Finite Group Databasebeta

← #25199688

Subgroups — #25199688

Order 11008.

746 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142974C211yesmaximal, characteristic, complemented
2#19137057C211yesmaximal, characteristic
3#19136094C211yesmaximal, characteristic, complemented
4#19135988C211yesmaximal, characteristic, complemented
5#19135981C211yesmaximal, characteristic
6#19135908C211yesmaximal, characteristic
7#19135328C211yesmaximal, characteristic, complemented
8#19135281C211yesmaximal, characteristic
9#19135274C211yesmaximal, characteristic, complemented
10#19135238C211yesmaximal, characteristic, complemented
11#19135175C211yesmaximal, characteristic, complemented
12#19134931C211yesmaximal, characteristic
13#19134844C211yesmaximal, characteristic
14C4×Dic43⋊C8C211yesmaximal, characteristic, complemented
15C43×#1968C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×#13063281—21no—
18C2×#13063259C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×C4×C43⋊C8C2211yescharacteristic
27#14582806C2211yescharacteristic
28#14582806C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582798C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582797C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582793—21no—
36#14582787—21no—
37#14582786—21no—
38#14582784—21no—
39#14582781—21no—
40#14582766—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C22⋊C4×Dic43—21no—
43C42×Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62D4×Dic43—22no—
63D4×Dic43—22no—
64#13063281—44no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43D411yescharacteristic
79C2×C4×Dic43D411yescharacteristic
80C2×C4×Dic43D411yescharacteristic
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84#13063259—22no—
85#13063259—41no—
86Dic43⋊C8—22no—
87Dic43⋊C8—22no—
88#13063249—22no—
89#13063249—41no—
90#13063246—22no—
91#13063246—41no—
92C4×C43⋊C8—41no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×Q8×C43C2311yescharacteristic
104C22×D4×C43C2311yescharacteristic
105C2×SD16×C43—22no—
106C2×SD16×C43—22no—
107C2×SD16×C43—41no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#106×C43—22no—
116#103×C43—22no—
117#102×C43—22no—
118C4×C8×C43—41no—
119#95×C43—21no—
120#95×C43—21no—
121C24×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43#4112yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—24no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151SD16×C43—44no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43#4112yes—
157C2×C8×C43#4112yes—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C22⋊C4×C43—42no—
163C22⋊C4×C43—42no—
164C42×C43—21no—
165C42×C43—21no—
166C22⋊Dic43—24no—
167C22⋊Dic43—42no—
168C22⋊Dic43—42no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—42no—
177C4⋊Dic43#4112yes—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182C4×Dic43—22no—
183C4×Dic43—22no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—22no—
189C4×Dic43—22no—
190C4×Dic43—42no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C23×C43—22no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43C22×D411yescharacteristic
205Q8×C43—41no—
206Q8×C43—41no—
207Q8×C43—41no—
208Q8×C43—41no—
209D4×C43—22no—
210D4×C43—22no—
211D4×C43—41no—
212D4×C43—41no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43AGL(1,ℤ/8)12yes—
227C2×C4×C43#13712yes—
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C2×C4×C432−1+411yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—48no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43#13512yes—
258C2×Dic43#13512yes—
259C8×C43—22no—
260C8×C43—22no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263#29433—431nomaximal, Sylow
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43#52511yescharacteristic
272C22×C43#53211yescharacteristic
273C22×C43#53711yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43C2×#13511yescharacteristic
276C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C43C2×#13711yescharacteristic
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#55111yescharacteristic
284C4×C43#55211yescharacteristic
285C4×C43#55311yescharacteristic
286C4×C43#55611yescharacteristic
287Dic43—22no—
288Dic43—22no—
289Dic43—42no—
290Dic43—41no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295#2863—431no—
296#2293—431no—
297#2088—431no—
298#2068—431no—
299#2067—431no—
300#2055—431no—
301#1968D4311yescharacteristic
302#1942—431no—
303#1934—431no—
304#1933—431no—
305#1928—431no—
306#1919—431no—
307#1877—431no—
308#1862—431no—
309C4×C4⋊C8—431no—
310C2×C43—82no—
311C2×C43#260111yescharacteristic
312C2×C43#310511yescharacteristic
313C2×C43#310711yescharacteristic
314C2×C43#316811yescharacteristic
315C2×C43#318211yescharacteristic
316C2×C43#324711yescharacteristic
317C2×C43#324811yescharacteristic
318C22×SD16C2×D4311yescharacteristic
319C2×C4×D4—431no—
320C2×#117—861no—
321C2×#107—431no—
322C2×#107—431no—
323C2×#106C2×D4311yescharacteristic
324C2×C4⋊C8—431no—
325C2×C4⋊C8—431no—
326C2×#103—431no—
327C2×#103—431no—
328C2×#103C2×D4311yescharacteristic
329C2×#102—431no—
330C2×#102—431no—
331C2×#102C2×D4311yescharacteristic
332C2×C4×C8—431no—
333C2×C4×C8C2×D4311yescharacteristic
334#391—431no—
335#391—431no—
336#391C2×D4311yescharacteristic
337#390—431no—
338#390C2×D4311yescharacteristic
339#389—431no—
340#389—431no—
341#389—431no—
342#389—431no—
343#389—431no—
344#388—861no—
345#388—861no—
346#387—861no—
347#387—861no—
348#387—861no—
349#383—861no—
350C4×C4⋊C4—431no—
351C4×C22⋊C4—861no—
352C43—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#336—431no—
360#336—431no—
361C43#2943311yescharacteristic, complemented, Sylow
362C22×Q8C22×D4311yescharacteristic
363C22×D4C22×D4311yescharacteristic
364C23×C4—861no—
365C2×SD16—22no—
366C2×SD16—22no—
367C2×SD16—41no—
368C22×C8—431no—
369C22×C8—431no—
370C22×C8C22×D4311yescharacteristic
371C22×C8C22×D4311yescharacteristic
372C4×D4—862no—
373C4×D4—862no—
374#117—1724no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—431no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—431no—
397C2×C42—861no—
398C2×C42C22×D4311yescharacteristic
399#107—862no—
400#107—1721no—
401#106—22no—
402C4⋊C8—862no—
403C4⋊C8—862no—
404#103—22no—
405#103—862no—
406#103—1721no—
407#102—22no—
408#102—862no—
409#102—1721no—
410C4×C8—41no—
411C4×C8—1721no—
412#95—21no—
413#95—21no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424C24—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4#1062189812yes—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—864no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—1722no—
450C22×C4—1722no—
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454SD16—44no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8#1062190012yes—
466C2×C8#1062190012yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—432no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—1722no—
480C4⋊C4—1722no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—864no—
487C22⋊C4—1722no—
488C22⋊C4—1722no—
489C42—21no—
490C42—21no—
491C42—862no—
492C42—862no—
493C42—862no—
494C42—862no—
495C42—861no—
496C42—861no—
497C42—861no—
498C42—861no—
499C42—1722no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C2×D4×D4311yescharacteristic
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—432no—
530C2×C4—432no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—862no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—1728no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4#1306335212yes—
555C2×C4#1306335412yes—
556C2×C4#41×D4311yescharacteristic
557C2×C4C2×#1062190011yescharacteristic
558C2×C4C2×#1062190011yescharacteristic
559C2×C4C2×#1062189811yescharacteristic
560C2×C4#1306337011yescharacteristic
561C2×C4#1306337211yescharacteristic
562C8—22no—
563C8—22no—
564C8—1721no—
565C8—1721no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#1458340811yescharacteristic
574C22#1458344711yescharacteristic
575C22#1458347611yescharacteristic
576C22#135×D4311yescharacteristic
577C22#135×D4311yescharacteristic
578C22C2×#1306335211yescharacteristic
579C22C2×#1306335411yescharacteristic
580C4—22no—
581C4—22no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—862no—
586C4—862no—
587C4—3441no—
588C4—3441no—
589C4—3441no—
590C4—1721no—
591C4—1722no—
592C4—1721no—
593C4#1458357511yescharacteristic
594C4#1458358911yescharacteristic
595C4#1458359211yescharacteristic
596C4#1458361811yescharacteristic
597C2—82no—
598C2#1914018911yescharacteristic
599C2#1914464611yescharacteristic
600C2#1914466211yescharacteristic
601C2#1914516211yescharacteristic
602C2#1914531111yescharacteristic
603C2#1914591611yescharacteristic
604C2#1914592511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1968C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1968D43
hypocenterC43#29433
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
1. #19142974C2semidirect
3. #19136094C2semidirect
4. #19135988C2semidirect
7. #19135328C2semidirect
9. #19135274C2semidirect
10. #19135238C2semidirect
11. #19135175C2semidirect
14. C4×Dic43⋊C8C2semidirect
361. C43#29433semidirect

Maximal subgroups

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

subgroupindex
#191429742
#191370572
#191360942
#191359882
#191359812
#191359082
#191353282
#191352812
#191352742
#191352382
#191351752
#191349312
#191348442
C4×Dic43⋊C82
C43×#19682
#2943343