Finite Group Databasebeta

← #14660279

Subgroups — #14660279

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×#66873C212yesmaximal, complemented
3C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
4C2×#10622167C212yesmaximal, complemented
5C2×C11×#380C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C23×C22⋊D11—21no—
8C23×D44C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×C11×C22⋊C4—21no—
11C2×#66983—22no—
12C2×#66983—24no—
13C2×#66983—24no—
14C2×#66983C414yescomplemented
15C22×(C2×D11)⋊C4—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C23×C11⋊C8C2212yes—
18C11×#380—24no—
19C2×C11×#95—21no—
20C2×C22⋊(C11⋊C8)—22no—
21C2×C22⋊(C11⋊C8)—24no—
22C2×#66873—24no—
23C2×#66873—24no—
24C2×#66873—24no—
25#10622167—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×C11—22no—
35C23×C4×C11C2×C412yes—
36C23×C4×C11D412yes—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—28no—
40C22×C22⋊D11—24no—
41C22×C22⋊D11—44no—
42C22×C22⋊D11—42no—
43C22×C22⋊D11—42no—
44C23×Dic11—21no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—22no—
49C22×D44—21no—
50C22×D44—22no—
51C22×D44C2×C412yes—
52C22×D44D414yes—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4D414yescomplemented
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—42no—
61C2×C11×C22⋊C4—42no—
62#66983—216no—
63#66983—28no—
64#66983—28no—
65C2×(C2×D11)⋊C4—28no—
66C2×(C2×D11)⋊C4—24no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11C2×C412yes—
70C2×C4⋊Dic11D414yes—
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
78C11×#95—24no—
79C22⋊(C11⋊C8)—28no—
80#66873—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—24no—
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×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C22⋊C412yes—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11#4112yes—
140C22×C4×C11#4112yes—
141C2×C22⋊D11—216no—
142C2×C22⋊D11—48no—
143C2×C22⋊D11—416no—
144C2×C22⋊D11—416no—
145C2×C22⋊D11—48no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—41no—
149C22×Dic11—41no—
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
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C22⋊C4—48no—
172(C2×D11)⋊C4—216no—
173C4⋊Dic11—22no—
174C4⋊Dic11—24no—
175C4⋊Dic11C22⋊C414yescomplemented
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×#121—111no—
184C22×#102—112no—
185C22×C22⋊C8—111no—
186C2×#380D1111yescharacteristic, complemented
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×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11—44no—
257C2×C4×C11—82no—
258C2×C4×C11—82no—
259C2×C4×C11—82no—
260C2×C4×C11—82no—
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C4×D412yes—
264C2×C4×C11C4×D412yes—
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12012yes—
267C2×C4×C11#12012yes—
268C2×C4×C11#12112yes—
269C2×C4×C11#12112yes—
270C2×C4×C11#12112yes—
271C2×C4×C11#12112yes—
272C2×C4×C11#12112yes—
273C2×C4×C11#12312yes—
274C2×C4×C11#12311yescharacteristic
275C2×C4×C11#12412yes—
276C2×C4×C11#12712yes—
277C22⋊D11—432no—
278C2×Dic11—24no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—44no—
282C2×Dic11—44no—
283D44—28no—
284D44—44no—
285D44—44no—
286D44—44no—
287C11⋊C8—44no—
288C23×D4—111no—
289C23×D4—221no—
290C24×C4C2×D1111yescharacteristic
291C23×C8—112no—
292C2×#121—114no—
293C2×#121—224no—
294C2×#121—224no—
295C2×#121—222no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4C2×D1112yes—
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—24no—
306C2×#95—21no—
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—84no—
355C4×C11#38612yes—
356C4×C11#39012yes—
357C4×C11#39212yes—
358C4×C11#39412yes—
359Dic11—44no—
360C25—221no—
361C25C22⋊D1111yescharacteristic
362C22×D4—112no—
363C22×D4—114no—
364C22×D4—228no—
365C22×D4—224no—
366C22×D4—221no—
367C22×D4—222no—
368C22×D4—222no—
369C22×D4—222no—
370C22×D4—222no—
371C22×D4—222no—
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—22no—
382C23×C4—221no—
383C23×C4C4×D1112yes—
384C23×C4D4412yes—
385C23×C4C22⋊D1111yescharacteristic
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—228no—
395#121—228no—
396#121—2216no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4C22⋊D1114yescomplemented
407C2×C22⋊C4—24no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—228no—
411C2×C22⋊C4—224no—
412#102—2216no—
413C22⋊C8—228no—
414#95—24no—
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—21no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—21no—
436C24—222no—
437C24—224no—
438C24—441no—
439C24—441no—
440C24—441no—
441C24—442no—
442C24—441no—
443C24—441no—
444C24—442no—
445C24—442no—
446C24—441no—
447C24(C2×D11)⋊C412yes—
448C24#432312yes—
449C24#432512yes—
450C24C2×C22⋊D1111yescharacteristic
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—441no—
466C2×D4—442no—
467C2×D4—442no—
468C2×D4—441no—
469C2×D4—442no—
470C2×D4—442no—
471C2×D4—442no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
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—42no—
498C22×C4—42no—
499C22×C4—222no—
500C22×C4—224no—
501C22×C4—441no—
502C22×C4—441no—
503C22×C4—442no—
504C22×C4(C2×D11)⋊C412yes—
505C22×C4C2×C4×D1111yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4#433912yes—
508C22×C4D4×D1112yes—
509C22×C4D4×D1112yes—
510C22×C4D4×D1112yes—
511C22×C4#434112yes—
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—24no—
521C4⋊C4—24no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—114no—
525C4⋊C4—222no—
526C4⋊C4—224no—
527C22⋊C4—48no—
528C22⋊C4—2216no—
529C11#1096911yescharacteristic, complemented, Sylow
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—224no—
553C23—442no—
554C23—442no—
555C23—444no—
556C23—442no—
557C23—442no—
558C23—444no—
559C23—442no—
560C23—442no—
561C23—444no—
562C23—444no—
563C23—444no—
564C23—444no—
565C23—881no—
566C23—881no—
567C23—881no—
568C23—881no—
569C23—882no—
570C23—882no—
571C23—882no—
572C23—882no—
573C23—882no—
574C23—882no—
575C23#6687314yescomplemented
576C23C2×(C2×D11)⋊C411yescharacteristic
577C23#6698211yescharacteristic
578C23C2×#432311yescharacteristic
579C23#6698511yescharacteristic
580C23#6699012yes—
581C23#6699212yes—
582C23C2×#432511yescharacteristic
583C23#6699511yescharacteristic
584C23#6700212yes—
585C23#6700312yes—
586C23#6700611yescharacteristic
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—44no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4—224no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—444no—
612C2×C4—444no—
613C2×C4C22⋊C4×D1111yescharacteristic
614C2×C4C22⋊C4×D1111yescharacteristic
615C2×C4(C22⋊D11)⋊C412yes—
616C2×C4#6693511yescharacteristic
617C2×C4#6693512yes—
618C2×C4#6693612yes—
619C2×C4#6693712yes—
620C2×C4#6693712yes—
621C2×C4#6693812yes—
622C2×C4#6693911yescharacteristic
623C2×C4C4×C22⋊D1112yes—
624C2×C4#6698312yes—
625C2×C4#6699012yes—
626C2×C4#6699112yes—
627C2×C4#6699212yes—
628C2×C4#6699312yes—
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—444no—
642C22—444no—
643C22—444no—
644C22—884no—
645C22—884no—
646C22—882no—
647C22—882no—
648C22—884no—
649C22—884no—
650C22—882no—
651C22—882no—
652C22#1062256811yescharacteristic
653C22#1062257111yescharacteristic
654C22#1062257212yes—
655C22C2×#6687311yescharacteristic
656C22#1062257911yescharacteristic
657C22#1062258011yescharacteristic
658C22#1062258111yescharacteristic
659C22#1062261411yescharacteristic
660C22#1062261511yescharacteristic
661C22#1062261612yes—
662C22#1062264912yes—
663C22#1062265012yes—
664C22#1062265112yes—
665C22#1062265212yes—
666C22#1062265912yes—
667C22#1062266012yes—
668C22#1062266112yes—
669C22#1062266212yes—
670C22#1062282611yescharacteristic
671C22#1062283011yescharacteristic
672C22#1062283612yes—
673C22#1062284011yescharacteristic
674C22#1062285112yes—
675C4—42no—
676C4—84no—
677C4—444no—
678C4#1062256912yes—
679C4#1062257012yes—
680C4#1062257312yes—
681C4#1062257412yes—
682C2—44no—
683C2—884no—
684C2#1306685511yescharacteristic
685C2#1306854611yescharacteristic
686C2#1306855411yescharacteristic
687C2#1306893311yescharacteristic
688C2#1306893811yescharacteristic
689C2#1306904211yescharacteristic
690C2#1306905211yescharacteristic
691C2#1306961212yes—
692C2#1306961712yes—
693C2#1306979812yes—
694C2#1306980512yes—
subgroupG/H
centerC24C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#380C2
socleC24×C11C2×D4
prime radicalC22×#66983C2
cosocleC23×C4×C11C23
hypercenterC2×#380D11
hypocenterC11#10969
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#66873C2semidirect
3. C22×C22⋊(C11⋊C8)C2semidirect
4. C2×#10622167C2semidirect
5. C2×C11×#380C2semidirect
14. C2×#66983C4semidirect
58. C2×C11×C4⋊C4D4semidirect
77. C22×C11⋊C8D4semidirect
166. C2×D44C22⋊C4semidirect
175. C4⋊Dic11C22⋊C4semidirect
186. C2×#380D11semidirect
210. C23×C11#102semidirect
406. C2×C4⋊C4C22⋊D11semidirect
529. C11#10969semidirect
575. C23#66873semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C22×#668732
C22×C22⋊(C11⋊C8)2
C2×#106221672
C2×C11×#3802
#1096911