Finite Group Databasebeta

← #28402366

Subgroups — #28402366

Order 14464.

460 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#20299410C211yesmaximal, characteristic, complemented
2#20299408C211yesmaximal, characteristic, complemented
3#20299407C211yesmaximal, characteristic, complemented
4#20299404C211yesmaximal, characteristic, complemented
5#20298969C211yesmaximal, characteristic, complemented
6#20298864C211yesmaximal, characteristic, complemented
7#20298862C211yesmaximal, characteristic, complemented
8#20298860C211yesmaximal, characteristic, complemented
9#20298783C211yesmaximal, characteristic, complemented
10#20298779C211yesmaximal, characteristic, complemented
11#20298768C211yesmaximal, characteristic, complemented
12#20298764C211yesmaximal, characteristic, complemented
13#20298714C211yesmaximal, characteristic, complemented
14#20298713C211yesmaximal, characteristic, complemented
15#471×C113C211yesmaximal, characteristic, complemented
16#16813670C2211yescharacteristic
17#16813669C2211yescharacteristic
18#16813668C2211yescharacteristic, complemented
19#16813667C2211yescharacteristic, complemented
20#16813655—21no—
21#16813655C2211yescharacteristic, complemented
22#16813655C2211yescharacteristic, complemented
23#16813654—21no—
24#16813653C2211yescharacteristic, complemented
25#16813651—21no—
26#16813651—21no—
27#16813650—21no—
28#16813650C2211yescharacteristic
29#16813650C2211yescharacteristic
30#16813649—21no—
31#16813649—21no—
32#16813648C2211yescharacteristic
33#16813646—21no—
34#16813645—21no—
35#16813644—21no—
36#16813644C2211yescharacteristic
37#16813643—21no—
38#16813642C2211yescharacteristic
39#16813641—21no—
40C2×#14268636—21no—
41C2×#14268636C2211yescharacteristic, complemented
42C2×#14268635C2211yescharacteristic, complemented
43C2×#14268634C2211yescharacteristic, complemented
44SD16×D113—21no—
45SD16×D113—21no—
46SD16×D113—21no—
47#16813630C2211yescharacteristic, complemented
48#16813630C2211yescharacteristic, complemented
49#16813628C2211yescharacteristic, complemented
50#16813620C2211yescharacteristic, complemented
51#16813618C2211yescharacteristic
52#16813557C2211yescharacteristic, complemented
53#16813549C2211yescharacteristic, complemented
54#16813548C2211yescharacteristic, complemented
55#16813548C2211yescharacteristic, complemented
56#16813548C2211yescharacteristic, complemented
57#16813540C2211yescharacteristic, complemented
58#16813538C2211yescharacteristic, complemented
59C8×Dic113C2211yescharacteristic, 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
67#14268648—21no—
68#14268648—21no—
69#14268648—21no—
70#14268647—21no—
71#14268647—21no—
72#14268647—41no—
73#14268647C2311yescharacteristic
74#14268647C2311yescharacteristic
75#14268647C2311yescharacteristic
76#14268646—21no—
77#14268646—21no—
78#14268646—21no—
79#14268646—41no—
80C2×Dic226—21no—
81C2×Dic226C2311yescharacteristic
82Q8×D113—21no—
83Q8×D113—21no—
84Q8×D113—21no—
85C2×D452—21no—
86C2×D452C2311yescharacteristic
87C2×C22⋊D113—41no—
88C2×C22⋊D113—41no—
89D4×D113—21no—
90D4×D113—21no—
91D4×D113—21no—
92D4×D113—41no—
93Dic452—21no—
94Dic452—21no—
95Dic452D411yescharacteristic, complemented
96#14268637—21no—
97#14268637D411yescharacteristic, complemented
98#14268636—21no—
99#14268636—21no—
100#14268636—21no—
101#14268636—21no—
102#14268636—21no—
103#14268636—21no—
104#14268636D411yescharacteristic, complemented
105#14268636D411yescharacteristic, complemented
106#14268635—21no—
107#14268635—21no—
108#14268635—21no—
109#14268635D411yescharacteristic, complemented
110#14268634—21no—
111#14268634—21no—
112#14268634—21no—
113#14268634D411yescharacteristic, complemented
114D904—21no—
115D904—21no—
116D904D411yescharacteristic, complemented
117#14268632—21no—
118#14268632D411yescharacteristic, complemented
119#14268631C2311yescharacteristic
120#14268630—21no—
121#14268630—21no—
122#14268630—21no—
123C2×#11744751C2311yescharacteristic
124C8×D113—21no—
125C8×D113—21no—
126C8×D113—21no—
127#14268626—41no—
128C4×Dic113C2311yescharacteristic
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—41no—
147C22×D113—41no—
148Q8×C113—21no—
149Q8×C113—21no—
150Q8×C113C2×D411yescharacteristic
151D4×C113—21no—
152D4×C113—21no—
153D4×C113—21no—
154D4×C113C2×D411yescharacteristic
155C2×C4×C113—21no—
156C2×C4×C113—21no—
157C2×C4×C113C2411yescharacteristic
158C22⋊D113—21no—
159C22⋊D113—21no—
160C22⋊D113—21no—
161C22⋊D113—41no—
162C22⋊D113—41no—
163C22⋊D113—41no—
164C22⋊D113—41no—
165C22⋊D113—82no—
166C2×Dic113—21no—
167C2×Dic113—21no—
168C2×Dic113—41no—
169C2×Dic113—41no—
170D452—21no—
171D452—21no—
172D452—41no—
173D452—41no—
174D452C2×D411yescharacteristic
175D452C2×D411yescharacteristic
176D452C2×D411yescharacteristic
177C4×D113—21no—
178C4×D113—21no—
179C4×D113—21no—
180C4×D113—41no—
181C4×D113—41no—
182C4×D113—41no—
183C4×D113—41no—
184Dic226—21no—
185Dic226—21no—
186Dic226—41no—
187Dic226—41no—
188Dic226C2×D411yescharacteristic
189Dic226C2×D411yescharacteristic
190Dic226C2×D411yescharacteristic
191C8×C113—21no—
192C8×C113—21no—
193C8×C113—21no—
194C8×C113C2×D411yescharacteristic
195C8×C113C2×D411yescharacteristic
196#11744751—21no—
197#11744751C2×D411yescharacteristic
198#11744751C2×D411yescharacteristic
199C22×C113—21no—
200C22×C113—41no—
201C22×C113—81no—
202C22×C113H(5,𝔽2)11yescharacteristic
203C2×D113—21no—
204C2×D113—21no—
205C2×D113—21no—
206C2×D113—41no—
207C2×D113—81no—
208C2×D113—161no—
209C2×D113—161no—
210C4×C113—21no—
211C4×C113—41no—
212C4×C113C22×D411yescharacteristic
213C4×C113C22×D411yescharacteristic
214Dic113—22no—
215Dic113—21no—
216Dic113—21no—
217Dic113—21no—
218Dic113—41no—
219C2×C113—21no—
220C2×C113—41no—
221C2×C113—81no—
222C2×C113D4211yescharacteristic
223D113—41no—
224D113—41no—
225D113—41no—
226D113—81no—
227#3291—1131nomaximal, Sylow
228C113#329111yescharacteristic, complemented, Sylow
229#577—1131no—
230#577—1131no—
231#577—1131no—
232#577—1131no—
233#492—1131no—
234#471—1131no—
235#471—1131no—
236#471—1131no—
237#471D11311yescharacteristic, complemented
238#456—1131no—
239#456—1131no—
240#453—1131no—
241#453—1131no—
242#443—1131no—
243#443—1131no—
2442−1+4—1131no—
2452−1+4—1131no—
246H(5,𝔽2)—1131no—
247H(5,𝔽2)—1131no—
248#137—1131no—
249#137—1131no—
250#137—1131no—
251#137—2261no—
252#137—2261no—
253#137—2261no—
254#137—2261no—
255#137C2×D11311yescharacteristic, complemented
256AGL(1,ℤ/8)—1131no—
257AGL(1,ℤ/8)—1131no—
258AGL(1,ℤ/8)—1131no—
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
264#135—1131no—
265#135—1131no—
266#135—2261no—
267#135—2261no—
268#135—2261no—
269#135—2261no—
270C2×SD16—1131no—
271C2×SD16—1131no—
272C2×SD16—1131no—
273C2×SD16—2261no—
274C2×SD16—2261no—
275C2×SD16—2261no—
276C2×SD16—2261no—
277C2×SD16C2×D11311yescharacteristic, complemented
278#131—1131no—
279#131—1131no—
280#131—1131no—
281#131C2×D11311yescharacteristic, complemented
282C4⋊Q8—1131no—
283#127—1131no—
284#108—1131no—
285#108C2×D11311yescharacteristic, complemented
286#104—1131no—
287#104—1131no—
288#104—1131no—
289#104—1131no—
290#101—1131no—
291#101C2×D11311yescharacteristic, complemented
292#100—1131no—
293#100C2×D11311yescharacteristic, complemented
294C4×C8—1131no—
295#41—1131no—
296#41—1131no—
297#41—1131no—
298#41—4521no—
299#41—4521no—
300#41—2261no—
301#41—2261no—
302#41—2261no—
303#41—2261no—
304#41—2261no—
305#41—2261no—
306#41—2261no—
307#41—2261no—
308#41C22×D11311yescharacteristic
309C2×Q8—1131no—
310C2×Q8—2261no—
311C2×Q8—2261no—
312C2×Q8—2261no—
313C2×Q8—2261no—
314C2×Q8C22×D11311yescharacteristic
315C2×D4—1131no—
316C2×D4—4521no—
317C2×D4—4521no—
318C2×D4—4521no—
319C2×D4—2261no—
320C2×D4—2261no—
321C2×D4—2261no—
322C2×D4—2261no—
323C2×D4C22×D11311yescharacteristic
324Q16—21no—
325Q16—1131no—
326Q16—1131no—
327Q16—2261no—
328Q16—2261no—
329Q16—2261no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—1131no—
335SD16—1131no—
336SD16—1131no—
337SD16—1131no—
338SD16—2261no—
339SD16—2261no—
340SD16—2261no—
341SD16—2261no—
342SD16—2261no—
343SD16—2261no—
344SD16—2261no—
345SD16—2261no—
346SD16—2261no—
347SD16—2261no—
348SD16—2261no—
349SD16—2261no—
350D8—21no—
351D8—1131no—
352D8—1131no—
353D8—2261no—
354D8—2261no—
355D8—2261no—
356M16—21no—
357M16—1131no—
358M16—2261no—
359M16—2261no—
360M16—2261no—
361M16C22×D11311yescharacteristic
362M16C22×D11311yescharacteristic
363M16C22×D11311yescharacteristic
364C2×C8—21no—
365C2×C8—1131no—
366C2×C8—2261no—
367C2×C8—2261no—
368C2×C8—2261no—
369C2×C8C22×D11311yescharacteristic
370C4⋊C4—4521no—
371C42—1131no—
372C23—21no—
373C23—4521no—
374C23—4521no—
375C23—2261no—
376Q8—21no—
377Q8—21no—
378Q8—1131no—
379Q8—1131no—
380Q8—1131no—
381Q8—4521no—
382Q8—4521no—
383Q8—2261no—
384Q8—2261no—
385Q8D4×D11311yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—1131no—
390D4—1131no—
391D4—1131no—
392D4—9042no—
393D4—4521no—
394D4—4521no—
395D4—4521no—
396D4—4521no—
397D4—4521no—
398D4—4521no—
399D4—2261no—
400D4—2261no—
401D4—2261no—
402D4—2261no—
403D4—2261no—
404D4D4×D11311yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—4521no—
408C2×C4—4521no—
409C2×C4—4521no—
410C2×C4—4521no—
411C2×C4—4521no—
412C2×C4—4521no—
413C2×C4—2261no—
414C2×C4—2261no—
415C2×C4—2261no—
416C2×C4—2261no—
417C2×C4—2261no—
418C2×C4C23×D11311yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—1131no—
423C8—1131no—
424C8—2261no—
425C8D4×D11311yescharacteristic
426C8D4×D11311yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—18081no—
431C22—18081no—
432C22—9041no—
433C22—4521no—
434C22—2261no—
435C22—2261no—
436C22—2261no—
437C22#1681366811yescharacteristic
438C4—21no—
439C4—41no—
440C4—4521no—
441C4—2262no—
442C4—2261no—
443C4—2261no—
444C4—2261no—
445C4C2×D4×D11311yescharacteristic
446C4C2×D4×D11311yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—9041no—
451C2—4521no—
452C2—4521no—
453C2—4521no—
454C2#2029923211yescharacteristic
subgroupG/H
centerC2#20299232
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#471×C113C2
socleC2×C113D42
hypercenter#471D113
hypocenterC113#3291
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. #20299410C2semidirect
2. #20299408C2semidirect
3. #20299407C2semidirect
4. #20299404C2semidirect
5. #20298969C2semidirect
6. #20298864C2semidirect
7. #20298862C2semidirect
8. #20298860C2semidirect
9. #20298783C2semidirect
10. #20298779C2semidirect
11. #20298768C2semidirect
12. #20298764C2semidirect
13. #20298714C2semidirect
14. #20298713C2semidirect
15. #471×C113C2semidirect
18. #16813668C22semidirect
19. #16813667C22semidirect
21. #16813655C22semidirect
22. #16813655C22semidirect
24. #16813653C22semidirect
41. C2×#14268636C22semidirect
42. C2×#14268635C22semidirect
43. C2×#14268634C22semidirect
47. #16813630C22semidirect
48. #16813630C22semidirect
49. #16813628C22semidirect
50. #16813620C22semidirect
52. #16813557C22semidirect
53. #16813549C22semidirect
54. #16813548C22semidirect
55. #16813548C22semidirect
56. #16813548C22semidirect
57. #16813540C22semidirect
58. #16813538C22semidirect
59. C8×Dic113C22semidirect
60. #137×C113C22semidirect
62. C2×SD16×C113C22semidirect
63. #131×C113C22semidirect
64. #108×C113C22semidirect
65. #101×C113C22semidirect
66. #100×C113C22semidirect
95. Dic452D4semidirect
97. #14268637D4semidirect
104. #14268636D4semidirect
105. #14268636D4semidirect
109. #14268635D4semidirect
113. #14268634D4semidirect
116. D904D4semidirect
118. #14268632D4semidirect
228. C113#3291semidirect
237. #471D113semidirect
255. #137C2×D113semidirect
277. C2×SD16C2×D113semidirect
281. #131C2×D113semidirect
285. #108C2×D113semidirect
291. #101C2×D113semidirect
293. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994102
#202994082
#202994072
#202994042
#202989692
#202988642
#202988622
#202988602
#202987832
#202987792
#202987682
#202987642
#202987142
#202987132
#471×C1132
#3291113