Finite Group Databasebeta

← #14660281

Subgroups — #14660281

Order 2816.

1922 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
1C22×#66896C212yesmaximal, complemented
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C2×#10622825C211yesmaximal, characteristic, complemented
4C2×#10622167C212yesmaximal, complemented
5C22×C11×#121C211yesmaximal, characteristic
6C23×D4×C11—21no—
7C23×D4×C11C2211yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C2×C11×#121—24no—
10C2×C11×#121—22no—
11C2×C11×#121—24no—
12C2×C11×#121C414yescomplemented
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4—21no—
15C22×C22⋊Dic11—21no—
16C22×C4⋊Dic11C2212yes—
17C23×C11⋊C8C2212yes—
18C2×#66896—24no—
19C2×#66896—24no—
20C2×#66896—24no—
21#10622825—24no—
22C2×C11⋊#95—21no—
23C2×C22⋊(C11⋊C8)—22no—
24C2×C22⋊(C11⋊C8)—24no—
25#10622167—24no—
26C25×C11—21no—
27C25×C11D411yescharacteristic
28C22×D4×C11—28no—
29C22×D4×C11—24no—
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—22no—
33C22×D4×C11—21no—
34C22×D4×C11—22no—
35C22×D4×C11—22no—
36C22×D4×C11—44no—
37C22×D4×C11—42no—
38C22×D4×C11—42no—
39C22×D4×C11C2×C412yes—
40C22×D4×C11D414yes—
41C23×C4×C11—21no—
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11C2×C412yes—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D412yes—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—22no—
53C11×#121—216no—
54C11×#121—28no—
55C11×#121—28no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2×C412yes—
59C2×C11×C4⋊C4D414yes—
60C2×C11×C22⋊C4—28no—
61C2×C11×C22⋊C4—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—42no—
64C2×C22⋊Dic11—42no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11D414yescomplemented
71C22×C11⋊C8—22no—
72C22×C11⋊C8—22no—
73C22×C11⋊C8—22no—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—22no—
76C22×C11⋊C8—22no—
77C22×C11⋊C8D414yescomplemented
78#66896—216no—
79C11⋊#95—24no—
80C22⋊(C11⋊C8)—28no—
81#10969—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11—21no—
88C24×C11—22no—
89C24×C11—21no—
90C24×C11—22no—
91C24×C11—24no—
92C24×C11—41no—
93C24×C11—42no—
94C24×C11—41no—
95C24×C11—41no—
96C24×C11—41no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11—41no—
100C24×C11—41no—
101C24×C11C22⋊C412yes—
102C24×C11D812yes—
103C24×C11SD1612yes—
104C24×C11C2×D411yescharacteristic
105C2×D4×C11—216no—
106C2×D4×C11—22no—
107C2×D4×C11—24no—
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—24no—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—48no—
115C2×D4×C11—416no—
116C2×D4×C11—416no—
117C2×D4×C11—48no—
118C2×D4×C11—41no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—41no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11C22⋊C414yescomplemented
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11C22⋊C412yes—
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4112yes—
159C22×C4×C11#4112yes—
160C22×Dic11—24no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C22×Dic11—42no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4C22⋊C414yescomplemented
170C11×C22⋊C4—216no—
171C22⋊Dic11—48no—
172C4⋊Dic11—24no—
173C4⋊Dic11—24no—
174C4⋊Dic11—42no—
175C4⋊Dic11—42no—
176C2×C11⋊C8—24no—
177C2×C11⋊C8—24no—
178C2×C11⋊C8—24no—
179C2×C11⋊C8—42no—
180C2×C11⋊C8—42no—
181C2×C11⋊C8—42no—
182C2×C11⋊C8—42no—
183C22×#121D1111yescharacteristic
184C22×#102—112no—
185C22×C22⋊C8—111no—
186C2×#380—111no—
187C2×#340—112no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—44no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—81no—
224C23×C11—81no—
225C23×C11—82no—
226C23×C11—82no—
227C23×C11—82no—
228C23×C11—82no—
229C23×C11—82no—
230C23×C11—81no—
231C23×C11—81no—
232C23×C11—82no—
233C23×C11#10214yescomplemented
234C23×C11C2×C22⋊C411yescharacteristic
235C23×C11#12011yescharacteristic
236C23×C11#12012yes—
237C23×C11#12112yes—
238C23×C11#12311yescharacteristic
239C23×C11C2×D811yescharacteristic
240C23×C11C2×SD1611yescharacteristic
241C23×C11#13512yes—
242C23×C11AGL(1,ℤ/8)12yes—
243C23×C11AGL(1,ℤ/8)11yescharacteristic
244C23×C11#13711yescharacteristic
245D4×C11—28no—
246D4×C11—432no—
247D4×C11—44no—
248D4×C11—44no—
249D4×C11—44no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—44no—
259C2×C4×C11—44no—
260C2×C4×C11—44no—
261C2×C4×C11—44no—
262C2×C4×C11—44no—
263C2×C4×C11—44no—
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C4×D412yes—
267C2×C4×C11C4×D412yes—
268C2×C4×C11#12012yes—
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12012yes—
271C2×C4×C11#12112yes—
272C2×C4×C11#12112yes—
273C2×C4×C11#12112yes—
274C2×C4×C11#12112yes—
275C2×C4×C11#12112yes—
276C2×C4×C11#12312yes—
277C2×C4×C11#12311yescharacteristic
278C2×C4×C11#12412yes—
279C2×C4×C11#12712yes—
280C2×Dic11—44no—
281C2×Dic11—44no—
282C2×Dic11—44no—
283C2×Dic11—82no—
284C2×Dic11—82no—
285C2×Dic11—82no—
286C2×Dic11—82no—
287C11⋊C8—44no—
288C23×D4—21no—
289C23×D4C2×D1111yescharacteristic
290C24×C4C2×D1111yescharacteristic
291C23×C8—112no—
292C2×#121—24no—
293C2×#121—22no—
294C2×#121—24no—
295C2×#121Dic1114yescomplemented
296C22×C4⋊C4—112no—
297C22×C4⋊C4C2×D1111yescharacteristic
298C22×C22⋊C4—21no—
299C22×C22⋊C4—221no—
300C2×#102—224no—
301C2×#102—224no—
302C2×#102—224no—
303C2×C22⋊C8—224no—
304C2×C22⋊C8—222no—
305#380—224no—
306C2×#95—221no—
307#340—224no—
308C22×C11—24no—
309C22×C11—24no—
310C22×C11—24no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—82no—
323C22×C11—82no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11—84no—
327C22×C11—84no—
328C22×C11—84no—
329C22×C11—84no—
330C22×C11#37911yescharacteristic
331C22×C11#38611yescharacteristic
332C22×C11#38611yescharacteristic
333C22×C11#39212yes—
334C22×C11#39412yes—
335C22×C11C2×#10211yescharacteristic
336C22×C11#41611yescharacteristic
337C22×C11#41711yescharacteristic
338C22×C11#41811yescharacteristic
339C22×C11#44712yes—
340C22×C11#44711yescharacteristic
341C22×C11#44811yescharacteristic
342C22×C11#44912yes—
343C22×C11#44912yes—
344C22×C11#45012yes—
345C22×C11#45212yes—
346C22×C11#46512yes—
347C22×C11#46612yes—
348C22×C11#46812yes—
349C22×C11#46912yes—
350C22×C11#48011yescharacteristic
351C22×C11#48111yescharacteristic
352C22×C11#48212yes—
353C4×C11—42no—
354C4×C11—44no—
355C4×C11#38612yes—
356C4×C11#39012yes—
357C4×C11#39212yes—
358C4×C11#39412yes—
359Dic11—84no—
360C25—21no—
361C25C22⋊D1111yescharacteristic
362C22×D4—28no—
363C22×D4—24no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—21no—
369C22×D4—22no—
370C22×D4—44no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4C2×Dic1112yes—
374C22×D4C22⋊D1114yes—
375C23×C4—21no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—222no—
383C23×C4C2×Dic1112yes—
384C23×C4C22⋊D1111yescharacteristic
385C23×C4C22⋊D1112yes—
386C23×C4C22×D1111yescharacteristic
387C22×C8—114no—
388C22×C8—222no—
389C22×C8—222no—
390C22×C8—222no—
391C22×C8—222no—
392C22×C8—222no—
393C22×C8—222no—
394#121—216no—
395#121—28no—
396#121—28no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4C2×Dic1112yes—
406C2×C4⋊C4C22⋊D1114yes—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—224no—
410C2×C22⋊C4—442no—
411C2×C22⋊C4—442no—
412#102—2216no—
413C22⋊C8—228no—
414#95—224no—
415C2×C11—44no—
416C2×C11—84no—
417C2×C11#143811yescharacteristic
418C2×C11#178611yescharacteristic
419C2×C11#178811yescharacteristic
420C2×C11#187411yescharacteristic
421C2×C11#187511yescharacteristic
422C2×C11#189311yescharacteristic
423C2×C11#189511yescharacteristic
424C2×C11#199912yes—
425C2×C11#200012yes—
426C2×C11#203312yes—
427C2×C11#203412yes—
428C24—22no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24—22no—
436C24—22no—
437C24—24no—
438C24—41no—
439C24—42no—
440C24—41no—
441C24—41no—
442C24—41no—
443C24—42no—
444C24—41no—
445C24—42no—
446C24—41no—
447C24#432312yes—
448C24#432412yes—
449C24C22⋊Dic1112yes—
450C24C2×C22⋊D1111yescharacteristic
451C2×D4—216no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4—24no—
460C2×D4—48no—
461C2×D4—416no—
462C2×D4—416no—
463C2×D4—48no—
464C2×D4—41no—
465C2×D4—42no—
466C2×D4—41no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4C22⋊Dic1114yescomplemented
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—41no—
487C22×C4—42no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—224no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4C22⋊Dic1112yes—
505C22×C4D4×D1112yes—
506C22×C4D4×D1112yes—
507C22×C4#434112yes—
508C22×C4#434112yes—
509C22×C4C22×Dic1111yescharacteristic
510C22×C4C2×C22⋊D1112yes—
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1112yes—
513C2×C8—224no—
514C2×C8—224no—
515C2×C8—224no—
516C2×C8—442no—
517C2×C8—442no—
518C2×C8—442no—
519C2×C8—442no—
520C4⋊C4—22no—
521C4⋊C4—24no—
522C4⋊C4—224no—
523C4⋊C4—224no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4C22⋊Dic1114yescomplemented
527C22⋊C4—216no—
528C22⋊C4—448no—
529C11#1096911yescharacteristic, complemented, Sylow
530C23—22no—
531C23—24no—
532C23—24no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—24no—
542C23—22no—
543C23—24no—
544C23—24no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—44no—
556C23—44no—
557C23—42no—
558C23—42no—
559C23—44no—
560C23—44no—
561C23—42no—
562C23—42no—
563C23—44no—
564C23—44no—
565C23—81no—
566C23—81no—
567C23—82no—
568C23—81no—
569C23—82no—
570C23—82no—
571C23—82no—
572C23—81no—
573C23—82no—
574C23—82no—
575C23#6689614yescomplemented
576C23C2×#432311yescharacteristic
577C23#6698512yes—
578C23C2×#432411yescharacteristic
579C23#6698811yescharacteristic
580C23#6699011yescharacteristic
581C23#6699212yes—
582C23#6700211yescharacteristic
583C23#6700312yes—
584C23#6700411yescharacteristic
585C23C2×C22⋊Dic1111yescharacteristic
586C23#6700612yes—
587D4—28no—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—444no—
607C2×C4—444no—
608C2×C4—444no—
609C2×C4—882no—
610C2×C4—882no—
611C2×C4—882no—
612C2×C4—882no—
613C2×C4D4×Dic1112yes—
614C2×C4D4×Dic1112yes—
615C2×C4#6698812yes—
616C2×C4#6698811yescharacteristic
617C2×C4#6698912yes—
618C2×C4#6699012yes—
619C2×C4#6699011yescharacteristic
620C2×C4#6699112yes—
621C2×C4#6699112yes—
622C2×C4#6699212yes—
623C2×C4#6699212yes—
624C2×C4#6699212yes—
625C2×C4#6699312yes—
626C2×C4C2×C22⋊Dic1111yescharacteristic
627C2×C4C2×C22⋊Dic1111yescharacteristic
628C2×C4#6700612yes—
629C8—444no—
630C22—24no—
631C22—24no—
632C22—24no—
633C22—42no—
634C22—44no—
635C22—44no—
636C22—42no—
637C22—42no—
638C22—44no—
639C22—44no—
640C22—42no—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—84no—
645C22—84no—
646C22—82no—
647C22—82no—
648C22—84no—
649C22—84no—
650C22—82no—
651C22—82no—
652C22#1062264611yescharacteristic
653C22#1062264711yescharacteristic
654C22#1062264812yes—
655C22#1062264911yescharacteristic
656C22#1062265012yes—
657C22#1062265112yes—
658C22#1062265212yes—
659C22#1062265311yescharacteristic
660C22#1062265412yes—
661C22#1062265512yes—
662C22C2×#6689611yescharacteristic
663C22#1062282811yescharacteristic
664C22#1062283012yes—
665C22#1062283112yes—
666C22#1062283311yescharacteristic
667C22#1062283311yescharacteristic
668C22#1062283512yes—
669C22#1062283612yes—
670C22#1062284511yescharacteristic
671C22#1062284611yescharacteristic
672C22#1062285112yes—
673C22#1062285212yes—
674C22#1062286011yescharacteristic
675C4—44no—
676C4—42no—
677C4—884no—
678C4#1062283312yes—
679C4#1062283412yes—
680C4#1062283512yes—
681C4#1062283612yes—
682C2—44no—
683C2—84no—
684C2#1306685711yescharacteristic
685C2#1306854711yescharacteristic
686C2#1306855611yescharacteristic
687C2#1306893411yescharacteristic
688C2#1306893911yescharacteristic
689C2#1306904511yescharacteristic
690C2#1306905511yescharacteristic
691C2#1306961212yes—
692C2#1306961912yes—
693C2#1306979512yes—
694C2#1306980212yes—
subgroupG/H
centerC24C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC22×C11×#121C2
socleC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC22×#121D11
hypocenterC11#10969
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66896C2semidirect
2. C22×C22⋊(C11⋊C8)C2semidirect
3. C2×#10622825C2semidirect
4. C2×#10622167C2semidirect
12. C2×C11×#121C4semidirect
70. C2×C4⋊Dic11D4semidirect
77. C22×C11⋊C8D4semidirect
125. C2×D4×C11C22⋊C4semidirect
169. C11×C4⋊C4C22⋊C4semidirect
233. C23×C11#102semidirect
295. C2×#121Dic11semidirect
471. C2×D4C22⋊Dic11semidirect
526. C4⋊C4C22⋊Dic11semidirect
529. C11#10969semidirect
575. C23#66896semidirect

Maximal subgroups

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

subgroupindex
C22×#668962
C22×C22⋊(C11⋊C8)2
C2×#106228252
C2×#106221672
C22×C11×#1212
#1096911