Finite Group Databasebeta

← #25080591

Subgroups — #25080591

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144918C211yesmaximal, characteristic, complemented
2#19144758C211yesmaximal, characteristic, complemented
3#19144747C211yesmaximal, characteristic
4C8×#10621898C211yesmaximal, characteristic, complemented
5#19134054C211yesmaximal, characteristic, complemented
6#19134047C211yesmaximal, characteristic, complemented
7#19134040C211yesmaximal, characteristic, complemented
8#19134033C211yesmaximal, characteristic, complemented
9#19134026C211yesmaximal, characteristic, complemented
10#19134019C211yesmaximal, characteristic, complemented
11#19134012C211yesmaximal, characteristic, complemented
12#19134005C211yesmaximal, characteristic, complemented
13#19133306C211yesmaximal, characteristic, complemented
14#19133301C211yesmaximal, characteristic, complemented
15C43×#1568C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583254—21no—
20#14583254—21no—
21#14583250C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583241—21no—
26#14583224—21no—
27#14583195C2211yescharacteristic
28#14583190C2211yescharacteristic
29#14583185C2211yescharacteristic
30#14583180C2211yescharacteristic
31#14583110C2211yescharacteristic
32#14583105C2211yescharacteristic
33#14583100C2211yescharacteristic
34#14583095C2211yescharacteristic
35#14583063—21no—
36#14583046—21no—
37C8×Dic86C2211yescharacteristic
38C8×Dic86C2211yescharacteristic
39#14583012—21no—
40#14583007—21no—
41#14583001—21no—
42#14583001—21no—
43C8×D172C2211yescharacteristic
44C8×D172C2211yescharacteristic
45C8×C22⋊D43—21no—
46C8×C22⋊D43—21no—
47#14582952C2211yescharacteristic
48#14582950—21no—
49#14582896—21no—
50#14582896—21no—
51C4×C8×D43—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69C2×Dic172—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×D344—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063317—21no—
80#13063313—21no—
81#13063304—21no—
82#13063304—21no—
83#13063299—21no—
84#13063299—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86D411yescharacteristic
88C4×Dic86C2311yescharacteristic
89C4×D172—21no—
90C4×D172—21no—
91C4×D172D411yescharacteristic
92C4×D172C2311yescharacteristic
93C4×C22⋊D43—21no—
94C4×C22⋊D43—21no—
95#13063284—21no—
96#13063284D411yescharacteristic
97#13063282—21no—
98C42×D43—21no—
99#13063259—21no—
100#13063259—21no—
101#13063257—21no—
102#13063257—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126C4×C43⋊C8—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C22×C8×C43D411yescharacteristic
130C22×C8×C43D411yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×C22⋊D43—41no—
149#10621898—22no—
150#10621898—22no—
151#10621898—42no—
152#10621898—42no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—41no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—41no—
170C2×C8×C43—41no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180C22⋊Dic43—41no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—41no—
184(C2×D43)⋊C4—41no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C2×D411yescharacteristic
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203Dic172—42no—
204D344—42no—
205#10621873—42no—
206#10621873—42no—
207C8×D43—42no—
208C8×D43—42no—
209C23×C43#12111yescharacteristic
210C22×D43—21no—
211C22×D43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—41no—
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C22⋊D43—24no—
224C22⋊D43—82no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231D172—21no—
232D172—41no—
233D172—41no—
234D172—41no—
235D172—41no—
236D172—81no—
237D172#13512yes—
238C4×D43—24no—
239C4×D43—42no—
240C4×D43—41no—
241C4×D43—41no—
242C4×D43—82no—
243Dic86—21no—
244Dic86—41no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—81no—
249Dic86#13512yes—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#19278—431nomaximal, Sylow
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43C2×#12111yescharacteristic
265C2×D43—22no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43C2×#13511yescharacteristic
276C4×C43C2×#13511yescharacteristic
277C4×C43#57511yescharacteristic
278C4×C43#57511yescharacteristic
279Dic43—22no—
280Dic43—41no—
281Dic43—41no—
282Dic43—81no—
283Dic43—81no—
284Dic43—81no—
285#3131—431no—
286#3116—431no—
287#3115—431no—
288C8×#41—431no—
289#1684—431no—
290#1683—431no—
291#1682—431no—
292#1681—431no—
293#1680—431no—
294#1679—431no—
295#1678—431no—
296#1677—431no—
297#1568D4311yescharacteristic, complemented
298#1554—431no—
299#1553—431no—
300C2×C43—41no—
301C2×C43#304011yescharacteristic
302C2×C43#305011yescharacteristic
303C2×C43#306711yescharacteristic
304D43—42no—
305D43—161no—
306#533—431no—
307#532—431no—
308C4×#41—431no—
309#488—861no—
310#488—861no—
311#487—431no—
312#487—431no—
313#486—431no—
314#486—431no—
315#485—861no—
316#482—861no—
317#477—431no—
318#476—431no—
319#475—431no—
320#474—431no—
321#462—431no—
322#461—431no—
323#460—431no—
324#459—431no—
325#452—861no—
326#449—861no—
327C8×Q8—431no—
328C8×Q8—431no—
329#442—861no—
330#441—861no—
331#440—861no—
332#440—861no—
333C8×D4—431no—
334C8×D4—431no—
335C8×D4—861no—
336C8×D4—861no—
337#432C2×D4311yescharacteristic
338#432C2×D4311yescharacteristic
339#431—431no—
340#431—861no—
341#416—861no—
342#416—861no—
343C2×C4×C8—861no—
344C2×C4×C8C2×D4311yescharacteristic
345#335C2×D4311yescharacteristic
346#335C2×D4311yescharacteristic
347#334C2×D4311yescharacteristic
348#334C2×D4311yescharacteristic
349#333—431no—
350#333—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#331—431no—
356#331—431no—
357C43#1927811yescharacteristic, complemented, Sylow
358C2×#41—431no—
359C2×#41—861no—
360C2×Q16—861no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×D8—861no—
364C22×C8—861no—
365C22×C8—861no—
366C22×C8D17211yescharacteristic
367C22×C8D17211yescharacteristic
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8—431no—
371#127—431no—
372#125—861no—
373#124—861no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—861no—
377#121—861no—
378C4×Q8—431no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—431no—
383C4×D4—431no—
384C4×D4—861no—
385C4×D4—861no—
386C4×D4—861no—
387C4×D4—861no—
388#117—431no—
389#117—861no—
390#117—861no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393#107—861no—
394#107—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8C22×D4311yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—21no—
427#97—21no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8D17211yescharacteristic
432C4×C8D17211yescharacteristic
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435#41—862no—
436#41—862no—
437#41—1722no—
438#41—1722no—
439C2×Q8—431no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—431no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—1721no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—1721no—
453C22×C4C2×D17211yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4#1062190211yescharacteristic
456Q16—1722no—
457SD16—1722no—
458SD16—1722no—
459D8—1722no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C2×C8—1722no—
470C2×C8C2×D17211yescharacteristic
471C2×C8C2×D17211yescharacteristic
472C2×C8C2×D17211yescharacteristic
473C2×C8C2×D17211yescharacteristic
474C4⋊C4—431no—
475C4⋊C4—431no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C22⋊C4—1721no—
492C42—861no—
493C42—861no—
494C42—861no—
495C42—1721no—
496C42C2×D17211yescharacteristic
497C42D4×D4311yescharacteristic
498C42#1062190211yescharacteristic
499C42C23×D4311yescharacteristic
500C23—861no—
501C23—1721no—
502C23#1306330011yescharacteristic
503Q8—432no—
504Q8—861no—
505Q8—3441no—
506Q8—1721no—
507Q8—1721no—
508Q8—1721no—
509Q8—1721no—
510D4—432no—
511D4—864no—
512D4—861no—
513D4—3441no—
514D4—3442no—
515D4—1721no—
516D4—1721no—
517D4—1721no—
518D4—1721no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—864no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—3442no—
529C2×C4—1722no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4#1306330011yescharacteristic
536C2×C4#1306330011yescharacteristic
537C2×C4#1306330011yescharacteristic
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4C22×D17211yescharacteristic
540C2×C4C2×#1062190211yescharacteristic
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—1721no—
550C8—1721no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—862no—
555C22—3441no—
556C22—3441no—
557C22—3441no—
558C22—1721no—
559C22—1721no—
560C22C2×#1306330011yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—862no—
566C4—3441no—
567C4—3441no—
568C4—3441no—
569C4—1721no—
570C4—1721no—
571C4#135×D4311yescharacteristic
572C4#135×D4311yescharacteristic
573C4#1458369911yescharacteristic
574C4#1458369911yescharacteristic
575C2—41no—
576C2—1722no—
577C2—6881no—
578C2#1914409011yescharacteristic
579C2#1914417711yescharacteristic
580C2#1914431611yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1568C2
socleC22×C43C2×#121
prime radical#19144747C2
hypercenter#1568D43
hypocenterC43#19278
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
1. #19144918C2semidirect
2. #19144758C2semidirect
4. C8×#10621898C2semidirect
5. #19134054C2semidirect
6. #19134047C2semidirect
7. #19134040C2semidirect
8. #19134033C2semidirect
9. #19134026C2semidirect
10. #19134019C2semidirect
11. #19134012C2semidirect
12. #19134005C2semidirect
13. #19133306C2semidirect
14. #19133301C2semidirect
15. C43×#1568C2semidirect
297. #1568D43semidirect
357. C43#19278semidirect

Maximal subgroups

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

subgroupindex
#191449182
#191447582
#191447472
C8×#106218982
#191340542
#191340472
#191340402
#191340332
#191340262
#191340192
#191340122
#191340052
#191333062
#191333012
C43×#15682
#1927843