Finite Group Databasebeta

← #14677268

Subgroups — #14677268

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66989C211yesmaximal, characteristic
2C22×D4×Dic11C211yesmaximal, characteristic
3C2×#10622542C211yesmaximal, characteristic, complemented
4C2×#10622587C211yesmaximal, characteristic, complemented
5#13066863C214yesmaximal, complemented
6#13066845C211yesmaximal, characteristic, complemented
7#13066838C214yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2212yes—
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2214yes—
15C22×C42×C11C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2214yes—
18C2×#66989—24no—
19C2×#66989—24no—
20C2×#66989C418yescomplemented
21C2×D4×Dic11—24no—
22C2×D4×Dic11—24no—
23C2×D4×Dic11—24no—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C11×#390—24no—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2214yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2214yes—
34#10622587—24no—
35#10622542—24no—
36C25×C11C2312yes—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11C2×C414yes—
42C22×D4×C11D414yes—
43C22×D4×C11D414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—24no—
48C23×Dic11—24no—
49C23×Dic11—24no—
50C23×Dic11—28no—
51C23×Dic11—44no—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C22×Dic22—22no—
58C22×Dic22—22no—
59C22×Dic22—22no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22C2×C414yescomplemented
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C22⋊C4—28no—
68C2×C11×C22⋊C4—28no—
69C2×C11×C22⋊C4—44no—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11—22no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—28no—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11C2×C4116yescomplemented
79#66989—232no—
80D4×Dic11—232no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11D414yes—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11C2×C414yescomplemented
89C2×C4×Dic11D414yes—
90C11⋊#95—24no—
91C11⋊#95—28no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—44no—
96#14027—111nomaximal, Sylow
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—24no—
100C24×C11—24no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—24no—
104C24×C11—24no—
105C24×C11C22×C414yes—
106C24×C11C2×D414yes—
107C24×C11C2×D414yes—
108C24×C11C2411yescharacteristic
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—28no—
112C2×D4×C11—28no—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11C22⋊C4116yes—
116C22×C4×C11—22no—
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—24no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11#4114yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×Dic11—216no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—21no—
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—24no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—416no—
160C22×Dic11—416no—
161C22×Dic11—48no—
162C22×Dic11—48no—
163C22×Dic11C22×C414yes—
164C22×Dic11C22×C414yes—
165C22×Dic11C2×D412yes—
166C22×Dic11C2×D414yes—
167C22×Dic11C2×D412yes—
168C22×Dic11#4114yes—
169C2×Dic22—28no—
170C2×Dic22—28no—
171C2×Dic22—28no—
172C2×Dic22—44no—
173C2×Dic22—44no—
174C2×Dic22—44no—
175C2×Dic22—44no—
176C11×C4⋊C4—44no—
177C11×C22⋊C4—416no—
178C42×C11—44no—
179C22⋊Dic11—216no—
180C22⋊Dic11—232no—
181C4⋊Dic11—28no—
182C4×Dic11—28no—
183C4×Dic11—28no—
184C22×#124—111no—
185C22×C4×D4—111no—
186C2×#391—111no—
187C2×#391—111no—
188C2×#390D1111yescharacteristic
189#1440—114no—
190C4⋊#95—111no—
191C22⋊#95—114no—
192C4×#95—111no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—28no—
196C23×C11—28no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—28no—
202C23×C11—28no—
203C23×C11—28no—
204C23×C11—28no—
205C23×C11—42no—
206C23×C11—44no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11C2×C22⋊C418yes—
216C23×C11C23×C411yescharacteristic
217C23×C11C22×D411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C22×D411yescharacteristic
220C23×C11C22×D411yescharacteristic
221C23×C11C2×#4111yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C23×C11C2×#4112yes—
224C23×C11C2×#4112yes—
225C23×C11H(5,𝔽2)12yes—
226C23×C112−1+412yes—
227D4×C11—232no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11C2×C22⋊C414yes—
241C2×C4×C11C4×D414yes—
242C2×C4×C11C4×D414yes—
243C2×C4×C11#12014yes—
244C2×C4×C11#12114yes—
245C2×C4×C11#12114yes—
246C2×C4×C11#12314yes—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—28no—
262C2×Dic11—432no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—44no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11#12414yescomplemented
277Dic22—416no—
278C23×Q8—111no—
279C23×D4C2×D1111yescharacteristic
280C24×C4—112no—
281C2×#124—118no—
282C2×#124—224no—
283C2×#124—224no—
284C2×C4×D4—224no—
285C2×C4×D4—224no—
286C2×C4×D4—224no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4C2×D1111yescharacteristic
289C22×C22⋊C4—114no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4C2×D1114yes—
292C22×C42—111no—
293C22×C42—111no—
294C22×C42C2×D1111yescharacteristic
295#391—224no—
296#391—224no—
297#390—24no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—114no—
302C2×#95—112no—
303C2×#95—114no—
304C22×C11—216no—
305C22×C11—28no—
306C22×C11—44no—
307C22×C11—48no—
308C22×C11—48no—
309C22×C11—44no—
310C22×C11—44no—
311C22×C11—48no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—44no—
315C22×C11C22×C22⋊C411yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11C2×C4×D411yescharacteristic
318C22×C11C4×#4112yes—
319C22×C11#52012yes—
320C22×C11C2×#12011yescharacteristic
321C22×C11C2×#12111yescharacteristic
322C22×C11C2×#12111yescharacteristic
323C22×C11C2×#12311yescharacteristic
324C22×C11C2×#12411yescharacteristic
325C22×C11#52912yes—
326C22×C11#53211yescharacteristic
327C22×C11#53511yescharacteristic
328C22×C11#53611yescharacteristic
329C22×C11#54212yes—
330C22×C11#54612yes—
331C22×C11#54612yes—
332C22×C11#54612yes—
333C22×C11#54712yes—
334C22×C11#54712yes—
335C22×C11#54812yes—
336C22×C11#55612yes—
337C22×C11#55912yes—
338C4×C11—44no—
339C4×C11—82no—
340C4×C11#38618yes—
341Dic11—24no—
342Dic11—44no—
343Dic11—42no—
344Dic11—44no—
345Dic11—44no—
346C25C22×D1112yes—
347C22×Q8—114no—
348C22×Q8—222no—
349C22×Q8—222no—
350C22×Q8—222no—
351C22×Q8—222no—
352C22×Q8—222no—
353C22×Q8—222no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4C4×D1114yes—
359C22×D4D4414yes—
360C22×D4C22⋊D1114yes—
361C23×C4—111no—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4—111no—
365C23×C4—112no—
366C23×C4—224no—
367C23×C4—224no—
368C23×C4—228no—
369C23×C4—224no—
370C23×C4—444no—
371C23×C4C22×D1112yes—
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374#124—2232no—
375C4×D4—2232no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—1116no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—228no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—114no—
395C2×C42—114no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42—222no—
399C2×C42—222no—
400#95—224no—
401#95—228no—
402#95—224no—
403#95—224no—
404#95—224no—
405#95—444no—
406C2×C11—48no—
407C2×C11C2×#38611yescharacteristic
408C2×C11C4×#12411yescharacteristic
409C2×C11#232611yescharacteristic
410C2×C11#233912yes—
411C2×C11#236712yes—
412C2×C11#242712yes—
413C2×C11#243211yescharacteristic
414C2×C11#243511yescharacteristic
415C2×C11#244712yes—
416C2×C11#254411yescharacteristic
417C2×C11#254711yescharacteristic
418C24—22no—
419C24—22no—
420C24—24no—
421C24—22no—
422C24—22no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24C2×C4×D1114yes—
427C24C2×D4414yes—
428C24C2×C22⋊D1114yes—
429C24C23×D1111yescharacteristic
430C2×Q8—228no—
431C2×Q8—228no—
432C2×Q8—228no—
433C2×Q8—444no—
434C2×Q8—444no—
435C2×Q8—444no—
436C2×Q8—444no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—28no—
443C2×D4(C2×D11)⋊C4116yes—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—112no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—112no—
460C22×C4—114no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—222no—
464C22×C4—2216no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—221no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—224no—
479C22×C4—222no—
480C22×C4—224no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—448no—
486C22×C4—4416no—
487C22×C4—4416no—
488C22×C4—448no—
489C22×C4C2×C4×D1112yes—
490C22×C4C2×D4412yes—
491C22×C4D4×D1112yes—
492C22×C4D4×D1112yes—
493C22×C4#434114yes—
494C22×C4#434112yes—
495C22×C4#434112yes—
496C22×C4C2×C22⋊D1112yes—
497C4⋊C4—44no—
498C4⋊C4—228no—
499C22⋊C4—416no—
500C22⋊C4—2216no—
501C22⋊C4—2232no—
502C42—44no—
503C42—228no—
504C42—228no—
505C11#1402711yescharacteristic, complemented, Sylow
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—28no—
511C23—28no—
512C23—24no—
513C23—24no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—44no—
519C23—42no—
520C23—42no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—42no—
527C23—42no—
528C23C2×(C2×D11)⋊C418yes—
529C23C22×C4×D1111yescharacteristic
530C23C22×D4411yescharacteristic
531C23C2×D4×D1111yescharacteristic
532C23C2×D4×D1111yescharacteristic
533C23C2×#434111yescharacteristic
534C23C2×#434112yes—
535C23C2×#434111yescharacteristic
536C23#6703712yes—
537C23#41×D1112yes—
538C23#6704312yes—
539C23C22×C22⋊D1111yescharacteristic
540Q8—4416no—
541D4—232no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—44no—
554C2×C4—114no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—228no—
569C2×C4—222no—
570C2×C4—4432no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—444no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4(C22⋊D11)⋊C414yes—
585C2×C4(C22⋊D11)⋊C414yes—
586C2×C4#6693514yes—
587C2×C4#6693914yes—
588C2×C4C2×(C2×D11)⋊C414yes—
589C2×C4#6699214yes—
590C2×C4#6699214yes—
591C22—216no—
592C22—28no—
593C22—48no—
594C22—44no—
595C22—48no—
596C22—48no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22C2×(C22⋊D11)⋊C411yescharacteristic
603C22C2×(C22⋊D11)⋊C411yescharacteristic
604C22C2×#6693511yescharacteristic
605C22C2×#6693911yescharacteristic
606C22C4×#434112yes—
607C22#1062307712yes—
608C22#1062308512yes—
609C22#1062308612yes—
610C22#1062312912yes—
611C22#1062313112yes—
612C22#1062313412yes—
613C22#1062314312yes—
614C22#1062320212yes—
615C22D11×#12411yescharacteristic
616C22#1062320611yescharacteristic
617C22#1062324412yes—
618C22#1062324611yescharacteristic
619C22#1062324711yescharacteristic
620C22C22×(C2×D11)⋊C411yescharacteristic
621C22C2×#6699211yescharacteristic
622C22C2×#6699211yescharacteristic
623C22#1062333712yes—
624C22#1062335512yes—
625C4—44no—
626C4—82no—
627C4—224no—
628C4—444no—
629C4—442no—
630C4—444no—
631C4—444no—
632C4#1062257118yes—
633C2—48no—
634C2C2×#1062257111yescharacteristic
635C2#1307116311yescharacteristic
636C2#1307132611yescharacteristic
637C2#1307144112yes—
638C2#1307168612yes—
639C2#1307219512yes—
640C2#1307224611yescharacteristic
641C2#1307226611yescharacteristic
642C2#1307240112yes—
643C2#1307358411yescharacteristic
644C2#1307360911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14027
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#10622542C2semidirect
4. C2×#10622587C2semidirect
5. #13066863C2semidirect
6. #13066845C2semidirect
7. #13066838C2semidirect
8. C4×C11⋊#95C2semidirect
20. C2×#66989C4semidirect
63. C22×Dic22C2×C4semidirect
78. C2×C22⋊Dic11C2×C4semidirect
88. C2×C4×Dic11C2×C4semidirect
276. C2×Dic11#124semidirect
505. C11#14027semidirect

Maximal subgroups

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

subgroupindex
C22×#669892
C22×D4×Dic112
C2×#106225422
C2×#106225872
#130668632
#130668452
#130668382
C4×C11⋊#952
C2×C11×#3902
#1402711