Finite Group Databasebeta

← C2×#22581758 #31821157

Subgroups — C2×#22581758 #31821157

Order 17792.

1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.

normal subgroups only

This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 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
1C2×#17984888C212yesmaximal, complemented
2#22581758C2116yesmaximal, direct product factor
3C2×#17984870C216yesmaximal, complemented
4C2×#17984864C213yesmaximal, complemented
5C22×D1112C213yesmaximal, complemented
6C2×#131×C139C211yesmaximal, characteristic, complemented
7#17984888—28no—
8#17984888C22116yescomplemented
9C2×#14555786—22no—
10C2×#14555785C2216yescomplemented
11C22×D556C2216yescomplemented
12C2×D4×D139—26no—
13#17984870C22148yescomplemented
14#17984864C22124yescomplemented
15C2×Dic556C2211yescharacteristic, complemented
16C2×#14555774C2216yescomplemented
17C2×D1112C2213yescomplemented
18C2×D1112C2216yescomplemented
19C2×D1112C22124yescomplemented
20C2×#41×C139C2211yescharacteristic
21#131×C139C2218yescomplemented
22C2×M16×C139C2213yescomplemented
23C22×C8×C139C2213yescomplemented
24C23×D139—26no—
25#14555786—216no—
26#14555785—212no—
27#14555785C23124yescomplemented
28C2×Dic278C2312yes—
29C2×D556—26no—
30C2×D556—212no—
31C2×D556C2316yes—
32C2×D556C23124yescomplemented
33C2×C22⋊D139—26no—
34D4×D139—248no—
35C2×C4×D139—26no—
36Dic556C2314yescomplemented
37#14555774C23124yescomplemented
38D1112C23112yescomplemented
39D1112C23124yescomplemented
40#41×C139D414yes—
41#41×C139C2314yes—
42C2×Q8×C139D411yescharacteristic
43C2×D4×C139D413yes—
44C22×C4×C139C2313yes—
45M16×C139C23112yescomplemented
46C2×C8×C139C2311yescharacteristic
47C2×C8×C139C2313yes—
48C2×C8×C139C23112yescomplemented
49C22×D139—26no—
50C22×D139—224no—
51C22×D139—812no—
52Dic278—22no—
53Dic278C2414yes—
54D556—224no—
55D556—26no—
56D556C24112yes—
57C22⋊D139—224no—
58C2×Dic139—22no—
59C4×D139—224no—
60C23×C139C2×D413yes—
61Q8×C139C2×D414yes—
62D4×C139C2×D4112yes—
63C2×C4×C139C2×D413yes—
64C2×C4×C139C2×D416yes—
65C2×C4×C139C2411yescharacteristic
66C2×C4×C139C2416yes—
67C8×C139C2412yes—
68C8×C139C2416yes—
69C22×C139—26no—
70C22×C139C22×D416yes—
71C22×C139C22×D411yescharacteristic
72C2×D139—212no—
73C2×D139—412no—
74C2×D139—824no—
75C4×C139C22×D411yescharacteristic
76C4×C139C22×D416yes—
77C4×C139C2511yescharacteristic
78Dic139—24no—
79C2×C139—26no—
80C2×C139#57612yescomplemented
81C2×C139C23×D411yescharacteristic
82D139—412no—
83C139C2×#57611yescharacteristic, complemented, Sylow
84C2×#576—1391nomaximal, Sylow
85C2×H(5,𝔽2)—1392no—
86#576—13916no—
87C2×AGL(1,ℤ/8)—1396no—
88C2×#135—1393no—
89C22×D8—1393no—
90C2×#131D13911yescharacteristic, complemented
91H(5,𝔽2)—2788no—
92H(5,𝔽2)—13916no—
93C2×#41—2782no—
94C2×#41—1396no—
95C2×#41C2×D13911yescharacteristic
96C22×D4—2786no—
97C22×D4—1396no—
98AGL(1,ℤ/8)—13948no—
99#135—13924no—
100C2×Q16—1391no—
101C2×SD16—1396no—
102C2×D8—1393no—
103C2×D8—1396no—
104C2×D8—13924no—
105#131C2×D13918yescomplemented
106C2×M16C2×D13913yescomplemented
107C22×C8C2×D13913yescomplemented
108C24—2786no—
109#41—27816no—
110#41—27812no—
111#41—13924no—
112#41D55614yes—
113#41C22×D13914yes—
114C2×Q8—1392no—
115C2×Q8D55611yescharacteristic
116C2×D4—2786no—
117C2×D4—27848no—
118C2×D4—2786no—
119C2×D4—27812no—
120C2×D4—1396no—
121C2×D4—13924no—
122C2×D4D55613yes—
123C22×C4—2786no—
124C22×C4C22×D13913yes—
125Q16—1394no—
126SD16—13924no—
127D8—13912no—
128D8—13924no—
129M16C22×D139112yescomplemented
130C2×C8C22×D13911yescharacteristic
131C2×C8C22×D13913yes—
132C2×C8C22×D139112yescomplemented
133C23—2786no—
134C23—27824no—
135C23—111212no—
136C23C2×D55613yes—
137Q8—2782no—
138Q8—1394no—
139Q8C2×D55614yes—
140D4—27824no—
141D4—27824no—
142D4—2786no—
143D4—13912no—
144D4C2×D556112yes—
145C2×C4—2782no—
146C2×C4—27824no—
147C2×C4C2×D55616yes—
148C2×C4C2×D55613yes—
149C2×C4C23×D13916yes—
150C2×C4C23×D13911yescharacteristic
151C8C23×D13912yes—
152C8C23×D13916yes—
153C22—26no—
154C22—27812no—
155C22—55612no—
156C22—111224no—
157C22C22×D55616yes—
158C22C22×D55611yescharacteristic
159C4—2784no—
160C4C22×D55616yes—
161C4C22×D55611yescharacteristic
162C4C24×D13911yescharacteristic
163C2—26no—
164C2—55612no—
165C2#2258175812yesdirect product factor
166C2C23×D55611yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC4×C139C25
FrattiniC4C24×D139
FittingC2×#131×C139C2
socleC22×C139C22×D4
hypercenterC2×#131D139
hypocenterC139C2×#576
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#17984888C2semidirect
2. #22581758C2direct (N × H)
3. C2×#17984870C2semidirect
4. C2×#17984864C2semidirect
5. C22×D1112C2semidirect
6. C2×#131×C139C2semidirect
8. #17984888C22semidirect
10. C2×#14555785C22semidirect
11. C22×D556C22semidirect
13. #17984870C22semidirect
14. #17984864C22semidirect
15. C2×Dic556C22semidirect
16. C2×#14555774C22semidirect
17. C2×D1112C22semidirect
18. C2×D1112C22semidirect
19. C2×D1112C22semidirect
21. #131×C139C22semidirect
22. C2×M16×C139C22semidirect
23. C22×C8×C139C22semidirect
27. #14555785C23semidirect
32. C2×D556C23semidirect
36. Dic556C23semidirect
37. #14555774C23semidirect
38. D1112C23semidirect
39. D1112C23semidirect
45. M16×C139C23semidirect
48. C2×C8×C139C23semidirect
80. C2×C139#576semidirect
83. C139C2×#576semidirect
90. C2×#131D139semidirect
105. #131C2×D139semidirect
106. C2×M16C2×D139semidirect
107. C22×C8C2×D139semidirect
129. M16C22×D139semidirect
132. C2×C8C22×D139semidirect
165. C2#22581758direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179848882
#225817582
C2×#179848702
C2×#179848642
C22×D11122
C2×#131×C1392
C2×#576139