Finite Group Databasebeta

← #25074358

Subgroups — #25074358

Order 11008.

946 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148444C211yesmaximal, characteristic
2#19145937C211yesmaximal, characteristic, complemented
3#19144388C211yesmaximal, characteristic, complemented
4#19133862C212yesmaximal, complemented
5#19133785C212yesmaximal, complemented
6#19133764C212yesmaximal, complemented
7#19133719C212yesmaximal, complemented
8#19133272C211yesmaximal, characteristic, complemented
9#19133051C211yesmaximal, characteristic, complemented
10C2×#14582628C211yesmaximal, characteristic, complemented
11C43×#3167C211yesmaximal, characteristic, complemented
12#14583631—22no—
13#14583623C2212yes—
14#14583614—21no—
15#14583595—22no—
16#14583569C2212yes—
17#14583553—21no—
18#14583486—22no—
19#14583463—21no—
20#14583456C2211yescharacteristic
21#14583409—22no—
22#14583382—21no—
23C2×C4×D172C2211yescharacteristic
24#14583196—22no—
25#14583194—21no—
26#14583191C2212yescomplemented
27#14583186C2212yes—
28#14583176C2212yes—
29#14583138—22no—
30#14583109—21no—
31#14583106C2212yescomplemented
32#14582942—21no—
33#14582923C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35#14582903—21no—
36#14582645C2212yescomplemented
37#14582643C2212yescomplemented
38#14582631C2212yescomplemented
39#14582631C2212yescomplemented
40#14582628C2212yes—
41#14582628C2212yes—
42C43×#533C2211yescharacteristic
43C43×#532C2211yescharacteristic
44C43×#498C2211yescharacteristic, complemented
45C43×#492C2211yescharacteristic, complemented
46C43×#487C2211yescharacteristic, complemented
47C43×#486C2211yescharacteristic, complemented
48C43×#465—22no—
49C4×SD16×C43—22no—
50C2×C4×C8×C43C2211yescharacteristic
51C2×#10621900—22no—
52C22×D172D411yescharacteristic
53C22×C4×D43—21no—
54C2×#10621885—22no—
55C2×#10621877—21no—
56C22×C43⋊C8—21no—
57#13063325D411yescharacteristic
58#13063325D411yescharacteristic
59#13063321—22no—
60#13063320—24no—
61#13063317—21no—
62#13063314—22no—
63#13063311—24no—
64#13063309—24no—
65#13063307—24no—
66#13063305—22no—
67#13063304—21no—
68#13063304D412yes—
69#13063299—22no—
70#13063299—22no—
71#13063297—24no—
72#13063296—22no—
73#13063293—24no—
74Q8×Dic43—22no—
75C4×Dic86—21no—
76C4×Dic86C2312yes—
77C4×D172—21no—
78C4×D172—21no—
79C4×D172D412yes—
80C4×D172C2312yes—
81D4×Dic43—24no—
82D4×Dic43—22no—
83(C22⋊D43)⋊C4—24no—
84#13063284—22no—
85#13063284—21no—
86#13063283—22no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43D411yescharacteristic
89C2×(C2×D43)⋊C4—21no—
90#13063258—22no—
91#13063258—22no—
92#13063256—22no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2312yes—
96C4⋊(C43⋊C8)C2312yes—
97#13063249—22no—
98#13063248—22no—
99#13063245—22no—
100#13063245—22no—
101C2×#41×C43—21no—
102C2×SD16×C43—22no—
103C22×C8×C43—21no—
104C4⋊Q8×C43C2311yescharacteristic
105C4⋊Q8×C43C2311yescharacteristic
106C4⋊Q8×C43C2311yescharacteristic
107#127×C43C2311yescharacteristic
108#125×C43—21no—
109#124×C43—21no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—21no—
112#121×C43—21no—
113#121×C43D412yes—
114C4×Q8×C43—21no—
115C4×Q8×C43—21no—
116C4×D4×C43—21no—
117C4×D4×C43D412yes—
118#117×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#106×C43—22no—
121#103×C43—22no—
122#102×C43—22no—
123C4×C8×C43—21no—
124C4×C8×C43C2311yescharacteristic
125C4×C8×C43C2311yescharacteristic
126C23×D43—21no—
127#41×C43—42no—
128#41×C43—42no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—22no—
135C2×D4×C43C2×D412yes—
136C22×C4×C43—22no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C2×C22⋊D43—24no—
141C2×C22⋊D43—24no—
142C22×Dic43—24no—
143C22×Dic43—21no—
144#10621900—82no—
145#10621900—82no—
146C2×D172—21no—
147C2×D172—22no—
148C2×D172—22no—
149C2×D172C2×D412yes—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—81no—
153C2×C4×D43—81no—
154C2×Dic86—21no—
155C2×Dic86C2×D412yes—
156SD16×C43—44no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—42no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—41no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43C2×D412yes—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—41no—
171C42×C43—41no—
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43C2411yescharacteristic
176C22⋊Dic43—24no—
177C22⋊Dic43—22no—
178#10621885—82no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—22no—
183C4⋊Dic43—24no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43C2×D412yes—
189C4⋊Dic43C2×D412yes—
190Dic43⋊C4—22no—
191Dic43⋊C4—22no—
192C4×Dic43—24no—
193C4×Dic43—22no—
194#10621877—42no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—81no—
198C23×C43—22no—
199C23×C43#12011yescharacteristic
200C22×D43—22no—
201C22×D43—42no—
202C22×D43—81no—
203C22×D43—81no—
204Q8×C43—42no—
205Q8×C43—41no—
206Q8×C43—41no—
207Q8×C43—41no—
208Q8×C43—41no—
209D4×C43—42no—
210D4×C43—44no—
211D4×C43—41no—
212D4×C43—41no—
213D4×C43—41no—
214D4×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—41no—
219C2×C4×C43—44no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43#12011yescharacteristic
225C2×C4×C43#13512yes—
226C2×C4×C43#13712yes—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C22⋊D43—84no—
231C22⋊D43—84no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—81no—
236C2×Dic43—84no—
237D172—22no—
238D172—22no—
239D172—42no—
240C4×D43—42no—
241C4×D43—42no—
242C4×D43—82no—
243Dic86—22no—
244Dic86—22no—
245Dic86—81no—
246C8×C43—22no—
247C8×C43—41no—
248C43⋊C8—42no—
249C43⋊C8—42no—
250#18679—431nomaximal, Sylow
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—42no—
254C22×C43—42no—
255C22×C43—42no—
256C22×C43#45212yes—
257C22×C43C2×#12011yescharacteristic
258C2×D43—42no—
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—84no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—42no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43#45212yes—
269C4×C43C2×#13511yescharacteristic
270C4×C43C2×#13711yescharacteristic
271C4×C43#57611yescharacteristic
272C4×C43#57711yescharacteristic
273Dic43—42no—
274Dic43—42no—
275Dic43—42no—
276#3506—431no—
277#3249—431no—
278#3167D4311yescharacteristic, complemented
279#3077—431no—
280#1652—432no—
281#1641—432no—
282#1638—432no—
283#1631—432no—
284#1547—431no—
285#1493—431no—
286C2×D4⋊C8—431no—
287C2×C43—22no—
288C2×C43—82no—
289C2×C43C2×#45211yescharacteristic
290C2×C43#301211yescharacteristic
291C2×C43#301811yescharacteristic
292D43—82no—
293#559—862no—
294#556—432no—
295#555—861no—
296#553—862no—
297#550—432no—
298#547—861no—
299#538—862no—
300#535—861no—
301#533—431no—
302#533C2×D4311yescharacteristic
303#532C2×D4311yescharacteristic
304#525—862no—
305#520—861no—
306C2×C4×D4—431no—
307#498C2×D4311yescharacteristic, complemented
308#492C2×D4311yescharacteristic, complemented
309#487C2×D4311yescharacteristic, complemented
310#486C2×D4311yescharacteristic, complemented
311#478—862no—
312#477—432no—
313#477—861no—
314#476—432no—
315#474—432no—
316#467—862no—
317#465—22no—
318#462—432no—
319#462—861no—
320C4×SD16—22no—
321#428—861no—
322#423—431no—
323C2×C4⋊C8—431no—
324#418—861no—
325C2×C4×C8C2×D4311yescharacteristic
326#332—432no—
327#331—432no—
328Q8⋊C8—432no—
329Q8⋊C8—432no—
330D4⋊C8—432no—
331D4⋊C8—432no—
332C43#1867911yescharacteristic, complemented, Sylow
333C2×#41—21no—
334C2×#41—862no—
335C22×D4—431no—
336C23×C4—861no—
337C2×Q16—862no—
338C2×SD16—22no—
339C2×M16—861no—
340C22×C8—21no—
341C22×C8—861no—
342C4⋊Q8—431no—
343C4⋊Q8—431no—
344C4⋊Q8C22×D4311yescharacteristic
345C4⋊Q8C22×D4311yescharacteristic
346C4⋊Q8C22×D4311yescharacteristic
347#127—862no—
348#127C22×D4311yescharacteristic
349#126—864no—
350#125—21no—
351#125—861no—
352#124—21no—
353#124—864no—
354#124—862no—
355#123—864no—
356#123—864no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—432no—
360C22⋊Q8—862no—
361C22⋊Q8—861no—
362#121—21no—
363#121—862no—
364#121—862no—
365#121—862no—
366#121—864no—
367#121C22⋊D4312yes—
368#120—864no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—432no—
372C4×Q8—862no—
373C4×Q8—861no—
374C4×D4—21no—
375C4×D4—432no—
376C4×D4—432no—
377C4×D4—864no—
378C4×D4—862no—
379C4×D4—864no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4C22⋊D4312yes—
383#117—21no—
384#117—862no—
385#117—862no—
386#117—861no—
387C2×C4⋊C4—431no—
388C2×C4⋊C4—862no—
389C2×C22⋊C4—861no—
390C2×C42C22×D4311yescharacteristic
391#107—862no—
392#107—862no—
393#106—22no—
394#106—862no—
395C4⋊C8—432no—
396C4⋊C8—432no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399#103—22no—
400#103—862no—
401#103—862no—
402#102—22no—
403#102—862no—
404#102—862no—
405C4×C8—21no—
406C4×C8C22×D4311yescharacteristic
407C4×C8C22×D4311yescharacteristic
408C24—861no—
409#41—42no—
410#41—42no—
411#41—3442no—
412#41—3442no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—432no—
417C2×Q8—861no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—432no—
422C2×D4—864no—
423C2×D4—864no—
424C2×D4—861no—
425C2×D4—862no—
426C2×D4—862no—
427C2×D4C2×C22⋊D4312yes—
428C22×C4—22no—
429C22×C4—864no—
430C22×C4—861no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—3441no—
434C22×C4—3441no—
435C22×C4D4×D4311yescharacteristic
436C22×C4D4×D4311yescharacteristic
437C22×C4C2×C22⋊D4311yescharacteristic
438Q16—3442no—
439SD16—44no—
440M16—1722no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—42no—
444C2×C8—862no—
445C2×C8—862no—
446C2×C8—3441no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—432no—
455C4⋊C4—432no—
456C4⋊C4—864no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—862no—
461C4⋊C4—861no—
462C4⋊C4—862no—
463C4⋊C4C2×C22⋊D4312yes—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—41no—
467C22⋊C4—864no—
468C22⋊C4—864no—
469C22⋊C4—864no—
470C22⋊C4—862no—
471C22⋊C4—862no—
472C22⋊C4—862no—
473C42—41no—
474C42—864no—
475C42—862no—
476C42D4×D4311yescharacteristic
477C42D4×D4311yescharacteristic
478C42C2×C22⋊D4311yescharacteristic
479C42C23×D4311yescharacteristic
480C23—22no—
481C23—862no—
482C23—3441no—
483C23—3441no—
484C23—1722no—
485C23#1306329311yescharacteristic
486Q8—42no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—862no—
492Q8—862no—
493Q8—3441no—
494D4—42no—
495D4—44no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—862no—
501D4—862no—
502D4—3444no—
503D4—3444no—
504D4—1722no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—44no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—3442no—
516C2×C4—3441no—
517C2×C4—3444no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4#1306329311yescharacteristic
521C2×C4#1306329311yescharacteristic
522C2×C4#1306329311yescharacteristic
523C2×C4#1306334612yes—
524C2×C4#1306335412yes—
525C2×C4C2×D4×D4311yescharacteristic
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C8—22no—
529C8—41no—
530C8—1722no—
531C8—1722no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—3444no—
538C22—1722no—
539C22—1722no—
540C22—1722no—
541C22#1458305812yes—
542C22C2×#1306329311yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—81no—
548C4—81no—
549C4—1722no—
550C4—1722no—
551C4—1722no—
552C4#1458305812yes—
553C4C2×#1306334611yescharacteristic
554C4C2×#1306335411yescharacteristic
555C4#1458370111yescharacteristic
556C4#1458370611yescharacteristic
557C2—22no—
558C2—82no—
559C2—3442no—
560C2C2×#1458305811yescharacteristic
561C2#1914389511yescharacteristic
562C2#1914394311yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3167C2
socleC22×C43C2×#120
prime radical#19148444C2
hypercenter#3167D43
hypocenterC43#18679
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
2. #19145937C2semidirect
3. #19144388C2semidirect
4. #19133862C2semidirect
5. #19133785C2semidirect
6. #19133764C2semidirect
7. #19133719C2semidirect
8. #19133272C2semidirect
9. #19133051C2semidirect
10. C2×#14582628C2semidirect
11. C43×#3167C2semidirect
26. #14583191C22semidirect
31. #14583106C22semidirect
36. #14582645C22semidirect
37. #14582643C22semidirect
38. #14582631C22semidirect
39. #14582631C22semidirect
44. C43×#498C22semidirect
45. C43×#492C22semidirect
46. C43×#487C22semidirect
47. C43×#486C22semidirect
278. #3167D43semidirect
307. #498C2×D43semidirect
308. #492C2×D43semidirect
309. #487C2×D43semidirect
310. #486C2×D43semidirect
332. C43#18679semidirect

Maximal subgroups

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

subgroupindex
#191484442
#191459372
#191443882
#191338622
#191337852
#191337642
#191337192
#191332722
#191330512
C2×#145826282
C43×#31672
#1867943