Finite Group Databasebeta

← #25138057

Subgroups — #25138057

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
2C2×#14583176C211yesmaximal, characteristic, complemented
3C4×#13063353C211yesmaximal, characteristic
4#19143263C211yesmaximal, characteristic, complemented
5#19136039C212yesmaximal, complemented
6#19135890C212yesmaximal
7#19135379C212yesmaximal, complemented
8#19135370C211yesmaximal, characteristic, complemented
9#19135255C212yesmaximal, complemented
10#19134584C211yesmaximal, characteristic, complemented
11C43×#1997C211yesmaximal, characteristic, complemented
12C2×#13063353C2211yescharacteristic
13C4×#10621898C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583191—21no—
16#14583186—21no—
17#14583181—21no—
18#14583176—21no—
19#14583176—21no—
20#14583176—21no—
21#14583176—22no—
22#14583012—21no—
23#14583001—21no—
24C4×#10621873—21no—
25C4×D344—21no—
26#14582959—22no—
27#14582955—21no—
28#14582951—21no—
29C2×#13063260C2212yes—
30#14582941C2211yescharacteristic
31#14582939C2212yes—
32C2×#13063258C2212yes—
33#14582923C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35#14582905C2211yescharacteristic
36#14582901C2211yescharacteristic
37#14582898C2212yes—
38C2×#13063245C2212yes—
39C2×#13063241C2212yes—
40#14582867C2212yes—
41#14582857C2212yes—
42#14582667C2212yes—
43#14582663C2212yes—
44C2×C4⋊Q8×C43C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C43×#343C2212yes—
48C43×#343C2212yes—
49C2×#10621898C2311yescharacteristic
50C22×D172C2311yescharacteristic
51C22×C4×D43—21no—
52#13063353—22no—
53#13063353—22no—
54C2×#10621873—21no—
55C2×D344—21no—
56C2×#10621877C2312yes—
57C22×C43⋊C8C2312yes—
58C4×Dic86D411yescharacteristic
59C4×Dic86D411yescharacteristic
60C4×D172—21no—
61C4×D172—21no—
62C4×D172—21no—
63C4×D172—21no—
64C4×D172D411yescharacteristic
65C4×D172D411yescharacteristic
66C4×C22⋊D43—21no—
67C4×C22⋊D43—21no—
68#13063284C2311yescharacteristic
69#13063282—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×(C2×D43)⋊C4—21no—
72C42×D43—21no—
73#13063260—24no—
74#13063259—21no—
75#13063258—22no—
76#13063258—22no—
77#13063258—22no—
78#13063257—21no—
79#13063256—22no—
80C4⋊(C43⋊C8)—21no—
81C4⋊(C43⋊C8)—21no—
82C4⋊(C43⋊C8)D411yescharacteristic
83C4⋊(C43⋊C8)D411yescharacteristic
84C4⋊(C43⋊C8)D412yes—
85#13063250—21no—
86#13063248—22no—
87#13063247—21no—
88#13063247—21no—
89#13063247—21no—
90#13063245—22no—
91#13063245—22no—
92#13063245—22no—
93#13063241—24no—
94(C2×D43)⋊C8—22no—
95(C2×D43)⋊C8—22no—
96#13063235—22no—
97C8×Dic43—22no—
98C22×Q8×C43—21no—
99C2×M16×C43C2312yes—
100C2×M16×C43C2311yescharacteristic
101C2×M16×C43C2311yescharacteristic
102C4⋊Q8×C43—21no—
103C4⋊Q8×C43—21no—
104C4⋊Q8×C43—21no—
105C4⋊Q8×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2312yes—
108C2×C42×C43C2311yescharacteristic
109C4⋊C8×C43—21no—
110C4⋊C8×C43—21no—
111#97×C43—21no—
112C4×C8×C43—21no—
113C23×D43—21no—
114C2×Q8×C43—41no—
115C2×Q8×C43—41no—
116C2×Q8×C43—82no—
117C22×C4×C43—22no—
118C22×C4×C43#4111yescharacteristic
119C22×C4×C43#4111yescharacteristic
120C22×C4×C43C2411yescharacteristic
121C2×C22⋊D43—21no—
122C22×Dic43—21no—
123#10621898—21no—
124#10621898—21no—
125#10621898—21no—
126#10621898—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172C2×D411yescharacteristic
133C2×D172#4112yes—
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—41no—
138C2×C4×D43—41no—
139C2×C4×D43—82no—
140C2×Dic86C2×D411yescharacteristic
141M16×C43—21no—
142M16×C43—22no—
143M16×C43—21no—
144M16×C43—22no—
145M16×C43—21no—
146M16×C43#4112yes—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—41no—
153C4⋊C4×C43—41no—
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C22⋊Dic43—21no—
159(C2×D43)⋊C4—21no—
160(C2×D43)⋊C4—21no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43C2×D411yescharacteristic
166C4⋊Dic43C2×D411yescharacteristic
167Dic43⋊C4—21no—
168Dic43⋊C4—21no—
169C4×Dic43—21no—
170C4×Dic43—21no—
171C4×Dic43—21no—
172#10621877—22no—
173#10621877—22no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8C2×D412yes—
178C2×C43⋊C8C2×D412yes—
179D344—24no—
180#10621873—24no—
181C23×C43C2×#4111yescharacteristic
182C22×D43—21no—
183C22×D43—22no—
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—81no—
187C22×D43—81no—
188Q8×C43—82no—
189Q8×C43—82no—
190C2×C4×C43—22no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—82no—
194C2×C4×C43#12111yescharacteristic
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43C22×D411yescharacteristic
199C2×C4×C43C22×D411yescharacteristic
200C2×C4×C43C2×#4111yescharacteristic
201C2×C4×C43C2×#4111yescharacteristic
202C2×C4×C432−1+411yescharacteristic
203C2×C4×C432−1+411yescharacteristic
204C22⋊D43—41no—
205C22⋊D43—41no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—21no—
209C2×Dic43—41no—
210C2×Dic43—81no—
211D172—22no—
212D172—21no—
213D172—21no—
214D172—22no—
215D172—41no—
216D172—41no—
217C4×D43—41no—
218C4×D43—41no—
219C4×D43—42no—
220C4×D43—81no—
221C4×D43—82no—
222C4×D43—82no—
223Dic86—21no—
224Dic86—21no—
225C8×C43—22no—
226C8×C43—41no—
227C8×C43—42no—
228C43⋊C8—22no—
229C43⋊C8—22no—
230C43⋊C8—42no—
231#24720—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43C2×#12111yescharacteristic
235C22×C43#55211yescharacteristic
236C22×C43#55611yescharacteristic
237C2×D43—42no—
238C2×D43—41no—
239C2×D43—41no—
240C2×D43—41no—
241C2×D43—82no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—82no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—82no—
249C4×C43#47212yes—
250C4×C43#52511yescharacteristic
251C4×C43#53611yescharacteristic
252C4×C43#54711yescharacteristic
253C4×C43#54811yescharacteristic
254Dic43—41no—
255Dic43—41no—
256Dic43—41no—
257Dic43—81no—
258#3079—431no—
259C2×#474—431no—
260C4×AGL(1,ℤ/8)—431no—
261#2925—431no—
262#2078—432no—
263#2051—432no—
264#1997D4311yescharacteristic, complemented
265#1952—432no—
266#1950—431no—
267#1931—432no—
268#1800—431no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43#241511yescharacteristic
272C2×C43C2×#47211yescharacteristic
273C2×C43#306911yescharacteristic
274D43—81no—
275D43—82no—
276C2×AGL(1,ℤ/8)—431no—
277C2×C4⋊Q8C2×D4311yescharacteristic
278C4×#41—431no—
279C2×C4×D4—431no—
280#477—861no—
281#476—861no—
282#475—861no—
283#474—861no—
284#474—861no—
285#474—862no—
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—431no—
296#428—432no—
297C2×#107—432no—
298#423—431no—
299#423C2×D4311yescharacteristic
300C2×C4⋊C8—431no—
301#418—431no—
302#417—431no—
303#417—432no—
304C2×#102—432no—
305C2×#100—432no—
306#408—432no—
307#405—432no—
308C4×M16C2×D4311yescharacteristic
309#343—432no—
310#343C2×D4312yes—
311#343C2×D4312yes—
312#341—432no—
313C43#2472011yescharacteristic, complemented, Sylow
314C2×#41—431no—
315C22×Q8—21no—
316C22×D4—431no—
317C23×C4—861no—
318AGL(1,ℤ/8)—862no—
319AGL(1,ℤ/8)—862no—
320C2×SD16—861no—
321C2×D8—861no—
322C2×M16—432no—
323C2×M16C22×D4311yescharacteristic
324C2×M16C22×D4312yes—
325C2×M16C22×D4311yescharacteristic
326C22×C8—432no—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4×Q8—431no—
332C4×Q8—431no—
333C4×D4—431no—
334C4×D4—431no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—861no—
338C4×D4—861no—
339C4×D4—861no—
340C4×D4—861no—
341#117—431no—
342#117—861no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—431no—
345C2×C4⋊C4C22×D4312yes—
346C2×C22⋊C4—861no—
347C2×C42—861no—
348C2×C42C22×D4311yescharacteristic
349#108—864no—
350#107—862no—
351#107—862no—
352#107—862no—
353#107—861no—
354#106—862no—
355#106—861no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—431no—
359C4⋊C8—431no—
360C4⋊C8—432no—
361C4⋊C8—861no—
362C4⋊C8—861no—
363#103—862no—
364#103—861no—
365#102—862no—
366#102—862no—
367#102—862no—
368#102—861no—
369#102—861no—
370#102—861no—
371#100—864no—
372C22⋊C8—862no—
373C22⋊C8—862no—
374#97—21no—
375#97—862no—
376C4×C8—21no—
377C4×C8—862no—
378C24—861no—
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—431no—
388C2×D4—432no—
389C2×D4—861no—
390C2×D4—861no—
391C2×D4—861no—
392C2×D4—861no—
393C2×D4—861no—
394C2×D4—861no—
395C22×C4—22no—
396C22×C4—861no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—861no—
400C22×C4—3442no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4#1062189811yescharacteristic
404C22×C4#1062189811yescharacteristic
405C22×C4C23×D4311yescharacteristic
406SD16—864no—
407D8—864no—
408M16—21no—
409M16—22no—
410M16—22no—
411M16—21no—
412M16—21no—
413M16—862no—
414M16—862no—
415M16#1062190212yes—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—22no—
419C2×C8—432no—
420C2×C8—432no—
421C2×C8—862no—
422C2×C8—862no—
423C2×C8—862no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—431no—
429C4⋊C4—431no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C4⋊C4—861no—
433C4⋊C4—861no—
434C22⋊C4—861no—
435C22⋊C4—861no—
436C22⋊C4—861no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C42—861no—
440C42—861no—
441C42—861no—
442C42D4×D4311yescharacteristic
443C42D4×D4311yescharacteristic
444C42D4×D4311yescharacteristic
445C42D4×D4311yescharacteristic
446C23—862no—
447C23—861no—
448C23—3441no—
449C23—3441no—
450C23—1721no—
451C23—1721no—
452C23C2×#1062189811yescharacteristic
453Q8—82no—
454Q8—82no—
455Q8—861no—
456Q8—861no—
457D4—862no—
458D4—861no—
459D4—862no—
460D4—861no—
461D4—1721no—
462D4—1721no—
463D4—1721no—
464D4—1721no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—82no—
469C2×C4—861no—
470C2×C4—861no—
471C2×C4—861no—
472C2×C4—3442no—
473C2×C4—3441no—
474C2×C4—3442no—
475C2×C4—3441no—
476C2×C4—1721no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1722no—
480C2×C4#1306329811yescharacteristic
481C2×C4#1306329811yescharacteristic
482C2×C4#1306329811yescharacteristic
483C2×C4#1306329811yescharacteristic
484C2×C4C2×D4×D4311yescharacteristic
485C2×C4C2×D4×D4311yescharacteristic
486C2×C4#41×D4311yescharacteristic
487C2×C4C2×#1062190211yescharacteristic
488C2×C4#1306337211yescharacteristic
489C2×C4#1306337311yescharacteristic
490C8—22no—
491C8—42no—
492C8—41no—
493C8—862no—
494C8—862no—
495C8—1722no—
496C22—21no—
497C22—21no—
498C22—3442no—
499C22—3442no—
500C22—3441no—
501C22—3441no—
502C22—1721no—
503C22—1721no—
504C22—1721no—
505C22—1722no—
506C22C2×#1306329811yescharacteristic
507C22#1458359011yescharacteristic
508C22#1458362211yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—82no—
513C4—3441no—
514C4—1721no—
515C4—1721no—
516C4—1721no—
517C4#1458316812yes—
518C4#1458341211yescharacteristic
519C4#1458347211yescharacteristic
520C4#1458355211yescharacteristic
521C4#1458355711yescharacteristic
522C2—21no—
523C2—21no—
524C2—3442no—
525C2—3441no—
526C2#1913802711yescharacteristic
527C2C2×#1458316811yescharacteristic
528C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1997C2
socleC22×C43C2×#121
prime radicalC2×#13063353C22
hypercenter#1997D43
hypocenterC43#24720
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
1. #19144404C2semidirect
2. C2×#14583176C2semidirect
4. #19143263C2semidirect
5. #19136039C2semidirect
7. #19135379C2semidirect
8. #19135370C2semidirect
9. #19135255C2semidirect
10. #19134584C2semidirect
11. C43×#1997C2semidirect
264. #1997D43semidirect
313. C43#24720semidirect

Maximal subgroups

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

subgroupindex
#191444042
C2×#145831762
C4×#130633532
#191432632
#191360392
#191358902
#191353792
#191353702
#191352552
#191345842
C43×#19972
#2472043