Finite Group Databasebeta

← #16857494

Subgroups — #16857494

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#14521861C211yesmaximal, characteristic, complemented
3#14521855C211yesmaximal, characteristic, complemented
4#14521853C211yesmaximal, characteristic, complemented
5#14521430C211yesmaximal, characteristic, complemented
6#14521323C211yesmaximal, characteristic, complemented
7#14521318C211yesmaximal, characteristic, complemented
8#14521313C211yesmaximal, characteristic, complemented
9#14521229C211yesmaximal, characteristic, complemented
10#14521225C211yesmaximal, characteristic, complemented
11#14521224C211yesmaximal, characteristic, complemented
12#14521220C211yesmaximal, characteristic, complemented
13#14521165C211yesmaximal, characteristic, complemented
14#14521164C211yesmaximal, characteristic, complemented
15C31×#471C211yesmaximal, characteristic, complemented
16#11758567C2211yescharacteristic, complemented
17#11758566C2211yescharacteristic
18#11758564C2211yescharacteristic, complemented
19#11758561C2211yescharacteristic
20C31×#137C2211yescharacteristic, complemented
21C31×AGL(1,ℤ/8)C2211yescharacteristic
22C2×SD16×C31C2211yescharacteristic, complemented
23C31×#131C2211yescharacteristic, complemented
24#11758527C2211yescharacteristic
25#11758524C2211yescharacteristic, complemented
26C2×#92482C2211yescharacteristic, complemented
27#11758519C2211yescharacteristic
28#11758513C2211yescharacteristic, complemented
29#11758509C2211yescharacteristic, complemented
30C2×#92479C2211yescharacteristic
31#11758495—21no—
32Q16×D31—21no—
33#11758493—21no—
34#11758493—21no—
35#11758493—21no—
36#11758492—21no—
37#11758492—21no—
38#11758491—21no—
39#11758491—21no—
40SD16×D31—21no—
41#11758488—21no—
42D8×D31—21no—
43#11758486—21no—
44#11758486C2211yescharacteristic
45#11758486C2211yescharacteristic, complemented
46#11758485—21no—
47#11758485C2211yescharacteristic
48#11758485C2211yescharacteristic, complemented
49#11758484C2211yescharacteristic
50#11758484C2211yescharacteristic, complemented
51#11758481—21no—
52#11758481C2211yescharacteristic
53C2×#92470—21no—
54C2×#92470C2211yescharacteristic, complemented
55#11758478C2211yescharacteristic, complemented
56C31×#108C2211yescharacteristic, complemented
57C31×#101C2211yescharacteristic, complemented
58C31×#100C2211yescharacteristic, complemented
59#11758425C2211yescharacteristic, complemented
60#11758413C2211yescharacteristic
61#11758413C2211yescharacteristic, complemented
62#11758413C2211yescharacteristic, complemented
63#11758412C2211yescharacteristic, complemented
64#11758411C2211yescharacteristic, complemented
65#11758410C2211yescharacteristic, complemented
66C8×Dic31C2211yescharacteristic, complemented
67#41×C31C2311yescharacteristic
68C2×Q8×C31C2311yescharacteristic
69C2×D4×C31C2311yescharacteristic
70C2×C22⋊D31—41no—
71#92499—21no—
72#92499—21no—
73#92499—21no—
74Q8×D31—21no—
75Q8×D31—21no—
76Q8×D31—21no—
77#92497—21no—
78#92497—21no—
79#92497—21no—
80#92497—41no—
81D4×D31—21no—
82D4×D31—21no—
83D4×D31—21no—
84D4×D31—41no—
85#92495—21no—
86#92495—21no—
87#92495—41no—
88#92495C2311yescharacteristic
89#92495C2311yescharacteristic
90#92495C2311yescharacteristic
91C2×D124—21no—
92C2×D124C2311yescharacteristic
93C2×Dic62—21no—
94C2×Dic62C2311yescharacteristic
95Q16×C31—21no—
96SD16×C31—21no—
97SD16×C31—21no—
98SD16×C31—21no—
99SD16×C31—21no—
100D8×C31—21no—
101M16×C31—21no—
102M16×C31C2311yescharacteristic
103M16×C31C2311yescharacteristic
104M16×C31C2311yescharacteristic
105C2×C8×C31—21no—
106C2×C8×C31C2311yescharacteristic
107C22⋊Dic31—41no—
108#92482—21no—
109#92482—21no—
110#92482—21no—
111#92482D411yescharacteristic
112#92481—21no—
113#92481D411yescharacteristic
114#92480—21no—
115#92480D411yescharacteristic
116#92479—21no—
117#92479—21no—
118#92479—21no—
119#92479D411yescharacteristic
120(C2×D31)⋊C4—41no—
121C4×Dic31C2311yescharacteristic
122#92474C2311yescharacteristic
123C2×C31⋊C8C2311yescharacteristic
124Dic124—21no—
125Dic124—21no—
126Dic124D411yescharacteristic
127D248—21no—
128D248—21no—
129D248D411yescharacteristic
130#92470—21no—
131#92470—21no—
132#92470—21no—
133#92470—21no—
134#92470—21no—
135#92470—21no—
136#92470D411yescharacteristic
137#92470D411yescharacteristic
138#92469—21no—
139#92469—21no—
140#92469—21no—
141C8×D31—21no—
142C8×D31—21no—
143C8×D31—21no—
144C23×C31—21no—
145C22×D31—21no—
146C22×D31—41no—
147C22×D31—41no—
148Q8×C31—21no—
149Q8×C31—21no—
150Q8×C31C2×D411yescharacteristic
151D4×C31—21no—
152D4×C31—21no—
153D4×C31—21no—
154D4×C31C2×D411yescharacteristic
155C2×C4×C31—21no—
156C2×C4×C31—21no—
157C2×C4×C31C2411yescharacteristic
158C22⋊D31—21no—
159C22⋊D31—21no—
160C22⋊D31—21no—
161C22⋊D31—41no—
162C22⋊D31—41no—
163C22⋊D31—41no—
164C22⋊D31—41no—
165C2×Dic31—21no—
166C2×Dic31—21no—
167C2×Dic31—41no—
168C2×Dic31—41no—
169D124—21no—
170D124—21no—
171D124—41no—
172D124—41no—
173D124C2×D411yescharacteristic
174D124C2×D411yescharacteristic
175D124C2×D411yescharacteristic
176C4×D31—21no—
177C4×D31—21no—
178C4×D31—21no—
179C4×D31—41no—
180C4×D31—41no—
181C4×D31—41no—
182C4×D31—41no—
183Dic62—21no—
184Dic62—21no—
185Dic62—41no—
186Dic62—41no—
187Dic62C2×D411yescharacteristic
188Dic62C2×D411yescharacteristic
189Dic62C2×D411yescharacteristic
190C8×C31—21no—
191C8×C31—21no—
192C8×C31—21no—
193C8×C31C2×D411yescharacteristic
194C8×C31C2×D411yescharacteristic
195C31⋊C8—21no—
196C31⋊C8C2×D411yescharacteristic
197C31⋊C8C2×D411yescharacteristic
198#3290—311nomaximal, Sylow
199C22×C31—21no—
200C22×C31—41no—
201C22×C31—81no—
202C22×C31H(5,𝔽2)11yescharacteristic
203C2×D31—21no—
204C2×D31—21no—
205C2×D31—21no—
206C2×D31—41no—
207C2×D31—81no—
208C2×D31—161no—
209C2×D31—161no—
210C4×C31—21no—
211C4×C31—41no—
212C4×C31C22×D411yescharacteristic
213C4×C31C22×D411yescharacteristic
214Dic31—21no—
215Dic31—21no—
216Dic31—21no—
217Dic31—41no—
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#471D3111yescharacteristic, complemented
228#455—311no—
229#455—311no—
230#454—311no—
231#454—311no—
232#443—311no—
233#443—311no—
234C2×C31—21no—
235C2×C31—41no—
236C2×C31—81no—
237C2×C31D4211yescharacteristic
238D31—41no—
239D31—41no—
240D31—41no—
241D31—81no—
2422−1+4—311no—
2432−1+4—311no—
244H(5,𝔽2)—311no—
245H(5,𝔽2)—311no—
246#137—311no—
247#137—311no—
248#137—311no—
249#137—621no—
250#137—621no—
251#137—621no—
252#137—621no—
253#137C2×D3111yescharacteristic, complemented
254AGL(1,ℤ/8)—311no—
255AGL(1,ℤ/8)—311no—
256AGL(1,ℤ/8)—311no—
257AGL(1,ℤ/8)—621no—
258AGL(1,ℤ/8)—621no—
259AGL(1,ℤ/8)—621no—
260AGL(1,ℤ/8)—621no—
261AGL(1,ℤ/8)C2×D3111yescharacteristic
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—621no—
272C2×SD16—621no—
273C2×SD16C2×D3111yescharacteristic, complemented
274C2×D8—311no—
275C2×D8—621no—
276#131—311no—
277#131—311no—
278#131—311no—
279#131C2×D3111yescharacteristic, complemented
280#124—311no—
281#124—311no—
282#108—311no—
283#108C2×D3111yescharacteristic, complemented
284#104—311no—
285#104—311no—
286#104—311no—
287#104—311no—
288#101—311no—
289#101C2×D3111yescharacteristic, complemented
290#100—311no—
291#100C2×D3111yescharacteristic, complemented
292C4×C8—311no—
293C31#329011yescharacteristic, complemented, Sylow
294#41—311no—
295#41—311no—
296#41—311no—
297#41—621no—
298#41—621no—
299#41—621no—
300#41—621no—
301#41—621no—
302#41—621no—
303#41—621no—
304#41—621no—
305#41—1241no—
306#41—1241no—
307#41C22×D3111yescharacteristic
308C2×Q8—311no—
309C2×Q8—621no—
310C2×Q8—621no—
311C2×Q8—621no—
312C2×Q8—621no—
313C2×Q8C22×D3111yescharacteristic
314C2×D4—311no—
315C2×D4—621no—
316C2×D4—621no—
317C2×D4—621no—
318C2×D4—621no—
319C2×D4—1241no—
320C2×D4—1241no—
321C2×D4C22×D3111yescharacteristic
322Q16—21no—
323Q16—311no—
324Q16—311no—
325Q16—621no—
326Q16—621no—
327Q16—621no—
328Q16—621no—
329Q16—621no—
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—311no—
335SD16—311no—
336SD16—311no—
337SD16—311no—
338SD16—621no—
339SD16—621no—
340SD16—621no—
341SD16—621no—
342SD16—621no—
343SD16—621no—
344SD16—621no—
345SD16—621no—
346D8—21no—
347D8—311no—
348D8—311no—
349D8—621no—
350D8—621no—
351D8—621no—
352D8—621no—
353D8—621no—
354M16—21no—
355M16—311no—
356M16—621no—
357M16—621no—
358M16—621no—
359M16C22×D3111yescharacteristic
360M16C22×D3111yescharacteristic
361M16C22×D3111yescharacteristic
362C2×C8—21no—
363C2×C8—311no—
364C2×C8—621no—
365C2×C8—621no—
366C2×C8—621no—
367C2×C8C22×D3111yescharacteristic
368C22⋊C4—1241no—
369C22⋊C4—1241no—
370C42—311no—
371C23—21no—
372C23—621no—
373C23—1241no—
374C23—1241no—
375Q8—21no—
376Q8—21no—
377Q8—311no—
378Q8—311no—
379Q8—311no—
380Q8—621no—
381Q8—621no—
382Q8—1241no—
383Q8—1241no—
384Q8D4×D3111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—311no—
389D4—311no—
390D4—311no—
391D4—621no—
392D4—621no—
393D4—621no—
394D4—621no—
395D4—621no—
396D4—1241no—
397D4—1241no—
398D4—1241no—
399D4—1241no—
400D4—1241no—
401D4—1241no—
402D4D4×D3111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—621no—
406C2×C4—621no—
407C2×C4—621no—
408C2×C4—621no—
409C2×C4—621no—
410C2×C4—1241no—
411C2×C4—1241no—
412C2×C4—1241no—
413C2×C4—1241no—
414C2×C4—1241no—
415C2×C4—1241no—
416C2×C4C23×D3111yescharacteristic
417C8—21no—
418C8—21no—
419C8—21no—
420C8—311no—
421C8—311no—
422C8—621no—
423C8D4×D3111yescharacteristic
424C8D4×D3111yescharacteristic
425C22—21no—
426C22—41no—
427C22—81no—
428C22—621no—
429C22—621no—
430C22—621no—
431C22—1241no—
432C22—4961no—
433C22—4961no—
434C22—2481no—
435C22#1175856611yescharacteristic
436C4—21no—
437C4—41no—
438C4—621no—
439C4—621no—
440C4—621no—
441C4—1241no—
442C4—1241no—
443C4C2×D4×D3111yescharacteristic
444C4C2×D4×D3111yescharacteristic
445C2—21no—
446C2—41no—
447C2—81no—
448C2—1241no—
449C2—1241no—
450C2—1241no—
451C2—2481no—
452C2#1452168311yescharacteristic
subgroupG/H
centerC2#14521683
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#471C2
socleC2×C31D42
hypercenter#471D31
hypocenterC31#3290
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #14521865C2semidirect
2. #14521861C2semidirect
3. #14521855C2semidirect
4. #14521853C2semidirect
5. #14521430C2semidirect
6. #14521323C2semidirect
7. #14521318C2semidirect
8. #14521313C2semidirect
9. #14521229C2semidirect
10. #14521225C2semidirect
11. #14521224C2semidirect
12. #14521220C2semidirect
13. #14521165C2semidirect
14. #14521164C2semidirect
15. C31×#471C2semidirect
16. #11758567C22semidirect
18. #11758564C22semidirect
20. C31×#137C22semidirect
22. C2×SD16×C31C22semidirect
23. C31×#131C22semidirect
25. #11758524C22semidirect
26. C2×#92482C22semidirect
28. #11758513C22semidirect
29. #11758509C22semidirect
45. #11758486C22semidirect
48. #11758485C22semidirect
50. #11758484C22semidirect
54. C2×#92470C22semidirect
55. #11758478C22semidirect
56. C31×#108C22semidirect
57. C31×#101C22semidirect
58. C31×#100C22semidirect
59. #11758425C22semidirect
61. #11758413C22semidirect
62. #11758413C22semidirect
63. #11758412C22semidirect
64. #11758411C22semidirect
65. #11758410C22semidirect
66. C8×Dic31C22semidirect
227. #471D31semidirect
253. #137C2×D31semidirect
273. C2×SD16C2×D31semidirect
279. #131C2×D31semidirect
283. #108C2×D31semidirect
289. #101C2×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
#145218612
#145218552
#145218532
#145214302
#145213232
#145213182
#145213132
#145212292
#145212252
#145212242
#145212202
#145211652
#145211642
C31×#4712
#329031