Finite Group Databasebeta

← #25082062

Subgroups — #25082062

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145720C211yesmaximal, characteristic, complemented
2#19144411C211yesmaximal, characteristic, complemented
3#19144044C211yesmaximal, characteristic
4#19143704C211yesmaximal, characteristic, complemented
5#19134010C212yesmaximal, complemented
6#19134003C212yesmaximal, complemented
7#19133976C212yesmaximal, complemented
8#19133969C212yesmaximal, complemented
9#19133367C211yesmaximal, characteristic, complemented
10C2×#14582647C211yesmaximal, characteristic, complemented
11C43×#1547C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13C2×#13063325C2211yescharacteristic
14C4×#10621898C2211yescharacteristic
15#14583295C2212yes—
16#14583245C2212yes—
17#14583215—22no—
18#14583195C2212yes—
19#14583190C2212yes—
20#14583189—21no—
21#14583189—21no—
22#14583185—21no—
23#14583180—21no—
24#14583118—21no—
25#14583111—21no—
26#14583106C2211yescharacteristic
27#14583101C2211yescharacteristic
28#14583096C2211yescharacteristic
29#14583091C2211yescharacteristic
30#14583023C2212yes—
31#14582964C2212yes—
32C8×C22⋊D43—22no—
33#14582952C2211yescharacteristic
34#14582951—21no—
35#14582941—21no—
36C2×C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊C8×D43—21no—
38#14582901—21no—
39#14582895—21no—
40#14582649C2212yes—
41#14582649C2212yes—
42#14582647C2212yes—
43#14582647C2212yes—
44C43×#532C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#332C2212yes—
48C43×#331C2212yes—
49C2×#10621898D411yescharacteristic
50C22×Dic86—21no—
51#13063345—44no—
52C2×#10621885—21no—
53C2×#10621883—21no—
54C2×#10621884—21no—
55C2×#10621882—21no—
56C22×C43⋊C8—21no—
57C2×C8×D43—22no—
58#13063325—21no—
59#13063325—21no—
60#13063325—21no—
61#13063325C2312yes—
62C4×Dic86D411yescharacteristic
63C4×Dic86C2311yescharacteristic
64C4×D172D411yescharacteristic
65C4×D172C2311yescharacteristic
66C4×C22⋊D43—21no—
67C4×C22⋊D43—21no—
68#13063284D411yescharacteristic
69#13063282—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C42×D43—21no—
73#13063259—22no—
74#13063257—22no—
75#13063256—22no—
76#13063256—22no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)D411yescharacteristic
79C4⋊(C43⋊C8)D411yescharacteristic
80C4⋊(C43⋊C8)C2311yescharacteristic
81C4⋊(C43⋊C8)C2311yescharacteristic
82Dic43⋊C8—22no—
83#13063250—22no—
84#13063249—21no—
85#13063249—21no—
86#13063247—22no—
87#13063246—21no—
88#13063246—21no—
89#13063246—22no—
90#13063246—22no—
91C22⋊(C43⋊C8)D412yes—
92(C2×D43)⋊C8—22no—
93C4×C43⋊C8C2312yes—
94C8×Dic43—22no—
95C2×#41×C43—21no—
96C2×M16×C43—21no—
97C22×C8×C43—21no—
98C4⋊Q8×C43C2311yescharacteristic
99#127×C43C2311yescharacteristic
100#124×C43—21no—
101#121×C43—21no—
102#121×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C2×C42×C43C2311yescharacteristic
106C4⋊C8×C43—21no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109C4⋊C8×C43C2312yes—
110#41×C43—42no—
111#41×C43—42no—
112C2×Q8×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C2×C22⋊D43—21no—
122C22×Dic43—41no—
123#10621898—22no—
124#10621898SD1614yes—
125C2×D172C2×D411yescharacteristic
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×Dic86—22no—
130C2×Dic86—41no—
131C2×Dic86—82no—
132C2×Dic86C2×D411yescharacteristic
133M16×C43—42no—
134C2×C8×C43—22no—
135C2×C8×C43—22no—
136C2×C8×C43—81no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C22⋊C4×C43—41no—
140C22⋊C4×C43—41no—
141C42×C43C2×D411yescharacteristic
142C42×C43C2×D411yescharacteristic
143C42×C43#4111yescharacteristic
144C42×C43C2411yescharacteristic
145C22⋊Dic43—21no—
146#10621885—42no—
147#10621884—42no—
148#10621883—42no—
149#10621882—42no—
150(C2×D43)⋊C4—21no—
151(C2×D43)⋊C4—21no—
152C4⋊Dic43—22no—
153C4⋊Dic43—22no—
154C4⋊Dic43—41no—
155C4⋊Dic43—41no—
156C4⋊Dic43C2×D411yescharacteristic
157C4⋊Dic43C2×D411yescharacteristic
158Dic43⋊C4—21no—
159Dic43⋊C4—21no—
160C4×Dic43—21no—
161C4×Dic43—21no—
162C4×Dic43—21no—
163C2×C43⋊C8—21no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8—42no—
166C2×C43⋊C8C2×D412yes—
167C2×C43⋊C8C2×D412yes—
168C8×D43—82no—
169C23×C43—41no—
170C23×C43#12111yescharacteristic
171C22×D43—21no—
172Q8×C43—41no—
173Q8×C43—41no—
174D4×C43—41no—
175D4×C43—41no—
176D4×C43—41no—
177D4×C43—41no—
178D4×C43—81no—
179D4×C43—82no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—82no—
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43C2×SD1612yes—
189C2×C4×C43#13512yes—
190C2×C4×C43C22×D411yescharacteristic
191C2×C4×C43C22×D411yescharacteristic
192C2×C4×C43C2×#4111yescharacteristic
193C22⋊D43—24no—
194C2×Dic43—21no—
195C2×Dic43—21no—
196C2×Dic43—21no—
197C2×Dic43—42no—
198C2×Dic43—82no—
199D172—21no—
200D172C2×SD1612yes—
201C4×D43—24no—
202C4×D43—41no—
203C4×D43—41no—
204C4×D43—81no—
205Dic86—21no—
206Dic86—82no—
207Dic86—82no—
208Dic86C2×SD1612yes—
209C8×C43—42no—
210C8×C43—42no—
211C43⋊C8—22no—
212C43⋊C8—22no—
213C43⋊C8—41no—
214C43⋊C8—41no—
215#19414—431nomaximal, Sylow
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—81no—
219C22×C43—81no—
220C22×C43—81no—
221C22×C43#46512yes—
222C22×C43C2×#12111yescharacteristic
223C2×D43—22no—
224C2×D43—41no—
225C2×D43—41no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—81no—
230C4×C43#46512yes—
231C4×C43C22×SD1611yescharacteristic
232C4×C43C2×#13511yescharacteristic
233C4×C43#57711yescharacteristic
234C4×C43#57811yescharacteristic
235Dic43—22no—
236Dic43—41no—
237Dic43—41no—
238Dic43—82no—
239#3227—431no—
240#3079—431no—
241#3035—431no—
242#2988—431no—
243#1678—432no—
244#1677—432no—
245#1672—432no—
246#1671—432no—
247#1570—431no—
248#1547D4311yescharacteristic, complemented
249C2×#333—431no—
250C2×C43—22no—
251C2×C43—161no—
252C2×C43#304611yescharacteristic
253C2×C43C2×#46511yescharacteristic
254C2×C43#306811yescharacteristic
255D43—42no—
256C2×#135—861no—
257#532C2×D4311yescharacteristic
258C2×C4⋊Q8—431no—
259C4×#41—431no—
260#498—432no—
261#486—432no—
262#481—862no—
263#477—432no—
264#476—432no—
265#476—861no—
266#476—861no—
267#475—861no—
268#474—861no—
269#464—861no—
270#463—861no—
271#462—431no—
272#461—431no—
273#460—431no—
274#459—431no—
275C8×Q8—432no—
276C8×D4—432no—
277C8×D4—862no—
278#431—431no—
279#431—861no—
280#428—861no—
281#423C2×D4311yescharacteristic
282C2×C4⋊C8—431no—
283C2×C4⋊C8—861no—
284C2×C4⋊C8C2×D4311yescharacteristic
285#417—861no—
286#416—861no—
287#334—432no—
288#334—432no—
289#333—432no—
290#333—432no—
291#332C2×D4312yes—
292#331C2×D4312yes—
293C43#1941411yescharacteristic, complemented, Sylow
294C2×#41—21no—
295C2×#41—431no—
296C22×Q8—861no—
297#135—1724no—
298C2×Q16—861no—
299C2×SD16—861no—
300C2×SD16—861no—
301C2×D8—861no—
302C2×M16—21no—
303C22×C8—21no—
304C22×C8—862no—
305C22×C8—861no—
306C4⋊Q8—432no—
307C4⋊Q8—861no—
308C4⋊Q8—861no—
309C4⋊Q8—861no—
310C4⋊Q8C22×D4311yescharacteristic
311#127C22×D4311yescharacteristic
312#124—21no—
313#121—21no—
314#121—21no—
315C4×Q8—431no—
316C4×Q8—431no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—431no—
320C4×D4—431no—
321C4×D4—861no—
322C4×D4—861no—
323#117—431no—
324#117—861no—
325C2×C4⋊C4—861no—
326C2×C4⋊C4—861no—
327C2×C42—861no—
328C2×C42C22×D4311yescharacteristic
329#107—862no—
330#106—862no—
331#106—862no—
332#106—862no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8—431no—
336C4⋊C8—431no—
337C4⋊C8—431no—
338C4⋊C8—431no—
339C4⋊C8—862no—
340C4⋊C8—861no—
341C4⋊C8C22×D4312yes—
342C4⋊C8C22×D4312yes—
343#103—861no—
344#103—861no—
345#103—862no—
346#102—861no—
347#102—861no—
348#102—862no—
349#102—862no—
350#102—862no—
351C22⋊C8—432no—
352C22⋊C8—862no—
353C4×C8—432no—
354C4×C8—862no—
355#41—42no—
356#41—42no—
357#41—434no—
358#41—862no—
359C2×Q8—21no—
360C2×Q8—431no—
361C2×Q8—862no—
362C2×Q8—3442no—
363C2×Q8—1721no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—431no—
369C2×D4—861no—
370C22×C4—41no—
371C22×C4—861no—
372C22×C4—861no—
373C22×C4—861no—
374C22×C4—1721no—
375C22×C4#1062189811yescharacteristic
376C22×C4D4×D4311yescharacteristic
377C22×C4D4×D4311yescharacteristic
378Q16—1722no—
379SD16—1722no—
380SD16—1722no—
381D8—1722no—
382M16—42no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—81no—
386C2×C8—432no—
387C2×C8—432no—
388C2×C8—861no—
389C2×C8—861no—
390C2×C8—3442no—
391C2×C8—1722no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—431no—
395C4⋊C4—431no—
396C4⋊C4—861no—
397C4⋊C4—861no—
398C4⋊C4—862no—
399C4⋊C4—862no—
400C4⋊C4—1721no—
401C4⋊C4—1721no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—861no—
405C22⋊C4—861no—
406C22⋊C4—861no—
407C42—861no—
408C42—861no—
409C42—861no—
410C42#1062189811yescharacteristic
411C42D4×D4311yescharacteristic
412C42D4×D4311yescharacteristic
413C42C23×D4311yescharacteristic
414C23—41no—
415C23—861no—
416C23#1306329811yescharacteristic
417Q8—41no—
418Q8—41no—
419Q8—432no—
420Q8—861no—
421Q8—3442no—
422Q8—3442no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—82no—
429D4—432no—
430D4—864no—
431D4—861no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—82no—
437C2×C4—861no—
438C2×C4—864no—
439C2×C4—861no—
440C2×C4—861no—
441C2×C4—3441no—
442C2×C4—3442no—
443C2×C4—1722no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4#1306329811yescharacteristic
447C2×C4#1306329811yescharacteristic
448C2×C4#1306329811yescharacteristic
449C2×C4SD16×D4312yes—
450C2×C4#1306334412yes—
451C2×C4C2×D4×D4311yescharacteristic
452C2×C4C2×D4×D4311yescharacteristic
453C2×C4C2×#1062189811yescharacteristic
454C8—42no—
455C8—42no—
456C8—862no—
457C8—862no—
458C8—1721no—
459C8—1721no—
460C22—21no—
461C22—21no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—862no—
466C22—1721no—
467C22—1721no—
468C22#1458312712yes—
469C22C2×#1306329811yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—81no—
474C4—862no—
475C4—3442no—
476C4—1721no—
477C4—1721no—
478C4#1458312712yes—
479C4C2×SD16×D4311yescharacteristic
480C4C2×#1306334411yescharacteristic
481C4#1458370911yescharacteristic
482C4#1458371511yescharacteristic
483C2—22no—
484C2—161no—
485C2—1722no—
486C2#1914414411yescharacteristic
487C2C2×#1458312711yescharacteristic
488C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1547C2
socleC22×C43C2×#121
prime radical#19144044C2
hypercenter#1547D43
hypocenterC43#19414
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
1. #19145720C2semidirect
2. #19144411C2semidirect
4. #19143704C2semidirect
5. #19134010C2semidirect
6. #19134003C2semidirect
7. #19133976C2semidirect
8. #19133969C2semidirect
9. #19133367C2semidirect
10. C2×#14582647C2semidirect
11. C43×#1547C2semidirect
248. #1547D43semidirect
293. C43#19414semidirect

Maximal subgroups

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

subgroupindex
#191457202
#191444112
#191440442
#191437042
#191340102
#191340032
#191339762
#191339692
#191333672
C2×#145826472
C43×#15472
#1941443