Finite Group Databasebeta

← #49133052

Subgroups — #49133052

Order 36224.

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#31827276C211yesmaximal, characteristic, complemented
2#31827273C211yesmaximal, characteristic, complemented
3#31827272C211yesmaximal, characteristic, complemented
4#31826836C211yesmaximal, characteristic, complemented
5#31826730C211yesmaximal, characteristic, complemented
6#31826728C211yesmaximal, characteristic, complemented
7#31826726C211yesmaximal, characteristic, complemented
8#31826725C211yesmaximal, characteristic, complemented
9#31826648C211yesmaximal, characteristic, complemented
10#31826646C211yesmaximal, characteristic, complemented
11#31826633C211yesmaximal, characteristic, complemented
12#31826631C211yesmaximal, characteristic, complemented
13#31826582C211yesmaximal, characteristic, complemented
14#31826580C211yesmaximal, characteristic, complemented
15#577×C283C211yesmaximal, characteristic, complemented
16#22583657C2211yescharacteristic
17#22583656C2211yescharacteristic, complemented
18#22583642—21no—
19#22583641—21no—
20#22583641C2211yescharacteristic, complemented
21#22583640—21no—
22#22583640C2211yescharacteristic, complemented
23#22583640C2211yescharacteristic, complemented
24#22583636—21no—
25#22583636C2211yescharacteristic
26#22583635—21no—
27#22583635C2211yescharacteristic
28#22583635C2211yescharacteristic
29#22583634—21no—
30#22583631—21no—
31#22583630—21no—
32#22583630—21no—
33#22583630C2211yescharacteristic
34C2×#17985381C2211yescharacteristic, complemented
35C2×#17985380—21no—
36C2×#17985380C2211yescharacteristic, complemented
37C2×#17985379—21no—
38C2×#17985379C2211yescharacteristic, complemented
39SD16×D283—21no—
40#22583617C2211yescharacteristic, complemented
41#22583617C2211yescharacteristic, complemented
42#22583616C2211yescharacteristic, complemented
43#22583608C2211yescharacteristic, complemented
44#22583606C2211yescharacteristic
45#22583546C2211yescharacteristic, complemented
46#22583545C2211yescharacteristic, complemented
47#22583537C2211yescharacteristic, complemented
48#22583537C2211yescharacteristic, complemented
49#22583537C2211yescharacteristic, complemented
50#22583536C2211yescharacteristic, complemented
51#22583529C2211yescharacteristic, complemented
52#22583528C2211yescharacteristic, complemented
53#22583527C2211yescharacteristic, complemented
54#22583526C2211yescharacteristic, complemented
55C8×Dic283C2211yescharacteristic, complemented
562−1+4×C283C2211yescharacteristic
57H(5,𝔽2)×C283C2211yescharacteristic, complemented
58#137×C283—21no—
59#137×C283C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C283—21no—
61AGL(1,ℤ/8)×C283C2211yescharacteristic
62#135×C283—21no—
63#135×C283C2211yescharacteristic
64C2×SD16×C283—21no—
65C2×SD16×C283C2211yescharacteristic, complemented
66#131×C283C2211yescharacteristic, complemented
67#17985393—21no—
68#17985392—21no—
69#17985392—21no—
70#17985392C2311yescharacteristic
71#17985391—21no—
72#17985391—41no—
73C2×Dic566—21no—
74C2×Dic566C2311yescharacteristic
75Q8×D283—21no—
76C2×D1132—21no—
77C2×D1132C2311yescharacteristic
78C2×C22⋊D283—41no—
79D4×D283—21no—
80D4×D283—41no—
81#17985382—21no—
82#17985382—21no—
83#17985382—21no—
84#17985382D411yescharacteristic, complemented
85#17985381—21no—
86#17985381—21no—
87#17985380—21no—
88#17985380—21no—
89#17985380—21no—
90#17985380—21no—
91#17985380—21no—
92#17985380D411yescharacteristic, complemented
93#17985379—21no—
94#17985379—21no—
95#17985379—21no—
96#17985379—21no—
97#17985379—21no—
98#17985379D411yescharacteristic, complemented
99#17985377—21no—
100#17985377—21no—
101#17985377—21no—
102#17985377D411yescharacteristic, complemented
103#17985376—21no—
104#17985376—21no—
105#17985376C2311yescharacteristic
106#17985376C2311yescharacteristic
107#17985376C2311yescharacteristic
108#17985375—21no—
109C2×C283⋊C8—21no—
110C2×C283⋊C8—21no—
111C2×C283⋊C8C2311yescharacteristic
112C8×D283—21no—
113Dic283⋊C4—41no—
114C4×Dic283C2311yescharacteristic
115#41×C283—21no—
116#41×C283—21no—
117#41×C283—21no—
118#41×C283—21no—
119#41×C283—41no—
120#41×C283C2311yescharacteristic
121#41×C283C2311yescharacteristic
122#41×C283C2311yescharacteristic
123C2×Q8×C283—21no—
124C2×Q8×C283—21no—
125C2×Q8×C283C2311yescharacteristic
126C2×D4×C283—21no—
127C2×D4×C283—21no—
128C2×D4×C283—41no—
129C2×D4×C283C2311yescharacteristic
130Q16×C283—21no—
131Q16×C283D411yescharacteristic, complemented
132SD16×C283—21no—
133SD16×C283—21no—
134SD16×C283—21no—
135SD16×C283—21no—
136SD16×C283D411yescharacteristic, complemented
137SD16×C283D411yescharacteristic, complemented
138D8×C283—21no—
139D8×C283D411yescharacteristic, complemented
140M16×C283—21no—
141M16×C283C2311yescharacteristic
142C2×C8×C283—21no—
143C2×C8×C283C2311yescharacteristic
144C22×D283—21no—
145C22×D283—41no—
146Dic566—21no—
147Dic566—21no—
148Dic566—41no—
149Dic566C2×D411yescharacteristic
150D1132—21no—
151D1132—21no—
152D1132—41no—
153D1132C2×D411yescharacteristic
154C22⋊D283—21no—
155C22⋊D283—41no—
156C22⋊D283—41no—
157C22⋊D283—82no—
158C2×Dic283—21no—
159C2×Dic283—21no—
160C2×Dic283—41no—
161C4×D283—21no—
162C4×D283—41no—
163C4×D283—41no—
164C283⋊C8—21no—
165C283⋊C8—21no—
166C283⋊C8—21no—
167C283⋊C8C2×D411yescharacteristic
168C283⋊C8C2×D411yescharacteristic
169C23×C283—21no—
170C23×C283—41no—
171Q8×C283—21no—
172Q8×C283—21no—
173Q8×C283—41no—
174Q8×C283C2×D411yescharacteristic
175Q8×C283C2×D411yescharacteristic
176Q8×C283C2×D411yescharacteristic
177D4×C283—21no—
178D4×C283—21no—
179D4×C283—21no—
180D4×C283—21no—
181D4×C283—21no—
182D4×C283—41no—
183D4×C283—41no—
184D4×C283—41no—
185D4×C283C2×D411yescharacteristic
186D4×C283C2×D411yescharacteristic
187D4×C283C2×D411yescharacteristic
188C2×C4×C283—21no—
189C2×C4×C283—21no—
190C2×C4×C283—21no—
191C2×C4×C283—21no—
192C2×C4×C283—41no—
193C2×C4×C283—41no—
194C2×C4×C283—41no—
195C2×C4×C283C2411yescharacteristic
196C8×C283—21no—
197C8×C283C2×D411yescharacteristic
198C8×C283C2×D411yescharacteristic
199C22×C283—21no—
200C22×C283—21no—
201C22×C283—21no—
202C22×C283—41no—
203C22×C283—81no—
204C22×C283—161no—
205C22×C283H(5,𝔽2)11yescharacteristic
206C2×D283—21no—
207C2×D283—41no—
208C2×D283—81no—
209C2×D283—161no—
210C4×C283—21no—
211C4×C283—21no—
212C4×C283—21no—
213C4×C283—41no—
214C4×C283C22×D411yescharacteristic
215C4×C283C22×D411yescharacteristic
216Dic283—22no—
217Dic283—21no—
218Dic283—41no—
219C2×C283—21no—
220C2×C283—41no—
221C2×C283—41no—
222C2×C283—41no—
223C2×C283—81no—
224C2×C283D4211yescharacteristic
225D283—41no—
226D283—81no—
227C283#329111yescharacteristic, complemented, Sylow
228#3291—2831nomaximal, Sylow
229#577—2831no—
230#577—2831no—
231#577—2831no—
232#577D28311yescharacteristic, complemented
233#492—2831no—
234#471—2831no—
235#471—2831no—
236#471—2831no—
237#471—2831no—
238#456—2831no—
239#456—2831no—
240#453—2831no—
241#453—2831no—
242#443—2831no—
243#443—2831no—
2442−1+4—2831no—
2452−1+4C2×D28311yescharacteristic
246H(5,𝔽2)—2831no—
247H(5,𝔽2)C2×D28311yescharacteristic, complemented
248#137—21no—
249#137—2831no—
250#137—2831no—
251#137—2831no—
252#137—5661no—
253#137—5661no—
254#137—5661no—
255#137C2×D28311yescharacteristic, complemented
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—2831no—
258AGL(1,ℤ/8)—2831no—
259AGL(1,ℤ/8)—2831no—
260AGL(1,ℤ/8)—5661no—
261AGL(1,ℤ/8)—5661no—
262AGL(1,ℤ/8)—5661no—
263AGL(1,ℤ/8)C2×D28311yescharacteristic
264#135—21no—
265#135—2831no—
266#135—5661no—
267#135—5661no—
268#135—5661no—
269#135C2×D28311yescharacteristic
270C2×SD16—21no—
271C2×SD16—2831no—
272C2×SD16—2831no—
273C2×SD16—2831no—
274C2×SD16—5661no—
275C2×SD16—5661no—
276C2×SD16—5661no—
277C2×SD16C2×D28311yescharacteristic, complemented
278#131—2831no—
279#131—2831no—
280#131—2831no—
281#131C2×D28311yescharacteristic, complemented
282C4⋊Q8—2831no—
283#127—2831no—
284#108—2831no—
285#108—2831no—
286#104—2831no—
287#104—2831no—
288#104—2831no—
289#104—2831no—
290#101—2831no—
291#101—2831no—
292#100—2831no—
293#100—2831no—
294C4×C8—2831no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—2831no—
301#41—5661no—
302#41—5661no—
303#41—5661no—
304#41—5661no—
305#41—11321no—
306#41C22×D28311yescharacteristic
307#41C22×D28311yescharacteristic
308#41C22×D28311yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—2831no—
312C2×Q8—5661no—
313C2×Q8—5661no—
314C2×Q8C22×D28311yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—2831no—
319C2×D4—5661no—
320C2×D4—5661no—
321C2×D4—11321no—
322C2×D4—11321no—
323C2×D4C22×D28311yescharacteristic
324Q16—21no—
325Q16—2831no—
326Q16—5661no—
327Q16—5661no—
328Q16—5661no—
329Q16C22⋊D28311yescharacteristic, complemented
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—2831no—
335SD16—2831no—
336SD16—5661no—
337SD16—5661no—
338SD16—5661no—
339SD16—5661no—
340SD16—5661no—
341SD16—5661no—
342SD16—5661no—
343SD16—5661no—
344SD16—5661no—
345SD16—5661no—
346SD16—5661no—
347SD16—5661no—
348SD16C22⋊D28311yescharacteristic, complemented
349SD16C22⋊D28311yescharacteristic, complemented
350D8—21no—
351D8—2831no—
352D8—5661no—
353D8—5661no—
354D8—5661no—
355D8C22⋊D28311yescharacteristic, complemented
356M16—21no—
357M16—2831no—
358M16—2831no—
359M16—2831no—
360M16—5661no—
361M16—5661no—
362M16—5661no—
363M16C22×D28311yescharacteristic
364C2×C8—21no—
365C2×C8—2831no—
366C2×C8—5661no—
367C2×C8—5661no—
368C2×C8—5661no—
369C2×C8C22×D28311yescharacteristic
370C4⋊C4—11321no—
371C42—2831no—
372C23—21no—
373C23—41no—
374C23—5661no—
375C23—11321no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—2831no—
380Q8—5661no—
381Q8—5661no—
382Q8—11321no—
383Q8D4×D28311yescharacteristic
384Q8C2×C22⋊D28311yescharacteristic
385Q8C2×C22⋊D28311yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—2831no—
395D4—5661no—
396D4—5661no—
397D4—5661no—
398D4—11321no—
399D4—11321no—
400D4—11321no—
401D4—22642no—
402D4D4×D28311yescharacteristic
403D4C2×C22⋊D28311yescharacteristic
404D4C2×C22⋊D28311yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—5661no—
413C2×C4—5661no—
414C2×C4—5661no—
415C2×C4—11321no—
416C2×C4—11321no—
417C2×C4—11321no—
418C2×C4C23×D28311yescharacteristic
419C8—21no—
420C8—2831no—
421C8—2831no—
422C8—5661no—
423C8—5661no—
424C8—5661no—
425C8C2×C22⋊D28311yescharacteristic
426C8C2×C22⋊D28311yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—5661no—
434C22—11321no—
435C22—45281no—
436C22—22641no—
437C22#2258365511yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—5662no—
443C4—5661no—
444C4—11321no—
445C4C2×D4×D28311yescharacteristic
446C4C22×C22⋊D28311yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—11321no—
453C2—22641no—
454C2D4×C22⋊D28311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#577×C283C2
socleC2×C283D42
hypercenter#577D283
hypocenterC283#3291
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #31827276C2semidirect
2. #31827273C2semidirect
3. #31827272C2semidirect
4. #31826836C2semidirect
5. #31826730C2semidirect
6. #31826728C2semidirect
7. #31826726C2semidirect
8. #31826725C2semidirect
9. #31826648C2semidirect
10. #31826646C2semidirect
11. #31826633C2semidirect
12. #31826631C2semidirect
13. #31826582C2semidirect
14. #31826580C2semidirect
15. #577×C283C2semidirect
17. #22583656C22semidirect
20. #22583641C22semidirect
22. #22583640C22semidirect
23. #22583640C22semidirect
34. C2×#17985381C22semidirect
36. C2×#17985380C22semidirect
38. C2×#17985379C22semidirect
40. #22583617C22semidirect
41. #22583617C22semidirect
42. #22583616C22semidirect
43. #22583608C22semidirect
45. #22583546C22semidirect
46. #22583545C22semidirect
47. #22583537C22semidirect
48. #22583537C22semidirect
49. #22583537C22semidirect
50. #22583536C22semidirect
51. #22583529C22semidirect
52. #22583528C22semidirect
53. #22583527C22semidirect
54. #22583526C22semidirect
55. C8×Dic283C22semidirect
57. H(5,𝔽2)×C283C22semidirect
59. #137×C283C22semidirect
65. C2×SD16×C283C22semidirect
66. #131×C283C22semidirect
84. #17985382D4semidirect
92. #17985380D4semidirect
98. #17985379D4semidirect
102. #17985377D4semidirect
131. Q16×C283D4semidirect
136. SD16×C283D4semidirect
137. SD16×C283D4semidirect
139. D8×C283D4semidirect
227. C283#3291semidirect
232. #577D283semidirect
247. H(5,𝔽2)C2×D283semidirect
255. #137C2×D283semidirect
277. C2×SD16C2×D283semidirect
281. #131C2×D283semidirect
329. Q16C22⋊D283semidirect
348. SD16C22⋊D283semidirect
349. SD16C22⋊D283semidirect
355. D8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318272762
#318272732
#318272722
#318268362
#318267302
#318267282
#318267262
#318267252
#318266482
#318266462
#318266332
#318266312
#318265822
#318265802
#577×C2832
#3291283