Finite Group Databasebeta

← #25124250

Subgroups — #25124250

Order 11008.

1442 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic
2C2×#14582916C211yesmaximal, characteristic, complemented
3C2×#14582915C211yesmaximal, characteristic, complemented
4#19143112C211yesmaximal, characteristic, complemented
5#19137215C211yesmaximal, characteristic, complemented
6#19135822C214yesmaximal, complemented
7#19135817C214yesmaximal, complemented
8C2×#14582667C211yesmaximal, characteristic, complemented
9C43×#2896C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12#14583477—22no—
13#14583477—22no—
14#14583477—22no—
15#14583477C2214yes—
16C2×#13063304—21no—
17C2×#13063301—21no—
18C2×#13063299—21no—
19C2×#13063297—22no—
20C2×#13063296—21no—
21C2×#13063284C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23#14582916—24no—
24#14582915—24no—
25C2×#13063252C2214yescomplemented
26C2×#13063251C2214yescomplemented
27#14582907—21no—
28#14582903—21no—
29#14582898C2212yescomplemented
30#14582898C2212yescomplemented
31#14582893—22no—
32#14582797—22no—
33#14582771—22no—
34#14582768C2212yescomplemented
35#14582764C2212yescomplemented
36#14582667C2214yescomplemented
37C22×#41×C43C2211yescharacteristic
38C22×M16×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C43×#419—21no—
41C43×#418—21no—
42C43×#417C2212yescomplemented
43C43×#417C2212yescomplemented
44C43×#416—22no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898D412yes—
52C2×#10621898C2312yes—
53C22×Dic86D411yescharacteristic
54C22×D172D411yescharacteristic
55C22×C22⋊D43—21no—
56C22×C22⋊D43—22no—
57C23×Dic43D412yes—
58C22×C4×D43—21no—
59C2×#10621877—21no—
60C2×#10621877—22no—
61C2×#10621877—22no—
62C2×#10621877C2312yes—
63C22×C43⋊C8—21no—
64#13063304—24no—
65#13063304—24no—
66#13063301—24no—
67#13063301—24no—
68#13063299—24no—
69#13063299—24no—
70#13063297—28no—
71#13063297—28no—
72#13063296—24no—
73#13063296—24no—
74#13063284—22no—
75#13063284D414yescomplemented
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43D412yes—
82C2×C4⋊Dic43C2312yes—
83C2×Dic43⋊C4—22no—
84C2×Dic43⋊C4—24no—
85C2×C22⋊Dic43—22no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—22no—
88C2×C4×Dic43C2312yes—
89#13063252—28no—
90#13063251—28no—
91#13063248—22no—
92#13063248—22no—
93#13063245—22no—
94#13063245—22no—
95C43⋊#95—24no—
96C2×#41×C43—21no—
97C2×#41×C43—21no—
98C2×#41×C43—22no—
99C2×#41×C43—22no—
100C2×#41×C43—22no—
101C2×#41×C43—22no—
102C2×#41×C43D412yes—
103C2×#41×C43C2312yes—
104C22×Q8×C43D411yescharacteristic
105C22×D4×C43—21no—
106C22×D4×C43D411yescharacteristic
107C23×C4×C43—21no—
108C23×C4×C43C2311yescharacteristic
109C2×M16×C43—21no—
110C2×M16×C43—22no—
111C2×M16×C43—22no—
112C2×M16×C43C2312yes—
113C22×C8×C43—21no—
114#117×C43—21no—
115#117×C43—21no—
116#117×C43—21no—
117#117×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C42×C43—21no—
122#103×C43—22no—
123#103×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C23×D43—21no—
129#41×C43—24no—
130#41×C43—24no—
131#41×C43—22no—
132#41×C43—22no—
133#41×C43—22no—
134#41×C43—22no—
135#41×C43—42no—
136#41×C43—42no—
137#41×C43—42no—
138#41×C43—42no—
139C2×Q8×C43—21no—
140C2×Q8×C43—22no—
141C2×Q8×C43—22no—
142C2×Q8×C43C2×D412yes—
143C2×D4×C43—21no—
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43—22no—
147C2×D4×C43—22no—
148C2×D4×C43—42no—
149C2×D4×C43—42no—
150C2×D4×C43C2×D412yes—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43#4112yes—
165C22×C4×C43#4112yes—
166C22×C4×C43#4112yes—
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—28no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—42no—
172C2×C22⋊D43—42no—
173C2×C22⋊D43—84no—
174C22×Dic43—22no—
175C22×Dic43—21no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—82no—
179C22×Dic43C2×D414yes—
180#10621898—24no—
181#10621898—24no—
182#10621898—22no—
183#10621898—22no—
184#10621898—22no—
185#10621898—22no—
186#10621898—42no—
187#10621898—42no—
188#10621898—42no—
189#10621898—42no—
190C2×D172—21no—
191C2×D172—22no—
192C2×D172—22no—
193C2×D172C2×D412yes—
194C2×C4×D43—22no—
195C2×C4×D43—22no—
196C2×C4×D43—42no—
197C2×C4×D43—42no—
198C2×Dic86—22no—
199C2×Dic86—22no—
200C2×Dic86—21no—
201C2×Dic86C2×D412yes—
202M16×C43—22no—
203M16×C43—22no—
204M16×C43—42no—
205C2×C8×C43—22no—
206C2×C8×C43—42no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C22⋊C4×C43—41no—
212C22⋊C4×C43—41no—
213C42×C43—41no—
214C42×C43—41no—
215C22⋊Dic43—28no—
216C22⋊Dic43—24no—
217(C2×D43)⋊C4—28no—
218C4⋊Dic43—22no—
219C4⋊Dic43—22no—
220C4⋊Dic43—24no—
221C4⋊Dic43—22no—
222C4⋊Dic43—22no—
223Dic43⋊C4—28no—
224Dic43⋊C4—84no—
225C4×Dic43—22no—
226C4×Dic43C2×D414yescomplemented
227#10621877—22no—
228#10621877—22no—
229#10621877—42no—
230C2×C43⋊C8—22no—
231C2×C43⋊C8—42no—
232C23×C43—22no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—42no—
236C23×C43—42no—
237C23×C43—42no—
238C23×C43#12011yescharacteristic
239C23×C43#12011yescharacteristic
240C23×C43#12112yes—
241C23×C43#12412yes—
242C23×C43C22×D411yescharacteristic
243C22×D43—22no—
244C22×D43—42no—
245C22×D43—42no—
246C22×D43—42no—
247Q8×C43—22no—
248Q8×C43—22no—
249Q8×C43—42no—
250D4×C43—22no—
251D4×C43—22no—
252D4×C43—42no—
253D4×C43—42no—
254D4×C43—44no—
255D4×C43—42no—
256C2×C4×C43—22no—
257C2×C4×C43—42no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—44no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43#12011yescharacteristic
266C2×C4×C43#12011yescharacteristic
267C2×C4×C43#12112yes—
268C2×C4×C43#12112yes—
269C2×C4×C43#12112yes—
270C2×C4×C43#12112yes—
271C2×C4×C43#12112yes—
272C2×C4×C43#12312yes—
273C2×C4×C43#12312yes—
274C2×C4×C43#12312yes—
275C2×C4×C43#12312yes—
276C2×C4×C43#12412yes—
277C2×C4×C43C22×D411yescharacteristic
278C2×C4×C43C22×D411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C22⋊D43—42no—
284C22⋊D43—42no—
285C22⋊D43—44no—
286C22⋊D43—88no—
287C2×Dic43—22no—
288C2×Dic43—24no—
289C2×Dic43—24no—
290C2×Dic43—42no—
291C2×Dic43—42no—
292C2×Dic43—44no—
293C2×Dic43—42no—
294C2×Dic43—44no—
295C2×Dic43—82no—
296D172—22no—
297D172—22no—
298D172—42no—
299C4×D43—42no—
300C4×D43—42no—
301C4×D43—44no—
302Dic86—22no—
303Dic86—22no—
304Dic86—42no—
305C8×C43—42no—
306C43⋊C8—42no—
307#23499—431nomaximal, Sylow
308C22×C43—21no—
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—42no—
315C22×C43—42no—
316C22×C43—42no—
317C22×C43—42no—
318C22×C43—42no—
319C22×C43—84no—
320C22×C43#39412yes—
321C22×C43#39412yes—
322C22×C43C2×#12011yescharacteristic
323C22×C43C2×#12111yescharacteristic
324C22×C43C2×#12411yescharacteristic
325C2×D43—42no—
326C2×D43—42no—
327C2×D43—42no—
328C2×D43—84no—
329C4×C43—42no—
330C4×C43—81no—
331C4×C43—81no—
332C4×C43#39412yes—
333C4×C43#39412yes—
334C4×C43C2×#12111yescharacteristic
335C4×C43C2×#12111yescharacteristic
336C4×C43C2×#12311yescharacteristic
337C4×C43C2×#12311yescharacteristic
338Dic43—44no—
339Dic43—42no—
340Dic43—44no—
341C2×#537—431no—
342C2×#421—431no—
343C2×#421—431no—
344#2896—431no—
345#2896D4311yescharacteristic, complemented
346#2317—431no—
347#2040—434no—
348#2039—434no—
349C2×#343—431no—
350C2×C43—21no—
351C2×C43—22no—
352C2×C43—21no—
353C2×C43—22no—
354C2×C43—82no—
355C2×C43C2×#39411yescharacteristic
356C2×C43#301911yescharacteristic
357C2×C43#302011yescharacteristic
358D43—82no—
359C22×#41—431no—
360C22×#41C2×D4311yescharacteristic
361C22×M16—431no—
362C22×M16C2×D4311yescharacteristic
363#537—434no—
364#537—862no—
365#537—862no—
366#537—862no—
367C2×C22⋊Q8—861no—
368C2×C22⋊Q8—861no—
369C2×#121—861no—
370C2×#121—862no—
371C2×#121—861no—
372C2×#117—431no—
373C2×#117C2×D4311yescharacteristic
374C22×C4⋊C4—431no—
375#421—864no—
376#421—864no—
377C2×#104—434no—
378C2×#104—434no—
379#419—21no—
380#419—861no—
381#418—21no—
382#418—861no—
383#417—432no—
384#417—432no—
385#417C2×D4312yescomplemented
386#417C2×D4312yescomplemented
387#416—22no—
388#416—862no—
389#389—862no—
390#385—862no—
391#384—432no—
392#382—432no—
393#343—434no—
394C43#2349911yescharacteristic, complemented, Sylow
395C2×#41—21no—
396C2×#41—21no—
397C2×#41—22no—
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—432no—
402C2×#41—432no—
403C2×#41—861no—
404C2×#41—861no—
405C2×#41—862no—
406C2×#41—862no—
407C2×#41—862no—
408C2×#41—862no—
409C2×#41C22⋊D4312yes—
410C2×#41C22×D4312yes—
411C22×Q8—431no—
412C22×Q8C22⋊D4311yescharacteristic
413C22×D4—21no—
414C22×D4—431no—
415C22×D4—862no—
416C22×D4—861no—
417C22×D4C22⋊D4311yescharacteristic
418C23×C4—21no—
419C23×C4—432no—
420C23×C4—861no—
421C23×C4C22×D4311yescharacteristic
422C2×M16—21no—
423C2×M16—22no—
424C2×M16—22no—
425C2×M16—432no—
426C2×M16—861no—
427C2×M16—862no—
428C2×M16—862no—
429C2×M16C22×D4312yes—
430C22×C8—21no—
431C22×C8—861no—
432C22⋊Q8—864no—
433C22⋊Q8—864no—
434C22⋊Q8—864no—
435C22⋊Q8—864no—
436#121—864no—
437#121—864no—
438#121—868no—
439#121—864no—
440#121—868no—
441#121—864no—
442#117—21no—
443#117—21no—
444#117—21no—
445#117—21no—
446#117—434no—
447#117—862no—
448C2×C4⋊C4—432no—
449C2×C4⋊C4—432no—
450C2×C4⋊C4—862no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—864no—
457C2×C4⋊C4C22×D4311yescharacteristic
458C2×C4⋊C4C22×D4311yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—862no—
461C2×C22⋊C4—862no—
462C2×C22⋊C4—861no—
463C2×C42—21no—
464C2×C42—432no—
465#104—868no—
466#104—868no—
467#103—22no—
468#103—22no—
469#103—862no—
470#103—862no—
471#102—22no—
472#102—22no—
473#102—862no—
474#102—862no—
475#95—864no—
476C24—21no—
477C24—861no—
478C24D4×D4311yescharacteristic
479#41—24no—
480#41—24no—
481#41—22no—
482#41—22no—
483#41—22no—
484#41—22no—
485#41—42no—
486#41—42no—
487#41—42no—
488#41—42no—
489#41—864no—
490#41—864no—
491#41—862no—
492#41—862no—
493#41—862no—
494#41—862no—
495#41—1722no—
496#41—1722no—
497#41—1722no—
498#41—1722no—
499C2×Q8—21no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—432no—
503C2×Q8—861no—
504C2×Q8—862no—
505C2×Q8—862no—
506C2×Q8C2×C22⋊D4312yes—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—21no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—432no—
515C2×D4—868no—
516C2×D4—862no—
517C2×D4—862no—
518C2×D4—861no—
519C2×D4—862no—
520C2×D4—862no—
521C2×D4—3444no—
522C2×D4—1722no—
523C2×D4—1722no—
524C2×D4C2×C22⋊D4312yes—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—434no—
533C22×C4—862no—
534C22×C4—862no—
535C22×C4—861no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—3442no—
540C22×C4—1722no—
541C22×C4—1722no—
542C22×C4#1062189812yes—
543C22×C4#1062189812yes—
544C22×C4D4×D4311yescharacteristic
545C22×C4D4×D4311yescharacteristic
546C22×C4D4×D4311yescharacteristic
547C22×C4D4×D4312yes—
548C22×C4#1062190012yes—
549C22×C4C2×C22⋊D4311yescharacteristic
550C22×C4C2×C22⋊D4311yescharacteristic
551C22×C4C23×D4311yescharacteristic
552M16—22no—
553M16—22no—
554M16—42no—
555M16—862no—
556M16—862no—
557M16—1722no—
558C2×C8—22no—
559C2×C8—42no—
560C2×C8—862no—
561C2×C8—1722no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—868no—
567C4⋊C4—862no—
568C4⋊C4—862no—
569C4⋊C4—864no—
570C4⋊C4—862no—
571C4⋊C4—862no—
572C4⋊C4—3444no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—868no—
576C22⋊C4—868no—
577C22⋊C4—864no—
578C42—41no—
579C42—41no—
580C42—434no—
581C42—862no—
582C23—22no—
583C23—41no—
584C23—41no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—862no—
589C23—1722no—
590C23—1722no—
591C23—1722no—
592C23#1306329311yescharacteristic
593C23#1306329311yescharacteristic
594C23#1306329812yes—
595C23#1306331112yes—
596C23C2×D4×D4311yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—42no—
600Q8—862no—
601Q8—862no—
602Q8—1722no—
603D4—22no—
604D4—22no—
605D4—44no—
606D4—42no—
607D4—42no—
608D4—42no—
609D4—862no—
610D4—862no—
611D4—3448no—
612D4—1724no—
613D4—1722no—
614D4—1722no—
615D4—1722no—
616C2×C4—22no—
617C2×C4—42no—
618C2×C4—44no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—864no—
626C2×C4—862no—
627C2×C4—864no—
628C2×C4—3442no—
629C2×C4—1722no—
630C2×C4—1724no—
631C2×C4—1722no—
632C2×C4—1722no—
633C2×C4—1724no—
634C2×C4—1722no—
635C2×C4—1722no—
636C2×C4—1724no—
637C2×C4#1306329311yescharacteristic
638C2×C4#1306329311yescharacteristic
639C2×C4#1306329712yes—
640C2×C4#1306329712yes—
641C2×C4#1306329812yes—
642C2×C4#1306329812yes—
643C2×C4#1306329812yes—
644C2×C4#1306330712yes—
645C2×C4#1306330712yes—
646C2×C4#1306330812yes—
647C2×C4#1306330812yes—
648C2×C4#1306331112yes—
649C2×C4C2×D4×D4311yescharacteristic
650C2×C4C2×D4×D4311yescharacteristic
651C2×C4C22×C22⋊D4311yescharacteristic
652C2×C4C2×#1062190011yescharacteristic
653C2×C4C2×#1062189811yescharacteristic
654C2×C4C2×#1062189811yescharacteristic
655C8—42no—
656C8—1722no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—84no—
669C22—3444no—
670C22—1722no—
671C22—1722no—
672C22—1722no—
673C22#1458281412yes—
674C22#1458281412yes—
675C22C2×#1306329311yescharacteristic
676C22C2×#1306329811yescharacteristic
677C22C2×#1306331111yescharacteristic
678C4—42no—
679C4—81no—
680C4—81no—
681C4—1724no—
682C4—1722no—
683C4—1724no—
684C4#1458281412yes—
685C4#1458281412yes—
686C4C2×#1306329711yescharacteristic
687C4C2×#1306329811yescharacteristic
688C4C2×#1306330711yescharacteristic
689C4C2×#1306330811yescharacteristic
690C2—21no—
691C2—22no—
692C2—22no—
693C2—21no—
694C2—82no—
695C2—3442no—
696C2C2×#1458281411yescharacteristic
697C2#1914395011yescharacteristic
698C2#1914395711yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2896C2
socleC22×C43C2×#120
prime radicalC2×#14583477C2
hypercenter#2896D43
hypocenterC43#23499
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. C2×#14582916C2semidirect
3. C2×#14582915C2semidirect
4. #19143112C2semidirect
5. #19137215C2semidirect
6. #19135822C2semidirect
7. #19135817C2semidirect
8. C2×#14582667C2semidirect
9. C43×#2896C2semidirect
25. C2×#13063252C22semidirect
26. C2×#13063251C22semidirect
29. #14582898C22semidirect
30. #14582898C22semidirect
34. #14582768C22semidirect
35. #14582764C22semidirect
36. #14582667C22semidirect
42. C43×#417C22semidirect
43. C43×#417C22semidirect
75. #13063284D4semidirect
226. C4×Dic43C2×D4semidirect
345. #2896D43semidirect
385. #417C2×D43semidirect
386. #417C2×D43semidirect
394. C43#23499semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
C2×#145829162
C2×#145829152
#191431122
#191372152
#191358222
#191358172
C2×#145826672
C43×#28962
#2349943