Finite Group Databasebeta

← #34082247

Subgroups — #34082247

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#23753013C212yesmaximal, complemented
2#23752648C212yesmaximal, complemented
3#23752646C214yesmaximal, complemented
4#23752644C211yesmaximal, characteristic, complemented
5#23752641C212yesmaximal, complemented
6D16×D151C212yesmaximal, complemented
7#23752628C211yesmaximal, characteristic, complemented
8C2×D16×C151C211yesmaximal, characteristic, complemented
9#18012784—22no—
10#18012765—22no—
11#18012763—24no—
12#18012761C2212yescomplemented
13#18012758C2214yescomplemented
14D8×D151C2214yescomplemented
15#18012745C2211yescharacteristic
16Dic1208C2211yescharacteristic, complemented
17#18012684C2212yescomplemented
18#18012683C2214yescomplemented
19D2416C2211yescharacteristic, complemented
20#18012680C2214yescomplemented
21#18012679C2211yescharacteristic, complemented
22#18012678C2212yescomplemented
23C16×D151C2212yescomplemented
24C2×D8×C151C2212yescomplemented
25D16×C151C2212yescomplemented
26D16×C151C2212yescomplemented
27C2×C16×C151C2211yescharacteristic, complemented
28#14559004—22no—
29#14559004D411yescharacteristic
30#14559003—24no—
31#14559003—42no—
32C2×C22⋊D151—44no—
33D4×D151—24no—
34D4×D151—42no—
35Dic604C2312yes—
36#14558993—22no—
37#14558992—24no—
38D1208C2312yes—
39#14558989—24no—
40#14558988D411yescharacteristic
41#14558987D412yes—
42C8×D151C2312yes—
43C151⋊C16C2312yes—
44C2×D4×C151—22no—
45D8×C151—22no—
46D8×C151C2314yes—
47C2×C8×C151C2311yescharacteristic
48C16×C151C2311yescharacteristic
49C16×C151C2311yescharacteristic
50C22×D151—44no—
51Dic302—22no—
52Dic302D811yescharacteristic
53D604—22no—
54D604D811yescharacteristic
55C22⋊D151—42no—
56C22⋊D151—44no—
57C22⋊D151—44no—
58C22⋊D151D812yes—
59C2×Dic151—44no—
60C4×D151—42no—
61C4×D151C2×D412yes—
62C151⋊C8C2×D412yes—
63C23×C151—42no—
64D4×C151—24no—
65D4×C151—42no—
66C2×C4×C151C2×D411yescharacteristic
67C8×C151C2×D411yescharacteristic
68C8×C151C2411yescharacteristic
69C22×C151—44no—
70C22×C151—162no—
71C22×C151C2×D811yescharacteristic
72C2×D151—42no—
73C2×D151—164no—
74C2×D151C2×D812yes—
75C4×C151C2×D811yescharacteristic
76C4×C151C22×D411yescharacteristic
77Dic151—42no—
78Dic151C2×D812yes—
79C2×C151—21no—
80C2×C151—84no—
81C2×C151C22×D811yescharacteristic
82D151—22no—
83D151—82no—
84C151#341511yescharacteristic, complemented, Sylow
85#3415—1511nomaximal, Sylow
86#576—1512no—
87#509—1512no—
88#509—1514no—
89#508—1512no—
90#508—1511no—
91C2×D16—1512no—
92C2×D16D15111yescharacteristic, complemented
93#504—1511no—
94H(5,𝔽2)—3022no—
95AGL(1,ℤ/8)—3024no—
96AGL(1,ℤ/8)—3022no—
97#135—1514no—
98#135—1512no—
99C2×D8—1514no—
100C2×D8C2×D15112yescomplemented
101#131—1511no—
102Q32—1511no—
103SD32—1514no—
104SD32—1512no—
105D16—1514no—
106D16—1511no—
107D16C2×D15112yescomplemented
108D16C2×D15112yescomplemented
109M32—1511no—
110M32—1512no—
111C2×C16—1512no—
112C2×C16C2×D15111yescharacteristic, complemented
113#41—3024no—
114#41—3022no—
115#41—6042no—
116#41—1511no—
117C2×D4—22no—
118C2×D4—3024no—
119C2×D4—6042no—
120C2×D4—6044no—
121Q16—1512no—
122SD16—3024no—
123SD16—3022no—
124D8—22no—
125D8—3024no—
126D8—1512no—
127D8C22×D15114yes—
128M16—1511no—
129M16—1512no—
130C2×C8—1512no—
131C2×C8C22×D15111yescharacteristic
132C16—1512no—
133C16C22×D15111yescharacteristic
134C16C22×D15111yescharacteristic
135C23—42no—
136C23—6044no—
137Q8—3022no—
138Q8—1511no—
139D4—24no—
140D4—42no—
141D4—3022no—
142D4—6044no—
143D4—6042no—
144D4—6044no—
145D4—1512no—
146D4—1511no—
147C2×C4—6044no—
148C2×C4—6042no—
149C2×C4—1512no—
150C2×C4D4×D15111yescharacteristic
151C8—1512no—
152C8D4×D15111yescharacteristic
153C8C23×D15111yescharacteristic
154C22—44no—
155C22—162no—
156C22—6042no—
157C22—24164no—
158C22—1512no—
159C22D8×D15111yescharacteristic
160C4—6042no—
161C4—1512no—
162C4D8×D15111yescharacteristic
163C4C2×D4×D15111yescharacteristic
164C2—21no—
165C2—84no—
166C2—3022no—
167C2—12082no—
168C2C2×D8×D15111yescharacteristic
subgroupG/H
centerC2C2×D8×D151
commutator, cosocleC8×C151C24
FrattiniC8C23×D151
FittingC2×D16×C151C2
socleC2×C151C22×D8
hypercenterC2×D16D151
hypocenterC151#3415
LCSG ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #23753013C2semidirect
2. #23752648C2semidirect
3. #23752646C2semidirect
4. #23752644C2semidirect
5. #23752641C2semidirect
6. D16×D151C2semidirect
7. #23752628C2semidirect
8. C2×D16×C151C2semidirect
12. #18012761C22semidirect
13. #18012758C22semidirect
14. D8×D151C22semidirect
16. Dic1208C22semidirect
17. #18012684C22semidirect
18. #18012683C22semidirect
19. D2416C22semidirect
20. #18012680C22semidirect
21. #18012679C22semidirect
22. #18012678C22semidirect
23. C16×D151C22semidirect
24. C2×D8×C151C22semidirect
25. D16×C151C22semidirect
26. D16×C151C22semidirect
27. C2×C16×C151C22semidirect
84. C151#3415semidirect
92. C2×D16D151semidirect
100. C2×D8C2×D151semidirect
107. D16C2×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
#237530132
#237526482
#237526462
#237526442
#237526412
D16×D1512
#237526282
C2×D16×C1512
#3415151