Finite Group Databasebeta

← #14926497

Subgroups — #14926497

Order 2816.

4346 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×#66935C211yesmaximal, characteristic
2C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
3#13076911C214yesmaximal, complemented
4#13074394C214yesmaximal, complemented
5#13072896C214yesmaximal, complemented
6#13072009C218yesmaximal, complemented
7#13071945C214yesmaximal, complemented
8#13071228C211yesmaximal, characteristic, complemented
9#13071191C211yesmaximal, characteristic, complemented
10#13071191C211yesmaximal, characteristic, complemented
11C2×#10622568C211yesmaximal, characteristic, complemented
12C11×#2315C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×D44C2212yes—
16C23×C4×D11C2212yescomplemented
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yescomplemented
24C22×(C2×D11)⋊C4C2214yescomplemented
25C2×#66947C2218yescomplemented
26C2×#66935—28no—
27C2×#66935C2214yes—
28C2×#66935C2212yes—
29C2×#66935C2212yes—
30C2×C22⋊C4×D11—28no—
31C2×C22⋊C4×D11C2214yes—
32C2×C22⋊C4×D11C2214yescomplemented
33C11×#385C2214yescomplemented
34C11×#385C2214yescomplemented
35C11×#380C2214yescomplemented
36#10622826C2214yescomplemented
37#10622826C2214yescomplemented
38#10622823C2214yescomplemented
39#10622606C2218yescomplemented
40#10622604C2218yescomplemented
41#10622602C2218yescomplemented
42#10622571C2214yescomplemented
43#10622571C2214yescomplemented
44#10622568C2214yes—
45#10622568C2212yescomplemented
46#10622568C2212yescomplemented
47#10622568C2212yescomplemented
48#10622568C2212yescomplemented
49#10622559C2214yescomplemented
50#10622556C2212yescomplemented
51#10622556C2212yescomplemented
52#10622555C2214yescomplemented
53#10622288C2218yescomplemented
54#10622285C2218yescomplemented
55#10622278C2218yescomplemented
56#10622277C2218yescomplemented
57C25×C11C2311yescharacteristic
58C24×D11—24no—
59C24×D11—24no—
60C24×D11—48no—
61C24×D11D418yes—
62C24×D11C2311yescharacteristic
63C24×D11C2312yes—
64C24×D11C2312yes—
65C24×D11C2311yescharacteristic
66C24×D11C2311yescharacteristic
67C23×C4×C11C2312yes—
68C23×C4×C11C2312yes—
69C23×C4×C11C2312yes—
70C22×C22⋊D11—24no—
71C22×C22⋊D11—24no—
72C22×C22⋊D11—24no—
73C22×C22⋊D11C2312yes—
74C22×C22⋊D11C2312yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2312yes—
77C23×Dic11C2312yes—
78C22×D44—28no—
79C22×D44—48no—
80C22×D44C2314yes—
81C22×D44C2314yes—
82C22×C4×D11—28no—
83C22×C4×D11—48no—
84C22×C4×D11C2314yes—
85C22×C4×D11C2314yes—
86C2×C11×C4⋊C4C2318yescomplemented
87C2×C11×C22⋊C4—24no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4C2312yes—
91C2×C11×C22⋊C4C2312yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C11×C22⋊C4C2312yes—
94C2×C11×C22⋊C4C2312yes—
95C2×C11×C22⋊C4C2312yes—
96C2×C22⋊Dic11—24no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2312yes—
100C2×C22⋊Dic11C2312yes—
101C2×C22⋊Dic11C2312yes—
102C2×(C2×D11)⋊C4—28no—
103C2×(C2×D11)⋊C4—28no—
104C2×(C2×D11)⋊C4—48no—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2318yes—
110C2×(C2×D11)⋊C4C2318yes—
111C2×(C2×D11)⋊C4C2318yescomplemented
112C2×(C2×D11)⋊C4C2318yescomplemented
113C2×Dic11⋊C4C2318yescomplemented
114#66947—416no—
115#66935—28no—
116#66935—216no—
117#66935—28no—
118C22⋊C4×D11—216no—
119C22⋊C4×D11—216no—
120C11×#95C2318yescomplemented
121C11⋊#95C2318yescomplemented
122C11⋊#95C2318yescomplemented
123C11⋊#95C2318yescomplemented
124#34992—111nomaximal, Sylow
125C24×C11—44no—
126C24×C11C2×D414yes—
127C24×C11#4114yes—
128C24×C11#4114yes—
129C24×C11C2411yescharacteristic
130C24×C11C2411yescharacteristic
131C24×C11C2411yescharacteristic
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—28no—
135C23×D11—232no—
136C23×D11—24no—
137C23×D11—24no—
138C23×D11—24no—
139C23×D11—24no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—28no—
143C23×D11—28no—
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11—432no—
148C23×D11—44no—
149C23×D11—44no—
150C23×D11—44no—
151C23×D11—44no—
152C23×D11—432no—
153C23×D11—432no—
154C23×D11C2×D414yes—
155C23×D11C2×D418yes—
156C23×D11C2×D418yes—
157C23×D11C2×D414yes—
158C23×D11C2412yes—
159C23×D11C2412yes—
160C23×D11C2412yes—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11—44no—
165C22×C4×C11—44no—
166C22×C4×C11—44no—
167C22×C4×C11C2414yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2414yes—
170C2×C22⋊D11—24no—
171C2×C22⋊D11—24no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11—24no—
175C2×C22⋊D11—24no—
176C2×C22⋊D11—416no—
177C22×Dic11—22no—
178C22×Dic11—24no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—24no—
182C22×Dic11—44no—
183C22×Dic11—44no—
184C22×Dic11C2412yes—
185C22×Dic11C2414yes—
186C22×Dic11C2414yes—
187C2×D44—28no—
188C2×D44—28no—
189C2×D44—216no—
190C2×D44—48no—
191C2×D44—432no—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×C4×D11—216no—
195C2×C4×D11—48no—
196C2×C4×D11—432no—
197C11×C4⋊C4—48no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C22⋊Dic11—24no—
205C22⋊Dic11—24no—
206C22⋊Dic11—24no—
207C22⋊Dic11—24no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—28no—
212(C2×D11)⋊C4—216no—
213(C2×D11)⋊C4—48no—
214(C2×D11)⋊C4—48no—
215(C2×D11)⋊C4—48no—
216Dic11⋊C4—48no—
217C22×#120—111no—
218C23×C22⋊C4—111no—
219#2849—114no—
220#2622—114no—
221#2483—114no—
222#2412—118no—
223#2405—114no—
224#2315—111no—
225#2315D1111yescharacteristic, complemented
226#2308—111no—
227#2308—111no—
228C2×#379—111no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—48no—
233C23×C11—48no—
234C23×C11—48no—
235C23×C11#123116yescomplemented
236C23×C11C22×D412yes—
237C23×C11C22×D412yes—
238C23×C11C22×D412yes—
239C23×C11C2×#4112yes—
240C23×C11C2×#4112yes—
241C23×C11C2×#4112yes—
242C23×C11C2×#4112yes—
243C23×C11C2×#4112yes—
244C23×C11C2×#4112yes—
245C23×C11C2511yescharacteristic
246C22×D11—216no—
247C22×D11—216no—
248C22×D11—28no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—24no—
252C22×D11—216no—
253C22×D11—216no—
254C22×D11—216no—
255C22×D11—28no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—216no—
261C22×D11—216no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—28no—
266C22×D11—48no—
267C22×D11—48no—
268C22×D11—48no—
269C22×D11—416no—
270C22×D11—416no—
271C22×D11—416no—
272C22×D11—416no—
273C22×D11—4128no—
274C22×D11—48no—
275C22×D11—48no—
276C22×D11—48no—
277C22×D11—44no—
278C22×D11—84no—
279C22×D11—84no—
280C22×D11C22×D414yes—
281C22×D11C22×D414yes—
282C22×D11H(5,𝔽2)18yes—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—28no—
287C2×C4×C11—28no—
288C2×C4×C11—28no—
289C2×C4×C11—48no—
290C2×C4×C11—48no—
291C2×C4×C11—84no—
292C22⋊D11—48no—
293C22⋊D11—48no—
294C2×Dic11—22no—
295C2×Dic11—24no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—28no—
300C2×Dic11—28no—
301C2×Dic11—48no—
302C2×Dic11—44no—
303C2×Dic11—84no—
304D44—416no—
305D44—416no—
306C4×D11—416no—
307C4×D11—416no—
308C26—111no—
309C23×D4—111no—
310C23×D4—112no—
311C24×C4—112no—
312C2×#123—118no—
313C2×#120—112no—
314C2×#120—112no—
315C2×#120—114no—
316C2×#120—228no—
317C22×C22⋊C4—111no—
318C22×C22⋊C4—111no—
319C22×C22⋊C4—112no—
320C22×C22⋊C4—112no—
321C22×C22⋊C4—114no—
322C22×C22⋊C4—114no—
323C22×C22⋊C4—114no—
324C22×C22⋊C4—228no—
325C22×C22⋊C4C2×D1111yescharacteristic
326C22×C22⋊C4C2×D1111yescharacteristic
327C22×C22⋊C4C2×D1111yescharacteristic
328#397—118no—
329#397—118no—
330#394—118no—
331#394—118no—
332#386—114no—
333#386—114no—
334#386—114no—
335#386—114no—
336#386—118no—
337#385—114no—
338#385—118no—
339#385—114no—
340#385C2×D1114yescomplemented
341#385C2×D1114yescomplemented
342#381—112no—
343#381—112no—
344#381—118no—
345#380—114no—
346#380C2×D1114yescomplemented
347#379—112no—
348#379—112no—
349#379—112no—
350#379—112no—
351#379—114no—
352C22×C11—24no—
353C22×C11—24no—
354C22×C11—24no—
355C22×C11—24no—
356C22×C11—24no—
357C22×C11—24no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—416no—
362C22×C11C2×#12314yes—
363C22×C11C2×#12314yes—
364C22×C11C2×#12314yes—
365C22×C11C23×D411yescharacteristic
366C22×C11C22×#4111yescharacteristic
367C22×C11C22×#4111yescharacteristic
368C22×C11C2×H(5,𝔽2)14yes—
369C2×D11—232no—
370C2×D11—24no—
371C2×D11—24no—
372C2×D11—28no—
373C2×D11—28no—
374C2×D11—24no—
375C2×D11—24no—
376C2×D11—24no—
377C2×D11—432no—
378C2×D11—432no—
379C2×D11—416no—
380C2×D11—44no—
381C2×D11—44no—
382C2×D11—42no—
383C2×D11—44no—
384C2×D11—44no—
385C2×D11—44no—
386C2×D11—88no—
387C2×D11#53418yes—
388C4×C11—44no—
389C4×C11—44no—
390C4×C11—44no—
391Dic11—42no—
392Dic11—44no—
393Dic11—44no—
394C25—111no—
395C25—112no—
396C25—112no—
397C25—118no—
398C25—111no—
399C25—111no—
400C25—224no—
401C25—224no—
402C25—448no—
403C25C22×D1111yescharacteristic
404C22×D4—112no—
405C22×D4—112no—
406C22×D4—114no—
407C22×D4—114no—
408C22×D4—228no—
409C22×D4—224no—
410C22×D4—224no—
411C22×D4—224no—
412C22×D4—448no—
413C23×C4—111no—
414C23×C4—112no—
415C23×C4—112no—
416C23×C4—114no—
417C23×C4—114no—
418C23×C4—228no—
419C23×C4—448no—
420C23×C4C22×D1112yes—
421C23×C4C22×D1112yes—
422C23×C4C22×D1112yes—
423#123—4416no—
424#120—228no—
425#120—2216no—
426#120—228no—
427C2×C4⋊C4—118no—
428C2×C4⋊C4C22×D1118yescomplemented
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—112no—
433C2×C22⋊C4—112no—
434C2×C22⋊C4—112no—
435C2×C22⋊C4—112no—
436C2×C22⋊C4—114no—
437C2×C22⋊C4—114no—
438C2×C22⋊C4—114no—
439C2×C22⋊C4—114no—
440C2×C22⋊C4—118no—
441C2×C22⋊C4—118no—
442C2×C22⋊C4—118no—
443C2×C22⋊C4—118no—
444C2×C22⋊C4—2216no—
445C2×C22⋊C4—2216no—
446C2×C22⋊C4—228no—
447C2×C22⋊C4—228no—
448C2×C22⋊C4—224no—
449C2×C22⋊C4—224no—
450C2×C22⋊C4—448no—
451C2×C22⋊C4C22×D1112yes—
452C2×C22⋊C4C22×D1112yes—
453C2×C22⋊C4C22×D1112yes—
454C2×C22⋊C4C22×D1112yes—
455C2×C22⋊C4C22×D1112yes—
456C2×C22⋊C4C22×D1112yes—
457#95—118no—
458#95—118no—
459#95—118no—
460#95C22×D1118yescomplemented
461C2×C11—24no—
462C2×C11—24no—
463C2×C11—24no—
464C2×C11C22×#12311yescharacteristic
465C2×C11C2×#53412yes—
466C2×C11#349012yes—
467C2×C11#349012yes—
468D11—28no—
469D11—44no—
470D11—82no—
471C24—44no—
472C24—112no—
473C24—114no—
474C24—112no—
475C24—118no—
476C24—118no—
477C24—114no—
478C24—112no—
479C24—228no—
480C24—228no—
481C24—228no—
482C24—222no—
483C24—222no—
484C24—2232no—
485C24—224no—
486C24—224no—
487C24—222no—
488C24—224no—
489C24—224no—
490C24—222no—
491C24—222no—
492C24—222no—
493C24—222no—
494C24—444no—
495C24—444no—
496C24—444no—
497C24—444no—
498C24—4432no—
499C24—4432no—
500C24—4432no—
501C24#433914yes—
502C24D4×D1114yes—
503C24#434314yes—
504C24C23×D1111yescharacteristic
505C24C23×D1111yescharacteristic
506C24C23×D1111yescharacteristic
507C2×D4—228no—
508C2×D4—228no—
509C2×D4—2216no—
510C2×D4—224no—
511C2×D4—224no—
512C2×D4—224no—
513C2×D4—224no—
514C2×D4—224no—
515C2×D4—224no—
516C2×D4—448no—
517C2×D4—4432no—
518C2×D4—4416no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—112no—
526C22×C4—114no—
527C22×C4—114no—
528C22×C4—228no—
529C22×C4—228no—
530C22×C4—2216no—
531C22×C4—222no—
532C22×C4—224no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—224no—
536C22×C4—448no—
537C22×C4—4432no—
538C22×C4—444no—
539C22×C4—444no—
540C22×C4C23×D1114yes—
541C22×C4C23×D1114yes—
542C22×C4C23×D1114yes—
543C4⋊C4—48no—
544C4⋊C4—448no—
545C22⋊C4—24no—
546C22⋊C4—24no—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—228no—
552C22⋊C4—228no—
553C22⋊C4—228no—
554C22⋊C4—228no—
555C22⋊C4—2216no—
556C22⋊C4—224no—
557C22⋊C4—224no—
558C22⋊C4—224no—
559C22⋊C4—224no—
560C22⋊C4—448no—
561C22⋊C4—448no—
562C22⋊C4—448no—
563C11#3499211yescharacteristic, complemented, Sylow
564C23—24no—
565C23—24no—
566C23—24no—
567C23—48no—
568C23—48no—
569C23—48no—
570C23—114no—
571C23—118no—
572C23—114no—
573C23—2216no—
574C23—2216no—
575C23—2216no—
576C23—2216no—
577C23—2216no—
578C23—228no—
579C23—222no—
580C23—222no—
581C23—224no—
582C23—2216no—
583C23—2216no—
584C23—228no—
585C23—222no—
586C23—222no—
587C23—224no—
588C23—224no—
589C23—222no—
590C23—222no—
591C23—222no—
592C23—228no—
593C23—448no—
594C23—448no—
595C23—448no—
596C23—4416no—
597C23—4416no—
598C23—4416no—
599C23—4416no—
600C23—448no—
601C23—448no—
602C23—448no—
603C23—44128no—
604C23—444no—
605C23—884no—
606C23—884no—
607C23#66947116yescomplemented
608C23C2×#433912yes—
609C23C2×#433912yes—
610C23C2×#433912yes—
611C23C2×D4×D1112yes—
612C23C2×D4×D1112yes—
613C23C2×D4×D1112yes—
614C23C2×#434312yes—
615C23C2×#434312yes—
616C23C2×#434312yes—
617C23C24×D1111yescharacteristic
618D4—4416no—
619D4—4416no—
620D4—448no—
621D4—448no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—48no—
629C2×C4—48no—
630C2×C4—84no—
631C2×C4—222no—
632C2×C4—224no—
633C2×C4—222no—
634C2×C4—224no—
635C2×C4—222no—
636C2×C4—228no—
637C2×C4—228no—
638C2×C4—4416no—
639C2×C4—4416no—
640C2×C4—448no—
641C2×C4—444no—
642C2×C4—884no—
643C22—24no—
644C22—24no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—24no—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—416no—
653C22—118no—
654C22—2232no—
655C22—224no—
656C22—228no—
657C22—228no—
658C22—224no—
659C22—224no—
660C22—224no—
661C22—224no—
662C22—4432no—
663C22—4432no—
664C22—4416no—
665C22—444no—
666C22—444no—
667C22—444no—
668C22—444no—
669C22—444no—
670C22—442no—
671C22—888no—
672C22C2×#6694714yes—
673C22C2×#6694714yes—
674C22C2×#6694714yes—
675C22C22×#433911yescharacteristic
676C22C22×D4×D1111yescharacteristic
677C22C22×#434311yescharacteristic
678C22D11×H(5,𝔽2)14yes—
679C4—44no—
680C4—44no—
681C4—44no—
682C4—444no—
683C4—444no—
684C4—442no—
685C2—24no—
686C2—24no—
687C2—24no—
688C2—228no—
689C2—444no—
690C2—882no—
691C2C22×#6694711yescharacteristic
692C2D11×#53412yes—
693C2#1308230112yes—
694C2#1308230612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2315C2
prime radicalC22×#66935C2
hypercenter#2315D11
hypocenterC11#34992
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊C4×D11C2semidirect
3. #13076911C2semidirect
4. #13074394C2semidirect
5. #13072896C2semidirect
6. #13072009C2semidirect
7. #13071945C2semidirect
8. #13071228C2semidirect
9. #13071191C2semidirect
10. #13071191C2semidirect
11. C2×#10622568C2semidirect
12. C11×#2315C2semidirect
16. C23×C4×D11C22semidirect
23. C22×(C2×D11)⋊C4C22semidirect
24. C22×(C2×D11)⋊C4C22semidirect
25. C2×#66947C22semidirect
32. C2×C22⋊C4×D11C22semidirect
33. C11×#385C22semidirect
34. C11×#385C22semidirect
35. C11×#380C22semidirect
36. #10622826C22semidirect
37. #10622826C22semidirect
38. #10622823C22semidirect
39. #10622606C22semidirect
40. #10622604C22semidirect
41. #10622602C22semidirect
42. #10622571C22semidirect
43. #10622571C22semidirect
45. #10622568C22semidirect
46. #10622568C22semidirect
47. #10622568C22semidirect
48. #10622568C22semidirect
49. #10622559C22semidirect
50. #10622556C22semidirect
51. #10622556C22semidirect
52. #10622555C22semidirect
53. #10622288C22semidirect
54. #10622285C22semidirect
55. #10622278C22semidirect
56. #10622277C22semidirect
86. C2×C11×C4⋊C4C23semidirect
111. C2×(C2×D11)⋊C4C23semidirect
112. C2×(C2×D11)⋊C4C23semidirect
113. C2×Dic11⋊C4C23semidirect
120. C11×#95C23semidirect
121. C11⋊#95C23semidirect
122. C11⋊#95C23semidirect
123. C11⋊#95C23semidirect
225. #2315D11semidirect
235. C23×C11#123semidirect
340. #385C2×D11semidirect
341. #385C2×D11semidirect
346. #380C2×D11semidirect
428. C2×C4⋊C4C22×D11semidirect
460. #95C22×D11semidirect
563. C11#34992semidirect
607. C23#66947semidirect

Maximal subgroups

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

subgroupindex
C22×#669352
C22×C22⋊C4×D112
#130769112
#130743942
#130728962
#130720092
#130719452
#130712282
#130711912
C2×#106225682
C11×#23152
#3499211