Finite Group Databasebeta

← #14675776

Subgroups — #14675776

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic11⋊C4C211yesmaximal, characteristic
2C2×#10622268C212yesmaximal, complemented
3C2×#10622825C211yesmaximal, characteristic
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic
5#13066882C212yesmaximal, complemented
6#13066870C212yesmaximal, complemented
7#13066847C212yesmaximal, complemented
8#13066838C211yesmaximal, characteristic
9#13066838C211yesmaximal, characteristic
10#13066838C211yesmaximal, characteristic
11C11×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×Dic11⋊C4—28no—
21C22×Dic11⋊C4C418yescomplemented
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29#10622825—24no—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C22⋊C4×Dic11—24no—
39#10622268—28no—
40C25×C11C2311yescharacteristic
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11—24no—
44C23×C4×C11—42no—
45C23×C4×C11C2×C414yes—
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—22no—
51C23×Dic11—22no—
52C23×Dic11—24no—
53C23×Dic11—24no—
54C23×Dic11—22no—
55C23×Dic11—22no—
56C23×Dic11—24no—
57C23×Dic11—42no—
58C23×Dic11C2×C414yes—
59C23×Dic11C2×C414yes—
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4Q814yes—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11D414yes—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—24no—
80C2×C4⋊Dic11—42no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4—232no—
85C2×Dic11⋊C4C2×C414yes—
86C2×Dic11⋊C4C2×C414yes—
87C2×Dic11⋊C4C2×C414yes—
88C2×Dic11⋊C4C2×C414yes—
89C2×Dic11⋊C4D418yes—
90C2×C4×Dic11—24no—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—42no—
93C11×#95—24no—
94C11×#95—42no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103#13882—111nomaximal, Sylow
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11C22×C412yes—
109C24×C11C2×D412yes—
110C24×C11C2×Q812yes—
111C24×C11#4112yes—
112C24×C11#4112yes—
113C24×C11#4112yes—
114C24×C11#4112yes—
115C24×C11C2411yescharacteristic
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—28no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—28no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—44no—
139C22×C4×C11—48no—
140C22×C4×C11—48no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2×Q814yes—
145C22×Dic11—216no—
146C22×Dic11—216no—
147C22×Dic11—28no—
148C22×Dic11—28no—
149C22×Dic11—28no—
150C22×Dic11—28no—
151C22×Dic11—28no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—44no—
179C22×Dic11—48no—
180C22×Dic11—48no—
181C22×Dic11C22×C412yes—
182C22×Dic11C22×C412yes—
183C22×Dic11C22×C412yes—
184C22×Dic11C22×C412yes—
185C22×Dic11C2×D414yes—
186C22×Dic11C2×D414yes—
187C22×Dic11C2×D414yes—
188C22×Dic11#4114yes—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—44no—
191C22⋊Dic11—28no—
192C22⋊Dic11—44no—
193C4⋊Dic11—48no—
194Dic11⋊C4—28no—
195Dic11⋊C4—28no—
196Dic11⋊C4—28no—
197Dic11⋊C4C22⋊C4116yescomplemented
198C4×Dic11—48no—
199C23×C4⋊C4—111no—
200C2×#387—112no—
201C2×#380—111no—
202C2×C4×C22⋊C4—111no—
203#1445—112no—
204#1441—112no—
205#1436—112no—
206C22⋊#95—111no—
207C22⋊#95—111no—
208C22⋊#95—111no—
209C22⋊#95D1111yescharacteristic
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—24no—
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×C11—24no—
225C23×C11—24no—
226C23×C11#11714yes—
227C23×C11C4×D414yes—
228C23×C11C4×Q814yes—
229C23×C11C22⋊Q814yes—
230C23×C11#12314yes—
231C23×C11#12514yes—
232C23×C11#12614yes—
233C23×C11C23×C411yescharacteristic
234C23×C11C22×D412yes—
235C23×C11C22×D411yescharacteristic
236C23×C11C22×Q811yescharacteristic
237C23×C11C2×#4111yescharacteristic
238C23×C11C2×#4111yescharacteristic
239C23×C11C2×#4111yescharacteristic
240C23×C11C2×#4111yescharacteristic
241C23×C11C2×#4112yes—
242C23×C11H(5,𝔽2)12yes—
243C23×C112−1+412yes—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
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—416no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
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×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11C2×C22⋊C414yes—
269C2×Dic11—232no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—416no—
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—
302C2×Dic11C2×C22⋊C414yes—
303C2×Dic11C2×C22⋊C414yes—
304C2×Dic11#11714yes—
305C24×C4—111no—
306C24×C4—111no—
307C24×C4C2×D1111yescharacteristic
308C22×C4⋊C4—111no—
309C22×C4⋊C4—111no—
310C22×C4⋊C4—111no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4—118no—
313C22×C4⋊C4—112no—
314C22×C4⋊C4—228no—
315C22×C22⋊C4—111no—
316C22×C22⋊C4—111no—
317C22×C22⋊C4C2×D1111yescharacteristic
318C22×C22⋊C4C2×D1111yescharacteristic
319C22×C42—112no—
320#387—228no—
321#380—224no—
322C4×C22⋊C4—224no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—112no—
328C2×#95—112no—
329C2×#95—112no—
330C2×#95—112no—
331C2×#95C2×D1112yes—
332C2×#95C2×D1112yes—
333C22×C11—24no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—28no—
339C22×C11—28no—
340C22×C11—28no—
341C22×C11—28no—
342C22×C11—24no—
343C22×C11#38718yescomplemented
344C22×C11C22×C22⋊C411yescharacteristic
345C22×C11C2×#11711yescharacteristic
346C22×C11C2×#11711yescharacteristic
347C22×C11C2×C4×D411yescharacteristic
348C22×C11C2×C4×Q811yescharacteristic
349C22×C11#51811yescharacteristic
350C22×C11#51911yescharacteristic
351C22×C11C2×C22⋊Q811yescharacteristic
352C22×C11C2×#12311yescharacteristic
353C22×C11#52512yes—
354C22×C11#52512yes—
355C22×C11C2×#12511yescharacteristic
356C22×C11C2×#12611yescharacteristic
357C22×C11#53912yes—
358C22×C11#53912yes—
359C22×C11D4212yes—
360C22×C11#54612yes—
361C22×C11#54712yes—
362C22×C11#54812yes—
363C22×C11D4×Q812yes—
364C22×C11#55212yes—
365C22×C11#55312yes—
366C22×C11#55412yes—
367C4×C11—24no—
368C4×C11—42no—
369C4×C11—44no—
370C4×C11—82no—
371Dic11—24no—
372Dic11—24no—
373Dic11—24no—
374Dic11—42no—
375Dic11—44no—
376Dic11—82no—
377C25C22×D1111yescharacteristic
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—42no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—114no—
386C23×C4—112no—
387C23×C4—111no—
388C23×C4—114no—
389C23×C4—112no—
390C23×C4—224no—
391C23×C4—224no—
392C23×C4—224no—
393C23×C4—222no—
394C23×C4—222no—
395C23×C4—222no—
396C23×C4—222no—
397C23×C4—442no—
398C23×C4C4×D1114yes—
399C23×C4C22×D1112yes—
400C23×C4C22×D1112yes—
401C23×C4C22×D1111yescharacteristic
402C23×C4C22×D1111yescharacteristic
403C2×C4⋊C4—114no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—2232no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4—224no—
411C2×C4⋊C4—224no—
412C2×C4⋊C4—224no—
413C2×C4⋊C4—224no—
414C2×C4⋊C4—442no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—114no—
421C2×C22⋊C4—222no—
422C2×C22⋊C4—222no—
423C2×C22⋊C4—222no—
424C2×C22⋊C4—222no—
425C2×C22⋊C4—222no—
426C2×C22⋊C4Dic2214yes—
427C2×C42—224no—
428C2×C42—224no—
429C2×C42—442no—
430#95—24no—
431#95—42no—
432#95—224no—
433#95—224no—
434#95—224no—
435#95—224no—
436#95—224no—
437#95—224no—
438#95—224no—
439#95—442no—
440C2×C11—28no—
441C2×C11#228011yescharacteristic
442C2×C11C2×#38711yescharacteristic
443C2×C11#231311yescharacteristic
444C2×C11D4×C22⋊C411yescharacteristic
445C2×C11Q8×C22⋊C411yescharacteristic
446C2×C11#234411yescharacteristic
447C2×C11#234511yescharacteristic
448C2×C11#244312yes—
449C2×C11#244912yes—
450C2×C11#247312yes—
451C2×C11#248112yes—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24C2×Dic2212yes—
457C24C2×C4×D1112yes—
458C24#433912yes—
459C24D4×D1112yes—
460C24#434112yes—
461C24#434112yes—
462C24#434312yes—
463C24C23×D1111yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—28no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—28no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—44no—
487C22×C4—48no—
488C22×C4—48no—
489C22×C4—112no—
490C22×C4—112no—
491C22×C4—112no—
492C22×C4—114no—
493C22×C4—114no—
494C22×C4—114no—
495C22×C4—112no—
496C22×C4—114no—
497C22×C4—228no—
498C22×C4—228no—
499C22×C4—228no—
500C22×C4—2216no—
501C22×C4—2216no—
502C22×C4—228no—
503C22×C4—221no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—222no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—222no—
512C22×C4—228no—
513C22×C4—222no—
514C22×C4—221no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—221no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—444no—
531C22×C4—448no—
532C22×C4—448no—
533C22×C4C2×Dic2214yes—
534C22×C4C2×C4×D1112yes—
535C22×C4C2×C4×D1112yes—
536C22×C4D4×D1114yes—
537C4⋊C4—1116no—
538C4⋊C4—228no—
539C4⋊C4—228no—
540C4⋊C4—228no—
541C4⋊C4—448no—
542C22⋊C4—28no—
543C22⋊C4—44no—
544C22⋊C4—228no—
545C22⋊C4—444no—
546C42—448no—
547C11#1388211yescharacteristic, complemented, Sylow
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23C4×Dic2214yes—
565C23#6693114yes—
566C23#6693214yes—
567C23(C22⋊D11)⋊C414yes—
568C23#6694314yes—
569C23#6694514yes—
570C23#6694714yes—
571C23C22×Dic2211yescharacteristic
572C23C22×C4×D1111yescharacteristic
573C23C2×#433911yescharacteristic
574C23C2×D4×D1111yescharacteristic
575C23C2×D4×D1112yes—
576C23C2×#434111yescharacteristic
577C23C2×#434111yescharacteristic
578C23#6703712yes—
579C23C2×#434311yescharacteristic
580C23#41×D1112yes—
581C23#6704312yes—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—416no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—114no—
607C2×C4—114no—
608C2×C4—114no—
609C2×C4—2232no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—224no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—224no—
626C2×C4—224no—
627C2×C4—224no—
628C2×C4—4416no—
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—442no—
638C2×C4—442no—
639C2×C4—442no—
640C2×C4—442no—
641C2×C4—442no—
642C2×C4C22⋊C4×D1114yes—
643C22—28no—
644C22—24no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—28no—
649C22—24no—
650C22—24no—
651C22—28no—
652C22—28no—
653C22#1062226818yescomplemented
654C22C2×C4×Dic2211yescharacteristic
655C22C2×#6693111yescharacteristic
656C22C2×#6693211yescharacteristic
657C22C2×C22⋊C4×D1111yescharacteristic
658C22C2×(C22⋊D11)⋊C411yescharacteristic
659C22#1062301711yescharacteristic
660C22C2×#6694311yescharacteristic
661C22C2×#6694511yescharacteristic
662C22C2×#6694711yescharacteristic
663C22#1062304711yescharacteristic
664C22D11×#11711yescharacteristic
665C22D4×Dic2212yes—
666C22#1062307012yes—
667C22#1062307112yes—
668C22#1062308312yes—
669C22#1062312112yes—
670C22#1062312212yes—
671C22#1062313312yes—
672C22#1062313712yes—
673C22#1062315812yes—
674C22#1062317612yes—
675C22#1062318112yes—
676C22#1062318612yes—
677C4—24no—
678C4—44no—
679C4—42no—
680C4—82no—
681C4—224no—
682C4—224no—
683C4—224no—
684C4—442no—
685C4—444no—
686C4—882no—
687C2—28no—
688C2#1307099811yescharacteristic
689C2C2×#1062226811yescharacteristic
690C2#1307121811yescharacteristic
691C2#1307143211yescharacteristic
692C2C22⋊C4×Dic2211yescharacteristic
693C2#1307148011yescharacteristic
694C2#1307149411yescharacteristic
695C2#1307235512yes—
696C2#1307242912yes—
697C2#1307276412yes—
698C2#1307288212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#13882
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622268C2semidirect
5. #13066882C2semidirect
6. #13066870C2semidirect
7. #13066847C2semidirect
21. C22×Dic11⋊C4C4semidirect
197. Dic11⋊C4C22⋊C4semidirect
343. C22×C11#387semidirect
547. C11#13882semidirect
653. C22#10622268semidirect

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106222682
C2×#106228252
C2×C22⋊C4×Dic112
#130668822
#130668702
#130668472
#130668382
C11×C22⋊#952
#1388211