Finite Group Databasebeta

← C2×#22581696 #31820525

Subgroups — C2×#22581696 #31820525

Order 17792.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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#22581696C2116yesmaximal, direct product factor
2C2×#17984829C213yesmaximal, complemented
3C2×#17984828C216yesmaximal, complemented
4C2×#17984811C212yesmaximal, complemented
5C2×#17984810C213yesmaximal, complemented
6C2×#120×C139C211yesmaximal, characteristic, complemented
7C24×D139C2211yescharacteristic, complemented
8C22×Dic278C2213yescomplemented
9C22×C22⋊D139C2216yes—
10#17984829C22124yescomplemented
11#17984828C22148yescomplemented
12#17984811C22116yescomplemented
13#17984810C22124yescomplemented
14C2×C22⋊Dic139C2213yescomplemented
15C2×C22⋊Dic139C2216yescomplemented
16C2×(C2×D139)⋊C4C2216yescomplemented
17C2×C4×Dic139C2213yescomplemented
18C25×C139C2211yescharacteristic, complemented
19C22×D4×C139C2213yes—
20#120×C139C2218yescomplemented
21C2×C22⋊C4×C139C2213yescomplemented
22C23×D139—46no—
23C23×D139C2312yes—
24C23×D139C2314yescomplemented
25C2×Dic278—46no—
26C2×Dic278C23112yescomplemented
27C2×C22⋊D139—412no—
28C2×C22⋊D139C23124yes—
29C22×Dic139C2316yes—
30C22⋊Dic139C23112yescomplemented
31C22⋊Dic139C23124yescomplemented
32(C2×D139)⋊C4C23124yescomplemented
33C4×Dic139C23112yescomplemented
34C24×C139—46no—
35C24×C139C2311yescharacteristic
36C24×C139C2313yes—
37C24×C139C2314yescomplemented
38C2×D4×C139—46no—
39C2×D4×C139C23112yes—
40C22×C4×C139C2313yes—
41C22⋊C4×C139C23112yescomplemented
42C22×D139—212no—
43C22×D139—412no—
44C22×D139—416no—
45C22×D139C2414yes—
46Dic278—412no—
47C22⋊D139—424no—
48C2×Dic139—212no—
49C2×Dic139C24112yes—
50C23×C139—26no—
51C23×C139—26no—
52C23×C139—212no—
53C23×C139—412no—
54C23×C139—416no—
55C23×C139C2416yes—
56C23×C139C2412yes—
57C23×C139C2411yescharacteristic
58D4×C139—412no—
59C2×C4×C139—26no—
60C2×C4×C139C2416yes—
61C22×C139—26no—
62C22×C139—26no—
63C22×C139—212no—
64C22×C139—416no—
65C22×C139—412no—
66C22×C139—44no—
67C22×C139H(5,𝔽2)16yes—
68C22×C139C2511yescharacteristic
69C2×D139—212no—
70C2×D139—416no—
71C2×D139—48no—
72C4×C139—26no—
73Dic139—212no—
74C2×C139—42no—
75C2×C139—46no—
76C2×C139H(3,𝔽4)14yescomplemented
77C2×C139C2×H(5,𝔽2)13yes—
78D139—44no—
79C139C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
80C2×H(3,𝔽4)—1391nomaximal, Sylow
81H(3,𝔽4)—13916no—
82C2×#124—1393no—
83C2×#124—1396no—
84C2×#120—1392no—
85C2×#120—1393no—
86C2×#120D13911yescharacteristic, complemented
87C25—1391no—
88C25C2×D13911yescharacteristic, complemented
89C22×Q8—1393no—
90C22×D4—1396no—
91C22×D4C2×D13913yes—
92#124—13924no—
93#124—13948no—
94#120—13916no—
95#120—13924no—
96#120C2×D13918yescomplemented
97C2×C22⋊C4—1393no—
98C2×C22⋊C4—1396no—
99C2×C22⋊C4—1396no—
100C2×C22⋊C4C2×D13913yescomplemented
101C2×C42—1393no—
102C24—46no—
103C24—5566no—
104C24—1392no—
105C24—1394no—
106C24C22×D13911yescharacteristic
107C24C22×D13913yes—
108C24C22×D13914yescomplemented
109C2×Q8—5566no—
110C2×Q8—13912no—
111C2×D4—46no—
112C2×D4—55612no—
113C2×D4—13924no—
114C2×D4C22×D139112yes—
115C22×C4—1396no—
116C22×C4C22×D13913yes—
117C22⋊C4—13912no—
118C22⋊C4—13924no—
119C22⋊C4—13924no—
120C22⋊C4C22×D139112yescomplemented
121C42—13912no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—27812no—
128C23—55612no—
129C23—55616no—
130C23—1394no—
131C23C23×D13912yes—
132C23C23×D13916yes—
133C23C23×D13911yescharacteristic
134Q8—55612no—
135D4—412no—
136D4—55624no—
137C2×C4—26no—
138C2×C4—27812no—
139C2×C4—13912no—
140C2×C4C23×D13916yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—27812no—
148C22—55616no—
149C22—5568no—
150C22#1798488716yes—
151C22C24×D13911yescharacteristic
152C4—26no—
153C4—27812no—
154C2—46no—
155C2—42no—
156C2—5564no—
157C2#2258169614yesdirect product factor
158C2C2×#1798488713yes—
subgroupG/H
centerC23C23×D139
commutator, cosocleC22×C139C25
FrattiniC22C24×D139
FittingC2×#120×C139C2
socleC23×C139C24
hypercenterC2×#120D139
hypocenterC139C2×H(3,𝔽4)
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #22581696C2direct (N × H)
2. C2×#17984829C2semidirect
3. C2×#17984828C2semidirect
4. C2×#17984811C2semidirect
5. C2×#17984810C2semidirect
6. C2×#120×C139C2semidirect
7. C24×D139C22semidirect
8. C22×Dic278C22semidirect
10. #17984829C22semidirect
11. #17984828C22semidirect
12. #17984811C22semidirect
13. #17984810C22semidirect
14. C2×C22⋊Dic139C22semidirect
15. C2×C22⋊Dic139C22semidirect
16. C2×(C2×D139)⋊C4C22semidirect
17. C2×C4×Dic139C22semidirect
18. C25×C139C22semidirect
20. #120×C139C22semidirect
21. C2×C22⋊C4×C139C22semidirect
24. C23×D139C23semidirect
26. C2×Dic278C23semidirect
30. C22⋊Dic139C23semidirect
31. C22⋊Dic139C23semidirect
32. (C2×D139)⋊C4C23semidirect
33. C4×Dic139C23semidirect
37. C24×C139C23semidirect
41. C22⋊C4×C139C23semidirect
76. C2×C139H(3,𝔽4)semidirect
79. C139C2×H(3,𝔽4)semidirect
86. C2×#120D139semidirect
88. C25C2×D139semidirect
96. #120C2×D139semidirect
100. C2×C22⋊C4C2×D139semidirect
108. C24C22×D139semidirect
120. C22⋊C4C22×D139semidirect
157. C2#22581696direct (N × H)

Maximal subgroups

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

subgroupindex
#225816962
C2×#179848292
C2×#179848282
C2×#179848112
C2×#179848102
C2×#120×C1392
C2×H(3,𝔽4)139