Finite Group Databasebeta

← #440×D283 #49130036

Subgroups — #440×D283 #49130036

Order 36224.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D283C211yesmaximal, characteristic
2C4×Q8×D283C211yesmaximal, characteristic, complemented
3C4×D4×D283C211yesmaximal, characteristic
4#31826568C211yesmaximal, characteristic, complemented
5#31826567C211yesmaximal, characteristic, complemented
6#31826566C211yesmaximal, characteristic, complemented
7#31826565C211yesmaximal, characteristic, complemented
8#31826564C211yesmaximal, characteristic, complemented
9#31826563C211yesmaximal, characteristic, complemented
10#31826562C211yesmaximal, characteristic, complemented
11#107×D283C211yesmaximal, characteristic, complemented
12#103×D283C211yesmaximal, characteristic, complemented
13#102×D283C211yesmaximal, characteristic
14#97×D283C211yesmaximal, characteristic, complemented
15#440×C283C211yesmaximal, characteristic, complemented
16C2×Q8×D283C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C22×C4×D283—21no—
19C2×#17985381C2211yescharacteristic
20C2×#17985380C2211yescharacteristic
21C2×#17985379C2211yescharacteristic
22SD16×D283C418yescomplemented
23C2×C8×D283C2211yescharacteristic
24C2×C8×D283C2211yescharacteristic
25Q8×Dic283C2211yescharacteristic, complemented
26C4×Dic566—21no—
27C4×Dic566C2211yescharacteristic, complemented
28#22583575—21no—
29#22583575C2211yescharacteristic, complemented
30C4×D1132C2211yescharacteristic
31D4×Dic283C2211yescharacteristic
32#22583572C2211yescharacteristic
33C4×C22⋊D283—21no—
34(C22⋊D283)⋊C4—21no—
35C4⋊C4×D283—21no—
36C4⋊C4×D283C2211yescharacteristic
37C4⋊C4×D283C2211yescharacteristic
38C22⋊C4×D283—21no—
39C42×D283—21no—
40C42×D283C2211yescharacteristic
41#22583544C2211yescharacteristic, complemented
42#22583543C2211yescharacteristic, complemented
43#22583543C2211yescharacteristic, complemented
44#22583535C2211yescharacteristic, complemented
45#22583534C2211yescharacteristic, complemented
46#22583533C2211yescharacteristic, complemented
47#22583532C2211yescharacteristic
48#22583531C2211yescharacteristic
49#22583530C2211yescharacteristic
50#22583521C2211yescharacteristic, complemented
51#22583520C2211yescharacteristic, complemented
52#22583520C2211yescharacteristic, complemented
53C2×SD16×C283C2211yescharacteristic
54C4×Q8×C283C2211yescharacteristic, complemented
55C4×D4×C283C2211yescharacteristic
56#107×C283C2211yescharacteristic, complemented
57#103×C283C2211yescharacteristic, complemented
58#102×C283C2211yescharacteristic
59#97×C283C2211yescharacteristic, complemented
60C23×D283—21no—
61C2×Dic566—21no—
62C2×Dic566C2311yescharacteristic
63Q8×D283—22no—
64Q8×D283C2×C414yescomplemented
65C2×D1132C2311yescharacteristic
66C2×C22⋊D283—21no—
67D4×D283—22no—
68D4×D283C2×C414yes—
69C22×Dic283—21no—
70C2×C4×D283—21no—
71C2×C4×D283—21no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283—21no—
75C2×C4×D283—44no—
76C2×C4×D283D411yescharacteristic
77C2×C4×D283D411yescharacteristic
78C2×C4×D283C2311yescharacteristic
79#17985381C2×C414yescomplemented
80#17985380C2×C414yescomplemented
81#17985379C2×C414yescomplemented
82C2×C283⋊C8C2311yescharacteristic
83C2×C283⋊C8C2311yescharacteristic
84C8×D283—22no—
85C8×D283C2×C414yescomplemented
86C4⋊Dic283—21no—
87C4⋊Dic283C2311yescharacteristic
88C4⋊Dic283C2311yescharacteristic
89Dic283⋊C4—21no—
90Dic283⋊C4—21no—
91Dic283⋊C4—21no—
92Dic283⋊C4—21no—
93C22⋊Dic283—21no—
94(C2×D283)⋊C4—21no—
95(C2×D283)⋊C4—21no—
96C4×Dic283—21no—
97C4×Dic283—21no—
98C4×Dic283—21no—
99C4×Dic283D411yescharacteristic
100C4×Dic283D411yescharacteristic
101C4×Dic283C2311yescharacteristic
102C2×Q8×C283C2311yescharacteristic
103C2×D4×C283C2311yescharacteristic
104C22×C4×C283—21no—
105SD16×C283C2×C414yescomplemented
106C2×C8×C283C2311yescharacteristic
107C2×C8×C283C2311yescharacteristic
108C4⋊C4×C283—21no—
109C4⋊C4×C283C2311yescharacteristic
110C4⋊C4×C283C2311yescharacteristic
111C22⋊C4×C283—21no—
112C42×C283—21no—
113C42×C283C2311yescharacteristic
114C22×D283—21no—
115C22×D283—24no—
116C22×D283—42no—
117C22×D283—42no—
118C22×D283C2×D411yescharacteristic
119Dic566—21no—
120Dic566—24no—
121Dic566C22×C412yescomplemented
122D1132—21no—
123D1132C22×C412yes—
124C22⋊D283—24no—
125C2×Dic283—21no—
126C2×Dic283—21no—
127C2×Dic283—21no—
128C2×Dic283—42no—
129C2×Dic283C2×D411yescharacteristic
130C2×Dic283C2×D411yescharacteristic
131C2×Dic283C2×D411yescharacteristic
132C4×D283—24no—
133C4×D283—22no—
134C4×D283—22no—
135C4×D283—42no—
136C4×D283—42no—
137C4×D283—42no—
138C4×D283—42no—
139C4×D283C22×C412yes—
140C4×D283#4112yes—
141C283⋊C8—21no—
142C283⋊C8C22×C412yescomplemented
143C23×C283—21no—
144Q8×C283—21no—
145Q8×C283C22×C412yescomplemented
146D4×C283—21no—
147D4×C283C22×C412yes—
148C2×C4×C283—21no—
149C2×C4×C283—21no—
150C2×C4×C283—21no—
151C2×C4×C283—42no—
152C2×C4×C283C2×D411yescharacteristic
153C2×C4×C283C2×D411yescharacteristic
154C2×C4×C283C2411yescharacteristic
155C8×C283—21no—
156C8×C283C22×C412yescomplemented
157C22×C283—22no—
158C22×C283—41no—
159C22×C283—41no—
160C22×C283C22×D411yescharacteristic
161C2×D283—22no—
162C2×D283—41no—
163C2×D283—41no—
164C2×D283—48no—
165C2×D283C4×D412yes—
166C2×D283AGL(1,ℤ/8)12yes—
167C2×D283#13712yes—
168C4×C283—22no—
169C4×C283—21no—
170C4×C283—21no—
171C4×C283—41no—
172C4×C283—41no—
173C4×C283C23×C411yescharacteristic
174C4×C283C2×#4111yescharacteristic
175Dic283—22no—
176Dic283—21no—
177Dic283—21no—
178Dic283—41no—
179Dic283—41no—
180Dic283C4×D412yes—
181C2×C283—42no—
182C2×C283C2×C4×D411yescharacteristic
183C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C283C2×#13711yescharacteristic
185D283—42no—
186D283#44014yesdirect product factor
187C283C2×#44011yescharacteristic, complemented, Sylow
188C2×#440—2831nomaximal, Sylow
189C22×SD16—2831no—
190C2×C4×Q8—2831no—
191C2×C4×D4—2831no—
192#440—2831no—
193#440—2831no—
194#440—2831no—
195#440—2831no—
196#440—2831no—
197#440—2831no—
198#440—2831no—
199#440D28311yescharacteristic, direct product factor
200C2×#107—2831no—
201C2×#103—2831no—
202C2×#102—2831no—
203C2×#97—2831no—
204C22×Q8—2831no—
205C22×D4—2831no—
206C23×C4—5661no—
207C2×SD16—2831no—
208C2×SD16—2831no—
209C2×SD16—2838no—
210C2×SD16—2831no—
211C2×SD16C2×D28311yescharacteristic
212C22×C8—2831no—
213C22×C8—2831no—
214C4×Q8—2831no—
215C4×Q8—2831no—
216C4×Q8—2831no—
217C4×Q8—5661no—
218C4×Q8—5661no—
219C4×Q8C2×D28311yescharacteristic, complemented
220C4×D4—2831no—
221C4×D4—2831no—
222C4×D4—2831no—
223C4×D4—5661no—
224C4×D4—5661no—
225C4×D4C2×D28311yescharacteristic
226C2×C4⋊C4—2831no—
227C2×C4⋊C4—2831no—
228C2×C4⋊C4—5661no—
229C2×C22⋊C4—5661no—
230C2×C42—2831no—
231C2×C42—5661no—
232#107—2831no—
233#107—2831no—
234#107—2831no—
235#107C2×D28311yescharacteristic, complemented
236#103—2831no—
237#103—2831no—
238#103—2831no—
239#103C2×D28311yescharacteristic, complemented
240#102—2831no—
241#102—2831no—
242#102—2831no—
243#102C2×D28311yescharacteristic
244#97—2831no—
245#97—2831no—
246#97—2831no—
247#97C2×D28311yescharacteristic, complemented
248C24—5661no—
249C2×Q8—2834no—
250C2×Q8—2831no—
251C2×Q8—5661no—
252C2×Q8—5662no—
253C2×Q8C22×D28311yescharacteristic
254C2×D4—2834no—
255C2×D4—2831no—
256C2×D4—5662no—
257C2×D4—5661no—
258C2×D4C22×D28311yescharacteristic
259C22×C4—21no—
260C22×C4—2831no—
261C22×C4—2831no—
262C22×C4—2831no—
263C22×C4—5661no—
264C22×C4—5661no—
265C22×C4—5661no—
266C22×C4—5661no—
267C22×C4—5661no—
268C22×C4—5661no—
269C22×C4—11324no—
270SD16—2834no—
271SD16—2834no—
272SD16—2834no—
273SD16C4×D28314yescomplemented
274C2×C8—2831no—
275C2×C8—2834no—
276C2×C8—2831no—
277C2×C8—5662no—
278C2×C8C22×D28311yescharacteristic
279C2×C8C22×D28311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—2831no—
282C4⋊C4—2831no—
283C4⋊C4—5661no—
284C4⋊C4—5661no—
285C4⋊C4—5661no—
286C4⋊C4—5661no—
287C4⋊C4—5661no—
288C4⋊C4C22×D28311yescharacteristic
289C4⋊C4C22×D28311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—5661no—
292C22⋊C4—5661no—
293C22⋊C4—5661no—
294C42—21no—
295C42—2831no—
296C42—2831no—
297C42—2831no—
298C42—5661no—
299C42—5661no—
300C42—5661no—
301C42C22×D28311yescharacteristic
302C23—21no—
303C23—2831no—
304C23—5664no—
305C23—5661no—
306C23—11322no—
307C23—11322no—
308Q8—21no—
309Q8—2832no—
310Q8—5664no—
311Q8—5661no—
312Q8C2×C4×D28312yescomplemented
313D4—21no—
314D4—2832no—
315D4—5664no—
316D4—5661no—
317D4C2×C4×D28312yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—2831no—
323C2×C4—2832no—
324C2×C4—2832no—
325C2×C4—2831no—
326C2×C4—2831no—
327C2×C4—5662no—
328C2×C4—5662no—
329C2×C4—5664no—
330C2×C4—5661no—
331C2×C4—5661no—
332C2×C4—5661no—
333C2×C4—11322no—
334C2×C4—11322no—
335C2×C4—11322no—
336C2×C4—11322no—
337C2×C4—11322no—
338C2×C4D4×D28311yescharacteristic
339C2×C4D4×D28311yescharacteristic
340C2×C4C23×D28311yescharacteristic
341C8—21no—
342C8—2832no—
343C8—5661no—
344C8C2×C4×D28312yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—2832no—
349C22—2832no—
350C22—2832no—
351C22—5662no—
352C22—11328no—
353C22—11321no—
354C22—11321no—
355C22C2×D4×D28311yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—2832no—
362C4—5661no—
363C4—5661no—
364C4—5662no—
365C4—11321no—
366C4—11321no—
367C4C22×C4×D28311yescharacteristic
368C4#41×D28311yescharacteristic
369C2—42no—
370C2—2834no—
371C2—11322no—
372C2C4×D4×D28311yescharacteristic
373C2AGL(1,ℤ/8)×D28311yescharacteristic
374C2#137×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#440×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×D283C22
cosocleC2×C4×C283C24
hypercenter#440D283
hypocenterC283C2×#440
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D283C2semidirect
4. #31826568C2semidirect
5. #31826567C2semidirect
6. #31826566C2semidirect
7. #31826565C2semidirect
8. #31826564C2semidirect
9. #31826563C2semidirect
10. #31826562C2semidirect
11. #107×D283C2semidirect
12. #103×D283C2semidirect
14. #97×D283C2semidirect
15. #440×C283C2semidirect
22. SD16×D283C4semidirect
25. Q8×Dic283C22semidirect
27. C4×Dic566C22semidirect
29. #22583575C22semidirect
41. #22583544C22semidirect
42. #22583543C22semidirect
43. #22583543C22semidirect
44. #22583535C22semidirect
45. #22583534C22semidirect
46. #22583533C22semidirect
50. #22583521C22semidirect
51. #22583520C22semidirect
52. #22583520C22semidirect
54. C4×Q8×C283C22semidirect
56. #107×C283C22semidirect
57. #103×C283C22semidirect
59. #97×C283C22semidirect
64. Q8×D283C2×C4semidirect
79. #17985381C2×C4semidirect
80. #17985380C2×C4semidirect
81. #17985379C2×C4semidirect
85. C8×D283C2×C4semidirect
105. SD16×C283C2×C4semidirect
121. Dic566C22×C4semidirect
142. C283⋊C8C22×C4semidirect
145. Q8×C283C22×C4semidirect
156. C8×C283C22×C4semidirect
186. D283#440direct (N × H)
187. C283C2×#440semidirect
199. #440D283direct (N × H)
219. C4×Q8C2×D283semidirect
235. #107C2×D283semidirect
239. #103C2×D283semidirect
247. #97C2×D283semidirect
273. SD16C4×D283semidirect
312. Q8C2×C4×D283semidirect
344. C8C2×C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D2832
C4×Q8×D2832
C4×D4×D2832
#318265682
#318265672
#318265662
#318265652
#318265642
#318265632
#318265622
#107×D2832
#103×D2832
#102×D2832
#97×D2832
#440×C2832
C2×#440283