Finite Group Databasebeta

← #14677482

Subgroups — #14677482

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622563C211yesmaximal, characteristic
2C2×#10622563C211yesmaximal, characteristic
3C2×#10622823C211yesmaximal, characteristic
4C22×C11⋊#95C211yesmaximal, characteristic
5#13066872C212yesmaximal, complemented
6#13066868C212yesmaximal, complemented
7#13066849C212yesmaximal, complemented
8#13066846C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic
10#13066838C211yesmaximal, characteristic
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C42×C11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2212yes—
21C22×C4⋊Dic11C2212yes—
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C4×C11×C22⋊C4—24no—
25C2×C11×#95C2212yes—
26#10622823—24no—
27C2×C11⋊#95—24no—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622563—24no—
39#10622563C418yescomplemented
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—24no—
44C23×C4×C11—42no—
45C23×C4×C11D414yes—
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—22no—
51C23×Dic11—22no—
52C23×Dic11—22no—
53C23×Dic11—24no—
54C23×Dic11—22no—
55C23×Dic11—22no—
56C23×Dic11—42no—
57C23×Dic11—42no—
58C23×Dic11—42no—
59C23×Dic11C2×C414yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2312yes—
65C23×Dic11C2312yes—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4C2×C414yes—
69C2×C11×C22⋊C4D414yes—
70C2×C11×C22⋊C4Q814yes—
71C2×C11×C22⋊C4Q814yes—
72C2×C42×C11—24no—
73C2×C42×C11—24no—
74C2×C42×C11—42no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11C2×C414yes—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11—42no—
84C2×C4⋊Dic11—42no—
85C2×C4⋊Dic11—42no—
86C2×C4⋊Dic11C2×C418yescomplemented
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—42no—
91C11×#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95—24no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100C11⋊#95—42no—
101C11⋊#95C2×C418yescomplemented
102#14044—111nomaximal, Sylow
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11C22×C412yes—
108C24×C11C2×D412yes—
109C24×C11C2×D412yes—
110C24×C11C2×Q812yes—
111C24×C11C2×Q812yes—
112C24×C11#4112yes—
113C24×C11#4112yes—
114C24×C11C2411yescharacteristic
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—28no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—28no—
134C22×C4×C11—44no—
135C22×C4×C11—48no—
136C22×C4×C11—48no—
137C22×C4×C11C22×C414yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×Q814yes—
142C22×C4×C11C2×Q814yes—
143C22×C4×C11#4114yes—
144C22×Dic11—28no—
145C22×Dic11—28no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—21no—
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×Dic11—22no—
176C22×Dic11—48no—
177C22×Dic11—48no—
178C22×Dic11—48no—
179C22×Dic11—44no—
180C22×Dic11—44no—
181C22×Dic11—44no—
182C22×Dic11—48no—
183C22×Dic11—44no—
184C22×Dic11C22×C412yes—
185C22×Dic11C22×C414yes—
186C22×Dic11C22×C412yes—
187C22×Dic11#4114yes—
188C11×C22⋊C4—28no—
189C11×C22⋊C4C4⋊C4116yescomplemented
190C42×C11—48no—
191C22⋊Dic11—28no—
192C22⋊Dic11—44no—
193C4⋊Dic11—48no—
194C4⋊Dic11—48no—
195Dic11⋊C4—44no—
196Dic11⋊C4—44no—
197C2×#385—111no—
198C2×#385—111no—
199C2×#385—111no—
200C2×C4×C22⋊C4D1111yescharacteristic
201C22×#95—111no—
202#1442—112no—
203#1441—112no—
204#1436—112no—
205C4⋊#95—112no—
206C22⋊#95—111no—
207C22⋊#95—111no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11C2×C4⋊C414yes—
225C23×C11C4×D414yes—
226C23×C11C4×Q814yes—
227C23×C11#12114yes—
228C23×C11C22⋊Q814yes—
229C23×C11#12514yes—
230C23×C11C4⋊Q814yes—
231C23×C11C23×C411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C22×Q811yescharacteristic
235C23×C11C22×Q811yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C23×C11C2×#4111yescharacteristic
238C23×C11C2×#4112yes—
239C23×C11C2×#4112yes—
240C23×C11H(5,𝔽2)12yes—
241C23×C11H(5,𝔽2)12yes—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—416no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11C2×C4⋊C418yes—
266C2×C4×C11#12314yes—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—416no—
278C2×Dic11—416no—
279C2×Dic11—42no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—42no—
283C2×Dic11—41no—
284C2×Dic11—42no—
285C2×Dic11—41no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302C2×Dic11—42no—
303C24×C4—111no—
304C24×C4—111no—
305C24×C4C2×D1111yescharacteristic
306C22×C4⋊C4—112no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—112no—
309C22×C4⋊C4—111no—
310C22×C22⋊C4—111no—
311C22×C22⋊C4—111no—
312C22×C22⋊C4C2×D1111yescharacteristic
313C22×C22⋊C4C2×D1111yescharacteristic
314C22×C42C2×D1112yes—
315#385—118no—
316#385—224no—
317#385—224no—
318C4×C22⋊C4—24no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—111no—
326C2×#95—112no—
327C2×#95—112no—
328C2×#95—112no—
329C2×#95—224no—
330C2×#95C2×D1112yes—
331C22×C11—24no—
332C22×C11—24no—
333C22×C11—28no—
334C22×C11—28no—
335C22×C11—24no—
336C22×C11—24no—
337C22×C11—28no—
338C22×C11—24no—
339C22×C11—28no—
340C22×C11—24no—
341C22×C11#38918yes—
342C22×C11C22×C4⋊C411yescharacteristic
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C2×C4×Q811yescharacteristic
345C22×C11C4×#4112yes—
346C22×C11#51812yes—
347C22×C11C2×#12111yescharacteristic
348C22×C11C2×C22⋊Q811yescharacteristic
349C22×C11C2×#12311yescharacteristic
350C22×C11#52511yescharacteristic
351C22×C11C2×#12511yescharacteristic
352C22×C11#52912yes—
353C22×C11C2×C4⋊Q811yescharacteristic
354C22×C11#53411yescharacteristic
355C22×C11#53511yescharacteristic
356C22×C11#53812yes—
357C22×C11#54612yes—
358C22×C11#54612yes—
359C22×C11#55112yes—
360C22×C11#55112yes—
361C22×C11#55412yes—
362C22×C11#55412yes—
363C22×C11#55412yes—
364C22×C11#55412yes—
365C4×C11—28no—
366C4×C11—24no—
367C4×C11—42no—
368C4×C11—44no—
369Dic11—42no—
370Dic11—44no—
371Dic11—44no—
372Dic11—42no—
373Dic11—81no—
374Dic11—81no—
375C25C22×D1111yescharacteristic
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—24no—
379C23×C4—42no—
380C23×C4—111no—
381C23×C4—111no—
382C23×C4—112no—
383C23×C4—112no—
384C23×C4—114no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—224no—
388C23×C4—222no—
389C23×C4—222no—
390C23×C4—222no—
391C23×C4—222no—
392C23×C4—222no—
393C23×C4—442no—
394C23×C4—442no—
395C23×C4—442no—
396C23×C4D4414yes—
397C23×C4C22×D1112yes—
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1112yes—
400C23×C4C22×D1111yescharacteristic
401C2×C4⋊C4—118no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—224no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—442no—
408C2×C4⋊C4—442no—
409C2×C4⋊C4—442no—
410C2×C4⋊C4—442no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4Dic2214yes—
420C2×C22⋊C4Dic2214yes—
421C2×C22⋊C4C4×D1114yes—
422C2×C22⋊C4C22⋊D1114yes—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—42no—
426#95—24no—
427#95—118no—
428#95—224no—
429#95—224no—
430#95—224no—
431#95—222no—
432#95—222no—
433#95—224no—
434#95—442no—
435#95—442no—
436#95—442no—
437C2×C11—28no—
438C2×C11C2×#38911yescharacteristic
439C2×C11C4×#12311yescharacteristic
440C2×C11#232111yescharacteristic
441C2×C11#234912yes—
442C2×C11#236812yes—
443C2×C11#241111yescharacteristic
444C2×C11#241211yescharacteristic
445C2×C11#245012yes—
446C2×C11#250211yescharacteristic
447C2×C11#250512yes—
448C2×C11#258311yescharacteristic
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24C2×Dic2212yes—
454C24C2×Dic2212yes—
455C24C2×C4×D1112yes—
456C24C2×D4412yes—
457C24#433912yes—
458C24#433912yes—
459C24C2×C22⋊D1112yes—
460C24C23×D1111yescharacteristic
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—28no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—28no—
480C22×C4—44no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—112no—
484C22×C4—114no—
485C22×C4—112no—
486C22×C4—114no—
487C22×C4—228no—
488C22×C4—228no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—448no—
520C22×C4—448no—
521C22×C4—448no—
522C22×C4—444no—
523C22×C4—444no—
524C22×C4—444no—
525C22×C4—448no—
526C22×C4—444no—
527C22×C4C2×Dic2214yes—
528C22×C4C2×Dic2214yes—
529C22×C4C2×C4×D1114yes—
530C22×C4C2×D4412yes—
531C22×C4C2×D4412yes—
532C22×C4#434114yes—
533C22×C4C2×C22⋊D1114yes—
534C4⋊C4—448no—
535C4⋊C4—448no—
536C4⋊C4—444no—
537C4⋊C4—444no—
538C22⋊C4—28no—
539C22⋊C4—228no—
540C22⋊C4—444no—
541C22⋊C4Dic11⋊C4116yescomplemented
542C42—48no—
543C11#1404411yescharacteristic, complemented, Sylow
544C23—22no—
545C23—22no—
546C23—24no—
547C23—22no—
548C23—22no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23C4×Dic2214yes—
561C23#6692214yes—
562C23#6692314yes—
563C23C4×D4414yes—
564C23C2×Dic11⋊C414yes—
565C23#6697714yes—
566C23#6698314yes—
567C23C22×Dic2211yescharacteristic
568C23C22×Dic2211yescharacteristic
569C23C22×C4×D1111yescharacteristic
570C23C22×D4411yescharacteristic
571C23C2×#433911yescharacteristic
572C23C2×#433911yescharacteristic
573C23C2×#434112yes—
574C23#6703712yes—
575C23#41×D1112yes—
576C23#6704212yes—
577C23C22×C22⋊D1111yescharacteristic
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—416no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—4416no—
612C2×C4—4416no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—442no—
616C2×C4—441no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—441no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—442no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—442no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4#6693914yes—
638C2×C4C2×Dic11⋊C418yes—
639C22—24no—
640C22—28no—
641C22—24no—
642C22—28no—
643C22—24no—
644C22—24no—
645C22—28no—
646C22—24no—
647C22—24no—
648C22—28no—
649C22#1062254118yes—
650C22C2×C4×Dic2211yescharacteristic
651C22C2×#6692211yescharacteristic
652C22C2×#6692311yescharacteristic
653C22C2×C4×D4411yescharacteristic
654C22C2×#6693911yescharacteristic
655C22#1062302411yescharacteristic
656C22#1062302612yes—
657C22#1062305511yescharacteristic
658C22#1062305611yescharacteristic
659C22#1062305812yes—
660C22C4×#434112yes—
661C22#1062306912yes—
662C22#1062307012yes—
663C22#1062307012yes—
664C22#1062307412yes—
665C22#1062307412yes—
666C22#1062307612yes—
667C22#1062309112yes—
668C22C22×Dic11⋊C411yescharacteristic
669C22C2×#6697711yescharacteristic
670C22C2×#6698311yescharacteristic
671C22#1062333712yes—
672C22#1062336012yes—
673C4—24no—
674C4—28no—
675C4—44no—
676C4—42no—
677C4—442no—
678C4—444no—
679C4—444no—
680C4—442no—
681C4—881no—
682C4—881no—
683C2—28no—
684C2C2×#1062254111yescharacteristic
685C2C4×#6693911yescharacteristic
686C2#1307127611yescharacteristic
687C2#1307152112yes—
688C2#1307169412yes—
689C2#1307199511yescharacteristic
690C2#1307200611yescharacteristic
691C2#1307243412yes—
692C2#1307309411yescharacteristic
693C2#1307311112yes—
694C2#1307399111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14044
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. #13066872C2semidirect
6. #13066868C2semidirect
7. #13066849C2semidirect
8. #13066846C2semidirect
39. #10622563C4semidirect
86. C2×C4⋊Dic11C2×C4semidirect
101. C11⋊#95C2×C4semidirect
189. C11×C22⋊C4C4⋊C4semidirect
541. C22⋊C4Dic11⋊C4semidirect
543. C11#14044semidirect

Maximal subgroups

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

subgroupindex
C2×#106225632
C2×#106228232
C22×C11⋊#952
#130668722
#130668682
#130668492
#130668462
#130668382
C2×C4×C11×C22⋊C42
#1404411