Finite Group Databasebeta

← #49133284

Subgroups — #49133284

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#31827155C211yesmaximal, characteristic, complemented
2D4×D1132C211yesmaximal, characteristic
3#31826830C211yesmaximal, characteristic, complemented
4#31826790C211yesmaximal, characteristic, complemented
5#31826779C211yesmaximal, characteristic, complemented
6#31826766C211yesmaximal, characteristic, complemented
7#31826711C211yesmaximal, characteristic, complemented
8#31826694C211yesmaximal, characteristic, complemented
9#31826666C211yesmaximal, characteristic, complemented
10#31826618C211yesmaximal, characteristic, complemented
11#31826618C211yesmaximal, characteristic, complemented
12#31826567C211yesmaximal, characteristic, complemented
13#31826471C211yesmaximal, characteristic, complemented
14C2×#22583532C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C22×D1132C2211yescharacteristic
18C2×D4×D283—21no—
19C2×#17985381C2211yescharacteristic
20C2×#17985381C2211yescharacteristic, complemented
21C2×#17985381C2211yescharacteristic, complemented
22#22583607C2211yescharacteristic
23#22583603—21no—
24#22583602C2211yescharacteristic, complemented
25#22583600—21no—
26#22583591—21no—
27#22583589C2211yescharacteristic, complemented
28#22583589C2211yescharacteristic, complemented
29#22583585—21no—
30#22583584C2211yescharacteristic
31#22583584C2211yescharacteristic
32#22583580—21no—
33#22583580—21no—
34C4×Dic566C2211yescharacteristic, complemented
35C4×D1132C2211yescharacteristic
36#22583569C2211yescharacteristic, complemented
37#22583566—21no—
38C2×C4⋊Dic283C2211yescharacteristic, complemented
39#22583544C2211yescharacteristic, complemented
40#22583544C2211yescharacteristic, complemented
41#22583542C2211yescharacteristic, complemented
42#22583535C2211yescharacteristic, complemented
43#22583532C2211yescharacteristic
44#22583532C2211yescharacteristic
45#22583532C2211yescharacteristic
46#22583532C2211yescharacteristic, complemented
47#22583532C2211yescharacteristic, complemented
48#22583532C2211yescharacteristic, complemented
49#22583532C2211yescharacteristic, complemented
50#22583532C2211yescharacteristic, complemented
51#22583532C2211yescharacteristic, complemented
52C2×M16×C283C2211yescharacteristic, complemented
53C22×C8×C283C2211yescharacteristic, complemented
54C4×D4×C283C2211yescharacteristic
55C4⋊C8×C283C2211yescharacteristic, complemented
56C22⋊C8×C283C2211yescharacteristic, complemented
57C22⋊C8×C283C2211yescharacteristic, complemented
58#97×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C23×D283—21no—
61C2×Dic566C2311yescharacteristic
62C2×D1132—22no—
63C2×D1132—22no—
64C2×D1132—21no—
65C2×D1132—21no—
66C2×D1132—21no—
67C2×D1132—21no—
68C2×D1132—41no—
69C2×D1132—41no—
70C2×D1132C2311yescharacteristic
71C2×D1132C2311yescharacteristic
72C2×D1132C2311yescharacteristic
73C2×C22⋊D283—21no—
74C2×C22⋊D283—21no—
75D4×D283—44no—
76C22×Dic283—21no—
77C2×C4×D283—21no—
78#17985381—22no—
79#17985381—41no—
80#17985381—41no—
81C4⋊Dic283—21no—
82C4⋊Dic283C2311yescharacteristic
83C4⋊Dic283C2311yescharacteristic
84C4⋊Dic283C2311yescharacteristic
85C4⋊Dic283C2311yescharacteristic
86Dic283⋊C4—21no—
87Dic283⋊C4—21no—
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91C22⋊Dic283—21no—
92C22⋊Dic283—21no—
93C22⋊Dic283—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97C4×Dic283—21no—
98C4×Dic283—21no—
99C2×D4×C283D411yescharacteristic
100C22×C4×C283C2311yescharacteristic
101C22×C4×C283C2311yescharacteristic
102M16×C283—41no—
103C2×C8×C283—41no—
104C2×C8×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283D411yescharacteristic
109C22⋊C4×C283D411yescharacteristic
110C22⋊C4×C283D411yescharacteristic
111C42×C283C2311yescharacteristic
112C22×D283—21no—
113C22×D283—21no—
114C22×D283—21no—
115C22×D283—42no—
116C22×D283—42no—
117C22×D283—42no—
118C22×D283—42no—
119C22×D283—81no—
120C22×D283—81no—
121Dic566—21no—
122Dic566—21no—
123D1132—21no—
124D1132—21no—
125D1132—21no—
126D1132—21no—
127D1132—21no—
128D1132—42no—
129D1132—42no—
130D1132—42no—
131D1132—81no—
132D1132#4112yes—
133C22⋊D283—42no—
134C22⋊D283—42no—
135C2×Dic283—21no—
136C2×Dic283—21no—
137C2×Dic283—21no—
138C2×Dic283—21no—
139C2×Dic283—21no—
140C2×Dic283—42no—
141C4×D283—42no—
142C23×C283C2×D411yescharacteristic
143C23×C283C2×D411yescharacteristic
144D4×C283—22no—
145C2×C4×C283—21no—
146C2×C4×C283—21no—
147C2×C4×C283—21no—
148C2×C4×C283—21no—
149C2×C4×C283C2×D411yescharacteristic
150C2×C4×C283C2×D411yescharacteristic
151C2×C4×C283C2×D411yescharacteristic
152C2×C4×C283C2×D411yescharacteristic
153C2×C4×C283C2411yescharacteristic
154C8×C283—21no—
155C8×C283—21no—
156C8×C283—21no—
157C8×C283—21no—
158C22×C283—21no—
159C22×C283—21no—
160C22×C283—21no—
161C22×C283—21no—
162C22×C283—21no—
163C22×C283AGL(1,ℤ/8)12yes—
164C22×C283C22×D411yescharacteristic
165C2×D283—22no—
166C2×D283—41no—
167C2×D283—41no—
168C2×D283—41no—
169C2×D283—41no—
170C2×D283—41no—
171C2×D283—41no—
172C2×D283—41no—
173C2×D283—41no—
174C2×D283—84no—
175C2×D283—84no—
176C4×C283—21no—
177C4×C283—21no—
178C4×C283—21no—
179C4×C283—21no—
180C4×C283C2×#4111yescharacteristic
181C4×C283H(5,𝔽2)11yescharacteristic
182Dic283—41no—
183Dic283—41no—
184Dic283—41no—
185Dic283—41no—
186Dic283—41no—
187C2×C283—22no—
188C2×C283—41no—
189C2×C283#54611yescharacteristic
190C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C283#57711yescharacteristic
192D283—42no—
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#440—2831no—
209#435D28311yescharacteristic, complemented
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×M16C2×D28311yescharacteristic, complemented
219C22×C8C2×D28311yescharacteristic, complemented
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×Q8—2831no—
233C4×D4—2831no—
234C4×D4C2×D28311yescharacteristic
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#102—2831no—
251#102—2831no—
252C22⋊C8C2×D28311yescharacteristic, complemented
253C22⋊C8C2×D28311yescharacteristic, complemented
254#97C2×D28311yescharacteristic, complemented
255C24—5661no—
256C24—5661no—
257C2×Q8—2831no—
258C2×D4—2831no—
259C2×D4—2831no—
260C2×D4—2831no—
261C2×D4—5662no—
262C2×D4—5662no—
263C2×D4—5661no—
264C2×D4—5661no—
265C2×D4—5661no—
266C2×D4—5661no—
267C2×D4—5661no—
268C2×D4—5661no—
269C2×D4—11321no—
270C2×D4—11321no—
271C2×D4—11324no—
272C2×D4D113211yescharacteristic
273C22×C4—5661no—
274C22×C4—5661no—
275C22×C4C22×D28311yescharacteristic
276C22×C4C22×D28311yescharacteristic
277SD16—5662no—
278SD16—11321no—
279SD16—11321no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D28311yescharacteristic
283C2×C8C22×D28311yescharacteristic
284C2×C8C22×D28311yescharacteristic
285C2×C8C22×D28311yescharacteristic
286C4⋊C4—2831no—
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⋊C4—5661no—
296C4⋊C4D113211yescharacteristic
297C22⋊C4—5661no—
298C22⋊C4—5661no—
299C22⋊C4—5661no—
300C22⋊C4—5661no—
301C22⋊C4—5661no—
302C22⋊C4—5661no—
303C22⋊C4D113211yescharacteristic
304C22⋊C4D113211yescharacteristic
305C42—5661no—
306C42—5661no—
307C42C22×D28311yescharacteristic
308C23—5661no—
309C23—5661no—
310C23—5661no—
311C23—11322no—
312C23—11322no—
313C23—11322no—
314C23—11322no—
315C23—22641no—
316C23—22641no—
317C23C2×D113211yescharacteristic
318C23C2×D113211yescharacteristic
319Q8—5661no—
320Q8—5661no—
321D4—22no—
322D4—2832no—
323D4—5661no—
324D4—5661no—
325D4—5661no—
326D4—5661no—
327D4—5661no—
328D4—11322no—
329D4—11322no—
330D4—11322no—
331D4—11322no—
332D4—11322no—
333D4—22641no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—5661no—
339C2×C4—5661no—
340C2×C4—5661no—
341C2×C4—5661no—
342C2×C4—5661no—
343C2×C4—11322no—
344C2×C4—11322no—
345C2×C4C2×D113211yescharacteristic
346C2×C4C2×D113211yescharacteristic
347C2×C4C2×D113211yescharacteristic
348C2×C4C2×D113211yescharacteristic
349C2×C4C23×D28311yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—5662no—
360C22—11321no—
361C22—11321no—
362C22—11321no—
363C22—11321no—
364C22—11321no—
365C22—11321no—
366C22—11321no—
367C22—11321no—
368C22—22644no—
369C22—22644no—
370C22#2258363812yes—
371C22C22×D113211yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—11321no—
377C4—11321no—
378C4—11321no—
379C4—11321no—
380C4—11321no—
381C4#41×D28311yescharacteristic
382C4#2258365511yescharacteristic
383C2—22no—
384C2—41no—
385C2—11322no—
386C2—22641no—
387C2—22641no—
388C2#3182711011yescharacteristic
389C2C2×#2258363811yescharacteristic
390C2#3182727711yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#435×C283C2
socleC22×C283C22×D4
prime radicalD4×D1132C2
hypercenter#435D283
hypocenterC283#3310
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #31827155C2semidirect
3. #31826830C2semidirect
4. #31826790C2semidirect
5. #31826779C2semidirect
6. #31826766C2semidirect
7. #31826711C2semidirect
8. #31826694C2semidirect
9. #31826666C2semidirect
10. #31826618C2semidirect
11. #31826618C2semidirect
12. #31826567C2semidirect
13. #31826471C2semidirect
14. C2×#22583532C2semidirect
15. #435×C283C2semidirect
20. C2×#17985381C22semidirect
21. C2×#17985381C22semidirect
24. #22583602C22semidirect
27. #22583589C22semidirect
28. #22583589C22semidirect
34. C4×Dic566C22semidirect
36. #22583569C22semidirect
38. C2×C4⋊Dic283C22semidirect
39. #22583544C22semidirect
40. #22583544C22semidirect
41. #22583542C22semidirect
42. #22583535C22semidirect
46. #22583532C22semidirect
47. #22583532C22semidirect
48. #22583532C22semidirect
49. #22583532C22semidirect
50. #22583532C22semidirect
51. #22583532C22semidirect
52. C2×M16×C283C22semidirect
53. C22×C8×C283C22semidirect
55. C4⋊C8×C283C22semidirect
56. C22⋊C8×C283C22semidirect
57. C22⋊C8×C283C22semidirect
58. #97×C283C22semidirect
195. C283#3310semidirect
209. #435D283semidirect
218. C2×M16C2×D283semidirect
219. C22×C8C2×D283semidirect
241. C4⋊C8C2×D283semidirect
252. C22⋊C8C2×D283semidirect
253. C22⋊C8C2×D283semidirect
254. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271552
D4×D11322
#318268302
#318267902
#318267792
#318267662
#318267112
#318266942
#318266662
#318266182
#318265672
#318264712
C2×#225835322
#435×C2832
#3310283