Finite Group Databasebeta

← #14810333

Subgroups — #14810333

Order 2816.

1442 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622668C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3#13073789C211yesmaximal, characteristic, complemented
4#13069816C212yesmaximal, complemented
5#13069795C212yesmaximal, 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×#66922C2211yescharacteristic, complemented
26C2×#66899C2212yescomplemented
27C2×#66899C2212yescomplemented
28#10622834—21no—
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#10622620—24no—
39#10622590—21no—
40C2×#66871C2212yescomplemented
41#10622560—21no—
42#10622560—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—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2312yes—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2312yes—
100C22×C11⋊C8C2312yes—
101#66922—22no—
102#66922—22no—
103#66899—24no—
104#66899—42no—
105#66896—24no—
106#66896—24no—
107#66896—24no—
108#66896—42no—
109C11⋊#95—21no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C22⋊(C11⋊C8)—42no—
113C22⋊(C11⋊C8)—42no—
114#66871—24no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117#25897—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11—24no—
120C24×C11—21no—
121C24×C11—44no—
122C24×C11—42no—
123C24×C11—42no—
124C24×C11—82no—
125C24×C11C2×D411yescharacteristic
126C24×C11C2×D411yescharacteristic
127C11×#41—48no—
128C11×#41—44no—
129C11×#41—44no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—41no—
145C2×D4×C11—44no—
146C2×D4×C11—48no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—44no—
150C2×D4×C11—82no—
151C2×D4×C11C2×D412yes—
152C2×D4×C11C2×D412yes—
153C2×D4×C11#4114yes—
154C22×C4×C11—24no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—24no—
166C22×C4×C11—44no—
167C22×C4×C11—82no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C22×Dic11—22no—
174C22×Dic11—22no—
175C2×Dic22—42no—
176C2×Dic22—82no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2×D412yes—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—24no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—22no—
188C42×C11C2×D412yes—
189C42×C11C2×D412yes—
190C22⋊Dic11—82no—
191C22⋊Dic11—82no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11—42no—
197C4×Dic11—42no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×#546D1111yescharacteristic
205C2×#489—111no—
206C2×#474—111no—
207#2563—111no—
208#2036—112no—
209#2033—112no—
210#1983—111no—
211#1955—111no—
212#1788—112no—
213#1786—112no—
214#1762—111no—
215C23×C11—21no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—21no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—42no—
236C23×C11—88no—
237C23×C11—84no—
238C23×C11—88no—
239C23×C11#13712yes—
240C23×C11C22×D411yescharacteristic
241Q8×C11—24no—
242Q8×C11—41no—
243Q8×C11—41no—
244D4×C11—22no—
245D4×C11—24no—
246D4×C11—24no—
247D4×C11—44no—
248D4×C11—48no—
249D4×C11—48no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—84no—
253D4×C11#12414yes—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—48no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—84no—
273C2×C4×C11#12012yes—
274C2×C4×C11#12012yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4112yes—
278C2×C4×C11H(5,𝔽2)12yes—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285Dic22—84no—
286C11⋊C8—42no—
287C11⋊C8—42no—
288C22×#41C2×D1111yescharacteristic
289C23×D4C2×D1111yescharacteristic
290#546—24no—
291#546—24no—
292C2×C4⋊Q8—111no—
293C2×#124C2×D1111yescharacteristic
294C2×#123—21no—
295C2×C22⋊Q8C2×D1111yescharacteristic
296C2×#121—21no—
297C2×#121C2×D1111yescharacteristic
298C2×#120—21no—
299C2×C4×D4C2×D1111yescharacteristic
300C2×C4×D4C2×D1111yescharacteristic
301C22×C22⋊C4—21no—
302#489—224no—
303#474—224no—
304C2×#107—112no—
305C2×C4⋊C8—111no—
306C2×#103—112no—
307C2×#103—112no—
308C2×#102—112no—
309C2×#102—112no—
310C2×#102—112no—
311C2×#102—112no—
312C2×C22⋊C8—112no—
313C2×C22⋊C8—112no—
314C2×#97—111no—
315#393—221no—
316#393—221no—
317#390—221no—
318#382—221no—
319#380—112no—
320#380—112no—
321C4×C4⋊C4—111no—
322#340—112no—
323C22×C11—24no—
324C22×C11—22no—
325C22×C11—24no—
326C22×C11—41no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—41no—
330C22×C11—44no—
331C22×C11—42no—
332C22×C11—44no—
333C22×C11—41no—
334C22×C11—42no—
335C22×C11—41no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—816no—
342C22×C11—82no—
343C22×C11—82no—
344C22×C11C2×#12011yescharacteristic
345C22×C11#54612yes—
346C22×C11C2×#13711yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57612yes—
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11C2×#12411yescharacteristic
356C4×C11#53511yescharacteristic
357C4×C11#54612yes—
358Dic11—82no—
359Dic11—82no—
360C25—21no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—24no—
364C2×#41—42no—
365C22×Q8—221no—
366C22×Q8C22×D1111yescharacteristic
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—24no—
372C22×D4—21no—
373C22×D4—42no—
374C22×D4C22⋊D1111yescharacteristic
375C22×D4C22×D1111yescharacteristic
376C22×D4C22×D1111yescharacteristic
377C23×C4—21no—
378C23×C4—21no—
379C23×C4C22×D1111yescharacteristic
380C23×C4C22×D1111yescharacteristic
381C22×C8—112no—
382C22×C8—112no—
383C4⋊Q8—222no—
384C4⋊Q8—222no—
385#124—22no—
386#124C22⋊D1114yes—
387#123—28no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390#121—28no—
391#121—22no—
392#121—22no—
393#120—28no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4C22⋊D1114yes—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—112no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22⋊D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—28no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—222no—
411C2×C22⋊C4—222no—
412C2×C22⋊C4C22⋊D1111yescharacteristic
413C2×C22⋊C4C22⋊D1111yescharacteristic
414C2×C42—221no—
415C2×C42C22×D1111yescharacteristic
416#107—224no—
417C4⋊C8—222no—
418#103—224no—
419#103—442no—
420#102—224no—
421#102—224no—
422#102—224no—
423#102—442no—
424C22⋊C8—442no—
425C22⋊C8—442no—
426#97—222no—
427#95—221no—
428#95—222no—
429#95—222no—
430C2×C11—42no—
431C2×C11—44no—
432C2×C11—81no—
433C2×C11—82no—
434C2×C11#243511yescharacteristic
435C2×C11#300711yescharacteristic
436C2×C11#300811yescharacteristic
437C2×C11#331412yes—
438C2×C11#331912yes—
439C24—21no—
440C24—24no—
441C24—21no—
442C24—44no—
443C24—42no—
444C24—42no—
445C24—82no—
446C24C2×C22⋊D1111yescharacteristic
447C24C2×C22⋊D1111yescharacteristic
448#41—48no—
449#41—44no—
450#41—44no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—442no—
455C2×Q8—882no—
456C2×Q8C2×C22⋊D1112yes—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—22no—
460C2×D4—24no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4—44no—
469C2×D4—48no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—82no—
474C2×D4#434114yes—
475C2×D4C2×C22⋊D1112yes—
476C2×D4C2×C22⋊D1112yes—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—24no—
489C22×C4—44no—
490C22×C4—82no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498C2×C8—222no—
499C2×C8—222no—
500C2×C8—222no—
501C2×C8—222no—
502C2×C8—222no—
503C2×C8—222no—
504C4⋊C4—24no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—442no—
512C4⋊C4C2×C22⋊D1112yes—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—22no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—22no—
520C22⋊C4—882no—
521C22⋊C4—882no—
522C42—442no—
523C42C2×C22⋊D1112yes—
524C42C2×C22⋊D1112yes—
525C11#2589711yescharacteristic, complemented, Sylow
526C23—22no—
527C23—24no—
528C23—21no—
529C23—22no—
530C23—21no—
531C23—22no—
532C23—22no—
533C23—21no—
534C23—21no—
535C23—22no—
536C23—22no—
537C23—21no—
538C23—48no—
539C23—48no—
540C23—41no—
541C23—41no—
542C23—42no—
543C23—42no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—88no—
548C23—84no—
549C23—88no—
550C23#6700412yes—
551C23C22×C22⋊D1111yescharacteristic
552Q8—24no—
553Q8—41no—
554Q8—41no—
555Q8—884no—
556D4—22no—
557D4—24no—
558D4—24no—
559D4—44no—
560D4—48no—
561D4—48no—
562D4—41no—
563D4—41no—
564D4—84no—
565D4#6698914yes—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—48no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—84no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4#6700612yes—
592C2×C4#6700612yes—
593C2×C4C2×#434112yes—
594C2×C4#6703712yes—
595C2×C4C22×C22⋊D1111yescharacteristic
596C2×C4C22×C22⋊D1111yescharacteristic
597C8—442no—
598C8—442no—
599C22—22no—
600C22—24no—
601C22—24no—
602C22—42no—
603C22—44no—
604C22—42no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—44no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22—42no—
614C22—41no—
615C22—42no—
616C22—42no—
617C22—816no—
618C22—82no—
619C22—82no—
620C22#1062333712yes—
621C22#1062335311yescharacteristic
622C22C2×#6700411yescharacteristic
623C22#1062336612yes—
624C22C2×#6700611yescharacteristic
625C4—22no—
626C4—22no—
627C4—42no—
628C4—41no—
629C4—41no—
630C4—42no—
631C4—882no—
632C4—882no—
633C4C2×#6698911yescharacteristic
634C4#1062333611yescharacteristic
635C4#1062333712yes—
636C2—42no—
637C2—44no—
638C2—81no—
639C2—82no—
640C2#1307226311yescharacteristic
641C2#1307787611yescharacteristic
642C2#1307788411yescharacteristic
643C2#1308069712yes—
644C2#1308077212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#546C2
socleC23×C11C22×D4
hypercenterC2×#546D11
hypocenterC11#25897
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×#10622620C2semidirect
3. #13073789C2semidirect
4. #13069816C2semidirect
5. #13069795C2semidirect
6. #13069549C2semidirect
7. #13069415C2semidirect
8. #13068556C2semidirect
9. #13068547C2semidirect
10. #13068441C2semidirect
25. C2×#66922C22semidirect
26. C2×#66899C22semidirect
27. C2×#66899C22semidirect
34. #10622825C22semidirect
36. C2×C22⋊(C11⋊C8)C22semidirect
40. C2×#66871C22semidirect
43. C4×C4⋊Dic11C22semidirect
44. C2×C4⋊(C11⋊C8)C22semidirect
45. C2×#66867C22semidirect
46. #10622167C22semidirect
525. C11#25897semidirect

Maximal subgroups

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

subgroupindex
C2×#106226682
C2×#106226202
#130737892
#130698162
#130697952
#130695492
#130694152
#130685562
#130685472
#130684412
C2×C11×#5462
#2589711