Finite Group Databasebeta

← #49130286

Subgroups — #49130286

Order 36224.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×D283C211yesmaximal, characteristic
2#31826539C211yesmaximal, characteristic, complemented
3#31826538C211yesmaximal, characteristic, complemented
4#31826537C211yesmaximal, characteristic, complemented
5#31826536C211yesmaximal, characteristic, complemented
6#31826535C211yesmaximal, characteristic, complemented
7#31826534C211yesmaximal, characteristic, complemented
8#31826533C211yesmaximal, characteristic, complemented
9#31826521C211yesmaximal, characteristic, complemented
10#31826520C211yesmaximal, characteristic, complemented
11#31826428C211yesmaximal, characteristic, complemented
12#31826427C211yesmaximal, characteristic, complemented
13C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
14C22⋊C8×D283C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C411yescharacteristic
17C22×C4×D283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19C2×#17985376C2211yescharacteristic, complemented
20C2×#17985375C2211yescharacteristic, complemented
21C2×#17985375C2211yescharacteristic, complemented
22C22×C283⋊C8C2211yescharacteristic, complemented
23C2×C8×D283C2211yescharacteristic, complemented
24C2×C8×D283C2211yescharacteristic, complemented
25C4×D1132C2211yescharacteristic
26D4×Dic283C411yescharacteristic
27#22583572C411yescharacteristic
28C4×C22⋊D283C2211yescharacteristic
29C4×C22⋊D283C2211yescharacteristic
30(C22⋊D283)⋊C4C411yescharacteristic
31(C22⋊D283)⋊C4C411yescharacteristic
32C4⋊C4×D283C411yescharacteristic
33C22⋊C4×D283C411yescharacteristic
34C22⋊C4×D283C411yescharacteristic
35C42×D283C2211yescharacteristic
36C4⋊(C283⋊C8)C2211yescharacteristic, complemented
37Dic283⋊C8C2211yescharacteristic, complemented
38Dic283⋊C8C2211yescharacteristic, complemented
39C22⋊(C283⋊C8)C2211yescharacteristic, complemented
40C22⋊(C283⋊C8)C2211yescharacteristic, complemented
41(C2×D283)⋊C8C2211yescharacteristic
42(C2×D283)⋊C8C2211yescharacteristic
43(C2×D283)⋊C8C2211yescharacteristic
44(C2×D283)⋊C8C2211yescharacteristic
45(C2×D283)⋊C8C2211yescharacteristic, complemented
46(C2×D283)⋊C8C2211yescharacteristic, complemented
47(C2×D283)⋊C8C2211yescharacteristic, complemented
48(C2×D283)⋊C8C2211yescharacteristic, complemented
49#22583521C2211yescharacteristic, complemented
50#22583520C2211yescharacteristic, complemented
51#22583520C2211yescharacteristic, 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×D283C2×C411yescharacteristic
60C23×D283C2×C411yescharacteristic
61C2×D1132C2×C411yescharacteristic
62C2×C22⋊D283C2×C411yescharacteristic
63C2×C22⋊D283C2×C411yescharacteristic
64D4×D283—24no—
65C22×Dic283C2×C411yescharacteristic
66C22×Dic283C2×C411yescharacteristic
67C2×C4×D283—41no—
68C2×C4×D283—41no—
69C2×C4×D283—41no—
70C2×C4×D283—41no—
71C2×C4×D283C2×C411yescharacteristic
72C2×C4×D283C2×C411yescharacteristic
73C2×C4×D283C2×C411yescharacteristic
74C2×C4×D283C2×C411yescharacteristic
75C2×C4×D283C2×C411yescharacteristic
76C2×C4×D283C2×C411yescharacteristic
77C2×C4×D283C2311yescharacteristic
78C2×C4×D283C2311yescharacteristic
79C2×C4×D283C2311yescharacteristic
80#17985376—41no—
81#17985375—41no—
82#17985375—41no—
83C2×C283⋊C8—41no—
84C2×C283⋊C8C2311yescharacteristic
85C2×C283⋊C8C2311yescharacteristic
86C2×C283⋊C8C2311yescharacteristic
87C2×C283⋊C8C2311yescharacteristic
88C8×D283—41no—
89C8×D283—41no—
90C4⋊Dic283C2×C411yescharacteristic
91Dic283⋊C4C2×C411yescharacteristic
92Dic283⋊C4C2×C411yescharacteristic
93C22⋊Dic283C2×C411yescharacteristic
94C22⋊Dic283C2×C411yescharacteristic
95(C2×D283)⋊C4C2×C411yescharacteristic
96(C2×D283)⋊C4C2×C411yescharacteristic
97(C2×D283)⋊C4C2×C411yescharacteristic
98(C2×D283)⋊C4C2×C411yescharacteristic
99C4×Dic283C2×C411yescharacteristic
100C4×Dic283C2×C411yescharacteristic
101C4×Dic283C2311yescharacteristic
102C2×D4×C283C2×C411yescharacteristic
103C22×C4×C283C2311yescharacteristic
104C22×C4×C283C2311yescharacteristic
105M16×C283—41no—
106C2×C8×C283—41no—
107C2×C8×C283C2311yescharacteristic
108C2×C8×C283C2311yescharacteristic
109C2×C8×C283C2311yescharacteristic
110C2×C8×C283C2311yescharacteristic
111C4⋊C4×C283C2×C411yescharacteristic
112C22⋊C4×C283C2×C411yescharacteristic
113C22⋊C4×C283C2×C411yescharacteristic
114C42×C283C2311yescharacteristic
115C22×D283—22no—
116C22×D283—41no—
117C22×D283—41no—
118C22×D283—41no—
119C22×D283—41no—
120C22×D283M1614yescomplemented
121C22×D283C22×C411yescharacteristic
122C22×D283C22×C411yescharacteristic
123C22×D283C22×C411yescharacteristic
124D1132—22no—
125C22⋊D283—22no—
126C22⋊D283—22no—
127C2×Dic283—41no—
128C2×Dic283—41no—
129C2×Dic283C22×C411yescharacteristic
130C2×Dic283C22×C411yescharacteristic
131C2×Dic283C22×C411yescharacteristic
132C2×Dic283C22×C411yescharacteristic
133C2×Dic283C22×C411yescharacteristic
134C4×D283—22no—
135C4×D283—21no—
136C4×D283—21no—
137C4×D283—21no—
138C4×D283—21no—
139C4×D283—21no—
140C4×D283—21no—
141C4×D283—41no—
142C4×D283—41no—
143C4×D283—41no—
144C4×D283—41no—
145C4×D283—41no—
146C283⋊C8—21no—
147C283⋊C8—21no—
148C283⋊C8—21no—
149C283⋊C8—21no—
150C23×C283C22×C411yescharacteristic
151C23×C283C22×C411yescharacteristic
152D4×C283—22no—
153C2×C4×C283—21no—
154C2×C4×C283—21no—
155C2×C4×C283—21no—
156C2×C4×C283—21no—
157C2×C4×C283C22×C411yescharacteristic
158C2×C4×C283C22×C411yescharacteristic
159C2×C4×C283C22×C411yescharacteristic
160C2×C4×C283C22×C411yescharacteristic
161C2×C4×C283C2411yescharacteristic
162C8×C283—21no—
163C8×C283—21no—
164C8×C283—21no—
165C8×C283—21no—
166C22×C283—21no—
167C22×C283—21no—
168C22×C283—21no—
169C22×C283—21no—
170C22×C283—21no—
171C22×C283C2×M1612yes—
172C22×C283C23×C411yescharacteristic
173C2×D283—21no—
174C2×D283—21no—
175C2×D283—21no—
176C2×D283—21no—
177C2×D283—21no—
178C2×D283—21no—
179C2×D283—21no—
180C2×D283—44no—
181C2×D283—44no—
182C2×D283C2×M1612yes—
183C2×D283C2×M1612yes—
184C4×C283—21no—
185C4×C283—21no—
186C4×C283—21no—
187C4×C283—21no—
188C4×C283H(5,𝔽2)11yescharacteristic
189C4×C283H(5,𝔽2)11yescharacteristic
190Dic283—21no—
191Dic283—21no—
192Dic283—21no—
193Dic283—21no—
194Dic283—21no—
195C2×C283—22no—
196C2×C283—41no—
197C2×C283#51811yescharacteristic
198C2×C283C22×M1611yescharacteristic
199C2×C283#56811yescharacteristic
200D283—22no—
201D283—22no—
202D283—41no—
203C283#297311yescharacteristic, complemented, Sylow
204#2973—2831nomaximal, Sylow
205C2×C4×D4—2831no—
206#435—2831no—
207#435—2831no—
208#435—2831no—
209#435—2831no—
210#435—2831no—
211#435—2831no—
212#435—2831no—
213#435D28311yescharacteristic, complemented
214#432—2831no—
215#432—2831no—
216#407—2831no—
217#407—2831no—
218C2×C22⋊C8—2831no—
219C2×C22⋊C8—2831no—
220C22×D4—2831no—
221C23×C4—2831no—
222C23×C4—2831no—
223C2×M16—2831no—
224C2×M16—2831no—
225C2×M16—2831no—
226C2×M16C2×D28311yescharacteristic, complemented
227C22×C8—2831no—
228C22×C8—2831no—
229C22×C8—2831no—
230C22×C8C2×D28311yescharacteristic, complemented
231C4×D4—2831no—
232C4×D4—2831no—
233C4×D4—2831no—
234C4×D4—2831no—
235C4×D4—2831no—
236C4×D4—2831no—
237C4×D4—2831no—
238C4×D4C2×D28311yescharacteristic
239C2×C4⋊C4—2831no—
240C2×C22⋊C4—2831no—
241C2×C22⋊C4—2831no—
242C2×C42—2831no—
243C4⋊C8—2831no—
244C4⋊C8—2831no—
245C4⋊C8—2831no—
246C4⋊C8C2×D28311yescharacteristic, complemented
247C22⋊C8—2831no—
248C22⋊C8—2831no—
249C22⋊C8—2831no—
250C22⋊C8—2831no—
251C22⋊C8—2831no—
252C22⋊C8—2831no—
253C22⋊C8—2831no—
254C22⋊C8—2831no—
255C22⋊C8—2831no—
256C22⋊C8—2831no—
257C22⋊C8C2×D28311yescharacteristic, complemented
258C22⋊C8C2×D28311yescharacteristic, complemented
259#97—2831no—
260#97—2831no—
261#97—2831no—
262#97C2×D28311yescharacteristic, complemented
263C24—2831no—
264C24—2831no—
265C2×D4—2831no—
266C2×D4—2831no—
267C2×D4—2831no—
268C2×D4—5664no—
269C2×D4C4×D28311yescharacteristic
270C22×C4—2831no—
271C22×C4—2831no—
272C22×C4—2831no—
273C22×C4—2831no—
274C22×C4—2831no—
275C22×C4—2831no—
276C22×C4—2831no—
277C22×C4—2831no—
278C22×C4—2831no—
279C22×C4—2831no—
280C22×C4—2831no—
281C22×C4—11321no—
282C22×C4—11321no—
283C22×C4—11321no—
284C22×C4—11321no—
285C22×C4C22×D28311yescharacteristic
286C22×C4C22×D28311yescharacteristic
287M16—41no—
288M16—11321no—
289M16—11321no—
290M16—11321no—
291C2×C8—41no—
292C2×C8—2831no—
293C2×C8—2831no—
294C2×C8—2831no—
295C2×C8—2831no—
296C2×C8—11321no—
297C2×C8—11321no—
298C2×C8—11321no—
299C2×C8C22×D28311yescharacteristic
300C2×C8C22×D28311yescharacteristic
301C2×C8C22×D28311yescharacteristic
302C2×C8C22×D28311yescharacteristic
303C4⋊C4—2831no—
304C4⋊C4—2831no—
305C4⋊C4—2831no—
306C4⋊C4C4×D28311yescharacteristic
307C22⋊C4—2831no—
308C22⋊C4—2831no—
309C22⋊C4—2831no—
310C22⋊C4—2831no—
311C22⋊C4—2831no—
312C22⋊C4—2831no—
313C22⋊C4C4×D28311yescharacteristic
314C22⋊C4C4×D28311yescharacteristic
315C42—2831no—
316C42—2831no—
317C42—2831no—
318C42C22×D28311yescharacteristic
319C23—2831no—
320C23—2831no—
321C23—2834no—
322C23—2831no—
323C23—5662no—
324C23—11321no—
325C23—11321no—
326C23—11321no—
327C23—11321no—
328C23C2×C4×D28311yescharacteristic
329C23C2×C4×D28311yescharacteristic
330D4—22no—
331D4—5662no—
332D4—5662no—
333D4—5662no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—2831no—
339C2×C4—2831no—
340C2×C4—2831no—
341C2×C4—2831no—
342C2×C4—2831no—
343C2×C4—5662no—
344C2×C4—5661no—
345C2×C4—5661no—
346C2×C4—5661no—
347C2×C4—5661no—
348C2×C4—5661no—
349C2×C4—5661no—
350C2×C4—11321no—
351C2×C4—11321no—
352C2×C4—11321no—
353C2×C4—11321no—
354C2×C4—11321no—
355C2×C4—11321no—
356C2×C4—11321no—
357C2×C4C2×C4×D28311yescharacteristic
358C2×C4C2×C4×D28311yescharacteristic
359C2×C4C2×C4×D28311yescharacteristic
360C2×C4C2×C4×D28311yescharacteristic
361C2×C4C23×D28311yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—21no—
366C8—5661no—
367C8—5661no—
368C8—5661no—
369C8—5661no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—2832no—
376C22—2832no—
377C22—5661no—
378C22—5661no—
379C22—5661no—
380C22—5661no—
381C22—5661no—
382C22—5661no—
383C22—5661no—
384C22—11324no—
385C22—11324no—
386C22M16×D28312yes—
387C22C22×C4×D28311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—5661no—
393C4—5661no—
394C4—5661no—
395C4—5661no—
396C4—5661no—
397C4#2258365511yescharacteristic
398C4#2258365611yescharacteristic
399C2—22no—
400C2—41no—
401C2—5662no—
402C2—5662no—
403C2—11321no—
404C2#3182693711yescharacteristic
405C2C2×M16×D28311yescharacteristic
406C2#3182723011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#435×C283C2
prime radicalC2×D4×D283C4
cosocleC2×C4×C283C24
hypercenter#435D283
hypocenterC283#2973
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #31826539C2semidirect
3. #31826538C2semidirect
4. #31826537C2semidirect
5. #31826536C2semidirect
6. #31826535C2semidirect
7. #31826534C2semidirect
8. #31826533C2semidirect
9. #31826521C2semidirect
10. #31826520C2semidirect
11. #31826428C2semidirect
12. #31826427C2semidirect
13. C2×(C2×D283)⋊C8C2semidirect
14. C22⋊C8×D283C2semidirect
15. #435×C283C2semidirect
19. C2×#17985376C22semidirect
20. C2×#17985375C22semidirect
21. C2×#17985375C22semidirect
22. C22×C283⋊C8C22semidirect
23. C2×C8×D283C22semidirect
24. C2×C8×D283C22semidirect
36. C4⋊(C283⋊C8)C22semidirect
37. Dic283⋊C8C22semidirect
38. Dic283⋊C8C22semidirect
39. C22⋊(C283⋊C8)C22semidirect
40. C22⋊(C283⋊C8)C22semidirect
45. (C2×D283)⋊C8C22semidirect
46. (C2×D283)⋊C8C22semidirect
47. (C2×D283)⋊C8C22semidirect
48. (C2×D283)⋊C8C22semidirect
49. #22583521C22semidirect
50. #22583520C22semidirect
51. #22583520C22semidirect
52. C2×M16×C283C22semidirect
53. C22×C8×C283C22semidirect
55. C4⋊C8×C283C22semidirect
56. C22⋊C8×C283C22semidirect
57. C22⋊C8×C283C22semidirect
58. #97×C283C22semidirect
120. C22×D283M16semidirect
203. C283#2973semidirect
213. #435D283semidirect
226. C2×M16C2×D283semidirect
230. C22×C8C2×D283semidirect
246. C4⋊C8C2×D283semidirect
257. C22⋊C8C2×D283semidirect
258. C22⋊C8C2×D283semidirect
262. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D2832
#318265392
#318265382
#318265372
#318265362
#318265352
#318265342
#318265332
#318265212
#318265202
#318264282
#318264272
C2×(C2×D283)⋊C82
C22⋊C8×D2832
#435×C2832
#2973283