Finite Group Databasebeta

← C2×H(5,𝔽2)×D83 #24922263

Subgroups — C2×H(5,𝔽2)×D83 #24922263

Order 10624.

6560 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.

normal subgroups only

This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3213 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×#14581838C216yesmaximal, complemented
2C2×#14581837C219yesmaximal, complemented
3H(5,𝔽2)×D83C2132yesmaximal, direct product factor
4C2×#41×D83C216yesmaximal, complemented
5C22×D4×D83C219yesmaximal, complemented
6C2×H(5,𝔽2)×C83C211yesmaximal, characteristic, complemented
7C24×D83C2216yescomplemented
8#14581838C22196yescomplemented
9#14581837C221144yescomplemented
10C2×#13050591C2216yescomplemented
11C2×#13050590C22118yescomplemented
12C2×#13050589C22118yescomplemented
13#41×D83C22196yescomplemented
14C2×Q8×D83C2212yescomplemented
15C22×D332C2219yescomplemented
16C22×C22⋊D83C22118yescomplemented
17C2×D4×D83C22118yescomplemented
18C2×D4×D83C221144yescomplemented
19C2×D4×D83C22136yescomplemented
20C22×C4×D83C2219yescomplemented
21H(5,𝔽2)×C83C22116yescomplemented
22C2×#41×C83C2216yescomplemented
23C22×D4×C83C2219yescomplemented
24C23×D83—424no—
25C23×D83C2319yes—
26C23×D83C23148yescomplemented
27C23×D83C23118yescomplemented
28#13050591C23148yescomplemented
29#13050590C231144yescomplemented
30#13050589C231144yescomplemented
31C2×Dic166C2316yescomplemented
32Q8×D83C23116yescomplemented
33C2×D332C23118yescomplemented
34C2×D332C23172yescomplemented
35C2×C22⋊D83C23136yescomplemented
36C2×C22⋊D83C231144yescomplemented
37D4×D83C231144yescomplemented
38D4×D83C231288yescomplemented
39C22×Dic83C2319yescomplemented
40C2×C4×D83C2316yes—
41C2×C4×D83C23172yescomplemented
42C2×C4×D83C23118yescomplemented
43C24×C83C2316yescomplemented
44#41×C83C23148yescomplemented
45C2×Q8×C83C2312yescomplemented
46C2×D4×C83C23118yescomplemented
47C2×D4×C83C23172yescomplemented
48C22×C4×C83C2319yescomplemented
49C23×C83—412no—
50C23×C83C2419yes—
51C23×C83C24124yescomplemented
52C22×D83—236no—
53C22×D83—496no—
54C22×D83—436no—
55C22×D83C24136yes—
56C22×D83C2419yes—
57C22×D83C2411yescharacteristic
58C22×D83C24172yescomplemented
59Q8×C83C2418yescomplemented
60D4×C83C24172yescomplemented
61C2×C4×C83C2416yes—
62C2×C4×C83C24136yescomplemented
63C22⋊D83C241144yescomplemented
64C2×Dic83C2416yes—
65C2×Dic83C24136yescomplemented
66D332C24172yescomplemented
67C4×D83C24124yes—
68C4×D83C24172yescomplemented
69Dic166C24124yescomplemented
70C22×C83—218no—
71C22×C83—424no—
72C22×C83C25118yes—
73C22×C83C2511yescharacteristic
74C2×D83—218no—
75C2×D83—272no—
76C2×D83—472no—
77C2×D83H(5,𝔽2)14yesdirect product factor
78C2×D83C25118yes—
79C2×D83C2512yes—
80C4×C83C25112yes—
81Dic83C25112yes—
82C2×C83—218no—
83C2×C83C2×H(5,𝔽2)12yescomplemented
84C2×C83C2611yescharacteristic
85D83—218no—
86D83C2×H(5,𝔽2)14yesdirect product factor
87C22×H(5,𝔽2)—831nomaximal, Sylow
88C83C22×H(5,𝔽2)11yescharacteristic, complemented, Sylow
89C2×H(5,𝔽2)—8332no—
90C2×H(5,𝔽2)—836no—
91C2×H(5,𝔽2)—839no—
92C2×H(5,𝔽2)D8311yescharacteristic, direct product factor
93C22×#41—836no—
94C23×D4—839no—
95C25—836no—
96H(5,𝔽2)—8396no—
97H(5,𝔽2)—83144no—
98H(5,𝔽2)C2×D83116yesdirect product factor
99C2×#41—8396no—
100C2×#41—836no—
101C2×#41—8318no—
102C2×#41—8318no—
103C2×#41C2×D8316yescomplemented
104C22×Q8—832no—
105C22×D4—8318no—
106C22×D4—8318no—
107C22×D4—8336no—
108C22×D4—83144no—
109C22×D4—839no—
110C22×D4C2×D8319yescomplemented
111C23×C4—839no—
112C24—33224no—
113C24—8318no—
114C24—8348no—
115C24—839no—
116C24C22×D8316yescomplemented
117#41—8348no—
118#41—83144no—
119#41—83144no—
120#41C22×D83148yescomplemented
121C2×Q8—8316no—
122C2×Q8—836no—
123C2×Q8C22×D8312yescomplemented
124C2×D4—8336no—
125C2×D4—83144no—
126C2×D4—83144no—
127C2×D4—83288no—
128C2×D4—8318no—
129C2×D4—8372no—
130C2×D4C22×D83118yescomplemented
131C2×D4C22×D83172yescomplemented
132C22×C4—839no—
133C22×C4—836no—
134C22×C4—8318no—
135C22×C4—8372no—
136C22×C4C22×D8319yescomplemented
137C23—412no—
138C23—33236no—
139C23—33296no—
140C23—8372no—
141C23—831no—
142C23—8336no—
143C23—839no—
144C23—16636no—
145C23C23×D8319yes—
146C23C23×D83124yescomplemented
147Q8—8324no—
148Q8C23×D8318yescomplemented
149D4—83144no—
150D4—8372no—
151D4C23×D83172yescomplemented
152C2×C4—8336no—
153C2×C4—836no—
154C2×C4—8324no—
155C2×C4—8372no—
156C2×C4C23×D8316yes—
157C2×C4C23×D83136yescomplemented
158C22—218no—
159C22—424no—
160C22—33272no—
161C22—834no—
162C22—832no—
163C22—8318no—
164C22—16672no—
165C22—16618no—
166C22C24×D83118yes—
167C22C24×D8311yescharacteristic
168C4—8312no—
169C4C24×D83112yes—
170C2—218no—
171C2—834no—
172C2—16618no—
173C2H(5,𝔽2)×D8312yesdirect product factor
174C2C25×D8311yescharacteristic
subgroupG/H
centerC22C24×D83
commutator, cosocleC2×C83C26
FrattiniC2C25×D83
FittingC2×H(5,𝔽2)×C83C2
socleC22×C83C25
hypercenterC2×H(5,𝔽2)D83
hypocenterC83C22×H(5,𝔽2)
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#14581838C2semidirect
2. C2×#14581837C2semidirect
3. H(5,𝔽2)×D83C2direct (N × H)
4. C2×#41×D83C2semidirect
5. C22×D4×D83C2semidirect
6. C2×H(5,𝔽2)×C83C2semidirect
7. C24×D83C22semidirect
8. #14581838C22semidirect
9. #14581837C22semidirect
10. C2×#13050591C22semidirect
11. C2×#13050590C22semidirect
12. C2×#13050589C22semidirect
13. #41×D83C22semidirect
14. C2×Q8×D83C22semidirect
15. C22×D332C22semidirect
16. C22×C22⋊D83C22semidirect
17. C2×D4×D83C22semidirect
18. C2×D4×D83C22semidirect
19. C2×D4×D83C22semidirect
20. C22×C4×D83C22semidirect
21. H(5,𝔽2)×C83C22semidirect
22. C2×#41×C83C22semidirect
23. C22×D4×C83C22semidirect
26. C23×D83C23semidirect
27. C23×D83C23semidirect
28. #13050591C23semidirect
29. #13050590C23semidirect
30. #13050589C23semidirect
31. C2×Dic166C23semidirect
32. Q8×D83C23semidirect
33. C2×D332C23semidirect
34. C2×D332C23semidirect
35. C2×C22⋊D83C23semidirect
36. C2×C22⋊D83C23semidirect
37. D4×D83C23semidirect
38. D4×D83C23semidirect
39. C22×Dic83C23semidirect
41. C2×C4×D83C23semidirect
42. C2×C4×D83C23semidirect
43. C24×C83C23semidirect
44. #41×C83C23semidirect
45. C2×Q8×C83C23semidirect
46. C2×D4×C83C23semidirect
47. C2×D4×C83C23semidirect
48. C22×C4×C83C23semidirect
51. C23×C83C24semidirect
58. C22×D83C24semidirect
59. Q8×C83C24semidirect
60. D4×C83C24semidirect
62. C2×C4×C83C24semidirect
63. C22⋊D83C24semidirect
65. C2×Dic83C24semidirect
66. D332C24semidirect
68. C4×D83C24semidirect
69. Dic166C24semidirect
77. C2×D83H(5,𝔽2)direct (N × H)
83. C2×C83C2×H(5,𝔽2)semidirect
86. D83C2×H(5,𝔽2)direct (N × H)
88. C83C22×H(5,𝔽2)semidirect
92. C2×H(5,𝔽2)D83direct (N × H)
98. H(5,𝔽2)C2×D83direct (N × H)
103. C2×#41C2×D83semidirect
110. C22×D4C2×D83semidirect
116. C24C22×D83semidirect
120. #41C22×D83semidirect
123. C2×Q8C22×D83semidirect
130. C2×D4C22×D83semidirect
131. C2×D4C22×D83semidirect
136. C22×C4C22×D83semidirect
146. C23C23×D83semidirect
148. Q8C23×D83semidirect
151. D4C23×D83semidirect
157. C2×C4C23×D83semidirect
173. C2H(5,𝔽2)×D83direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145818382
C2×#145818372
H(5,𝔽2)×D832
C2×#41×D832
C22×D4×D832
C2×H(5,𝔽2)×C832
C22×H(5,𝔽2)83