Finite Group Databasebeta

← #490×D89 #26030584

Subgroups — #490×D89 #26030584

Order 11392.

488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#127×D89C211yesmaximal, characteristic
2#125×D89C211yesmaximal, characteristic, complemented
3#19151964C211yesmaximal, characteristic, complemented
4#19151963C211yesmaximal, characteristic, complemented
5#19151962C211yesmaximal, characteristic, complemented
6#19151961C214yesmaximal, complemented
7#102×D89C214yesmaximal, complemented
8#97×D89C211yesmaximal, characteristic, complemented
9#490×C89C211yesmaximal, characteristic, complemented
10C2×D4×D89—22no—
11C2×D4×D89C2212yes—
12C2×C8×D89C2212yes—
13#15668009C2211yescharacteristic
14#15668008—22no—
15#15668008C2212yes—
16#15668004C2211yescharacteristic, complemented
17#15668003C2212yescomplemented
18#15668002—22no—
19C4⋊C4×D89—22no—
20C4⋊C4×D89C2212yes—
21C42×D89C2211yescharacteristic
22#15667934C2214yescomplemented
23#15667933C2214yescomplemented
24#15667932C2214yescomplemented
25#15667923C2211yescharacteristic, complemented
26#15667922C2212yescomplemented
27#127×C89C2211yescharacteristic
28#125×C89C2211yescharacteristic, complemented
29#102×C89C2214yescomplemented
30#97×C89C2211yescharacteristic, complemented
31C23×D89—22no—
32C2×D356—22no—
33C2×D356C2312yes—
34C2×C22⋊D89—22no—
35C2×C22⋊D89—24no—
36D4×D89—28no—
37D4×D89—48no—
38C2×C4×D89—22no—
39C2×C4×D89D412yes—
40C2×C4×D89C2311yescharacteristic
41C2×#10623494C2312yes—
42C8×D89—24no—
43C4⋊Dic89—22no—
44C4⋊Dic89C2312yes—
45#13083553—22no—
46#13083553—22no—
47#13083553—22no—
48C4×Dic89D412yes—
49C4×Dic89C2311yescharacteristic
50C2×D4×C89—22no—
51C2×D4×C89C2312yes—
52C2×C8×C89C2312yes—
53C4⋊C4×C89—22no—
54C4⋊C4×C89C2312yes—
55C42×C89C2311yescharacteristic
56C23×C89—22no—
57C22×D89—22no—
58C22×D89—44no—
59C22×D89—48no—
60C22×D89C2×D411yescharacteristic
61D4×C89—24no—
62D4×C89—44no—
63C2×C4×C89—22no—
64C2×C4×C89C2×D412yes—
65C2×C4×C89C2411yescharacteristic
66C22⋊D89—48no—
67C22⋊D89—44no—
68C2×Dic89—22no—
69C2×Dic89C2×D412yes—
70C2×Dic89C2×D411yescharacteristic
71D356—24no—
72D356—44no—
73C4×D89—24no—
74C4×D89—44no—
75C4×D89#4114yes—
76C8×C89—22no—
77#10623494—22no—
78C22×C89—42no—
79C22×C89—44no—
80C22×C89C22×D411yescharacteristic
81C2×D89—42no—
82C2×D89—44no—
83C2×D89—88no—
84C2×D89#12412yes—
85C2×D89AGL(1,ℤ/8)14yes—
86C4×C89—22no—
87C4×C89—42no—
88C4×C89C2×#4112yes—
89Dic89—22no—
90Dic89—42no—
91Dic89#12412yes—
92C2×C89—82no—
93C2×C89C2×#12411yescharacteristic
94C2×C89C2×AGL(1,ℤ/8)12yes—
95D89—82no—
96D89#49014yesdirect product factor
97C2×#490—891nomaximal, Sylow
98C89C2×#49011yescharacteristic, complemented, Sylow
99C2×#127—891no—
100C2×#125—891no—
101#490—891no—
102#490—891no—
103#490—894no—
104#490—891no—
105#490D8911yescharacteristic, direct product factor
106C2×#102—894no—
107C2×#97—891no—
108C22×D4—892no—
109C22×D4—1782no—
110C22×C8—892no—
111#127—892no—
112#127—891no—
113#127—1782no—
114#127C2×D8911yescharacteristic
115#125—892no—
116#125—891no—
117#125—1782no—
118#125C2×D8911yescharacteristic, complemented
119C2×C4⋊C4—892no—
120C2×C4⋊C4—1782no—
121C2×C42—891no—
122#102—894no—
123#102—894no—
124#102—894no—
125#102C2×D8914yescomplemented
126#97—892no—
127#97—891no—
128#97C2×D8911yescharacteristic, complemented
129C24—1782no—
130C2×D4—22no—
131C2×D4—892no—
132C2×D4—3568no—
133C2×D4—1788no—
134C2×D4—1784no—
135C2×D4—1782no—
136C2×D4—1782no—
137C2×D4C22×D8912yes—
138C22×C4—891no—
139C22×C4—892no—
140C22×C4—1782no—
141C2×C8—892no—
142C2×C8—1784no—
143C2×C8C22×D8912yes—
144C4⋊C4—22no—
145C4⋊C4—892no—
146C4⋊C4—1782no—
147C4⋊C4—1782no—
148C4⋊C4—1782no—
149C4⋊C4—1782no—
150C4⋊C4C22×D8912yes—
151C42—892no—
152C42—891no—
153C42C22×D8911yescharacteristic
154C23—22no—
155C23—891no—
156C23—3568no—
157C23—3564no—
158C23—1782no—
159D4—24no—
160D4—44no—
161D4—3564no—
162D4—3564no—
163D4—3568no—
164D4—1784no—
165C2×C4—22no—
166C2×C4—891no—
167C2×C4—894no—
168C2×C4—892no—
169C2×C4—3564no—
170C2×C4—1784no—
171C2×C4—1782no—
172C2×C4D4×D8912yes—
173C2×C4C23×D8911yescharacteristic
174C8—22no—
175C8—1782no—
176C22—42no—
177C22—44no—
178C22—892no—
179C22—894no—
180C22—3562no—
181C22—3564no—
182C22—7128no—
183C22C2×D4×D8911yescharacteristic
184C4—22no—
185C4—42no—
186C4—892no—
187C4—3562no—
188C4—1782no—
189C4#41×D8912yes—
190C2—82no—
191C2—894no—
192C2—7122no—
193C2#124×D8911yescharacteristic
194C2AGL(1,ℤ/8)×D8912yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#490×C89C2
socleC22×C89C22×D4
prime radical#127×D89C2
hypercenter#490D89
hypocenterC89C2×#490
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D89C2semidirect
3. #19151964C2semidirect
4. #19151963C2semidirect
5. #19151962C2semidirect
6. #19151961C2semidirect
7. #102×D89C2semidirect
8. #97×D89C2semidirect
9. #490×C89C2semidirect
16. #15668004C22semidirect
17. #15668003C22semidirect
22. #15667934C22semidirect
23. #15667933C22semidirect
24. #15667932C22semidirect
25. #15667923C22semidirect
26. #15667922C22semidirect
28. #125×C89C22semidirect
29. #102×C89C22semidirect
30. #97×C89C22semidirect
96. D89#490direct (N × H)
98. C89C2×#490semidirect
105. #490D89direct (N × H)
118. #125C2×D89semidirect
125. #102C2×D89semidirect
128. #97C2×D89semidirect

Maximal subgroups

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

subgroupindex
#127×D892
#125×D892
#191519642
#191519632
#191519622
#191519612
#102×D892
#97×D892
#490×C892
C2×#49089