Finite Group Databasebeta

← #25129621

Subgroups — #25129621

Order 11008.

1484 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583543C211yesmaximal, characteristic
2C2×#14583234C211yesmaximal, characteristic, complemented
3#19138906C211yesmaximal, characteristic, complemented
4#19135834C212yesmaximal, complemented
5#19135775C212yesmaximal, complemented
6#19135018C211yesmaximal, characteristic, complemented
7#19134887C211yesmaximal, characteristic, complemented
8#19134840C212yesmaximal, complemented
9#19134532C212yesmaximal, complemented
10#19134526C211yesmaximal, characteristic, complemented
11C22×#102×C43C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13#14583543—24no—
14#14583543—24no—
15C2×#13063312C2211yescharacteristic
16C2×#13063306—21no—
17C2×#13063304C2211yescharacteristic
18C2×#13063297—21no—
19C2×#13063296C2211yescharacteristic
20C2×#13063294—21no—
21C2×D4×Dic43C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23C22×C22⋊Dic43—21no—
24#14583234—24no—
25C2×#13063258C2212yescomplemented
26C2×#13063250C2212yescomplemented
27C2×#13063248C2212yescomplemented
28C2×#13063246C2212yes—
29C2×#13063246C2212yes—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×(C2×D43)⋊C8C2212yescomplemented
32#14582837—21no—
33#14582834—21no—
34#14582795C2212yescomplemented
35#14582778—21no—
36#14582772—21no—
37#14582759C2211yescharacteristic
38#14582756C2212yescomplemented
39#14582662C2212yescomplemented
40#14582653C2212yescomplemented
41C23×D4×C43C2211yescharacteristic
42C23×C8×C43C2211yescharacteristic
43C22×C4⋊C4×C43C2211yescharacteristic
44C2×#102×C43—24no—
45C2×#102×C43C2212yes—
46C2×#102×C43C2212yes—
47C2×#10621900—22no—
48C2×#10621900—24no—
49C2×#10621900—22no—
50C2×#10621900—42no—
51C22×Dic86C2311yescharacteristic
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C22×C22⋊D43D411yescharacteristic
55C23×Dic43—21no—
56C23×Dic43—21no—
57C22×C4×D43C2311yescharacteristic
58C22×C43⋊C8C2312yes—
59#13063312—22no—
60#13063312—22no—
61#13063306—28no—
62#13063304—22no—
63#13063304D414yes—
64#13063297—28no—
65#13063296—22no—
66#13063296—22no—
67#13063294—28no—
68D4×Dic43—22no—
69D4×Dic43—22no—
70C4×C22⋊D43—22no—
71C4×C22⋊D43—22no—
72C2×C4⋊Dic43C2312yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4D411yescharacteristic
77C2×C22⋊Dic43—28no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43D411yescharacteristic
85C2×(C2×D43)⋊C4—22no—
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063258—24no—
89#13063250—42no—
90#13063248—24no—
91#13063246—24no—
92#13063246—42no—
93C22⋊(C43⋊C8)—22no—
94(C2×D43)⋊C8—42no—
95C43⋊#95—21no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C25×C43—21no—
99C22×D4×C43—24no—
100C22×D4×C43—21no—
101C22×D4×C43—22no—
102C22×D4×C43—42no—
103C22×D4×C43D414yes—
104C22×D4×C43C2311yescharacteristic
105C22×D4×C43C2311yescharacteristic
106C23×C4×C43—21no—
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43—22no—
109C22×C8×C43—42no—
110C22×C8×C43C2312yes—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43C2312yes—
115#102×C43—24no—
116#102×C43—24no—
117C24×C43—21no—
118C24×C43—21no—
119C24×C43—24no—
120C24×C43—44no—
121C24×C43—42no—
122C24×C43—42no—
123C24×C43—82no—
124C24×C43C2×D411yescharacteristic
125C23×D43C2×D411yescharacteristic
126C2×D4×C43—24no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—22no—
130C2×D4×C43—28no—
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—44no—
134C2×D4×C43—44no—
135C2×D4×C43—48no—
136C2×D4×C43C2×D412yes—
137C2×D4×C43C2×D412yes—
138C2×D4×C43#4114yes—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—42no—
143C22×C4×C43—82no—
144C22×C4×C43C2×D412yes—
145C22×C4×C43C2×D412yes—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—24no—
149C2×C22⋊D43—24no—
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43—44no—
154C2×C22⋊D43—82no—
155C22×Dic43—24no—
156C22×Dic43—24no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—22no—
160C22×Dic43—44no—
161C22×Dic43—82no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165#10621900—48no—
166#10621900—44no—
167#10621900—44no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×Dic86—22no—
173C2×Dic86—22no—
174C2×Dic86—21no—
175C2×Dic86C2×D412yes—
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C2×C8×C43—22no—
179C2×C8×C43—44no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—42no—
183C22⋊Dic43—24no—
184C22⋊Dic43—24no—
185C22⋊Dic43—24no—
186C22⋊Dic43—24no—
187C22⋊Dic43—22no—
188C22⋊Dic43—24no—
189C22⋊Dic43—42no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—82no—
192C4⋊Dic43—21no—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43C2×D412yes—
196Dic43⋊C4—24no—
197Dic43⋊C4—22no—
198Dic43⋊C4—82no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—24no—
208C23×C43—22no—
209C23×C43—48no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—42no—
217C23×C43—48no—
218C23×C43—84no—
219C23×C43—88no—
220C23×C43—88no—
221C23×C43#12012yes—
222C23×C43#13512yes—
223C23×C43#13712yes—
224C23×C43C22×D411yescharacteristic
225C22×D43—21no—
226C22×D43—22no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—22no—
230D4×C43—22no—
231D4×C43—22no—
232D4×C43—22no—
233D4×C43—24no—
234D4×C43—48no—
235D4×C43—42no—
236D4×C43#12314yes—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—24no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—84no—
245C2×C4×C43#12012yes—
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4112yes—
249C2×C4×C43H(5,𝔽2)12yes—
250C22⋊D43—48no—
251C22⋊D43—44no—
252C22⋊D43—84no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—22no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—22no—
262C2×Dic43—48no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—84no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—42no—
272Dic86—24no—
273Dic86—41no—
274Dic86—41no—
275C8×C43—42no—
276C43⋊C8—42no—
277#24039—431nomaximal, Sylow
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—24no—
281C22×C43—24no—
282C22×C43—24no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—44no—
286C22×C43—44no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—816no—
291C22×C43—82no—
292C22×C43—82no—
293C22×C43#45214yes—
294C22×C43C2×#12011yescharacteristic
295C22×C43#54612yes—
296C22×C43C2×#13511yescharacteristic
297C22×C43C2×#13711yescharacteristic
298C22×C43#57612yes—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—42no—
303C2×D43—42no—
304C4×C43—22no—
305C4×C43—82no—
306C4×C43C2×#12311yescharacteristic
307C4×C43#53411yescharacteristic
308C4×C43#54612yes—
309Dic43—42no—
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313Dic43—42no—
314Dic43—82no—
315C2×#546—431no—
316C2×#484—431no—
317C22×#102D4311yescharacteristic, complemented
318#2487—431no—
319#2042—432no—
320#2033—432no—
321#1892—431no—
322#1869—431no—
323#1862—432no—
324#1788—432no—
325#1786—431no—
326C2×C43—24no—
327C2×C43—44no—
328C2×C43—82no—
329C2×C43#240511yescharacteristic
330C2×C43C2×#45211yescharacteristic
331C2×C43#300811yescharacteristic
332C2×C43#329712yes—
333C2×C43#331412yes—
334D43—81no—
335C22×#41—431no—
336C23×D4C2×D4311yescharacteristic
337C23×C8C2×D4311yescharacteristic
338#546—864no—
339#546—864no—
340C2×#124—431no—
341C2×#123—861no—
342C2×C22⋊Q8—431no—
343C2×#121—431no—
344C2×#121—861no—
345C2×#120—861no—
346C2×C4×D4—431no—
347C2×C4×D4—431no—
348C22×C4⋊C4C2×D4311yescharacteristic
349C22×C22⋊C4—861no—
350#484—864no—
351C2×#107—432no—
352C2×#103—432no—
353C2×#103—432no—
354C2×#102—24no—
355C2×#102—432no—
356C2×#102—432no—
357C2×#102C2×D4312yes—
358C2×#102C2×D4312yes—
359C2×C22⋊C8—431no—
360C2×C22⋊C8—432no—
361#400—861no—
362#399—861no—
363#389—432no—
364#386—861no—
365#385—861no—
366#380—431no—
367#380—432no—
368#340—432no—
369#336—432no—
370C43#2403911yescharacteristic, complemented, Sylow
371C25—21no—
372C2×#41—862no—
373C2×#41—862no—
374C2×#41—864no—
375C2×#41—1722no—
376C22×Q8—431no—
377C22×D4—24no—
378C22×D4—21no—
379C22×D4—22no—
380C22×D4—42no—
381C22×D4—431no—
382C22×D4—861no—
383C22×D4—861no—
384C22×D4C22⋊D4314yes—
385C22×D4C22×D4311yescharacteristic
386C22×D4C22×D4311yescharacteristic
387C23×C4—21no—
388C23×C4—431no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4C22×D4311yescharacteristic
392C22×C8—22no—
393C22×C8—42no—
394C22×C8—432no—
395C22×C8C22×D4312yes—
396#124—862no—
397#124—862no—
398#123—868no—
399C22⋊Q8—434no—
400C22⋊Q8—862no—
401#121—862no—
402#121—868no—
403#121—862no—
404#120—868no—
405C4×D4—862no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—862no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—432no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4C22×D4312yes—
418C2×C22⋊C4—431no—
419C2×C22⋊C4—431no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—868no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—862no—
427C2×C22⋊C4—861no—
428C2×C42—431no—
429#107—864no—
430#103—864no—
431#103—1722no—
432#102—24no—
433#102—24no—
434#102—864no—
435#102—1722no—
436C22⋊C8—862no—
437C22⋊C8—1722no—
438#95—862no—
439#95—862no—
440#95—861no—
441C24—21no—
442C24—21no—
443C24—24no—
444C24—44no—
445C24—42no—
446C24—42no—
447C24—82no—
448C24—431no—
449C24D4×D4311yescharacteristic
450#41—1728no—
451#41—1724no—
452#41—1724no—
453C2×Q8—432no—
454C2×Q8—861no—
455C2×Q8—862no—
456C2×Q8—862no—
457C2×D4—28no—
458C2×D4—24no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—44no—
465C2×D4—48no—
466C2×D4—44no—
467C2×D4—864no—
468C2×D4—864no—
469C2×D4—862no—
470C2×D4—862no—
471C2×D4—862no—
472C2×D4—3442no—
473C2×D4—1724no—
474C2×D4#1062189814yes—
475C2×D4C2×C22⋊D4312yes—
476C2×D4C2×C22⋊D4312yes—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—42no—
481C22×C4—82no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—864no—
486C22×C4—864no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—862no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—3442no—
495C22×C4—1724no—
496C22×C4D4×D4311yescharacteristic
497C22×C4D4×D4312yes—
498C22×C4C2×C22⋊D4312yes—
499C22×C4C23×D4311yescharacteristic
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—44no—
504C2×C8—862no—
505C2×C8—862no—
506C2×C8—862no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—42no—
510C4⋊C4—432no—
511C4⋊C4—862no—
512C4⋊C4—864no—
513C4⋊C4—861no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—3442no—
517C22⋊C4—864no—
518C22⋊C4—864no—
519C22⋊C4—864no—
520C22⋊C4—864no—
521C22⋊C4—862no—
522C22⋊C4—864no—
523C22⋊C4—862no—
524C22⋊C4—3442no—
525C22⋊C4—1722no—
526C42—861no—
527C42—861no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—24no—
532C23—22no—
533C23—48no—
534C23—41no—
535C23—41no—
536C23—42no—
537C23—48no—
538C23—41no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—84no—
543C23—88no—
544C23—88no—
545C23—861no—
546C23—861no—
547C23—861no—
548C23—862no—
549C23—862no—
550C23#1306329312yes—
551C23#1306334612yes—
552C23#1306335412yes—
553C23C2×D4×D4311yescharacteristic
554Q8—864no—
555Q8—1721no—
556Q8—1721no—
557D4—22no—
558D4—22no—
559D4—22no—
560D4—24no—
561D4—48no—
562D4—42no—
563D4—3444no—
564D4—1728no—
565D4—1724no—
566D4#1306330814yes—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—84no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—862no—
578C2×C4—861no—
579C2×C4—862no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—3444no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1728no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1722no—
594C2×C4#1306329312yes—
595C2×C4C2×D4×D4311yescharacteristic
596C2×C4C22×C22⋊D4311yescharacteristic
597C2×C4C2×#1062189812yes—
598C2×C4#1306337012yes—
599C8—42no—
600C8—1722no—
601C22—22no—
602C22—24no—
603C22—22no—
604C22—24no—
605C22—24no—
606C22—42no—
607C22—44no—
608C22—42no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—816no—
614C22—82no—
615C22—82no—
616C22—1721no—
617C22—1721no—
618C22—1722no—
619C22—1721no—
620C22—1722no—
621C22#1458305814yes—
622C22C2×#1306329311yescharacteristic
623C22#1458353912yes—
624C22C2×#1306334611yescharacteristic
625C22C2×#1306335411yescharacteristic
626C22#1458370012yes—
627C4—22no—
628C4—82no—
629C4—3442no—
630C4—1721no—
631C4—1721no—
632C4—1722no—
633C4—1721no—
634C4—1722no—
635C4C2×#1306330811yescharacteristic
636C4#1458345811yescharacteristic
637C4#1458353912yes—
638C2—24no—
639C2—44no—
640C2—82no—
641C2—3441no—
642C2#1913792211yescharacteristic
643C2C2×#1458305811yescharacteristic
644C2#1914385911yescharacteristic
645C2#1914644112yes—
646C2#1914667212yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583543C2
hypercenterC22×#102D43
hypocenterC43#24039
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14583234C2semidirect
3. #19138906C2semidirect
4. #19135834C2semidirect
5. #19135775C2semidirect
6. #19135018C2semidirect
7. #19134887C2semidirect
8. #19134840C2semidirect
9. #19134532C2semidirect
10. #19134526C2semidirect
11. C22×#102×C43C2semidirect
25. C2×#13063258C22semidirect
26. C2×#13063250C22semidirect
27. C2×#13063248C22semidirect
31. C2×(C2×D43)⋊C8C22semidirect
34. #14582795C22semidirect
38. #14582756C22semidirect
39. #14582662C22semidirect
40. #14582653C22semidirect
317. C22×#102D43semidirect
370. C43#24039semidirect

Maximal subgroups

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

subgroupindex
C2×#145835432
C2×#145832342
#191389062
#191358342
#191357752
#191350182
#191348872
#191348402
#191345322
#191345262
C22×#102×C432
#2403943