Finite Group Databasebeta

← #25138050

Subgroups — #25138050

Order 11008.

706 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#19144404C211yesmaximal, characteristic, complemented
2C4×#13063351C211yesmaximal, characteristic
3#19143260C211yesmaximal, characteristic, complemented
4#19136036C212yesmaximal, complemented
5#19135888C212yesmaximal
6#19135585C211yesmaximal, characteristic, complemented
7#19135378C212yesmaximal, complemented
8#19135371C211yesmaximal, characteristic, complemented
9#19135254C212yesmaximal, complemented
10#19134587C211yesmaximal, characteristic, complemented
11C2×C43×#474C211yesmaximal, characteristic, complemented
12C2×#13063351C2211yescharacteristic
13C4×#10621898C2211yescharacteristic
14#14583191—21no—
15#14583186—21no—
16#14583181—21no—
17#14583176—21no—
18#14583009—21no—
19#14582999—21no—
20C4×#10621883—21no—
21C4×#10621882—21no—
22#14582959—22no—
23#14582955—21no—
24#14582951—21no—
25C2×#13063261C2212yes—
26#14582939C2212yes—
27#14582939C2211yescharacteristic
28#14582923C2211yescharacteristic
29#14582923C2211yescharacteristic
30#14582904C2211yescharacteristic
31#14582898C2211yescharacteristic
32#14582898C2212yes—
33C2×#13063242C2212yes—
34#14582865C2212yes—
35#14582854C2212yes—
36C4×#10621877C2211yescharacteristic
37#14582668C2212yes—
38#14582668C2212yes—
39#14582668C2212yes—
40#14582664C2212yes—
41C2×C4⋊Q8×C43C2211yescharacteristic
42C2×C4×D4×C43C2211yescharacteristic
43C43×#474—21no—
44C43×#474—21no—
45C43×#474—22no—
46C2×#107×C43C2212yes—
47C2×C4⋊C8×C43C2211yescharacteristic
48C2×#102×C43C2212yes—
49C2×#10621898C2311yescharacteristic
50#13063351—22no—
51#13063351—22no—
52C2×#10621883—21no—
53C2×#10621882—21no—
54C2×#10621877C2311yescharacteristic
55C2×#10621877C2312yes—
56C2×#10621877C2312yes—
57C2×#10621877C2311yescharacteristic
58C4×Dic86D411yescharacteristic
59C4×Dic86D411yescharacteristic
60C4×D172D411yescharacteristic
61C4×D172D411yescharacteristic
62C4×C22⋊D43—21no—
63C4×C22⋊D43—21no—
64#13063284C2311yescharacteristic
65#13063282—21no—
66C42×D43—21no—
67#13063261—24no—
68#13063258—22no—
69#13063258—21no—
70#13063256—22no—
71#13063256—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)—21no—
74C4⋊(C43⋊C8)—21no—
75C4⋊(C43⋊C8)—21no—
76#13063248—22no—
77#13063248—21no—
78#13063246—21no—
79#13063246—21no—
80#13063245—22no—
81#13063245—21no—
82#13063242—24no—
83(C2×D43)⋊C8—22no—
84(C2×D43)⋊C8—22no—
85#13063236—21no—
86#13063235—22no—
87C4×C43⋊C8—21no—
88C8×Dic43—22no—
89C22×Q8×C43—21no—
90C22×D4×C43C2311yescharacteristic
91C23×C4×C43—21no—
92C22×C8×C43C2312yes—
93C4⋊Q8×C43—21no—
94C4⋊Q8×C43—21no—
95C4⋊Q8×C43—21no—
96C4⋊Q8×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2312yes—
104C2×C22⋊C4×C43—21no—
105C2×C42×C43C2311yescharacteristic
106#107×C43—22no—
107#107×C43—22no—
108C4⋊C8×C43D411yescharacteristic
109C4⋊C8×C43D411yescharacteristic
110C4⋊C8×C43D412yes—
111#102×C43—22no—
112#102×C43—22no—
113C24×C43—21no—
114C2×Q8×C43—41no—
115C2×Q8×C43—41no—
116C2×Q8×C43—82no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43#4112yes—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—82no—
128C22×C4×C43#4111yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C2×C22⋊D43—21no—
132#10621898—21no—
133#10621898—21no—
134#10621898—21no—
135#10621898—21no—
136C2×D172C2×D411yescharacteristic
137C2×C4×D43—21no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×Dic86C2×D411yescharacteristic
141C2×C8×C43—22no—
142C2×C8×C43—22no—
143C2×C8×C43C2×D412yes—
144C2×C8×C43C2×D412yes—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—41no—
150C4⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C22⋊Dic43—21no—
158#10621883—24no—
159#10621882—24no—
160(C2×D43)⋊C4—21no—
161(C2×D43)⋊C4—21no—
162C4⋊Dic43C2×D411yescharacteristic
163C4⋊Dic43C2×D411yescharacteristic
164Dic43⋊C4—21no—
165Dic43⋊C4—21no—
166C4×Dic43—21no—
167C4×Dic43—21no—
168C4×Dic43—21no—
169#10621877—21no—
170#10621877—22no—
171#10621877—22no—
172#10621877—22no—
173#10621877—21no—
174#10621877—21no—
175#10621877—22no—
176#10621877#4112yes—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—21no—
180C2×C43⋊C8—22no—
181C23×C43—22no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—81no—
185C23×C43—81no—
186C23×C43C2×#4111yescharacteristic
187C22×D43—21no—
188Q8×C43—82no—
189Q8×C43—82no—
190D4×C43—22no—
191D4×C43—22no—
192D4×C43—41no—
193D4×C43—41no—
194C2×C4×C43—22no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—42no—
198C2×C4×C43—82no—
199C2×C4×C43—82no—
200C2×C4×C43—81no—
201C2×C4×C43—82no—
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C2×#4111yescharacteristic
209C2×C4×C43C2×#4111yescharacteristic
210C2×C4×C432−1+411yescharacteristic
211C2×C4×C432−1+411yescharacteristic
212C22⋊D43—41no—
213C22⋊D43—41no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—21no—
217D172—21no—
218D172—21no—
219C4×D43—41no—
220C4×D43—41no—
221C4×D43—42no—
222C4×D43—81no—
223Dic86—21no—
224Dic86—21no—
225C8×C43—22no—
226C8×C43—22no—
227C43⋊C8—22no—
228C43⋊C8—42no—
229C43⋊C8—41no—
230C43⋊C8—42no—
231#24720—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—42no—
235C22×C43—82no—
236C22×C43—82no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43C2×#12111yescharacteristic
240C22×C43#55211yescharacteristic
241C22×C43#55611yescharacteristic
242C2×D43—41no—
243C2×D43—41no—
244C2×D43—41no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—81no—
249C4×C43—82no—
250C4×C43#47212yes—
251C4×C43#52511yescharacteristic
252C4×C43#53611yescharacteristic
253C4×C43#54711yescharacteristic
254C4×C43#54811yescharacteristic
255Dic43—41no—
256Dic43—41no—
257Dic43—41no—
258#3079—431no—
259C2×#474D4311yescharacteristic, complemented
260C4×AGL(1,ℤ/8)—431no—
261#2925—431no—
262#2078—432no—
263#2051—432no—
264#1997—431no—
265#1952—432no—
266#1950—431no—
267#1931—432no—
268#1800—431no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43—82no—
272C2×C43#241511yescharacteristic
273C2×C43C2×#47211yescharacteristic
274C2×C43#306911yescharacteristic
275D43—81no—
276C2×AGL(1,ℤ/8)—431no—
277C2×C4⋊Q8C2×D4311yescharacteristic
278C4×#41—431no—
279C2×C4×D4C2×D4311yescharacteristic
280#477—861no—
281#476—861no—
282#475—861no—
283#474—21no—
284#474—21no—
285#474—22no—
286#474—861no—
287#442—861no—
288#440—861no—
289C4×SD16—861no—
290C4×D8—861no—
291#433—862no—
292#432—861no—
293#431—861no—
294C2×#108—432no—
295#428—432no—
296#428—431no—
297C2×#107C2×D4312yes—
298#423—431no—
299#423—431no—
300C2×C4⋊C8C2×D4311yescharacteristic
301#418—431no—
302#417—432no—
303#417—431no—
304C2×#102C2×D4312yes—
305C2×#100—432no—
306#408—432no—
307#405—432no—
308C4×M16—431no—
309#343—432no—
310#343—432no—
311#343—432no—
312#341—432no—
313C43#2472011yescharacteristic, complemented, Sylow
314C2×#41—431no—
315C22×Q8—21no—
316C22×D4C22×D4311yescharacteristic
317C23×C4—21no—
318AGL(1,ℤ/8)—862no—
319AGL(1,ℤ/8)—862no—
320C2×SD16—861no—
321C2×D8—861no—
322C2×M16—431no—
323C2×M16—431no—
324C2×M16—432no—
325C2×M16—432no—
326C22×C8C22×D4312yes—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4×Q8—431no—
332C4×Q8—431no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—431no—
338C4×D4—431no—
339C4×D4—861no—
340C4×D4—861no—
341#117—431no—
342#117—861no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4C22×D4311yescharacteristic
345C2×C4⋊C4C22×D4312yes—
346C2×C22⋊C4—21no—
347C2×C42—861no—
348C2×C42C22×D4311yescharacteristic
349#108—864no—
350#107—22no—
351#107—22no—
352#107—861no—
353#107—862no—
354#106—861no—
355#106—862no—
356C4⋊C8—861no—
357C4⋊C8—861no—
358C4⋊C8—861no—
359C4⋊C8—861no—
360C4⋊C8C22⋊D4311yescharacteristic
361C4⋊C8C22⋊D4311yescharacteristic
362C4⋊C8C22⋊D4312yes—
363#103—861no—
364#103—862no—
365#102—22no—
366#102—22no—
367#102—861no—
368#102—862no—
369#102—861no—
370#102—861no—
371#100—864no—
372C22⋊C8—862no—
373C22⋊C8—862no—
374#97—862no—
375#97—861no—
376C4×C8—862no—
377C4×C8—861no—
378C24—21no—
379#41—861no—
380#41—861no—
381#41—861no—
382#41—861no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—82no—
386C2×Q8—431no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—431no—
393C2×D4—861no—
394C2×D4#1062190212yes—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—82no—
400C22×C4—861no—
401C22×C4—861no—
402C22×C4—861no—
403C22×C4#1062190011yescharacteristic
404C22×C4#1062190011yescharacteristic
405C22×C4C23×D4311yescharacteristic
406SD16—864no—
407D8—864no—
408M16—432no—
409M16—861no—
410M16—862no—
411M16—862no—
412M16—862no—
413M16—861no—
414M16—862no—
415M16—861no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—861no—
419C2×C8—861no—
420C2×C8—862no—
421C2×C8—862no—
422C2×C8C2×C22⋊D4312yes—
423C2×C8C2×C22⋊D4312yes—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—431no—
431C4⋊C4—431no—
432C4⋊C4—861no—
433C4⋊C4—861no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—861no—
437C22⋊C4—861no—
438C22⋊C4—861no—
439C42—861no—
440C42—861no—
441C42—861no—
442C42D4×D4311yescharacteristic
443C42D4×D4311yescharacteristic
444C42C2×C22⋊D4311yescharacteristic
445C42C2×C22⋊D4311yescharacteristic
446C23—22no—
447C23—41no—
448C23—41no—
449C23—81no—
450C23—81no—
451C23—861no—
452C23C2×#1062190011yescharacteristic
453Q8—82no—
454Q8—82no—
455Q8—861no—
456Q8—861no—
457D4—22no—
458D4—22no—
459D4—41no—
460D4—41no—
461D4—861no—
462D4—861no—
463D4—1721no—
464D4—1721no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—81no—
472C2×C4—82no—
473C2×C4—861no—
474C2×C4—861no—
475C2×C4—861no—
476C2×C4—3441no—
477C2×C4—1721no—
478C2×C4—1722no—
479C2×C4—1721no—
480C2×C4#1306329611yescharacteristic
481C2×C4#1306329611yescharacteristic
482C2×C4#1306329611yescharacteristic
483C2×C4#1306329611yescharacteristic
484C2×C4C2×D4×D4311yescharacteristic
485C2×C4C22×C22⋊D4311yescharacteristic
486C2×C4#41×D4311yescharacteristic
487C2×C4C2×#1062190211yescharacteristic
488C2×C4#1306337211yescharacteristic
489C2×C4#1306337311yescharacteristic
490C8—22no—
491C8—22no—
492C8—862no—
493C8—1722no—
494C8—1722no—
495C8—1721no—
496C22—21no—
497C22—21no—
498C22—42no—
499C22—82no—
500C22—82no—
501C22—81no—
502C22—81no—
503C22—1721no—
504C22—1721no—
505C22—1721no—
506C22C2×#1306329611yescharacteristic
507C22#1458359111yescharacteristic
508C22#1458362011yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—81no—
513C4—82no—
514C4—1721no—
515C4—1721no—
516C4—1721no—
517C4#1458316612yes—
518C4#1458341211yescharacteristic
519C4#1458347211yescharacteristic
520C4#1458354811yescharacteristic
521C4#1458356011yescharacteristic
522C2—21no—
523C2—21no—
524C2—82no—
525C2—3441no—
526C2#1913802011yescharacteristic
527C2C2×#1458316611yescharacteristic
528C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#474C2
socleC22×C43C2×#121
prime radicalC2×#13063351C22
hypercenterC2×#474D43
hypocenterC43#24720
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #19144404C2semidirect
3. #19143260C2semidirect
4. #19136036C2semidirect
6. #19135585C2semidirect
7. #19135378C2semidirect
8. #19135371C2semidirect
9. #19135254C2semidirect
10. #19134587C2semidirect
11. C2×C43×#474C2semidirect
259. C2×#474D43semidirect
313. C43#24720semidirect

Maximal subgroups

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

subgroupindex
#191444042
C4×#130633512
#191432602
#191360362
#191358882
#191355852
#191353782
#191353712
#191352542
#191345872
C2×C43×#4742
#2472043