Finite Group Databasebeta

← #25085931

Subgroups — #25085931

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145329C211yesmaximal, characteristic
2#19145313C211yesmaximal, characteristic, complemented
3#19145309C211yesmaximal, characteristic, complemented
4#19144991C211yesmaximal, characteristic, complemented
5#19144975C211yesmaximal, characteristic, complemented
6#19134250C211yesmaximal, characteristic, complemented
7#19134247C211yesmaximal, characteristic, complemented
8#19134244C211yesmaximal, characteristic, complemented
9#19134238C211yesmaximal, characteristic, complemented
10#19134236C211yesmaximal, characteristic, complemented
11#19134231C211yesmaximal, characteristic, complemented
12#19134208C211yesmaximal, characteristic, complemented
13#19134206C211yesmaximal, characteristic, complemented
14#19132898C211yesmaximal, characteristic, complemented
15C43×#3141C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583275C2211yescharacteristic
22#14583272C2211yescharacteristic
23#14583271C2211yescharacteristic
24#14583267—22no—
25#14583261—22no—
26#14583251C2211yescharacteristic
27#14583251C2211yescharacteristic
28#14583251C2211yescharacteristic
29#14583250C2211yescharacteristic
30#14583249C2211yescharacteristic
31#14583249C2211yescharacteristic
32#14583249C2211yescharacteristic
33#14583249C2211yescharacteristic
34#14583247C2211yescharacteristic
35#14583247C2211yescharacteristic
36#14583247C2211yescharacteristic
37#14583246C2211yescharacteristic
38#14583245C2211yescharacteristic
39#14583245C2211yescharacteristic
40#14583150—22no—
41#14583145—22no—
42#14583143—22no—
43#14583009—22no—
44#14583001—22no—
45#14582999—22no—
46#14582908—22no—
47#14582898—22no—
48C4×#10621877C2211yescharacteristic
49C4×#10621877C2211yescharacteristic
50#14582621C2211yescharacteristic
51#14582621C2211yescharacteristic
52#14582620C2211yescharacteristic
53C8×C43⋊C8C2211yescharacteristic
54C43×#532C2211yescharacteristic
55C2×C4⋊Q8×C43C2211yescharacteristic
56C43×#489—22no—
57C43×#487C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#486C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#417—22no—
62C4×M16×C43C2211yescharacteristic
63C2×#10621898—21no—
64C2×#10621873—22no—
65C2×#10621883—22no—
66C2×#10621882—22no—
67C2×#10621877D412yes—
68C2×#10621877D412yes—
69#13063325C2311yescharacteristic
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063322C2311yescharacteristic
73#13063317—21no—
74#13063313—21no—
75#13063304—21no—
76#13063304—21no—
77#13063299—21no—
78#13063299—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×D172—21no—
82C4×D172—21no—
83#13063284—21no—
84#13063259—22no—
85#13063258—22no—
86#13063256—22no—
87#13063250—22no—
88#13063249—22no—
89#13063249—22no—
90#13063249—22no—
91#13063249—22no—
92#13063248—22no—
93#13063248—22no—
94#13063248—22no—
95#13063247—22no—
96#13063246—22no—
97#13063246—22no—
98#13063245—22no—
99#13063245—22no—
100#13063245—22no—
101#13063236D412yes—
102#13063236D412yes—
103C4×C43⋊C8C2311yescharacteristic
104C4×C43⋊C8C2311yescharacteristic
105C4×C43⋊C8C2311yescharacteristic
106C4×C43⋊C8C2311yescharacteristic
107C2×#41×C43—21no—
108C22×Q8×C43—21no—
109C2×M16×C43D412yes—
110C4⋊Q8×C43—21no—
111C4⋊Q8×C43—21no—
112C4⋊Q8×C43—21no—
113C4⋊Q8×C43C2311yescharacteristic
114C4⋊Q8×C43C2311yescharacteristic
115C4⋊Q8×C43C2311yescharacteristic
116#127×C43C2311yescharacteristic
117#124×C43—21no—
118#121×C43—21no—
119#121×C43—21no—
120C4×D4×C43—21no—
121C4×D4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C42×C43C2311yescharacteristic
125#103×C43—22no—
126#103×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129#97×C43D412yes—
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132#41×C43—44no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—44no—
137C2×Q8×C43—41no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—41no—
142C22×C4×C43—41no—
143C22×C4×C43—41no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C2×C22⋊D43—41no—
148#10621898—44no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—21no—
152C2×C4×D43—41no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156M16×C43—42no—
157C2×C8×C43C2×D412yes—
158C2×C8×C43C2×D412yes—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—41no—
166C4⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C42×C43C2×D411yescharacteristic
170C42×C43C2×D411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43C2411yescharacteristic
173C22⋊Dic43—41no—
174#10621883—44no—
175#10621882—44no—
176(C2×D43)⋊C4—41no—
177(C2×D43)⋊C4—41no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184Dic43⋊C4—41no—
185Dic43⋊C4—41no—
186C4×Dic43—41no—
187#10621877—42no—
188#10621877—42no—
189C2×C43⋊C8C2×D412yes—
190C2×C43⋊C8C2×D412yes—
191C2×C43⋊C8C2×D412yes—
192C2×C43⋊C8C2×D412yes—
193#10621873—44no—
194C23×C43—41no—
195C23×C43#12711yescharacteristic
196C22×D43—41no—
197Q8×C43—42no—
198Q8×C43—42no—
199Q8×C43—42no—
200Q8×C43—82no—
201D4×C43—42no—
202D4×C43—42no—
203D4×C43—42no—
204D4×C43—82no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—82no—
212C2×C4×C43—82no—
213C2×C4×C43#12711yescharacteristic
214C2×C4×C43#12711yescharacteristic
215C2×C4×C43#12711yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C22⋊D43—82no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223D172—42no—
224D172—42no—
225D172—42no—
226C4×D43—82no—
227Dic86—42no—
228Dic86—42no—
229Dic86—42no—
230C8×C43—22no—
231C8×C43—22no—
232C43⋊C8—22no—
233C43⋊C8—22no—
234C43⋊C8—22no—
235C43⋊C8—22no—
236#19754—431nomaximal, Sylow
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—81no—
241C22×C43—81no—
242C22×C43—81no—
243C22×C43C2×#12711yescharacteristic
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C4×C43—21no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—81no—
251C4×C43—81no—
252C4×C43—81no—
253C4×C43#57512yes—
254C4×C43#57512yes—
255C4×C43#57512yes—
256Dic43—81no—
257Dic43—81no—
258Dic43—81no—
259#3184—431no—
260#3182—431no—
261#3182—431no—
262#3141—431no—
263#3141D4311yescharacteristic, complemented
264#3139—431no—
265#1719—431no—
266#1719—431no—
267#1718—431no—
268#1718—431no—
269#1717—431no—
270#1717—431no—
271#1711—431no—
272#1711—431no—
273#1455—431no—
274C2×C43—41no—
275C2×C43—161no—
276C2×C43#315311yescharacteristic
277C2×C43#315311yescharacteristic
278C2×C43#315311yescharacteristic
279D43—161no—
280#533—431no—
281#532—431no—
282#532C2×D4311yescharacteristic
283C2×C4⋊Q8C2×D4311yescharacteristic
284#500—431no—
285#500—431no—
286#498—431no—
287#493—431no—
288#492—431no—
289#492—431no—
290#491—862no—
291#489—22no—
292#489—862no—
293#487—431no—
294#487—431no—
295#487—431no—
296#487—431no—
297#487—431no—
298#487—431no—
299#487—431no—
300#487—431no—
301#487C2×D4311yescharacteristic
302#487C2×D4311yescharacteristic
303#486—431no—
304#486—431no—
305#486—431no—
306#486—431no—
307#486—431no—
308#486—431no—
309#486C2×D4311yescharacteristic
310#486C2×D4311yescharacteristic
311#469—862no—
312#468—862no—
313#468—862no—
314#442—862no—
315#440—862no—
316#440—862no—
317#419—862no—
318#417—22no—
319#417—862no—
320C4×M16—431no—
321C4×M16—431no—
322C4×M16C2×D4311yescharacteristic
323#322—431no—
324#322—431no—
325#322—431no—
326C82—431no—
327C43#1975411yescharacteristic, complemented, Sylow
328C2×#41—21no—
329C2×#41—861no—
330C22×Q8—21no—
331C2×SD16—862no—
332C2×SD16—862no—
333C2×D8—862no—
334C2×M16—432no—
335C2×M16—432no—
336C2×M16C22⋊D4312yes—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—431no—
341C4⋊Q8—431no—
342C4⋊Q8—431no—
343C4⋊Q8C22×D4311yescharacteristic
344C4⋊Q8C22×D4311yescharacteristic
345C4⋊Q8C22×D4311yescharacteristic
346#127—431no—
347#127C22×D4311yescharacteristic
348#125—861no—
349#124—21no—
350#124—861no—
351C22⋊Q8—861no—
352C22⋊Q8—861no—
353#121—21no—
354#121—21no—
355#121—861no—
356#121—861no—
357C4×Q8—861no—
358C4×Q8—861no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—861no—
362C4×D4—861no—
363#117—861no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C42C22×D4311yescharacteristic
367#107—862no—
368#107—862no—
369#106—862no—
370#103—22no—
371#103—22no—
372#103—862no—
373#103—862no—
374#103—862no—
375#103—862no—
376#103—862no—
377#103—862no—
378#103—862no—
379#103—862no—
380#102—22no—
381#102—22no—
382#102—862no—
383#102—862no—
384#102—862no—
385#102—862no—
386#102—862no—
387#102—862no—
388#97—432no—
389#97—432no—
390#97C22⋊D4312yes—
391C4×C8—431no—
392C4×C8—431no—
393C4×C8—431no—
394C4×C8—431no—
395C4×C8C22×D4311yescharacteristic
396C4×C8C22×D4311yescharacteristic
397#41—44no—
398#41—1724no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—44no—
403C2×Q8—41no—
404C2×Q8—861no—
405C2×Q8—861no—
406C2×Q8—861no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—41no—
411C2×D4—861no—
412C2×D4—861no—
413C2×D4—861no—
414C2×D4—1721no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—1721no—
418C22×C4D4×D4311yescharacteristic
419C22×C4D4×D4311yescharacteristic
420C22×C4C2×C22⋊D4311yescharacteristic
421SD16—1724no—
422SD16—1724no—
423D8—1724no—
424M16—42no—
425M16—1722no—
426M16—1722no—
427C2×C8—432no—
428C2×C8—432no—
429C2×C8—432no—
430C2×C8—432no—
431C2×C8C2×C22⋊D4312yes—
432C2×C8C2×C22⋊D4312yes—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—861no—
442C4⋊C4—861no—
443C4⋊C4—861no—
444C4⋊C4—861no—
445C4⋊C4—861no—
446C4⋊C4—861no—
447C4⋊C4—1721no—
448C4⋊C4—1721no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—1721no—
452C22⋊C4—1721no—
453C22⋊C4—1721no—
454C42—1721no—
455C42D4×D4311yescharacteristic
456C42D4×D4311yescharacteristic
457C42C2×C22⋊D4311yescharacteristic
458C42C23×D4311yescharacteristic
459C23—41no—
460C23—1721no—
461C23#1306332111yescharacteristic
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—82no—
466Q8—1722no—
467Q8—1722no—
468Q8—1722no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—82no—
473D4—3442no—
474D4—1722no—
475D4—1722no—
476D4—1722no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4—3442no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4—1721no—
489C2×C4#1306332111yescharacteristic
490C2×C4#1306332111yescharacteristic
491C2×C4#1306332111yescharacteristic
492C2×C4C2×D4×D4311yescharacteristic
493C2×C4C2×D4×D4311yescharacteristic
494C2×C4C22×C22⋊D4311yescharacteristic
495C8—22no—
496C8—22no—
497C8—862no—
498C8—862no—
499C8—862no—
500C8—862no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—3441no—
508C22—3441no—
509C22—3441no—
510C22C2×#1306332111yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—81no—
515C4—81no—
516C4—81no—
517C4—3441no—
518C4—3441no—
519C4—3441no—
520C4#1458369512yes—
521C4#1458369712yes—
522C4#1458369812yes—
523C2—41no—
524C2—161no—
525C2—6881no—
526C2#1914505711yescharacteristic
527C2#1914505911yescharacteristic
528C2#1914506211yescharacteristic
subgroupG/H
centerC22C2×#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3141C2
socleC22×C43C2×#127
prime radical#19145329C2
hypercenter#3141D43
hypocenterC43#19754
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #19145313C2semidirect
3. #19145309C2semidirect
4. #19144991C2semidirect
5. #19144975C2semidirect
6. #19134250C2semidirect
7. #19134247C2semidirect
8. #19134244C2semidirect
9. #19134238C2semidirect
10. #19134236C2semidirect
11. #19134231C2semidirect
12. #19134208C2semidirect
13. #19134206C2semidirect
14. #19132898C2semidirect
15. C43×#3141C2semidirect
263. #3141D43semidirect
327. C43#19754semidirect

Maximal subgroups

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

subgroupindex
#191453292
#191453132
#191453092
#191449912
#191449752
#191342502
#191342472
#191342442
#191342382
#191342362
#191342312
#191342082
#191342062
#191328982
C43×#31412
#1975443