Finite Group Databasebeta

← #49133287

Subgroups — #49133287

Order 36224.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827156C211yesmaximal, characteristic, complemented
2D4×D1132C211yesmaximal, characteristic
3#31826830C211yesmaximal, characteristic, complemented
4#31826792C211yesmaximal, characteristic, complemented
5#31826780C211yesmaximal, characteristic, complemented
6#31826765C211yesmaximal, characteristic, complemented
7#31826714C211yesmaximal, characteristic, complemented
8#31826697C211yesmaximal, characteristic, complemented
9#31826665C211yesmaximal, characteristic, complemented
10#31826614C211yesmaximal, characteristic, complemented
11#31826614C211yesmaximal, characteristic, complemented
12#31826538C211yesmaximal, characteristic, complemented
13#31826468C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C22×D1132—21no—
17C2×D4×D283C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19C2×#17985379C2211yescharacteristic, complemented
20C2×#17985379C2211yescharacteristic, complemented
21C2×#17985375C2211yescharacteristic, complemented
22C2×C8×D283C2211yescharacteristic, complemented
23#22583607C2211yescharacteristic
24#22583604—21no—
25#22583602C2211yescharacteristic, complemented
26#22583600—21no—
27#22583595—21no—
28#22583586C2211yescharacteristic, complemented
29#22583586C2211yescharacteristic, complemented
30#22583585C2211yescharacteristic
31#22583585C2211yescharacteristic
32#22583584—21no—
33#22583580—21no—
34#22583580—21no—
35C4×D1132C2211yescharacteristic
36#22583568C2211yescharacteristic, complemented
37#22583567—21no—
38C4⋊C4×D283C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41C4⋊(C283⋊C8)C2211yescharacteristic, complemented
42#22583532C2211yescharacteristic, complemented
43#22583532C2211yescharacteristic, complemented
44#22583532C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic, complemented
46#22583531C2211yescharacteristic
47#22583531C2211yescharacteristic
48#22583530C2211yescharacteristic, complemented
49#22583530C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51(C2×D283)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C283C2211yescharacteristic
53C4×Q8×C283C2211yescharacteristic, complemented
54C4×D4×C283C2211yescharacteristic
55#107×C283C2211yescharacteristic, complemented
56#103×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic
58#97×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C23×D283—21no—
61C2×D1132—21no—
62C2×D1132—21no—
63C2×D1132—21no—
64C2×D1132—21no—
65C2×D1132—44no—
66C2×D1132D411yescharacteristic
67C2×D1132C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71D4×D283—22no—
72D4×D283—22no—
73D4×D283—41no—
74D4×D283—41no—
75C2×C4×D283—21no—
76C2×C4×D283C2311yescharacteristic
77C2×C4×D283C2311yescharacteristic
78#17985379—41no—
79#17985379—41no—
80#17985375—41no—
81C2×C283⋊C8C2311yescharacteristic
82C2×C283⋊C8C2311yescharacteristic
83C8×D283—41no—
84C4⋊Dic283D411yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86C4⋊Dic283C2311yescharacteristic
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91Dic283⋊C4—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4D411yescharacteristic
98(C2×D283)⋊C4D411yescharacteristic
99C4×Dic283—21no—
100C2×Q8×C283C2311yescharacteristic
101C2×D4×C283C2311yescharacteristic
102C22×C4×C283—21no—
103SD16×C283—22no—
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C4⋊C4×C283—21no—
107C4⋊C4×C283C2311yescharacteristic
108C4⋊C4×C283C2311yescharacteristic
109C22⋊C4×C283—21no—
110C42×C283—21no—
111C42×C283C2311yescharacteristic
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—42no—
115C22×D283—42no—
116C22×D283—42no—
117C22×D283—42no—
118C22×D283—81no—
119C22×D283—81no—
120C22×D283C2×D411yescharacteristic
121C22×D283C2×D411yescharacteristic
122D1132—22no—
123D1132—21no—
124D1132—21no—
125D1132—21no—
126D1132—21no—
127D1132—42no—
128D1132—42no—
129D1132—42no—
130D1132—81no—
131C22⋊D283—42no—
132C22⋊D283—42no—
133C2×Dic283—21no—
134C2×Dic283—21no—
135C2×Dic283C2×D411yescharacteristic
136C2×Dic283C2×D411yescharacteristic
137C4×D283—21no—
138C4×D283—21no—
139C4×D283—21no—
140C4×D283—21no—
141C4×D283—42no—
142C283⋊C8—21no—
143C283⋊C8—21no—
144C23×C283—21no—
145Q8×C283—21no—
146Q8×C283—21no—
147D4×C283—21no—
148D4×C283#4112yes—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—42no—
153C2×C4×C283C2×D411yescharacteristic
154C2×C4×C283C2×D411yescharacteristic
155C2×C4×C283C2411yescharacteristic
156C8×C283—21no—
157C8×C283—21no—
158C22×C283—22no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283C22×D411yescharacteristic
162C2×D283—21no—
163C2×D283—21no—
164C2×D283—21no—
165C2×D283—21no—
166C2×D283—21no—
167C2×D283—41no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—41no—
171C2×D283—41no—
172C2×D283—41no—
173C2×D283—84no—
174C2×D283—84no—
175C2×D283AGL(1,ℤ/8)12yes—
176C4×C283—21no—
177C4×C283—21no—
178C4×C283—41no—
179C4×C283—41no—
180C4×C283—41no—
181C4×C283C2×#4111yescharacteristic
182C4×C283H(5,𝔽2)11yescharacteristic
183Dic283—21no—
184Dic283—21no—
185Dic283—41no—
186Dic283—41no—
187C2×C283—42no—
188C2×C283#54611yescharacteristic
189C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C283#57711yescharacteristic
191D283—22no—
192D283—41no—
193D283—81no—
194D283—81no—
195C283#331011yescharacteristic, complemented, Sylow
196#3310—2831nomaximal, Sylow
197#552—2831no—
198D42—2831no—
199#490—2831no—
200#482—2831no—
201#480—2831no—
202#478—2831no—
203#468—2831no—
204#465—2831no—
205#460—2831no—
206#450—2831no—
207#450—2831no—
208#440D28311yescharacteristic, complemented
209#435—2831no—
210#418—2831no—
211C2×#102—2831no—
212C22×D4—2831no—
213C22×D4—2831no—
214C22×D4—5661no—
215C2×SD16—2831no—
216C2×SD16—2831no—
217C2×SD16C2×D28311yescharacteristic
218C2×M16—2831no—
219C22×C8—2831no—
220#127—2831no—
221#126—5661no—
222#125—2831no—
223#125—5661no—
224#123—5661no—
225C22⋊Q8—2831no—
226C22⋊Q8—2831no—
227#121—2831no—
228#121—2831no—
229#121—5661no—
230#120—5661no—
231#120—5661no—
232C4×Q8C2×D28311yescharacteristic, complemented
233C4×D4—2831no—
234C4×D4C2×D28311yescharacteristic
235#117—2831no—
236#117—5661no—
237C2×C4⋊C4—2831no—
238#107—2831no—
239#107C2×D28311yescharacteristic, complemented
240#106—2831no—
241C4⋊C8—2831no—
242#103C2×D28311yescharacteristic, complemented
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102—2831no—
247#102—2831no—
248#102—2831no—
249#102—2831no—
250#102—2831no—
251#102C2×D28311yescharacteristic
252C22⋊C8—2831no—
253C22⋊C8—2831no—
254#97C2×D28311yescharacteristic, complemented
255C24—5661no—
256C24—5661no—
257C2×Q8C22×D28311yescharacteristic
258C2×D4—2831no—
259C2×D4—2831no—
260C2×D4—2831no—
261C2×D4—5661no—
262C2×D4—5661no—
263C2×D4—5661no—
264C2×D4—5661no—
265C2×D4—5662no—
266C2×D4—5662no—
267C2×D4—5661no—
268C2×D4—5661no—
269C2×D4—11324no—
270C2×D4—11321no—
271C2×D4—11321no—
272C2×D4C22×D28311yescharacteristic
273C22×C4—21no—
274C22×C4—2831no—
275C22×C4—2831no—
276C22×C4—5661no—
277SD16—22no—
278SD16—11321no—
279SD16—11321no—
280M16—11321no—
281C2×C8—2831no—
282C2×C8—2831no—
283C2×C8—11321no—
284C2×C8C22×D28311yescharacteristic
285C2×C8C22×D28311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—2831no—
288C4⋊C4—2831no—
289C4⋊C4—2831no—
290C4⋊C4—5661no—
291C4⋊C4—5661no—
292C4⋊C4—5661no—
293C4⋊C4—5661no—
294C4⋊C4—5661no—
295C4⋊C4C22×D28311yescharacteristic
296C4⋊C4C22×D28311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—2831no—
299C22⋊C4—2831no—
300C22⋊C4—5661no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4—5661no—
304C22⋊C4—5661no—
305C42—21no—
306C42—5661no—
307C42C22×D28311yescharacteristic
308C23—21no—
309C23—2831no—
310C23—2831no—
311C23—5661no—
312C23—5661no—
313C23—11322no—
314C23—11322no—
315C23—11322no—
316C23—11322no—
317C23—22641no—
318C23—22641no—
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—5662no—
323D4—5661no—
324D4—5661no—
325D4—5661no—
326D4—5661no—
327D4—11322no—
328D4—11322no—
329D4—11322no—
330D4—11322no—
331D4—11322no—
332D4—22641no—
333D4#1798539212yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—2831no—
339C2×C4—2831no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—5661no—
344C2×C4—5661no—
345C2×C4—5661no—
346C2×C4—11322no—
347C2×C4D4×D28311yescharacteristic
348C2×C4D4×D28311yescharacteristic
349C2×C4C23×D28311yescharacteristic
350C8—21no—
351C8—21no—
352C8—5661no—
353C8—5661no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—2832no—
358C22—5661no—
359C22—5661no—
360C22—5661no—
361C22—5661no—
362C22—5661no—
363C22—11321no—
364C22—11321no—
365C22—11321no—
366C22—11321no—
367C22—11321no—
368C22—11321no—
369C22—22644no—
370C22—22644no—
371C22C2×D4×D28311yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—5661no—
378C4—5661no—
379C4—11321no—
380C4—11321no—
381C4C2×#1798539211yescharacteristic
382C4#2258365611yescharacteristic
383C2—42no—
384C2—5662no—
385C2—11321no—
386C2—22641no—
387C2—22641no—
388C2#3182711111yescharacteristic
389C2AGL(1,ℤ/8)×D28311yescharacteristic
390C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radicalD4×D1132C2
hypercenter#440D283
hypocenterC283#3310
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #31827156C2semidirect
3. #31826830C2semidirect
4. #31826792C2semidirect
5. #31826780C2semidirect
6. #31826765C2semidirect
7. #31826714C2semidirect
8. #31826697C2semidirect
9. #31826665C2semidirect
10. #31826614C2semidirect
11. #31826614C2semidirect
12. #31826538C2semidirect
13. #31826468C2semidirect
14. #102×D283C2semidirect
15. #440×C283C2semidirect
19. C2×#17985379C22semidirect
20. C2×#17985379C22semidirect
21. C2×#17985375C22semidirect
22. C2×C8×D283C22semidirect
25. #22583602C22semidirect
28. #22583586C22semidirect
29. #22583586C22semidirect
36. #22583568C22semidirect
38. C4⋊C4×D283C22semidirect
39. #22583543C22semidirect
40. #22583541C22semidirect
41. C4⋊(C283⋊C8)C22semidirect
42. #22583532C22semidirect
43. #22583532C22semidirect
44. #22583532C22semidirect
45. #22583532C22semidirect
48. #22583530C22semidirect
49. #22583530C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. (C2×D283)⋊C8C22semidirect
53. C4×Q8×C283C22semidirect
55. #107×C283C22semidirect
56. #103×C283C22semidirect
58. #97×C283C22semidirect
195. C283#3310semidirect
208. #440D283semidirect
232. C4×Q8C2×D283semidirect
239. #107C2×D283semidirect
242. #103C2×D283semidirect
254. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271562
D4×D11322
#318268302
#318267922
#318267802
#318267652
#318267142
#318266972
#318266652
#318266142
#318265382
#318264682
#102×D2832
#440×C2832
#3310283