Finite Group Databasebeta

← #31819541

Subgroups — #31819541

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#22581754C212yesmaximal, complemented
2#22581389C212yesmaximal, complemented
3#22581387C214yesmaximal, complemented
4#22581385C211yesmaximal, characteristic, complemented
5#22581382C212yesmaximal, complemented
6D16×D139C212yesmaximal, complemented
7#22581369C211yesmaximal, characteristic, complemented
8C2×D16×C139C211yesmaximal, characteristic, complemented
9#17984887—22no—
10#17984868—22no—
11#17984866—24no—
12#17984864C2212yescomplemented
13#17984861C2214yescomplemented
14D8×D139C2214yescomplemented
15#17984848C2211yescharacteristic
16Dic1112C2211yescharacteristic, complemented
17#17984787C2212yescomplemented
18#17984786C2214yescomplemented
19D2224C2211yescharacteristic, complemented
20#17984783C2214yescomplemented
21#17984782C2211yescharacteristic, complemented
22#17984781C2212yescomplemented
23C16×D139C2212yescomplemented
24C2×D8×C139C2212yescomplemented
25D16×C139C2212yescomplemented
26D16×C139C2212yescomplemented
27C2×C16×C139C2211yescharacteristic, complemented
28#14555785—22no—
29#14555785D411yescharacteristic
30#14555784—24no—
31#14555784—42no—
32C2×C22⋊D139—44no—
33D4×D139—24no—
34D4×D139—42no—
35Dic556C2312yes—
36#14555774—22no—
37#14555773—24no—
38D1112C2312yes—
39#14555770—24no—
40#14555769D411yescharacteristic
41#14555768D412yes—
42C8×D139C2312yes—
43C139⋊C16C2312yes—
44C2×D4×C139—22no—
45D8×C139—22no—
46D8×C139C2314yes—
47C2×C8×C139C2311yescharacteristic
48C16×C139C2311yescharacteristic
49C16×C139C2311yescharacteristic
50C22×D139—44no—
51Dic278—22no—
52Dic278D811yescharacteristic
53D556—22no—
54D556D811yescharacteristic
55C22⋊D139—42no—
56C22⋊D139—44no—
57C22⋊D139—44no—
58C22⋊D139D812yes—
59C2×Dic139—44no—
60C4×D139—42no—
61C4×D139C2×D412yes—
62C139⋊C8C2×D412yes—
63C23×C139—42no—
64D4×C139—24no—
65D4×C139—42no—
66C2×C4×C139C2×D411yescharacteristic
67C8×C139C2×D411yescharacteristic
68C8×C139C2411yescharacteristic
69C22×C139—44no—
70C22×C139—162no—
71C22×C139C2×D811yescharacteristic
72C2×D139—42no—
73C2×D139—164no—
74C2×D139C2×D812yes—
75C4×C139C2×D811yescharacteristic
76C4×C139C22×D411yescharacteristic
77Dic139—42no—
78Dic139C2×D812yes—
79C2×C139—21no—
80C2×C139—84no—
81C2×C139C22×D811yescharacteristic
82D139—22no—
83D139—82no—
84C139#341511yescharacteristic, complemented, Sylow
85#3415—1391nomaximal, Sylow
86#576—1392no—
87#509—1392no—
88#509—1394no—
89#508—1392no—
90#508—1391no—
91C2×D16—1392no—
92C2×D16D13911yescharacteristic, complemented
93#504—1391no—
94H(5,𝔽2)—2782no—
95AGL(1,ℤ/8)—2784no—
96AGL(1,ℤ/8)—2782no—
97#135—1394no—
98#135—1392no—
99C2×D8—1394no—
100C2×D8C2×D13912yescomplemented
101#131—1391no—
102Q32—1391no—
103SD32—1394no—
104SD32—1392no—
105D16—1394no—
106D16—1391no—
107D16C2×D13912yescomplemented
108D16C2×D13912yescomplemented
109M32—1391no—
110M32—1392no—
111C2×C16—1392no—
112C2×C16C2×D13911yescharacteristic, complemented
113#41—2784no—
114#41—2782no—
115#41—5562no—
116#41—1391no—
117C2×D4—22no—
118C2×D4—2784no—
119C2×D4—5562no—
120C2×D4—5564no—
121Q16—1392no—
122SD16—2784no—
123SD16—2782no—
124D8—22no—
125D8—2784no—
126D8—1392no—
127D8C22×D13914yes—
128M16—1391no—
129M16—1392no—
130C2×C8—1392no—
131C2×C8C22×D13911yescharacteristic
132C16—1392no—
133C16C22×D13911yescharacteristic
134C16C22×D13911yescharacteristic
135C23—42no—
136C23—5564no—
137Q8—2782no—
138Q8—1391no—
139D4—24no—
140D4—42no—
141D4—2782no—
142D4—5564no—
143D4—5562no—
144D4—5564no—
145D4—1392no—
146D4—1391no—
147C2×C4—5564no—
148C2×C4—5562no—
149C2×C4—1392no—
150C2×C4D4×D13911yescharacteristic
151C8—1392no—
152C8D4×D13911yescharacteristic
153C8C23×D13911yescharacteristic
154C22—44no—
155C22—162no—
156C22—5562no—
157C22—1392no—
158C22—22244no—
159C22D8×D13911yescharacteristic
160C4—5562no—
161C4—1392no—
162C4D8×D13911yescharacteristic
163C4C2×D4×D13911yescharacteristic
164C2—21no—
165C2—84no—
166C2—2782no—
167C2—11122no—
168C2C2×D8×D13911yescharacteristic
subgroupG/H
centerC2C2×D8×D139
commutator, cosocleC8×C139C24
FrattiniC8C23×D139
FittingC2×D16×C139C2
socleC2×C139C22×D8
hypercenterC2×D16D139
hypocenterC139#3415
LCSG ▷ C8×C139 ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #22581754C2semidirect
2. #22581389C2semidirect
3. #22581387C2semidirect
4. #22581385C2semidirect
5. #22581382C2semidirect
6. D16×D139C2semidirect
7. #22581369C2semidirect
8. C2×D16×C139C2semidirect
12. #17984864C22semidirect
13. #17984861C22semidirect
14. D8×D139C22semidirect
16. Dic1112C22semidirect
17. #17984787C22semidirect
18. #17984786C22semidirect
19. D2224C22semidirect
20. #17984783C22semidirect
21. #17984782C22semidirect
22. #17984781C22semidirect
23. C16×D139C22semidirect
24. C2×D8×C139C22semidirect
25. D16×C139C22semidirect
26. D16×C139C22semidirect
27. C2×C16×C139C22semidirect
84. C139#3415semidirect
92. C2×D16D139semidirect
100. C2×D8C2×D139semidirect
107. D16C2×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
#225817542
#225813892
#225813872
#225813852
#225813822
D16×D1392
#225813692
C2×D16×C1392
#3415139