Finite Group Databasebeta

← #14810344

Subgroups — #14810344

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622668C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3#13073608C211yesmaximal, characteristic, complemented
4#13069809C212yesmaximal, complemented
5#13069802C212yesmaximal, complemented
6#13069549C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068556C212yesmaximal, complemented
9#13068547C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×C11×#546C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C11×#546—24no—
15C11×#546—24no—
16C2×C11×#124C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121—21no—
20C2×C11×#121C2211yescharacteristic
21C2×C11×#120—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C22⋊C4—21no—
25C2×#66989—21no—
26C2×#66922C2211yescharacteristic, complemented
27C2×#66899C2212yescomplemented
28C2×#66899C2212yescomplemented
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2212yes—
32C2×#66896C2212yes—
33#10622825C2212yes—
34#10622825C2212yescomplemented
35C2×C22⋊(C11⋊C8)C2212yes—
36C2×C22⋊(C11⋊C8)C2212yescomplemented
37#10622668—24no—
38#10622621—24no—
39#10622587—21no—
40C2×#66872C2212yescomplemented
41#10622566—21no—
42#10622566—21no—
43C4×C4⋊Dic11C2211yescharacteristic, complemented
44C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
45C2×#66867C2211yescharacteristic, complemented
46#10622167C2212yescomplemented
47C25×C11—21no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—24no—
51C2×C11×#41—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—24no—
58C22×D4×C11—21no—
59C22×D4×C11—42no—
60C22×D4×C11D411yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×Dic22—21no—
68C11×#124—22no—
69C11×#124D414yes—
70C11×#123—28no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×#121—28no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#120—28no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11D414yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95#66989—44no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2312yes—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2312yes—
101C22×C11⋊C8C2312yes—
102#66922—22no—
103#66922—22no—
104#66899—24no—
105#66899—42no—
106#66896—24no—
107#66896—24no—
108#66896—24no—
109#66896—42no—
110C11⋊#95—21no—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C22⋊(C11⋊C8)—42no—
114C22⋊(C11⋊C8)—42no—
115#66872—24no—
116C4⋊(C11⋊C8)—22no—
117#66867—22no—
118#25898—111nomaximal, Sylow
119C24×C11—21no—
120C24×C11—24no—
121C24×C11—21no—
122C24×C11—44no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—82no—
126C24×C11C2×D411yescharacteristic
127C24×C11C2×D411yescharacteristic
128C11×#41—48no—
129C11×#41—44no—
130C11×#41—44no—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11—22no—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—41no—
146C2×D4×C11—44no—
147C2×D4×C11—48no—
148C2×D4×C11—44no—
149C2×D4×C11—44no—
150C2×D4×C11—44no—
151C2×D4×C11—82no—
152C2×D4×C11C2×D412yes—
153C2×D4×C11C2×D412yes—
154C2×D4×C11#4114yes—
155C22×C4×C11—24no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—24no—
167C22×C4×C11—44no—
168C22×C4×C11—82no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×Dic11—22no—
175C22×Dic11—22no—
176C2×Dic22—42no—
177C2×Dic22—42no—
178C2×Dic22—42no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4C2×D412yes—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—22no—
190C42×C11C2×D412yes—
191C42×C11C2×D412yes—
192C22⋊Dic11—44no—
193C22⋊Dic11—44no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11—22no—
197C4⋊Dic11—22no—
198C4⋊Dic11—42no—
199C4×Dic11—42no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×#546D1111yescharacteristic
207C2×#489—111no—
208C2×#476—111no—
209#2547—111no—
210#2035—112no—
211#2034—112no—
212#1983—111no—
213#1955—111no—
214#1788—112no—
215#1786—112no—
216#1762—111no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—21no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—21no—
225C23×C11—22no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—48no—
230C23×C11—48no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—42no—
238C23×C11—88no—
239C23×C11—84no—
240C23×C11—88no—
241C23×C11AGL(1,ℤ/8)12yes—
242C23×C11C22×D411yescharacteristic
243Q8×C11—24no—
244Q8×C11—41no—
245Q8×C11—41no—
246D4×C11—22no—
247D4×C11—24no—
248D4×C11—24no—
249D4×C11—44no—
250D4×C11—48no—
251D4×C11—48no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—84no—
255D4×C11#12414yescomplemented
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—48no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—84no—
275C2×C4×C11#12012yes—
276C2×C4×C11#12012yes—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4112yes—
280C2×C4×C11H(5,𝔽2)12yes—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287Dic22—84no—
288C11⋊C8—42no—
289C11⋊C8—42no—
290C22×#41C2×D1111yescharacteristic
291C23×D4C2×D1111yescharacteristic
292#546—24no—
293#546—24no—
294C2×C4⋊Q8—111no—
295C2×#124—221no—
296C2×#124C2×D1111yescharacteristic
297C2×#123—21no—
298C2×C22⋊Q8C2×D1111yescharacteristic
299C2×#121—21no—
300C2×#121C2×D1111yescharacteristic
301C2×#120—21no—
302C2×C4×D4C2×D1111yescharacteristic
303C2×C4×D4C2×D1111yescharacteristic
304C22×C22⋊C4—21no—
305#489—224no—
306#476—224no—
307C2×#106—112no—
308C2×C4⋊C8—111no—
309C2×#103—112no—
310C2×#103—112no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—112no—
315C2×C22⋊C8—112no—
316C2×C22⋊C8—112no—
317C2×#97—111no—
318#397—221no—
319#397—221no—
320#391—221no—
321#380—112no—
322#380—112no—
323C4×C4⋊C4—111no—
324#340—112no—
325C22×C11—24no—
326C22×C11—22no—
327C22×C11—24no—
328C22×C11—41no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—41no—
332C22×C11—44no—
333C22×C11—42no—
334C22×C11—44no—
335C22×C11—41no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11—42no—
339C22×C11—41no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—816no—
344C22×C11—82no—
345C22×C11—82no—
346C22×C11C2×#12011yescharacteristic
347C22×C11#54612yes—
348C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57712yes—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11C2×#12411yescharacteristic
358C4×C11#53511yescharacteristic
359C4×C11#54612yes—
360Dic11—82no—
361Dic11—82no—
362C25—21no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—24no—
366C2×#41—42no—
367C22×Q8—221no—
368C22×Q8C22×D1111yescharacteristic
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—24no—
374C22×D4—21no—
375C22×D4—42no—
376C22×D4C22⋊D1111yescharacteristic
377C22×D4C22×D1111yescharacteristic
378C22×D4C22×D1111yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C22×C8—112no—
384C22×C8—112no—
385C4⋊Q8—222no—
386C4⋊Q8—222no—
387#124—22no—
388#124—444no—
389#124C22⋊D1114yes—
390#123—28no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393#121—28no—
394#121—22no—
395#121—22no—
396#120—28no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4C22⋊D1114yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22⋊D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C22⋊C4—28no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4C22⋊D1111yescharacteristic
416C2×C22⋊C4C22⋊D1111yescharacteristic
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#106—224no—
420C4⋊C8—222no—
421#103—224no—
422#103—442no—
423#102—224no—
424#102—224no—
425#102—224no—
426#102—442no—
427C22⋊C8—442no—
428C22⋊C8—442no—
429#97—222no—
430#95—221no—
431#95—222no—
432#95—222no—
433C2×C11—42no—
434C2×C11—44no—
435C2×C11—81no—
436C2×C11—82no—
437C2×C11#243511yescharacteristic
438C2×C11#300611yescharacteristic
439C2×C11#300911yescharacteristic
440C2×C11#330612yes—
441C2×C11#331112yes—
442C24—21no—
443C24—24no—
444C24—21no—
445C24—44no—
446C24—42no—
447C24—42no—
448C24—82no—
449C24C2×C22⋊D1111yescharacteristic
450C24C2×C22⋊D1111yescharacteristic
451#41—48no—
452#41—44no—
453#41—44no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—442no—
458C2×Q8—442no—
459C2×Q8—442no—
460C2×Q8C2×C22⋊D1112yes—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—41no—
472C2×D4—44no—
473C2×D4—48no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—82no—
478C2×D4#434114yes—
479C2×D4C2×C22⋊D1112yes—
480C2×D4C2×C22⋊D1112yes—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—82no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502C2×C8—222no—
503C2×C8—222no—
504C2×C8—222no—
505C2×C8—222no—
506C2×C8—222no—
507C2×C8—222no—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—442no—
516C4⋊C4C2×C22⋊D1112yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—22no—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—24no—
523C22⋊C4—22no—
524C22⋊C4—444no—
525C22⋊C4—444no—
526C42—442no—
527C42C2×C22⋊D1112yes—
528C42C2×C22⋊D1112yes—
529C11#2589811yescharacteristic, complemented, Sylow
530C23—22no—
531C23—24no—
532C23—21no—
533C23—22no—
534C23—21no—
535C23—22no—
536C23—22no—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—22no—
541C23—21no—
542C23—48no—
543C23—48no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23—41no—
549C23—41no—
550C23—42no—
551C23—88no—
552C23—84no—
553C23—88no—
554C23#6700212yes—
555C23C22×C22⋊D1111yescharacteristic
556Q8—24no—
557Q8—41no—
558Q8—41no—
559Q8—884no—
560D4—22no—
561D4—24no—
562D4—24no—
563D4—44no—
564D4—48no—
565D4—48no—
566D4—41no—
567D4—41no—
568D4—84no—
569D4#6698914yescomplemented
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—48no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—84no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4#6700612yes—
596C2×C4#6700612yes—
597C2×C4C2×#434112yes—
598C2×C4#6703712yes—
599C2×C4C22×C22⋊D1111yescharacteristic
600C2×C4C22×C22⋊D1111yescharacteristic
601C8—442no—
602C8—442no—
603C22—24no—
604C22—22no—
605C22—24no—
606C22—44no—
607C22—42no—
608C22—44no—
609C22—42no—
610C22—42no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—41no—
616C22—42no—
617C22—41no—
618C22—42no—
619C22—41no—
620C22—42no—
621C22—816no—
622C22—82no—
623C22—82no—
624C22#1062333712yes—
625C22C2×#6700211yescharacteristic
626C22#1062335311yescharacteristic
627C22#1062336712yes—
628C22C2×#6700611yescharacteristic
629C4—22no—
630C4—22no—
631C4—42no—
632C4—41no—
633C4—41no—
634C4—42no—
635C4—882no—
636C4—882no—
637C4C2×#6698911yescharacteristic
638C4#1062333611yescharacteristic
639C4#1062333712yes—
640C2—42no—
641C2—44no—
642C2—81no—
643C2—82no—
644C2#1307226311yescharacteristic
645C2#1307786811yescharacteristic
646C2#1307789311yescharacteristic
647C2#1308057712yes—
648C2#1308065212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11#25898
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#10622668C2semidirect
2. C2×#10622621C2semidirect
3. #13073608C2semidirect
4. #13069809C2semidirect
5. #13069802C2semidirect
6. #13069549C2semidirect
7. #13069415C2semidirect
8. #13068556C2semidirect
9. #13068547C2semidirect
10. #13068441C2semidirect
26. C2×#66922C22semidirect
27. C2×#66899C22semidirect
28. C2×#66899C22semidirect
34. #10622825C22semidirect
36. C2×C22⋊(C11⋊C8)C22semidirect
40. C2×#66872C22semidirect
43. C4×C4⋊Dic11C22semidirect
44. C2×C4⋊(C11⋊C8)C22semidirect
45. C2×#66867C22semidirect
46. #10622167C22semidirect
255. D4×C11#124semidirect
529. C11#25898semidirect
569. D4#66989semidirect

Maximal subgroups

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

subgroupindex
C2×#106226682
C2×#106226212
#130736082
#130698092
#130698022
#130695492
#130694152
#130685562
#130685472
#130684412
C2×C11×#5462
#2589811