no—
223C23×C11—28no—
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—216no—
229C23×C11—216no—
230C23×C11—232no—
231C23×C11—232no—
232C23×C11—416no—
233C23×C11—464no—
234C23×C11—464no—
235C23×C11—432no—
236C23×C11—432no—
237C23×C11—464no—
238C23×C11—416no—
239C23×C11—432no—
240C23×C11—432no—
241C23×C11—464no—
242C23×C11—42no—
243C23×C11—44no—
244C23×C11—42no—
245C23×C11—44no—
246C23×C11—44no—
247C23×C11—48no—
248C23×C11—48no—
249C23×C11—48no—
250C23×C11—48no—
251C23×C11—416no—
252C23×C11C2×C22⋊C414yes—
253C23×C11C2×C22⋊C414yes—
254C23×C11C2×C22⋊C418yes—
255C23×C11C2×C22⋊C414yes—
256C23×C11C2×C22⋊C418yescomplemented
257C23×C11C4×D418yes—
258C23×C11#12014yes—
259C23×C11#12018yes—
260C23×C11#12018yes—
261C23×C11#12118yes—
262C23×C11#12314yes—
263C23×C11C23×C411yescharacteristic
264C23×C11C22×D412yes—
265C23×C11C22×D411yescharacteristic
266C23×C11C22×D411yescharacteristic
267C23×C11C22×D414yes—
268C23×C11C2×#4112yes—
269C23×C11H(5,𝔽2)14yes—
270D4×C11—264no—
271D4×C11—264no—
272C2×C4×C11—232no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—28no—
276C2×C4×C11—28no—
277C2×C4×C11C2×C22⋊C418yescomplemented
278C2×Dic11—28no—
279C2×Dic11—216no—
280C2×Dic11—432no—
281C2×Dic11—44no—
282C2×Dic11—44no—
283C2×Dic11—48no—
284C2×Dic11—44no—
285C2×Dic11—44no—
286C2×Dic11—44no—
287C2×Dic11—48no—
288C2×Dic11—48no—
289C26C2×D1111yescharacteristic
290C26C2×D1111yescharacteristic
291C23×D4—24no—
292C23×D4—24no—
293C23×D4—216no—
294C23×D4Dic1118yescomplemented
295C23×D4C2×D1112yes—
296C23×D4C2×D1112yes—
297C24×C4—112no—
298C24×C4C2×D1111yescharacteristic
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4—112no—
302C22×C22⋊C4—112no—
303C22×C22⋊C4—118no—
304C22×C22⋊C4—112no—
305C22×C22⋊C4—228no—
306C22×C22⋊C4—224no—
307#386—2216no—
308#379—228no—
309#379—224no—
310C2×#95—118no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—216no—
314C22×C11—216no—
315C22×C11—28no—
316C22×C11—28no—
317C22×C11—28no—
318C22×C11—28no—
319C22×C11—216no—
320C22×C11—216no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—24no—
324C22×C11—216no—
325C22×C11—24no—
326C22×C11—28no—
327C22×C11—24no—
328C22×C11—464no—
329C22×C11—464no—
330C22×C11—44no—
331C22×C11—48no—
332C22×C11—48no—
333C22×C11—44no—
334C22×C11—48no—
335C22×C11—44no—
336C22×C11—48no—
337C22×C11—48no—
338C22×C11—416no—
339C22×C11—44no—
340C22×C11#37918yescomplemented
341C22×C11#38618yescomplemented
342C22×C11C22×C22⋊C411yescharacteristic
343C22×C11C22×C22⋊C412yes—
344C22×C11C2×C4×D412yes—
345C22×C11#51812yes—
346C22×C11C2×#12011yescharacteristic
347C22×C11C2×#12012yes—
348C22×C11C2×#12012yes—
349C22×C11C2×#12112yes—
350C22×C11C2×#12311yescharacteristic
351C22×C11#53412yes—
352C22×C11#53412yes—
353C22×C11D4218yes—
354C22×C11#54618yes—
355C4×C11—28no—
356Dic11—48no—
357Dic11—84no—
358C25—24no—
359C25—24no—
360C25—28no—
361C25—28no—
362C25—22no—
363C25—22no—
364C25—24no—
365C25—24no—
366C25—44no—
367C25—44no—
368C25C2×Dic1114yes—
369C25C2×Dic1114yescomplemented
370C25C22⋊D1114yes—
371C25C22⋊D1114yes—
372C25C22×D1111yescharacteristic
373C25C22×D1112yes—
374C25C22×D1111yescharacteristic
375C25C22×D1111yescharacteristic
376C22×D4—264no—
377C22×D4—264no—
378C22×D4—232no—
379C22×D4—24no—
380C22×D4—24no—
381C22×D4—28no—
382C22×D4—24no—
383C22×D4—28no—
384C22×D4—24no—
385C22×D4—264no—
386C22×D4—28no—
387C22×D4C2×Dic1118yes—
388C22×D4C2×Dic1118yescomplemented
389C22×D4C22⋊D11116yes—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—28no—
393C23×C4—114no—
394C23×C4—114no—
395C23×C4—228no—
396C23×C4—224no—
397C23×C4—228no—
398C23×C4—444no—
399C23×C4C2×Dic1114yescomplemented
400C23×C4C22×D1112yes—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—228no—
403C2×C22⋊C4—2232no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—2216no—
408C2×C22⋊C4—224no—
409C2×C22⋊C4—224no—
410C2×C22⋊C4—224no—
411C2×C22⋊C4—224no—
412C2×C22⋊C4—224no—
413C2×C22⋊C4—2216no—
414C2×C22⋊C4—228no—
415C2×C22⋊C4—448no—
416C2×C22⋊C4—444no—
417#95—2216no—
418C2×C11—28no—
419C2×C11—28no—
420C2×C11—44no—
421C2×C11—48no—
422C2×C11C2×#37911yescharacteristic
423C2×C11C2×#38611yescharacteristic
424C2×C11#230811yescharacteristic
425C2×C11D4×C22⋊C414yes—
426C2×C11#240312yes—
427C2×C11#240512yes—
428C2×C11#241014yes—
429C24—22no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—216no—
435C24—216no—
436C24—216no—
437C24—28no—
438C24—28no—
439C24—216no—
440C24—216no—
441C24—28no—
442C24—216no—
443C24—216no—
444C24—216no—
445C24—22no—
446C24—24no—
447C24—22no—
448C24—24no—
449C24—28no—
450C24—24no—
451C24—22no—
452C24—24no—
453C24—24no—
454C24—22no—
455C24—216no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—48no—
460C24—432no—
461C24—432no—
462C24—432no—
463C24—432no—
464C24—48no—
465C24—48no—
466C24—44no—
467C24—44no—
468C24—48no—
469C24C22⋊Dic11116yescomplemented
470C24D4×D1114yes—
471C24#434114yes—
472C24C22×Dic1112yes—
473C24C22×Dic1114yes—
474C24C22×Dic1112yes—
475C24C22×Dic1112yes—
476C24C2×C22⋊D1112yes—
477C24C2×C22⋊D1112yes—
478C24C2×C22⋊D1118yes—
479C24C2×C22⋊D1112yes—
480C24C2×C22⋊D1112yes—
481C24C2×C22⋊D1112yes—
482C24C2×C22⋊D1118yes—
483C24C2×C22⋊D1112yes—
484C24C23×D1111yescharacteristic
485C2×D4—2256no—
486C2×D4—232no—
487C2×D4—232no—
488C2×D4—216no—
489C2×D4—216no—
490C2×D4—216no—
491C2×D4—216no—
492C2×D4—232no—
493C2×D4—232no—
494C2×D4—216no—
495C2×D4C22⋊Dic11132yescomplemented
496C22×C4—216no—
497C22×C4—216no—
498C22×C4—28no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—216no—
503C22×C4—118no—
504C22×C4—2216no—
505C22×C4—224no—
506C22×C4—228no—
507C22×C4—228no—
508C22×C4—224no—
509C22×C4—224no—
510C22×C4—224no—
511C22×C4—228no—
512C22×C4—228no—
513C22×C4—224no—
514C22×C4—4432no—
515C22×C4—448no—
516C22×C4—448no—
517C22×C4C22×Dic1114yes—
518C22×C4C2×C22⋊D1118yes—
519C22⋊C4—2216no—
520C22⋊C4—2216no—
521C22⋊C4—4432no—
522C22⋊C4—448no—
523C22⋊C4—448no—
524C22⋊C4—448no—
525C11#1386711yescharacteristic, complemented, Sylow
526C23—24no—
527C23—22no—
528C23—24no—
529C23—24no—
530C23—22no—
531C23—216no—
532C23—216no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—216no—
539C23—216no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—232no—
544C23—28no—
545C23—24no—
546C23—22no—
547C23—28no—
548C23—24no—
549C23—22no—
550C23—216no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—216no—
555C23—232no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—28no—
562C23—28no—
563C23—232no—
564C23—416no—
565C23—432no—
566C23—432no—
567C23—464no—
568C23—464no—
569C23—464no—
570C23—432no—
571C23—432no—
572C23—416no—
573C23—464no—
574C23—42no—
575C23—42no—
576C23—48no—
577C23—48no—
578C23—44no—
579C23—44no—
580C23—44no—
581C23—48no—
582C23—48no—
583C23—416no—
584C23D4×Dic1118yes—
585C23#6698814yes—
586C23#6699014yes—
587C23#6699218yes—
588C23C2×C22⋊Dic1114yes—
589C23C2×C22⋊Dic1114yes—
590C23C2×C22⋊Dic1114yes—
591C23C2×C22⋊Dic1118yes—
592C23C2×C22⋊Dic1118yescomplemented
593C23#6700618yes—
594C23#6700618yes—
595C23C2×D4×D1112yes—
596C23C2×#434112yes—
597C23#6703714yes—
598C23C23×Dic1111yescharacteristic
599C23C22×C22⋊D1111yescharacteristic
600C23C22×C22⋊D1114yes—
601C23C22×C22⋊D1111yescharacteristic
602D4—264no—
603D4—264no—
604C2×C4—232no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—28no—
608C2×C4—28no—
609C2×C4—228no—
610C2×C4—2216no—
611C2×C4—4432no—
612C2×C4—448no—
613C2×C4—444no—
614C2×C4—444no—
615C2×C4—448no—
616C2×C4—444no—
617C2×C4—444no—
618C2×C4—448no—
619C2×C4—444no—
620C2×C4C2×C22⋊Dic1118yescomplemented
621C22—28no—
622C22—28no—
623C22—28no—
624C22—28no—
625C22—216no—
626C22—216no—
627C22—24no—
628C22—24no—
629C22—216no—
630C22—216no—
631C22—24no—
632C22—24no—
633C22—216no—
634C22—24no—
635C22—24no—
636C22—28no—
637C22—24no—
638C22—464no—
639C22—464no—
640C22—44no—
641C22—48no—
642C22—44no—
643C22—48no—
644C22—48no—
645C22—48no—
646C22—44no—
647C22—416no—
648C22—48no—
649C22—44no—
650C22#1062283318yescomplemented
651C22#1062286018yescomplemented
652C22C2×D4×Dic1112yes—
653C22C2×#6698811yescharacteristic
654C22#1062332912yes—
655C22C2×#6699011yescharacteristic
656C22D4×C22⋊D1118yes—
657C22C2×#6699212yes—
658C22#1062333512yes—
659C22#1062333512yes—
660C22#1062333718yes—
661C22C22×C22⋊Dic1112yes—
662C22C22×C22⋊Dic1111yescharacteristic
663C22C2×#6700612yes—
664C22C2×#6700612yes—
665C4—28no—
666C4—448no—
667C4—884no—
668C2—28no—
669C2—28no—
670C2—48no—
671C2—44no—
672C2C2×#1062286011yescharacteristic
673C2C2×#1062283311yescharacteristic
674C2#1307119411yescharacteristic
675C2D4×C22⋊Dic1114yes—
676C2#1307192612yes—
677C2#1307193912yes—
678C2#1307199014yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC24×D4×C11C2
socle, cosocleC24×C11C24
hypercenterC24×D4D11
hypocenterC11#13867
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊Dic11C2semidirect
2. C2×#10622833C2semidirect
3. C2×#10622860C2semidirect
4. C2×#10622860C2semidirect
5. #13066857C2semidirect
6. #13066839C2semidirect
13. C23×D4×C11C4semidirect
17. C24×Dic11C22semidirect
22. C22×C22⋊Dic11C22semidirect
23. C22×C22⋊Dic11C22semidirect
24. C22×C22⋊Dic11C22semidirect
25. C22×C22⋊Dic11C22semidirect
29. C2×C11⋊#95C22semidirect
41. C25×C11C2×C4semidirect
60. C22×D4×C11C2×C4semidirect
65. C23×C4×C11C2×C4semidirect
88. C2×C22⋊Dic11D4semidirect
131. C24×C11C22⋊C4semidirect
157. C2×D4×C11C22⋊C4semidirect
180. C22×Dic11C2×D4semidirect
256. C23×C11C2×C22⋊C4semidirect
277. C2×C4×C11C2×C22⋊C4semidirect
294. C23×D4Dic11semidirect
340. C22×C11#379semidirect
341. C22×C11#386semidirect
369. C25C2×Dic11semidirect
388. C22×D4C2×Dic11semidirect
399. C23×C4C2×Dic11semidirect
469. C24C22⋊Dic11semidirect
495. C2×D4C22⋊Dic11semidirect
525. C11#13867semidirect
592. C23C2×C22⋊Dic11semidirect
620. C2×C4C2×C22⋊Dic11semidirect
650. C22#10622833semidirect
651. C22#10622860semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Dic112
C2×#106228332
C2×#106228602
#130668572
#130668392
C24×D4×C112
#1386711