Finite Group Databasebeta

← #49133281

Subgroups — #49133281

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#31827153C211yesmaximal, characteristic, complemented
2#31827100C211yesmaximal, characteristic
3#31826787C211yesmaximal, characteristic, complemented
4#31826777C211yesmaximal, characteristic, complemented
5#31826762C211yesmaximal, characteristic, complemented
6#31826710C211yesmaximal, characteristic, complemented
7#31826693C211yesmaximal, characteristic, complemented
8#31826662C211yesmaximal, characteristic, complemented
9#31826617C211yesmaximal, characteristic, complemented
10#31826617C211yesmaximal, characteristic, complemented
11#31826567C211yesmaximal, characteristic, complemented
12#31826538C211yesmaximal, characteristic, complemented
13#31826468C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#490×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283—21no—
17C2×D4×D283C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×#17985380C2211yescharacteristic, complemented
21C2×#17985380C2211yescharacteristic, complemented
22C2×#17985375C2211yescharacteristic, complemented
23C2×C8×D283C2211yescharacteristic, complemented
24#22583605—21no—
25#22583601—21no—
26#22583595—21no—
27#22583590C2211yescharacteristic, complemented
28#22583590C2211yescharacteristic, complemented
29#22583581—21no—
30#22583581C2211yescharacteristic
31#22583581C2211yescharacteristic
32#22583578—21no—
33#22583578—21no—
34C4×Dic566C2211yescharacteristic, complemented
35C4×D1132C2211yescharacteristic
36C4×D1132C2211yescharacteristic
37#22583568—21no—
38#22583568C2211yescharacteristic, complemented
39C4⋊C4×D283C2211yescharacteristic, complemented
40#22583544C2211yescharacteristic, complemented
41#22583543C2211yescharacteristic, complemented
42#22583541C2211yescharacteristic, complemented
43C4⋊(C283⋊C8)C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583532C2211yescharacteristic
46#22583531C2211yescharacteristic, complemented
47#22583531C2211yescharacteristic, complemented
48#22583530C2211yescharacteristic
49#22583530C2211yescharacteristic
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51(C2×D283)⋊C8C2211yescharacteristic, complemented
52#127×C283C2211yescharacteristic
53#125×C283C2211yescharacteristic, complemented
54#102×C283C2211yescharacteristic, complemented
55#102×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic, complemented
58#97×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C23×D283—21no—
61C2×Dic566C2311yescharacteristic
62C2×D1132D411yescharacteristic
63C2×D1132C2311yescharacteristic
64C2×C22⋊D283—21no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283—21no—
68D4×D283—22no—
69D4×D283—22no—
70D4×D283—41no—
71D4×D283—41no—
72D4×D283—44no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283C2311yescharacteristic
76C2×C4×D283C2311yescharacteristic
77#17985381—22no—
78#17985380—41no—
79#17985380—41no—
80#17985375—41no—
81C2×C283⋊C8C2311yescharacteristic
82C2×C283⋊C8C2311yescharacteristic
83C8×D283—41no—
84C4⋊Dic283—21no—
85C4⋊Dic283—21no—
86C4⋊Dic283D411yescharacteristic
87C4⋊Dic283C2311yescharacteristic
88C4⋊Dic283C2311yescharacteristic
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91C22⋊Dic283—21no—
92C22⋊Dic283—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—
100C4×Dic283—21no—
101C2×D4×C283—21no—
102C2×D4×C283—21no—
103C2×D4×C283C2311yescharacteristic
104C2×D4×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283—21no—
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
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
121Dic566—21no—
122Dic566—21no—
123D1132—22no—
124D1132—21no—
125D1132#4112yes—
126C22⋊D283—42no—
127C22⋊D283—42no—
128C22⋊D283—42no—
129C22⋊D283—42no—
130C2×Dic283—21no—
131C2×Dic283—21no—
132C2×Dic283—21no—
133C2×Dic283C2×D411yescharacteristic
134C2×Dic283C2×D411yescharacteristic
135C4×D283—21no—
136C4×D283—21no—
137C4×D283—21no—
138C4×D283—21no—
139C4×D283—42no—
140C4×D283—42no—
141C283⋊C8—21no—
142C283⋊C8—21no—
143C23×C283—21no—
144C23×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#490D28311yescharacteristic, complemented
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#440—2831no—
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×SD16—2831no—
218C2×M16—2831no—
219C22×C8—2831no—
220#127C2×D28311yescharacteristic
221#126—5661no—
222#125—5661no—
223#125C2×D28311yescharacteristic, complemented
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×Q8—2831no—
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⋊C8—2831no—
242#103—2831no—
243#102—2831no—
244#102—2831no—
245#102—2831no—
246#102—2831no—
247#102—2831no—
248#102C2×D28311yescharacteristic, complemented
249#102C2×D28311yescharacteristic, complemented
250#102C2×D28311yescharacteristic, complemented
251#102C2×D28311yescharacteristic, complemented
252C22⋊C8—2831no—
253C22⋊C8—2831no—
254#97C2×D28311yescharacteristic, complemented
255C24—5661no—
256C24—5661no—
257C2×Q8—2831no—
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—5662no—
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—21no—
288C4⋊C4—2831no—
289C4⋊C4—2831no—
290C4⋊C4—2831no—
291C4⋊C4—5661no—
292C4⋊C4—5661no—
293C4⋊C4—5661no—
294C4⋊C4—5661no—
295C4⋊C4C22×D28311yescharacteristic
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—5661no—
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—5661no—
320Q8—5661no—
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#2258365611yescharacteristic
383C2—81no—
384C2—81no—
385C2—5662no—
386C2—11321no—
387C2—11322no—
388C2#3182710811yescharacteristic
389C2AGL(1,ℤ/8)×D28311yescharacteristic
390C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#490×C283C2
socleC22×C283C22×D4
prime radical#31827100C2
hypercenter#490D283
hypocenterC283#3310
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #31827153C2semidirect
3. #31826787C2semidirect
4. #31826777C2semidirect
5. #31826762C2semidirect
6. #31826710C2semidirect
7. #31826693C2semidirect
8. #31826662C2semidirect
9. #31826617C2semidirect
10. #31826617C2semidirect
11. #31826567C2semidirect
12. #31826538C2semidirect
13. #31826468C2semidirect
14. #102×D283C2semidirect
15. #490×C283C2semidirect
20. C2×#17985380C22semidirect
21. C2×#17985380C22semidirect
22. C2×#17985375C22semidirect
23. C2×C8×D283C22semidirect
27. #22583590C22semidirect
28. #22583590C22semidirect
34. C4×Dic566C22semidirect
38. #22583568C22semidirect
39. C4⋊C4×D283C22semidirect
40. #22583544C22semidirect
41. #22583543C22semidirect
42. #22583541C22semidirect
43. C4⋊(C283⋊C8)C22semidirect
44. #22583535C22semidirect
46. #22583531C22semidirect
47. #22583531C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. (C2×D283)⋊C8C22semidirect
53. #125×C283C22semidirect
54. #102×C283C22semidirect
55. #102×C283C22semidirect
56. #102×C283C22semidirect
57. #102×C283C22semidirect
58. #97×C283C22semidirect
195. C283#3310semidirect
199. #490D283semidirect
223. #125C2×D283semidirect
248. #102C2×D283semidirect
249. #102C2×D283semidirect
250. #102C2×D283semidirect
251. #102C2×D283semidirect
254. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271532
#318271002
#318267872
#318267772
#318267622
#318267102
#318266932
#318266622
#318266172
#318265672
#318265382
#318264682
#102×D2832
#490×C2832
#3310283