Finite Group Databasebeta

← #25080364

Subgroups — #25080364

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145922C211yesmaximal, characteristic
2#19145776C211yesmaximal, characteristic, complemented
3#19145313C211yesmaximal, characteristic, complemented
4#19143599C211yesmaximal, characteristic, complemented
5#19134178C211yesmaximal, characteristic, complemented
6#19134136C211yesmaximal, characteristic, complemented
7#19134119C211yesmaximal, characteristic, complemented
8#19134061C211yesmaximal, characteristic, complemented
9#19134047C211yesmaximal, characteristic, complemented
10#19134005C211yesmaximal, characteristic, complemented
11#19134000C211yesmaximal, characteristic, complemented
12#19133944C211yesmaximal, characteristic, complemented
13#19133255C211yesmaximal, characteristic, complemented
14#19133253C211yesmaximal, characteristic, complemented
15C43×#1565C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583301—21no—
21#14583272C2211yescharacteristic
22#14583254—21no—
23#14583250C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583241—21no—
26#14583224—21no—
27#14583200—21no—
28#14583195C2211yescharacteristic
29#14583195C2211yescharacteristic
30#14583190C2211yescharacteristic
31#14583190C2211yescharacteristic
32#14583185C2211yescharacteristic
33#14583180C2211yescharacteristic
34#14583145—21no—
35#14583145—21no—
36#14583135—21no—
37#14583128—21no—
38#14583115—21no—
39#14583100C2211yescharacteristic
40#14583095C2211yescharacteristic
41#14583029C2211yescharacteristic
42C8×Dic86C2211yescharacteristic
43#14583001—21no—
44#14583001—21no—
45#14582978C2211yescharacteristic
46#14582975—21no—
47#14582968—21no—
48C8×D172C2211yescharacteristic
49#14582961—21no—
50#14582952C2211yescharacteristic
51#14582856—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621873—21no—
69C2×#10621873—21no—
70C2×#10621873—21no—
71C2×D344—21no—
72C2×#10621872—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063319—21no—
79#13063317—21no—
80#13063317D411yescharacteristic
81#13063313—21no—
82#13063313D411yescharacteristic
83#13063308—21no—
84#13063304—21no—
85#13063304—21no—
86#13063304D411yescharacteristic
87#13063299—21no—
88#13063299—21no—
89#13063299D411yescharacteristic
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86C2311yescharacteristic
93C4×D172—21no—
94C4×D172—21no—
95C4×D172C2311yescharacteristic
96C4×C22⋊D43—21no—
97#13063284—21no—
98#13063282—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—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×C43D411yescharacteristic
130C2×M16×C43D411yescharacteristic
131C22×C8×C43—21no—
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×C43D411yescharacteristic
140#97×C43D411yescharacteristic
141C4×C8×C43—21no—
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—
149#10621898—82no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C2×D411yescharacteristic
154C2×C4×D43—21no—
155C2×C4×D43—41no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C2×D411yescharacteristic
160M16×C43—22no—
161M16×C43—41no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43#4111yescharacteristic
174C42×C43C2411yescharacteristic
175C22⋊Dic43—21no—
176C22⋊Dic43—41no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C2×D411yescharacteristic
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201D344—81no—
202#10621873—42no—
203#10621873—42no—
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—
229D172—21no—
230D172—21no—
231D172—41no—
232D172—41no—
233D172—41no—
234D172—41no—
235D172—81no—
236C4×D43—41no—
237C4×D43—41no—
238C4×D43—82no—
239Dic86—21no—
240Dic86—21no—
241Dic86—41no—
242Dic86—41no—
243Dic86—81no—
244Dic86—81no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43#13512yes—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#19253—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43C2×#12111yescharacteristic
260C2×D43—41no—
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43C2×#13511yescharacteristic
271C4×C43#57511yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277Dic43—81no—
278Dic43—81no—
279Dic43—81no—
280#3247—431no—
281#3233—431no—
282#3182—431no—
283#2969—431no—
284#1704—431no—
285#1698—431no—
286#1695—431no—
287#1685—431no—
288#1683—431no—
289#1677—431no—
290#1676—431no—
291#1666—431no—
292#1565D4311yescharacteristic, complemented
293#1543—431no—
294#1542—431no—
295C2×C43—41no—
296C2×C43#303511yescharacteristic
297C2×C43#306311yescharacteristic
298C2×C43#306811yescharacteristic
299D43—81no—
300D43—161no—
301#533—431no—
302#532—431no—
303#529—431no—
304#500—431no—
305#499—861no—
306#492—431no—
307#488—861no—
308#487—431no—
309#486—431no—
310#485—861no—
311#482—861no—
312#478—861no—
313#477—431no—
314#477—431no—
315#476—431no—
316#476—431no—
317#475—431no—
318#474—431no—
319#468—861no—
320#468—861no—
321#466—861no—
322#465—861no—
323#463—861no—
324#460—431no—
325#459—431no—
326#446—431no—
327C8×Q8—431no—
328#440—861no—
329#440—861no—
330#436—431no—
331#436—861no—
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#431—431no—
336#431C2×D4311yescharacteristic
337C2×C4⋊C8C2×D4311yescharacteristic
338#405—861no—
339C4×M16C2×D4311yescharacteristic
340#335C2×D4311yescharacteristic
341#335C2×D4311yescharacteristic
342#334C2×D4311yescharacteristic
343#334C2×D4311yescharacteristic
344#333—431no—
345#333—431no—
346#333—431no—
347#333—431no—
348#332—431no—
349#332—431no—
350#331—431no—
351#331—431no—
352C43#1925311yescharacteristic, complemented, Sylow
353C2×#41—861no—
354C2×SD16—861no—
355C2×SD16—861no—
356C2×SD16—861no—
357C2×D8—861no—
358C2×M16—861no—
359C2×M16D17211yescharacteristic
360C2×M16D17211yescharacteristic
361C22×C8—21no—
362C22×C8—861no—
363C4⋊Q8—431no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366#127—431no—
367#126—861no—
368#125—431no—
369#125—861no—
370#124—431no—
371#124—861no—
372#123—861no—
373C22⋊Q8—431no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—431no—
377#121—861no—
378#121—861no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—431no—
383C4×D4—861no—
384C4×D4—861no—
385C4×D4—861no—
386#117—861no—
387#117—861no—
388C2×C42C22×D4311yescharacteristic
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#107—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—21no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
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—
418C22⋊C8—21no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—861no—
423#97D17211yescharacteristic
424#97D17211yescharacteristic
425C4×C8—21no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8C22×D4311yescharacteristic
429C4×C8C22×D4311yescharacteristic
430#41—3442no—
431C2×Q8—431no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×D4—431no—
436C2×D4—861no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—1721no—
441C22×C4—861no—
442C22×C4—1721no—
443C22×C4C2×D17211yescharacteristic
444C22×C4D4×D4311yescharacteristic
445C22×C4#1062190211yescharacteristic
446SD16—3441no—
447SD16—1722no—
448SD16—1722no—
449D8—3441no—
450M16—22no—
451M16—41no—
452M16—1722no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—81no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—1722no—
461C2×C8C2×D17211yescharacteristic
462C2×C8C2×D17211yescharacteristic
463C2×C8C2×D17211yescharacteristic
464C2×C8C2×D17211yescharacteristic
465C4⋊C4—431no—
466C4⋊C4—431no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—861no—
488C42—1721no—
489C42C2×D17211yescharacteristic
490C42D4×D4311yescharacteristic
491C42#1062190211yescharacteristic
492C42C23×D4311yescharacteristic
493C23—861no—
494C23—1721no—
495C23#1306330011yescharacteristic
496Q8—861no—
497Q8—861no—
498Q8—3441no—
499Q8—3441no—
500Q8—1721no—
501Q8—1721no—
502D4—861no—
503D4—861no—
504D4—3441no—
505D4—3442no—
506D4—3441no—
507D4—1721no—
508D4—1721no—
509D4—1721no—
510D4—1721no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—3442no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4#1306330011yescharacteristic
526C2×C4#1306330011yescharacteristic
527C2×C4#1306330011yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C22×D17211yescharacteristic
530C2×C4C2×#1062190211yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—1721no—
539C8—1721no—
540C8#1306334712yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—3441no—
545C22—3441no—
546C22—3441no—
547C22—1721no—
548C22—1721no—
549C22—1721no—
550C22C2×#1306330011yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—3441no—
556C4—3441no—
557C4—3441no—
558C4—1721no—
559C4—1721no—
560C4—1721no—
561C4C2×#1306334711yescharacteristic
562C4#1458369911yescharacteristic
563C4#1458370911yescharacteristic
564C4#1458371511yescharacteristic
565C2—41no—
566C2—3441no—
567C2—6881no—
568C2#1914405211yescharacteristic
569C2#1914428711yescharacteristic
570C2#1914432411yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1565C2
socleC22×C43C2×#121
prime radical#19145922C2
hypercenter#1565D43
hypocenterC43#19253
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
2. #19145776C2semidirect
3. #19145313C2semidirect
4. #19143599C2semidirect
5. #19134178C2semidirect
6. #19134136C2semidirect
7. #19134119C2semidirect
8. #19134061C2semidirect
9. #19134047C2semidirect
10. #19134005C2semidirect
11. #19134000C2semidirect
12. #19133944C2semidirect
13. #19133255C2semidirect
14. #19133253C2semidirect
15. C43×#1565C2semidirect
292. #1565D43semidirect
352. C43#19253semidirect

Maximal subgroups

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

subgroupindex
#191459222
#191457762
#191453132
#191435992
#191341782
#191341362
#191341192
#191340612
#191340472
#191340052
#191340002
#191339442
#191332552
#191332532
C43×#15652
#1925343