Finite Group Databasebeta

← #49129994

Subgroups — #49129994

Order 36224.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#17985375C211yesmaximal, characteristic, complemented
2C2×M16×D283C211yesmaximal, characteristic, complemented
3C4×D4×D283C211yesmaximal, characteristic
4#31826541C211yesmaximal, characteristic, complemented
5#31826540C211yesmaximal, characteristic, complemented
6#31826538C211yesmaximal, characteristic, complemented
7#31826537C211yesmaximal, characteristic, complemented
8#31826535C211yesmaximal, characteristic, complemented
9C8×C22⋊D283C211yesmaximal, characteristic, complemented
10(C22⋊D283)⋊C8C211yesmaximal, characteristic, complemented
11#31826487C211yesmaximal, characteristic, complemented
12#31826427C211yesmaximal, characteristic, complemented
13#31826427C211yesmaximal, characteristic, complemented
14#31826417C211yesmaximal, characteristic, complemented
15#435×C283C211yesmaximal, characteristic, complemented
16C2×D4×D283C411yescharacteristic
17C22×C4×D283C2211yescharacteristic
18C22×C4×D283C2211yescharacteristic
19C2×#17985376C2211yescharacteristic, complemented
20C2×#17985375—24no—
21C2×#17985375C2211yescharacteristic
22C2×#17985375C2211yescharacteristic
23C2×#17985375C2211yescharacteristic
24C2×#17985375C2211yescharacteristic
25C2×#17985375C2211yescharacteristic, complemented
26C2×#17985375C2211yescharacteristic, complemented
27M16×D283—24no—
28C22×C283⋊C8C2211yescharacteristic, complemented
29C2×C8×D283C2211yescharacteristic, complemented
30C2×C8×D283C2211yescharacteristic, complemented
31C4×D1132C2211yescharacteristic
32D4×Dic283C411yescharacteristic
33#22583572C411yescharacteristic
34C4×C22⋊D283C2211yescharacteristic
35C4×C22⋊D283C2211yescharacteristic
36(C22⋊D283)⋊C4C411yescharacteristic
37(C22⋊D283)⋊C4C411yescharacteristic
38C4⋊C4×D283C411yescharacteristic
39C22⋊C4×D283C411yescharacteristic
40C22⋊C4×D283C411yescharacteristic
41C42×D283C2211yescharacteristic
42C4⋊(C283⋊C8)C2211yescharacteristic, complemented
43Dic283⋊C8C2211yescharacteristic, complemented
44Dic283⋊C8C2211yescharacteristic, complemented
45C22⋊(C283⋊C8)C2211yescharacteristic, complemented
46C22⋊(C283⋊C8)C2211yescharacteristic, complemented
47(C2×D283)⋊C8C2211yescharacteristic, complemented
48(C2×D283)⋊C8C2211yescharacteristic, complemented
49(C2×D283)⋊C8C2211yescharacteristic, complemented
50(C2×D283)⋊C8C2211yescharacteristic, complemented
51#22583521C2211yescharacteristic, complemented
52C8×Dic283C2211yescharacteristic, complemented
53C8×Dic283C2211yescharacteristic, complemented
54C2×M16×C283C2211yescharacteristic, complemented
55C22×C8×C283C2211yescharacteristic, complemented
56C4×D4×C283C2211yescharacteristic
57C4⋊C8×C283C2211yescharacteristic, complemented
58C22⋊C8×C283C2211yescharacteristic, complemented
59C22⋊C8×C283C2211yescharacteristic, complemented
60#97×C283C2211yescharacteristic, complemented
61C23×D283C2×C411yescharacteristic
62C23×D283C2×C411yescharacteristic
63C2×D1132C2×C411yescharacteristic
64C2×C22⋊D283C2×C411yescharacteristic
65C2×C22⋊D283C2×C411yescharacteristic
66D4×D283—24no—
67C22×Dic283C2×C411yescharacteristic
68C22×Dic283C2×C411yescharacteristic
69C2×C4×D283—22no—
70C2×C4×D283—22no—
71C2×C4×D283—22no—
72C2×C4×D283—22no—
73C2×C4×D283C2×C411yescharacteristic
74C2×C4×D283C2×C411yescharacteristic
75C2×C4×D283C2×C411yescharacteristic
76C2×C4×D283C2×C411yescharacteristic
77C2×C4×D283C2×C411yescharacteristic
78C2×C4×D283C2×C411yescharacteristic
79C2×C4×D283C2311yescharacteristic
80C2×C4×D283C2311yescharacteristic
81C2×C4×D283C2311yescharacteristic
82#17985376—22no—
83#17985375—22no—
84#17985375—22no—
85#17985375—22no—
86#17985375—22no—
87#17985375—22no—
88#17985375D414yescomplemented
89C2×C283⋊C8—22no—
90C2×C283⋊C8C2311yescharacteristic
91C2×C283⋊C8C2311yescharacteristic
92C2×C283⋊C8C2311yescharacteristic
93C2×C283⋊C8C2311yescharacteristic
94C8×D283—22no—
95C8×D283—22no—
96C4⋊Dic283C2×C411yescharacteristic
97Dic283⋊C4C2×C411yescharacteristic
98Dic283⋊C4C2×C411yescharacteristic
99C22⋊Dic283C2×C411yescharacteristic
100C22⋊Dic283C2×C411yescharacteristic
101(C2×D283)⋊C4C2×C411yescharacteristic
102(C2×D283)⋊C4C2×C411yescharacteristic
103(C2×D283)⋊C4C2×C411yescharacteristic
104(C2×D283)⋊C4C2×C411yescharacteristic
105C4×Dic283C2×C411yescharacteristic
106C4×Dic283C2×C411yescharacteristic
107C4×Dic283C2311yescharacteristic
108C2×D4×C283C2×C411yescharacteristic
109C22×C4×C283C2311yescharacteristic
110C22×C4×C283C2311yescharacteristic
111M16×C283—22no—
112C2×C8×C283—22no—
113C2×C8×C283C2311yescharacteristic
114C2×C8×C283C2311yescharacteristic
115C2×C8×C283C2311yescharacteristic
116C2×C8×C283C2311yescharacteristic
117C4⋊C4×C283C2×C411yescharacteristic
118C22⋊C4×C283C2×C411yescharacteristic
119C22⋊C4×C283C2×C411yescharacteristic
120C42×C283C2311yescharacteristic
121C22×D283—22no—
122C22×D283—22no—
123C22×D283—22no—
124C22×D283—22no—
125C22×D283—41no—
126C22×D283—41no—
127C22×D283C22×C411yescharacteristic
128C22×D283C22×C411yescharacteristic
129C22×D283C22×C411yescharacteristic
130D1132—22no—
131C22⋊D283—22no—
132C22⋊D283M1614yescomplemented
133C2×Dic283—22no—
134C2×Dic283—22no—
135C2×Dic283C22×C411yescharacteristic
136C2×Dic283C22×C411yescharacteristic
137C2×Dic283C22×C411yescharacteristic
138C2×Dic283C22×C411yescharacteristic
139C2×Dic283C22×C411yescharacteristic
140C4×D283—22no—
141C4×D283—22no—
142C4×D283—21no—
143C4×D283—21no—
144C4×D283—21no—
145C4×D283—21no—
146C4×D283—22no—
147C4×D283—22no—
148C4×D283—22no—
149C4×D283—41no—
150C4×D283C2×D412yes—
151C4×D283#4112yes—
152C283⋊C8—21no—
153C283⋊C8—21no—
154C283⋊C8—21no—
155C283⋊C8C2×D412yescomplemented
156C23×C283C22×C411yescharacteristic
157C23×C283C22×C411yescharacteristic
158D4×C283—22no—
159C2×C4×C283—21no—
160C2×C4×C283—21no—
161C2×C4×C283—21no—
162C2×C4×C283—21no—
163C2×C4×C283C22×C411yescharacteristic
164C2×C4×C283C22×C411yescharacteristic
165C2×C4×C283C22×C411yescharacteristic
166C2×C4×C283C22×C411yescharacteristic
167C2×C4×C283C2411yescharacteristic
168C8×C283—21no—
169C8×C283—21no—
170C8×C283—21no—
171C8×C283C2×D412yescomplemented
172C22×C283—21no—
173C22×C283—21no—
174C22×C283—21no—
175C22×C283—21no—
176C22×C283—21no—
177C22×C283C2×M1612yescomplemented
178C22×C283C23×C411yescharacteristic
179C2×D283—21no—
180C2×D283—21no—
181C2×D283—21no—
182C2×D283—21no—
183C2×D283—21no—
184C2×D283—21no—
185C2×D283—21no—
186C2×D283—44no—
187C2×D283—44no—
188C2×D283C4×D412yes—
189C2×D283C2×M1612yescomplemented
190C4×C283—21no—
191C4×C283—21no—
192C4×C283—21no—
193C4×C283—21no—
194C4×C283C22×D411yescharacteristic
195C4×C283C2×#4111yescharacteristic
196Dic283—21no—
197Dic283—21no—
198Dic283—21no—
199Dic283C4×D412yes—
200Dic283C2×M1612yescomplemented
201C2×C283—22no—
202C2×C283—41no—
203C2×C283C2×C4×D411yescharacteristic
204C2×C283C22×M1611yescharacteristic
205C2×C283#56811yescharacteristic
206D283—22no—
207D283—22no—
208D283—41no—
209C283D4×M1611yescharacteristic, complemented, Sylow
210D4×M16—2831nomaximal, Sylow
211C22×M16—2831no—
212C22×M16—2831no—
213C2×C4×D4—2831no—
214#436—2831no—
215#436—2831no—
216#435—2831no—
217#435—2831no—
218#435—2831no—
219#435D28311yescharacteristic, complemented
220C8×D4—2831no—
221C8×D4—2831no—
222#423—2831no—
223#407—2831no—
224#407—2831no—
225C4×M16—2831no—
226C22×D4—2831no—
227C23×C4—2831no—
228C23×C4—2831no—
229C2×M16—2831no—
230C2×M16—2831no—
231C2×M16—2831no—
232C2×M16—2831no—
233C2×M16—2831no—
234C2×M16—2831no—
235C2×M16—2831no—
236C2×M16—5664no—
237C2×M16—5664no—
238C2×M16C2×D28311yescharacteristic, complemented
239C22×C8—2831no—
240C22×C8—2831no—
241C22×C8—2831no—
242C22×C8C2×D28311yescharacteristic, complemented
243C4×D4—2831no—
244C4×D4—2831no—
245C4×D4—2831no—
246C4×D4—2831no—
247C4×D4—2831no—
248C4×D4—2831no—
249C4×D4—2831no—
250C4×D4C2×D28311yescharacteristic
251C2×C4⋊C4—2831no—
252C2×C22⋊C4—2831no—
253C2×C22⋊C4—2831no—
254C2×C42—2831no—
255C4⋊C8—2831no—
256C4⋊C8—2831no—
257C4⋊C8—2831no—
258C4⋊C8C2×D28311yescharacteristic, complemented
259C22⋊C8—2831no—
260C22⋊C8—2831no—
261C22⋊C8—2831no—
262C22⋊C8—2831no—
263C22⋊C8—2831no—
264C22⋊C8—2831no—
265C22⋊C8C2×D28311yescharacteristic, complemented
266C22⋊C8C2×D28311yescharacteristic, complemented
267#97—2831no—
268#97C2×D28311yescharacteristic, complemented
269C4×C8—2831no—
270C4×C8—2831no—
271C24—2831no—
272C24—2831no—
273C2×D4—2831no—
274C2×D4—2831no—
275C2×D4—2831no—
276C2×D4—5664no—
277C2×D4C4×D28311yescharacteristic
278C22×C4—2831no—
279C22×C4—2831no—
280C22×C4—2831no—
281C22×C4—2831no—
282C22×C4—2831no—
283C22×C4—2831no—
284C22×C4—2831no—
285C22×C4—2831no—
286C22×C4—2831no—
287C22×C4—2831no—
288C22×C4—2831no—
289C22×C4—5662no—
290C22×C4—5662no—
291C22×C4—5662no—
292C22×C4—5662no—
293C22×C4C22×D28311yescharacteristic
294C22×C4C22×D28311yescharacteristic
295M16—22no—
296M16—2834no—
297M16—5662no—
298M16—5662no—
299M16—5662no—
300M16—5662no—
301M16—5662no—
302M16—5662no—
303C2×C8—22no—
304C2×C8—2831no—
305C2×C8—2831no—
306C2×C8—2831no—
307C2×C8—2831no—
308C2×C8—5662no—
309C2×C8—5662no—
310C2×C8—5662no—
311C2×C8C22×D28311yescharacteristic
312C2×C8C22×D28311yescharacteristic
313C2×C8C22×D28311yescharacteristic
314C2×C8C22×D28311yescharacteristic
315C4⋊C4—2831no—
316C4⋊C4—2831no—
317C4⋊C4—2831no—
318C4⋊C4C4×D28311yescharacteristic
319C22⋊C4—2831no—
320C22⋊C4—2831no—
321C22⋊C4—2831no—
322C22⋊C4—2831no—
323C22⋊C4—2831no—
324C22⋊C4—2831no—
325C22⋊C4C4×D28311yescharacteristic
326C22⋊C4C4×D28311yescharacteristic
327C42—2831no—
328C42—2831no—
329C42—2831no—
330C42C22×D28311yescharacteristic
331C23—2831no—
332C23—2831no—
333C23—2831no—
334C23—5662no—
335C23—5662no—
336C23—5662no—
337C23—5662no—
338C23—11321no—
339C23—11321no—
340C23C2×C4×D28311yescharacteristic
341C23C2×C4×D28311yescharacteristic
342D4—22no—
343D4—2834no—
344D4—5662no—
345D4—5662no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—2831no—
351C2×C4—2831no—
352C2×C4—2832no—
353C2×C4—2832no—
354C2×C4—2831no—
355C2×C4—2831no—
356C2×C4—2831no—
357C2×C4—5662no—
358C2×C4—5662no—
359C2×C4—5662no—
360C2×C4—5662no—
361C2×C4—5662no—
362C2×C4—5662no—
363C2×C4—5662no—
364C2×C4—5661no—
365C2×C4—5661no—
366C2×C4—5661no—
367C2×C4—5661no—
368C2×C4—11321no—
369C2×C4C2×C4×D28311yescharacteristic
370C2×C4C2×C4×D28311yescharacteristic
371C2×C4C2×C4×D28311yescharacteristic
372C2×C4C2×C4×D28311yescharacteristic
373C2×C4C23×D28311yescharacteristic
374C8—21no—
375C8—21no—
376C8—21no—
377C8—2832no—
378C8—5661no—
379C8—5661no—
380C8—5661no—
381C8D4×D28312yescomplemented
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—2832no—
388C22—2832no—
389C22—5661no—
390C22—5661no—
391C22—5661no—
392C22—5661no—
393C22—5661no—
394C22—5661no—
395C22—5661no—
396C22—11324no—
397C22—11324no—
398C22M16×D28312yescomplemented
399C22C22×C4×D28311yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—2832no—
405C4—2832no—
406C4—5661no—
407C4—5661no—
408C4—5661no—
409C4C2×D4×D28311yescharacteristic
410C4#41×D28311yescharacteristic
411C2—22no—
412C2—41no—
413C2—5662no—
414C2—5662no—
415C2—11321no—
416C2C4×D4×D28311yescharacteristic
417C2C2×M16×D28311yescharacteristic
418C2#3182723011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D283
commutator, socleC22×C283C23×C4
Fitting#435×C283C2
prime radicalC2×D4×D283C4
cosocleC2×C4×C283C24
hypercenter#435D283
hypocenterC283D4×M16
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C22×#17985375C2semidirect
2. C2×M16×D283C2semidirect
4. #31826541C2semidirect
5. #31826540C2semidirect
6. #31826538C2semidirect
7. #31826537C2semidirect
8. #31826535C2semidirect
9. C8×C22⋊D283C2semidirect
10. (C22⋊D283)⋊C8C2semidirect
11. #31826487C2semidirect
12. #31826427C2semidirect
13. #31826427C2semidirect
14. #31826417C2semidirect
15. #435×C283C2semidirect
19. C2×#17985376C22semidirect
25. C2×#17985375C22semidirect
26. C2×#17985375C22semidirect
28. C22×C283⋊C8C22semidirect
29. C2×C8×D283C22semidirect
30. C2×C8×D283C22semidirect
42. C4⋊(C283⋊C8)C22semidirect
43. Dic283⋊C8C22semidirect
44. Dic283⋊C8C22semidirect
45. C22⋊(C283⋊C8)C22semidirect
46. C22⋊(C283⋊C8)C22semidirect
47. (C2×D283)⋊C8C22semidirect
48. (C2×D283)⋊C8C22semidirect
49. (C2×D283)⋊C8C22semidirect
50. (C2×D283)⋊C8C22semidirect
51. #22583521C22semidirect
52. C8×Dic283C22semidirect
53. C8×Dic283C22semidirect
54. C2×M16×C283C22semidirect
55. C22×C8×C283C22semidirect
57. C4⋊C8×C283C22semidirect
58. C22⋊C8×C283C22semidirect
59. C22⋊C8×C283C22semidirect
60. #97×C283C22semidirect
88. #17985375D4semidirect
132. C22⋊D283M16semidirect
155. C283⋊C8C2×D4semidirect
171. C8×C283C2×D4semidirect
177. C22×C283C2×M16semidirect
189. C2×D283C2×M16semidirect
200. Dic283C2×M16semidirect
209. C283D4×M16semidirect
219. #435D283semidirect
238. C2×M16C2×D283semidirect
242. C22×C8C2×D283semidirect
258. C4⋊C8C2×D283semidirect
265. C22⋊C8C2×D283semidirect
266. C22⋊C8C2×D283semidirect
268. #97C2×D283semidirect
381. C8D4×D283semidirect
398. C22M16×D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853752
C2×M16×D2832
C4×D4×D2832
#318265412
#318265402
#318265382
#318265372
#318265352
C8×C22⋊D2832
(C22⋊D283)⋊C82
#318264872
#318264272
#318264172
#435×C2832
D4×M16283