Finite Group Databasebeta

← #25097845

Subgroups — #25097845

Order 11008.

2278 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063300C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic, complemented
3C2×#14582905C211yesmaximal, characteristic, complemented
4C2×#14582903C211yesmaximal, characteristic, complemented
5C2×#14582862C211yesmaximal, characteristic, complemented
6#19134916C214yesmaximal, complemented
7#19134911C214yesmaximal, complemented
8#19134314C211yesmaximal, characteristic, complemented
9C43×#1736C211yesmaximal, characteristic, complemented
10C23×D172—21no—
11C23×D172C2211yescharacteristic
12C23×C4×D43C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C2×#13063300—24no—
15C2×#13063300—21no—
16C2×#13063300—21no—
17C2×#13063300C418yescomplemented
18C2×#13063300C2212yes—
19C2×#13063300C2212yes—
20C2×#13063284C2211yescharacteristic
21C2×#13063283C2212yescomplemented
22C2×#13063282—21no—
23C2×#13063281—21no—
24#117×D43—24no—
25#117×D43—24no—
26C2×C4⋊C4×D43C2212yescomplemented
27C22×(C2×D43)⋊C4—21no—
28C2×C22⋊C4×D43—21no—
29C2×C42×D43—21no—
30#14582905—24no—
31#14582903—24no—
32C2×#13063247C2214yescomplemented
33C2×#13063245C2214yescomplemented
34#14582862—24no—
35C2×(C2×D43)⋊C8C2212yescomplemented
36C2×(C2×D43)⋊C8C2212yescomplemented
37#14582661C2214yescomplemented
38C22×M16×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C22×C4⋊C4×C43C2211yescharacteristic
41C43×#340C2214yescomplemented
42C24×D43—21no—
43C24×D43D411yescharacteristic
44C22×D172—22no—
45C22×D172—22no—
46C22×D172—22no—
47C22×D172—22no—
48C22×D172—28no—
49C22×D172—22no—
50C22×D172—22no—
51C22×D172—21no—
52C22×D172—22no—
53C22×D172—48no—
54C22×D172C2×C414yescomplemented
55C22×D172C2312yes—
56C23×Dic43D411yescharacteristic
57C22×C4×D43—22no—
58C22×C4×D43—22no—
59C22×C4×D43—22no—
60C22×C4×D43—22no—
61C22×C4×D43—22no—
62C22×C4×D43C2×C414yes—
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D414yes—
66C22×C4×D43C2311yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C2×#10621877—22no—
69C2×#10621877—22no—
70C2×#10621877—22no—
71C22×C43⋊C8C2312yes—
72#13063300—28no—
73#13063300—28no—
74#13063300—24no—
75#13063300—24no—
76#13063300C2×C418yes—
77#13063300C2×C418yescomplemented
78#13063284—22no—
79#13063284D414yescomplemented
80#13063283—24no—
81#13063283—24no—
82#13063282—28no—
83#13063281—28no—
84C2×C4⋊Dic43C2312yes—
85C2×Dic43⋊C4—22no—
86C4⋊C4×D43—24no—
87C4⋊C4×D43—24no—
88C2×C22⋊Dic43—21no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—28no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C22⋊C4×D43—28no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—22no—
96C42×D43—28no—
97#13063247—28no—
98#13063245—28no—
99(C2×D43)⋊C8—24no—
100(C2×D43)⋊C8—24no—
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103C2×M16×C43—22no—
104C2×M16×C43—22no—
105C2×M16×C43—22no—
106C22×C8×C43C2312yes—
107#117×C43—22no—
108#117×C43D414yescomplemented
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43C2×C414yescomplemented
112C2×C4⋊C4×C43C2312yes—
113C2×C4⋊C4×C43C2312yes—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43—21no—
116C24×C43C2×D411yescharacteristic
117C23×D43—22no—
118C23×D43—22no—
119C23×D43—24no—
120C23×D43—24no—
121C23×D43—22no—
122C23×D43—42no—
123C23×D43—44no—
124C23×D43—44no—
125C23×D43—42no—
126C23×D43—42no—
127C23×D43C22⋊C414yes—
128C23×D43C2×D411yescharacteristic
129C23×D43C2×D411yescharacteristic
130C22×C4×C43—24no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—44no—
134C22×C4×C43C22×C412yes—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43#4112yes—
140C22×C4×C43#4112yes—
141C22×C4×C43C2411yescharacteristic
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43C22⋊C414yes—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×D172—24no—
149C2×D172—22no—
150C2×D172—28no—
151C2×D172—28no—
152C2×D172—28no—
153C2×D172—28no—
154C2×D172—22no—
155C2×D172—22no—
156C2×D172—22no—
157C2×D172—22no—
158C2×D172—48no—
159C2×D172—432no—
160C2×D172—42no—
161C2×D172—44no—
162C2×D172—44no—
163C2×D172—42no—
164C2×D172—48no—
165C2×D172C22×C414yes—
166C2×C4×D43—28no—
167C2×C4×D43—28no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—28no—
171C2×C4×D43—28no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—28no—
183C2×C4×D43—44no—
184C2×C4×D43—44no—
185C2×C4×D43C22⋊C414yes—
186C2×C4×D43C22⋊C414yes—
187C2×C4×D43C22×C412yes—
188C2×C4×D43C22×C412yes—
189C2×C4×D43C2×D412yes—
190C2×C4×D43C2×D412yes—
191M16×C43—44no—
192C2×C8×C43—22no—
193C2×C8×C43—22no—
194C2×C8×C43—22no—
195C4⋊C4×C43—24no—
196C4⋊C4×C43—22no—
197C4⋊C4×C43—22no—
198C4⋊C4×C43C22×C414yes—
199C4⋊C4×C43C2×D414yescomplemented
200C22⋊C4×C43—24no—
201C42×C43—24no—
202C22⋊Dic43—24no—
203(C2×D43)⋊C4—28no—
204(C2×D43)⋊C4—28no—
205(C2×D43)⋊C4—28no—
206C4⋊Dic43—22no—
207C4⋊Dic43C2×D414yescomplemented
208Dic43⋊C4—28no—
209C4×Dic43—28no—
210C4×Dic43—24no—
211#10621877—44no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—22no—
214C2×C43⋊C8—22no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43C2×C22⋊C412yes—
218C23×C43#12012yes—
219C23×C43#12312yes—
220C23×C43C22×D411yescharacteristic
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—22no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—28no—
229C22×D43—28no—
230C22×D43—24no—
231C22×D43—44no—
232C22×D43—48no—
233C22×D43—48no—
234C22×D43—48no—
235C22×D43—48no—
236C22×D43—42no—
237C22×D43—42no—
238C22×D43—44no—
239C22×D43—44no—
240C22×D43—48no—
241C22×D43—88no—
242C22×D43—88no—
243C22×D43C2×C22⋊C412yes—
244C22×D43C2×C22⋊C412yes—
245C22×D43AGL(1,ℤ/8)14yes—
246C2×C4×C43—24no—
247C2×C4×C43—24no—
248C2×C4×C43—48no—
249C2×C4×C43—42no—
250C2×C4×C43—44no—
251C2×C4×C43—42no—
252C2×C4×C43C2×C22⋊C412yes—
253C2×C4×C43C4×D414yes—
254C2×C4×C43C4×D414yes—
255C2×C4×C43#12012yes—
256C2×C4×C43#12114yes—
257C2×C4×C43#12114yes—
258C2×C4×C43#12312yes—
259C2×C4×C43C23×C411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—28no—
270C2×Dic43—24no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43C2×C22⋊C412yes—
274C2×Dic43C2×C22⋊C412yes—
275D172—24no—
276D172—24no—
277D172—416no—
278D172—416no—
279D172—42no—
280D172—42no—
281D172—48no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—22no—
287C4×D43—22no—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—28no—
291C4×D43—28no—
292C4×D43—416no—
293C8×C43—42no—
294C43⋊C8—42no—
295#20912—431nomaximal, Sylow
296C22×C43—24no—
297C22×C43—22no—
298C22×C43—22no—
299C22×C43—24no—
300C22×C43#38614yes—
301C22×C43C22×C22⋊C411yescharacteristic
302C22×C43C2×#12011yescharacteristic
303C22×C43C2×#12311yescharacteristic
304C22×C43C2×AGL(1,ℤ/8)12yes—
305C22×C43#57512yes—
306C2×D43—24no—
307C2×D43—22no—
308C2×D43—24no—
309C2×D43—22no—
310C2×D43—22no—
311C2×D43—22no—
312C2×D43—22no—
313C2×D43—416no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—44no—
317C2×D43—44no—
318C2×D43—44no—
319C2×D43—816no—
320C2×D43—84no—
321C2×D43—84no—
322C2×D43#41814yescomplemented
323C4×C43—44no—
324C4×C43—44no—
325C4×C43#38614yes—
326C4×C43C2×C4×D411yescharacteristic
327C4×C43C2×C4×D411yescharacteristic
328C4×C43C2×#12111yescharacteristic
329C4×C43C2×#12111yescharacteristic
330Dic43—22no—
331Dic43—22no—
332Dic43—44no—
333C22×#121—431no—
334C22×#117—431no—
335C2×#418—431no—
336C2×#418—431no—
337C2×#407—431no—
338#1875—434no—
339#1874—434no—
340#1736—431no—
341#1736D4311yescharacteristic, complemented
342C2×C43—24no—
343C2×C43C2×#38611yescharacteristic
344C2×C43C2×#41811yescharacteristic
345C2×C43#289611yescharacteristic
346C2×C43#300612yes—
347C2×C43#309412yes—
348D43—24no—
349D43—42no—
350D43—84no—
351C23×D4—431no—
352C23×D4—861no—
353C24×C4—431no—
354C22×M16—431no—
355C22×M16C2×D4311yescharacteristic
356C2×#121—432no—
357C2×#121—432no—
358C2×#121—438no—
359C2×#121—861no—
360C2×#121—864no—
361C2×#121—861no—
362C2×#117—431no—
363C2×#117—432no—
364C2×#117—861no—
365C2×#117—861no—
366C2×#117—864no—
367C2×#117—864no—
368C2×#117C2×D4311yescharacteristic
369C22×C4⋊C4—432no—
370C22×C4⋊C4C2×D4311yescharacteristic
371C22×C22⋊C4—861no—
372C22×C22⋊C4—861no—
373C22×C42—861no—
374#418—864no—
375#418—864no—
376C2×#102—434no—
377C2×#102—434no—
378#407—864no—
379C2×C22⋊C8—432no—
380C2×C22⋊C8—432no—
381#340—434no—
382#340C2×D4314yescomplemented
383C43#2091211yescharacteristic, complemented, Sylow
384C25—431no—
385C25—861no—
386C22×D4—434no—
387C22×D4—432no—
388C22×D4—868no—
389C22×D4—862no—
390C22×D4—862no—
391C22×D4—862no—
392C22×D4—862no—
393C22×D4—862no—
394C22×D4—861no—
395C22×D4—862no—
396C22×D4—862no—
397C22×D4—1728no—
398C23×C4—21no—
399C23×C4—431no—
400C23×C4—434no—
401C23×C4—431no—
402C23×C4—434no—
403C23×C4—431no—
404C23×C4—431no—
405C23×C4—431no—
406C23×C4—862no—
407C23×C4—862no—
408C23×C4—862no—
409C23×C4—862no—
410C23×C4—862no—
411C23×C4C22×D4311yescharacteristic
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—22no—
415C2×M16—862no—
416C2×M16—862no—
417C2×M16—862no—
418C22×C8—432no—
419C22×C8C22×D4312yes—
420#121—438no—
421#121—438no—
422#121—868no—
423#121—868no—
424#121—864no—
425#121—864no—
426#117—22no—
427#117—434no—
428#117—868no—
429#117—868no—
430#117—864no—
431#117—862no—
432#117—864no—
433#117D17214yescomplemented
434C2×C4⋊C4—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—432no—
437C2×C4⋊C4—864no—
438C2×C4⋊C4—862no—
439C2×C4⋊C4—864no—
440C2×C4⋊C4C4×D4314yescomplemented
441C2×C4⋊C4C22×D4312yes—
442C2×C4⋊C4C22×D4312yes—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—868no—
445C2×C22⋊C4—868no—
446C2×C22⋊C4—862no—
447C2×C22⋊C4—862no—
448C2×C22⋊C4—862no—
449C2×C22⋊C4—861no—
450C2×C42—21no—
451C2×C42—868no—
452C2×C42—862no—
453C2×C42—861no—
454#102—868no—
455#102—868no—
456C22⋊C8—864no—
457C22⋊C8—864no—
458C24—431no—
459C24—431no—
460C24—434no—
461C24—864no—
462C24—862no—
463C24—862no—
464C24—864no—
465C24—862no—
466C24—1722no—
467C24—1724no—
468C24—1724no—
469C24—1722no—
470C24—1722no—
471C24D4×D4311yescharacteristic
472C2×D4—434no—
473C2×D4—868no—
474C2×D4—868no—
475C2×D4—864no—
476C2×D4—868no—
477C2×D4—868no—
478C2×D4—862no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—862no—
482C2×D4—862no—
483C2×D4—1728no—
484C2×D4—17232no—
485C2×D4—1728no—
486C2×D4—1722no—
487C2×D4—1724no—
488C2×D4—1724no—
489C2×D4—1722no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—44no—
494C22×C4—434no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—434no—
498C22×C4—434no—
499C22×C4—432no—
500C22×C4—432no—
501C22×C4—432no—
502C22×C4—432no—
503C22×C4—868no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—868no—
507C22×C4—868no—
508C22×C4—862no—
509C22×C4—862no—
510C22×C4—868no—
511C22×C4—868no—
512C22×C4—862no—
513C22×C4—862no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—862no—
523C22×C4—1724no—
524C22×C4—1724no—
525C22×C4C2×C4×D4312yes—
526C22×C4C2×D17212yes—
527C22×C4#1062189812yes—
528C22×C4D4×D4311yescharacteristic
529C22×C4D4×D4312yes—
530C22×C4D4×D4312yes—
531C22×C4#1062190212yes—
532C22×C4C23×D4311yescharacteristic
533M16—44no—
534M16—1724no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—862no—
539C2×C8—862no—
540C2×C8—862no—
541C4⋊C4—24no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—434no—
545C4⋊C4—868no—
546C4⋊C4—862no—
547C4⋊C4C2×C4×D4314yes—
548C4⋊C4C2×D17214yescomplemented
549C22⋊C4—24no—
550C22⋊C4—868no—
551C22⋊C4—868no—
552C22⋊C4—868no—
553C22⋊C4—864no—
554C42—24no—
555C42—868no—
556C42—864no—
557C23—22no—
558C23—22no—
559C23—432no—
560C23—434no—
561C23—432no—
562C23—868no—
563C23—861no—
564C23—861no—
565C23—862no—
566C23—861no—
567C23—861no—
568C23—862no—
569C23—862no—
570C23—868no—
571C23—864no—
572C23—3448no—
573C23—3448no—
574C23—1724no—
575C23—1728no—
576C23—1728no—
577C23—1728no—
578C23—1728no—
579C23—1722no—
580C23—1722no—
581C23—1724no—
582C23—1724no—
583C23—1728no—
584C23C22⋊C4×D4312yes—
585C23#1306329512yes—
586C23#1306331012yes—
587C23C2×D4×D4311yescharacteristic
588D4—864no—
589D4—864no—
590D4—17216no—
591D4—17216no—
592D4—1722no—
593D4—1722no—
594D4—1728no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—48no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—432no—
602C2×C4—432no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—861no—
606C2×C4—861no—
607C2×C4—868no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—868no—
617C2×C4—868no—
618C2×C4—864no—
619C2×C4—17216no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4C22⋊C4×D4312yes—
623C2×C4#1306328714yes—
624C2×C4C4×D17214yes—
625C2×C4#1306329512yes—
626C2×C4#1306329814yes—
627C2×C4#1306330014yes—
628C2×C4#1306331012yes—
629C2×C4C22×C4×D4311yescharacteristic
630C2×C4C2×D4×D4311yescharacteristic
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4C22×D17211yescharacteristic
633C2×C4C2×#1062189811yescharacteristic
634C2×C4C2×#1062190211yescharacteristic
635C8—42no—
636C8—1722no—
637C22—24no—
638C22—24no—
639C22—22no—
640C22—22no—
641C22—434no—
642C22—864no—
643C22—864no—
644C22—862no—
645C22—862no—
646C22—862no—
647C22—862no—
648C22—862no—
649C22—34416no—
650C22—3444no—
651C22—3444no—
652C22—17216no—
653C22—1724no—
654C22—1724no—
655C22—1724no—
656C22—1722no—
657C22—1722no—
658C22#1458277714yes—
659C22C2×C22⋊C4×D4311yescharacteristic
660C22C2×#1306329511yescharacteristic
661C22C2×#1306331011yescharacteristic
662C22AGL(1,ℤ/8)×D4312yes—
663C22#1458369812yes—
664C4—44no—
665C4—44no—
666C4—862no—
667C4—862no—
668C4—1724no—
669C4#1458277714yes—
670C4C2×#1306328711yescharacteristic
671C4C2×C4×D17211yescharacteristic
672C4C2×#1306329811yescharacteristic
673C4C2×#1306330011yescharacteristic
674C2—24no—
675C2—864no—
676C2—3444no—
677C2—1722no—
678C2C2×#1458277711yescharacteristic
679C2#418×D4311yescharacteristic
680C2#1914311311yescharacteristic
681C2#1914384812yes—
682C2#1914453712yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC22×#13063300C2
cosocleC22×C4×C43C24
hypercenter#1736D43
hypocenterC43#20912
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#117×D43C2semidirect
3. C2×#14582905C2semidirect
4. C2×#14582903C2semidirect
5. C2×#14582862C2semidirect
6. #19134916C2semidirect
7. #19134911C2semidirect
8. #19134314C2semidirect
9. C43×#1736C2semidirect
17. C2×#13063300C4semidirect
21. C2×#13063283C22semidirect
26. C2×C4⋊C4×D43C22semidirect
32. C2×#13063247C22semidirect
33. C2×#13063245C22semidirect
35. C2×(C2×D43)⋊C8C22semidirect
36. C2×(C2×D43)⋊C8C22semidirect
37. #14582661C22semidirect
41. C43×#340C22semidirect
54. C22×D172C2×C4semidirect
77. #13063300C2×C4semidirect
79. #13063284D4semidirect
108. #117×C43D4semidirect
111. C2×C4⋊C4×C43C2×C4semidirect
199. C4⋊C4×C43C2×D4semidirect
207. C4⋊Dic43C2×D4semidirect
322. C2×D43#418semidirect
341. #1736D43semidirect
382. #340C2×D43semidirect
383. C43#20912semidirect
433. #117D172semidirect
440. C2×C4⋊C4C4×D43semidirect
548. C4⋊C4C2×D172semidirect

Maximal subgroups

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

subgroupindex
C22×#130633002
C2×#117×D432
C2×#145829052
C2×#145829032
C2×#145828622
#191349162
#191349112
#191343142
C43×#17362
#2091243