Finite Group Databasebeta

← #25081731

Subgroups — #25081731

Order 11008.

594 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#19145958C211yesmaximal, characteristic
2#19145818C211yesmaximal, characteristic, complemented
3#19144989C211yesmaximal, characteristic, complemented
4#19143599C211yesmaximal, characteristic, complemented
5#19134178C211yesmaximal, characteristic, complemented
6#19134171C211yesmaximal, characteristic, complemented
7#19134136C211yesmaximal, characteristic, complemented
8#19134129C211yesmaximal, characteristic, complemented
9#19134054C211yesmaximal, characteristic, complemented
10#19134047C211yesmaximal, characteristic, complemented
11#19134012C211yesmaximal, characteristic, complemented
12#19134005C211yesmaximal, characteristic, complemented
13#19133301C211yesmaximal, characteristic, complemented
14#19133277C211yesmaximal, characteristic, complemented
15C43×#1569C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583308—21no—
20#14583259—21no—
21#14583259—21no—
22#14583259—21no—
23#14583250C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583246C2211yescharacteristic
26#14583246C2211yescharacteristic
27#14583230—21no—
28#14583213—21no—
29#14583200—21no—
30#14583195C2211yescharacteristic
31#14583195C2211yescharacteristic
32#14583190C2211yescharacteristic
33#14583190C2211yescharacteristic
34#14583185C2211yescharacteristic
35#14583180C2211yescharacteristic
36#14583152—21no—
37#14583145—21no—
38#14583115—21no—
39#14583100C2211yescharacteristic
40#14583095C2211yescharacteristic
41#14583029C2211yescharacteristic
42C8×Dic86C2211yescharacteristic
43#14582978C2211yescharacteristic
44#14582975—21no—
45#14582968—21no—
46C8×D172C2211yescharacteristic
47#14582961—21no—
48#14582952C2211yescharacteristic
49#14582901—21no—
50#14582901—21no—
51#14582856—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C22×Dic86—21no—
69C2×#10621873—21no—
70C2×D344—21no—
71C2×#10621872—21no—
72C2×C8×D43—21no—
73#13063325—21no—
74#13063325—21no—
75#13063325—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063319—21no—
81#13063317D411yescharacteristic
82#13063313—21no—
83#13063313D411yescharacteristic
84#13063308—21no—
85#13063304D411yescharacteristic
86#13063299—21no—
87#13063299—21no—
88#13063299D411yescharacteristic
89C4×Dic86C2311yescharacteristic
90C4×D172—21no—
91C4×D172—21no—
92C4×D172C2311yescharacteristic
93C4×C22⋊D43—21no—
94#13063282—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063257—21no—
101#13063257—21no—
102#13063257—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063247—21no—
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126#13063235—21no—
127C4×C43⋊C8—21no—
128C8×Dic43—21no—
129C2×M16×C43—21no—
130C2×M16×C43D411yescharacteristic
131C2×M16×C43D411yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139#97×C43—21no—
140#97×C43D411yescharacteristic
141#97×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×C22⋊D43—41no—
149C22×Dic43—41no—
150#10621898—42no—
151#10621898—42no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86—82no—
163C2×Dic86C2×D411yescharacteristic
164M16×C43—41no—
165M16×C43—41no—
166M16×C43—81no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43—41no—
194C4⋊Dic43C2×D411yescharacteristic
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200C4×Dic43—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203D344—81no—
204#10621873—81no—
205#10621872—42no—
206C8×D43—42no—
207C23×C43#12111yescharacteristic
208C22×D43—21no—
209C22×D43—41no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C22⋊D43—81no—
222C22⋊D43—82no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—82no—
230D172—21no—
231D172—21no—
232D172—41no—
233D172—41no—
234D172—41no—
235D172—41no—
236D172—81no—
237C4×D43—41no—
238C4×D43—41no—
239C4×D43—82no—
240Dic86—21no—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244Dic86—82no—
245Dic86—81no—
246Dic86—81no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19382—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43C2×#12111yescharacteristic
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43#57511yescharacteristic
273C4×C43#57511yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—41no—
277Dic43—41no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281Dic43—81no—
282#3251—431no—
283#3238—431no—
284#3141—431no—
285#2969—431no—
286#1704—431no—
287#1703—431no—
288#1698—431no—
289#1697—431no—
290#1684—431no—
291#1683—431no—
292#1678—431no—
293#1677—431no—
294#1569D4311yescharacteristic, complemented
295#1553—431no—
296#1548—431no—
297C2×C43—41no—
298C2×C43#304011yescharacteristic
299C2×C43#306311yescharacteristic
300C2×C43#306811yescharacteristic
301D43—81no—
302D43—161no—
303#532—431no—
304C2×C4⋊Q8—431no—
305#529—431no—
306#501—861no—
307#489—861no—
308#489—861no—
309#489—861no—
310#487—431no—
311#487—431no—
312#486—431no—
313#486—431no—
314#483—861no—
315#480—861no—
316#478—861no—
317#477—431no—
318#477—431no—
319#476—431no—
320#476—431no—
321#475—431no—
322#474—431no—
323#469—861no—
324#468—861no—
325#463—861no—
326#460—431no—
327#459—431no—
328#446—431no—
329C8×Q8—431no—
330#436—431no—
331#436—861no—
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#432C2×D4311yescharacteristic
336#431—431no—
337#423C2×D4311yescharacteristic
338#417—861no—
339#417—861no—
340#405—861no—
341C4×M16C2×D4311yescharacteristic
342#335C2×D4311yescharacteristic
343#335C2×D4311yescharacteristic
344#334C2×D4311yescharacteristic
345#334C2×D4311yescharacteristic
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#1938211yescharacteristic, complemented, Sylow
355C2×#41—861no—
356C22×Q8—861no—
357C2×SD16—861no—
358C2×D8—861no—
359C2×M16—21no—
360C2×M16—861no—
361C2×M16D17211yescharacteristic
362C2×M16D17211yescharacteristic
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—431no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8—861no—
370#127—431no—
371#126—861no—
372#125—431no—
373#124—431no—
374#124—861no—
375#123—861no—
376C22⋊Q8—431no—
377#121—431no—
378#121—861no—
379#121—861no—
380C4×Q8—431no—
381C4×D4—431no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4—861no—
385#117—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C42C22×D4311yescharacteristic
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—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—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—21no—
425#97—861no—
426#97D17211yescharacteristic
427#97D17211yescharacteristic
428C4×C8—861no—
429C4×C8—861no—
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432#41—1722no—
433#41—1722no—
434C2×Q8—431no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—3442no—
439C2×Q8—1721no—
440C2×D4—431no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—1721no—
446C22×C4—861no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4C2×D17211yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4#1062190211yescharacteristic
452SD16—3441no—
453D8—3441no—
454M16—41no—
455M16—41no—
456M16—81no—
457M16—1722no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—1722no—
465C2×C8C2×D17211yescharacteristic
466C2×C8C2×D17211yescharacteristic
467C2×C8C2×D17211yescharacteristic
468C2×C8C2×D17211yescharacteristic
469C4⋊C4—431no—
470C4⋊C4—431no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C42—861no—
491C42C2×D17211yescharacteristic
492C42D4×D4311yescharacteristic
493C42#1062190211yescharacteristic
494C42C23×D4311yescharacteristic
495C23—861no—
496C23—1721no—
497C23#1306330011yescharacteristic
498Q8—861no—
499Q8—861no—
500Q8—3441no—
501Q8—3441no—
502Q8—3442no—
503Q8—1721no—
504Q8—1721no—
505D4—861no—
506D4—861no—
507D4—3441no—
508D4—3442no—
509D4—3441no—
510D4—1721no—
511D4—1721no—
512D4—1721no—
513D4—1721no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—3442no—
523C2×C4—3442no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306330011yescharacteristic
530C2×C4#1306330011yescharacteristic
531C2×C4#1306330011yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C22×D17211yescharacteristic
534C2×C4C2×#1062190211yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—3441no—
549C22—3441no—
550C22—3441no—
551C22—1721no—
552C22—1721no—
553C22—1721no—
554C22C2×#1306330011yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—3441no—
560C4—3441no—
561C4—3441no—
562C4—1721no—
563C4—1721no—
564C4—1721no—
565C4#1458369911yescharacteristic
566C4#1458369911yescharacteristic
567C4#1458370911yescharacteristic
568C4#1458371511yescharacteristic
569C2—41no—
570C2—3441no—
571C2—6881no—
572C2#1914409011yescharacteristic
573C2#1914428711yescharacteristic
574C2#1914432411yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1569C2
socleC22×C43C2×#121
prime radical#19145958C2
hypercenter#1569D43
hypocenterC43#19382
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
2. #19145818C2semidirect
3. #19144989C2semidirect
4. #19143599C2semidirect
5. #19134178C2semidirect
6. #19134171C2semidirect
7. #19134136C2semidirect
8. #19134129C2semidirect
9. #19134054C2semidirect
10. #19134047C2semidirect
11. #19134012C2semidirect
12. #19134005C2semidirect
13. #19133301C2semidirect
14. #19133277C2semidirect
15. C43×#1569C2semidirect
294. #1569D43semidirect
354. C43#19382semidirect

Maximal subgroups

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

subgroupindex
#191459582
#191458182
#191449892
#191435992
#191341782
#191341712
#191341362
#191341292
#191340542
#191340472
#191340122
#191340052
#191333012
#191332772
C43×#15692
#1938243