Finite Group Databasebeta

← #25125764

Subgroups — #25125764

Order 11008.

1016 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×#14582990C211yesmaximal, characteristic, complemented
2C2×#14582986C211yesmaximal, characteristic, complemented
3#19137159C211yesmaximal, characteristic
4#19137066C211yesmaximal, characteristic, complemented
5#19136074C211yesmaximal, characteristic, complemented
6#19136007C211yesmaximal, characteristic, complemented
7#19135966C211yesmaximal, characteristic, complemented
8#19135913C211yesmaximal, characteristic, complemented
9#19135912C211yesmaximal, characteristic, complemented
10#19135828C211yesmaximal, characteristic
11#19135684C211yesmaximal, characteristic
12C4⋊C8×Dic43C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#2065C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063321C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×(C22⋊D43)⋊C4—21no—
23C2×(C22⋊D43)⋊C4—21no—
24#14582990—24no—
25#14582986—24no—
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36#14582805C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582799—21no—
40#14582799—21no—
41#14582798C2211yescharacteristic
42#14582786—21no—
43#14582780—21no—
44#14582768C2211yescharacteristic
45C4⋊C4×Dic43—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47#14582744—21no—
48C42×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43—21no—
65C23×Dic43—21no—
66C22×C4×D43—21no—
67C2×#10621873—22no—
68C2×#10621873—22no—
69C2×#10621873—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063321—22no—
76#13063321—22no—
77#13063290—22no—
78#13063290D414yescomplemented
79D4×Dic43—22no—
80D4×Dic43—22no—
81#13063287—22no—
82#13063287—22no—
83(C22⋊D43)⋊C4—44no—
84(C22⋊D43)⋊C4—44no—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43D411yescharacteristic
99C2×C4×Dic43D411yescharacteristic
100C2×C4×Dic43D411yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103#13063256—22no—
104C4⋊(C43⋊C8)—22no—
105#13063250—22no—
106#13063248—22no—
107#13063247—22no—
108#13063246—22no—
109#13063245—22no—
110#13063245—22no—
111C8×Dic43—22no—
112C8×Dic43—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×D4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C42×C43C2311yescharacteristic
129#106×C43—22no—
130C4⋊C8×C43—22no—
131#102×C43—22no—
132#102×C43—22no—
133#95×C43—21no—
134C24×C43—21no—
135C23×D43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43#4112yes—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—24no—
149C2×C22⋊D43—24no—
150C2×C22⋊D43—42no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—42no—
153C2×C22⋊D43—42no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172#4112yes—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86C2×D412yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43#4112yes—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43C2×D412yes—
192C22⋊C4×C43—42no—
193C22⋊C4×C43—42no—
194C42×C43—21no—
195C42×C43—21no—
196C22⋊Dic43—42no—
197#10621883—28no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—42no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—42no—
206Dic43⋊C4—24no—
207Dic43⋊C4—42no—
208Dic43⋊C4—42no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—24no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214C4×Dic43—41no—
215C4×Dic43—42no—
216C4×Dic43SD1614yescomplemented
217C4×Dic43C2×D412yes—
218C4×Dic43#4112yes—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8#4112yes—
225#10621873—28no—
226C23×C43—22no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43C22×D411yescharacteristic
234C22×D43—22no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—41no—
244D4×C43—41no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43C2×SD1612yes—
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C22⋊D43—48no—
267C22⋊D43—48no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—84no—
284C2×Dic43#12112yes—
285C2×Dic43#12112yes—
286C2×Dic43C2×SD1612yes—
287C2×Dic43C2×SD1612yes—
288C2×Dic43#13512yes—
289C2×Dic43AGL(1,ℤ/8)12yes—
290D172—22no—
291D172—22no—
292D172—41no—
293D172—41no—
294C4×D43—84no—
295Dic86—22no—
296Dic86—22no—
297Dic86—41no—
298Dic86—41no—
299C8×C43—22no—
300C8×C43—41no—
301C43⋊C8—22no—
302C43⋊C8—41no—
303#23678—431nomaximal, Sylow
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—42no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43C2×#12111yescharacteristic
312C22×C43#52511yescharacteristic
313C22×C43#53211yescharacteristic
314C22×C43C22×SD1611yescharacteristic
315C22×C43C2×#13511yescharacteristic
316C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
317C22×C43#57511yescharacteristic
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—81no—
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C4×C43—22no—
326C4×C43—41no—
327C4×C43—42no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43#52511yescharacteristic
331C4×C43#52511yescharacteristic
332C4×C43#52911yescharacteristic
333C4×C43#52911yescharacteristic
334Dic43—22no—
335Dic43—22no—
336Dic43—22no—
337Dic43—42no—
338Dic43—81no—
339Dic43—81no—
340Dic43#46014yes—
341C2×C4×SD16—431no—
342C2×C4×SD16—431no—
343C4×#127—431no—
344#2295—431no—
345#2084—431no—
346#2072—431no—
347#2065—431no—
348#2065D4311yescharacteristic, complemented
349#2055—431no—
350#2055—431no—
351#2041—431no—
352#2014—431no—
353C4×C4⋊C8—431no—
354C4×#102—431no—
355C4×#102—431no—
356C2×C43—82no—
357C2×C43#239211yescharacteristic
358C2×C43C2×#46011yescharacteristic
359C2×C43#303511yescharacteristic
360C2×C43#310111yescharacteristic
361C2×C43#310511yescharacteristic
362C2×C43#316711yescharacteristic
363C2×C43#317111yescharacteristic
364D43—82no—
365C22×SD16—431no—
366C22×SD16—431no—
367C2×#127—431no—
368C2×C4×Q8—431no—
369C2×C4×D4—431no—
370C2×C4×D4—431no—
371C2×C4×D4—861no—
372C2×C4×D4—861no—
373C4×SD16—864no—
374C4×SD16—864no—
375C2×#106—431no—
376C2×#106C2×D4311yescharacteristic
377C2×C4⋊C8—431no—
378C2×C4⋊C8C2×D4311yescharacteristic
379C2×#103—431no—
380C2×#103—431no—
381C2×#102—431no—
382C2×#102—431no—
383C2×#102—431no—
384C2×#102—431no—
385C2×#102C2×D4311yescharacteristic
386C2×#102C2×D4311yescharacteristic
387C2×C4×C8—431no—
388C2×C4×C8—431no—
389#391—431no—
390#391—431no—
391#390—431no—
392#390—861no—
393#390—861no—
394#390C2×D4311yescharacteristic
395#389—431no—
396#389C2×D4311yescharacteristic
397#387—861no—
398#387—861no—
399#384—431no—
400C4×C4⋊C4—431no—
401C4×C4⋊C4—861no—
402#376—861no—
403C43—431no—
404#340—431no—
405#340—431no—
406#340—431no—
407#340C2×D4311yescharacteristic
408#336—431no—
409#336—431no—
410C43#2367811yescharacteristic, complemented, Sylow
411C22×Q8—431no—
412C22×D4—431no—
413C22×D4—861no—
414C22×D4—861no—
415C22×D4C22×D4311yescharacteristic
416C23×C4—861no—
417C23×C4—861no—
418C2×SD16—862no—
419C2×SD16—862no—
420C2×SD16—862no—
421C2×SD16—862no—
422C2×SD16—862no—
423C2×SD16—862no—
424C22×C8—431no—
425C22×C8—431no—
426C22×C8C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428#127—862no—
429#127—862no—
430C4×Q8—434no—
431C4×Q8—862no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4—862no—
435C4×D4—862no—
436C4×D4—1724no—
437C4×D4—1724no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—861no—
461C2×C42—861no—
462C2×C42C22×D4311yescharacteristic
463#106—22no—
464#106—862no—
465C4⋊C8—22no—
466C4⋊C8—862no—
467#103—862no—
468#103—862no—
469#102—22no—
470#102—22no—
471#102—862no—
472#102—862no—
473#102—862no—
474#102—862no—
475C4×C8—862no—
476C4×C8—862no—
477#95—21no—
478#95—861no—
479#95—861no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484C24—21no—
485C24—861no—
486C2×Q8—432no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—432no—
498C2×D4—864no—
499C2×D4—864no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4—861no—
503C2×D4—861no—
504C2×D4—861no—
505C2×D4—1722no—
506C2×D4—1722no—
507C2×D4—1722no—
508C2×D4—1722no—
509C2×D4#1062190212yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—1722no—
521C22×C4—1722no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4D4×D4311yescharacteristic
527C22×C4D4×D4311yescharacteristic
528C22×C4C23×D4311yescharacteristic
529SD16—868no—
530SD16—868no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—432no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8#1062190012yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—864no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—861no—
554C4⋊C4—1722no—
555C4⋊C4—1722no—
556C4⋊C4—1722no—
557C4⋊C4D4×D4312yes—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—1722no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C42—21no—
565C42—21no—
566C42—434no—
567C42—432no—
568C42—432no—
569C42—862no—
570C42—862no—
571C42—864no—
572C42—861no—
573C42—861no—
574C42—1721no—
575C42—1722no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—862no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23C2×D4×D4311yescharacteristic
591Q8—862no—
592Q8—862no—
593Q8—1721no—
594Q8—1721no—
595D4—22no—
596D4—22no—
597D4—41no—
598D4—41no—
599D4—862no—
600D4—862no—
601D4—1728no—
602D4—1728no—
603D4—1721no—
604D4—1721no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—432no—
620C2×C4—432no—
621C2×C4—432no—
622C2×C4—432no—
623C2×C4—432no—
624C2×C4—432no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—862no—
632C2×C4—3444no—
633C2×C4—3444no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4SD16×D4312yes—
643C2×C4C2×D4×D4311yescharacteristic
644C2×C4#41×D4311yescharacteristic
645C2×C4#41×D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4C2×#1062190011yescharacteristic
648C2×C4C2×#1062190211yescharacteristic
649C8—22no—
650C8—41no—
651C8—862no—
652C8—1721no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—3441no—
664C22—1722no—
665C22—1722no—
666C22—1722no—
667C22#121×D4311yescharacteristic
668C22#1458341211yescharacteristic
669C22#1458344411yescharacteristic
670C22C2×SD16×D4311yescharacteristic
671C22#135×D4311yescharacteristic
672C22AGL(1,ℤ/8)×D4311yescharacteristic
673C22#1458369511yescharacteristic
674C4—22no—
675C4—42no—
676C4—41no—
677C4—81no—
678C4—81no—
679C4—434no—
680C4—862no—
681C4—862no—
682C4—862no—
683C4—3441no—
684C4—3441no—
685C4—1722no—
686C4#1458340911yescharacteristic
687C4#1458341211yescharacteristic
688C4#1458343211yescharacteristic
689C4#1458343511yescharacteristic
690C2—82no—
691C2—3442no—
692C2#1913784011yescharacteristic
693C2#460×D4311yescharacteristic
694C2#1914404711yescharacteristic
695C2#1914460511yescharacteristic
696C2#1914464711yescharacteristic
697C2#1914514911yescharacteristic
698C2#1914518511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2065C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenter#2065D43
hypocenterC43#23678
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. C2×#14582990C2semidirect
2. C2×#14582986C2semidirect
4. #19137066C2semidirect
5. #19136074C2semidirect
6. #19136007C2semidirect
7. #19135966C2semidirect
8. #19135913C2semidirect
9. #19135912C2semidirect
12. C4⋊C8×Dic43C2semidirect
13. #102×Dic43C2semidirect
14. #19134409C2semidirect
15. C43×#2065C2semidirect
78. #13063290D4semidirect
216. C4×Dic43SD16semidirect
348. #2065D43semidirect
410. C43#23678semidirect

Maximal subgroups

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

subgroupindex
C2×#145829902
C2×#145829862
#191371592
#191370662
#191360742
#191360072
#191359662
#191359132
#191359122
#191358282
#191356842
C4⋊C8×Dic432
#102×Dic432
#191344092
C43×#20652
#2367843