Finite Group Databasebeta

← #14677267

Subgroups — #14677267

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×D4×Dic11C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic, complemented
3C2×#10622843C211yesmaximal, characteristic, complemented
4C2×#10622834C211yesmaximal, characteristic
5#13066865C214yesmaximal, complemented
6#13066846C211yesmaximal, characteristic, complemented
7#13066838C214yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C22×C11×#124C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C24×Dic11C2212yes—
13C2×C11×#124—24no—
14C2×C11×#124—24no—
15C2×C11×#124C418yescomplemented
16C22×C11×C22⋊C4C2214yes—
17C22×C42×C11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2214yes—
20C2×D4×Dic11—24no—
21C2×D4×Dic11—24no—
22C2×D4×Dic11—24no—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27#10622843—24no—
28#10622843—24no—
29#10622834—24no—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2214yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2214yes—
36C25×C11C2312yes—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11C2×C414yescomplemented
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11C2×C414yes—
49C22×D4×C11D414yes—
50C22×D4×C11D414yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—24no—
55C23×Dic11—24no—
56C23×Dic11—24no—
57C23×Dic11—28no—
58C23×Dic11—44no—
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C11×#124—232no—
65C2×C11×C22⋊C4—28no—
66C2×C11×C22⋊C4—28no—
67C2×C11×C22⋊C4C2×C4116yescomplemented
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11C2×C414yescomplemented
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—28no—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11—44no—
77D4×Dic11—232no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
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×Dic11—22no—
89C2×C4×Dic11D414yes—
90C11⋊#95—28no—
91C11⋊#95—24no—
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×Q8×C11—28no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—44no—
113C2×Q8×C11—44no—
114C2×Q8×C11—44no—
115C2×Q8×C11—44no—
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—28no—
119C2×D4×C11—28no—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11C22⋊C4116yes—
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×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4112yes—
143C22×C4×C11#4112yes—
144C22×Dic11—216no—
145C22×Dic11—21no—
146C22×Dic11—21no—
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—24no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—416no—
168C22×Dic11—416no—
169C22×Dic11—48no—
170C22×Dic11—48no—
171C22×Dic11C2×D412yes—
172C22×Dic11C2×D414yes—
173C22×Dic11C2×D412yes—
174C22×Dic11#4114yes—
175C22×Dic11#4114yes—
176C11×C22⋊C4—232no—
177C42×C11—28no—
178C22⋊Dic11—216no—
179C22⋊Dic11—416no—
180C4⋊Dic11—28no—
181C4⋊Dic11—44no—
182C4×Dic11—28no—
183C4×Dic11—44no—
184C22×#124D1111yescharacteristic
185C22×C4×D4—111no—
186C2×#391—111no—
187C2×#391—111no—
188C2×#390—111no—
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—
227Q8×C11—416no—
228D4×C11—232no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11C2×C22⋊C414yes—
244C2×C4×C11C4×D414yes—
245C2×C4×C11C4×D414yes—
246C2×C4×C11#12014yes—
247C2×C4×C11#12114yes—
248C2×C4×C11#12114yes—
249C2×C4×C11#12314yes—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—28no—
261C2×Dic11—24no—
262C2×Dic11—432no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—44no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C2×Dic11#12414yescomplemented
278C23×Q8C2×D1111yescharacteristic
279C23×D4C2×D1111yescharacteristic
280C24×C4—112no—
281C2×#124—24no—
282C2×#124—24no—
283C2×#124Dic1118yescomplemented
284C2×C4×D4—224no—
285C2×C4×D4—224no—
286C2×C4×D4—224no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—111no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—114no—
291C22×C22⋊C4C2×D1114yes—
292C22×C42—111no—
293C22×C42—111no—
294C22×C42C2×D1111yescharacteristic
295#391—224no—
296#391—224no—
297#390—224no—
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—44no—
340C4×C11#38618yes—
341Dic11—24no—
342Dic11—44no—
343Dic11—42no—
344Dic11—44no—
345Dic11—82no—
346C25C22×D1112yes—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8C2×Dic1114yescomplemented
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4C2×Dic1114yes—
359C22×D4C22⋊D1114yes—
360C22×D4C22⋊D1114yes—
361C23×C4—111no—
362C23×C4—111no—
363C23×C4—112no—
364C23×C4—112no—
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—232no—
375C4×D4—2232no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—228no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—444no—
390C2×C22⋊C4C2×Dic11116yescomplemented
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—114no—
394C2×C42—222no—
395C2×C42—222no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42—222no—
399C2×C42C2×Dic1114yescomplemented
400#95—224no—
401#95—224no—
402#95—224no—
403#95—224no—
404#95—228no—
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—22no—
421C24—22no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24C22×Dic1114yes—
427C24C2×C22⋊D1114yes—
428C24C2×C22⋊D1114yes—
429C24C23×D1111yescharacteristic
430C2×Q8—28no—
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—28no—
443C2×D4C22⋊Dic11116yes—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—221no—
462C22×C4—222no—
463C22×C4—221no—
464C22×C4—2216no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—221no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—222no—
484C22×C4—448no—
485C22×C4—4416no—
486C22×C4—4416no—
487C22×C4—448no—
488C22×C4D4×D1112yes—
489C22×C4D4×D1112yes—
490C22×C4#434112yes—
491C22×C4#434112yes—
492C22×C4C22×Dic1114yes—
493C22×C4C22×Dic1114yes—
494C22×C4C22×Dic1112yes—
495C22×C4C2×C22⋊D1112yes—
496C22×C4C2×C22⋊D1112yes—
497C4⋊C4—228no—
498C4⋊C4—444no—
499C22⋊C4—232no—
500C22⋊C4—2216no—
501C22⋊C4—4416no—
502C42—28no—
503C42—228no—
504C42—444no—
505C11#1402711yescharacteristic, complemented, Sylow
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—28no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—42no—
519C23—44no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23C2×C22⋊Dic1118yes—
529C23C2×D4×D1111yescharacteristic
530C23C2×D4×D1111yescharacteristic
531C23C2×#434111yescharacteristic
532C23C2×#434111yescharacteristic
533C23#41×D1112yes—
534C23#41×D1112yes—
535C23#6704212yes—
536C23#6704312yes—
537C23C23×Dic1111yescharacteristic
538C23C22×C22⋊D1111yescharacteristic
539C23C22×C22⋊D1111yescharacteristic
540Q8—416no—
541D4—232no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—114no—
557C2×C4—222no—
558C2×C4—224no—
559C2×C4—222no—
560C2×C4—224no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—228no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—4432no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—444no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—444no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—444no—
584C2×C4D4×Dic1114yes—
585C2×C4D4×Dic1114yes—
586C2×C4#6698814yes—
587C2×C4#6699014yes—
588C2×C4#6699214yes—
589C2×C4#6699214yes—
590C2×C4C2×C22⋊Dic1114yes—
591C22—216no—
592C22—28no—
593C22—48no—
594C22—44no—
595C22—48no—
596C22—48no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22#1062319911yescharacteristic
603C22#1062320212yes—
604C22D11×#12411yescharacteristic
605C22#1062320511yescharacteristic
606C22#1062320611yescharacteristic
607C22#1062320712yes—
608C22#1062320812yes—
609C22#1062321112yes—
610C22#1062321212yes—
611C22#1062321312yes—
612C22C2×D4×Dic1111yescharacteristic
613C22C2×D4×Dic1111yescharacteristic
614C22C2×#6698811yescharacteristic
615C22C2×#6699011yescharacteristic
616C22C2×#6699211yescharacteristic
617C22C2×#6699211yescharacteristic
618C22#1062335512yes—
619C22#1062335512yes—
620C22#41×Dic1112yes—
621C22#1062335812yes—
622C22#1062336012yes—
623C22#1062336012yes—
624C22C22×C22⋊Dic1111yescharacteristic
625C4—44no—
626C4—44no—
627C4—224no—
628C4—444no—
629C4—442no—
630C4—444no—
631C4—882no—
632C4#1062283318yes—
633C2—48no—
634C2C2×#1062283311yescharacteristic
635C2#124×Dic1111yescharacteristic
636C2#1307132911yescharacteristic
637C2#1307144612yes—
638C2#1307169112yes—
639C2#1307219612yes—
640C2#1307224711yescharacteristic
641C2#1307226411yescharacteristic
642C2#1307239912yes—
643C2#1307358611yescharacteristic
644C2#1307360911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#124C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#124D11
hypocenterC11#14027
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
2. C2×#10622843C2semidirect
3. C2×#10622843C2semidirect
5. #13066865C2semidirect
6. #13066846C2semidirect
7. #13066838C2semidirect
8. C4×C11⋊#95C2semidirect
15. C2×C11×#124C4semidirect
43. C22×Q8×C11C2×C4semidirect
67. C2×C11×C22⋊C4C2×C4semidirect
70. C2×C42×C11C2×C4semidirect
277. C2×Dic11#124semidirect
283. C2×#124Dic11semidirect
353. C22×Q8C2×Dic11semidirect
390. C2×C22⋊C4C2×Dic11semidirect
399. C2×C42C2×Dic11semidirect
505. C11#14027semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228432
C2×#106228342
#130668652
#130668462
#130668382
C4×C11⋊#952
C22×C11×#1242
#1402711