Finite Group Databasebeta

← C2×#20299433 #28405381

Subgroups — C2×#20299433 #28405381

Order 14464.

5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.

normal subgroups only

This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 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#20299433C2132yesmaximal, direct product factor
2C2×#16813669C216yesmaximal, complemented
3C2×#16813667C219yesmaximal, complemented
4C22×#14268646C219yesmaximal, complemented
5C2×#41×D113C216yesmaximal, complemented
6C2×H(5,𝔽2)×C113C211yesmaximal, characteristic, complemented
7#16813669C22196yescomplemented
8#16813667C221144yescomplemented
9C2×#14268648C2212yescomplemented
10C2×#14268647C22118yescomplemented
11C2×#14268646C22118yescomplemented
12C2×#14268646C22136yescomplemented
13C2×#14268646C221144yescomplemented
14#41×D113C22196yescomplemented
15C22×Dic226C2219yescomplemented
16C2×Q8×D113C2216yescomplemented
17C22×C22⋊D113C22118yescomplemented
18C2×D4×D113C22118yescomplemented
19C23×Dic113C2216yescomplemented
20C22×C4×D113C2219yescomplemented
21H(5,𝔽2)×C113C22116yescomplemented
22C2×#41×C113C2216yescomplemented
23C22×D4×C113C2219yescomplemented
24C23×D113C2319yes—
25#14268648C23116yescomplemented
26#14268647C231144yescomplemented
27#14268646C231144yescomplemented
28#14268646C231288yescomplemented
29C2×Dic226C23118yes—
30C2×Dic226C23172yescomplemented
31Q8×D113C23148yescomplemented
32C2×D452C2316yes—
33C2×C22⋊D113C23136yes—
34C2×C22⋊D113C231144yescomplemented
35D4×D113C231144yescomplemented
36C22×Dic113C2319yes—
37C22×Dic113C23118yes—
38C22×Dic113C23148yescomplemented
39C2×C4×D113C2316yes—
40C2×C4×D113C23118yes—
41C2×C4×D113C23172yescomplemented
42C24×C113C2316yes—
43#41×C113C23148yescomplemented
44C2×Q8×C113C2312yes—
45C2×D4×C113C23118yes—
46C2×D4×C113C23172yescomplemented
47C22×C4×C113C2319yes—
48C23×C113—412no—
49C23×C113C2419yes—
50C23×C113C24124yes—
51C22×D113—418no—
52C22×D113C2416yes—
53C22×D113C24136yes—
54Q8×C113C2418yes—
55D4×C113C24172yes—
56C2×C4×C113C2416yes—
57C2×C4×C113C24136yes—
58C22⋊D113C241144yes—
59C2×Dic113C2411yescharacteristic
60C2×Dic113C2419yes—
61C2×Dic113C24136yes—
62C2×Dic113C24172yes—
63D452C24124yes—
64C4×D113C24124yes—
65C4×D113C24172yes—
66Dic226C24172yes—
67C22×C113—218no—
68C22×C113—424no—
69C22×C113C25118yes—
70C22×C113C2511yescharacteristic
71C2×D113—212no—
72C2×D113—436no—
73C2×D113C25112yes—
74C4×C113C25112yes—
75Dic113C25118yes—
76Dic113C2512yes—
77C2×C113—218no—
78C2×C113#58512yescomplemented
79C2×C113C2611yescharacteristic
80D113—212no—
81C2×#585—1131nomaximal, Sylow
82C113C2×#58511yescharacteristic, complemented, Sylow
83#585—11332no—
84C2×2−1+4—1136no—
85C2×H(5,𝔽2)—1139no—
86C2×H(5,𝔽2)D11311yescharacteristic, complemented
87C22×#41—1136no—
88C22×#41—1139no—
892−1+4—11396no—
90H(5,𝔽2)—113144no—
91H(5,𝔽2)C2×D113116yescomplemented
92C2×#41—11396no—
93C2×#41—1132no—
94C2×#41—11318no—
95C2×#41—11336no—
96C2×#41—113144no—
97C2×#41—11318no—
98C2×#41C2×D11316yescomplemented
99C22×Q8—1136no—
100C22×Q8—1139no—
101C22×D4—11318no—
102C22×D4—11318no—
103C22×D4C2×D11319yescomplemented
104C23×C4—1136no—
105C23×C4—1139no—
106C24—1139no—
107C24C22×D11316yes—
108#41—11316no—
109#41—113144no—
110#41—113288no—
111#41—113144no—
112#41C22×D113148yescomplemented
113C2×Q8—11348no—
114C2×Q8—11318no—
115C2×Q8—11372no—
116C2×Q8C22×D11312yes—
117C2×D4—11336no—
118C2×D4—113144no—
119C2×D4—113144no—
120C2×D4—1136no—
121C2×D4C22×D113118yes—
122C2×D4C22×D113172yescomplemented
123C22×C4—1139no—
124C22×C4—11318no—
125C22×C4—11348no—
126C22×C4—1136no—
127C22×C4—11318no—
128C22×C4—11372no—
129C22×C4C22×D11319yes—
130C23—412no—
131C23—11336no—
132C23—1136no—
133C23—45218no—
134C23C23×D11319yes—
135C23C23×D113124yes—
136Q8—11372no—
137Q8C23×D11318yes—
138D4—113144no—
139D4—11324no—
140D4C23×D113172yes—
141C2×C4—11336no—
142C2×C4—11372no—
143C2×C4—1131no—
144C2×C4—1139no—
145C2×C4—11324no—
146C2×C4—11372no—
147C2×C4C23×D113136yes—
148C2×C4C23×D11316yes—
149C22—218no—
150C22—424no—
151C22—11312no—
152C22—45236no—
153C22—22612no—
154C22C24×D113118yes—
155C22C24×D11311yescharacteristic
156C4—1132no—
157C4—11318no—
158C4C24×D113112yes—
159C2—218no—
160C2—22612no—
161C2#2029943312yesdirect product factor
162C2C25×D11311yescharacteristic
subgroupG/H
centerC22C24×D113
commutator, cosocleC2×C113C26
FrattiniC2C25×D113
FittingC2×H(5,𝔽2)×C113C2
socleC22×C113C25
hypercenterC2×H(5,𝔽2)D113
hypocenterC113C2×#585
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #20299433C2direct (N × H)
2. C2×#16813669C2semidirect
3. C2×#16813667C2semidirect
4. C22×#14268646C2semidirect
5. C2×#41×D113C2semidirect
6. C2×H(5,𝔽2)×C113C2semidirect
7. #16813669C22semidirect
8. #16813667C22semidirect
9. C2×#14268648C22semidirect
10. C2×#14268647C22semidirect
11. C2×#14268646C22semidirect
12. C2×#14268646C22semidirect
13. C2×#14268646C22semidirect
14. #41×D113C22semidirect
15. C22×Dic226C22semidirect
16. C2×Q8×D113C22semidirect
17. C22×C22⋊D113C22semidirect
18. C2×D4×D113C22semidirect
19. C23×Dic113C22semidirect
20. C22×C4×D113C22semidirect
21. H(5,𝔽2)×C113C22semidirect
22. C2×#41×C113C22semidirect
23. C22×D4×C113C22semidirect
25. #14268648C23semidirect
26. #14268647C23semidirect
27. #14268646C23semidirect
28. #14268646C23semidirect
30. C2×Dic226C23semidirect
31. Q8×D113C23semidirect
34. C2×C22⋊D113C23semidirect
35. D4×D113C23semidirect
38. C22×Dic113C23semidirect
41. C2×C4×D113C23semidirect
43. #41×C113C23semidirect
46. C2×D4×C113C23semidirect
78. C2×C113#585semidirect
82. C113C2×#585semidirect
86. C2×H(5,𝔽2)D113semidirect
91. H(5,𝔽2)C2×D113semidirect
98. C2×#41C2×D113semidirect
103. C22×D4C2×D113semidirect
112. #41C22×D113semidirect
122. C2×D4C22×D113semidirect
161. C2#20299433direct (N × H)

Maximal subgroups

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

subgroupindex
#202994332
C2×#168136692
C2×#168136672
C22×#142686462
C2×#41×D1132
C2×H(5,𝔽2)×C1132
C2×#585113