Finite Group Databasebeta

← #25199727

Subgroups — #25199727

Order 11008.

724 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142959C211yesmaximal, characteristic
2#19137069C211yesmaximal, characteristic, complemented
3#19136098C211yesmaximal, characteristic, complemented
4#19135985C211yesmaximal, characteristic, complemented
5#19135981C211yesmaximal, characteristic
6#19135911C211yesmaximal, characteristic
7#19135450C211yesmaximal, characteristic
8#19135326C211yesmaximal, characteristic, complemented
9#19135275C211yesmaximal, characteristic
10#19135269C211yesmaximal, characteristic, complemented
11#19135180C211yesmaximal, characteristic, complemented
12#19134953C211yesmaximal, characteristic
13#19134852C211yesmaximal, characteristic, complemented
14#19134443C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063318—21no—
18C2×C4×Dic86C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582804C2211yescharacteristic
30#14582804C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582793—21no—
39#14582792—21no—
40#14582787—21no—
41#14582781—21no—
42#14582781—21no—
43C4×Dic43⋊C4—21no—
44#14582745—21no—
45C42×Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621883—22no—
61C2×#10621883—22no—
62C2×#10621883—41no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063318—44no—
66C4×Dic86—22no—
67C4×Dic86—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43D411yescharacteristic
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88#13063259—22no—
89#13063256—22no—
90Dic43⋊C8—22no—
91Dic43⋊C8—22no—
92#13063250—22no—
93#13063250—22no—
94#13063248—41no—
95#13063246—22no—
96C8×Dic43—41no—
97C8×Dic43—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×D4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#107×C43—41no—
118#102×C43—22no—
119#102×C43—41no—
120#95×C43—21no—
121C24×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86#4112yes—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43#4112yes—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C22⋊C4×C43—42no—
161C22⋊C4×C43—42no—
162C42×C43—21no—
163C42×C43—21no—
164C42×C43—42no—
165C22⋊Dic43—42no—
166C22⋊Dic43—42no—
167C22⋊Dic43—42no—
168C22⋊Dic43—42no—
169#10621883—44no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—42no—
176C4⋊Dic43#4112yes—
177Dic43⋊C4—24no—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182C4×Dic43—24no—
183C4×Dic43—22no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—22no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8#4112yes—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43C22×D411yescharacteristic
205D4×C43—41no—
206D4×C43—41no—
207D4×C43—41no—
208D4×C43—41no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
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#13512yes—
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43#13512yes—
252C2×Dic43AGL(1,ℤ/8)12yes—
253C2×Dic43#13712yes—
254Dic86—22no—
255Dic86—22no—
256Dic86—41no—
257Dic86—41no—
258C8×C43—22no—
259C8×C43—41no—
260C43⋊C8—22no—
261C43⋊C8—41no—
262#29435—431nomaximal, Sylow
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43#52511yescharacteristic
271C22×C43#53211yescharacteristic
272C22×C43#53711yescharacteristic
273C22×C43C2×#13511yescharacteristic
274C22×C43C2×#13511yescharacteristic
275C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C43C2×#13711yescharacteristic
277C4×C43—22no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43#55111yescharacteristic
283C4×C43#55211yescharacteristic
284C4×C43#55311yescharacteristic
285C4×C43#55611yescharacteristic
286Dic43—22no—
287Dic43—22no—
288Dic43—22no—
289Dic43—42no—
290Dic43—42no—
291Dic43—41no—
292Dic43—81no—
293Dic43—81no—
294#2860—431no—
295#2295—431no—
296#2088—431no—
297#2068—431no—
298#2067—431no—
299#2055—431no—
300#1968—431no—
301#1942—431no—
302#1934—431no—
303#1933—431no—
304#1925D4311yescharacteristic
305#1920—431no—
306#1880—431no—
307#1863—431no—
308C4×C4⋊C8—431no—
309C2×C43—161no—
310C2×C43#260111yescharacteristic
311C2×C43#310611yescharacteristic
312C2×C43#310811yescharacteristic
313C2×C43#316811yescharacteristic
314C2×C43#318211yescharacteristic
315C2×C43#324711yescharacteristic
316C2×C43#324811yescharacteristic
317C22×SD16—431no—
318C2×#126—861no—
319C2×C4×Q8—431no—
320C2×#107—431no—
321C2×#107C2×D4311yescharacteristic
322C2×#106—431no—
323C2×C4⋊C8—431no—
324C2×C4⋊C8—431no—
325C2×#103—431no—
326C2×#103—431no—
327C2×#103—431no—
328C2×#102—431no—
329C2×#102C2×D4311yescharacteristic
330C2×#102C2×D4311yescharacteristic
331C2×C4×C8—431no—
332C2×C4×C8—431no—
333#391—431no—
334#391—431no—
335#390—431no—
336#390—431no—
337#390C2×D4311yescharacteristic
338#389—431no—
339#389—431no—
340#389—431no—
341#389—431no—
342#389—431no—
343#388—861no—
344#388—861no—
345#388—861no—
346#387—861no—
347#387—861no—
348C4×C4⋊C4—861no—
349C4×C4⋊C4C2×D4311yescharacteristic
350#376—861no—
351C43—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340C2×D4311yescharacteristic
358#336—431no—
359#336C2×D4311yescharacteristic
360C43#2943511yescharacteristic, complemented, Sylow
361C22×Q8—431no—
362C22×D4C22×D4311yescharacteristic
363C2×SD16—862no—
364C2×SD16—862no—
365C2×SD16—1721no—
366C22×C8—431no—
367C22×C8—431no—
368C22×C8C22×D4311yescharacteristic
369C22×C8C22×D4311yescharacteristic
370#126—1724no—
371C4×Q8—862no—
372C4×Q8—862no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C42—21no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—431no—
397C2×C42—431no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400#107—41no—
401#107—862no—
402#106—862no—
403C4⋊C8—862no—
404C4⋊C8—862no—
405#103—862no—
406#103—862no—
407#103—1721no—
408#102—22no—
409#102—41no—
410#102—862no—
411C4×C8—1721no—
412C4×C8—1721no—
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—
423C24—21no—
424C2×Q8—432no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4D4×D4311yescharacteristic
448C22×C4D4×D4311yescharacteristic
449C22×C4C23×D4311yescharacteristic
450SD16—1724no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—432no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8#1062189812yes—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—432no—
470C4⋊C4—864no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—1722no—
477C4⋊C4—1722no—
478C4⋊C4—1722no—
479C4⋊C4—1722no—
480C4⋊C4—1722no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—1722no—
484C22⋊C4—1722no—
485C22⋊C4—1722no—
486C22⋊C4—1722no—
487C42—21no—
488C42—21no—
489C42—42no—
490C42—862no—
491C42—862no—
492C42—862no—
493C42—864no—
494C42—862no—
495C42—861no—
496C42—861no—
497C42—861no—
498C42—861no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23C2×D4×D4311yescharacteristic
507Q8—862no—
508Q8—862no—
509Q8—1721no—
510Q8—1721no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515C2×C4—21no—
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—432no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
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#1306334412yes—
554C2×C4#41×D4311yescharacteristic
555C2×C4#41×D4311yescharacteristic
556C2×C4#41×D4311yescharacteristic
557C2×C4C2×#1062189811yescharacteristic
558C2×C4#1306337011yescharacteristic
559C2×C4#1306337211yescharacteristic
560C8—22no—
561C8—41no—
562C8—862no—
563C8—1721no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22#1458340711yescharacteristic
572C22#1458344611yescharacteristic
573C22#1458347811yescharacteristic
574C22#135×D4311yescharacteristic
575C22C2×#1306334411yescharacteristic
576C22AGL(1,ℤ/8)×D4311yescharacteristic
577C22#137×D4311yescharacteristic
578C4—22no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—862no—
584C4—862no—
585C4—862no—
586C4—3441no—
587C4—3441no—
588C4—1721no—
589C4—1722no—
590C4—1722no—
591C4#1458357911yescharacteristic
592C4#1458358811yescharacteristic
593C4#1458359811yescharacteristic
594C4#1458361611yescharacteristic
595C2—161no—
596C2#1914019811yescharacteristic
597C2#1914465011yescharacteristic
598C2#1914467211yescharacteristic
599C2#1914516311yescharacteristic
600C2#1914531011yescharacteristic
601C2#1914591711yescharacteristic
602C2#1914592911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1925D43
hypocenterC43#29435
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. #19137069C2semidirect
3. #19136098C2semidirect
4. #19135985C2semidirect
8. #19135326C2semidirect
10. #19135269C2semidirect
11. #19135180C2semidirect
13. #19134852C2semidirect
14. #19134443C2semidirect
360. C43#29435semidirect

Maximal subgroups

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

subgroupindex
#191429592
#191370692
#191360982
#191359852
#191359812
#191359112
#191354502
#191353262
#191352752
#191352692
#191351802
#191349532
#191348522
#191344432
C43×#19252
#2943543