Finite Group Databasebeta

← #442×D283 #49130050

Subgroups — #442×D283 #49130050

Order 36224.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×D283C211yesmaximal, characteristic
2C4×D4×D283C212yesmaximal, complemented
3#31826578C211yesmaximal, characteristic, complemented
4#31826577C211yesmaximal, characteristic, complemented
5#31826576C211yesmaximal, characteristic, complemented
6#31826575C212yesmaximal, complemented
7#31826574C212yesmaximal, complemented
8#106×D283C211yesmaximal, characteristic, complemented
9#102×D283C212yesmaximal, complemented
10#97×D283C211yesmaximal, characteristic, complemented
11#442×C283C211yesmaximal, characteristic, complemented
12C2×D4×D283C2212yes—
13C22×C4×D283—22no—
14C2×D2264C2211yescharacteristic
15C2×#17985377C2212yes—
16D8×D283C418yescomplemented
17C2×C8×D283C2211yescharacteristic
18C2×C8×D283C2211yescharacteristic
19C4×D1132C2212yescomplemented
20D4×Dic283C2212yescomplemented
21#22583572C2212yescomplemented
22C4×C22⋊D283—22no—
23(C22⋊D283)⋊C4—22no—
24C4⋊C4×D283C2212yes—
25C22⋊C4×D283—22no—
26C42×D283C2211yescharacteristic
27#22583542C2211yescharacteristic, complemented
28#22583541C2212yescomplemented
29#22583532C2212yescomplemented
30#22583531C2212yescomplemented
31#22583530C2212yescomplemented
32#22583521C2211yescharacteristic, complemented
33#22583520C2211yescharacteristic, complemented
34#22583520C2211yescharacteristic, complemented
35C2×D8×C283C2211yescharacteristic
36C4×D4×C283C2212yescomplemented
37#106×C283C2211yescharacteristic, complemented
38#102×C283C2212yescomplemented
39#97×C283C2211yescharacteristic, complemented
40C23×D283—22no—
41C2×D1132C2312yes—
42C2×C22⋊D283—22no—
43D4×D283—24no—
44D4×D283C2×C418yescomplemented
45C22×Dic283—22no—
46C2×C4×D283—22no—
47C2×C4×D283—22no—
48C2×C4×D283—22no—
49C2×C4×D283—48no—
50C2×C4×D283D412yes—
51C2×C4×D283C2311yescharacteristic
52D2264C2×C414yescomplemented
53#17985377C2×C418yescomplemented
54C2×C283⋊C8C2311yescharacteristic
55C2×C283⋊C8C2311yescharacteristic
56C8×D283—22no—
57C8×D283C2×C414yescomplemented
58C4⋊Dic283C2312yes—
59Dic283⋊C4—22no—
60C22⋊Dic283—22no—
61(C2×D283)⋊C4—22no—
62(C2×D283)⋊C4—22no—
63C4×Dic283D412yes—
64C4×Dic283C2311yescharacteristic
65C2×D4×C283C2312yes—
66C22×C4×C283—22no—
67D8×C283C2×C414yescomplemented
68C2×C8×C283C2311yescharacteristic
69C2×C8×C283C2311yescharacteristic
70C4⋊C4×C283C2312yes—
71C22⋊C4×C283—22no—
72C42×C283C2311yescharacteristic
73C22×D283—22no—
74C22×D283—28no—
75C22×D283—44no—
76C22×D283—44no—
77C22×D283C2×D411yescharacteristic
78D1132—22no—
79D1132C22×C414yescomplemented
80C22⋊D283—28no—
81C2×Dic283—22no—
82C2×Dic283—44no—
83C2×Dic283C2×D412yes—
84C2×Dic283C2×D411yescharacteristic
85C4×D283—24no—
86C4×D283—44no—
87C4×D283—44no—
88C4×D283—44no—
89C4×D283C22×C412yes—
90C4×D283#4112yes—
91C283⋊C8—21no—
92C283⋊C8C22×C412yescomplemented
93C23×C283—22no—
94D4×C283—22no—
95D4×C283C22×C414yescomplemented
96C2×C4×C283—22no—
97C2×C4×C283—44no—
98C2×C4×C283C2×D412yes—
99C2×C4×C283C2411yescharacteristic
100C8×C283—21no—
101C8×C283C22×C412yescomplemented
102C22×C283—24no—
103C22×C283—42no—
104C22×C283—42no—
105C22×C283C22×D411yescharacteristic
106C2×D283—24no—
107C2×D283—42no—
108C2×D283—42no—
109C2×D283—416no—
110C2×D283C4×D412yes—
111C2×D283AGL(1,ℤ/8)14yes—
112C4×C283—22no—
113C4×C283—42no—
114C4×C283C23×C411yescharacteristic
115C4×C283C2×#4111yescharacteristic
116Dic283—22no—
117Dic283—42no—
118Dic283C4×D412yes—
119C2×C283—44no—
120C2×C283C2×C4×D411yescharacteristic
121C2×C283C2×AGL(1,ℤ/8)12yes—
122D283—44no—
123D283#44214yesdirect product factor
124C283C2×#44211yescharacteristic, complemented, Sylow
125C2×#442—2831nomaximal, Sylow
126C22×D8—2831no—
127C2×C4×D4—2832no—
128#442—2831no—
129#442—2832no—
130#442—2831no—
131#442—2832no—
132#442—2831no—
133#442D28311yescharacteristic, direct product factor
134C2×#106—2831no—
135C2×#102—2832no—
136C2×#97—2831no—
137C22×D4—2832no—
138C23×C4—5662no—
139C2×D8—2832no—
140C2×D8—2838no—
141C2×D8—2831no—
142C2×D8C2×D28311yescharacteristic
143C22×C8—2831no—
144C22×C8—2831no—
145C4×D4—2832no—
146C4×D4—2832no—
147C4×D4—2832no—
148C4×D4—5662no—
149C4×D4—5662no—
150C4×D4C2×D28312yescomplemented
151C2×C4⋊C4—2832no—
152C2×C22⋊C4—5662no—
153C2×C42—2831no—
154#106—2831no—
155#106—2832no—
156#106C2×D28311yescharacteristic, complemented
157#102—2832no—
158#102—2832no—
159#102—2832no—
160#102C2×D28312yescomplemented
161#97—2831no—
162#97—2831no—
163#97—2831no—
164#97C2×D28311yescharacteristic, complemented
165C24—5662no—
166C2×D4—2838no—
167C2×D4—2832no—
168C2×D4—5664no—
169C2×D4—5662no—
170C2×D4C22×D28312yes—
171C22×C4—22no—
172C22×C4—2831no—
173C22×C4—2832no—
174C22×C4—5662no—
175C22×C4—5662no—
176C22×C4—5662no—
177C22×C4—5662no—
178C22×C4—11328no—
179D8—2838no—
180D8—2834no—
181D8C4×D28314yescomplemented
182C2×C8—2831no—
183C2×C8—2834no—
184C2×C8—2831no—
185C2×C8—5662no—
186C2×C8C22×D28311yescharacteristic
187C2×C8C22×D28311yescharacteristic
188C4⋊C4—2832no—
189C4⋊C4—5662no—
190C4⋊C4C22×D28312yes—
191C22⋊C4—22no—
192C22⋊C4—5662no—
193C22⋊C4—5662no—
194C22⋊C4—5662no—
195C42—2832no—
196C42—2831no—
197C42C22×D28311yescharacteristic
198C23—22no—
199C23—2831no—
200C23—5668no—
201C23—5662no—
202C23—11324no—
203C23—11324no—
204D4—22no—
205D4—2834no—
206D4—5668no—
207D4—5662no—
208D4C2×C4×D28314yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—2831no—
212C2×C4—2832no—
213C2×C4—2832no—
214C2×C4—2832no—
215C2×C4—5664no—
216C2×C4—5662no—
217C2×C4—11324no—
218C2×C4—11324no—
219C2×C4—11324no—
220C2×C4—11324no—
221C2×C4D4×D28312yes—
222C2×C4C23×D28311yescharacteristic
223C8—21no—
224C8—2832no—
225C8—5661no—
226C8C2×C4×D28312yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—2834no—
231C22—2832no—
232C22—5664no—
233C22—113216no—
234C22—11322no—
235C22—11322no—
236C22C2×D4×D28311yescharacteristic
237C4—22no—
238C4—42no—
239C4—2832no—
240C4—5662no—
241C4—11322no—
242C4C22×C4×D28311yescharacteristic
243C4#41×D28311yescharacteristic
244C2—44no—
245C2—2834no—
246C2—11324no—
247C2C4×D4×D28311yescharacteristic
248C2AGL(1,ℤ/8)×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#442×C283C2
socleC22×C283C22×D4
prime radicalC2×D8×D283C2
cosocleC2×C4×C283C24
hypercenter#442D283
hypocenterC283C2×#442
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D283C2semidirect
3. #31826578C2semidirect
4. #31826577C2semidirect
5. #31826576C2semidirect
6. #31826575C2semidirect
7. #31826574C2semidirect
8. #106×D283C2semidirect
9. #102×D283C2semidirect
10. #97×D283C2semidirect
11. #442×C283C2semidirect
16. D8×D283C4semidirect
19. C4×D1132C22semidirect
20. D4×Dic283C22semidirect
21. #22583572C22semidirect
27. #22583542C22semidirect
28. #22583541C22semidirect
29. #22583532C22semidirect
30. #22583531C22semidirect
31. #22583530C22semidirect
32. #22583521C22semidirect
33. #22583520C22semidirect
34. #22583520C22semidirect
36. C4×D4×C283C22semidirect
37. #106×C283C22semidirect
38. #102×C283C22semidirect
39. #97×C283C22semidirect
44. D4×D283C2×C4semidirect
52. D2264C2×C4semidirect
53. #17985377C2×C4semidirect
57. C8×D283C2×C4semidirect
67. D8×C283C2×C4semidirect
79. D1132C22×C4semidirect
92. C283⋊C8C22×C4semidirect
95. D4×C283C22×C4semidirect
101. C8×C283C22×C4semidirect
123. D283#442direct (N × H)
124. C283C2×#442semidirect
133. #442D283direct (N × H)
150. C4×D4C2×D283semidirect
156. #106C2×D283semidirect
160. #102C2×D283semidirect
164. #97C2×D283semidirect
181. D8C4×D283semidirect
208. D4C2×C4×D283semidirect
226. C8C2×C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D2832
C4×D4×D2832
#318265782
#318265772
#318265762
#318265752
#318265742
#106×D2832
#102×D2832
#97×D2832
#442×C2832
C2×#442283