Finite Group Databasebeta

← #25084220

Subgroups — #25084220

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145813C211yesmaximal, characteristic, complemented
2#19145713C211yesmaximal, characteristic, complemented
3#19143755C211yesmaximal, characteristic, complemented
4#19134133C211yesmaximal, characteristic, complemented
5#19134126C211yesmaximal, characteristic, complemented
6#19134121C211yesmaximal, characteristic, complemented
7#19134116C211yesmaximal, characteristic, complemented
8#19134009C211yesmaximal, characteristic, complemented
9#19134002C211yesmaximal, characteristic, complemented
10#19133997C211yesmaximal, characteristic, complemented
11#19133992C211yesmaximal, characteristic, complemented
12#19133378C211yesmaximal, characteristic, complemented
13#19133290C211yesmaximal, characteristic, complemented
14C2×#14582647C211yesmaximal, characteristic, complemented
15C43×#3247C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17#14583309—21no—
18#14583302C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583258—21no—
21#14583245C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583227—21no—
24#14583210—21no—
25#14583210—21no—
26#14583210—21no—
27#14583194C2211yescharacteristic
28#14583194C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583179—21no—
32#14583179—21no—
33#14583030C2211yescharacteristic
34Q8×C43⋊C8C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582956C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582926—21no—
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#478—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#466—21no—
62C43×#465—21no—
63C43×#463—21no—
64C43×#460C2211yescharacteristic
65C43×#459C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621877—21no—
69C22×C43⋊C8—21no—
70C22×C43⋊C8—21no—
71#13063325—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78#13063258—21no—
79#13063258—21no—
80#13063258—21no—
81#13063258—21no—
82#13063258—21no—
83#13063258—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#13063249—21no—
97#13063246—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—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43—21no—
114C2×SD16×C43—21no—
115C2×D8×C43—21no—
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43—21no—
122#124×C43D411yescharacteristic
123#123×C43—21no—
124C22⋊Q8×C43D411yescharacteristic
125#121×C43—21no—
126#121×C43—21no—
127#121×C43D411yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×Dic43—41no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86—82no—
163SD16×C43—81no—
164D8×C43—81no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C42×C43—21no—
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43#4111yescharacteristic
187C42×C43C2411yescharacteristic
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43—41no—
194#10621877—81no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C23×C43—21no—
206C23×C43—41no—
207C23×C43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—81no—
211D4×C43—21no—
212D4×C43—21no—
213D4×C43—42no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—81no—
219D4×C43—82no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—82no—
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—82no—
241Dic86—82no—
242Dic86—81no—
243Dic86—81no—
244C8×C43—41no—
245C8×C43—41no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#19591—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43#47212yes—
264C22×C43C2×#12111yescharacteristic
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—81no—
273C4×C43#57711yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57811yescharacteristic
276C4×C43#57811yescharacteristic
277Dic43—81no—
278Dic43—81no—
279#3247D4311yescharacteristic
280#3238—431no—
281#3226—431no—
282#2994—431no—
283#1698—431no—
284#1697—431no—
285#1696—431no—
286#1695—431no—
287#1678—431no—
288#1677—431no—
289#1676—431no—
290#1675—431no—
291#1573—431no—
292#1551—431no—
293C2×#333—431no—
294C2×C43—22no—
295C2×C43—81no—
296C2×C43—161no—
297C2×C43#304611yescharacteristic
298C2×C43#306311yescharacteristic
299C2×C43C2×#47211yescharacteristic
300#532C2×D4311yescharacteristic
301C2×C4⋊Q8—431no—
302#529C2×D4311yescharacteristic
303#501—861no—
304#500—431no—
305#500—431no—
306#489—861no—
307#486—431no—
308#486—431no—
309#483—861no—
310#480—861no—
311#480—861no—
312#480—861no—
313#478—21no—
314#477—431no—
315#477—431no—
316#477C2×D4311yescharacteristic
317#476—431no—
318#476—431no—
319#476C2×D4311yescharacteristic
320#474—861no—
321#474—861no—
322#466—21no—
323#465—21no—
324#463—21no—
325#460C2×D4311yescharacteristic
326#459C2×D4311yescharacteristic
327#446—431no—
328C8×Q8—431no—
329#436—431no—
330#435—861no—
331C8×D4—431no—
332C8×D4—861no—
333#433—861no—
334#432—431no—
335#431—431no—
336#424—861no—
337C2×C4⋊C8—431no—
338C2×C4⋊C8C2×D4311yescharacteristic
339#335—431no—
340#335—431no—
341#334—431no—
342#334—431no—
343#333—431no—
344#333—431no—
345#333—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#331—431no—
350#331—431no—
351C43#1959111yescharacteristic, complemented, Sylow
352C2×#41—21no—
353C22×Q8—861no—
354C2×SD16—21no—
355C2×D8—21no—
356C2×M16—861no—
357C22×C8—21no—
358C22×C8—861no—
359C22×C8—861no—
360C4⋊Q8—431no—
361C4⋊Q8—431no—
362C4⋊Q8—861no—
363C4⋊Q8—861no—
364C4⋊Q8—861no—
365C4⋊Q8C22×D4311yescharacteristic
366#127C22×D4311yescharacteristic
367#126—21no—
368#125C22⋊D4311yescharacteristic
369#124—21no—
370#124C22⋊D4311yescharacteristic
371#123—21no—
372C22⋊Q8C22⋊D4311yescharacteristic
373#121—21no—
374#121—21no—
375#121C22⋊D4311yescharacteristic
376C4×Q8C22×D4311yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C22×D4311yescharacteristic
381#117—21no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C42C22×D4311yescharacteristic
385#107—21no—
386#107—861no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—21no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—21no—
408#103—861no—
409#103—861no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—431no—
420C22⋊C8—431no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—861no—
425#97—861no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—861no—
429#41—82no—
430C2×Q8—21no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—3442no—
434C2×Q8—1721no—
435C2×Q8C2×C22⋊D4311yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4C2×C22⋊D4311yescharacteristic
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—1721no—
445C22×C4D4×D4311yescharacteristic
446C22×C4#1062190011yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448SD16—81no—
449D8—81no—
450M16—3441no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—3441no—
463C2×C8—3441no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4C2×C22⋊D4311yescharacteristic
477C4⋊C4C2×C22⋊D4311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42D4×D4311yescharacteristic
487C42#1062190011yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—21no—
491C23—41no—
492C23#1306329711yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—81no—
496Q8—3441no—
497Q8—3441no—
498Q8—3442no—
499D4—21no—
500D4—21no—
501D4—42no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507D4—82no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—3442no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4#1306329711yescharacteristic
524C2×C4#1306329711yescharacteristic
525C2×C4#1306329711yescharacteristic
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C2×C4C2×#1062190011yescharacteristic
529C8—41no—
530C8—41no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22#1458316712yes—
548C22C2×#1306329711yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—3441no—
558C4—3441no—
559C4#1458370611yescharacteristic
560C4#1458371011yescharacteristic
561C4#1458371311yescharacteristic
562C4#1458371411yescharacteristic
563C2—22no—
564C2—81no—
565C2—161no—
566C2#1914414311yescharacteristic
567C2#1914428811yescharacteristic
568C2C2×#1458316711yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3247C2
socleC22×C43C2×#121
hypercenter#3247D43
hypocenterC43#19591
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3247

Complements

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

NH ≅ G/Ntype
1. #19145813C2semidirect
2. #19145713C2semidirect
3. #19143755C2semidirect
4. #19134133C2semidirect
5. #19134126C2semidirect
6. #19134121C2semidirect
7. #19134116C2semidirect
8. #19134009C2semidirect
9. #19134002C2semidirect
10. #19133997C2semidirect
11. #19133992C2semidirect
12. #19133378C2semidirect
13. #19133290C2semidirect
14. C2×#14582647C2semidirect
351. C43#19591semidirect

Maximal subgroups

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

subgroupindex
#191458132
#191457132
#191437552
#191341332
#191341262
#191341212
#191341162
#191340092
#191340022
#191339972
#191339922
#191333782
#191332902
C2×#145826472
C43×#32472
#1959143