Finite Group Databasebeta

← #25079679

Subgroups — #25079679

Order 11008.

746 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145902C211yesmaximal, characteristic, complemented
2#19145021C211yesmaximal, characteristic, complemented
3#19143307C211yesmaximal, characteristic, complemented
4#19134082C212yesmaximal, complemented
5#19134072C212yesmaximal, complemented
6#19133938C212yesmaximal, complemented
7#19133934C212yesmaximal, complemented
8C2×#14582649C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10#19133270C211yesmaximal, characteristic, complemented
11C43×#3245C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13C2×#13063345—21no—
14C2×#13063332—21no—
15#14583449C2211yescharacteristic
16#14583281—21no—
17#14583281—21no—
18#14583278C2211yescharacteristic
19#14583275C2211yescharacteristic
20#14583273C2211yescharacteristic
21#14583271C2211yescharacteristic
22#14583179C2212yes—
23#14583176—21no—
24#14583133—22no—
25#14583094C2212yes—
26#14583091—21no—
27#14582977—21no—
28#14582977C2212yes—
29D4×C43⋊C8—21no—
30D4×C43⋊C8C2212yes—
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582866—21no—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582649C2212yes—
36#14582649C2212yes—
37#14582645C2212yes—
38#14582644C2212yes—
39#14582643C2212yes—
40#14582642C2212yes—
41C43×#532C2211yescharacteristic
42C43×#532C2211yescharacteristic
43C43×#474—21no—
44C43×#474C2212yes—
45C43×#466—22no—
46C43×#459—21no—
47C43×#459C2212yes—
48C2×C4⋊C8×C43C2211yescharacteristic
49C2×#10621898—21no—
50#13063345—44no—
51#13063345—44no—
52C2×#10621885—21no—
53C2×#10621885—21no—
54C2×#10621883—21no—
55C2×#10621883—21no—
56C2×#10621884—21no—
57C2×#10621884—21no—
58C2×#10621882—22no—
59C2×#10621882—21no—
60C2×#10621882—21no—
61#13063332—44no—
62C2×#10621877—21no—
63C2×#10621877—22no—
64C22×C43⋊C8—21no—
65C22×C43⋊C8—22no—
66C22×C43⋊C8D411yescharacteristic
67C22×C43⋊C8D411yescharacteristic
68#13063325C2311yescharacteristic
69#13063322C2311yescharacteristic
70#13063313—21no—
71#13063299—21no—
72#13063299—21no—
73C4×D172—21no—
74C4×D172—21no—
75#13063258—22no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)C2312yes—
79C4⋊(C43⋊C8)C2312yes—
80#13063246—22no—
81#13063245—22no—
82C22⋊(C43⋊C8)—22no—
83C22⋊(C43⋊C8)—22no—
84C4×C43⋊C8D411yescharacteristic
85C4×C43⋊C8D411yescharacteristic
86C4×C43⋊C8C2311yescharacteristic
87C4×C43⋊C8C2311yescharacteristic
88C2×#41×C43—21no—
89C2×#41×C43—21no—
90C2×D8×C43—22no—
91C22×C8×C43—21no—
92C4⋊Q8×C43D411yescharacteristic
93C4⋊Q8×C43C2311yescharacteristic
94#127×C43D411yescharacteristic
95#127×C43C2311yescharacteristic
96#124×C43—21no—
97#124×C43—21no—
98#121×C43—21no—
99#121×C43—21no—
100#121×C43—21no—
101#121×C43D412yes—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43C2312yes—
106C2×C42×C43C2311yescharacteristic
107#107×C43—22no—
108C4⋊C8×C43—21no—
109C4⋊C8×C43C2312yes—
110#102×C43—22no—
111#102×C43—22no—
112#41×C43—42no—
113#41×C43—42no—
114#41×C43—42no—
115#41×C43—42no—
116C2×Q8×C43—21no—
117C2×Q8×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—41no—
125C2×D4×C43C2×D412yes—
126C22×C4×C43—22no—
127C22×C4×C43—41no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43#4111yescharacteristic
131C2×C22⋊D43—41no—
132#10621898—42no—
133#10621898—42no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×C4×D43—41no—
138C2×Dic86—21no—
139D8×C43—82no—
140C2×C8×C43—22no—
141C2×C8×C43—81no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43C2×D412yes—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43#4111yescharacteristic
153C42×C43C2411yescharacteristic
154#10621885—42no—
155#10621885—42no—
156#10621884—42no—
157#10621884—42no—
158#10621883—42no—
159#10621883—42no—
160#10621882—42no—
161#10621882—42no—
162#10621882—82no—
163(C2×D43)⋊C4—41no—
164(C2×D43)⋊C4—41no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167#10621877—42no—
168#10621877—44no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—44no—
173C2×C43⋊C8—81no—
174C2×C43⋊C8D814yescomplemented
175C2×C43⋊C8C2×D411yescharacteristic
176C2×C43⋊C8C2×D411yescharacteristic
177C2×C43⋊C8C2×D411yescharacteristic
178C2×C43⋊C8C2×D411yescharacteristic
179C23×C43—22no—
180C23×C43—41no—
181C23×C43#12111yescharacteristic
182C22×D43—41no—
183Q8×C43—42no—
184Q8×C43—41no—
185Q8×C43—41no—
186D4×C43—22no—
187D4×C43—22no—
188D4×C43—42no—
189D4×C43—44no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—41no—
193D4×C43—41no—
194D4×C43—42no—
195D4×C43—81no—
196D4×C43—82no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—22no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—41no—
204C2×C4×C43—82no—
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43#12111yescharacteristic
207C2×C4×C43#12111yescharacteristic
208C2×C4×C43C2×D812yes—
209C2×C4×C43AGL(1,ℤ/8)12yes—
210C2×C4×C43C22×D411yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C2×C4×C43C2×#4111yescharacteristic
213C22⋊D43—82no—
214C2×Dic43—41no—
215D172—41no—
216D172—41no—
217D172—41no—
218D172—41no—
219D172—81no—
220C4×D43—82no—
221Dic86—41no—
222Dic86—41no—
223C8×C43—42no—
224C43⋊C8—21no—
225C43⋊C8—21no—
226C43⋊C8—42no—
227C43⋊C8—42no—
228C43⋊C8C2×D812yes—
229C43⋊C8C2×D812yes—
230#19189—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—42no—
234C22×C43—42no—
235C22×C43—42no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43#45912yes—
240C22×C43C2×#12111yescharacteristic
241C2×D43—81no—
242C2×D43—81no—
243C2×D43—81no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—42no—
248C4×C43—81no—
249C4×C43#45912yes—
250C4×C43C22×D811yescharacteristic
251C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C43#57711yescharacteristic
253C4×C43#57711yescharacteristic
254Dic43—81no—
255#3245—431no—
256#3245D4311yescharacteristic, complemented
257#3147—431no—
258#2931—431no—
259#1689—432no—
260#1687—432no—
261#1665—432no—
262#1665—432no—
263C2×#334—431no—
264#1547—431no—
265#1547—431no—
266C2×C43—22no—
267C2×C43—82no—
268C2×C43—161no—
269C2×C43C2×#45911yescharacteristic
270C2×C43#306011yescharacteristic
271C2×C43#306711yescharacteristic
272D43—161no—
273C2×#135—861no—
274C2×#135—861no—
275C2×#131—861no—
276#532—431no—
277#532C2×D4311yescharacteristic
278#532C2×D4311yescharacteristic
279#495—861no—
280#495—861no—
281#494—431no—
282#493—431no—
283#492—431no—
284#492—431no—
285#474—21no—
286#474—432no—
287#474—861no—
288#474C2×D4312yes—
289#466—22no—
290#466—862no—
291#459—21no—
292#459—432no—
293#459—861no—
294#459C2×D4312yes—
295#436—432no—
296#436—861no—
297C8×D4—432no—
298C8×D4—861no—
299#423—431no—
300C2×C4⋊C8—431no—
301C2×C4⋊C8C2×D4311yescharacteristic
302#408—861no—
303C2×C4×C8—431no—
304#334—432no—
305#334—432no—
306#332—432no—
307#332—432no—
308#331—432no—
309#331—432no—
310C43#1918911yescharacteristic, complemented, Sylow
311C2×#41—21no—
312C2×#41—21no—
313C2×#41—861no—
314#135—1724no—
315#135—1724no—
316C2×Q16—861no—
317C2×Q16—861no—
318C2×SD16—861no—
319C2×SD16—861no—
320C2×SD16—861no—
321C2×SD16—861no—
322C2×D8—22no—
323C2×D8—861no—
324C2×D8—861no—
325C2×D8—862no—
326#131—1724no—
327C2×M16—862no—
328C2×M16—861no—
329C22×C8—21no—
330C22×C8—431no—
331C22×C8—431no—
332C22×C8—862no—
333C22×C8—861no—
334C4⋊Q8—431no—
335C4⋊Q8C22⋊D4311yescharacteristic
336C4⋊Q8C22×D4311yescharacteristic
337#127—431no—
338#127C22⋊D4311yescharacteristic
339#127C22×D4311yescharacteristic
340#124—21no—
341#124—21no—
342#124—861no—
343#121—21no—
344#121—21no—
345#121—21no—
346#121—861no—
347#121—861no—
348#121C22⋊D4312yes—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—861no—
353C4×D4—861no—
354C4×D4C22×D4312yes—
355C2×C42C22×D4311yescharacteristic
356#107—22no—
357#107—862no—
358C4⋊C8—21no—
359C4⋊C8—432no—
360C4⋊C8—432no—
361C4⋊C8—861no—
362C4⋊C8—861no—
363C4⋊C8C22×D4312yes—
364#102—22no—
365#102—22no—
366#102—862no—
367#102—862no—
368C22⋊C8—862no—
369C22⋊C8—862no—
370C4×C8—431no—
371C4×C8—431no—
372C4×C8—431no—
373C4×C8—431no—
374#41—42no—
375#41—42no—
376#41—42no—
377#41—42no—
378#41—1722no—
379#41—1722no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—861no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—41no—
390C2×D4—861no—
391C2×D4—861no—
392C2×D4—861no—
393C2×D4—1721no—
394C2×D4C2×C22⋊D4312yes—
395C22×C4—22no—
396C22×C4—41no—
397C22×C4—1721no—
398C22×C4D4×D4311yescharacteristic
399C22×C4#1062190011yescharacteristic
400C22×C4C2×C22⋊D4311yescharacteristic
401Q16—1722no—
402Q16—1722no—
403SD16—1722no—
404SD16—1722no—
405SD16—1722no—
406SD16—1722no—
407D8—82no—
408D8—3442no—
409D8—1722no—
410D8—1722no—
411M16—1724no—
412M16—1722no—
413C2×C8—22no—
414C2×C8—81no—
415C2×C8—434no—
416C2×C8—431no—
417C2×C8—431no—
418C2×C8—431no—
419C2×C8—431no—
420C2×C8—862no—
421C2×C8—862no—
422C2×C8—862no—
423C2×C8—3441no—
424C2×C8—1724no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4C2×C22⋊D4312yes—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C42D4×D4311yescharacteristic
438C42#1062190011yescharacteristic
439C42C2×C22⋊D4311yescharacteristic
440C42C23×D4311yescharacteristic
441C23—22no—
442C23—41no—
443C23—1721no—
444C23#1306329711yescharacteristic
445Q8—42no—
446Q8—41no—
447Q8—41no—
448Q8—1721no—
449Q8—1721no—
450D4—22no—
451D4—22no—
452D4—42no—
453D4—44no—
454D4—42no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—41no—
459D4—81no—
460D4—82no—
461D4—3441no—
462D4—3442no—
463D4—1721no—
464D4—1721no—
465D4—1721no—
466D4—1721no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4—3442no—
476C2×C4—1721no—
477C2×C4#1306329711yescharacteristic
478C2×C4#1306329711yescharacteristic
479C2×C4#1306329711yescharacteristic
480C2×C4D8×D4312yes—
481C2×C4#1306334912yes—
482C2×C4C2×D4×D4311yescharacteristic
483C2×C4C22×C22⋊D4311yescharacteristic
484C2×C4C2×#1062190011yescharacteristic
485C8—42no—
486C8—432no—
487C8—432no—
488C8—861no—
489C8—861no—
490C8—1722no—
491C8—1722no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—3441no—
501C22—3441no—
502C22—3441no—
503C22#1458309212yes—
504C22C2×#1306329711yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—42no—
509C4—81no—
510C4—3441no—
511C4#1458309212yes—
512C4C2×D8×D4311yescharacteristic
513C4C2×#1306334911yescharacteristic
514C4#1458370711yescharacteristic
515C4#1458371011yescharacteristic
516C2—22no—
517C2—82no—
518C2—161no—
519C2—6881no—
520C2C2×#1458309211yescharacteristic
521C2#1914425411yescharacteristic
522C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3245C2
socleC22×C43C2×#121
hypercenter#3245D43
hypocenterC43#19189
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #19145902C2semidirect
2. #19145021C2semidirect
3. #19143307C2semidirect
4. #19134082C2semidirect
5. #19134072C2semidirect
6. #19133938C2semidirect
7. #19133934C2semidirect
8. C2×#14582649C2semidirect
9. #19133272C2semidirect
10. #19133270C2semidirect
11. C43×#3245C2semidirect
174. C2×C43⋊C8D8semidirect
256. #3245D43semidirect
310. C43#19189semidirect

Maximal subgroups

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

subgroupindex
#191459022
#191450212
#191433072
#191340822
#191340722
#191339382
#191339342
C2×#145826492
#191332722
#191332702
C43×#32452
#1918943