Finite Group Databasebeta

← #49133289

Subgroups — #49133289

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
2#31827100C211yesmaximal, characteristic
3#31826829C211yesmaximal, characteristic, complemented
4#31826788C211yesmaximal, characteristic, complemented
5#31826777C211yesmaximal, characteristic, complemented
6#31826766C211yesmaximal, characteristic, complemented
7#31826708C211yesmaximal, characteristic, complemented
8#31826691C211yesmaximal, characteristic, complemented
9#31826614C211yesmaximal, characteristic, complemented
10#31826614C211yesmaximal, characteristic, complemented
11#31826563C211yesmaximal, characteristic, complemented
12#31826535C211yesmaximal, characteristic, complemented
13#31826468C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#460×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283—21no—
17C2×D4×D283C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19C2×#17985379C2211yescharacteristic
20C2×#17985375C2211yescharacteristic, complemented
21C2×C8×D283C2211yescharacteristic, complemented
22#22583604—21no—
23#22583602C2211yescharacteristic, complemented
24#22583600—21no—
25#22583595—21no—
26#22583586C2211yescharacteristic, complemented
27#22583586C2211yescharacteristic, complemented
28#22583581—21no—
29#22583581C2211yescharacteristic
30#22583581C2211yescharacteristic
31#22583578—21no—
32#22583578—21no—
33C4×D1132C2211yescharacteristic
34C4×D1132C2211yescharacteristic
35#22583568C2211yescharacteristic, complemented
36#22583567—21no—
37C4⋊C4×D283C2211yescharacteristic, complemented
38#22583544C2211yescharacteristic, complemented
39#22583543C2211yescharacteristic, complemented
40#22583542C2211yescharacteristic, complemented
41#22583534C2211yescharacteristic, complemented
42#22583532C2211yescharacteristic
43#22583532C2211yescharacteristic
44#22583531C2211yescharacteristic, complemented
45#22583531C2211yescharacteristic, complemented
46#22583531C2211yescharacteristic, complemented
47#22583531C2211yescharacteristic, complemented
48#22583530C2211yescharacteristic
49(C2×D283)⋊C8C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51#22583521C2211yescharacteristic, complemented
52C2×SD16×C283C2211yescharacteristic, complemented
53C2×SD16×C283C2211yescharacteristic, complemented
54#127×C283C2211yescharacteristic
55C4×Q8×C283C2211yescharacteristic, complemented
56C4⋊C8×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic, complemented
58#102×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C23×D283—21no—
61C2×D1132D411yescharacteristic
62C2×D1132C2311yescharacteristic
63C2×C22⋊D283—21no—
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67D4×D283—22no—
68D4×D283—22no—
69D4×D283—41no—
70D4×D283—41no—
71D4×D283—44no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2311yescharacteristic
75C2×C4×D283C2311yescharacteristic
76#17985379—22no—
77#17985375—41no—
78C2×C283⋊C8C2311yescharacteristic
79C2×C283⋊C8C2311yescharacteristic
80C8×D283—41no—
81C4⋊Dic283D411yescharacteristic
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85Dic283⋊C4—21no—
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90C22⋊Dic283—21no—
91C22⋊Dic283—21no—
92(C2×D283)⋊C4—21no—
93(C2×D283)⋊C4—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4D411yescharacteristic
97(C2×D283)⋊C4D411yescharacteristic
98C4×Dic283—21no—
99C2×Q8×C283C2311yescharacteristic
100C2×D4×C283—21no—
101C2×D4×C283—21no—
102C2×D4×C283C2311yescharacteristic
103C2×D4×C283C2311yescharacteristic
104SD16×C283—41no—
105SD16×C283—41no—
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C42×C283—21no—
111C42×C283C2311yescharacteristic
112C22×D283—21no—
113C22×D283—42no—
114C22×D283—42no—
115C22×D283—42no—
116C22×D283—42no—
117C22×D283—81no—
118C22×D283—81no—
119C22×D283C2×D411yescharacteristic
120C22×D283C2×D411yescharacteristic
121D1132—22no—
122D1132—21no—
123D1132#4112yes—
124C22⋊D283—42no—
125C22⋊D283—42no—
126C22⋊D283—42no—
127C22⋊D283—42no—
128C2×Dic283—21no—
129C2×Dic283—21no—
130C2×Dic283—21no—
131C2×Dic283C2×D411yescharacteristic
132C2×Dic283C2×D411yescharacteristic
133C4×D283—21no—
134C4×D283—21no—
135C4×D283—21no—
136C4×D283—21no—
137C4×D283—42no—
138C4×D283—42no—
139C283⋊C8—21no—
140C283⋊C8—21no—
141C23×C283—21no—
142C23×C283—21no—
143Q8×C283—21no—
144Q8×C283—21no—
145D4×C283—21no—
146D4×C283—21no—
147D4×C283—21no—
148D4×C283—21no—
149D4×C283—42no—
150D4×C283—81no—
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283C2×D411yescharacteristic
154C2×C4×C283C2×D411yescharacteristic
155C2×C4×C283C2411yescharacteristic
156C8×C283—21no—
157C8×C283—21no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283—41no—
161C22×C283—41no—
162C22×C283—41no—
163C22×C283—41no—
164C22×C283C22×D411yescharacteristic
165C2×D283—21no—
166C2×D283—21no—
167C2×D283—21no—
168C2×D283—22no—
169C2×D283—21no—
170C2×D283—21no—
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×C283C2×#4111yescharacteristic
181C4×C283H(5,𝔽2)11yescharacteristic
182Dic283—21no—
183Dic283—21no—
184Dic283—41no—
185Dic283—41no—
186Dic283—41no—
187C2×C283—81no—
188C2×C283—81no—
189C2×C283#54611yescharacteristic
190C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C283#57711yescharacteristic
192D283—22no—
193D283—41no—
194D283—42no—
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#460D28311yescharacteristic, complemented
206#450—2831no—
207#450—2831no—
208#440—2831no—
209#435—2831no—
210#418—2831no—
211C2×#102—2831no—
212C22×D4—2831no—
213C22×D4—2831no—
214C22×D4—5661no—
215C2×SD16—2831no—
216C2×SD16C2×D28311yescharacteristic, complemented
217C2×SD16C2×D28311yescharacteristic, complemented
218C2×M16—2831no—
219C22×C8—2831no—
220#127C2×D28311yescharacteristic
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×D4—2831no—
235#117—2831no—
236#117—5661no—
237C2×C4⋊C4—2831no—
238#107—2831no—
239#107—2831no—
240#106—2831no—
241C4⋊C8C2×D28311yescharacteristic, complemented
242#103—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102—2831no—
247#102—2831no—
248#102—2831no—
249#102—2831no—
250#102C2×D28311yescharacteristic, complemented
251#102C2×D28311yescharacteristic, complemented
252C22⋊C8—2831no—
253C22⋊C8—2831no—
254#97—2831no—
255C24—5661no—
256C24—5661no—
257C2×Q8C22×D28311yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—2831no—
261C2×D4—2831no—
262C2×D4—5661no—
263C2×D4—5661no—
264C2×D4—5662no—
265C2×D4—5662no—
266C2×D4—5661no—
267C2×D4—5661no—
268C2×D4—11321no—
269C2×D4—11321no—
270C2×D4—11324no—
271C2×D4C22×D28311yescharacteristic
272C2×D4C22×D28311yescharacteristic
273C22×C4—2831no—
274C22×C4—2831no—
275C22×C4—5661no—
276C22×C4—5661no—
277SD16—41no—
278SD16—41no—
279SD16—5662no—
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—2831no—
291C4⋊C4—5661no—
292C4⋊C4—5661no—
293C4⋊C4—5661no—
294C4⋊C4—5661no—
295C4⋊C4—5661no—
296C4⋊C4C22×D28311yescharacteristic
297C22⋊C4—2831no—
298C22⋊C4—2831no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4—5661no—
304C22⋊C4—5661no—
305C42—21no—
306C42—5661no—
307C42C22×D28311yescharacteristic
308C23—21no—
309C23—21no—
310C23—2831no—
311C23—2831no—
312C23—5661no—
313C23—11322no—
314C23—11322no—
315C23—11322no—
316C23—11322no—
317C23—22641no—
318C23—22641no—
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—2832no—
328D4—5662no—
329D4—5661no—
330D4—11322no—
331D4—11322no—
332D4—11322no—
333D4—11322no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—2831no—
337C2×C4—2831no—
338C2×C4—5661no—
339C2×C4—5661no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—5661no—
344C2×C4—5661no—
345C2×C4—11322no—
346C2×C4—11322no—
347C2×C4D4×D28311yescharacteristic
348C2×C4D4×D28311yescharacteristic
349C2×C4C23×D28311yescharacteristic
350C8—21no—
351C8—21no—
352C8—5661no—
353C8—5661no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—2832no—
361C22—5661no—
362C22—5661no—
363C22—5661no—
364C22—5661no—
365C22—5661no—
366C22—5662no—
367C22—11321no—
368C22—11321no—
369C22—22644no—
370C22—22644no—
371C22C2×D4×D28311yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—5661no—
377C4—5661no—
378C4—11321no—
379C4—11321no—
380C4—11321no—
381C4#41×D28311yescharacteristic
382C4#2258365511yescharacteristic
383C2—81no—
384C2—81no—
385C2—5662no—
386C2—11321no—
387C2—11322no—
388C2#3182711211yescharacteristic
389C2AGL(1,ℤ/8)×D28311yescharacteristic
390C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#460×C283C2
socleC22×C283C22×D4
prime radical#31827100C2
hypercenter#460D283
hypocenterC283#3310
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #31827156C2semidirect
3. #31826829C2semidirect
4. #31826788C2semidirect
5. #31826777C2semidirect
6. #31826766C2semidirect
7. #31826708C2semidirect
8. #31826691C2semidirect
9. #31826614C2semidirect
10. #31826614C2semidirect
11. #31826563C2semidirect
12. #31826535C2semidirect
13. #31826468C2semidirect
14. #102×D283C2semidirect
15. #460×C283C2semidirect
20. C2×#17985375C22semidirect
21. C2×C8×D283C22semidirect
23. #22583602C22semidirect
26. #22583586C22semidirect
27. #22583586C22semidirect
35. #22583568C22semidirect
37. C4⋊C4×D283C22semidirect
38. #22583544C22semidirect
39. #22583543C22semidirect
40. #22583542C22semidirect
41. #22583534C22semidirect
44. #22583531C22semidirect
45. #22583531C22semidirect
46. #22583531C22semidirect
47. #22583531C22semidirect
49. (C2×D283)⋊C8C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. #22583521C22semidirect
52. C2×SD16×C283C22semidirect
53. C2×SD16×C283C22semidirect
55. C4×Q8×C283C22semidirect
56. C4⋊C8×C283C22semidirect
57. #102×C283C22semidirect
58. #102×C283C22semidirect
195. C283#3310semidirect
205. #460D283semidirect
216. C2×SD16C2×D283semidirect
217. C2×SD16C2×D283semidirect
232. C4×Q8C2×D283semidirect
241. C4⋊C8C2×D283semidirect
250. #102C2×D283semidirect
251. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271562
#318271002
#318268292
#318267882
#318267772
#318267662
#318267082
#318266912
#318266142
#318265632
#318265352
#318264682
#102×D2832
#460×C2832
#3310283