Finite Group Databasebeta

← #14660282

Subgroups — #14660282

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×#66983C211yesmaximal, characteristic
2C22×#66885C212yesmaximal, complemented
3C2×#10622825C211yesmaximal, characteristic, complemented
4C2×#10622189C212yesmaximal, complemented
5C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C23×C22⋊D11—21no—
8C23×D44C2211yescharacteristic
9C23×C8×C11C2212yes—
10C22×C22⋊Dic11—21no—
11C2×#66983—22no—
12C2×#66983—24no—
13C2×#66983—24no—
14C2×#66983C414yescomplemented
15C22×(C2×D11)⋊C4—21no—
16C22×C4⋊Dic11C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C2×C11×C22⋊C8—22no—
19C2×C11×C22⋊C8—24no—
20#10622825—24no—
21C2×C11⋊#95—21no—
22C2×#66885—24no—
23C2×#66885—24no—
24C2×#66885—24no—
25#10622189—24no—
26C25×C11D411yescharacteristic
27C24×D11—21no—
28C23×C4×C11—22no—
29C23×C4×C11—22no—
30C23×C4×C11—22no—
31C23×C4×C11—22no—
32C23×C4×C11—22no—
33C23×C4×C11—22no—
34C23×C4×C11C2×C412yes—
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D412yes—
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11—28no—
39C22×C22⋊D11—24no—
40C22×C22⋊D11—44no—
41C22×C22⋊D11—42no—
42C22×C22⋊D11—42no—
43C23×Dic11—21no—
44C23×Dic11—22no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44—22no—
50C22×D44—21no—
51C22×D44C2×C412yes—
52C22×D44D414yes—
53C22×C8×C11—22no—
54C22×C8×C11—22no—
55C22×C8×C11—22no—
56C22×C8×C11—22no—
57C22×C8×C11—22no—
58C22×C8×C11—22no—
59C22×C8×C11D414yescomplemented
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—42no—
62C2×C22⋊Dic11—42no—
63#66983—216no—
64#66983—28no—
65#66983—28no—
66C2×(C2×D11)⋊C4—28no—
67C2×(C2×D11)⋊C4—24no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11C2×C412yes—
76C2×C4⋊Dic11D414yes—
77C2×C4⋊Dic11D414yescomplemented
78C11×C22⋊C8—28no—
79C11⋊#95—24no—
80#66885—216no—
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×C11C22⋊C412yes—
91C24×C11D812yes—
92C24×C11SD1612yes—
93C24×C11C2×D411yescharacteristic
94C23×D11—22no—
95C23×D11—24no—
96C23×D11—41no—
97C23×D11—42no—
98C23×D11—41no—
99C23×D11—41no—
100C23×D11—41no—
101C23×D11—42no—
102C23×D11—42no—
103C23×D11—41no—
104C23×D11—41no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11C22⋊C412yes—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C2×C22⋊D11—216no—
135C2×C22⋊D11—48no—
136C2×C22⋊D11—416no—
137C2×C22⋊D11—416no—
138C2×C22⋊D11—48no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—41no—
145C22×Dic11—42no—
146C22×Dic11—41no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C2×D44—22no—
152C2×D44—24no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—24no—
158C2×D44—24no—
159C2×D44—41no—
160C2×D44—42no—
161C2×D44—42no—
162C2×D44—42no—
163C2×D44—41no—
164C2×D44—42no—
165C2×D44—42no—
166C2×D44C22⋊C414yescomplemented
167C2×C8×C11—24no—
168C2×C8×C11—24no—
169C2×C8×C11—24no—
170C2×C8×C11—42no—
171C2×C8×C11—42no—
172C2×C8×C11—42no—
173C2×C8×C11—42no—
174C22⋊Dic11—48no—
175(C2×D11)⋊C4—216no—
176C4⋊Dic11—22no—
177C4⋊Dic11—24no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11—42no—
181C4⋊Dic11—42no—
182C4⋊Dic11C22⋊C414yescomplemented
183C22×#121—111no—
184C22×#102—112no—
185C22×C22⋊C8D1111yescharacteristic, complemented
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—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11#10214yescomplemented
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11#12012yes—
213C23×C11#12011yescharacteristic
214C23×C11#12112yes—
215C23×C11#12311yescharacteristic
216C23×C11C2×D811yescharacteristic
217C23×C11C2×SD1611yescharacteristic
218C23×C11#13512yes—
219C23×C11AGL(1,ℤ/8)11yescharacteristic
220C23×C11AGL(1,ℤ/8)12yes—
221C23×C11#13711yescharacteristic
222C22×D11—24no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—44no—
235C22×D11—81no—
236C22×D11—81no—
237C22×D11—82no—
238C22×D11—82no—
239C22×D11—82no—
240C22×D11—82no—
241C22×D11—82no—
242C22×D11—81no—
243C22×D11—81no—
244C22×D11—82no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—44no—
251C2×C4×C11—44no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C4×D412yes—
257C2×C4×C11C4×D412yes—
258C2×C4×C11#12012yes—
259C2×C4×C11#12012yes—
260C2×C4×C11#12011yescharacteristic
261C2×C4×C11#12112yes—
262C2×C4×C11#12112yes—
263C2×C4×C11#12112yes—
264C2×C4×C11#12112yes—
265C2×C4×C11#12112yes—
266C2×C4×C11#12312yes—
267C2×C4×C11#12311yescharacteristic
268C2×C4×C11#12412yes—
269C2×C4×C11#12712yes—
270C22⋊D11—432no—
271C2×Dic11—24no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C2×Dic11—44no—
278C2×Dic11—44no—
279C2×Dic11—82no—
280C2×Dic11—82no—
281C2×Dic11—82no—
282C2×Dic11—82no—
283D44—28no—
284D44—44no—
285D44—44no—
286D44—44no—
287C8×C11—44no—
288C23×D4—111no—
289C23×D4—221no—
290C24×C4C2×D1111yescharacteristic
291C23×C8C2×D1112yes—
292C2×#121—114no—
293C2×#121—224no—
294C2×#121—224no—
295C2×#121—222no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4—112no—
298C22×C22⋊C4—221no—
299C22×C22⋊C4—221no—
300C2×#102—224no—
301C2×#102—224no—
302C2×#102—224no—
303C2×C22⋊C8—22no—
304C2×C22⋊C8—24no—
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#37911yescharacteristic
320C22×C11#38611yescharacteristic
321C22×C11#38611yescharacteristic
322C22×C11#39212yes—
323C22×C11#39412yes—
324C22×C11C2×#10211yescharacteristic
325C22×C11#41611yescharacteristic
326C22×C11#41711yescharacteristic
327C22×C11#41811yescharacteristic
328C22×C11#44711yescharacteristic
329C22×C11#44712yes—
330C22×C11#44811yescharacteristic
331C22×C11#44912yes—
332C22×C11#44912yes—
333C22×C11#45012yes—
334C22×C11#45212yes—
335C22×C11#46512yes—
336C22×C11#46612yes—
337C22×C11#46812yes—
338C22×C11#46912yes—
339C22×C11#48011yescharacteristic
340C22×C11#48111yescharacteristic
341C22×C11#48212yes—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—82no—
346C2×D11—82no—
347C2×D11—82no—
348C2×D11—82no—
349C2×D11—84no—
350C2×D11—84no—
351C2×D11—84no—
352C2×D11—84no—
353C4×C11—42no—
354C4×C11#38612yes—
355C4×C11#39012yes—
356C4×C11#39212yes—
357C4×C11#39412yes—
358Dic11—44no—
359Dic11—84no—
360C25—221no—
361C25D4411yescharacteristic
362C22×D4—112no—
363C22×D4—114no—
364C22×D4—228no—
365C22×D4—224no—
366C22×D4—222no—
367C22×D4—222no—
368C22×D4—222no—
369C22×D4—222no—
370C22×D4—222no—
371C22×D4—221no—
372C22×D4—444no—
373C22×D4—442no—
374C22×D4—442no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—221no—
382C23×C4—222no—
383C23×C4C4×D1112yes—
384C23×C4D4411yescharacteristic
385C23×C4C22⋊D1112yes—
386C23×C4C22×D1111yescharacteristic
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8C22⋊D1114yescomplemented
394#121—228no—
395#121—228no—
396#121—2216no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C22⋊C4—228no—
408C2×C22⋊C4—224no—
409C2×C22⋊C4—224no—
410C2×C22⋊C4—442no—
411C2×C22⋊C4—442no—
412#102—2216no—
413C22⋊C8—28no—
414#95—224no—
415C2×C11—44no—
416C2×C11#143811yescharacteristic
417C2×C11#178611yescharacteristic
418C2×C11#178811yescharacteristic
419C2×C11#187411yescharacteristic
420C2×C11#187511yescharacteristic
421C2×C11#189311yescharacteristic
422C2×C11#189511yescharacteristic
423C2×C11#199912yes—
424C2×C11#200012yes—
425C2×C11#203312yes—
426C2×C11#203412yes—
427D11—84no—
428C24—21no—
429C24—22no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24—22no—
436C24—224no—
437C24—222no—
438C24—441no—
439C24—441no—
440C24—441no—
441C24—441no—
442C24—442no—
443C24—442no—
444C24—441no—
445C24—441no—
446C24—442no—
447C24#431412yes—
448C24D8812yes—
449C24(C2×D11)⋊C412yes—
450C24C2×D4411yescharacteristic
451C2×D4—114no—
452C2×D4—2216no—
453C2×D4—222no—
454C2×D4—224no—
455C2×D4—224no—
456C2×D4—224no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—224no—
460C2×D4—224no—
461C2×D4—448no—
462C2×D4—4416no—
463C2×D4—4416no—
464C2×D4—448no—
465C2×D4—442no—
466C2×D4—442no—
467C2×D4—441no—
468C2×D4—442no—
469C2×D4—442no—
470C2×D4—442no—
471C2×D4—441no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—224no—
493C22×C4—222no—
494C22×C4—224no—
495C22×C4—441no—
496C22×C4—441no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4(C2×D11)⋊C412yes—
505C22×C4C2×C4×D1111yescharacteristic
506C22×C4#433912yes—
507C22×C4D4×D1112yes—
508C22×C4D4×D1112yes—
509C22×C4D4×D1112yes—
510C22×C4#434112yes—
511C22×C4C2×C22⋊D1112yes—
512C22×C4C2×C22⋊D1111yescharacteristic
513C2×C8—24no—
514C2×C8—24no—
515C2×C8—24no—
516C2×C8—42no—
517C2×C8—42no—
518C2×C8—42no—
519C2×C8—42no—
520C4⋊C4—114no—
521C4⋊C4—222no—
522C4⋊C4—224no—
523C4⋊C4—224no—
524C4⋊C4—224no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C22⋊C4—2216no—
528C22⋊C4—448no—
529C11#1096911yescharacteristic, complemented, Sylow
530C23—22no—
531C23—24no—
532C23—24no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—24no—
539C23—22no—
540C23—24no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—224no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23—442no—
557C23—442no—
558C23—442no—
559C23—444no—
560C23—444no—
561C23—444no—
562C23—444no—
563C23—444no—
564C23—444no—
565C23—882no—
566C23—882no—
567C23—882no—
568C23—882no—
569C23—881no—
570C23—882no—
571C23—881no—
572C23—881no—
573C23—882no—
574C23—881no—
575C23#6688514yescomplemented
576C23#6693512yes—
577C23#6693511yescharacteristic
578C23#6693911yescharacteristic
579C23C2×#431411yescharacteristic
580C23C2×D8811yescharacteristic
581C23#6695712yes—
582C23#6696112yes—
583C23#6696111yescharacteristic
584C23#6696211yescharacteristic
585C23C2×(C2×D11)⋊C411yescharacteristic
586C23#6698312yes—
587D4—228no—
588D4—4432no—
589D4—444no—
590D4—444no—
591D4—444no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—224no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—444no—
605C2×C4—444no—
606C2×C4—444no—
607C2×C4—444no—
608C2×C4—444no—
609C2×C4—882no—
610C2×C4—882no—
611C2×C4—882no—
612C2×C4—882no—
613C2×C4C22⋊C4×D1111yescharacteristic
614C2×C4C22⋊C4×D1111yescharacteristic
615C2×C4(C22⋊D11)⋊C412yes—
616C2×C4#6693612yes—
617C2×C4#6693712yes—
618C2×C4#6693712yes—
619C2×C4#6693812yes—
620C2×C4C4×C22⋊D1112yes—
621C2×C4#6698211yescharacteristic
622C2×C4#6699012yes—
623C2×C4#6699012yes—
624C2×C4#6699112yes—
625C2×C4#6699212yes—
626C2×C4#6699212yes—
627C2×C4#6699312yes—
628C2×C4#6700611yescharacteristic
629C8—44no—
630C22—24no—
631C22—24no—
632C22—24no—
633C22—42no—
634C22—44no—
635C22—44no—
636C22—42no—
637C22—42no—
638C22—44no—
639C22—44no—
640C22—42no—
641C22—444no—
642C22—444no—
643C22—444no—
644C22—884no—
645C22—884no—
646C22—882no—
647C22—882no—
648C22—884no—
649C22—884no—
650C22—882no—
651C22—882no—
652C22#1062234412yes—
653C22#1062234512yes—
654C22#1062234511yescharacteristic
655C22#1062234612yes—
656C22#1062234712yes—
657C22#1062234712yes—
658C22#1062234811yescharacteristic
659C22#1062234911yescharacteristic
660C22#1062235012yes—
661C22#1062235111yescharacteristic
662C22#1062256811yescharacteristic
663C22#1062257111yescharacteristic
664C22#1062257312yes—
665C22#1062257412yes—
666C22C2×#6688511yescharacteristic
667C22#1062272611yescharacteristic
668C22#1062272712yes—
669C22#1062272812yes—
670C22#1062274411yescharacteristic
671C22#1062274611yescharacteristic
672C22#1062274712yes—
673C22#1062274812yes—
674C22#1062282611yescharacteristic
675C4—42no—
676C4—444no—
677C4—884no—
678C4#1062256912yes—
679C4#1062257012yes—
680C4#1062257212yes—
681C4#1062283612yes—
682C2—44no—
683C2—884no—
684C2#1306685511yescharacteristic
685C2#1306854811yescharacteristic
686C2#1306855711yescharacteristic
687C2#1306893111yescharacteristic
688C2#1306893611yescharacteristic
689C2#1306904411yescharacteristic
690C2#1306905411yescharacteristic
691C2#1306961412yes—
692C2#1306962112yes—
693C2#1306979912yes—
694C2#1306980612yes—
subgroupG/H
centerC24C2×D44
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×C22⋊C8C2
socleC24×C11C2×D4
prime radicalC22×#66983C2
cosocleC23×C4×C11C23
hypercenterC22×C22⋊C8D11
hypocenterC11#10969
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#66885C2semidirect
3. C2×#10622825C2semidirect
4. C2×#10622189C2semidirect
5. C22×C11×C22⋊C8C2semidirect
14. C2×#66983C4semidirect
59. C22×C8×C11D4semidirect
77. C2×C4⋊Dic11D4semidirect
166. C2×D44C22⋊C4semidirect
182. C4⋊Dic11C22⋊C4semidirect
185. C22×C22⋊C8D11semidirect
210. C23×C11#102semidirect
393. C22×C8C22⋊D11semidirect
529. C11#10969semidirect
575. C23#66885semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C22×#668852
C2×#106228252
C2×#106221892
C22×C11×C22⋊C82
#1096911