Finite Group Databasebeta

← #31819542

Subgroups — #31819542

Order 17792.

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#22581755C212yesmaximal, complemented
2#22581390C214yesmaximal, complemented
3#22581388C212yesmaximal, complemented
4#22581386C212yesmaximal, complemented
5C2×D2224C211yesmaximal, characteristic, complemented
6D16×D139C212yesmaximal, complemented
7#22581369C211yesmaximal, characteristic, complemented
8#508×C139C211yesmaximal, characteristic, complemented
9#17984888—22no—
10#17984869—24no—
11#17984867—22no—
12#17984865C2214yescomplemented
13C2×D1112C2212yescomplemented
14D8×D139C2214yescomplemented
15#17984848C2211yescharacteristic
16#17984785C2214yescomplemented
17D2224C2212yescomplemented
18D2224C2212yescomplemented
19#17984783C2214yescomplemented
20#17984782C2211yescharacteristic, complemented
21#17984781C2212yescomplemented
22C16×D139C2212yescomplemented
23#135×C139C2212yescomplemented
24Q32×C139C2211yescharacteristic, complemented
25SD32×C139C2212yescomplemented
26D16×C139C2211yescharacteristic, complemented
27C2×C16×C139C2211yescharacteristic, complemented
28#14555786—24no—
29#14555785—42no—
30#14555785D411yescharacteristic
31C2×D556—22no—
32C2×D556—42no—
33D4×D139—24no—
34D4×D139—44no—
35#14555772—24no—
36D1112—22no—
37D1112C2314yes—
38#14555770—24no—
39#14555769D411yescharacteristic
40#14555768D412yes—
41C8×D139C2312yes—
42C139⋊C16C2312yes—
43#41×C139—22no—
44Q16×C139C2312yes—
45SD16×C139—22no—
46D8×C139C2312yes—
47C2×C8×C139C2311yescharacteristic
48C16×C139C2311yescharacteristic
49C16×C139C2311yescharacteristic
50C22×D139—42no—
51C22×D139—44no—
52Dic278D811yescharacteristic
53D556—24no—
54D556—44no—
55D556—42no—
56D556D811yescharacteristic
57C22⋊D139—44no—
58C22⋊D139D812yes—
59C4×D139—44no—
60C4×D139C2×D412yes—
61C139⋊C8C2×D412yes—
62Q8×C139—22no—
63D4×C139—22no—
64D4×C139—42no—
65C2×C4×C139—42no—
66C2×C4×C139C2×D411yescharacteristic
67C8×C139C2×D411yescharacteristic
68C8×C139C2411yescharacteristic
69C22×C139—42no—
70C22×C139C2×D811yescharacteristic
71C2×D139—44no—
72C2×D139—164no—
73C2×D139—162no—
74C2×D139C2×D812yes—
75C4×C139—42no—
76C4×C139C2×D811yescharacteristic
77C4×C139C22×D411yescharacteristic
78Dic139C2×D812yes—
79C2×C139—21no—
80C2×C139—82no—
81C2×C139C22×D811yescharacteristic
82D139—22no—
83D139—84no—
84C139#341511yescharacteristic, complemented, Sylow
85#3415—1391nomaximal, Sylow
86#576—1392no—
87#509—1392no—
88#509—1394no—
89#508—1392no—
90#508D13911yescharacteristic, complemented
91C2×D16—1392no—
92C2×D16—1391no—
93#504—1391no—
94H(5,𝔽2)—2782no—
95AGL(1,ℤ/8)—2784no—
96AGL(1,ℤ/8)—2782no—
97#135—1394no—
98#135C2×D13912yescomplemented
99C2×D8—1394no—
100C2×D8—1392no—
101#131—1391no—
102Q32C2×D13911yescharacteristic, complemented
103SD32—1394no—
104SD32C2×D13912yescomplemented
105D16—1394no—
106D16—1392no—
107D16—1392no—
108D16C2×D13911yescharacteristic, complemented
109M32—1391no—
110M32—1392no—
111C2×C16—1392no—
112C2×C16C2×D13911yescharacteristic, complemented
113#41—22no—
114#41—2784no—
115#41—5562no—
116#41—1391no—
117C2×D4—2784no—
118C2×D4—2782no—
119C2×D4—5562no—
120C2×D4—5564no—
121Q16C22×D13912yes—
122SD16—22no—
123SD16—2784no—
124D8—2784no—
125D8—2782no—
126D8—1394no—
127D8C22×D13912yes—
128M16—1391no—
129M16—1392no—
130C2×C8—1392no—
131C2×C8C22×D13911yescharacteristic
132C16—1392no—
133C16C22×D13911yescharacteristic
134C16C22×D13911yescharacteristic
135C23—5564no—
136C23—5562no—
137Q8—22no—
138Q8—1391no—
139D4—22no—
140D4—42no—
141D4—2784no—
142D4—5564no—
143D4—5564no—
144D4—5562no—
145D4—1392no—
146D4—1391no—
147C2×C4—42no—
148C2×C4—5564no—
149C2×C4—1392no—
150C2×C4D4×D13911yescharacteristic
151C8—1392no—
152C8D4×D13911yescharacteristic
153C8C23×D13911yescharacteristic
154C22—42no—
155C22—5564no—
156C22—1392no—
157C22—22242no—
158C22—22244no—
159C22D8×D13911yescharacteristic
160C4—42no—
161C4—1392no—
162C4D8×D13911yescharacteristic
163C4C2×D4×D13911yescharacteristic
164C2—21no—
165C2—82no—
166C2—2782no—
167C2—11124no—
168C2C2×D8×D13911yescharacteristic
subgroupG/H
centerC2C2×D8×D139
commutator, cosocleC8×C139C24
FrattiniC8C23×D139
Fitting#508×C139C2
socleC2×C139C22×D8
hypercenter#508D139
hypocenterC139#3415
LCSG ▷ C8×C139 ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #22581755C2semidirect
2. #22581390C2semidirect
3. #22581388C2semidirect
4. #22581386C2semidirect
5. C2×D2224C2semidirect
6. D16×D139C2semidirect
7. #22581369C2semidirect
8. #508×C139C2semidirect
12. #17984865C22semidirect
13. C2×D1112C22semidirect
14. D8×D139C22semidirect
16. #17984785C22semidirect
17. D2224C22semidirect
18. D2224C22semidirect
19. #17984783C22semidirect
20. #17984782C22semidirect
21. #17984781C22semidirect
22. C16×D139C22semidirect
23. #135×C139C22semidirect
24. Q32×C139C22semidirect
25. SD32×C139C22semidirect
26. D16×C139C22semidirect
27. C2×C16×C139C22semidirect
84. C139#3415semidirect
90. #508D139semidirect
98. #135C2×D139semidirect
102. Q32C2×D139semidirect
104. SD32C2×D139semidirect
108. D16C2×D139semidirect
112. C2×C16C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225817552
#225813902
#225813882
#225813862
C2×D22242
D16×D1392
#225813692
#508×C1392
#3415139