Finite Group Databasebeta

← #25082120

Subgroups — #25082120

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145727C211yesmaximal, characteristic, complemented
2#19144757C211yesmaximal, characteristic, complemented
3#19143706C211yesmaximal, characteristic, complemented
4#19134037C211yesmaximal, characteristic, complemented
5#19134030C211yesmaximal, characteristic, complemented
6#19134009C211yesmaximal, characteristic, complemented
7#19134002C211yesmaximal, characteristic, complemented
8#19133997C211yesmaximal, characteristic, complemented
9#19133992C211yesmaximal, characteristic, complemented
10#19133979C211yesmaximal, characteristic, complemented
11#19133972C211yesmaximal, characteristic, complemented
12#19133373C211yesmaximal, characteristic, complemented
13#19133290C211yesmaximal, characteristic, complemented
14#19133250C211yesmaximal, characteristic, complemented
15C43×#3106C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583245C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583240—21no—
22#14583220—21no—
23#14583220—21no—
24#14583199—21no—
25#14583199—21no—
26#14583194C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583109C2211yescharacteristic
29#14583104C2211yescharacteristic
30#14583061—21no—
31Q8×C43⋊C8C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14583004—21no—
34#14582999—21no—
35D4×C43⋊C8—21no—
36D4×C43⋊C8—21no—
37D4×C43⋊C8C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582956C2211yescharacteristic
40#14582952—21no—
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)—21no—
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#482—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C4×SD16×C43—21no—
65C4×D8×C43—21no—
66C43×#431C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621883—21no—
69C22×C43⋊C8—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063317—21no—
75#13063304—21no—
76#13063304—21no—
77C4×Dic86—21no—
78C4×Dic86—21no—
79#13063284—21no—
80#13063258—21no—
81#13063258—21no—
82#13063258—21no—
83#13063256—21no—
84#13063256—21no—
85#13063256—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)D411yescharacteristic
90C4⋊(C43⋊C8)D411yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063248—21no—
97#13063248—21no—
98#13063246—21no—
99#13063246—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)D411yescharacteristic
107C22⋊(C43⋊C8)D411yescharacteristic
108#13063236—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×#41×C43D411yescharacteristic
115C2×SD16×C43—21no—
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#124×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43D411yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—82no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164SD16×C43—42no—
165D8×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43#4111yescharacteristic
185C42×C43C2411yescharacteristic
186C22⋊Dic43—41no—
187#10621885—42no—
188#10621883—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—41no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43—41no—
209C23×C43#12111yescharacteristic
210Q8×C43—21no—
211Q8×C43—81no—
212Q8×C43#13512yes—
213D4×C43—24no—
214D4×C43—21no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—81no—
220D4×C43—82no—
221D4×C43#13512yes—
222C2×C4×C43—24no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—81no—
235C2×C4×C43—82no—
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×Dic43—41no—
243C2×Dic43—41no—
244Dic86—41no—
245Dic86—41no—
246Dic86—81no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19419—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—22no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43C2×#12111yescharacteristic
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—22no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43C2×#13511yescharacteristic
277C4×C43C2×#13511yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57811yescharacteristic
280Dic43—81no—
281Dic43—81no—
282#3228—431no—
283#3116—431no—
284#3106D4311yescharacteristic
285#2988—431no—
286#1682—431no—
287#1681—431no—
288#1678—431no—
289#1677—431no—
290#1676—431no—
291#1675—431no—
292#1672—431no—
293#1671—431no—
294#1572—431no—
295#1551—431no—
296#1542—431no—
297C2×C43—41no—
298C2×C43—42no—
299C2×C43—161no—
300C2×C43#304611yescharacteristic
301C2×C43#305011yescharacteristic
302C2×C43#306811yescharacteristic
303#533—431no—
304#532C2×D4311yescharacteristic
305C4×#41C2×D4311yescharacteristic
306#500—431no—
307#498—431no—
308#486—431no—
309#486—431no—
310#485—861no—
311#482—21no—
312#482—861no—
313#482—861no—
314#478—861no—
315#478—861no—
316#477—431no—
317#477C2×D4311yescharacteristic
318#476—431no—
319#476C2×D4311yescharacteristic
320#462—431no—
321#461—431no—
322#460C2×D4311yescharacteristic
323#459C2×D4311yescharacteristic
324#452—861no—
325#449—21no—
326C8×Q8—431no—
327C8×Q8—431no—
328#441—861no—
329#440—861no—
330C4×SD16—21no—
331C4×D8—21no—
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335C8×D4—861no—
336#432—431no—
337#431—431no—
338#431—861no—
339#431C2×D4311yescharacteristic
340C2×C4⋊C8—431no—
341C2×C4⋊C8—861no—
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#331—431no—
353#331—431no—
354C43#1941911yescharacteristic, complemented, Sylow
355C2×#41—21no—
356C2×#41C22⋊D4311yescharacteristic
357C2×Q16—861no—
358C2×SD16—21no—
359C2×SD16—861no—
360C2×D8—21no—
361C22×C8—861no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8C22×D4311yescharacteristic
367#127C22×D4311yescharacteristic
368#125—861no—
369#124—21no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—21no—
373#121—21no—
374C4×Q8—861no—
375C4×Q8—861no—
376C4×Q8C22⋊D4311yescharacteristic
377C4×Q8C22×D4311yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C22⋊D4311yescharacteristic
383C4×D4C22×D4311yescharacteristic
384#117—21no—
385#117—861no—
386#117C22⋊D4311yescharacteristic
387C2×C42—21no—
388C2×C42C22×D4311yescharacteristic
389#107—21no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—21no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—21no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—431no—
422C22⋊C8—431no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427C4×C8—21no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—861no—
431C4×C8—861no—
432#41—22no—
433#41—22no—
434#41—82no—
435C2×Q8—21no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8C2×C22⋊D4311yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4C2×C22⋊D4311yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4D4×D4311yescharacteristic
450C22×C4#1062190011yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452Q16—1722no—
453SD16—42no—
454SD16—1722no—
455D8—42no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—3441no—
467C2×C8—3441no—
468C2×C8—3441no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4C2×C22⋊D4311yescharacteristic
480C4⋊C4C2×C22⋊D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—1721no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—1721no—
491C42D4×D4311yescharacteristic
492C42#1062190011yescharacteristic
493C42C2×C22⋊D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—21no—
496C23—41no—
497C23#1306329711yescharacteristic
498Q8—21no—
499Q8—81no—
500Q8—3441no—
501Q8—1721no—
502Q8—1721no—
503Q8#1306334512yes—
504D4—24no—
505D4—21no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—81no—
511D4—82no—
512D4#1306334512yes—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—81no—
526C2×C4—82no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306329711yescharacteristic
530C2×C4#1306329711yescharacteristic
531C2×C4#1306329711yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C22×C22⋊D4311yescharacteristic
534C2×C4C2×#1062190011yescharacteristic
535C8—41no—
536C8—41no—
537C8—861no—
538C8—861no—
539C8—861no—
540C8—861no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22C2×#1306329711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—3441no—
564C4—3441no—
565C4C2×#1306334511yescharacteristic
566C4C2×#1306334511yescharacteristic
567C4#1458370611yescharacteristic
568C4#1458371311yescharacteristic
569C2—41no—
570C2—42no—
571C2—161no—
572C2#1914414311yescharacteristic
573C2#1914417311yescharacteristic
574C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3106C2
socleC22×C43C2×#121
hypercenter#3106D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #19145727C2semidirect
2. #19144757C2semidirect
3. #19143706C2semidirect
4. #19134037C2semidirect
5. #19134030C2semidirect
6. #19134009C2semidirect
7. #19134002C2semidirect
8. #19133997C2semidirect
9. #19133992C2semidirect
10. #19133979C2semidirect
11. #19133972C2semidirect
12. #19133373C2semidirect
13. #19133290C2semidirect
14. #19133250C2semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191457272
#191447572
#191437062
#191340372
#191340302
#191340092
#191340022
#191339972
#191339922
#191339792
#191339722
#191333732
#191332902
#191332502
C43×#31062
#1941943