Finite Group Databasebeta

← #34082248

Subgroups — #34082248

Order 19328.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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#23753014C212yesmaximal, complemented
2#23752649C214yesmaximal, complemented
3#23752647C212yesmaximal, complemented
4#23752645C212yesmaximal, complemented
5C2×D2416C211yesmaximal, characteristic, complemented
6D16×D151C212yesmaximal, complemented
7#23752628C211yesmaximal, characteristic, complemented
8#508×C151C211yesmaximal, characteristic, complemented
9#18012785—22no—
10#18012766—24no—
11#18012764—22no—
12#18012762C2214yescomplemented
13C2×D1208C2212yescomplemented
14D8×D151C2214yescomplemented
15#18012745C2211yescharacteristic
16#18012682C2214yescomplemented
17D2416C2212yescomplemented
18D2416C2212yescomplemented
19#18012680C2214yescomplemented
20#18012679C2211yescharacteristic, complemented
21#18012678C2212yescomplemented
22C16×D151C2212yescomplemented
23#135×C151C2212yescomplemented
24Q32×C151C2211yescharacteristic, complemented
25SD32×C151C2212yescomplemented
26D16×C151C2211yescharacteristic, complemented
27C2×C16×C151C2211yescharacteristic, complemented
28#14559005—24no—
29#14559004—42no—
30#14559004D411yescharacteristic
31C2×D604—22no—
32C2×D604—42no—
33D4×D151—24no—
34D4×D151—44no—
35#14558991—24no—
36D1208—22no—
37D1208C2314yes—
38#14558989—24no—
39#14558988D411yescharacteristic
40#14558987D412yes—
41C8×D151C2312yes—
42C151⋊C16C2312yes—
43#41×C151—22no—
44Q16×C151C2312yes—
45SD16×C151—22no—
46D8×C151C2312yes—
47C2×C8×C151C2311yescharacteristic
48C16×C151C2311yescharacteristic
49C16×C151C2311yescharacteristic
50C22×D151—42no—
51C22×D151—44no—
52Dic302D811yescharacteristic
53D604—24no—
54D604—44no—
55D604—42no—
56D604D811yescharacteristic
57C22⋊D151—44no—
58C22⋊D151D812yes—
59C4×D151—44no—
60C4×D151C2×D412yes—
61C151⋊C8C2×D412yes—
62Q8×C151—22no—
63D4×C151—22no—
64D4×C151—42no—
65C2×C4×C151—42no—
66C2×C4×C151C2×D411yescharacteristic
67C8×C151C2×D411yescharacteristic
68C8×C151C2411yescharacteristic
69C22×C151—42no—
70C22×C151C2×D811yescharacteristic
71C2×D151—44no—
72C2×D151—164no—
73C2×D151—162no—
74C2×D151C2×D812yes—
75C4×C151—42no—
76C4×C151C2×D811yescharacteristic
77C4×C151C22×D411yescharacteristic
78Dic151C2×D812yes—
79C2×C151—21no—
80C2×C151—82no—
81C2×C151C22×D811yescharacteristic
82D151—22no—
83D151—84no—
84C151#341511yescharacteristic, complemented, Sylow
85#3415—1511nomaximal, Sylow
86#576—1512no—
87#509—1512no—
88#509—1514no—
89#508—1512no—
90#508D15111yescharacteristic, complemented
91C2×D16—1512no—
92C2×D16—1511no—
93#504—1511no—
94H(5,𝔽2)—3022no—
95AGL(1,ℤ/8)—3024no—
96AGL(1,ℤ/8)—3022no—
97#135—1514no—
98#135C2×D15112yescomplemented
99C2×D8—1514no—
100C2×D8—1512no—
101#131—1511no—
102Q32C2×D15111yescharacteristic, complemented
103SD32—1514no—
104SD32C2×D15112yescomplemented
105D16—1514no—
106D16—1512no—
107D16—1512no—
108D16C2×D15111yescharacteristic, complemented
109M32—1511no—
110M32—1512no—
111C2×C16—1512no—
112C2×C16C2×D15111yescharacteristic, complemented
113#41—22no—
114#41—3024no—
115#41—6042no—
116#41—1511no—
117C2×D4—3024no—
118C2×D4—3022no—
119C2×D4—6042no—
120C2×D4—6044no—
121Q16C22×D15112yes—
122SD16—22no—
123SD16—3024no—
124D8—3024no—
125D8—3022no—
126D8—1514no—
127D8C22×D15112yes—
128M16—1511no—
129M16—1512no—
130C2×C8—1512no—
131C2×C8C22×D15111yescharacteristic
132C16—1512no—
133C16C22×D15111yescharacteristic
134C16C22×D15111yescharacteristic
135C23—6044no—
136C23—6042no—
137Q8—22no—
138Q8—1511no—
139D4—22no—
140D4—42no—
141D4—3024no—
142D4—6044no—
143D4—6044no—
144D4—6042no—
145D4—1512no—
146D4—1511no—
147C2×C4—42no—
148C2×C4—6044no—
149C2×C4—1512no—
150C2×C4D4×D15111yescharacteristic
151C8—1512no—
152C8D4×D15111yescharacteristic
153C8C23×D15111yescharacteristic
154C22—42no—
155C22—6044no—
156C22—24162no—
157C22—24164no—
158C22—1512no—
159C22D8×D15111yescharacteristic
160C4—42no—
161C4—1512no—
162C4D8×D15111yescharacteristic
163C4C2×D4×D15111yescharacteristic
164C2—21no—
165C2—82no—
166C2—3022no—
167C2—12084no—
168C2C2×D8×D15111yescharacteristic
subgroupG/H
centerC2C2×D8×D151
commutator, cosocleC8×C151C24
FrattiniC8C23×D151
Fitting#508×C151C2
socleC2×C151C22×D8
hypercenter#508D151
hypocenterC151#3415
LCSG ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #23753014C2semidirect
2. #23752649C2semidirect
3. #23752647C2semidirect
4. #23752645C2semidirect
5. C2×D2416C2semidirect
6. D16×D151C2semidirect
7. #23752628C2semidirect
8. #508×C151C2semidirect
12. #18012762C22semidirect
13. C2×D1208C22semidirect
14. D8×D151C22semidirect
16. #18012682C22semidirect
17. D2416C22semidirect
18. D2416C22semidirect
19. #18012680C22semidirect
20. #18012679C22semidirect
21. #18012678C22semidirect
22. C16×D151C22semidirect
23. #135×C151C22semidirect
24. Q32×C151C22semidirect
25. SD32×C151C22semidirect
26. D16×C151C22semidirect
27. C2×C16×C151C22semidirect
84. C151#3415semidirect
90. #508D151semidirect
98. #135C2×D151semidirect
102. Q32C2×D151semidirect
104. SD32C2×D151semidirect
108. D16C2×D151semidirect
112. C2×C16C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530142
#237526492
#237526472
#237526452
C2×D24162
D16×D1512
#237526282
#508×C1512
#3415151