Finite Group Databasebeta

← #25129861

Subgroups — #25129861

Order 11008.

1424 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×#14583444C211yesmaximal, characteristic
2C2×#14583212C211yesmaximal, characteristic, complemented
3C2×#14582795C211yesmaximal, characteristic, complemented
4#19135921C212yesmaximal, complemented
5#19135827C212yesmaximal, complemented
6#19134913C211yesmaximal, characteristic, complemented
7#19134910C211yesmaximal, characteristic, complemented
8#19134840C212yesmaximal, complemented
9#19134839C212yesmaximal, complemented
10#19134661C211yesmaximal, characteristic, complemented
11C2×C43×#480C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13#14583444—24no—
14#14583444—24no—
15C2×#13063324C2211yescharacteristic
16C2×#13063321C2211yescharacteristic
17C2×#13063311—21no—
18C2×#13063299C2211yescharacteristic
19C2×#13063297—21no—
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×(C22⋊D43)⋊C4—21no—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×Dic43⋊C4—21no—
25C22×C4×Dic43C2211yescharacteristic
26#14583212—24no—
27C2×#13063258C2212yes—
28C2×#13063247C2212yes—
29C2×#13063246C2212yes—
30C2×#13063245C2212yes—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32#14582795—21no—
33#14582795—21no—
34#14582795C2212yes—
35#14582795C2212yes—
36C2×C43⋊#95—21no—
37#14582662C2212yes—
38#14582661C2212yes—
39#14582653C2212yes—
40#14582653C2212yes—
41C2×#121×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C43×#480—24no—
44C2×#107×C43C2212yes—
45C2×#102×C43C2212yes—
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×#10621900—28no—
48C2×#10621900—44no—
49C2×#10621900—44no—
50C22×Dic86—21no—
51C22×D172C2311yescharacteristic
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C22×C22⋊D43—21no—
55C23×Dic43—21no—
56C23×Dic43—21no—
57C23×Dic43D411yescharacteristic
58C23×Dic43D411yescharacteristic
59C22×C4×D43—21no—
60C22×C43⋊C8C2312yes—
61#13063324—22no—
62#13063324—22no—
63#13063321—22no—
64#13063321—22no—
65#13063311—28no—
66#13063299—22no—
67#13063299D414yes—
68#13063297—28no—
69D4×Dic43—22no—
70D4×Dic43—22no—
71#13063287—22no—
72#13063287—22no—
73(C22⋊D43)⋊C4—28no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—24no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2312yes—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—44no—
82C2×C22⋊Dic43—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×C4×Dic43—22no—
86C2×C4×Dic43—22no—
87C2×C4×Dic43D411yescharacteristic
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063258—24no—
92#13063247—24no—
93#13063246—24no—
94#13063245—24no—
95C22⋊(C43⋊C8)—22no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C22×D4×C43—21no—
99C22×D4×C43C2311yescharacteristic
100C23×C4×C43—21no—
101C23×C4×C43C2311yescharacteristic
102C22×C8×C43C2312yes—
103#121×C43—22no—
104#121×C43D414yes—
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43—22no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43C2312yes—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—21no—
111#107×C43—24no—
112#102×C43—24no—
113C22⋊C8×C43—22no—
114C24×C43—21no—
115C24×C43C2×D411yescharacteristic
116C23×D43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—24no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—42no—
122C2×D4×C43—42no—
123C2×D4×C43C2×D412yes—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43C2×D412yes—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C2×C22⋊D43—24no—
136C2×C22⋊D43—24no—
137C2×C22⋊D43—24no—
138C2×C22⋊D43—42no—
139C2×C22⋊D43—42no—
140C2×C22⋊D43—42no—
141C2×C22⋊D43—42no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—42no—
144C22×Dic43—24no—
145C22×Dic43—24no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—21no—
152C22×Dic43—41no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43D814yes—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162#10621900—432no—
163C2×D172—21no—
164C2×D172—22no—
165C2×D172—22no—
166C2×D172C2×D412yes—
167C2×C4×D43—24no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×Dic86—24no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C2×C8×C43—22no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—42no—
180C4⋊C4×C43C2×D412yes—
181C22⋊C4×C43—24no—
182C22⋊Dic43—24no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—24no—
185C4⋊Dic43—24no—
186C4⋊Dic43—21no—
187C4⋊Dic43—22no—
188C4⋊Dic43C2×D412yes—
189C4⋊Dic43#4114yescomplemented
190Dic43⋊C4—24no—
191Dic43⋊C4—44no—
192Dic43⋊C4—44no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C2×C43⋊C8—22no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—22no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43#12012yes—
214C23×C43C2×D812yes—
215C23×C43AGL(1,ℤ/8)12yes—
216C23×C43C22×D411yescharacteristic
217C22×D43—22no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224D4×C43—24no—
225D4×C43—48no—
226D4×C43—42no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—22no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—84no—
238C2×C4×C43#12012yes—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4112yes—
242C2×C4×C432−1+412yes—
243C22⋊D43—48no—
244C22⋊D43—48no—
245C22⋊D43—48no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—28no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—24no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—44no—
259C2×Dic43—48no—
260C2×Dic43—48no—
261C2×Dic43—42no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—42no—
265C2×Dic43C2×D812yes—
266C2×Dic43C2×D812yes—
267C2×Dic43#13712yes—
268D172—24no—
269D172—42no—
270C4×D43—48no—
271Dic86—48no—
272C8×C43—42no—
273C43⋊C8—42no—
274#24060—431nomaximal, Sylow
275C22×C43—22no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43#44714yes—
289C22×C43C2×#12011yescharacteristic
290C22×C43#52511yescharacteristic
291C22×C43#53611yescharacteristic
292C22×C43C22×D811yescharacteristic
293C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C43C2×#13711yescharacteristic
295C22×C43#57511yescharacteristic
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C4×C43—22no—
304C4×C43—42no—
305C4×C43—82no—
306C4×C43#54712yes—
307C4×C43#54712yes—
308Dic43—22no—
309Dic43—22no—
310Dic43—22no—
311Dic43—44no—
312Dic43—42no—
313Dic43—41no—
314C2×#532—431no—
315C2×#480—431no—
316C2×#480D4311yescharacteristic, complemented
317C2×#389—431no—
318#2057—432no—
319#2041—432no—
320#1874—431no—
321#1874—431no—
322#1862—432no—
323#1862—432no—
324#1817—431no—
325C2×C43—24no—
326C2×C43—82no—
327C2×C43#240611yescharacteristic
328C2×C43C2×#44711yescharacteristic
329C2×C43#300711yescharacteristic
330C2×C43#310011yescharacteristic
331C2×C43#311211yescharacteristic
332C2×C43#322611yescharacteristic
333C2×C43#323411yescharacteristic
334D43—82no—
335C22×#41—861no—
336#532—864no—
337#532—864no—
338C2×C4⋊Q8—431no—
339C2×#127—431no—
340C2×#124—861no—
341C2×#121—431no—
342C2×#121—861no—
343C2×#121C2×D4311yescharacteristic
344C2×C4×D4—431no—
345C2×C4×D4—431no—
346C2×C4×D4—861no—
347C22×C4⋊C4—431no—
348C22×C4⋊C4—861no—
349C22×C4⋊C4C2×D4311yescharacteristic
350C22×C42—431no—
351#480—24no—
352#480—864no—
353C2×#107—432no—
354C2×#107C2×D4312yes—
355C2×#102—432no—
356C2×#102—432no—
357C2×#102—432no—
358C2×#102C2×D4312yes—
359C2×C22⋊C8—431no—
360C2×C22⋊C8C2×D4311yescharacteristic
361#389—432no—
362#389—432no—
363#389—861no—
364#389—861no—
365C2×#95—861no—
366#340—432no—
367#340—432no—
368#336—432no—
369#336—432no—
370C43#2406011yescharacteristic, complemented, Sylow
371C2×#41—868no—
372C2×#41—1724no—
373C2×#41—1724no—
374C22×Q8—861no—
375C22×D4—21no—
376C22×D4—431no—
377C22×D4—861no—
378C22×D4—861no—
379C22×D4—861no—
380C22×D4C22×D4311yescharacteristic
381C23×C4—21no—
382C23×C4—431no—
383C23×C4—431no—
384C23×C4—861no—
385C23×C4—861no—
386C23×C4—861no—
387C23×C4C22×D4311yescharacteristic
388C22×C8—432no—
389C22×C8C22×D4312yes—
390C4⋊Q8—862no—
391C4⋊Q8—862no—
392#127—862no—
393#127—862no—
394#124—868no—
395#121—22no—
396#121—434no—
397#121—868no—
398#121—862no—
399#121C22⋊D4314yes—
400C4×D4—868no—
401C4×D4—862no—
402C4×D4—862no—
403C4×D4—862no—
404C4×D4—862no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—432no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—864no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—1724no—
416C2×C4⋊C4C22×D4312yes—
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C42—431no—
423C2×C42—431no—
424C2×C42—431no—
425C2×C42—431no—
426C2×C42—862no—
427C2×C42—862no—
428#107—24no—
429#107—864no—
430#102—24no—
431#102—864no—
432#102—864no—
433#102—864no—
434C22⋊C8—22no—
435C22⋊C8—862no—
436#95—862no—
437#95—862no—
438C24—21no—
439C24—861no—
440C24D4×D4311yescharacteristic
441#41—17232no—
442C2×Q8—864no—
443C2×Q8—1722no—
444C2×Q8—1722no—
445C2×D4—24no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—432no—
452C2×D4—864no—
453C2×D4—864no—
454C2×D4—864no—
455C2×D4—861no—
456C2×D4—862no—
457C2×D4—862no—
458C2×D4—1722no—
459C2×D4—1722no—
460C2×D4—1722no—
461C2×D4—1722no—
462C2×D4—1722no—
463C2×D4—1722no—
464C2×D4C2×C22⋊D4312yes—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—434no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—864no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—864no—
482C22×C4—864no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—861no—
486C22×C4—1722no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4—1721no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4312yes—
495C22×C4C2×C22⋊D4312yes—
496C22×C4C23×D4311yescharacteristic
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—862no—
501C2×C8—862no—
502C2×C8—862no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—42no—
507C4⋊C4—432no—
508C4⋊C4—434no—
509C4⋊C4—864no—
510C4⋊C4—864no—
511C4⋊C4—861no—
512C4⋊C4—862no—
513C4⋊C4—1724no—
514C4⋊C4—1724no—
515C4⋊C4C2×C22⋊D4312yes—
516C22⋊C4—24no—
517C22⋊C4—864no—
518C22⋊C4—864no—
519C22⋊C4—864no—
520C42—862no—
521C42—862no—
522C42—861no—
523C42—861no—
524C42—861no—
525C42—861no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—862no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23—1721no—
542C23—1721no—
543C23—1721no—
544C23#1306329312yes—
545C23D8×D4312yes—
546C23#1306334912yes—
547C23C2×D4×D4311yescharacteristic
548Q8—1728no—
549D4—24no—
550D4—48no—
551D4—42no—
552D4—864no—
553D4—1728no—
554D4—1728no—
555D4—1728no—
556D4—1722no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—84no—
568C2×C4—432no—
569C2×C4—432no—
570C2×C4—432no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—868no—
578C2×C4—861no—
579C2×C4—862no—
580C2×C4—864no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—1728no—
584C2×C4—1724no—
585C2×C4—1728no—
586C2×C4—1728no—
587C2×C4—1722no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1722no—
591C2×C4#1306329312yes—
592C2×C4C2×D4×D4311yescharacteristic
593C2×C4C22×C22⋊D4311yescharacteristic
594C2×C4#41×D4312yes—
595C2×C4#1306337212yes—
596C8—42no—
597C8—1722no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—3441no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22#1458303114yes—
619C22C2×#1306329311yescharacteristic
620C22#1458340711yescharacteristic
621C22#1458347111yescharacteristic
622C22C2×D8×D4311yescharacteristic
623C22C2×#1306334911yescharacteristic
624C22#137×D4311yescharacteristic
625C22#1458369811yescharacteristic
626C4—22no—
627C4—42no—
628C4—82no—
629C4—862no—
630C4—862no—
631C4—862no—
632C4—1722no—
633C4—1724no—
634C4—1721no—
635C4#1458354712yes—
636C4#1458354812yes—
637C2—24no—
638C2—82no—
639C2—3442no—
640C2#1913792711yescharacteristic
641C2C2×#1458303111yescharacteristic
642C2#1914385111yescharacteristic
643C2#1914459211yescharacteristic
644C2#1914471411yescharacteristic
645C2#1914571411yescharacteristic
646C2#1914578211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#480C2
socleC23×C43C22×D4
prime radicalC2×#14583444C2
hypercenterC2×#480D43
hypocenterC43#24060
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#14583212C2semidirect
3. C2×#14582795C2semidirect
4. #19135921C2semidirect
5. #19135827C2semidirect
6. #19134913C2semidirect
7. #19134910C2semidirect
8. #19134840C2semidirect
9. #19134839C2semidirect
10. #19134661C2semidirect
11. C2×C43×#480C2semidirect
189. C4⋊Dic43#41semidirect
316. C2×#480D43semidirect
370. C43#24060semidirect

Maximal subgroups

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

subgroupindex
C2×#145834442
C2×#145832122
C2×#145827952
#191359212
#191358272
#191349132
#191349102
#191348402
#191348392
#191346612
C2×C43×#4802
#2406043