Finite Group Databasebeta

← #25084224

Subgroups — #25084224

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#19145921C211yesmaximal, characteristic
2#19145813C211yesmaximal, characteristic, complemented
3#19145718C211yesmaximal, characteristic, complemented
4#19134135C211yesmaximal, characteristic, complemented
5#19134128C211yesmaximal, characteristic, complemented
6#19134123C211yesmaximal, characteristic, complemented
7#19134118C211yesmaximal, characteristic, complemented
8#19134011C211yesmaximal, characteristic, complemented
9#19134004C211yesmaximal, characteristic, complemented
10#19133999C211yesmaximal, characteristic, complemented
11#19133994C211yesmaximal, characteristic, complemented
12#19133380C211yesmaximal, characteristic, complemented
13#19133288C211yesmaximal, characteristic, complemented
14C2×#14582647C211yesmaximal, characteristic, complemented
15C43×#2994C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583309—21no—
19#14583304C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583258—21no—
22#14583246C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583227—21no—
25#14583213—21no—
26#14583213—21no—
27#14583210—21no—
28#14583196—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583194C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583189C2211yescharacteristic
34#14583189C2211yescharacteristic
35#14583180—21no—
36#14583180—21no—
37#14583133—21no—
38#14583130—21no—
39#14583111—21no—
40#14583099C2211yescharacteristic
41#14583094C2211yescharacteristic
42#14582956C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436C2211yescharacteristic
60C43×#435—21no—
61C8×D4×C43—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#424—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C22×Dic86—21no—
69C2×#10621884—21no—
70C2×#10621882—21no—
71C22×C43⋊C8—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063313—21no—
80#13063299—21no—
81#13063299—21no—
82C4×D172—21no—
83C4×D172—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43—21no—
86#13063259—21no—
87#13063259—21no—
88#13063259—21no—
89#13063259—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063247—21no—
105#13063247—21no—
106#13063247—21no—
107#13063247—21no—
108#13063246—21no—
109#13063246—21no—
110#13063246—21no—
111#13063245—21no—
112#13063245—21no—
113C22⋊(C43⋊C8)—21no—
114#13063236—21no—
115C2×M16×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118#126×C43—21no—
119#125×C43D411yescharacteristic
120#124×C43D411yescharacteristic
121#123×C43—21no—
122C22⋊Q8×C43D411yescharacteristic
123#121×C43D411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—41no—
152C22×Dic43—41no—
153#10621898—82no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86—82no—
163M16×C43—81no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
167C2×C8×C43—81no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C42×C43—21no—
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43#4111yescharacteristic
187C42×C43C2411yescharacteristic
188#10621884—81no—
189#10621882—81no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C23×C43—21no—
206C23×C43#12111yescharacteristic
207C22×D43—41no—
208Q8×C43—21no—
209Q8×C43—21no—
210D4×C43—21no—
211D4×C43—21no—
212D4×C43—42no—
213C2×C4×C43—22no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C22⋊D43—82no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—82no—
234D172—41no—
235D172—41no—
236D172—41no—
237D172—41no—
238D172—81no—
239C4×D43—82no—
240Dic86—82no—
241Dic86—81no—
242Dic86—81no—
243Dic86—81no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C8×C43—41no—
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#47212yes—
261C22×C43C2×#12111yescharacteristic
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43#57711yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—81no—
277Dic43—81no—
278Dic43—81no—
279#3247—431no—
280#3238—431no—
281#3226—431no—
282#2994D4311yescharacteristic, complemented
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#304611yescharacteristic
297C2×C43#306311yescharacteristic
298C2×C43C2×#47211yescharacteristic
299D43—161no—
300#532—431no—
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—861no—
314#477—431no—
315#477—431no—
316#477—431no—
317#476—431no—
318#476—431no—
319#476—431no—
320#474—861no—
321#474—861no—
322#466—861no—
323#465—861no—
324#463—861no—
325#460—431no—
326#459—431no—
327#446C2×D4311yescharacteristic
328C8×Q8C2×D4311yescharacteristic
329#436C2×D4311yescharacteristic
330#435—21no—
331C8×D4—21no—
332C8×D4C2×D4311yescharacteristic
333#433—21no—
334#432—431no—
335#431C2×D4311yescharacteristic
336#424—21no—
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—861no—
353C22×Q8—861no—
354C2×SD16—861no—
355C2×D8—861no—
356C2×M16—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—861no—
360C4⋊Q8—431no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363C4⋊Q8—861no—
364C4⋊Q8—861no—
365C4⋊Q8—861no—
366#127—431no—
367#126—21no—
368#125D17211yescharacteristic
369#124—861no—
370#124D17211yescharacteristic
371#123—21no—
372C22⋊Q8D17211yescharacteristic
373#121—861no—
374#121—861no—
375#121D17211yescharacteristic
376C4×Q8C22×D4311yescharacteristic
377C4×D4—21no—
378C4×D4—861no—
379C4×D4—861no—
380C4×D4C22×D4311yescharacteristic
381#117—21no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C42C22×D4311yescharacteristic
385#107—861no—
386#107—861no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8C22⋊D4311yescharacteristic
404C4⋊C8C22⋊D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—861no—
408#103—861no—
409#103—861no—
410#102—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—861no—
422C22⋊C8C22⋊D4311yescharacteristic
423C22⋊C8C22⋊D4311yescharacteristic
424#97—21no—
425#97—861no—
426C4×C8—21no—
427C4×C8C22×D4311yescharacteristic
428C4×C8C22×D4311yescharacteristic
429#41—3442no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—3442no—
434C2×Q8—1721no—
435C2×Q8C2×D17211yescharacteristic
436C2×D4—21no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—1721no—
441C2×D4C2×D17211yescharacteristic
442C22×C4—21no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4C2×D17211yescharacteristic
446C22×C4#1062189811yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448SD16—3441no—
449D8—3441no—
450M16—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8—81no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—3441no—
460C2×C8C2×C22⋊D4311yescharacteristic
461C2×C8C2×C22⋊D4311yescharacteristic
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4C2×D17211yescharacteristic
477C4⋊C4C2×D17211yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C42—21no—
486C42C2×D17211yescharacteristic
487C42#1062189811yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—21no—
491C23—1721no—
492C23#1306329911yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—3441no—
496Q8—3441no—
497Q8—3441no—
498Q8—3442no—
499D4—21no—
500D4—21no—
501D4—42no—
502D4—3441no—
503D4—3442no—
504D4—1721no—
505D4—1721no—
506D4—1721no—
507D4—1721no—
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—3442no—
519C2×C4—3442no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4#1306329911yescharacteristic
524C2×C4#1306329911yescharacteristic
525C2×C4#1306329911yescharacteristic
526C2×C4C22×C22⋊D4311yescharacteristic
527C2×C4C22×D17211yescharacteristic
528C2×C4C2×#1062189811yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—3441no—
545C22—3441no—
546C22—3441no—
547C22#1458316912yes—
548C22C2×#1306329911yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—3441no—
557C4—3441no—
558C4—3441no—
559C4#1458371011yescharacteristic
560C4#1458371111yescharacteristic
561C4#1458371411yescharacteristic
562C4#1458371611yescharacteristic
563C2—22no—
564C2—81no—
565C2—6881no—
566C2#1914414511yescharacteristic
567C2#1914428611yescharacteristic
568C2C2×#1458316911yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2994C2
socleC22×C43C2×#121
prime radical#19145921C2
hypercenter#2994D43
hypocenterC43#19591
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #19145813C2semidirect
3. #19145718C2semidirect
4. #19134135C2semidirect
5. #19134128C2semidirect
6. #19134123C2semidirect
7. #19134118C2semidirect
8. #19134011C2semidirect
9. #19134004C2semidirect
10. #19133999C2semidirect
11. #19133994C2semidirect
12. #19133380C2semidirect
13. #19133288C2semidirect
14. C2×#14582647C2semidirect
15. C43×#2994C2semidirect
282. #2994D43semidirect
351. C43#19591semidirect

Maximal subgroups

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

subgroupindex
#191459212
#191458132
#191457182
#191341352
#191341282
#191341232
#191341182
#191340112
#191340042
#191339992
#191339942
#191333802
#191332882
C2×#145826472
C43×#29942
#1959143