Finite Group Databasebeta

← #14675649

Subgroups — #14675649

Order 2816.

3686 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66930C211yesmaximal, characteristic, complemented
2C23×(C2×D11)⋊C4C211yesmaximal, characteristic
3C2×#10622556C211yesmaximal, characteristic, complemented
4C2×#10622568C211yesmaximal, characteristic
5C2×#10622568C211yesmaximal, characteristic
6#13066860C214yesmaximal, complemented
7#13066852C214yesmaximal, complemented
8#13066839C211yesmaximal, characteristic, complemented
9C11×C22⋊#95C211yesmaximal, characteristic, complemented
10C25×D11C2211yescharacteristic
11C24×C4×C11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×(C2×D11)⋊C4—24no—
18C22×(C2×D11)⋊C4—24no—
19C22×(C2×D11)⋊C4C418yescomplemented
20C22×(C2×D11)⋊C4C2214yes—
21C22×(C2×D11)⋊C4C2214yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×Dic11⋊C4C2212yescomplemented
25C22×C4×Dic11C2212yescomplemented
26C2×#66930—24no—
27C2×#66930—24no—
28C2×#66930—24no—
29C2×C11×#95C2214yescomplemented
30C2×C11⋊#95C2212yescomplemented
31C2×C11⋊#95C2212yescomplemented
32C2×C11⋊#95C2214yescomplemented
33#10622568—24no—
34#10622568—24no—
35#10622556—24no—
36C25×C11C2311yescharacteristic
37C24×D11—22no—
38C24×D11—22no—
39C24×D11—28no—
40C24×D11—22no—
41C24×D11—22no—
42C24×D11—22no—
43C24×D11—22no—
44C24×D11—44no—
45C24×D11C2×C414yes—
46C24×D11C2312yes—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—44no—
50C23×C4×C11C2×C414yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×Dic11—22no—
55C23×Dic11—22no—
56C23×Dic11—22no—
57C23×Dic11—22no—
58C23×Dic11C2×C414yes—
59C23×Dic11D414yes—
60C23×Dic11D414yes—
61C23×Dic11C2312yes—
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4D414yes—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11D414yes—
77C2×(C2×D11)⋊C4—232no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4C2×C418yes—
89C2×(C2×D11)⋊C4C2×C418yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—24no—
96#66930—232no—
97C11×#95—44no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—44no—
101#13868—111nomaximal, Sylow
102C24×C11—24no—
103C24×C11—24no—
104C24×C11C22×C412yes—
105C24×C11C2×D412yes—
106C24×C11C2×D412yes—
107C24×C11C2×D412yes—
108C24×C11C2×D412yes—
109C24×C11#4112yes—
110C24×C11#4112yes—
111C24×C11C2411yescharacteristic
112C23×D11—216no—
113C23×D11—216no—
114C23×D11—28no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—24no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—216no—
125C23×D11—28no—
126C23×D11—28no—
127C23×D11—48no—
128C23×D11—416no—
129C23×D11—416no—
130C23×D11—416no—
131C23×D11—416no—
132C23×D11—48no—
133C23×D11—48no—
134C23×D11—44no—
135C23×D11—44no—
136C23×D11—44no—
137C23×D11—44no—
138C23×D11C22×C414yes—
139C23×D11#4118yes—
140C22×C4×C11—28no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—22no—
153C22×C4×C11—24no—
154C22×C4×C11—48no—
155C22×C4×C11—48no—
156C22×C4×C11—48no—
157C22×C4×C11C22×C414yes—
158C22×C4×C11C2×D414yes—
159C22×Dic11—28no—
160C22×Dic11—28no—
161C22×Dic11—28no—
162C22×Dic11—28no—
163C22×Dic11—28no—
164C22×Dic11—28no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—24no—
178C22×Dic11—24no—
179C22×Dic11—22no—
180C22×Dic11—24no—
181C22×Dic11—24no—
182C22×Dic11C22⋊C4116yescomplemented
183C22×Dic11C22×C412yes—
184C22×Dic11C22×C412yes—
185C22×Dic11C2×D414yes—
186C22×Dic11C2×D412yes—
187C22×Dic11C2×D412yes—
188C22×Dic11C2×D412yes—
189C22×Dic11C2×D412yes—
190C11×C22⋊C4—28no—
191C11×C22⋊C4—44no—
192C22⋊Dic11—28no—
193C22⋊Dic11—44no—
194(C2×D11)⋊C4—216no—
195(C2×D11)⋊C4—216no—
196(C2×D11)⋊C4—416no—
197(C2×D11)⋊C4—416no—
198Dic11⋊C4—216no—
199C4×Dic11—216no—
200C22×#117—111no—
201C23×C22⋊C4—111no—
202C2×#381—111no—
203C2×#379—111no—
204C2×#379—111no—
205#1439—114no—
206#1437—114no—
207C22⋊#95—111no—
208C22⋊#95D1111yescharacteristic, complemented
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—28no—
216C23×C11—28no—
217C23×C11—28no—
218C23×C11—28no—
219C23×C11C2×C22⋊C414yes—
220C23×C11C4×D414yes—
221C23×C11C4×D414yes—
222C23×C11#12014yes—
223C23×C11#12114yes—
224C23×C11#12114yes—
225C23×C11#12314yes—
226C23×C11C23×C411yescharacteristic
227C23×C11C22×D411yescharacteristic
228C23×C11C22×D411yescharacteristic
229C23×C11C22×D411yescharacteristic
230C23×C11C22×D411yescharacteristic
231C23×C11C2×#4111yescharacteristic
232C23×C11C2×#4111yescharacteristic
233C23×C11C2×#4114yes—
234C23×C11H(5,𝔽2)14yes—
235C22×D11—232no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—28no—
243C22×D11—28no—
244C22×D11—28no—
245C22×D11—28no—
246C22×D11—28no—
247C22×D11—28no—
248C22×D11—432no—
249C22×D11—432no—
250C22×D11—416no—
251C22×D11—432no—
252C22×D11—432no—
253C22×D11—432no—
254C22×D11—432no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—42no—
259C22×D11—44no—
260C22×D11—44no—
261C22×D11—44no—
262C22×D11—44no—
263C22×D11—44no—
264C22×D11—44no—
265C22×D11—416no—
266C22×D11#11718yescomplemented
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—28no—
272C2×C4×C11—416no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—44no—
276C2×C4×C11—44no—
277C2×C4×C11—44no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—44no—
282C2×C4×C11—44no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—232no—
296C2×Dic11—24no—
297C2×Dic11—28no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—44no—
301C2×Dic11—42no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11—44no—
305C2×Dic11—44no—
306C2×Dic11C2×C22⋊C414yes—
307C2×Dic11C2×C22⋊C414yes—
308C26—111no—
309C24×C4—111no—
310C24×C4C2×D1111yescharacteristic
311C2×#117—224no—
312C2×#117—224no—
313C2×#117—224no—
314C22×C4⋊C4—112no—
315C22×C22⋊C4—111no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—112no—
318C22×C22⋊C4—118no—
319C22×C22⋊C4—111no—
320C22×C22⋊C4—114no—
321C22×C22⋊C4—114no—
322C22×C22⋊C4—224no—
323C22×C22⋊C4—224no—
324C22×C22⋊C4C2×D1111yescharacteristic
325C22×C22⋊C4C2×D1111yescharacteristic
326C22×C42—112no—
327#381—224no—
328#379—224no—
329#379—224no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95—114no—
333C2×#95C2×D1114yescomplemented
334C22×C11—24no—
335C22×C11—28no—
336C22×C11—28no—
337C22×C11—28no—
338C22×C11—28no—
339C22×C11—28no—
340C22×C11—28no—
341C22×C11—24no—
342C22×C11#38618yes—
343C22×C11C22×C22⋊C411yescharacteristic
344C22×C11C2×#11712yes—
345C22×C11C2×C4×D411yescharacteristic
346C22×C11C2×C4×D411yescharacteristic
347C22×C11#51812yes—
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×#12111yescharacteristic
350C22×C11C2×#12111yescharacteristic
351C22×C11C2×#12311yescharacteristic
352C22×C11#52512yes—
353C22×C11#52512yes—
354C22×C11#53512yes—
355C22×C11#53512yes—
356C22×C11#54614yes—
357C22×C11#54614yes—
358C22×C11#55114yes—
359C22×C11#55114yes—
360C2×D11—28no—
361C2×D11—28no—
362C2×D11—28no—
363C2×D11—464no—
364C2×D11—44no—
365C2×D11—44no—
366C2×D11—44no—
367C2×D11—48no—
368C2×D11—48no—
369C2×D11—48no—
370C2×D11—48no—
371C2×D11—44no—
372C4×C11—44no—
373C4×C11—44no—
374C4×C11—82no—
375Dic11—24no—
376Dic11—24no—
377Dic11—44no—
378Dic11—82no—
379C25—112no—
380C25—114no—
381C25—228no—
382C25—222no—
383C25—222no—
384C25—222no—
385C25—222no—
386C25—222no—
387C25—222no—
388C25—444no—
389C25C22×D1111yescharacteristic
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—44no—
393C23×C4—114no—
394C23×C4—114no—
395C23×C4—114no—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—112no—
399C23×C4—112no—
400C23×C4—222no—
401C23×C4—222no—
402C23×C4—222no—
403C23×C4—222no—
404C23×C4C4×D1114yes—
405C23×C4C22×D1112yes—
406C23×C4C22×D1112yes—
407C23×C4C22×D1112yes—
408#117—2232no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4—224no—
411C2×C4⋊C4—224no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—114no—
418C2×C22⋊C4—118no—
419C2×C22⋊C4—118no—
420C2×C22⋊C4—2232no—
421C2×C22⋊C4—224no—
422C2×C22⋊C4—224no—
423C2×C22⋊C4—224no—
424C2×C22⋊C4—224no—
425C2×C22⋊C4—222no—
426C2×C22⋊C4—222no—
427C2×C22⋊C4—228no—
428C2×C22⋊C4—228no—
429C2×C22⋊C4—228no—
430C2×C22⋊C4—222no—
431C2×C22⋊C4—222no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—228no—
434C2×C22⋊C4—444no—
435C2×C22⋊C4—444no—
436C2×C22⋊C4D4414yes—
437C2×C42—224no—
438C2×C42—224no—
439C2×C42—224no—
440#95—44no—
441#95—224no—
442#95—224no—
443#95—444no—
444C2×C11—28no—
445C2×C11#228011yescharacteristic
446C2×C11C2×#38611yescharacteristic
447C2×C11#230911yescharacteristic
448C2×C11#234212yes—
449C2×C11#234212yes—
450C2×C11#240412yes—
451C2×C11#241112yes—
452C2×C11#241112yes—
453C2×C11#248212yes—
454D11—48no—
455C24—24no—
456C24—24no—
457C24—114no—
458C24—118no—
459C24—2216no—
460C24—2216no—
461C24—2216no—
462C24—228no—
463C24—222no—
464C24—222no—
465C24—222no—
466C24—222no—
467C24—222no—
468C24—224no—
469C24—224no—
470C24—222no—
471C24—224no—
472C24—228no—
473C24—228no—
474C24—448no—
475C24—4416no—
476C24—4416no—
477C24—4416no—
478C24—4416no—
479C24—448no—
480C24—448no—
481C24—444no—
482C24—444no—
483C24—444no—
484C24—444no—
485C24C2×C4×D1112yes—
486C24C2×D4412yes—
487C24#433912yes—
488C24D4×D1112yes—
489C24D4×D1112yes—
490C24D4×D1112yes—
491C24#434312yes—
492C24C23×D1111yescharacteristic
493C22×C4—28no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—48no—
508C22×C4—48no—
509C22×C4—48no—
510C22×C4—1116no—
511C22×C4—112no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—112no—
517C22×C4—114no—
518C22×C4—228no—
519C22×C4—228no—
520C22×C4—228no—
521C22×C4—228no—
522C22×C4—228no—
523C22×C4—228no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—222no—
533C22×C4—222no—
534C22×C4—224no—
535C22×C4—224no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—224no—
539C22×C4—222no—
540C22×C4—224no—
541C22×C4C2×C4×D1114yes—
542C22×C4C2×D4414yes—
543C4⋊C4—2216no—
544C22⋊C4—28no—
545C22⋊C4—44no—
546C22⋊C4—2216no—
547C22⋊C4—2216no—
548C22⋊C4—228no—
549C22⋊C4—4416no—
550C22⋊C4—4416no—
551C22⋊C4—444no—
552C42—2216no—
553C11#1386811yescharacteristic, complemented, Sylow
554C23—24no—
555C23—24no—
556C23—28no—
557C23—28no—
558C23—24no—
559C23—24no—
560C23—28no—
561C23—28no—
562C23—24no—
563C23—24no—
564C23—118no—
565C23—2232no—
566C23—224no—
567C23—224no—
568C23—224no—
569C23—224no—
570C23—224no—
571C23—224no—
572C23—228no—
573C23—228no—
574C23—228no—
575C23—228no—
576C23—228no—
577C23—228no—
578C23—4432no—
579C23—4432no—
580C23—4432no—
581C23—4416no—
582C23—4432no—
583C23—4432no—
584C23—4432no—
585C23—442no—
586C23—442no—
587C23—442no—
588C23—442no—
589C23—4416no—
590C23—444no—
591C23—444no—
592C23—444no—
593C23—444no—
594C23—444no—
595C23—444no—
596C23C4×D4414yes—
597C23C22⋊C4×D1114yes—
598C23#6693514yes—
599C23#6693714yes—
600C23#6694614yes—
601C23#6694714yes—
602C23#6694814yes—
603C23C22×C4×D1111yescharacteristic
604C23C22×D4411yescharacteristic
605C23C2×#433911yescharacteristic
606C23C2×D4×D1111yescharacteristic
607C23C2×D4×D1111yescharacteristic
608C23C2×D4×D1111yescharacteristic
609C23#6703714yes—
610C23C2×#434311yescharacteristic
611C23#41×D1114yes—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—28no—
617C2×C4—416no—
618C2×C4—42no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—44no—
625C2×C4—42no—
626C2×C4—44no—
627C2×C4—42no—
628C2×C4—114no—
629C2×C4—114no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—222no—
634C2×C4—222no—
635C2×C4—222no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—2232no—
643C2×C4—224no—
644C2×C4—228no—
645C2×C4—444no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—442no—
649C2×C4—444no—
650C2×C4—442no—
651C2×C4—444no—
652C2×C4—442no—
653C22—28no—
654C22—24no—
655C22—28no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22—24no—
660C22—28no—
661C22—228no—
662C22—228no—
663C22—228no—
664C22—4464no—
665C22—448no—
666C22—444no—
667C22—444no—
668C22—444no—
669C22—448no—
670C22—448no—
671C22—444no—
672C22—448no—
673C22#1062227818yes—
674C22C2×C4×D4411yescharacteristic
675C22C2×C22⋊C4×D1111yescharacteristic
676C22#1062301712yes—
677C22C2×#6693511yescharacteristic
678C22C2×#6693711yescharacteristic
679C22C2×#6694611yescharacteristic
680C22C2×#6694711yescharacteristic
681C22C2×#6694811yescharacteristic
682C22D11×#11712yes—
683C22#1062308514yes—
684C22#1062308714yes—
685C22#1062312312yes—
686C22#1062312312yes—
687C22#1062314114yes—
688C22#1062316814yes—
689C22#1062318712yes—
690C22#1062318712yes—
691C4—44no—
692C4—44no—
693C4—82no—
694C4—224no—
695C4—224no—
696C4—444no—
697C4—882no—
698C2—28no—
699C2—448no—
700C2#1307099611yescharacteristic
701C2C2×#1062227811yescharacteristic
702C2#1307119711yescharacteristic
703C2#1307146212yes—
704C2#1307146812yes—
705C2#1307193412yes—
706C2#1307199912yes—
707C2#1307200412yes—
708C2#1307288912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenterC22⋊#95D11
hypocenterC11#13868
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#66930C2semidirect
3. C2×#10622556C2semidirect
6. #13066860C2semidirect
7. #13066852C2semidirect
8. #13066839C2semidirect
9. C11×C22⋊#95C2semidirect
19. C22×(C2×D11)⋊C4C4semidirect
24. C22×Dic11⋊C4C22semidirect
25. C22×C4×Dic11C22semidirect
29. C2×C11×#95C22semidirect
30. C2×C11⋊#95C22semidirect
31. C2×C11⋊#95C22semidirect
32. C2×C11⋊#95C22semidirect
182. C22×Dic11C22⋊C4semidirect
208. C22⋊#95D11semidirect
266. C22×D11#117semidirect
333. C2×#95C2×D11semidirect
553. C11#13868semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
C23×(C2×D11)⋊C42
C2×#106225562
C2×#106225682
#130668602
#130668522
#130668392
C11×C22⋊#952
#1386811