Finite Group Databasebeta

← C2×#126×D139 #31819658

Subgroups — C2×#126×D139 #31819658

Order 17792.

1320 conjugacy classes of subgroups; only the 517 normal subgroups are shown.

normal subgroups only

This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 517 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×#17984837C213yesmaximal, complemented
2C2×#17984836C211yesmaximal, characteristic, complemented
3C2×#17984835C213yesmaximal, complemented
4#126×D139C2116yesmaximal, direct product factor
5C2×C4⋊C4×D139C213yesmaximal, complemented
6C2×C22⋊C4×D139C213yesmaximal
7C2×C42×D139C211yesmaximal, characteristic, complemented
8C2×#126×C139C211yesmaximal, characteristic, complemented
9C24×D139C2211yescharacteristic
10C22×C4×D139C2213yes—
11C22×C4×D139C2213yes—
12#17984837C22124yescomplemented
13#17984836C2218yescomplemented
14#17984835C22124yescomplemented
15C2×C4⋊Dic139C2213yescomplemented
16C2×Dic139⋊C4C2213yescomplemented
17C2×Dic139⋊C4C2213yescomplemented
18C4⋊C4×D139C22124yescomplemented
19C2×C22⋊Dic139C2213yes—
20C2×(C2×D139)⋊C4C2213yes—
21C2×(C2×D139)⋊C4C2213yes—
22C22⋊C4×D139C22124yes—
23C2×C4×Dic139C2213yescomplemented
24C42×D139C2218yescomplemented
25#126×C139C2218yescomplemented
26C2×C4⋊C4×C139C2213yescomplemented
27C2×C22⋊C4×C139C2213yes—
28C2×C42×C139C2211yescharacteristic, complemented
29C23×D139—212no—
30C23×D139C2314yes—
31C23×D139C2311yescharacteristic
32C23×D139C2311yescharacteristic
33C22×Dic139C2313yes—
34C22×Dic139C2313yes—
35C2×C4×D139—212no—
36C2×C4×D139—212no—
37C2×C4×D139C23112yes—
38C2×C4×D139C23112yes—
39C4⋊Dic139C23112yescomplemented
40Dic139⋊C4C23112yescomplemented
41Dic139⋊C4C23112yescomplemented
42C22⋊Dic139C23112yes—
43(C2×D139)⋊C4C23112yes—
44(C2×D139)⋊C4C23112yes—
45C4×Dic139C23112yescomplemented
46C24×C139C2311yescharacteristic
47C22×C4×C139C2313yes—
48C22×C4×C139C2313yes—
49C4⋊C4×C139C23112yescomplemented
50C22⋊C4×C139C23112yes—
51C42×C139C2314yescomplemented
52C22×D139—26no—
53C22×D139—224no—
54C22×D139—416no—
55C22×D139#41112yes—
56C22×D139C2412yes—
57C22×D139C2412yes—
58C2×Dic139—26no—
59C2×Dic139—26no—
60C2×Dic139C2416yes—
61C2×Dic139C2416yes—
62C4×D139—224no—
63C4×D139—224no—
64C23×C139—26no—
65C23×C139C2412yes—
66C23×C139C2411yescharacteristic
67C2×C4×C139—26no—
68C2×C4×C139—26no—
69C2×C4×C139C2416yes—
70C2×C4×C139C2416yes—
71C22×C139—26no—
72C22×C139—44no—
73C22×C139C2×#4116yes—
74C22×C139C2511yescharacteristic
75C2×D139—26no—
76C2×D139—44no—
77C2×D139—416no—
78C2×D139#126116yesdirect product factor
79C2×D139C2×#41112yes—
80C4×C139—26no—
81C4×C139—26no—
82Dic139—26no—
83Dic139—26no—
84C2×C139—42no—
85C2×C139C2×#12614yescomplemented
86C2×C139C22×#4113yes—
87D139—42no—
88D139C2×#12618yesdirect product factor
89C139C22×#12611yescharacteristic, complemented, Sylow
90C22×#126—1391nomaximal, Sylow
91C2×#126—13916no—
92C2×#126—1393no—
93C2×#126—1393no—
94C2×#126—1391no—
95C2×#126D13911yescharacteristic, direct product factor
96C22×C4⋊C4—1393no—
97C22×C22⋊C4—1393no—
98C22×C42—1391no—
99C25—1391no—
100C23×C4—1393no—
101C23×C4—1393no—
102#126—13924no—
103#126—13924no—
104#126—1398no—
105#126C2×D13918yesdirect product factor
106C2×C4⋊C4—1393no—
107C2×C4⋊C4—1393no—
108C2×C4⋊C4—1393no—
109C2×C4⋊C4—13924no—
110C2×C4⋊C4C2×D13913yescomplemented
111C2×C22⋊C4—1393no—
112C2×C22⋊C4—1393no—
113C2×C22⋊C4—1393no—
114C2×C22⋊C4—13924no—
115C2×C22⋊C4C2×D13913yes—
116C2×C42—1393no—
117C2×C42—1398no—
118C2×C42C2×D13911yescharacteristic, complemented
119C24—27812no—
120C24—1394no—
121C24—1391no—
122C24—1391no—
123C24C22×D13911yescharacteristic
124C22×C4—27812no—
125C22×C4—27812no—
126C22×C4—1393no—
127C22×C4—1393no—
128C22×C4—13912no—
129C22×C4—13912no—
130C22×C4C22×D13913yes—
131C22×C4C22×D13913yes—
132C4⋊C4—13912no—
133C4⋊C4—13912no—
134C4⋊C4—13912no—
135C4⋊C4C22×D139112yescomplemented
136C22⋊C4—13912no—
137C22⋊C4—13912no—
138C22⋊C4—13912no—
139C22⋊C4C22×D139112yes—
140C42—13912no—
141C42C22×D13914yescomplemented
142C23—26no—
143C23—27824no—
144C23—2786no—
145C23—55616no—
146C23—1392no—
147C23—13912no—
148C23—1392no—
149C23C23×D13912yes—
150C23C23×D13911yescharacteristic
151C2×C4—26no—
152C2×C4—26no—
153C2×C4—27824no—
154C2×C4—27824no—
155C2×C4—2786no—
156C2×C4—2786no—
157C2×C4—1396no—
158C2×C4—1396no—
159C2×C4C23×D13916yes—
160C2×C4C23×D13916yes—
161C22—26no—
162C22—44no—
163C22—2786no—
164C22—55616no—
165C22—5564no—
166C22—13912no—
167C22—13916no—
168C22#41×D13916yes—
169C22C24×D13911yescharacteristic
170C4—26no—
171C4—26no—
172C4—2786no—
173C4—2786no—
174C2—42no—
175C2—5562no—
176C2—1398no—
177C2#126×D13914yesdirect product factor
178C2C2×#41×D13913yes—
subgroupG/H
centerC23C23×D139
commutator, cosocleC22×C139C25
FrattiniC22C24×D139
FittingC2×#126×C139C2
socleC23×C139C24
prime radicalC24×D139C22
hypercenterC2×#126D139
hypocenterC139C22×#126
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#17984837C2semidirect
2. C2×#17984836C2semidirect
3. C2×#17984835C2semidirect
4. #126×D139C2direct (N × H)
5. C2×C4⋊C4×D139C2semidirect
7. C2×C42×D139C2semidirect
8. C2×#126×C139C2semidirect
12. #17984837C22semidirect
13. #17984836C22semidirect
14. #17984835C22semidirect
15. C2×C4⋊Dic139C22semidirect
16. C2×Dic139⋊C4C22semidirect
17. C2×Dic139⋊C4C22semidirect
18. C4⋊C4×D139C22semidirect
23. C2×C4×Dic139C22semidirect
24. C42×D139C22semidirect
25. #126×C139C22semidirect
26. C2×C4⋊C4×C139C22semidirect
28. C2×C42×C139C22semidirect
39. C4⋊Dic139C23semidirect
40. Dic139⋊C4C23semidirect
41. Dic139⋊C4C23semidirect
45. C4×Dic139C23semidirect
49. C4⋊C4×C139C23semidirect
51. C42×C139C23semidirect
78. C2×D139#126direct (N × H)
85. C2×C139C2×#126semidirect
88. D139C2×#126direct (N × H)
89. C139C22×#126semidirect
95. C2×#126D139direct (N × H)
105. #126C2×D139direct (N × H)
110. C2×C4⋊C4C2×D139semidirect
118. C2×C42C2×D139semidirect
135. C4⋊C4C22×D139semidirect
141. C42C22×D139semidirect
177. C2#126×D139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179848372
C2×#179848362
C2×#179848352
#126×D1392
C2×C4⋊C4×D1392
C2×C22⋊C4×D1392
C2×C42×D1392
C2×#126×C1392
C22×#126139