Finite Group Databasebeta

← #471×D113 #28400269

Subgroups — #471×D113 #28400269

Order 14464.

468 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#137×D113C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×D113C211yesmaximal, characteristic
3C2×SD16×D113C211yesmaximal, characteristic, complemented
4#131×D113C211yesmaximal, characteristic, complemented
5#20298864C211yesmaximal, characteristic, complemented
6#20298863C211yesmaximal, characteristic, complemented
7#20298862C211yesmaximal, characteristic, complemented
8#20298861C211yesmaximal, characteristic, complemented
9#20298860C211yesmaximal, characteristic, complemented
10#20298859C211yesmaximal, characteristic, complemented
11#20298858C211yesmaximal, characteristic, complemented
12#108×D113C211yesmaximal, characteristic, complemented
13#101×D113C211yesmaximal, characteristic, complemented
14#100×D113C211yesmaximal, characteristic, complemented
15#471×C113C211yesmaximal, characteristic, complemented
16#41×D113C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813655C2211yescharacteristic, complemented
20#16813654—21no—
21#16813653C2211yescharacteristic, complemented
22#16813652C2211yescharacteristic, complemented
23#16813651—21no—
24#16813650C2211yescharacteristic
25#16813649—21no—
26#16813648C2211yescharacteristic
27#16813647C2211yescharacteristic
28#16813646—21no—
29Q16×D113—21no—
30C2×#14268636C2211yescharacteristic, complemented
31C2×#14268635C2211yescharacteristic, complemented
32C2×#14268634C2211yescharacteristic, complemented
33SD16×D113—21no—
34SD16×D113—21no—
35SD16×D113—21no—
36SD16×D113—21no—
37SD16×D113—21no—
38SD16×D113—21no—
39D8×D113—21no—
40#16813630—21no—
41#16813630C2211yescharacteristic, complemented
42#16813629C2211yescharacteristic, complemented
43#16813628—21no—
44#16813628C2211yescharacteristic, complemented
45M16×D113—21no—
46M16×D113C2211yescharacteristic
47M16×D113C2211yescharacteristic
48M16×D113C2211yescharacteristic
49C2×C8×D113—21no—
50C2×C8×D113C2211yescharacteristic
51#16813558C2211yescharacteristic, complemented
52#16813557C2211yescharacteristic, complemented
53#16813557C2211yescharacteristic, complemented
54#16813541C2211yescharacteristic, complemented
55#16813540C2211yescharacteristic, complemented
56#16813540C2211yescharacteristic, complemented
57#16813539C2211yescharacteristic, complemented
58#16813538C2211yescharacteristic, complemented
59#16813538C2211yescharacteristic, complemented
60#137×C113C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C113C2211yescharacteristic
62C2×SD16×C113C2211yescharacteristic, complemented
63#131×C113C2211yescharacteristic, complemented
64#108×C113C2211yescharacteristic, complemented
65#101×C113C2211yescharacteristic, complemented
66#100×C113C2211yescharacteristic, complemented
67C23×D113—21no—
68#14268648D411yescharacteristic
69#14268647—21no—
70#14268647C2311yescharacteristic
71#14268646—21no—
72#14268646D411yescharacteristic
73C2×Dic226—21no—
74C2×Dic226C2311yescharacteristic
75Q8×D113—21no—
76Q8×D113—21no—
77Q8×D113—21no—
78Q8×D113—21no—
79Q8×D113D411yescharacteristic
80C2×D452C2311yescharacteristic
81C2×C22⋊D113—21no—
82D4×D113—21no—
83D4×D113—21no—
84D4×D113—21no—
85D4×D113—21no—
86D4×D113—21no—
87D4×D113D411yescharacteristic
88C2×C4×D113—21no—
89C2×C4×D113—21no—
90C2×C4×D113C2311yescharacteristic
91Dic452—21no—
92#14268637—21no—
93#14268637—21no—
94#14268636—21no—
95#14268636—21no—
96#14268636—21no—
97#14268636—21no—
98#14268635—21no—
99#14268635—21no—
100#14268635—21no—
101#14268635—21no—
102#14268634—21no—
103#14268634—21no—
104#14268634—21no—
105#14268634—21no—
106D904—21no—
107#14268632—21no—
108#14268632—21no—
109#14268631—21no—
110#14268631C2311yescharacteristic
111#14268631C2311yescharacteristic
112#14268631C2311yescharacteristic
113#14268630—21no—
114#14268630—21no—
115#14268630—21no—
116#14268630—21no—
117#14268630—21no—
118C2×#11744751—21no—
119C2×#11744751C2311yescharacteristic
120C8×D113—21no—
121C8×D113—21no—
122C8×D113—21no—
123C8×D113—21no—
124C8×D113—21no—
125C8×D113D411yescharacteristic
126C8×D113D411yescharacteristic
127C8×D113D411yescharacteristic
128C8×D113D411yescharacteristic
129#41×C113C2311yescharacteristic
130C2×Q8×C113C2311yescharacteristic
131C2×D4×C113C2311yescharacteristic
132Q16×C113—21no—
133SD16×C113—21no—
134SD16×C113—21no—
135SD16×C113—21no—
136SD16×C113—21no—
137D8×C113—21no—
138M16×C113—21no—
139M16×C113C2311yescharacteristic
140M16×C113C2311yescharacteristic
141M16×C113C2311yescharacteristic
142C2×C8×C113—21no—
143C2×C8×C113C2311yescharacteristic
144C23×C113—21no—
145C22×D113—21no—
146C22×D113—21no—
147C22×D113—41no—
148C22×D113—41no—
149C22×D113—82no—
150C22×D113#4111yescharacteristic
151Q8×C113—21no—
152Q8×C113—21no—
153Q8×C113C2×D411yescharacteristic
154D4×C113—21no—
155D4×C113—21no—
156D4×C113—21no—
157D4×C113C2×D411yescharacteristic
158C2×C4×C113—21no—
159C2×C4×C113—21no—
160C2×C4×C113C2411yescharacteristic
161C22⋊D113—21no—
162C22⋊D113—21no—
163C22⋊D113—21no—
164C22⋊D113—41no—
165C22⋊D113—41no—
166C2×Dic113—21no—
167C2×Dic113—21no—
168C2×Dic113#4111yescharacteristic
169D452—21no—
170D452—21no—
171D452—21no—
172D452C2×D411yescharacteristic
173C4×D113—21no—
174C4×D113—21no—
175C4×D113—21no—
176C4×D113—41no—
177C4×D113—41no—
178C4×D113C2×D411yescharacteristic
179C4×D113C2×D411yescharacteristic
180C4×D113C2×D411yescharacteristic
181C4×D113C2×D411yescharacteristic
182Dic226—21no—
183Dic226—21no—
184Dic226—21no—
185Dic226—41no—
186Dic226—41no—
187Dic226C2×D411yescharacteristic
188C8×C113—21no—
189C8×C113—21no—
190C8×C113—21no—
191C8×C113C2×D411yescharacteristic
192C8×C113C2×D411yescharacteristic
193#11744751—21no—
194#11744751—21no—
195#11744751—21no—
196#11744751C2×D411yescharacteristic
197#11744751C2×D411yescharacteristic
198C22×C113—21no—
199C22×C113—41no—
200C22×C113—81no—
201C22×C113C2×#4111yescharacteristic
202C2×D113—22no—
203C2×D113—21no—
204C2×D113—42no—
205C2×D113—41no—
206C2×D113—82no—
207C2×D113—82no—
208C2×D113—81no—
209C2×D113#12111yescharacteristic
210C2×D113#12111yescharacteristic
211C4×C113—21no—
212C4×C113—41no—
213C4×C113C22×D411yescharacteristic
214C4×C113C22×D411yescharacteristic
215Dic113—21no—
216Dic113—41no—
217Dic113#12111yescharacteristic
218Dic113#12111yescharacteristic
219C2×C113—21no—
220C2×C113—41no—
221C2×C113—81no—
222C2×C113C2×#12111yescharacteristic
223D113—21no—
224D113—41no—
225D113—81no—
226D113#47112yesdirect product factor
227C2×#471—1131nomaximal, Sylow
228C113C2×#47111yescharacteristic, complemented, Sylow
229C2×#137—1131no—
230C2×AGL(1,ℤ/8)—1131no—
231C22×SD16—1131no—
232C2×#131—1131no—
233#471—1131no—
234#471—1131no—
235#471—1131no—
236#471—1131no—
237#471—1131no—
238#471—1131no—
239#471—1131no—
240#471D11311yescharacteristic, direct product factor
241C2×#108—1131no—
242C2×#101—1131no—
243C2×#100—1131no—
244C2×#41—1131no—
245C22×Q8—1131no—
246C22×D4—1131no—
247#137—1131no—
248#137—1131no—
249#137—1131no—
250#137—2261no—
251#137—2261no—
252#137C2×D11311yescharacteristic, complemented
253AGL(1,ℤ/8)—1131no—
254AGL(1,ℤ/8)—1131no—
255AGL(1,ℤ/8)—1131no—
256AGL(1,ℤ/8)—2261no—
257AGL(1,ℤ/8)—2261no—
258AGL(1,ℤ/8)C2×D11311yescharacteristic
259C2×Q16—2261no—
260C2×SD16—1131no—
261C2×SD16—1131no—
262C2×SD16—1131no—
263C2×SD16—2261no—
264C2×SD16—2261no—
265C2×SD16—2261no—
266C2×SD16—2261no—
267C2×SD16—2261no—
268C2×SD16—2261no—
269C2×SD16C2×D11311yescharacteristic, complemented
270C2×D8—2261no—
271#131—1131no—
272#131—1131no—
273#131—1131no—
274#131—2261no—
275#131—2261no—
276#131C2×D11311yescharacteristic, complemented
277C2×M16—1131no—
278C2×M16—1131no—
279C2×M16—1131no—
280C2×M16—2261no—
281C22×C8—1131no—
282C22×C8—2261no—
283#108—1131no—
284#108—1131no—
285#108—1131no—
286#108C2×D11311yescharacteristic, complemented
287#101—1131no—
288#101—1131no—
289#101—1131no—
290#101C2×D11311yescharacteristic, complemented
291#100—1131no—
292#100—1131no—
293#100—1131no—
294#100C2×D11311yescharacteristic, complemented
295C24—2261no—
296#41—1131no—
297#41—1131no—
298#41—1131no—
299#41—2261no—
300#41—2261no—
301#41C22×D11311yescharacteristic
302C2×Q8—1131no—
303C2×Q8—1131no—
304C2×Q8—2261no—
305C2×Q8—2261no—
306C2×Q8—2261no—
307C2×Q8—2261no—
308C2×Q8—2261no—
309C2×Q8C22×D11311yescharacteristic
310C2×D4—1131no—
311C2×D4—1131no—
312C2×D4—2261no—
313C2×D4—2261no—
314C2×D4—2261no—
315C2×D4—2261no—
316C2×D4—2261no—
317C2×D4—2261no—
318C2×D4C22×D11311yescharacteristic
319C22×C4—1131no—
320C22×C4—2261no—
321C22×C4—2261no—
322Q16—21no—
323Q16—2261no—
324Q16—2261no—
325Q16—2261no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—2261no—
331SD16—2261no—
332SD16—2261no—
333SD16—2261no—
334SD16—2261no—
335SD16—2261no—
336SD16—2261no—
337SD16—2261no—
338SD16—2261no—
339SD16—2261no—
340SD16—2261no—
341SD16—2261no—
342D8—21no—
343D8—2261no—
344D8—2261no—
345D8—2261no—
346M16—21no—
347M16—1131no—
348M16—1131no—
349M16—1131no—
350M16—2261no—
351M16—2261no—
352M16—2261no—
353M16—2261no—
354M16—2261no—
355M16—2261no—
356M16C22×D11311yescharacteristic
357M16C22×D11311yescharacteristic
358M16C22×D11311yescharacteristic
359C2×C8—21no—
360C2×C8—1131no—
361C2×C8—1131no—
362C2×C8—1131no—
363C2×C8—1131no—
364C2×C8—1131no—
365C2×C8—2261no—
366C2×C8—2261no—
367C2×C8—2261no—
368C2×C8—2261no—
369C2×C8—2261no—
370C2×C8—2261no—
371C2×C8C22×D11311yescharacteristic
372C23—21no—
373C23—1131no—
374C23—9042no—
375C23—4521no—
376C23—4521no—
377C23—2261no—
378C23—2261no—
379Q8—21no—
380Q8—21no—
381Q8—1131no—
382Q8—4521no—
383Q8—4521no—
384Q8—2261no—
385Q8—2261no—
386Q8—2261no—
387Q8D4×D11311yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—1131no—
392D4—4521no—
393D4—4521no—
394D4—2261no—
395D4—2261no—
396D4—2261no—
397D4—2261no—
398D4—2261no—
399D4—2261no—
400D4D4×D11311yescharacteristic
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—1131no—
404C2×C4—1131no—
405C2×C4—1131no—
406C2×C4—1131no—
407C2×C4—1131no—
408C2×C4—4521no—
409C2×C4—4521no—
410C2×C4—2261no—
411C2×C4—2261no—
412C2×C4—2261no—
413C2×C4—2261no—
414C2×C4—2261no—
415C2×C4C23×D11311yescharacteristic
416C8—21no—
417C8—21no—
418C8—21no—
419C8—1131no—
420C8—1131no—
421C8—2261no—
422C8—2261no—
423C8—2261no—
424C8D4×D11311yescharacteristic
425C8D4×D11311yescharacteristic
426C22—21no—
427C22—41no—
428C22—81no—
429C22—1131no—
430C22—1131no—
431C22—9041no—
432C22—9042no—
433C22—9042no—
434C22—4522no—
435C22—4521no—
436C22—2262no—
437C22—2261no—
438C22#41×D11311yescharacteristic
439C4—21no—
440C4—41no—
441C4—1131no—
442C4—1131no—
443C4—4521no—
444C4—2261no—
445C4C2×D4×D11311yescharacteristic
446C4C2×D4×D11311yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—1132no—
451C2—9041no—
452C2—4521no—
453C2—2261no—
454C2#121×D11311yescharacteristic
subgroupG/H
centerC2#121×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#471×C113C2
socleC2×C113C2×#121
prime radicalAGL(1,ℤ/8)×D113C2
hypercenter#471D113
hypocenterC113C2×#471
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #137×D113C2semidirect
3. C2×SD16×D113C2semidirect
4. #131×D113C2semidirect
5. #20298864C2semidirect
6. #20298863C2semidirect
7. #20298862C2semidirect
8. #20298861C2semidirect
9. #20298860C2semidirect
10. #20298859C2semidirect
11. #20298858C2semidirect
12. #108×D113C2semidirect
13. #101×D113C2semidirect
14. #100×D113C2semidirect
15. #471×C113C2semidirect
19. #16813655C22semidirect
21. #16813653C22semidirect
22. #16813652C22semidirect
30. C2×#14268636C22semidirect
31. C2×#14268635C22semidirect
32. C2×#14268634C22semidirect
41. #16813630C22semidirect
42. #16813629C22semidirect
44. #16813628C22semidirect
51. #16813558C22semidirect
52. #16813557C22semidirect
53. #16813557C22semidirect
54. #16813541C22semidirect
55. #16813540C22semidirect
56. #16813540C22semidirect
57. #16813539C22semidirect
58. #16813538C22semidirect
59. #16813538C22semidirect
60. #137×C113C22semidirect
62. C2×SD16×C113C22semidirect
63. #131×C113C22semidirect
64. #108×C113C22semidirect
65. #101×C113C22semidirect
66. #100×C113C22semidirect
226. D113#471direct (N × H)
228. C113C2×#471semidirect
240. #471D113direct (N × H)
252. #137C2×D113semidirect
269. C2×SD16C2×D113semidirect
276. #131C2×D113semidirect
286. #108C2×D113semidirect
290. #101C2×D113semidirect
294. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#137×D1132
AGL(1,ℤ/8)×D1132
C2×SD16×D1132
#131×D1132
#202988642
#202988632
#202988622
#202988612
#202988602
#202988592
#202988582
#108×D1132
#101×D1132
#100×D1132
#471×C1132
C2×#471113