Finite Group Databasebeta

← #16857495

Subgroups — #16857495

Order 3968.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521865C211yesmaximal, characteristic, complemented
2#14521860C211yesmaximal, characteristic, complemented
3#14521858C211yesmaximal, characteristic, complemented
4#14521852C211yesmaximal, characteristic, complemented
5#14521431C211yesmaximal, characteristic, complemented
6#14521322C211yesmaximal, characteristic, complemented
7#14521318C211yesmaximal, characteristic, complemented
8#14521314C211yesmaximal, characteristic, complemented
9#14521311C211yesmaximal, characteristic, complemented
10#14521228C211yesmaximal, characteristic, complemented
11#14521223C211yesmaximal, characteristic, complemented
12#14521221C211yesmaximal, characteristic, complemented
13#14521163C211yesmaximal, characteristic, complemented
14#14521163C211yesmaximal, characteristic, complemented
15C31×#455C211yesmaximal, characteristic, complemented
16C31×H(5,𝔽2)C2211yescharacteristic
17#11758567C2211yescharacteristic, complemented
18#11758566C2211yescharacteristic
19#11758564C2211yescharacteristic, complemented
20C31×#137C2211yescharacteristic
21C31×#137C2211yescharacteristic, complemented
22C31×#124C2211yescharacteristic, complemented
23#11758528—21no—
24#11758528C2211yescharacteristic
25#11758527—21no—
26#11758527—21no—
27#11758527C2211yescharacteristic
28#11758527C2211yescharacteristic
29#11758526—21no—
30#11758526C2211yescharacteristic
31#11758525C2211yescharacteristic
32#11758525C2211yescharacteristic, complemented
33C2×#92482C2211yescharacteristic, complemented
34C2×#92481C2211yescharacteristic, complemented
35C2×#92480—21no—
36C2×#92480C2211yescharacteristic, complemented
37#11758509—21no—
38#11758509—21no—
39#11758509C2211yescharacteristic
40#11758509C2211yescharacteristic, complemented
41C2×#92479—21no—
42C2×#92479C2211yescharacteristic
43#11758496—21no—
44#11758495—21no—
45#11758495—21no—
46Q16×D31—21no—
47#11758493—21no—
48#11758492—21no—
49#11758491—21no—
50SD16×D31—21no—
51#11758486C2211yescharacteristic, complemented
52#11758485C2211yescharacteristic, complemented
53#11758484C2211yescharacteristic, complemented
54#11758484C2211yescharacteristic, complemented
55#11758452C2211yescharacteristic, complemented
56C31×#104C2211yescharacteristic
57C31×#104C2211yescharacteristic, complemented
58C31×#100C2211yescharacteristic, complemented
59#11758424C2211yescharacteristic, complemented
60#11758412C2211yescharacteristic, complemented
61#11758411C2211yescharacteristic, complemented
62#11758410C2211yescharacteristic, complemented
63#11758410C2211yescharacteristic, complemented
64#11758393C2211yescharacteristic, complemented
65#11758393C2211yescharacteristic, complemented
66C4×C31⋊C8C2211yescharacteristic, complemented
67#41×C31—21no—
68#41×C31—21no—
69#41×C31C2311yescharacteristic
70#41×C31C2311yescharacteristic
71C2×Q8×C31C2311yescharacteristic
72C2×D4×C31—21no—
73C2×D4×C31—21no—
74C2×D4×C31—41no—
75C2×D4×C31C2311yescharacteristic
76#92499—21no—
77#92499—21no—
78#92499—21no—
79Q8×D31—21no—
80Q8×D31—21no—
81Q8×D31—21no—
82#92497—21no—
83#92497—41no—
84D4×D31—21no—
85D4×D31—41no—
86#92495—21no—
87#92495—21no—
88#92495—41no—
89#92495C2311yescharacteristic
90#92495C2311yescharacteristic
91C2×D124—21no—
92C2×D124C2311yescharacteristic
93C2×Dic62—21no—
94C2×Dic62C2311yescharacteristic
95Q16×C31—21no—
96Q16×C31—21no—
97SD16×C31—21no—
98SD16×C31—21no—
99M16×C31C2311yescharacteristic
100M16×C31C2311yescharacteristic
101C22⋊C4×C31—41no—
102C42×C31C2311yescharacteristic
103#92482—21no—
104#92482—21no—
105#92482—21no—
106#92482D411yescharacteristic
107#92482D411yescharacteristic
108#92481—21no—
109#92481—21no—
110#92481—21no—
111#92481D411yescharacteristic
112#92481D411yescharacteristic
113#92480—21no—
114#92480—21no—
115#92480—21no—
116#92480—21no—
117#92480—21no—
118#92480D411yescharacteristic
119#92480D411yescharacteristic
120#92479—21no—
121#92479—21no—
122#92479—21no—
123#92479—21no—
124#92479—21no—
125#92479D411yescharacteristic
126#92479D411yescharacteristic
127(C2×D31)⋊C4—41no—
128#92474—21no—
129#92474—21no—
130#92474C2311yescharacteristic
131#92474C2311yescharacteristic
132C2×C31⋊C8—21no—
133C2×C31⋊C8—21no—
134C2×C31⋊C8C2311yescharacteristic
135C2×C31⋊C8C2311yescharacteristic
136Dic124—21no—
137D248—21no—
138#92470—21no—
139#92470—21no—
140#92469—21no—
141#92469—21no—
142C8×D31—21no—
143C8×D31—21no—
144C23×C31—21no—
145C23×C31—41no—
146C22×D31—21no—
147C22×D31—41no—
148Q8×C31—21no—
149Q8×C31—21no—
150Q8×C31C2×D411yescharacteristic
151Q8×C31C2×D411yescharacteristic
152D4×C31—21no—
153D4×C31—21no—
154D4×C31—21no—
155D4×C31—21no—
156D4×C31—41no—
157D4×C31—41no—
158D4×C31C2×D411yescharacteristic
159D4×C31C2×D411yescharacteristic
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—41no—
165C2×C4×C31C2411yescharacteristic
166C22⋊D31—21no—
167C22⋊D31—21no—
168C22⋊D31—41no—
169C22⋊D31—41no—
170C2×Dic31—21no—
171C2×Dic31—41no—
172D124—21no—
173D124—21no—
174D124—41no—
175D124—41no—
176D124C2×D411yescharacteristic
177D124C2×D411yescharacteristic
178C4×D31—21no—
179C4×D31—21no—
180C4×D31—41no—
181C4×D31—41no—
182C4×D31—41no—
183C4×D31—41no—
184Dic62—21no—
185Dic62—21no—
186Dic62—41no—
187Dic62—41no—
188Dic62C2×D411yescharacteristic
189Dic62C2×D411yescharacteristic
190C8×C31—21no—
191C8×C31—21no—
192C31⋊C8—21no—
193C31⋊C8—21no—
194C31⋊C8C2×D411yescharacteristic
195C31⋊C8C2×D411yescharacteristic
196C31⋊C8C2×D411yescharacteristic
197C31⋊C8C2×D411yescharacteristic
198#3290—311nomaximal, Sylow
199C22×C31—21no—
200C22×C31—21no—
201C22×C31—41no—
202C22×C31—81no—
203C22×C31—161no—
204C22×C31H(5,𝔽2)11yescharacteristic
205C2×D31—21no—
206C2×D31—21no—
207C2×D31—41no—
208C2×D31—81no—
209C2×D31—161no—
210C4×C31—21no—
211C4×C31—21no—
212C4×C31—41no—
213C4×C31—41no—
214C4×C31C22×D411yescharacteristic
215C4×C31C22×D411yescharacteristic
216Dic31—21no—
217Dic31—21no—
218Dic31—41no—
219#578—311no—
220#577—311no—
221#577—311no—
222#576—311no—
223#495—311no—
224#473—311no—
225#472—311no—
226#471—311no—
227#471—311no—
228#455—311no—
229#455D3111yescharacteristic, complemented
230#454—311no—
231#454—311no—
232#443—311no—
233#443—311no—
234C2×C31—21no—
235C2×C31—41no—
236C2×C31—41no—
237C2×C31—81no—
238C2×C31D4211yescharacteristic
239D31—41no—
240D31—41no—
241D31—81no—
2422−1+4—311no—
2432−1+4—311no—
244H(5,𝔽2)—311no—
245H(5,𝔽2)C2×D3111yescharacteristic
246#137—311no—
247#137—311no—
248#137—621no—
249#137—621no—
250#137—621no—
251#137—621no—
252#137C2×D3111yescharacteristic
253#137C2×D3111yescharacteristic, complemented
254AGL(1,ℤ/8)—311no—
255AGL(1,ℤ/8)—311no—
256AGL(1,ℤ/8)—311no—
257AGL(1,ℤ/8)—311no—
258AGL(1,ℤ/8)—621no—
259AGL(1,ℤ/8)—621no—
260AGL(1,ℤ/8)—621no—
261AGL(1,ℤ/8)—621no—
262#135—311no—
263#135—311no—
264#135—621no—
265#135—621no—
266#135—621no—
267#135—621no—
268C2×Q16—311no—
269C2×Q16—621no—
270C2×SD16—311no—
271C2×SD16—311no—
272C2×SD16—621no—
273C2×SD16—621no—
274C2×D8—311no—
275C2×D8—621no—
276#131—311no—
277#131—311no—
278#131—311no—
279#131—311no—
280#124—311no—
281#124C2×D3111yescharacteristic, complemented
282#108—311no—
283#108—311no—
284#104—311no—
285#104—311no—
286#104C2×D3111yescharacteristic
287#104C2×D3111yescharacteristic, complemented
288#101—311no—
289#101—311no—
290#100—311no—
291#100C2×D3111yescharacteristic, complemented
292C4×C8—311no—
293C31#329011yescharacteristic, complemented, Sylow
294#41—21no—
295#41—21no—
296#41—311no—
297#41—311no—
298#41—621no—
299#41—621no—
300#41—621no—
301#41—621no—
302#41—621no—
303#41—621no—
304#41—1241no—
305#41—1241no—
306#41C22×D3111yescharacteristic
307#41C22×D3111yescharacteristic
308C2×Q8—311no—
309C2×Q8—621no—
310C2×Q8—621no—
311C2×Q8—621no—
312C2×Q8—621no—
313C2×Q8C22×D3111yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—311no—
318C2×D4—621no—
319C2×D4—621no—
320C2×D4—1241no—
321C2×D4C22×D3111yescharacteristic
322Q16—21no—
323Q16—21no—
324Q16—311no—
325Q16—311no—
326Q16—621no—
327Q16—621no—
328Q16—621no—
329Q16—621no—
330SD16—21no—
331SD16—21no—
332SD16—311no—
333SD16—311no—
334SD16—311no—
335SD16—311no—
336SD16—621no—
337SD16—621no—
338SD16—621no—
339SD16—621no—
340SD16—621no—
341SD16—621no—
342SD16—621no—
343SD16—621no—
344SD16—621no—
345SD16—621no—
346D8—311no—
347D8—311no—
348D8—621no—
349D8—621no—
350D8—621no—
351D8—621no—
352D8—621no—
353D8—621no—
354M16—311no—
355M16—311no—
356M16—621no—
357M16—621no—
358M16—621no—
359M16—621no—
360M16C22×D3111yescharacteristic
361M16C22×D3111yescharacteristic
362C2×C8—311no—
363C2×C8—311no—
364C2×C8—621no—
365C2×C8—621no—
366C2×C8—621no—
367C2×C8—621no—
368C22⋊C4—41no—
369C22⋊C4—1241no—
370C42C22×D3111yescharacteristic
371C23—21no—
372C23—41no—
373C23—621no—
374C23—1241no—
375Q8—21no—
376Q8—21no—
377Q8—311no—
378Q8—311no—
379Q8—621no—
380Q8—621no—
381Q8—1241no—
382Q8—1241no—
383Q8D4×D3111yescharacteristic
384Q8D4×D3111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—41no—
391D4—311no—
392D4—311no—
393D4—621no—
394D4—621no—
395D4—621no—
396D4—621no—
397D4—1241no—
398D4—1241no—
399D4—1241no—
400D4—1241no—
401D4D4×D3111yescharacteristic
402D4D4×D3111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—621no—
409C2×C4—621no—
410C2×C4—621no—
411C2×C4—1241no—
412C2×C4—1241no—
413C2×C4—1241no—
414C2×C4—1241no—
415C2×C4—1241no—
416C2×C4C23×D3111yescharacteristic
417C8—21no—
418C8—21no—
419C8—311no—
420C8—311no—
421C8—311no—
422C8—311no—
423C8—621no—
424C8—621no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—81no—
429C22—161no—
430C22—621no—
431C22—621no—
432C22—1241no—
433C22—4961no—
434C22—2481no—
435C22#1175856111yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—621no—
441C4—621no—
442C4—1241no—
443C4C2×D4×D3111yescharacteristic
444C4C2×D4×D3111yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—81no—
449C2—1241no—
450C2—1241no—
451C2—2481no—
452C2#1452168111yescharacteristic
subgroupG/H
centerC2#14521681
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#455C2
socleC2×C31D42
hypercenter#455D31
hypocenterC31#3290
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #14521865C2semidirect
2. #14521860C2semidirect
3. #14521858C2semidirect
4. #14521852C2semidirect
5. #14521431C2semidirect
6. #14521322C2semidirect
7. #14521318C2semidirect
8. #14521314C2semidirect
9. #14521311C2semidirect
10. #14521228C2semidirect
11. #14521223C2semidirect
12. #14521221C2semidirect
13. #14521163C2semidirect
14. #14521163C2semidirect
15. C31×#455C2semidirect
17. #11758567C22semidirect
19. #11758564C22semidirect
21. C31×#137C22semidirect
22. C31×#124C22semidirect
32. #11758525C22semidirect
33. C2×#92482C22semidirect
34. C2×#92481C22semidirect
36. C2×#92480C22semidirect
40. #11758509C22semidirect
51. #11758486C22semidirect
52. #11758485C22semidirect
53. #11758484C22semidirect
54. #11758484C22semidirect
55. #11758452C22semidirect
57. C31×#104C22semidirect
58. C31×#100C22semidirect
59. #11758424C22semidirect
60. #11758412C22semidirect
61. #11758411C22semidirect
62. #11758410C22semidirect
63. #11758410C22semidirect
64. #11758393C22semidirect
65. #11758393C22semidirect
66. C4×C31⋊C8C22semidirect
229. #455D31semidirect
253. #137C2×D31semidirect
281. #124C2×D31semidirect
287. #104C2×D31semidirect
291. #100C2×D31semidirect
293. C31#3290semidirect

Maximal subgroups

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

subgroupindex
#145218652
#145218602
#145218582
#145218522
#145214312
#145213222
#145213182
#145213142
#145213112
#145212282
#145212232
#145212212
#145211632
C31×#4552
#329031