Finite Group Databasebeta

← #49133045

Subgroups — #49133045

Order 36224.

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#31827281C211yesmaximal, characteristic, complemented
2#31827276C211yesmaximal, characteristic, complemented
3#31827274C211yesmaximal, characteristic, complemented
4#31827268C211yesmaximal, characteristic, complemented
5#31826847C211yesmaximal, characteristic, complemented
6#31826738C211yesmaximal, characteristic, complemented
7#31826734C211yesmaximal, characteristic, complemented
8#31826730C211yesmaximal, characteristic, complemented
9#31826727C211yesmaximal, characteristic, complemented
10#31826644C211yesmaximal, characteristic, complemented
11#31826639C211yesmaximal, characteristic, complemented
12#31826637C211yesmaximal, characteristic, complemented
13#31826579C211yesmaximal, characteristic, complemented
14#31826579C211yesmaximal, characteristic, complemented
15#455×C283C211yesmaximal, characteristic, complemented
16#22583658C2211yescharacteristic, complemented
17#22583657C2211yescharacteristic, complemented
18#22583656C2211yescharacteristic
19#22583643C2211yescharacteristic, complemented
20#22583642—21no—
21#22583642—21no—
22#22583640—21no—
23#22583640C2211yescharacteristic
24#22583639—21no—
25#22583638C2211yescharacteristic, complemented
26#22583637—21no—
27#22583636—21no—
28#22583636—21no—
29#22583636C2211yescharacteristic
30#22583636C2211yescharacteristic, complemented
31#22583635—21no—
32#22583635C2211yescharacteristic
33#22583633—21no—
34#22583631—21no—
35#22583630—21no—
36#22583630—21no—
37#22583630C2211yescharacteristic
38#22583630C2211yescharacteristic
39C2×#17985382C2211yescharacteristic, complemented
40Q16×D283—21no—
41C2×#17985380—21no—
42C2×#17985380C2211yescharacteristic, complemented
43C2×#17985379C2211yescharacteristic, complemented
44SD16×D283—21no—
45C2×#17985377—21no—
46C2×#17985377C2211yescharacteristic
47#22583618C2211yescharacteristic, complemented
48#22583618C2211yescharacteristic, complemented
49#22583617C2211yescharacteristic
50#22583617C2211yescharacteristic, complemented
51#22583598C2211yescharacteristic, complemented
52#22583545C2211yescharacteristic, complemented
53#22583545C2211yescharacteristic, complemented
54#22583538C2211yescharacteristic, complemented
55#22583538C2211yescharacteristic, complemented
56#22583529C2211yescharacteristic, complemented
57#22583528C2211yescharacteristic, complemented
58#22583526C2211yescharacteristic, complemented
59C4×C283⋊C8C2211yescharacteristic, complemented
60H(5,𝔽2)×C283C2211yescharacteristic
61#137×C283C2211yescharacteristic
62#137×C283C2211yescharacteristic, complemented
63#124×C283C2211yescharacteristic, complemented
64#104×C283C2211yescharacteristic
65#104×C283C2211yescharacteristic, complemented
66#100×C283C2211yescharacteristic, complemented
67#17985393—21no—
68#17985393—21no—
69#17985393—21no—
70#17985392—21no—
71#17985392—21no—
72#17985392—41no—
73#17985392C2311yescharacteristic
74#17985392C2311yescharacteristic
75#17985391—21no—
76#17985391—41no—
77C2×Dic566—21no—
78C2×Dic566C2311yescharacteristic
79Q8×D283—21no—
80Q8×D283—21no—
81Q8×D283—21no—
82C2×D1132—21no—
83C2×D1132C2311yescharacteristic
84D4×D283—21no—
85D4×D283—41no—
86Dic1132—21no—
87#17985382—21no—
88#17985382—21no—
89#17985382—21no—
90#17985382D411yescharacteristic
91#17985382D411yescharacteristic
92#17985381—21no—
93#17985381—21no—
94#17985380—21no—
95#17985380—21no—
96#17985380—21no—
97#17985380—21no—
98#17985380—21no—
99#17985380D411yescharacteristic
100#17985380D411yescharacteristic
101#17985379—21no—
102#17985379—21no—
103#17985379—21no—
104#17985379D411yescharacteristic
105#17985379D411yescharacteristic
106D2264—21no—
107#17985377—21no—
108#17985377—21no—
109#17985377—21no—
110#17985377—21no—
111#17985377—21no—
112#17985377D411yescharacteristic
113#17985377D411yescharacteristic
114#17985376—21no—
115#17985376—21no—
116#17985376C2311yescharacteristic
117#17985376C2311yescharacteristic
118#17985375—21no—
119#17985375—21no—
120C2×C283⋊C8—21no—
121C2×C283⋊C8—21no—
122C2×C283⋊C8C2311yescharacteristic
123C2×C283⋊C8C2311yescharacteristic
124C8×D283—21no—
125C8×D283—21no—
126(C2×D283)⋊C4—41no—
127#41×C283—21no—
128#41×C283—21no—
129#41×C283C2311yescharacteristic
130#41×C283C2311yescharacteristic
131C2×Q8×C283C2311yescharacteristic
132C2×D4×C283—21no—
133C2×D4×C283—21no—
134C2×D4×C283—41no—
135C2×D4×C283C2311yescharacteristic
136Q16×C283—21no—
137Q16×C283—21no—
138SD16×C283—21no—
139SD16×C283—21no—
140M16×C283C2311yescharacteristic
141M16×C283C2311yescharacteristic
142C22⋊C4×C283—41no—
143C42×C283C2311yescharacteristic
144C22×D283—21no—
145C22×D283—41no—
146Dic566—21no—
147Dic566—21no—
148Dic566—41no—
149Dic566—41no—
150Dic566C2×D411yescharacteristic
151Dic566C2×D411yescharacteristic
152D1132—21no—
153D1132—21no—
154D1132—41no—
155D1132—41no—
156D1132C2×D411yescharacteristic
157D1132C2×D411yescharacteristic
158C22⋊D283—21no—
159C22⋊D283—21no—
160C22⋊D283—41no—
161C22⋊D283—41no—
162C2×Dic283—21no—
163C2×Dic283—41no—
164C4×D283—21no—
165C4×D283—21no—
166C4×D283—41no—
167C4×D283—41no—
168C4×D283—41no—
169C4×D283—41no—
170C283⋊C8—21no—
171C283⋊C8—21no—
172C283⋊C8C2×D411yescharacteristic
173C283⋊C8C2×D411yescharacteristic
174C283⋊C8C2×D411yescharacteristic
175C283⋊C8C2×D411yescharacteristic
176C23×C283—21no—
177C23×C283—41no—
178Q8×C283—21no—
179Q8×C283—21no—
180Q8×C283C2×D411yescharacteristic
181Q8×C283C2×D411yescharacteristic
182D4×C283—21no—
183D4×C283—21no—
184D4×C283—21no—
185D4×C283—21no—
186D4×C283—41no—
187D4×C283—41no—
188D4×C283C2×D411yescharacteristic
189D4×C283C2×D411yescharacteristic
190C2×C4×C283—21no—
191C2×C4×C283—21no—
192C2×C4×C283—21no—
193C2×C4×C283—21no—
194C2×C4×C283—41no—
195C2×C4×C283C2411yescharacteristic
196C8×C283—21no—
197C8×C283—21no—
198C22×C283—21no—
199C22×C283—21no—
200C22×C283—41no—
201C22×C283—81no—
202C22×C283—161no—
203C22×C283H(5,𝔽2)11yescharacteristic
204C2×D283—21no—
205C2×D283—21no—
206C2×D283—41no—
207C2×D283—81no—
208C2×D283—161no—
209C4×C283—21no—
210C4×C283—21no—
211C4×C283—41no—
212C4×C283—41no—
213C4×C283C22×D411yescharacteristic
214C4×C283C22×D411yescharacteristic
215Dic283—21no—
216Dic283—21no—
217Dic283—41no—
218C2×C283—21no—
219C2×C283—41no—
220C2×C283—41no—
221C2×C283—81no—
222C2×C283D4211yescharacteristic
223D283—41no—
224D283—41no—
225D283—81no—
226C283#329011yescharacteristic, complemented, Sylow
227#3290—2831nomaximal, Sylow
228#578—2831no—
229#577—2831no—
230#577—2831no—
231#576—2831no—
232#495—2831no—
233#473—2831no—
234#472—2831no—
235#471—2831no—
236#471—2831no—
237#455—2831no—
238#455D28311yescharacteristic, complemented
239#454—2831no—
240#454—2831no—
241#443—2831no—
242#443—2831no—
2432−1+4—2831no—
2442−1+4—2831no—
245H(5,𝔽2)—2831no—
246H(5,𝔽2)C2×D28311yescharacteristic
247#137—2831no—
248#137—2831no—
249#137—5661no—
250#137—5661no—
251#137—5661no—
252#137—5661no—
253#137C2×D28311yescharacteristic
254#137C2×D28311yescharacteristic, complemented
255AGL(1,ℤ/8)—2831no—
256AGL(1,ℤ/8)—2831no—
257AGL(1,ℤ/8)—2831no—
258AGL(1,ℤ/8)—2831no—
259AGL(1,ℤ/8)—5661no—
260AGL(1,ℤ/8)—5661no—
261AGL(1,ℤ/8)—5661no—
262AGL(1,ℤ/8)—5661no—
263#135—2831no—
264#135—2831no—
265#135—5661no—
266#135—5661no—
267#135—5661no—
268#135—5661no—
269C2×Q16—2831no—
270C2×Q16—5661no—
271C2×SD16—2831no—
272C2×SD16—2831no—
273C2×SD16—5661no—
274C2×SD16—5661no—
275C2×D8—2831no—
276C2×D8—5661no—
277#131—2831no—
278#131—2831no—
279#131—2831no—
280#131—2831no—
281#124—2831no—
282#124C2×D28311yescharacteristic, complemented
283#108—2831no—
284#108—2831no—
285#104—2831no—
286#104—2831no—
287#104C2×D28311yescharacteristic
288#104C2×D28311yescharacteristic, complemented
289#101—2831no—
290#101—2831no—
291#100—2831no—
292#100C2×D28311yescharacteristic, complemented
293C4×C8—2831no—
294#41—21no—
295#41—21no—
296#41—2831no—
297#41—2831no—
298#41—5661no—
299#41—5661no—
300#41—5661no—
301#41—5661no—
302#41—5661no—
303#41—5661no—
304#41—11321no—
305#41—11321no—
306#41C22×D28311yescharacteristic
307#41C22×D28311yescharacteristic
308C2×Q8—2831no—
309C2×Q8—5661no—
310C2×Q8—5661no—
311C2×Q8—5661no—
312C2×Q8—5661no—
313C2×Q8C22×D28311yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—2831no—
318C2×D4—5661no—
319C2×D4—5661no—
320C2×D4—11321no—
321C2×D4C22×D28311yescharacteristic
322Q16—21no—
323Q16—21no—
324Q16—2831no—
325Q16—2831no—
326Q16—5661no—
327Q16—5661no—
328Q16—5661no—
329Q16—5661no—
330SD16—21no—
331SD16—21no—
332SD16—2831no—
333SD16—2831no—
334SD16—2831no—
335SD16—2831no—
336SD16—5661no—
337SD16—5661no—
338SD16—5661no—
339SD16—5661no—
340SD16—5661no—
341SD16—5661no—
342SD16—5661no—
343SD16—5661no—
344SD16—5661no—
345SD16—5661no—
346D8—2831no—
347D8—2831no—
348D8—5661no—
349D8—5661no—
350D8—5661no—
351D8—5661no—
352D8—5661no—
353D8—5661no—
354M16—2831no—
355M16—2831no—
356M16—5661no—
357M16—5661no—
358M16—5661no—
359M16—5661no—
360M16C22×D28311yescharacteristic
361M16C22×D28311yescharacteristic
362C2×C8—2831no—
363C2×C8—2831no—
364C2×C8—5661no—
365C2×C8—5661no—
366C2×C8—5661no—
367C2×C8—5661no—
368C22⋊C4—41no—
369C22⋊C4—11321no—
370C42C22×D28311yescharacteristic
371C23—21no—
372C23—41no—
373C23—5661no—
374C23—11321no—
375Q8—21no—
376Q8—21no—
377Q8—2831no—
378Q8—2831no—
379Q8—5661no—
380Q8—5661no—
381Q8—11321no—
382Q8—11321no—
383Q8D4×D28311yescharacteristic
384Q8D4×D28311yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—41no—
391D4—2831no—
392D4—2831no—
393D4—5661no—
394D4—5661no—
395D4—5661no—
396D4—5661no—
397D4—11321no—
398D4—11321no—
399D4—11321no—
400D4—11321no—
401D4D4×D28311yescharacteristic
402D4D4×D28311yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—5661no—
409C2×C4—5661no—
410C2×C4—5661no—
411C2×C4—11321no—
412C2×C4—11321no—
413C2×C4—11321no—
414C2×C4—11321no—
415C2×C4—11321no—
416C2×C4C23×D28311yescharacteristic
417C8—21no—
418C8—21no—
419C8—2831no—
420C8—2831no—
421C8—2831no—
422C8—2831no—
423C8—5661no—
424C8—5661no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—81no—
429C22—161no—
430C22—5661no—
431C22—5661no—
432C22—11321no—
433C22—45281no—
434C22—22641no—
435C22#2258365511yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—5661no—
441C4—5661no—
442C4—11321no—
443C4C2×D4×D28311yescharacteristic
444C4C2×D4×D28311yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—81no—
449C2—11321no—
450C2—11321no—
451C2—22641no—
452C2#3182709711yescharacteristic
subgroupG/H
centerC2#31827097
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#455×C283C2
socleC2×C283D42
hypercenter#455D283
hypocenterC283#3290
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #31827281C2semidirect
2. #31827276C2semidirect
3. #31827274C2semidirect
4. #31827268C2semidirect
5. #31826847C2semidirect
6. #31826738C2semidirect
7. #31826734C2semidirect
8. #31826730C2semidirect
9. #31826727C2semidirect
10. #31826644C2semidirect
11. #31826639C2semidirect
12. #31826637C2semidirect
13. #31826579C2semidirect
14. #31826579C2semidirect
15. #455×C283C2semidirect
16. #22583658C22semidirect
17. #22583657C22semidirect
19. #22583643C22semidirect
25. #22583638C22semidirect
30. #22583636C22semidirect
39. C2×#17985382C22semidirect
42. C2×#17985380C22semidirect
43. C2×#17985379C22semidirect
47. #22583618C22semidirect
48. #22583618C22semidirect
50. #22583617C22semidirect
51. #22583598C22semidirect
52. #22583545C22semidirect
53. #22583545C22semidirect
54. #22583538C22semidirect
55. #22583538C22semidirect
56. #22583529C22semidirect
57. #22583528C22semidirect
58. #22583526C22semidirect
59. C4×C283⋊C8C22semidirect
62. #137×C283C22semidirect
63. #124×C283C22semidirect
65. #104×C283C22semidirect
66. #100×C283C22semidirect
226. C283#3290semidirect
238. #455D283semidirect
254. #137C2×D283semidirect
282. #124C2×D283semidirect
288. #104C2×D283semidirect
292. #100C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272812
#318272762
#318272742
#318272682
#318268472
#318267382
#318267342
#318267302
#318267272
#318266442
#318266392
#318266372
#318265792
#455×C2832
#3290283