Finite Group Databasebeta

← C2×#31827207 #49135381

Subgroups — C2×#31827207 #49135381

Order 36224.

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#31827207C2116yesmaximal, direct product factor
2C2×#22583599C212yesmaximal, complemented
3C2×#22583598C212yesmaximal, complemented
4C2×#22583596C214yesmaximal, complemented
5C2×#22583580C214yesmaximal, complemented
6C2×#22583578C212yesmaximal, complemented
7C2×#124×C283C211yesmaximal, characteristic, complemented
8C24×D283C2212yescomplemented
9C22×Dic566C2212yescomplemented
10C22×D1132C2212yes—
11C22×D1132C2212yes—
12C22×C22⋊D283C2214yes—
13#22583599C22116yescomplemented
14#22583598C22116yescomplemented
15#22583596C22132yescomplemented
16#22583580C22132yescomplemented
17#22583578C22116yescomplemented
18C2×C22⋊Dic283C2212yescomplemented
19C2×(C2×D283)⋊C4C2214yescomplemented
20C2×(C2×D283)⋊C4C2214yescomplemented
21C2×(C2×D283)⋊C4C2214yescomplemented
22C2×C4×Dic283C2212yescomplemented
23C22×Q8×C283C2211yescharacteristic, complemented
24C22×D4×C283C2211yescharacteristic
25#124×C283C2218yescomplemented
26C2×C22⋊C4×C283C2214yescomplemented
27C2×C42×C283C2211yescharacteristic, complemented
28C23×D283—44no—
29C23×D283—48no—
30C23×D283C2314yes—
31C23×D283C2318yescomplemented
32C2×Dic566—44no—
33C2×Dic566C2318yescomplemented
34C2×D1132—44no—
35C2×D1132—44no—
36C2×D1132C2318yes—
37C2×D1132C2318yes—
38C2×C22⋊D283—48no—
39C2×C22⋊D283C23116yes—
40C22×Dic283C2314yes—
41C22⋊Dic283C2318yescomplemented
42(C2×D283)⋊C4C23116yescomplemented
43(C2×D283)⋊C4C23116yescomplemented
44(C2×D283)⋊C4C23116yescomplemented
45C4×Dic283C2318yescomplemented
46C24×C283C2312yes—
47C2×Q8×C283—42no—
48C2×Q8×C283C2314yescomplemented
49C2×D4×C283—42no—
50C2×D4×C283C2314yes—
51C22×C4×C283C2312yes—
52C22×C4×C283C2311yescharacteristic
53C22×C4×C283C2312yes—
54C22⋊C4×C283C23116yescomplemented
55C42×C283C2314yescomplemented
56C22×D283—28no—
57C22×D283—28no—
58C22×D283—28no—
59C22×D283—416no—
60C22×D283—48no—
61C22×D283—432no—
62C22×D283C2418yes—
63Dic566—48no—
64D1132—48no—
65D1132—48no—
66C22⋊D283—416no—
67C2×Dic283—28no—
68C2×Dic283C2418yes—
69C23×C283—24no—
70C23×C283—28no—
71C23×C283C2414yes—
72C23×C283C2411yescharacteristic
73Q8×C283—44no—
74D4×C283—44no—
75C2×C4×C283—22no—
76C2×C4×C283—24no—
77C2×C4×C283—24no—
78C2×C4×C283C2414yes—
79C2×C4×C283C2412yes—
80C2×C4×C283C2414yes—
81C22×C283—24no—
82C22×C283—28no—
83C22×C283—48no—
84C22×C283H(5,𝔽2)12yes—
85C22×C283H(5,𝔽2)14yes—
86C22×C283C2511yescharacteristic
87C2×D283—28no—
88C2×D283—28no—
89C2×D283—28no—
90C2×D283—432no—
91C2×D283—416no—
92C4×C283—22no—
93C4×C283—24no—
94C4×C283—24no—
95Dic283—28no—
96C2×C283—44no—
97C2×C283H(3,𝔽4)14yescomplemented
98C2×C283C2×H(5,𝔽2)11yescharacteristic
99C2×C283C2×H(5,𝔽2)12yes—
100D283—48no—
101C283C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
102C2×H(3,𝔽4)—2831nomaximal, Sylow
103H(3,𝔽4)—28316no—
104C2×#124—2832no—
105C2×#124—2834no—
106C2×#124—2832no—
107C2×#124D28311yescharacteristic, complemented
108C2×#120—2832no—
109C2×#120—2834no—
110C25—2832no—
111C22×Q8—2832no—
112C22×Q8C2×D28311yescharacteristic, complemented
113C22×D4—2834no—
114C22×D4—2832no—
115C22×D4—2832no—
116C22×D4C2×D28311yescharacteristic
117#124—28316no—
118#124—28332no—
119#124—28316no—
120#124C2×D28318yescomplemented
121#120—28316no—
122#120—28332no—
123C2×C22⋊C4—2832no—
124C2×C22⋊C4—2834no—
125C2×C22⋊C4—2834no—
126C2×C22⋊C4—2834no—
127C2×C22⋊C4C2×D28314yescomplemented
128C2×C42—2832no—
129C2×C42C2×D28311yescharacteristic, complemented
130C24—2834no—
131C24—2838no—
132C24—11324no—
133C24—11328no—
134C24C22×D28312yes—
135C2×Q8—42no—
136C2×Q8—2838no—
137C2×Q8—11324no—
138C2×Q8C22×D28314yescomplemented
139C2×D4—42no—
140C2×D4—28316no—
141C2×D4—2838no—
142C2×D4—2838no—
143C2×D4—11324no—
144C2×D4—11324no—
145C2×D4—11328no—
146C2×D4C22×D28314yes—
147C22×C4—2834no—
148C22×C4C22×D28312yes—
149C22×C4C22×D28311yescharacteristic
150C22×C4C22×D28312yes—
151C22⋊C4—2838no—
152C22⋊C4—28316no—
153C22⋊C4—28316no—
154C22⋊C4—28316no—
155C22⋊C4C22×D283116yescomplemented
156C42—2838no—
157C42C22×D28314yescomplemented
158C23—24no—
159C23—28no—
160C23—2838no—
161C23—5668no—
162C23—5668no—
163C23—5668no—
164C23—11328no—
165C23—113216no—
166C23—113232no—
167C23C23×D28314yes—
168C23C23×D28311yescharacteristic
169Q8—44no—
170Q8—11328no—
171D4—44no—
172D4—11328no—
173D4—11328no—
174D4—113216no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—2838no—
179C2×C4—5668no—
180C2×C4C23×D28314yes—
181C2×C4C23×D28312yes—
182C2×C4C23×D28314yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—5668no—
187C22—5668no—
188C22—5668no—
189C22—113232no—
190C22—113216no—
191C22#2258365512yes—
192C22#2258365614yes—
193C22C24×D28311yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—5668no—
198C2—44no—
199C2—11328no—
200C2#3182720714yesdirect product factor
201C2C2×#2258365511yescharacteristic
202C2C2×#2258365612yes—
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×#124×C283C2
socleC23×C283C24
hypercenterC2×#124D283
hypocenterC283C2×H(3,𝔽4)
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #31827207C2direct (N × H)
2. C2×#22583599C2semidirect
3. C2×#22583598C2semidirect
4. C2×#22583596C2semidirect
5. C2×#22583580C2semidirect
6. C2×#22583578C2semidirect
7. C2×#124×C283C2semidirect
8. C24×D283C22semidirect
9. C22×Dic566C22semidirect
13. #22583599C22semidirect
14. #22583598C22semidirect
15. #22583596C22semidirect
16. #22583580C22semidirect
17. #22583578C22semidirect
18. C2×C22⋊Dic283C22semidirect
19. C2×(C2×D283)⋊C4C22semidirect
20. C2×(C2×D283)⋊C4C22semidirect
21. C2×(C2×D283)⋊C4C22semidirect
22. C2×C4×Dic283C22semidirect
23. C22×Q8×C283C22semidirect
25. #124×C283C22semidirect
26. C2×C22⋊C4×C283C22semidirect
27. C2×C42×C283C22semidirect
31. C23×D283C23semidirect
33. C2×Dic566C23semidirect
41. C22⋊Dic283C23semidirect
42. (C2×D283)⋊C4C23semidirect
43. (C2×D283)⋊C4C23semidirect
44. (C2×D283)⋊C4C23semidirect
45. C4×Dic283C23semidirect
48. C2×Q8×C283C23semidirect
54. C22⋊C4×C283C23semidirect
55. C42×C283C23semidirect
97. C2×C283H(3,𝔽4)semidirect
101. C283C2×H(3,𝔽4)semidirect
107. C2×#124D283semidirect
112. C22×Q8C2×D283semidirect
120. #124C2×D283semidirect
127. C2×C22⋊C4C2×D283semidirect
129. C2×C42C2×D283semidirect
138. C2×Q8C22×D283semidirect
155. C22⋊C4C22×D283semidirect
157. C42C22×D283semidirect
200. C2#31827207direct (N × H)

Maximal subgroups

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

subgroupindex
#318272072
C2×#225835992
C2×#225835982
C2×#225835962
C2×#225835802
C2×#225835782
C2×#124×C2832
C2×H(3,𝔽4)283