Finite Group Databasebeta

← #49130987

Subgroups — #49130987

Order 36224.

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#31827261C211yesmaximal, characteristic, complemented
2C2×#22583634C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×D283C211yesmaximal, characteristic, complemented
4#31827230C211yesmaximal, characteristic, complemented
5#31826734C211yesmaximal, characteristic, complemented
6#31826733C211yesmaximal, characteristic, complemented
7#31826732C211yesmaximal, characteristic, complemented
8#31826729C211yesmaximal, characteristic, complemented
9#31826728C211yesmaximal, characteristic, complemented
10#31826727C211yesmaximal, characteristic, complemented
11#31826726C211yesmaximal, characteristic, complemented
12#31826512C211yesmaximal, characteristic, complemented
13#31826446C211yesmaximal, characteristic, complemented
14#100×D283C211yesmaximal, characteristic, complemented
15#472×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17#41×D283C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19#22583643C2211yescharacteristic, complemented
20#22583640C2211yescharacteristic, complemented
21#22583639—21no—
22#22583638C2211yescharacteristic
23#22583637—21no—
24#22583636C2211yescharacteristic
25#22583636C2211yescharacteristic, complemented
26#22583635C2211yescharacteristic
27#22583634—21no—
28#22583634—21no—
29#22583634—21no—
30#22583634—21no—
31#22583634—21no—
32#22583634—21no—
33#22583631—21no—
34#22583629—21no—
35C2×#17985381C2211yescharacteristic, complemented
36C2×#17985380C2211yescharacteristic, complemented
37SD16×D283—21no—
38C2×#17985377C2211yescharacteristic, complemented
39D8×D283—21no—
40#22583618—21no—
41#22583618C2211yescharacteristic, complemented
42#22583617C2211yescharacteristic, complemented
43#22583616—21no—
44#22583616C2211yescharacteristic, complemented
45C2×#17985375—21no—
46C2×#17985375C2211yescharacteristic
47M16×D283—21no—
48M16×D283C2211yescharacteristic
49M16×D283C2211yescharacteristic
50M16×D283C2211yescharacteristic
51#22583546C2211yescharacteristic, complemented
52#22583545C2211yescharacteristic, complemented
53#22583545C2211yescharacteristic, complemented
54#22583528C2211yescharacteristic, complemented
55#22583528C2211yescharacteristic, complemented
56#22583527C2211yescharacteristic, complemented
57#22583527C2211yescharacteristic, complemented
58#22583526C2211yescharacteristic, complemented
59#22583526C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C283C2211yescharacteristic
61AGL(1,ℤ/8)×C283C2211yescharacteristic, complemented
62C2×D8×C283C2211yescharacteristic, complemented
63#131×C283C2211yescharacteristic, complemented
64#108×C283C2211yescharacteristic, complemented
65#100×C283C2211yescharacteristic, complemented
66#100×C283C2211yescharacteristic, complemented
67C23×D283—21no—
68#17985393D411yescharacteristic
69#17985392—21no—
70#17985392C2311yescharacteristic
71#17985391—21no—
72#17985391—21no—
73#17985391—21no—
74#17985391—21no—
75#17985391—21no—
76#17985391D411yescharacteristic
77C2×Dic566C2311yescharacteristic
78Q8×D283D411yescharacteristic
79C2×D1132C2311yescharacteristic
80C2×C22⋊D283—21no—
81C2×C22⋊D283—21no—
82D4×D283—21no—
83D4×D283—21no—
84D4×D283—21no—
85D4×D283—21no—
86D4×D283—21no—
87D4×D283D411yescharacteristic
88C22×Dic283—21no—
89C2×C4×D283—21no—
90C2×C4×D283C2311yescharacteristic
91Dic1132—21no—
92#17985382—21no—
93#17985381—21no—
94#17985381—21no—
95#17985381—21no—
96#17985381—21no—
97#17985380—21no—
98#17985380—21no—
99#17985380—21no—
100#17985380—21no—
101#17985380—21no—
102#17985379—21no—
103D2264—21no—
104#17985377—21no—
105#17985377—21no—
106#17985377—21no—
107#17985377—21no—
108#17985377—21no—
109#17985376—21no—
110#17985376C2311yescharacteristic
111#17985376C2311yescharacteristic
112#17985376C2311yescharacteristic
113#17985375—21no—
114#17985375—21no—
115#17985375—21no—
116#17985375—21no—
117#17985375—21no—
118#17985375D411yescharacteristic
119#17985375D411yescharacteristic
120#17985375D411yescharacteristic
121#17985375D411yescharacteristic
122C2×C283⋊C8—21no—
123C2×C283⋊C8C2311yescharacteristic
124C8×D283—21no—
125C8×D283—21no—
126C8×D283—21no—
127C8×D283—21no—
128C8×D283—21no—
129#41×C283C2311yescharacteristic
130C2×D4×C283C2311yescharacteristic
131C2×D4×C283C2311yescharacteristic
132SD16×C283—21no—
133SD16×C283—21no—
134D8×C283—21no—
135D8×C283—21no—
136D8×C283—21no—
137D8×C283—21no—
138M16×C283—21no—
139M16×C283C2311yescharacteristic
140M16×C283C2311yescharacteristic
141M16×C283C2311yescharacteristic
142C2×C8×C283—21no—
143C2×C8×C283C2311yescharacteristic
144C22×D283—21no—
145C22×D283—21no—
146C22×D283—41no—
147C22×D283—41no—
148C22×D283—82no—
149C22×D283#4111yescharacteristic
150Dic566—21no—
151Dic566—21no—
152Dic566—21no—
153Dic566C2×D411yescharacteristic
154D1132—21no—
155D1132—21no—
156D1132—21no—
157D1132C2×D411yescharacteristic
158C22⋊D283—21no—
159C22⋊D283—21no—
160C22⋊D283—21no—
161C22⋊D283—41no—
162C22⋊D283—41no—
163C22⋊D283—41no—
164C22⋊D283—41no—
165C2×Dic283—21no—
166C2×Dic283—21no—
167C2×Dic283—41no—
168C2×Dic283—41no—
169C2×Dic283#4111yescharacteristic
170C4×D283—21no—
171C4×D283—21no—
172C4×D283—21no—
173C4×D283C2×D411yescharacteristic
174C4×D283C2×D411yescharacteristic
175C4×D283C2×D411yescharacteristic
176C4×D283C2×D411yescharacteristic
177C283⋊C8—21no—
178C283⋊C8—21no—
179C283⋊C8—21no—
180C283⋊C8C2×D411yescharacteristic
181C283⋊C8C2×D411yescharacteristic
182C23×C283—21no—
183C23×C283—21no—
184Q8×C283C2×D411yescharacteristic
185D4×C283—21no—
186D4×C283—21no—
187D4×C283—21no—
188D4×C283—21no—
189D4×C283—21no—
190D4×C283C2×D411yescharacteristic
191C2×C4×C283—21no—
192C2×C4×C283C2411yescharacteristic
193C8×C283—21no—
194C8×C283—21no—
195C8×C283—21no—
196C8×C283C2×D411yescharacteristic
197C8×C283C2×D411yescharacteristic
198C22×C283—21no—
199C22×C283—41no—
200C22×C283—41no—
201C22×C283—81no—
202C22×C283—81no—
203C22×C283C2×#4111yescharacteristic
204C2×D283—21no—
205C2×D283—41no—
206C2×D283—41no—
207C2×D283—81no—
208C2×D283—82no—
209C2×D283—82no—
210C2×D283—81no—
211C2×D283#12111yescharacteristic
212C2×D283#12111yescharacteristic
213C4×C283—21no—
214C4×C283C22×D411yescharacteristic
215C4×C283C22×D411yescharacteristic
216Dic283—21no—
217Dic283—41no—
218Dic283#12111yescharacteristic
219Dic283#12111yescharacteristic
220C2×C283—21no—
221C2×C283—41no—
222C2×C283—81no—
223C2×C283—81no—
224C2×C283C2×#12111yescharacteristic
225D283—21no—
226D283—21no—
227D283—41no—
228D283—81no—
229C283#306811yescharacteristic, complemented, Sylow
230#3068—2831nomaximal, Sylow
231#575—2831no—
232C2×AGL(1,ℤ/8)—2831no—
233C2×AGL(1,ℤ/8)—2831no—
234#568—2831no—
235#472—2831no—
236#472—2831no—
237#472—2831no—
238#472D28311yescharacteristic, complemented
239#471—2831no—
240#471—2831no—
241#471—2831no—
242#471—2831no—
243#430—2831no—
244#413—2831no—
245C2×#100—2831no—
246C2×#41—2831no—
247C2×#41—2831no—
248C22×D4—2831no—
249#137—2831no—
250#137—2831no—
251#137—5661no—
252AGL(1,ℤ/8)—2831no—
253AGL(1,ℤ/8)—2831no—
254AGL(1,ℤ/8)—2831no—
255AGL(1,ℤ/8)—2831no—
256AGL(1,ℤ/8)—5661no—
257AGL(1,ℤ/8)—5661no—
258AGL(1,ℤ/8)—5661no—
259AGL(1,ℤ/8)—5661no—
260AGL(1,ℤ/8)—5661no—
261AGL(1,ℤ/8)—5661no—
262AGL(1,ℤ/8)—5661no—
263AGL(1,ℤ/8)C2×D28311yescharacteristic
264AGL(1,ℤ/8)C2×D28311yescharacteristic, complemented
265#135—5661no—
266#135—5661no—
267C2×SD16—2831no—
268C2×SD16—2831no—
269C2×SD16—5661no—
270C2×D8—2831no—
271C2×D8—5661no—
272C2×D8C2×D28311yescharacteristic, complemented
273#131—2831no—
274#131—2831no—
275#131—2831no—
276#131—5661no—
277#131—5661no—
278#131C2×D28311yescharacteristic, complemented
279C2×M16—2831no—
280C2×M16—2831no—
281C2×M16—2831no—
282C2×M16—2831no—
283C2×M16—5661no—
284C2×M16—5661no—
285#108—2831no—
286#108—2831no—
287#108—2831no—
288#108C2×D28311yescharacteristic, complemented
289#101—2831no—
290#101—2831no—
291#100—2831no—
292#100—2831no—
293#100—2831no—
294#100—2831no—
295#100C2×D28311yescharacteristic, complemented
296#100C2×D28311yescharacteristic, complemented
297C24—5661no—
298#41—2831no—
299#41—2831no—
300#41—2831no—
301#41—5661no—
302#41—5661no—
303#41—5661no—
304#41—5661no—
305#41—5661no—
306#41—5661no—
307#41C22×D28311yescharacteristic
308C2×Q8—2831no—
309C2×Q8—2831no—
310C2×D4—2831no—
311C2×D4—2831no—
312C2×D4—5661no—
313C2×D4—5661no—
314C2×D4—5661no—
315C2×D4—5661no—
316C2×D4—5661no—
317C2×D4—5661no—
318C2×D4—5661no—
319C2×D4C22×D28311yescharacteristic
320C2×D4C22×D28311yescharacteristic
321C22×C4—2831no—
322C22×C4—5661no—
323C22×C4—5661no—
324Q16—5661no—
325Q16—5661no—
326SD16—21no—
327SD16—21no—
328SD16—5661no—
329SD16—5661no—
330SD16—5661no—
331SD16—5661no—
332SD16—5661no—
333SD16—5661no—
334SD16—5661no—
335SD16—5661no—
336SD16—5661no—
337SD16—5661no—
338D8—21no—
339D8—21no—
340D8—21no—
341D8—21no—
342D8—5661no—
343D8—5661no—
344D8—5661no—
345D8—5661no—
346D8—5661no—
347D8—5661no—
348M16—21no—
349M16—2831no—
350M16—2831no—
351M16—2831no—
352M16—2831no—
353M16—2831no—
354M16—2831no—
355M16—2831no—
356M16—5661no—
357M16—5661no—
358M16—5661no—
359M16—5661no—
360M16—5661no—
361M16—5661no—
362M16C22×D28311yescharacteristic
363M16C22×D28311yescharacteristic
364M16C22×D28311yescharacteristic
365C2×C8—21no—
366C2×C8—2831no—
367C2×C8—5661no—
368C2×C8—5661no—
369C2×C8—5661no—
370C2×C8—5661no—
371C2×C8—5661no—
372C2×C8—5661no—
373C2×C8C22×D28311yescharacteristic
374C23—21no—
375C23—21no—
376C23—2831no—
377C23—5661no—
378C23—5661no—
379C23—11321no—
380C23—11321no—
381C23—22642no—
382Q8—2831no—
383Q8—5661no—
384Q8—5661no—
385Q8—5661no—
386Q8D4×D28311yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—2831no—
393D4—5661no—
394D4—5661no—
395D4—5661no—
396D4—5661no—
397D4—5661no—
398D4—5661no—
399D4—11321no—
400D4—11321no—
401D4—11321no—
402D4—11321no—
403D4D4×D28311yescharacteristic
404C2×C4—21no—
405C2×C4—2831no—
406C2×C4—2831no—
407C2×C4—2831no—
408C2×C4—2831no—
409C2×C4—2831no—
410C2×C4—5661no—
411C2×C4—5661no—
412C2×C4—5661no—
413C2×C4—5661no—
414C2×C4—5661no—
415C2×C4—11321no—
416C2×C4—11321no—
417C2×C4C23×D28311yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—2831no—
422C8—2831no—
423C8—5661no—
424C8—5661no—
425C8—5661no—
426C8D4×D28311yescharacteristic
427C8D4×D28311yescharacteristic
428C22—21no—
429C22—41no—
430C22—41no—
431C22—81no—
432C22—81no—
433C22—2831no—
434C22—2831no—
435C22—5661no—
436C22—11321no—
437C22—11321no—
438C22—22641no—
439C22—22641no—
440C22—22642no—
441C22—22642no—
442C22#41×D28311yescharacteristic
443C4—21no—
444C4—2831no—
445C4—2831no—
446C4—5661no—
447C4—11321no—
448C4C2×D4×D28311yescharacteristic
449C4C2×D4×D28311yescharacteristic
450C2—21no—
451C2—41no—
452C2—81no—
453C2—81no—
454C2—5661no—
455C2—5661no—
456C2—11321no—
457C2—22641no—
458C2#121×D28311yescharacteristic
subgroupG/H
centerC2#121×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#472×C283C2
socleC2×C283C2×#121
hypercenter#472D283
hypocenterC283#3068
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #31827261C2semidirect
2. C2×#22583634C2semidirect
3. AGL(1,ℤ/8)×D283C2semidirect
4. #31827230C2semidirect
5. #31826734C2semidirect
6. #31826733C2semidirect
7. #31826732C2semidirect
8. #31826729C2semidirect
9. #31826728C2semidirect
10. #31826727C2semidirect
11. #31826726C2semidirect
12. #31826512C2semidirect
13. #31826446C2semidirect
14. #100×D283C2semidirect
15. #472×C283C2semidirect
19. #22583643C22semidirect
20. #22583640C22semidirect
25. #22583636C22semidirect
35. C2×#17985381C22semidirect
36. C2×#17985380C22semidirect
38. C2×#17985377C22semidirect
41. #22583618C22semidirect
42. #22583617C22semidirect
44. #22583616C22semidirect
51. #22583546C22semidirect
52. #22583545C22semidirect
53. #22583545C22semidirect
54. #22583528C22semidirect
55. #22583528C22semidirect
56. #22583527C22semidirect
57. #22583527C22semidirect
58. #22583526C22semidirect
59. #22583526C22semidirect
61. AGL(1,ℤ/8)×C283C22semidirect
62. C2×D8×C283C22semidirect
63. #131×C283C22semidirect
64. #108×C283C22semidirect
65. #100×C283C22semidirect
66. #100×C283C22semidirect
229. C283#3068semidirect
238. #472D283semidirect
264. AGL(1,ℤ/8)C2×D283semidirect
272. C2×D8C2×D283semidirect
278. #131C2×D283semidirect
288. #108C2×D283semidirect
295. #100C2×D283semidirect
296. #100C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272612
C2×#225836342
AGL(1,ℤ/8)×D2832
#318272302
#318267342
#318267332
#318267322
#318267292
#318267282
#318267272
#318267262
#318265122
#318264462
#100×D2832
#472×C2832
#3068283