Finite Group Databasebeta

← #14675647

Subgroups — #14675647

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×C22⋊Dic11C211yesmaximal, characteristic
3C2×#10622556C211yesmaximal, characteristic, complemented
4C2×#10622860C211yesmaximal, characteristic
5#13066859C214yesmaximal, complemented
6#13066853C214yesmaximal, complemented
7#13066838C211yesmaximal, characteristic, complemented
8#13066838C211yesmaximal, characteristic, complemented
9C2×C11×#379C211yesmaximal, characteristic
10C26×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2214yes—
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic11—24no—
17C22×C22⋊Dic11—24no—
18C22×C22⋊Dic11C418yescomplemented
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2214yes—
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2212yescomplemented
25C22×C4×Dic11C2212yescomplemented
26C2×#66930—24no—
27C2×#66930—24no—
28C2×#66930—24no—
29C11×#379—24no—
30#10622860—24no—
31C2×C11⋊#95C2212yescomplemented
32C2×C11⋊#95C2212yescomplemented
33C2×C11⋊#95C2214yescomplemented
34C2×C11⋊#95C2214yescomplemented
35#10622556—24no—
36C25×C11—22no—
37C25×C11—22no—
38C25×C11—28no—
39C25×C11—22no—
40C25×C11—22no—
41C25×C11—22no—
42C25×C11—22no—
43C25×C11—44no—
44C25×C11C2×C414yes—
45C25×C11C2312yes—
46C25×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×Dic11—22no—
50C23×Dic11—22no—
51C23×Dic11—22no—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11—22no—
55C23×Dic11—44no—
56C23×Dic11C2×C414yes—
57C23×Dic11C2×C414yes—
58C23×Dic11D414yes—
59C23×Dic11D414yes—
60C23×Dic11C2312yes—
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—28no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—28no—
72C2×C11×C22⋊C4—44no—
73C2×C11×C22⋊C4D414yes—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—232no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11—44no—
87C2×C22⋊Dic11C2×C418yes—
88C2×C22⋊Dic11C2×C418yes—
89C2×C22⋊Dic11D414yes—
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—24no—
98C11⋊#95—24no—
99C11⋊#95—44no—
100C11⋊#95—44no—
101#13868—111nomaximal, Sylow
102C24×C11—24no—
103C24×C11—24no—
104C24×C11—216no—
105C24×C11—216no—
106C24×C11—28no—
107C24×C11—216no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—24no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—28no—
118C24×C11—28no—
119C24×C11—48no—
120C24×C11—416no—
121C24×C11—416no—
122C24×C11—416no—
123C24×C11—416no—
124C24×C11—48no—
125C24×C11—48no—
126C24×C11—44no—
127C24×C11—44no—
128C24×C11—44no—
129C24×C11—44no—
130C24×C11C22×C414yes—
131C24×C11C22×C412yes—
132C24×C11C2×D412yes—
133C24×C11C2×D412yes—
134C24×C11C2×D412yes—
135C24×C11C2×D412yes—
136C24×C11#4118yes—
137C24×C11#4112yes—
138C24×C11#4112yes—
139C24×C11C2411yescharacteristic
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11C2×D414yes—
150C22×Dic11—28no—
151C22×Dic11—28no—
152C22×Dic11—28no—
153C22×Dic11—28no—
154C22×Dic11—28no—
155C22×Dic11—28no—
156C22×Dic11—28no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—24no—
172C22×Dic11—22no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11—48no—
179C22×Dic11—48no—
180C22×Dic11—48no—
181C22×Dic11C22⋊C4116yescomplemented
182C22×Dic11C22×C414yes—
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—416no—
192C11×C22⋊C4—44no—
193C22⋊Dic11—216no—
194C22⋊Dic11—216no—
195C22⋊Dic11—28no—
196C22⋊Dic11—416no—
197C22⋊Dic11—44no—
198Dic11⋊C4—216no—
199C4×Dic11—216no—
200C22×#117—111no—
201C23×C22⋊C4—111no—
202C2×#381—111no—
203C2×#379—111no—
204C2×#379D1111yescharacteristic
205#1439—114no—
206#1437—114no—
207C22⋊#95—111no—
208C22⋊#95—111no—
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×C11—232no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—28no—
227C23×C11—28no—
228C23×C11—28no—
229C23×C11—28no—
230C23×C11—28no—
231C23×C11—28no—
232C23×C11—432no—
233C23×C11—432no—
234C23×C11—416no—
235C23×C11—432no—
236C23×C11—432no—
237C23×C11—432no—
238C23×C11—432no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—44no—
244C23×C11—44no—
245C23×C11—44no—
246C23×C11—44no—
247C23×C11—44no—
248C23×C11—44no—
249C23×C11—416no—
250C23×C11C2×C22⋊C414yes—
251C23×C11#11718yescomplemented
252C23×C11C4×D414yes—
253C23×C11C4×D414yes—
254C23×C11#12014yes—
255C23×C11#12114yes—
256C23×C11#12114yes—
257C23×C11#12314yes—
258C23×C11C23×C411yescharacteristic
259C23×C11C22×D411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C22×D411yescharacteristic
262C23×C11C22×D411yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4114yes—
265C23×C11C2×#4111yescharacteristic
266C23×C11H(5,𝔽2)14yes—
267C2×C4×C11—24no—
268C2×C4×C11—28no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—44no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—44no—
276C2×C4×C11—44no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—232no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—24no—
294C2×Dic11—28no—
295C2×Dic11—416no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—44no—
299C2×Dic11—44no—
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—
308C26C2×D1111yescharacteristic
309C24×C4—111no—
310C24×C4—111no—
311C2×#117—224no—
312C2×#117—224no—
313C2×#117—224no—
314C22×C4⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—111no—
318C22×C22⋊C4—118no—
319C22×C22⋊C4—111no—
320C22×C22⋊C4—114no—
321C22×C22⋊C4—224no—
322C22×C22⋊C4—224no—
323C22×C22⋊C4C2×D1111yescharacteristic
324C22×C22⋊C4C2×D1114yes—
325C22×C22⋊C4C2×D1111yescharacteristic
326C22×C42—112no—
327#381—224no—
328#379—24no—
329#379—224no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95—114no—
333C2×#95—114no—
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—28no—
343C22×C11—28no—
344C22×C11—28no—
345C22×C11—464no—
346C22×C11—44no—
347C22×C11—44no—
348C22×C11—44no—
349C22×C11—48no—
350C22×C11—48no—
351C22×C11—48no—
352C22×C11—48no—
353C22×C11—44no—
354C22×C11#38618yes—
355C22×C11C22×C22⋊C411yescharacteristic
356C22×C11C2×#11712yes—
357C22×C11C2×C4×D411yescharacteristic
358C22×C11C2×C4×D411yescharacteristic
359C22×C11#51812yes—
360C22×C11C2×#12011yescharacteristic
361C22×C11C2×#12111yescharacteristic
362C22×C11C2×#12111yescharacteristic
363C22×C11C2×#12311yescharacteristic
364C22×C11#52512yes—
365C22×C11#52512yes—
366C22×C11#53512yes—
367C22×C11#53512yes—
368C22×C11#54614yes—
369C22×C11#54614yes—
370C22×C11#55114yes—
371C22×C11#55114yes—
372C4×C11—44no—
373C4×C11—82no—
374Dic11—24no—
375Dic11—24no—
376Dic11—44no—
377Dic11—44no—
378Dic11—82no—
379C25—22no—
380C25—22no—
381C25—28no—
382C25—22no—
383C25—22no—
384C25—22no—
385C25—22no—
386C25—44no—
387C25C4×D1114yes—
388C25C22×D1112yes—
389C25C22×D1111yescharacteristic
390C23×C4—114no—
391C23×C4—114no—
392C23×C4—114no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—112no—
396C23×C4—112no—
397C23×C4—114no—
398C23×C4—112no—
399C23×C4—222no—
400C23×C4—222no—
401C23×C4—222no—
402C23×C4—222no—
403C23×C4—222no—
404C23×C4—222no—
405C23×C4—444no—
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—28no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—118no—
421C2×C22⋊C4—118no—
422C2×C22⋊C4—114no—
423C2×C22⋊C4—2232no—
424C2×C22⋊C4—224no—
425C2×C22⋊C4—224no—
426C2×C22⋊C4—224no—
427C2×C22⋊C4—224no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—222no—
430C2×C22⋊C4—228no—
431C2×C22⋊C4—222no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—222no—
434C2×C22⋊C4—228no—
435C2×C22⋊C4—444no—
436C2×C22⋊C4C22⋊D1114yes—
437C2×C42—224no—
438C2×C42—224no—
439C2×C42—224no—
440#95—224no—
441#95—224no—
442#95—444no—
443#95—444no—
444C2×C11—28no—
445C2×C11—48no—
446C2×C11#228011yescharacteristic
447C2×C11C2×#38611yescharacteristic
448C2×C11#230911yescharacteristic
449C2×C11#234212yes—
450C2×C11#234212yes—
451C2×C11#240412yes—
452C2×C11#241112yes—
453C2×C11#241112yes—
454C2×C11#248212yes—
455C24—24no—
456C24—24no—
457C24—216no—
458C24—216no—
459C24—216no—
460C24—28no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—24no—
466C24—22no—
467C24—24no—
468C24—24no—
469C24—22no—
470C24—28no—
471C24—28no—
472C24—48no—
473C24—416no—
474C24—416no—
475C24—416no—
476C24—416no—
477C24—48no—
478C24—48no—
479C24—44no—
480C24—44no—
481C24—44no—
482C24—44no—
483C24C2×C4×D1114yes—
484C24C2×C4×D1112yes—
485C24#433912yes—
486C24D4×D1112yes—
487C24D4×D1112yes—
488C24D4×D1112yes—
489C24#434118yes—
490C24#434112yes—
491C24C2×C22⋊D1112yes—
492C24C23×D1111yescharacteristic
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—1116no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—114no—
510C22×C4—114no—
511C22×C4—228no—
512C22×C4—228no—
513C22×C4—228no—
514C22×C4—228no—
515C22×C4—228no—
516C22×C4—228no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—228no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—224no—
530C22×C4—224no—
531C22×C4—224no—
532C22×C4—224no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—224no—
538C22×C4—224no—
539C22×C4—448no—
540C22×C4—448no—
541C22×C4—448no—
542C22×C4C2×C22⋊D1114yes—
543C4⋊C4—2216no—
544C22⋊C4—28no—
545C22⋊C4—416no—
546C22⋊C4—44no—
547C22⋊C4—2216no—
548C22⋊C4—2216no—
549C22⋊C4—228no—
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—232no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—28no—
571C23—24no—
572C23—28no—
573C23—28no—
574C23—28no—
575C23—28no—
576C23—28no—
577C23—432no—
578C23—432no—
579C23—432no—
580C23—416no—
581C23—432no—
582C23—432no—
583C23—432no—
584C23—42no—
585C23—42no—
586C23—44no—
587C23—42no—
588C23—42no—
589C23—416no—
590C23—44no—
591C23—44no—
592C23—44no—
593C23—44no—
594C23—44no—
595C23#6693018yescomplemented
596C23C22⋊C4×D1114yes—
597C23(C22⋊D11)⋊C414yes—
598C23#6693614yes—
599C23#6693714yes—
600C23C4×C22⋊D1114yes—
601C23#6699014yes—
602C23#6699114yes—
603C23C22×C4×D1111yescharacteristic
604C23C2×#433911yescharacteristic
605C23C2×D4×D1111yescharacteristic
606C23C2×D4×D1111yescharacteristic
607C23C2×D4×D1111yescharacteristic
608C23C2×#434114yes—
609C23C2×#434111yescharacteristic
610C23#6703714yes—
611C23C22×C22⋊D1111yescharacteristic
612C2×C4—24no—
613C2×C4—28no—
614C2×C4—42no—
615C2×C4—44no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—44no—
619C2×C4—42no—
620C2×C4—44no—
621C2×C4—42no—
622C2×C4—114no—
623C2×C4—114no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—222no—
634C2×C4—222no—
635C2×C4—222no—
636C2×C4—2232no—
637C2×C4—224no—
638C2×C4—224no—
639C2×C4—224no—
640C2×C4—224no—
641C2×C4—228no—
642C2×C4—4416no—
643C2×C4—444no—
644C2×C4—442no—
645C2×C4—444no—
646C2×C4—444no—
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—28no—
662C22—28no—
663C22—28no—
664C22—464no—
665C22—48no—
666C22—44no—
667C22—44no—
668C22—44no—
669C22—48no—
670C22—48no—
671C22—44no—
672C22—48no—
673C22#1062256918yes—
674C22C2×#6693012yes—
675C22C2×C22⋊C4×D1111yescharacteristic
676C22C2×(C22⋊D11)⋊C411yescharacteristic
677C22#1062301712yes—
678C22C2×#6693611yescharacteristic
679C22C2×#6693711yescharacteristic
680C22#1062302614yes—
681C22#1062311712yes—
682C22#1062311712yes—
683C22#1062311814yes—
684C22#1062312214yes—
685C22#1062312312yes—
686C22#1062312312yes—
687C22C2×C4×C22⋊D1111yescharacteristic
688C22C2×#6699011yescharacteristic
689C22C2×#6699111yescharacteristic
690C22#1062333714yes—
691C4—44no—
692C4—82no—
693C4—224no—
694C4—224no—
695C4—444no—
696C4—444no—
697C4—882no—
698C2—28no—
699C2—48no—
700C2#1307099411yescharacteristic
701C2C2×#1062256911yescharacteristic
702C2#1307119711yescharacteristic
703C2#1307146112yes—
704C2#1307146712yes—
705C2#1307193212yes—
706C2#1307199712yes—
707C2#1307200312yes—
708C2#1307288712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#379C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11#13868
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#66930C2semidirect
3. C2×#10622556C2semidirect
5. #13066859C2semidirect
6. #13066853C2semidirect
7. #13066838C2semidirect
8. #13066838C2semidirect
18. C22×C22⋊Dic11C4semidirect
24. C22×Dic11⋊C4C22semidirect
25. C22×C4×Dic11C22semidirect
31. C2×C11⋊#95C22semidirect
32. C2×C11⋊#95C22semidirect
33. C2×C11⋊#95C22semidirect
34. C2×C11⋊#95C22semidirect
181. C22×Dic11C22⋊C4semidirect
251. C23×C11#117semidirect
553. C11#13868semidirect
595. C23#66930semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
C23×C22⋊Dic112
C2×#106225562
C2×#106228602
#130668592
#130668532
#130668382
C2×C11×#3792
#1386811