Finite Group Databasebeta

← #25098303

Subgroups — #25098303

Order 11008.

1894 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10621872C211yesmaximal, characteristic
2C2×C22⋊Q8×D43C211yesmaximal, characteristic
3C2×#14582906C212yesmaximal, complemented
4#19136977C211yesmaximal, characteristic
5#19135027C212yesmaximal, complemented
6#19135025C212yesmaximal, complemented
7#19135019C211yesmaximal, characteristic, complemented
8#19135018C211yesmaximal, characteristic, complemented
9#19135016C211yesmaximal, characteristic, complemented
10#19134313C212yesmaximal, complemented
11C43×#1892C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C22×#10621872—24no—
15C22×#10621872—28no—
16C22×#10621872C2212yes—
17C22×#10621872C2212yes—
18C23×C43⋊C8C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063303—21no—
22C2×#13063302—21no—
23C2×#13063301C2211yescharacteristic
24C22⋊Q8×D43—24no—
25C22⋊Q8×D43C418yescomplemented
26C2×#13063283C2212yes—
27C2×C4⋊C4×D43—21no—
28C2×C4⋊C4×D43C2211yescharacteristic
29C2×C22⋊C4×D43—21no—
30#14582906—28no—
31C2×#13063250C2212yescomplemented
32C2×#13063249C2212yescomplemented
33C2×#13063248C2212yescomplemented
34#14582761—21no—
35#14582759C2211yescharacteristic
36#14582756C2212yes—
37#14582754—21no—
38C22⋊C4×Dic43—21no—
39#14582746—21no—
40#14582662C2212yescomplemented
41#14582661C2212yescomplemented
42#14582661C2212yescomplemented
43C23×C8×C43C2211yescharacteristic
44C2×C22⋊Q8×C43C2211yescharacteristic
45C2×#103×C43C2212yescomplemented
46C43×#380C2211yescharacteristic
47C43×#340C2212yescomplemented
48C24×D43D411yescharacteristic
49C22×Dic86—21no—
50C22×Dic86C2311yescharacteristic
51C2×Q8×D43—22no—
52C2×Q8×D43—24no—
53C2×Q8×D43—24no—
54C2×Q8×D43C2×C414yes—
55C23×Dic43D411yescharacteristic
56C22×C4×D43—24no—
57C22×C4×D43—24no—
58C22×C4×D43—21no—
59C22×C4×D43—21no—
60C22×C4×D43C2×C414yes—
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D414yes—
64C22×C4×D43C2311yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C2×#10621872—232no—
67C2×#10621872—24no—
68C2×#10621872—24no—
69C2×#10621872—24no—
70C2×#10621872—24no—
71C2×#10621872—24no—
72C2×#10621872D418yes—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—24no—
75C22×C43⋊C8C2312yes—
76#13063305—22no—
77#13063305C2×C414yes—
78#13063304—22no—
79#13063304C2×C414yes—
80#13063303—28no—
81#13063302—28no—
82#13063301—22no—
83#13063301C2×C414yes—
84#13063283—24no—
85#13063283—24no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2312yes—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C4⋊C4×D43—28no—
93C4⋊C4×D43—22no—
94C4⋊C4×D43C2×C414yes—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C22⋊C4×D43—28no—
102C2×C4×Dic43—22no—
103#13063250—24no—
104#13063249—24no—
105#13063248—24no—
106C43⋊#95—21no—
107C43⋊#95—22no—
108C22×Q8×C43C2311yescharacteristic
109C23×C4×C43C2311yescharacteristic
110C22×C8×C43—22no—
111C22×C8×C43—24no—
112C22×C8×C43C2312yes—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43C2×C414yes—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2312yes—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43—21no—
120#103×C43—24no—
121#95×C43—21no—
122C24×C43C2×D411yescharacteristic
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—24no—
126C23×D43—42no—
127C23×D43C22⋊C414yes—
128C23×D43C2×D411yescharacteristic
129C23×D43C2×D411yescharacteristic
130C2×Q8×C43—21no—
131C2×Q8×C43—22no—
132C2×Q8×C43—22no—
133C2×Q8×C43C22×C412yes—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43C22×C412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—24no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43C22⋊C414yes—
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150Q8×D43—216no—
151Q8×D43—44no—
152Q8×D43—44no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—24no—
156C2×C4×D43—216no—
157C2×C4×D43—28no—
158C2×C4×D43—28no—
159C2×C4×D43—24no—
160C2×C4×D43—24no—
161C2×C4×D43—24no—
162C2×C4×D43—44no—
163C2×C4×D43—44no—
164C2×C4×D43C22⋊C414yes—
165C2×C4×D43C22⋊C414yes—
166C2×C4×D43C22×C412yes—
167C2×C4×D43C22×C412yes—
168C2×C4×D43C2×D412yes—
169C2×C4×D43C2×D412yes—
170C2×C4×D43C2×D414yes—
171C2×C4×D43#4114yes—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—21no—
175C2×Dic86—24no—
176C2×Dic86—44no—
177C2×Dic86C22×C412yes—
178C2×C8×C43—28no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43C2×D414yes—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43C22×C412yes—
187C22⋊C4×C43—24no—
188C22⋊C4×C43—42no—
189C22⋊Dic43—24no—
190C22⋊Dic43—42no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—44no—
194(C2×D43)⋊C4—44no—
195C4⋊Dic43—21no—
196C4⋊Dic43—24no—
197C4⋊Dic43—22no—
198C4⋊Dic43—22no—
199C4⋊Dic43C22×C412yes—
200Dic43⋊C4—24no—
201Dic43⋊C4—24no—
202Dic43⋊C4—24no—
203C4×Dic43—44no—
204C2×C43⋊C8—28no—
205C2×C43⋊C8—22no—
206C2×C43⋊C8—22no—
207C2×C43⋊C8C2×D414yes—
208#10621872—216no—
209#10621872—216no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43C2×C22⋊C412yes—
213C23×C43#13712yes—
214C23×C43#13712yes—
215C23×C43C22×D411yescharacteristic
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—22no—
223C22×D43—28no—
224C22×D43—28no—
225C22×D43—44no—
226C22×D43—48no—
227C22×D43—48no—
228C22×D43C2×C22⋊C412yes—
229C22×D43C2×C22⋊C412yes—
230C22×D43#12114yes—
231Q8×C43—24no—
232Q8×C43—41no—
233Q8×C43—41no—
234C2×C4×C43—22no—
235C2×C4×C43—24no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43C2×C22⋊C412yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C22×D412yes—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4112yes—
250C2×Dic43—22no—
251C2×Dic43—28no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43C2×C22⋊C412yes—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43#12114yes—
262C4×D43—28no—
263C4×D43—24no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—28no—
267C4×D43—48no—
268C4×D43—48no—
269C4×D43C4×D418yes—
270C4×D43#12014yes—
271C4×D43#12314yes—
272Dic86—24no—
273Dic86—41no—
274Dic86—41no—
275Dic86—48no—
276C8×C43—24no—
277C43⋊C8—24no—
278#20972—431nomaximal, Sylow
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—24no—
282C22×C43—24no—
283C22×C43#41914yescomplemented
284C22×C43C22×C22⋊C411yescharacteristic
285C22×C43C2×#12112yes—
286C22×C43C2×#13711yescharacteristic
287C22×C43C2×#13711yescharacteristic
288C22×C43#57512yes—
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—24no—
292C2×D43—24no—
293C2×D43—22no—
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—416no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43#38614yes—
300C4×C43—22no—
301C4×C43—42no—
302C4×C43—42no—
303C4×C43—82no—
304C4×C43C2×C4×D412yes—
305C4×C43C2×#12011yescharacteristic
306C4×C43C2×#12311yescharacteristic
307Dic43—22no—
308Dic43—42no—
309Dic43—42no—
310Dic43—82no—
311Dic43#38614yes—
312C23×M16—431no—
313C22×C22⋊Q8—431no—
314C2×#419—432no—
315#2280—431no—
316#1894—432no—
317#1894—432no—
318#1892—431no—
319#1892—431no—
320#1892—431no—
321#1892D4311yescharacteristic, complemented
322#1736—432no—
323C2×C43—24no—
324C2×C43C2×#38611yescharacteristic
325C2×C43C2×#41911yescharacteristic
326C2×C43#289611yescharacteristic
327C2×C43#305612yes—
328C2×C43#305612yes—
329D43—24no—
330D43—42no—
331C23×Q8—431no—
332C24×C4—431no—
333C22×M16—432no—
334C22×M16—432no—
335C22×M16—868no—
336C22×M16—864no—
337C23×C8—431no—
338C23×C8C2×D4311yescharacteristic
339C2×C22⋊Q8—431no—
340C2×C22⋊Q8—431no—
341C2×C22⋊Q8—438no—
342C2×C22⋊Q8—431no—
343C2×C22⋊Q8—861no—
344C2×C22⋊Q8—861no—
345C2×C22⋊Q8—864no—
346C2×C22⋊Q8C2×D4311yescharacteristic
347C2×#117—432no—
348C22×C4⋊C4—431no—
349C22×C4⋊C4—861no—
350C22×C22⋊C4—861no—
351#419—868no—
352C2×#103—432no—
353C2×#103—432no—
354C2×#103—432no—
355C2×#103C2×D4312yescomplemented
356#381—861no—
357#380—431no—
358#380—432no—
359#380C2×D4311yescharacteristic
360#379—861no—
361C4×C22⋊C4—861no—
362C4×C22⋊C4—861no—
363#340—432no—
364#340—432no—
365#340—432no—
366#340C2×D4312yescomplemented
367C43#2097211yescharacteristic, complemented, Sylow
368C25—431no—
369C22×Q8—434no—
370C22×Q8—431no—
371C22×Q8—861no—
372C22×Q8—862no—
373C22×Q8—864no—
374C22×Q8—864no—
375C22×Q8C22×D4311yescharacteristic
376C23×C4—431no—
377C23×C4—431no—
378C23×C4—434no—
379C23×C4—431no—
380C23×C4—434no—
381C23×C4—431no—
382C23×C4—431no—
383C23×C4—864no—
384C23×C4—864no—
385C23×C4—861no—
386C23×C4—861no—
387C23×C4C22×D4311yescharacteristic
388C2×M16—438no—
389C2×M16—864no—
390C2×M16—864no—
391C2×M16—864no—
392C2×M16—864no—
393C2×M16—8632no—
394C2×M16—864no—
395C22×C8—22no—
396C22×C8—24no—
397C22×C8—432no—
398C22×C8—864no—
399C22×C8—862no—
400C22×C8C22×D4312yes—
401C22⋊Q8—22no—
402C22⋊Q8—434no—
403C22⋊Q8—434no—
404C22⋊Q8—434no—
405C22⋊Q8—868no—
406C22⋊Q8—868no—
407C22⋊Q8—862no—
408C22⋊Q8—862no—
409C22⋊Q8—862no—
410C22⋊Q8C4×D4314yes—
411#117—864no—
412#117—864no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—434no—
416C2×C4⋊C4—432no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—868no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4C22×D4312yes—
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—868no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—862no—
432C2×C22⋊C4—862no—
433C2×C22⋊C4—861no—
434C2×C42—862no—
435#103—24no—
436#103—864no—
437#103—864no—
438#103—864no—
439#95—21no—
440#95—862no—
441#95—861no—
442C24—431no—
443C24—431no—
444C24—434no—
445C24—864no—
446C24—862no—
447C24—862no—
448C24—1722no—
449C24D4×D4311yescharacteristic
450C2×Q8—21no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—432no—
454C2×Q8—864no—
455C2×Q8—8616no—
456C2×Q8—861no—
457C2×Q8—862no—
458C2×Q8—862no—
459C2×Q8—1724no—
460C2×Q8—1724no—
461C2×Q8—1724no—
462C2×Q8C2×C4×D4312yes—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—431no—
469C22×C4—432no—
470C22×C4—432no—
471C22×C4—434no—
472C22×C4—434no—
473C22×C4—434no—
474C22×C4—431no—
475C22×C4—434no—
476C22×C4—434no—
477C22×C4—432no—
478C22×C4—432no—
479C22×C4—868no—
480C22×C4—864no—
481C22×C4—8616no—
482C22×C4—868no—
483C22×C4—864no—
484C22×C4—864no—
485C22×C4—864no—
486C22×C4—864no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—862no—
492C22×C4—1724no—
493C22×C4—1724no—
494C22×C4C2×C4×D4312yes—
495C22×C4D4×D4311yescharacteristic
496C22×C4D4×D4312yes—
497C22×C4C23×D4311yescharacteristic
498M16—8616no—
499M16—8616no—
500C2×C8—28no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—434no—
504C2×C8—868no—
505C2×C8—862no—
506C2×C8—862no—
507C2×C8D4×D4314yes—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—432no—
513C4⋊C4—864no—
514C4⋊C4—864no—
515C4⋊C4—864no—
516C4⋊C4—864no—
517C4⋊C4—861no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4C2×C4×D4312yes—
521C22⋊C4—24no—
522C22⋊C4—42no—
523C22⋊C4—864no—
524C22⋊C4—864no—
525C22⋊C4—864no—
526C22⋊C4—1724no—
527C22⋊C4—1724no—
528C22⋊C4—1722no—
529C42—1724no—
530C23—22no—
531C23—22no—
532C23—432no—
533C23—434no—
534C23—432no—
535C23—868no—
536C23—861no—
537C23—861no—
538C23—862no—
539C23—862no—
540C23—868no—
541C23—861no—
542C23—861no—
543C23—862no—
544C23—1724no—
545C23—1728no—
546C23—1728no—
547C23C22⋊C4×D4312yes—
548C23#1306335412yes—
549C23#1306335712yes—
550C23C2×D4×D4311yescharacteristic
551Q8—24no—
552Q8—41no—
553Q8—41no—
554Q8—864no—
555Q8—1728no—
556Q8—1721no—
557Q8—1721no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—432no—
570C2×C4—434no—
571C2×C4—438no—
572C2×C4—434no—
573C2×C4—434no—
574C2×C4—432no—
575C2×C4—868no—
576C2×C4—868no—
577C2×C4—868no—
578C2×C4—862no—
579C2×C4—864no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—1728no—
585C2×C4—1728no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4C22⋊C4×D4312yes—
592C2×C4C22×C4×D4311yescharacteristic
593C2×C4C2×D4×D4312yes—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4#41×D4312yes—
596C8—24no—
597C8—864no—
598C22—24no—
599C22—24no—
600C22—22no—
601C22—22no—
602C22—434no—
603C22—864no—
604C22—864no—
605C22—862no—
606C22—862no—
607C22—862no—
608C22—862no—
609C22—862no—
610C22—17216no—
611C22—1722no—
612C22—1722no—
613C22#1458290614yescomplemented
614C22C2×C22⋊C4×D4311yescharacteristic
615C22#121×D4312yes—
616C22C2×#1306335411yescharacteristic
617C22C2×#1306335711yescharacteristic
618C22#1458369612yes—
619C4—22no—
620C4—42no—
621C4—42no—
622C4—82no—
623C4—434no—
624C4—862no—
625C4—3442no—
626C4—1722no—
627C4—1722no—
628C4C4×D4×D4312yes—
629C4#120×D4311yescharacteristic
630C4#123×D4311yescharacteristic
631C2—24no—
632C2—864no—
633C2—1722no—
634C2#386×D4311yescharacteristic
635C2C2×#1458290611yescharacteristic
636C2#1914311011yescharacteristic
637C2#1914421812yes—
638C2#1914422212yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1892C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1892D43
hypocenterC43#20972
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
3. C2×#14582906C2semidirect
5. #19135027C2semidirect
6. #19135025C2semidirect
7. #19135019C2semidirect
8. #19135018C2semidirect
9. #19135016C2semidirect
10. #19134313C2semidirect
11. C43×#1892C2semidirect
25. C22⋊Q8×D43C4semidirect
31. C2×#13063250C22semidirect
32. C2×#13063249C22semidirect
33. C2×#13063248C22semidirect
40. #14582662C22semidirect
41. #14582661C22semidirect
42. #14582661C22semidirect
45. C2×#103×C43C22semidirect
47. C43×#340C22semidirect
283. C22×C43#419semidirect
321. #1892D43semidirect
355. C2×#103C2×D43semidirect
366. #340C2×D43semidirect
367. C43#20972semidirect
613. C22#14582906semidirect

Maximal subgroups

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

subgroupindex
C23×#106218722
C2×C22⋊Q8×D432
C2×#145829062
#191369772
#191350272
#191350252
#191350192
#191350182
#191350162
#191343132
C43×#18922
#2097243