Finite Group Databasebeta

← #490×D151 #34079442

Subgroups — #490×D151 #34079442

Order 19328.

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×D151C211yesmaximal, characteristic
2#125×D151C211yesmaximal, characteristic, complemented
3#23752578C211yesmaximal, characteristic, complemented
4#23752577C211yesmaximal, characteristic, complemented
5#23752576C211yesmaximal, characteristic, complemented
6#23752575C214yesmaximal, complemented
7#102×D151C214yesmaximal, complemented
8#97×D151C211yesmaximal, characteristic, complemented
9#490×C151C211yesmaximal, characteristic, complemented
10C2×D4×D151—22no—
11C2×D4×D151C2212yes—
12C2×C8×D151C2212yes—
13#18012736C2211yescharacteristic
14#18012735—22no—
15#18012735C2212yes—
16#18012731C2211yescharacteristic, complemented
17#18012730C2212yescomplemented
18#18012729—22no—
19C4⋊C4×D151—22no—
20C4⋊C4×D151C2212yes—
21C42×D151C2211yescharacteristic
22#18012661C2214yescomplemented
23#18012660C2214yescomplemented
24#18012659C2214yescomplemented
25#18012650C2211yescharacteristic, complemented
26#18012649C2212yescomplemented
27#127×C151C2211yescharacteristic
28#125×C151C2211yescharacteristic, complemented
29#102×C151C2214yescomplemented
30#97×C151C2211yescharacteristic, complemented
31C23×D151—22no—
32C2×D604—22no—
33C2×D604C2312yes—
34C2×C22⋊D151—22no—
35C2×C22⋊D151—24no—
36D4×D151—28no—
37D4×D151—48no—
38C2×C4×D151—22no—
39C2×C4×D151D412yes—
40C2×C4×D151C2311yescharacteristic
41C2×C151⋊C8C2312yes—
42C8×D151—24no—
43C4⋊Dic151—22no—
44C4⋊Dic151C2312yes—
45Dic151⋊C4—22no—
46Dic151⋊C4—22no—
47Dic151⋊C4—22no—
48C4×Dic151D412yes—
49C4×Dic151C2311yescharacteristic
50C2×D4×C151—22no—
51C2×D4×C151C2312yes—
52C2×C8×C151C2312yes—
53C4⋊C4×C151—22no—
54C4⋊C4×C151C2312yes—
55C42×C151C2311yescharacteristic
56C22×D151—22no—
57C22×D151—44no—
58C22×D151—48no—
59C22×D151C2×D411yescharacteristic
60D604—24no—
61D604—44no—
62C22⋊D151—48no—
63C22⋊D151—44no—
64C2×Dic151—22no—
65C2×Dic151C2×D412yes—
66C2×Dic151C2×D411yescharacteristic
67C4×D151—24no—
68C4×D151—44no—
69C4×D151#4114yes—
70C151⋊C8—22no—
71C23×C151—22no—
72D4×C151—24no—
73D4×C151—44no—
74C2×C4×C151—22no—
75C2×C4×C151C2×D412yes—
76C2×C4×C151C2411yescharacteristic
77C8×C151—22no—
78C22×C151—42no—
79C22×C151—44no—
80C22×C151C22×D411yescharacteristic
81C2×D151—42no—
82C2×D151—44no—
83C2×D151—88no—
84C2×D151#12412yes—
85C2×D151AGL(1,ℤ/8)14yes—
86C4×C151—22no—
87C4×C151—42no—
88C4×C151C2×#4112yes—
89Dic151—22no—
90Dic151—42no—
91Dic151#12412yes—
92C2×C151—82no—
93C2×C151C2×#12411yescharacteristic
94C2×C151C2×AGL(1,ℤ/8)12yes—
95D151—82no—
96D151#49014yesdirect product factor
97C151C2×#49011yescharacteristic, complemented, Sylow
98C2×#490—1511nomaximal, Sylow
99C2×#127—1511no—
100C2×#125—1511no—
101#490—1511no—
102#490—1511no—
103#490—1514no—
104#490—1511no—
105#490D15111yescharacteristic, direct product factor
106C2×#102—1514no—
107C2×#97—1511no—
108C22×D4—3022no—
109C22×D4—1512no—
110C22×C8—1512no—
111#127—3022no—
112#127—1512no—
113#127—1511no—
114#127C2×D15111yescharacteristic
115#125—3022no—
116#125—1512no—
117#125—1511no—
118#125C2×D15111yescharacteristic, complemented
119C2×C4⋊C4—3022no—
120C2×C4⋊C4—1512no—
121C2×C42—1511no—
122#102—1514no—
123#102—1514no—
124#102—1514no—
125#102C2×D15114yescomplemented
126#97—1512no—
127#97—1511no—
128#97C2×D15111yescharacteristic, complemented
129C24—3022no—
130C2×D4—22no—
131C2×D4—3028no—
132C2×D4—3022no—
133C2×D4—3024no—
134C2×D4—3022no—
135C2×D4—6048no—
136C2×D4—1512no—
137C2×D4C22×D15112yes—
138C22×C4—3022no—
139C22×C4—1512no—
140C22×C4—1511no—
141C2×C8—3024no—
142C2×C8—1512no—
143C2×C8C22×D15112yes—
144C4⋊C4—22no—
145C4⋊C4—3022no—
146C4⋊C4—3022no—
147C4⋊C4—3022no—
148C4⋊C4—3022no—
149C4⋊C4—1512no—
150C4⋊C4C22×D15112yes—
151C42—1512no—
152C42—1511no—
153C42C22×D15111yescharacteristic
154C23—22no—
155C23—3022no—
156C23—6044no—
157C23—6048no—
158C23—1511no—
159D4—24no—
160D4—44no—
161D4—3024no—
162D4—6044no—
163D4—6048no—
164D4—6044no—
165C2×C4—22no—
166C2×C4—3024no—
167C2×C4—3022no—
168C2×C4—6044no—
169C2×C4—1512no—
170C2×C4—1511no—
171C2×C4—1514no—
172C2×C4D4×D15112yes—
173C2×C4C23×D15111yescharacteristic
174C8—22no—
175C8—3022no—
176C22—42no—
177C22—44no—
178C22—6042no—
179C22—6044no—
180C22—1512no—
181C22—1514no—
182C22—12088no—
183C22C2×D4×D15111yescharacteristic
184C4—22no—
185C4—42no—
186C4—3022no—
187C4—6042no—
188C4—1512no—
189C4#41×D15112yes—
190C2—82no—
191C2—1514no—
192C2—12082no—
193C2#124×D15111yescharacteristic
194C2AGL(1,ℤ/8)×D15112yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#490×C151C2
socleC22×C151C22×D4
prime radical#127×D151C2
hypercenter#490D151
hypocenterC151C2×#490
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D151C2semidirect
3. #23752578C2semidirect
4. #23752577C2semidirect
5. #23752576C2semidirect
6. #23752575C2semidirect
7. #102×D151C2semidirect
8. #97×D151C2semidirect
9. #490×C151C2semidirect
16. #18012731C22semidirect
17. #18012730C22semidirect
22. #18012661C22semidirect
23. #18012660C22semidirect
24. #18012659C22semidirect
25. #18012650C22semidirect
26. #18012649C22semidirect
28. #125×C151C22semidirect
29. #102×C151C22semidirect
30. #97×C151C22semidirect
96. D151#490direct (N × H)
97. C151C2×#490semidirect
105. #490D151direct (N × H)
118. #125C2×D151semidirect
125. #102C2×D151semidirect
128. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#127×D1512
#125×D1512
#237525782
#237525772
#237525762
#237525752
#102×D1512
#97×D1512
#490×C1512
C2×#490151