Finite Group Databasebeta

← #49133083

Subgroups — #49133083

Order 36224.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827170C211yesmaximal, characteristic, complemented
2#31827099C211yesmaximal, characteristic
3#31826810C211yesmaximal, characteristic, complemented
4#31826785C211yesmaximal, characteristic, complemented
5#31826754C211yesmaximal, characteristic, complemented
6#31826695C211yesmaximal, characteristic, complemented
7#31826692C211yesmaximal, characteristic, complemented
8#31826664C211yesmaximal, characteristic, complemented
9#31826618C211yesmaximal, characteristic, complemented
10#31826617C211yesmaximal, characteristic, complemented
11#31826552C211yesmaximal, characteristic, complemented
12(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
13C2×#22583530C211yesmaximal, characteristic, complemented
14#102×D283C211yesmaximal, characteristic, complemented
15#481×C283C211yesmaximal, characteristic, complemented
16C22×D1132C2211yescharacteristic
17C2×D4×D283—21no—
18C2×D4×D283C2211yescharacteristic
19C2×#17985381C2211yescharacteristic
20C2×#17985381C2211yescharacteristic, complemented
21C2×#17985380C2211yescharacteristic, complemented
22C22×C283⋊C8C2211yescharacteristic, complemented
23C2×C8×D283C2211yescharacteristic, complemented
24#22583609C2211yescharacteristic, complemented
25#22583606C2211yescharacteristic
26#22583600—21no—
27#22583590C2211yescharacteristic, complemented
28#22583589—21no—
29#22583589C2211yescharacteristic, complemented
30#22583588—21no—
31#22583585C2211yescharacteristic
32#22583583—21no—
33#22583580—21no—
34#22583578—21no—
35#22583575C2211yescharacteristic, complemented
36#22583572C2211yescharacteristic
37C4×C22⋊D283—21no—
38C4×C22⋊D283C2211yescharacteristic
39C4⋊C4×D283C2211yescharacteristic, complemented
40#22583541C2211yescharacteristic, complemented
41Dic283⋊C8C2211yescharacteristic, complemented
42#22583533C2211yescharacteristic, complemented
43#22583532C2211yescharacteristic
44#22583532C2211yescharacteristic, complemented
45#22583531C2211yescharacteristic, complemented
46#22583530C2211yescharacteristic
47#22583530C2211yescharacteristic
48#22583530C2211yescharacteristic, complemented
49#22583530C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51C8×Dic283C2211yescharacteristic, complemented
52#121×C283C2211yescharacteristic
53C2×C4⋊C4×C283C2211yescharacteristic, complemented
54#106×C283C2211yescharacteristic, complemented
55#106×C283C2211yescharacteristic, complemented
56#102×C283C2211yescharacteristic, complemented
57#102×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic, complemented
59C23×D283—21no—
60C23×D283—21no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63C2×D1132—22no—
64C2×D1132—21no—
65C2×D1132—21no—
66C2×D1132—41no—
67C2×D1132C2311yescharacteristic
68C2×D1132C2311yescharacteristic
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C22⋊D283D411yescharacteristic
73D4×D283—22no—
74D4×D283—41no—
75D4×D283—44no—
76C2×C4×D283—21no—
77C2×C4×D283—21no—
78C2×C4×D283C2311yescharacteristic
79#17985381—22no—
80#17985381—41no—
81#17985380—41no—
82C2×C283⋊C8—41no—
83C2×C283⋊C8C2311yescharacteristic
84C2×C283⋊C8C2311yescharacteristic
85C8×D283—41no—
86C4⋊Dic283—21no—
87C4⋊Dic283C2311yescharacteristic
88Dic283⋊C4—21no—
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91Dic283⋊C4—21no—
92Dic283⋊C4D411yescharacteristic
93C22⋊Dic283—21no—
94C22⋊Dic283D411yescharacteristic
95(C2×D283)⋊C4—21no—
96(C2×D283)⋊C4—21no—
97(C2×D283)⋊C4—21no—
98(C2×D283)⋊C4D411yescharacteristic
99C4×Dic283—21no—
100C4×Dic283C2311yescharacteristic
101C2×D4×C283—21no—
102C2×D4×C283C2311yescharacteristic
103C22×C4×C283—21no—
104C22×C4×C283C2311yescharacteristic
105C2×C8×C283C2311yescharacteristic
106C2×C8×C283C2311yescharacteristic
107C4⋊C4×C283—21no—
108C4⋊C4×C283C2311yescharacteristic
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22⋊C4×C283—21no—
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
121Dic566—21no—
122Dic566—21no—
123Dic566—81no—
124D1132—21no—
125D1132—21no—
126D1132—21no—
127D1132—42no—
128D1132—42no—
129D1132#4112yes—
130C22⋊D283—42no—
131C22⋊D283—42no—
132C22⋊D283—81no—
133C22⋊D283SD1614yescomplemented
134C2×Dic283—21no—
135C2×Dic283—21no—
136C2×Dic283C2×D411yescharacteristic
137C2×Dic283C2×D411yescharacteristic
138C2×Dic283C2×D411yescharacteristic
139C4×D283—21no—
140C4×D283—21no—
141C4×D283—42no—
142C4×D283—81no—
143C283⋊C8—21no—
144C283⋊C8—21no—
145C23×C283—21no—
146C23×C283C2×D411yescharacteristic
147D4×C283—21no—
148D4×C283—21no—
149D4×C283—42no—
150C2×C4×C283—21no—
151C2×C4×C283—21no—
152C2×C4×C283—21no—
153C2×C4×C283—21no—
154C2×C4×C283—21no—
155C2×C4×C283—81no—
156C2×C4×C283C2×D411yescharacteristic
157C2×C4×C283C2411yescharacteristic
158C8×C283—21no—
159C8×C283—21no—
160C22×C283—21no—
161C22×C283—21no—
162C22×C283—41no—
163C22×C283—41no—
164C22×C283—41no—
165C22×C283C2×SD1612yes—
166C22×C283C22×D411yescharacteristic
167C2×D283—21no—
168C2×D283—21no—
169C2×D283—22no—
170C2×D283—41no—
171C2×D283—41no—
172C2×D283—41no—
173C2×D283—41no—
174C2×D283—41no—
175C2×D283—84no—
176C2×D283—84no—
177C2×D283C2×SD1612yes—
178C4×C283—21no—
179C4×C283—41no—
180C4×C283—41no—
181C4×C283—41no—
182C4×C283C2×#4111yescharacteristic
183C4×C283H(5,𝔽2)11yescharacteristic
184Dic283—21no—
185Dic283—21no—
186Dic283—41no—
187Dic283—41no—
188Dic283C2×SD1612yes—
189C2×C283—22no—
190C2×C283—81no—
191C2×C283#54611yescharacteristic
192C2×C283C22×SD1611yescharacteristic
193C2×C283#57611yescharacteristic
194D283—22no—
195D283—42no—
196D283—81no—
197C283#329511yescharacteristic, complemented, Sylow
198#3295—2831nomaximal, Sylow
199#554—2831no—
200D42—2831no—
201#486—2831no—
202#481—2831no—
203#481D28311yescharacteristic, complemented
204#476—2831no—
205#465—2831no—
206#465—2831no—
207#460—2831no—
208#450—2831no—
209#450—2831no—
210C4×SD16—2831no—
211C8×D4—2831no—
212C2×#102—2831no—
213C2×#102—2831no—
214C22×D4—2831no—
215C22×D4—2831no—
216C22×D4—5661no—
217C2×SD16—2831no—
218C2×SD16—2831no—
219C2×SD16—2831no—
220C22×C8—2831no—
221C22×C8—2831no—
222C4⋊Q8—2831no—
223#127—2831no—
224#125—5661no—
225C22⋊Q8—2831no—
226C22⋊Q8—2831no—
227C22⋊Q8—5661no—
228C22⋊Q8—5661no—
229#121—2831no—
230#121—5661no—
231#121C2×D28311yescharacteristic
232#120—5661no—
233#120—5661no—
234C4×Q8—2831no—
235C4×D4—2831no—
236C4×D4—2831no—
237C4×D4—5661no—
238C2×C4⋊C4—2831no—
239C2×C4⋊C4C2×D28311yescharacteristic, complemented
240#106—2831no—
241#106C2×D28311yescharacteristic, complemented
242#106C2×D28311yescharacteristic, complemented
243C4⋊C8—2831no—
244#103—2831no—
245#102—2831no—
246#102—2831no—
247#102—2831no—
248#102—2831no—
249#102—2831no—
250#102—2831no—
251#102—2831no—
252#102C2×D28311yescharacteristic, complemented
253#102C2×D28311yescharacteristic, complemented
254C22⋊C8—2831no—
255C22⋊C8C2×D28311yescharacteristic, complemented
256C4×C8—2831no—
257C24—5661no—
258C24—5661no—
259C2×Q8—2831no—
260C2×Q8—5661no—
261C2×D4—21no—
262C2×D4—2831no—
263C2×D4—2831no—
264C2×D4—2831no—
265C2×D4—5662no—
266C2×D4—5661no—
267C2×D4—5661no—
268C2×D4—5661no—
269C2×D4—5661no—
270C2×D4—5662no—
271C2×D4—5661no—
272C2×D4—11321no—
273C2×D4—11321no—
274C2×D4—11324no—
275C2×D4C22×D28311yescharacteristic
276C22×C4—21no—
277C22×C4—2831no—
278C22×C4—5661no—
279C22×C4—5661no—
280C22×C4C22×D28311yescharacteristic
281SD16—5662no—
282SD16—11321no—
283SD16—11321no—
284C2×C8—2831no—
285C2×C8—2831no—
286C2×C8—11321no—
287C2×C8—11321no—
288C2×C8C22×D28311yescharacteristic
289C2×C8C22×D28311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—2831no—
292C4⋊C4—2831no—
293C4⋊C4—5661no—
294C4⋊C4—5661no—
295C4⋊C4—5661no—
296C4⋊C4—5661no—
297C4⋊C4—5661no—
298C4⋊C4C22×D28311yescharacteristic
299C4⋊C4C22×D28311yescharacteristic
300C4⋊C4C22×D28311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—2831no—
303C22⋊C4—2831no—
304C22⋊C4—5661no—
305C22⋊C4—5661no—
306C22⋊C4—5661no—
307C22⋊C4—5661no—
308C42—2831no—
309C42—5661no—
310C23—21no—
311C23—2831no—
312C23—5661no—
313C23—5661no—
314C23—11322no—
315C23—11322no—
316C23—11322no—
317C23—11322no—
318C23—22641no—
319C23—22641no—
320C23D4×D28311yescharacteristic
321Q8—5661no—
322Q8—5661no—
323Q8—22641no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—2834no—
328D4—2832no—
329D4—5661no—
330D4—5661no—
331D4—5661no—
332D4—11322no—
333D4—11322no—
334D4—11322no—
335D4—11322no—
336D4—22641no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—81no—
343C2×C4—2831no—
344C2×C4—2831no—
345C2×C4—2831no—
346C2×C4—5661no—
347C2×C4—5661no—
348C2×C4—5661no—
349C2×C4—5661no—
350C2×C4—11322no—
351C2×C4—22641no—
352C2×C4D4×D28311yescharacteristic
353C2×C4C23×D28311yescharacteristic
354C8—21no—
355C8—21no—
356C8—5661no—
357C8—5661no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—2832no—
364C22—5661no—
365C22—5661no—
366C22—5662no—
367C22—11321no—
368C22—11321no—
369C22—11321no—
370C22—11321no—
371C22—11321no—
372C22—22644no—
373C22—22644no—
374C22SD16×D28312yes—
375C22C2×D4×D28311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—2832no—
381C4—5661no—
382C4—5661no—
383C4—11321no—
384C4—11321no—
385C4#41×D28311yescharacteristic
386C4#2258365611yescharacteristic
387C2—22no—
388C2—81no—
389C2—5662no—
390C2—11322no—
391C2—22641no—
392C2#3182710711yescharacteristic
393C2C2×SD16×D28311yescharacteristic
394C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#481×C283C2
socleC22×C283C22×D4
prime radical#31827099C2
hypercenter#481D283
hypocenterC283#3295
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #31827170C2semidirect
3. #31826810C2semidirect
4. #31826785C2semidirect
5. #31826754C2semidirect
6. #31826695C2semidirect
7. #31826692C2semidirect
8. #31826664C2semidirect
9. #31826618C2semidirect
10. #31826617C2semidirect
11. #31826552C2semidirect
12. (C22⋊D283)⋊C8C2semidirect
13. C2×#22583530C2semidirect
14. #102×D283C2semidirect
15. #481×C283C2semidirect
20. C2×#17985381C22semidirect
21. C2×#17985380C22semidirect
22. C22×C283⋊C8C22semidirect
23. C2×C8×D283C22semidirect
24. #22583609C22semidirect
27. #22583590C22semidirect
29. #22583589C22semidirect
35. #22583575C22semidirect
39. C4⋊C4×D283C22semidirect
40. #22583541C22semidirect
41. Dic283⋊C8C22semidirect
42. #22583533C22semidirect
44. #22583532C22semidirect
45. #22583531C22semidirect
48. #22583530C22semidirect
49. #22583530C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. C8×Dic283C22semidirect
53. C2×C4⋊C4×C283C22semidirect
54. #106×C283C22semidirect
55. #106×C283C22semidirect
56. #102×C283C22semidirect
57. #102×C283C22semidirect
58. C22⋊C8×C283C22semidirect
133. C22⋊D283SD16semidirect
197. C283#3295semidirect
203. #481D283semidirect
239. C2×C4⋊C4C2×D283semidirect
241. #106C2×D283semidirect
242. #106C2×D283semidirect
252. #102C2×D283semidirect
253. #102C2×D283semidirect
255. C22⋊C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318271702
#318270992
#318268102
#318267852
#318267542
#318266952
#318266922
#318266642
#318266182
#318266172
#318265522
(C22⋊D283)⋊C82
C2×#225835302
#102×D2832
#481×C2832
#3295283