Finite Group Databasebeta

← #28400300

Subgroups — #28400300

Order 14464.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299394C211yesmaximal, characteristic, complemented
2C2×#16813646C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×D113C211yesmaximal, characteristic, complemented
4#20299363C211yesmaximal, characteristic, complemented
5#20298867C211yesmaximal, characteristic, complemented
6#20298866C211yesmaximal, characteristic, complemented
7#20298865C211yesmaximal, characteristic, complemented
8#20298862C211yesmaximal, characteristic, complemented
9#20298861C211yesmaximal, characteristic, complemented
10#20298860C211yesmaximal, characteristic, complemented
11#20298859C211yesmaximal, characteristic, complemented
12#20298645C211yesmaximal, characteristic, complemented
13#20298579C211yesmaximal, characteristic, complemented
14#100×D113C211yesmaximal, characteristic, complemented
15#472×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17#41×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813655C2211yescharacteristic, complemented
20#16813652C2211yescharacteristic, complemented
21#16813651—21no—
22#16813650C2211yescharacteristic
23#16813649—21no—
24#16813648C2211yescharacteristic
25#16813648C2211yescharacteristic, complemented
26#16813647C2211yescharacteristic
27#16813646—21no—
28#16813646—21no—
29#16813646—21no—
30#16813646—21no—
31#16813646—21no—
32#16813646—21no—
33#16813643—21no—
34#16813641—21no—
35C2×#14268636C2211yescharacteristic, complemented
36C2×#14268635C2211yescharacteristic, complemented
37SD16×D113—21no—
38C2×#14268632C2211yescharacteristic, complemented
39D8×D113—21no—
40#16813630—21no—
41#16813630C2211yescharacteristic, complemented
42#16813629C2211yescharacteristic, complemented
43#16813628—21no—
44#16813628C2211yescharacteristic, complemented
45C2×#14268630—21no—
46C2×#14268630C2211yescharacteristic
47M16×D113—21no—
48M16×D113C2211yescharacteristic
49M16×D113C2211yescharacteristic
50M16×D113C2211yescharacteristic
51#16813558C2211yescharacteristic, complemented
52#16813557C2211yescharacteristic, complemented
53#16813557C2211yescharacteristic, complemented
54#16813540C2211yescharacteristic, complemented
55#16813540C2211yescharacteristic, complemented
56#16813539C2211yescharacteristic, complemented
57#16813539C2211yescharacteristic, complemented
58#16813538C2211yescharacteristic, complemented
59#16813538C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C113C2211yescharacteristic
61AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
62C2×D8×C113C2211yescharacteristic, complemented
63#131×C113C2211yescharacteristic, complemented
64#108×C113C2211yescharacteristic, complemented
65#100×C113C2211yescharacteristic, complemented
66#100×C113C2211yescharacteristic, complemented
67C23×D113—21no—
68#14268648D411yescharacteristic
69#14268647—21no—
70#14268647C2311yescharacteristic
71#14268646—21no—
72#14268646—21no—
73#14268646—21no—
74#14268646—21no—
75#14268646—21no—
76#14268646D411yescharacteristic
77C2×Dic226C2311yescharacteristic
78Q8×D113D411yescharacteristic
79C2×D452C2311yescharacteristic
80C2×C22⋊D113—21no—
81C2×C22⋊D113—21no—
82D4×D113—21no—
83D4×D113—21no—
84D4×D113—21no—
85D4×D113—21no—
86D4×D113—21no—
87D4×D113D411yescharacteristic
88C22×Dic113—21no—
89C2×C4×D113—21no—
90C2×C4×D113C2311yescharacteristic
91Dic452—21no—
92#14268637—21no—
93#14268636—21no—
94#14268636—21no—
95#14268636—21no—
96#14268636—21no—
97#14268635—21no—
98#14268635—21no—
99#14268635—21no—
100#14268635—21no—
101#14268635—21no—
102#14268634—21no—
103D904—21no—
104#14268632—21no—
105#14268632—21no—
106#14268632—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—
118#14268630D411yescharacteristic
119#14268630D411yescharacteristic
120#14268630D411yescharacteristic
121#14268630D411yescharacteristic
122C2×#11744751—21no—
123C2×#11744751C2311yescharacteristic
124C8×D113—21no—
125C8×D113—21no—
126C8×D113—21no—
127C8×D113—21no—
128C8×D113—21no—
129#41×C113C2311yescharacteristic
130C2×D4×C113C2311yescharacteristic
131C2×D4×C113C2311yescharacteristic
132SD16×C113—21no—
133SD16×C113—21no—
134D8×C113—21no—
135D8×C113—21no—
136D8×C113—21no—
137D8×C113—21no—
138M16×C113—21no—
139M16×C113C2311yescharacteristic
140M16×C113C2311yescharacteristic
141M16×C113C2311yescharacteristic
142C2×C8×C113—21no—
143C2×C8×C113C2311yescharacteristic
144C23×C113—21no—
145C23×C113—21no—
146C22×D113—21no—
147C22×D113—21no—
148C22×D113—41no—
149C22×D113—41no—
150C22×D113—82no—
151C22×D113#4111yescharacteristic
152Q8×C113C2×D411yescharacteristic
153D4×C113—21no—
154D4×C113—21no—
155D4×C113—21no—
156D4×C113—21no—
157D4×C113—21no—
158D4×C113C2×D411yescharacteristic
159C2×C4×C113—21no—
160C2×C4×C113C2411yescharacteristic
161C22⋊D113—21no—
162C22⋊D113—21no—
163C22⋊D113—21no—
164C22⋊D113—41no—
165C22⋊D113—41no—
166C22⋊D113—41no—
167C22⋊D113—41no—
168C2×Dic113—21no—
169C2×Dic113—21no—
170C2×Dic113—41no—
171C2×Dic113—41no—
172C2×Dic113#4111yescharacteristic
173D452—21no—
174D452—21no—
175D452—21no—
176D452C2×D411yescharacteristic
177C4×D113—21no—
178C4×D113—21no—
179C4×D113—21no—
180C4×D113C2×D411yescharacteristic
181C4×D113C2×D411yescharacteristic
182C4×D113C2×D411yescharacteristic
183C4×D113C2×D411yescharacteristic
184Dic226—21no—
185Dic226—21no—
186Dic226—21no—
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—41no—
201C22×C113—81no—
202C22×C113—81no—
203C22×C113C2×#4111yescharacteristic
204C2×D113—21no—
205C2×D113—41no—
206C2×D113—41no—
207C2×D113—81no—
208C2×D113—82no—
209C2×D113—82no—
210C2×D113—81no—
211C2×D113#12111yescharacteristic
212C2×D113#12111yescharacteristic
213C4×C113—21no—
214C4×C113C22×D411yescharacteristic
215C4×C113C22×D411yescharacteristic
216Dic113—21no—
217Dic113—41no—
218Dic113#12111yescharacteristic
219Dic113#12111yescharacteristic
220C2×C113—21no—
221C2×C113—41no—
222C2×C113—81no—
223C2×C113—81no—
224C2×C113C2×#12111yescharacteristic
225D113—21no—
226D113—21no—
227D113—41no—
228D113—81no—
229#3068—1131nomaximal, Sylow
230C113#306811yescharacteristic, complemented, Sylow
231#575—1131no—
232C2×AGL(1,ℤ/8)—1131no—
233C2×AGL(1,ℤ/8)—1131no—
234#568—1131no—
235#472—1131no—
236#472—1131no—
237#472—1131no—
238#472D11311yescharacteristic, complemented
239#471—1131no—
240#471—1131no—
241#471—1131no—
242#471—1131no—
243#430—1131no—
244#413—1131no—
245C2×#100—1131no—
246C2×#41—1131no—
247C2×#41—1131no—
248C22×D4—1131no—
249#137—1131no—
250#137—1131no—
251#137—2261no—
252AGL(1,ℤ/8)—1131no—
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)—2261no—
259AGL(1,ℤ/8)—2261no—
260AGL(1,ℤ/8)—2261no—
261AGL(1,ℤ/8)—2261no—
262AGL(1,ℤ/8)—2261no—
263AGL(1,ℤ/8)C2×D11311yescharacteristic
264AGL(1,ℤ/8)C2×D11311yescharacteristic, complemented
265#135—2261no—
266#135—2261no—
267C2×SD16—1131no—
268C2×SD16—1131no—
269C2×SD16—2261no—
270C2×D8—1131no—
271C2×D8—2261no—
272C2×D8C2×D11311yescharacteristic, complemented
273#131—1131no—
274#131—1131no—
275#131—1131no—
276#131—2261no—
277#131—2261no—
278#131C2×D11311yescharacteristic, complemented
279C2×M16—1131no—
280C2×M16—1131no—
281C2×M16—1131no—
282C2×M16—1131no—
283C2×M16—2261no—
284C2×M16—2261no—
285#108—1131no—
286#108—1131no—
287#108—1131no—
288#108C2×D11311yescharacteristic, complemented
289#101—1131no—
290#101—1131no—
291#100—1131no—
292#100—1131no—
293#100—1131no—
294#100—1131no—
295#100C2×D11311yescharacteristic, complemented
296#100C2×D11311yescharacteristic, complemented
297C24—2261no—
298#41—1131no—
299#41—1131no—
300#41—1131no—
301#41—2261no—
302#41—2261no—
303#41—2261no—
304#41—2261no—
305#41—2261no—
306#41—2261no—
307#41C22×D11311yescharacteristic
308C2×Q8—1131no—
309C2×Q8—1131no—
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×D4—2261no—
319C2×D4C22×D11311yescharacteristic
320C2×D4C22×D11311yescharacteristic
321C22×C4—1131no—
322C22×C4—2261no—
323C22×C4—2261no—
324Q16—2261no—
325Q16—2261no—
326SD16—21no—
327SD16—21no—
328SD16—2261no—
329SD16—2261no—
330SD16—2261no—
331SD16—2261no—
332SD16—2261no—
333SD16—2261no—
334SD16—2261no—
335SD16—2261no—
336SD16—2261no—
337SD16—2261no—
338D8—21no—
339D8—21no—
340D8—21no—
341D8—21no—
342D8—2261no—
343D8—2261no—
344D8—2261no—
345D8—2261no—
346D8—2261no—
347D8—2261no—
348M16—21no—
349M16—1131no—
350M16—1131no—
351M16—1131no—
352M16—1131no—
353M16—1131no—
354M16—1131no—
355M16—1131no—
356M16—2261no—
357M16—2261no—
358M16—2261no—
359M16—2261no—
360M16—2261no—
361M16—2261no—
362M16C22×D11311yescharacteristic
363M16C22×D11311yescharacteristic
364M16C22×D11311yescharacteristic
365C2×C8—21no—
366C2×C8—1131no—
367C2×C8—2261no—
368C2×C8—2261no—
369C2×C8—2261no—
370C2×C8—2261no—
371C2×C8—2261no—
372C2×C8—2261no—
373C2×C8C22×D11311yescharacteristic
374C23—21no—
375C23—21no—
376C23—1131no—
377C23—9042no—
378C23—4521no—
379C23—4521no—
380C23—2261no—
381C23—2261no—
382Q8—1131no—
383Q8—2261no—
384Q8—2261no—
385Q8—2261no—
386Q8D4×D11311yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—1131no—
393D4—4521no—
394D4—4521no—
395D4—4521no—
396D4—4521no—
397D4—2261no—
398D4—2261no—
399D4—2261no—
400D4—2261no—
401D4—2261no—
402D4—2261no—
403D4D4×D11311yescharacteristic
404C2×C4—21no—
405C2×C4—1131no—
406C2×C4—1131no—
407C2×C4—1131no—
408C2×C4—1131no—
409C2×C4—1131no—
410C2×C4—4521no—
411C2×C4—4521no—
412C2×C4—2261no—
413C2×C4—2261no—
414C2×C4—2261no—
415C2×C4—2261no—
416C2×C4—2261no—
417C2×C4C23×D11311yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—1131no—
422C8—1131no—
423C8—2261no—
424C8—2261no—
425C8—2261no—
426C8D4×D11311yescharacteristic
427C8D4×D11311yescharacteristic
428C22—21no—
429C22—41no—
430C22—41no—
431C22—81no—
432C22—81no—
433C22—1131no—
434C22—1131no—
435C22—9041no—
436C22—9041no—
437C22—9042no—
438C22—9042no—
439C22—4521no—
440C22—4521no—
441C22—2261no—
442C22#41×D11311yescharacteristic
443C4—21no—
444C4—1131no—
445C4—1131no—
446C4—4521no—
447C4—2261no—
448C4C2×D4×D11311yescharacteristic
449C4C2×D4×D11311yescharacteristic
450C2—21no—
451C2—41no—
452C2—81no—
453C2—81no—
454C2—9041no—
455C2—4521no—
456C2—2261no—
457C2—2261no—
458C2#121×D11311yescharacteristic
subgroupG/H
centerC2#121×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#472×C113C2
socleC2×C113C2×#121
hypercenter#472D113
hypocenterC113#3068
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #20299394C2semidirect
2. C2×#16813646C2semidirect
3. AGL(1,ℤ/8)×D113C2semidirect
4. #20299363C2semidirect
5. #20298867C2semidirect
6. #20298866C2semidirect
7. #20298865C2semidirect
8. #20298862C2semidirect
9. #20298861C2semidirect
10. #20298860C2semidirect
11. #20298859C2semidirect
12. #20298645C2semidirect
13. #20298579C2semidirect
14. #100×D113C2semidirect
15. #472×C113C2semidirect
19. #16813655C22semidirect
20. #16813652C22semidirect
25. #16813648C22semidirect
35. C2×#14268636C22semidirect
36. C2×#14268635C22semidirect
38. C2×#14268632C22semidirect
41. #16813630C22semidirect
42. #16813629C22semidirect
44. #16813628C22semidirect
51. #16813558C22semidirect
52. #16813557C22semidirect
53. #16813557C22semidirect
54. #16813540C22semidirect
55. #16813540C22semidirect
56. #16813539C22semidirect
57. #16813539C22semidirect
58. #16813538C22semidirect
59. #16813538C22semidirect
61. AGL(1,ℤ/8)×C113C22semidirect
62. C2×D8×C113C22semidirect
63. #131×C113C22semidirect
64. #108×C113C22semidirect
65. #100×C113C22semidirect
66. #100×C113C22semidirect
230. C113#3068semidirect
238. #472D113semidirect
264. AGL(1,ℤ/8)C2×D113semidirect
272. C2×D8C2×D113semidirect
278. #131C2×D113semidirect
288. #108C2×D113semidirect
295. #100C2×D113semidirect
296. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993942
C2×#168136462
AGL(1,ℤ/8)×D1132
#202993632
#202988672
#202988662
#202988652
#202988622
#202988612
#202988602
#202988592
#202986452
#202985792
#100×D1132
#472×C1132
#3068113