Finite Group Databasebeta

← #25064177

Subgroups — #25064177

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148683C211yesmaximal, characteristic
2#19143682C211yesmaximal, characteristic, complemented
3#19137241C211yesmaximal, characteristic, complemented
4#19133171C212yesmaximal
5#19133157C212yesmaximal, complemented
6#19133144C212yesmaximal, complemented
7#19133132C212yesmaximal
8#19133118C211yesmaximal, characteristic
9#19133107C211yesmaximal, characteristic, complemented
10#19133082C211yesmaximal, characteristic
11C43×#1503C211yesmaximal, characteristic, complemented
12#14583625C412yescomplemented
13#14583624C411yescharacteristic, complemented
14#14583624C411yescharacteristic, complemented
15#14583623C411yescharacteristic, complemented
16#14583621C412yescomplemented
17#14583591—21no—
18#14583582—22no—
19#14583564C411yescharacteristic, complemented
20#14583562—21no—
21#14583508—22no—
22#14583507—21no—
23#14583451C2212yes—
24#14583435C2212yes—
25#14583433C2211yescharacteristic
26#14583375—21no—
27C2×C4×Dic86C2211yescharacteristic
28#14583029—21no—
29#14583028—22no—
30C8×Dic86—21no—
31#14582956C2211yescharacteristic
32#14582953C2212yes—
33#14582949C2212yes—
34#14582804—21no—
35#14582795—21no—
36#14582783—22no—
37#14582766C2212yes—
38#14582763C2212yes—
39#14582745C2211yescharacteristic
40#14582637C2211yescharacteristic
41#14582637C2211yescharacteristic
42#14582636C2212yes—
43#14582636C2212yes—
44#14582635C2212yes—
45#14582634C2211yescharacteristic
46#14582634C2211yescharacteristic
47#14582632C2212yes—
48C43×#533C2211yescharacteristic
49C43×#431C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C43×#328C2212yes—
52C43×#328C2212yes—
53C22×Dic86D411yescharacteristic
54C2×Q8×D43—21no—
55#13063324—22no—
56#13063324C2×C412yes—
57#13063323—21no—
58#13063323C2×C412yes—
59#13063320—22no—
60#13063320—22no—
61#13063320—22no—
62#13063319—21no—
63#13063319—22no—
64#13063317—22no—
65#13063317C2×C411yescharacteristic
66#13063316—21no—
67#13063316—22no—
68#13063316C2×C412yes—
69#13063315—22no—
70#13063315—22no—
71#13063315—22no—
72#13063314C2×C412yes—
73#13063313C2×C411yescharacteristic
74#13063309—22no—
75#13063308—21no—
76#13063305—21no—
77#13063304C2311yescharacteristic
78#13063303—22no—
79#13063303—22no—
80#13063302—22no—
81#13063301—21no—
82#13063299C2311yescharacteristic
83Q8×Dic43—21no—
84Q8×Dic43C2×C412yes—
85Q8×Dic43C2×C412yes—
86C4×Dic86—22no—
87C4×Dic86C2×C411yescharacteristic
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86C2×C412yes—
90C4×Dic86C2×C411yescharacteristic
91C4×Dic86D411yescharacteristic
92C4×Dic86D411yescharacteristic
93C4×Dic86D412yes—
94#13063290—21no—
95#13063290—22no—
96#13063290C2×C412yes—
97C4×D172C2×C411yescharacteristic
98#13063287C2×C412yes—
99C4×C22⋊D43—21no—
100(C22⋊D43)⋊C4—22no—
101#13063283—21no—
102#13063283—22no—
103#13063282—21no—
104#13063282—22no—
105#13063281—22no—
106C2×C4⋊Dic43D411yescharacteristic
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4D412yes—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2312yes—
111C4⋊(C43⋊C8)—21no—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114C22⋊(C43⋊C8)C2312yes—
115#13063236—21no—
116#13063235—22no—
117C8×Dic43—22no—
118C43⋊#95—21no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95C2311yescharacteristic
123C43⋊#95C2311yescharacteristic
124C4⋊Q8×C43C2×C411yescharacteristic
125C4⋊Q8×C43C2×C411yescharacteristic
126#125×C43—21no—
127C22⋊Q8×C43—21no—
128C22⋊Q8×C43C2312yes—
129C4×Q8×C43—21no—
130C4×Q8×C43C2×C412yes—
131#117×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2311yescharacteristic
137C22⋊C8×C43C2311yescharacteristic
138C4×C8×C43—21no—
139#95×C43C2312yes—
140C2×Q8×C43—21no—
141C2×Q8×C43C22×C412yes—
142C22×C4×C43—22no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D412yes—
150C22×Dic43C2×D412yes—
151Q8×D43—44no—
152C2×D172C22×C411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—22no—
155C2×Dic86—22no—
156C2×Dic86—42no—
157C2×Dic86C22⋊C411yescharacteristic
158C2×Dic86C22⋊C411yescharacteristic
159C2×Dic86C22⋊C412yes—
160C2×Dic86C22×C411yescharacteristic
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43C22×C412yes—
170C22⋊C4×C43—22no—
171C42×C43—22no—
172C42×C43—81no—
173C42×C43C22×C411yescharacteristic
174C42×C43C22×C411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C22⋊Dic43—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—22no—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43C22⋊C411yescharacteristic
189C4⋊Dic43C22⋊C411yescharacteristic
190C4⋊Dic43C22⋊C412yes—
191C4⋊Dic43C22×C411yescharacteristic
192C4⋊Dic43C22×C411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—82no—
203Dic43⋊C4C22⋊C412yes—
204Dic43⋊C4C22⋊C412yes—
205Dic43⋊C4C22⋊C412yes—
206Dic43⋊C4C22⋊C412yes—
207C4×Dic43—21no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—42no—
212C4×Dic43C22×C412yes—
213C4×Dic43C22×C412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43C2×D412yes—
216C2×C43⋊C8—22no—
217C23×C43C22×D411yescharacteristic
218C22×D43—21no—
219Q8×C43—42no—
220Q8×C43—42no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—41no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43C2×C22⋊C411yescharacteristic
231C2×C4×C43C2×C22⋊C411yescharacteristic
232C2×C4×C43C2×C22⋊C411yescharacteristic
233C2×C4×C43C2×C22⋊C411yescharacteristic
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C22⋊D43—41no—
237C22⋊D43—41no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—42no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43C2×C22⋊C412yes—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43C2×C22⋊C412yes—
253C2×Dic43C2×C22⋊C412yes—
254D172—41no—
255C4×D43—44no—
256C4×D43—42no—
257Dic86—22no—
258Dic86—22no—
259Dic86—42no—
260Dic86—44no—
261Dic86—41no—
262C8×C43—41no—
263C8×C43—41no—
264C43⋊C8—42no—
265#17601—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43C22×C22⋊C411yescharacteristic
269C22×C43#57711yescharacteristic
270C22×C43#57811yescharacteristic
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—41no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—42no—
280C4×C43—42no—
281C4×C43—82no—
282C4×C43#42112yes—
283Dic43—22no—
284Dic43—22no—
285Dic43—22no—
286Dic43—22no—
287Dic43—41no—
288Dic43—41no—
289Dic43—41no—
290Dic43—81no—
291Dic43—81no—
292#3523—431no—
293#2984—431no—
294#2320—431no—
295#1521—432no—
296#1518—432no—
297#1515—432no—
298#1512—432no—
299#1509—431no—
300#1506—431no—
301#1503D4311yescharacteristic, complemented
302#1500—431no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43#288411yescharacteristic
306C2×C43#289811yescharacteristic
307C2×C43C2×#42111yescharacteristic
308D43—81no—
309#557—431no—
310#557—431no—
311#557—432no—
312#556—431no—
313#556—432no—
314#552—862no—
315#552—861no—
316D4×Q8—431no—
317D4×Q8—861no—
318#541—861no—
319#541—862no—
320#533—432no—
321#533C2×D4311yescharacteristic
322#529—432no—
323#529—431no—
324#519—861no—
325C2×C4×Q8—431no—
326#446—861no—
327#446—862no—
328C8×Q8—861no—
329#432—431no—
330#432—432no—
331#431—432no—
332#431C2×D4311yescharacteristic
333#391—861no—
334#389—861no—
335#387—862no—
336#383—432no—
337#382—432no—
338C4×C4⋊C4C2×D4311yescharacteristic
339#376—431no—
340#328—432no—
341#328—432no—
342#328—431no—
343#328—431no—
344#328—432no—
345#328C2×D4312yes—
346#328C2×D4312yes—
347#327—431no—
348#327—431no—
349#327—432no—
350C43#1760111yescharacteristic, complemented, Sylow
351C22×Q8—431no—
352C22×Q8—861no—
353C4⋊Q8—432no—
354C4⋊Q8—432no—
355C4⋊Q8—862no—
356C4⋊Q8—861no—
357C4⋊Q8C4×D4311yescharacteristic
358C4⋊Q8C4×D4311yescharacteristic
359#126—862no—
360#126—862no—
361#126—862no—
362#126—862no—
363#126—861no—
364#125—21no—
365#125—432no—
366#125—431no—
367#125—862no—
368#125—862no—
369#125—862no—
370#125—862no—
371#125—862no—
372#125—861no—
373#124—432no—
374#124—431no—
375#123—862no—
376#123—861no—
377C22⋊Q8—21no—
378C22⋊Q8—431no—
379C22⋊Q8—862no—
380C22⋊Q8—862no—
381C22⋊Q8—862no—
382C22⋊Q8—861no—
383C22⋊Q8—861no—
384C22⋊Q8C22×D4312yes—
385#121—431no—
386C4×Q8—21no—
387C4×Q8—431no—
388C4×Q8—432no—
389C4×Q8—431no—
390C4×Q8—431no—
391C4×Q8—431no—
392C4×Q8—432no—
393C4×Q8—432no—
394C4×Q8—432no—
395C4×Q8—432no—
396C4×Q8—431no—
397C4×Q8—862no—
398C4×Q8—862no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8C4×D4312yes—
402C4×D4—432no—
403C4×D4—431no—
404C4×D4—862no—
405C4×D4—861no—
406#117—21no—
407#117—862no—
408#117—862no—
409#117—862no—
410#117—861no—
411#117—861no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—432no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—862no—
416C2×C42—21no—
417C2×C42—432no—
418C2×C42—861no—
419C2×C42C22×D4311yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—862no—
422C4⋊C8—862no—
423C4⋊C8—861no—
424C22⋊C8—432no—
425C22⋊C8C22×D4311yescharacteristic
426C22⋊C8C22×D4311yescharacteristic
427#97—862no—
428#97—861no—
429C4×C8—21no—
430C4×C8—862no—
431#95—431no—
432#95—431no—
433#95—862no—
434#95—862no—
435#95—862no—
436#95—861no—
437#95C22×D4312yes—
438C2×Q8—21no—
439C2×Q8—431no—
440C2×Q8—431no—
441C2×Q8—432no—
442C2×Q8—431no—
443C2×Q8—862no—
444C2×Q8—1722no—
445C2×Q8—1724no—
446C2×Q8C2×C4×D4312yes—
447C2×D4—431no—
448C2×D4—861no—
449C22×C4—22no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—862no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4C23×D4311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—862no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—432no—
469C4⋊C4—431no—
470C4⋊C4—432no—
471C4⋊C4—431no—
472C4⋊C4—432no—
473C4⋊C4—432no—
474C4⋊C4—432no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—3442no—
490C4⋊C4C2×C4×D4312yes—
491C22⋊C4—22no—
492C22⋊C4—862no—
493C22⋊C4—862no—
494C22⋊C4—862no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C42—22no—
501C42—81no—
502C42—432no—
503C42—432no—
504C42—432no—
505C42—432no—
506C42—862no—
507C42—862no—
508C42—862no—
509C42—861no—
510C42—1722no—
511C42C2×C4×D4311yescharacteristic
512C42C2×C4×D4311yescharacteristic
513C42D4×D4311yescharacteristic
514C42D4×D4311yescharacteristic
515C23—861no—
516C23C2×D4×D4311yescharacteristic
517Q8—42no—
518Q8—42no—
519Q8—862no—
520Q8—862no—
521Q8—1722no—
522Q8—1721no—
523Q8—1724no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—862no—
541C2×C4—862no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—1724no—
546C2×C4—1722no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1722no—
554C2×C4C22⋊C4×D4311yescharacteristic
555C2×C4C22⋊C4×D4311yescharacteristic
556C2×C4C22⋊C4×D4311yescharacteristic
557C2×C4C22⋊C4×D4311yescharacteristic
558C2×C4C22×C4×D4311yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C8—41no—
561C8—41no—
562C8—1722no—
563C22—21no—
564C22—21no—
565C22—1721no—
566C22—1721no—
567C22—1721no—
568C22C2×C22⋊C4×D4311yescharacteristic
569C22#1458370511yescharacteristic
570C22#1458371211yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—862no—
580C4—862no—
581C4—862no—
582C4—862no—
583C4—3441no—
584C4—3441no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4#1458291412yes—
589C2—21no—
590C2—21no—
591C2—3441no—
592C2#1914305711yescharacteristic
593C2#1914312311yescharacteristic
594C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1503C2
socleC22×C43C22×C22⋊C4
prime radical#13063299C23
cosocleC22×C4×C43C24
hypercenter#1503D43
hypocenterC43#17601
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. #19143682C2semidirect
3. #19137241C2semidirect
5. #19133157C2semidirect
6. #19133144C2semidirect
9. #19133107C2semidirect
11. C43×#1503C2semidirect
12. #14583625C4semidirect
13. #14583624C4semidirect
14. #14583624C4semidirect
15. #14583623C4semidirect
16. #14583621C4semidirect
19. #14583564C4semidirect
301. #1503D43semidirect
350. C43#17601semidirect

Maximal subgroups

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

subgroupindex
#191486832
#191436822
#191372412
#191331712
#191331572
#191331442
#191331322
#191331182
#191331072
#191330822
C43×#15032
#1760143