Finite Group Databasebeta

← #25129295

Subgroups — #25129295

Order 11008.

1772 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583220C212yesmaximal, complemented
2#19136978C211yesmaximal, characteristic, complemented
3#19135781C212yesmaximal, complemented
4#19135774C212yesmaximal, complemented
5#19134918C212yesmaximal, complemented
6#19134788C211yesmaximal, characteristic, complemented
7#19134783C211yesmaximal, characteristic, complemented
8#19134526C211yesmaximal, characteristic, complemented
9#19134526C211yesmaximal, characteristic, complemented
10#19134505C211yesmaximal, characteristic, complemented
11C22×#121×C43C211yesmaximal, characteristic
12C2×#13063284C2211yescharacteristic, complemented
13C2×#13063284C2211yescharacteristic, complemented
14#14583220—28no—
15C2×#13063258C2212yescomplemented
16C2×#13063256C2212yescomplemented
17C2×#13063246C2212yescomplemented
18C2×#13063246C2212yescomplemented
19C2×#13063246C2212yescomplemented
20C2×#13063246C2212yescomplemented
21C2×C22⋊(C43⋊C8)C2211yescharacteristic
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2212yescomplemented
24C2×C22⋊(C43⋊C8)C2212yescomplemented
25#14582762—21no—
26#14582759C2211yescharacteristic
27#14582759C2211yescharacteristic
28#14582759C2211yescharacteristic, complemented
29#14582759C2211yescharacteristic, complemented
30#14582755—21no—
31C4×C22⋊Dic43—21no—
32C4×C22⋊Dic43—21no—
33#14582661C2212yescomplemented
34#14582661C2212yescomplemented
35C23×D4×C43—21no—
36C23×D4×C43C2211yescharacteristic
37C24×C4×C43C2211yescharacteristic
38C2×#121×C43—21no—
39C2×#121×C43—21no—
40C2×#121×C43—28no—
41C2×#121×C43C2212yes—
42C2×#121×C43C2212yes—
43C22×C4⋊C4×C43C2211yescharacteristic
44C22×C22⋊C4×C43—21no—
45C22×C43⋊C8C2312yes—
46C22×C43⋊C8C2312yes—
47#13063284—24no—
48#13063284—42no—
49C2×C4⋊Dic43C2311yescharacteristic
50C2×C4⋊Dic43C2311yescharacteristic
51C2×C4⋊Dic43C2311yescharacteristic
52C2×C4⋊Dic43C2311yescharacteristic
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—21no—
59C2×C4×Dic43—21no—
60C2×C4×Dic43—21no—
61#13063258—24no—
62#13063256—24no—
63#13063246—24no—
64#13063246—24no—
65#13063246—42no—
66#13063246—42no—
67C22⋊(C43⋊C8)—24no—
68C22⋊(C43⋊C8)—22no—
69C22⋊(C43⋊C8)—22no—
70C22⋊(C43⋊C8)—42no—
71C43⋊#95—21no—
72C43⋊#95—21no—
73C43⋊#95—21no—
74C43⋊#95—21no—
75C25×C43—21no—
76C25×C43D411yescharacteristic
77C22×D4×C43—28no—
78C22×D4×C43—22no—
79C22×D4×C43—22no—
80C22×D4×C43—24no—
81C22×D4×C43—21no—
82C22×D4×C43—22no—
83C22×D4×C43—22no—
84C22×D4×C43—42no—
85C22×D4×C43—44no—
86C22×D4×C43—44no—
87C22×D4×C43C2312yes—
88C23×C4×C43—21no—
89C23×C4×C43—24no—
90C23×C4×C43—22no—
91C23×C4×C43—22no—
92C23×C4×C43—42no—
93C23×C4×C43D411yescharacteristic
94C23×C4×C43D411yescharacteristic
95C23×C4×C43D411yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C23×C4×C43C2311yescharacteristic
98C23×C4×C43C2311yescharacteristic
99#121×C43—28no—
100#121×C43—28no—
101#121×C43—24no—
102#121×C43—24no—
103#121×C43—24no—
104#121×C43D418yes—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—24no—
107C2×C4⋊C4×C43C2312yes—
108C2×C22⋊C4×C43—28no—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—22no—
111C24×C43—22no—
112C24×C43—22no—
113C24×C43—22no—
114C24×C43—24no—
115C24×C43—22no—
116C24×C43—22no—
117C24×C43—22no—
118C24×C43—41no—
119C24×C43—41no—
120C24×C43—42no—
121C24×C43—42no—
122C24×C43—42no—
123C24×C43—42no—
124C24×C43—42no—
125C24×C43—42no—
126C24×C43C2×D411yescharacteristic
127C24×C43C2×D411yescharacteristic
128C24×C43C2×D411yescharacteristic
129C2×D4×C43—28no—
130C2×D4×C43—24no—
131C2×D4×C43—22no—
132C2×D4×C43—28no—
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43—432no—
138C2×D4×C43—44no—
139C2×D4×C43—44no—
140C2×D4×C43—44no—
141C2×D4×C43—48no—
142C2×D4×C43—48no—
143C2×D4×C43—42no—
144C2×D4×C43—42no—
145C2×D4×C43—44no—
146C2×D4×C43C2×D414yes—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—24no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—41no—
165C22×C4×C43—41no—
166C22×C4×C43—41no—
167C22×C4×C43—42no—
168C22×C4×C43—48no—
169C22×C4×C43—48no—
170C22×C4×C43—42no—
171C22×C4×C43C2×D414yes—
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43#4112yes—
176C22×C4×C43#4112yes—
177C22×C4×C43C2411yescharacteristic
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43C2×D414yes—
185C22⋊C4×C43—28no—
186C22⋊C4×C43—28no—
187C22⋊Dic43—42no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—42no—
192C22⋊Dic43—42no—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
196C4⋊Dic43—22no—
197C4×Dic43—42no—
198C4×Dic43—42no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—28no—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43—21no—
219C23×C43—21no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—24no—
223C23×C43—44no—
224C23×C43—44no—
225C23×C43—44no—
226C23×C43—44no—
227C23×C43—44no—
228C23×C43—48no—
229C23×C43—48no—
230C23×C43—48no—
231C23×C43—44no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43—42no—
235C23×C43—42no—
236C23×C43—42no—
237C23×C43—42no—
238C23×C43—84no—
239C23×C43—84no—
240C23×C43—84no—
241C23×C43—84no—
242C23×C43#12012yes—
243C23×C43#12312yes—
244C23×C43#13512yes—
245C23×C43AGL(1,ℤ/8)12yes—
246C23×C43AGL(1,ℤ/8)12yes—
247C23×C43C22×D411yescharacteristic
248D4×C43—24no—
249D4×C43—24no—
250D4×C43—48no—
251D4×C43—416no—
252D4×C43—416no—
253D4×C43—42no—
254D4×C43—42no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—24no—
260C2×C4×C43—24no—
261C2×C4×C43—24no—
262C2×C4×C43—24no—
263C2×C4×C43—21no—
264C2×C4×C43—24no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—44no—
268C2×C4×C43—44no—
269C2×C4×C43—44no—
270C2×C4×C43—48no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—42no—
275C2×C4×C43#12012yes—
276C2×C4×C43#12312yes—
277C2×C4×C43C22×D412yes—
278C2×C4×C43C2×#4111yescharacteristic
279C2×C4×C43C2×#4111yescharacteristic
280C2×C4×C43H(5,𝔽2)12yes—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C43⋊C8—42no—
294C43⋊C8—42no—
295#24009—431nomaximal, Sylow
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—22no—
301C22×C43—22no—
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—416no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43—44no—
318C22×C43—44no—
319C22×C43—44no—
320C22×C43—816no—
321C22×C43—82no—
322C22×C43—82no—
323C22×C43—82no—
324C22×C43—82no—
325C22×C43#48214yescomplemented
326C22×C43C2×#12011yescharacteristic
327C22×C43C2×#12311yescharacteristic
328C22×C43#53411yescharacteristic
329C22×C43C2×#13511yescharacteristic
330C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C43#57511yescharacteristic
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—41no—
336C4×C43—44no—
337C4×C43#54612yes—
338C4×C43#54612yes—
339Dic43—81no—
340Dic43—81no—
341Dic43—81no—
342Dic43—81no—
343C22×#121D4311yescharacteristic
344C2×#482—432no—
345#2280—431no—
346#2034—432no—
347#2033—432no—
348#1875—432no—
349#1853—431no—
350#1852—431no—
351#1786—431no—
352#1786—431no—
353#1779—431no—
354C2×C43—24no—
355C2×C43—42no—
356C2×C43—42no—
357C2×C43—84no—
358C2×C43#240511yescharacteristic
359C2×C43#300211yescharacteristic
360C2×C43#300311yescharacteristic
361C2×C43C2×#48211yescharacteristic
362C2×C43#309411yescharacteristic
363C2×C43#318811yescharacteristic
364C2×C43#319411yescharacteristic
365C23×D4—21no—
366C23×D4C2×D4311yescharacteristic
367C24×C4C2×D4311yescharacteristic
368C2×#121—21no—
369C2×#121—21no—
370C2×#121—28no—
371C2×#121C2×D4312yes—
372C2×#121C2×D4312yes—
373C2×#117—431no—
374C2×#117—431no—
375C22×C4⋊C4C2×D4311yescharacteristic
376C22×C22⋊C4—21no—
377#482—868no—
378C2×#107—432no—
379C2×#106—432no—
380C2×#102—432no—
381C2×#102—432no—
382C2×#102—432no—
383C2×#102—432no—
384C2×C22⋊C8—432no—
385C2×C22⋊C8—431no—
386C2×C22⋊C8—431no—
387C2×C22⋊C8—432no—
388#381—861no—
389#380—431no—
390#380—431no—
391#380—431no—
392#380—431no—
393#379—861no—
394C4×C22⋊C4—861no—
395C4×C22⋊C4—861no—
396#340—432no—
397#340—432no—
398C43#2400911yescharacteristic, complemented, Sylow
399C25—21no—
400C25C22⋊D4311yescharacteristic
401C22×D4—28no—
402C22×D4—22no—
403C22×D4—22no—
404C22×D4—24no—
405C22×D4—22no—
406C22×D4—22no—
407C22×D4—21no—
408C22×D4—42no—
409C22×D4—44no—
410C22×D4—44no—
411C22×D4C22×D4312yes—
412C23×C4—21no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—24no—
416C23×C4—42no—
417C23×C4C22⋊D4311yescharacteristic
418C23×C4C22⋊D4311yescharacteristic
419C23×C4C22⋊D4311yescharacteristic
420C23×C4C22×D4311yescharacteristic
421C23×C4C22×D4311yescharacteristic
422C23×C4C22×D4311yescharacteristic
423C22×C8—432no—
424C22×C8—432no—
425#121—28no—
426#121—28no—
427#121—24no—
428#121—24no—
429#121—24no—
430#121C22⋊D4318yes—
431#117—864no—
432#117—1722no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4C22×D4312yes—
440C2×C22⋊C4—28no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—861no—
449C2×C42—861no—
450C2×C42—861no—
451#107—864no—
452#106—864no—
453#102—864no—
454#102—864no—
455#102—1722no—
456#102—1722no—
457C22⋊C8—862no—
458C22⋊C8—862no—
459C22⋊C8—864no—
460C22⋊C8—1722no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—24no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—41no—
473C24—41no—
474C24—42no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24C2×C22⋊D4311yescharacteristic
481C24C2×C22⋊D4311yescharacteristic
482C24C2×C22⋊D4311yescharacteristic
483C2×D4—24no—
484C2×D4—28no—
485C2×D4—28no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—42no—
494C2×D4—432no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—42no—
500C2×D4C2×C22⋊D4314yes—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4#1062190012yes—
530C22×C4#1062190012yes—
531C22×C4C2×C22⋊D4311yescharacteristic
532C22×C4C2×C22⋊D4311yescharacteristic
533C22×C4C2×C22⋊D4314yes—
534C22×C4C2×C22⋊D4311yescharacteristic
535C22×C4C23×D4311yescharacteristic
536C2×C8—862no—
537C2×C8—862no—
538C2×C8—862no—
539C2×C8—862no—
540C2×C8—862no—
541C2×C8—862no—
542C4⋊C4—24no—
543C4⋊C4—22no—
544C4⋊C4—862no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—862no—
548C4⋊C4C2×C22⋊D4314yes—
549C22⋊C4—28no—
550C22⋊C4—28no—
551C22⋊C4—1722no—
552C22⋊C4—1722no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C42—1722no—
558C42—1722no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—28no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—24no—
577C23—44no—
578C23—44no—
579C23—44no—
580C23—44no—
581C23—44no—
582C23—48no—
583C23—48no—
584C23—48no—
585C23—44no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—84no—
593C23—84no—
594C23—84no—
595C23—84no—
596C23#1306329412yes—
597C23#1306330612yes—
598C23#1306334512yes—
599C23#1306335112yes—
600C23#1306335112yes—
601C23C22×C22⋊D4311yescharacteristic
602D4—24no—
603D4—24no—
604D4—48no—
605D4—416no—
606D4—416no—
607D4—42no—
608D4—42no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—21no—
618C2×C4—24no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—48no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4#1306329412yes—
642C2×C4#1306330612yes—
643C2×C4C22×C22⋊D4312yes—
644C2×C4C2×#1062190011yescharacteristic
645C2×C4C2×#1062190011yescharacteristic
646C2×C4#1306337012yes—
647C8—1722no—
648C8—1722no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—416no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—44no—
671C22—44no—
672C22—44no—
673C22—816no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—82no—
678C22#1458322014yescomplemented
679C22C2×#1306329411yescharacteristic
680C22C2×#1306330611yescharacteristic
681C22#1458345811yescharacteristic
682C22C2×#1306334511yescharacteristic
683C22C2×#1306335111yescharacteristic
684C22C2×#1306335111yescharacteristic
685C22#1458369711yescharacteristic
686C4—22no—
687C4—22no—
688C4—41no—
689C4—44no—
690C4—3441no—
691C4—3441no—
692C4—3441no—
693C4—3441no—
694C4#1458354312yes—
695C4#1458354312yes—
696C2—24no—
697C2—42no—
698C2—42no—
699C2—84no—
700C2#1913791811yescharacteristic
701C2#1914381311yescharacteristic
702C2#1914382211yescharacteristic
703C2C2×#1458322011yescharacteristic
704C2#1914453111yescharacteristic
705C2#1914536011yescharacteristic
706C2#1914540911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC22×#121×C43C2
socleC23×C43C22×D4
hypercenterC22×#121D43
hypocenterC43#24009
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14583220C2semidirect
2. #19136978C2semidirect
3. #19135781C2semidirect
4. #19135774C2semidirect
5. #19134918C2semidirect
6. #19134788C2semidirect
7. #19134783C2semidirect
8. #19134526C2semidirect
9. #19134526C2semidirect
10. #19134505C2semidirect
12. C2×#13063284C22semidirect
13. C2×#13063284C22semidirect
15. C2×#13063258C22semidirect
16. C2×#13063256C22semidirect
17. C2×#13063246C22semidirect
18. C2×#13063246C22semidirect
19. C2×#13063246C22semidirect
20. C2×#13063246C22semidirect
23. C2×C22⋊(C43⋊C8)C22semidirect
24. C2×C22⋊(C43⋊C8)C22semidirect
28. #14582759C22semidirect
29. #14582759C22semidirect
33. #14582661C22semidirect
34. #14582661C22semidirect
325. C22×C43#482semidirect
398. C43#24009semidirect
678. C22#14583220semidirect

Maximal subgroups

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

subgroupindex
C2×#145832202
#191369782
#191357812
#191357742
#191349182
#191347882
#191347832
#191345262
#191345052
C22×#121×C432
#2400943