Finite Group Databasebeta

← C2×#30632322 #44563804

Subgroups — C2×#30632322 #44563804

Order 32128.

2536 conjugacy classes of subgroups; only the 581 normal subgroups are shown.

normal subgroups only

This group has 2536 conjugacy classes of subgroups — too many to draw. Only its 581 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
1C22×D4×D251C214yesmaximal, complemented
2#30632322C2116yesmaximal, direct product factor
3C2×#22548686C214yesmaximal, complemented
4C2×#22548683C214yesmaximal, complemented
5C2×C4×D1004C212yesmaximal, complemented
6C2×#127×C251C211yesmaximal, characteristic, complemented
7C24×D251C2214yescomplemented
8C22×D1004C2212yes—
9C22×C22⋊D251C2218yescomplemented
10C2×D4×D251—232no—
11C2×D4×D251C22132yescomplemented
12C22×C4×D251C2214yescomplemented
13#22548686C22132yescomplemented
14#22548683C22132yescomplemented
15C4×D1004C22116yescomplemented
16C2×C4⋊Dic251C2212yescomplemented
17C2×C22⋊Dic251C2214yescomplemented
18C2×(C2×D251)⋊C4C2214yescomplemented
19C22×D4×C251C2214yescomplemented
20C22×D4×C251C2212yescomplemented
21#127×C251C2218yescomplemented
22C2×C42×C251C2211yescharacteristic, complemented
23C23×D251—232no—
24C23×D251—48no—
25C23×D251C2314yes—
26C23×D251C23116yescomplemented
27C2×D1004D4116yescomplemented
28C2×D1004C2318yes—
29C2×C22⋊D251—232no—
30C2×C22⋊D251C23132yescomplemented
31D4×D251—2128no—
32C22×Dic251C2314yes—
33C2×C4×D251—216no—
34C2×C4×D251C23116yescomplemented
35C4⋊Dic251C2318yescomplemented
36C22⋊Dic251C23116yescomplemented
37(C2×D251)⋊C4C23116yescomplemented
38C24×C251C2314yes—
39C2×D4×C251—216no—
40C2×D4×C251—44no—
41C2×D4×C251C23116yescomplemented
42C2×D4×C251C2318yescomplemented
43C22×C4×C251C2311yescharacteristic
44C22×C4×C251C2312yes—
45C42×C251C2314yescomplemented
46C22×D251—28no—
47C22×D251—28no—
48C22×D251—264no—
49C22×D251—416no—
50C22×D251—464no—
51C22×D251C2×D4116yescomplemented
52C22×D251C2418yes—
53D1004C2×D4132yescomplemented
54C22⋊D251—264no—
55C2×Dic251—28no—
56C2×Dic251C2418yes—
57C4×D251—232no—
58C23×C251—216no—
59C23×C251—28no—
60C23×C251C2418yes—
61C23×C251C2411yescharacteristic
62D4×C251—232no—
63D4×C251—48no—
64C2×C4×C251—22no—
65C2×C4×C251C2×D418yescomplemented
66C2×C4×C251C2412yes—
67C2×C4×C251C2414yes—
68C22×C251—216no—
69C22×C251—28no—
70C22×C251—416no—
71C22×C251C22×D414yes—
72C22×C251H(5,𝔽2)12yes—
73C22×C251C2511yescharacteristic
74C2×D251—232no—
75C2×D251—28no—
76C2×D251—28no—
77C2×D251—464no—
78C2×D251C22×D4116yescomplemented
79C4×C251—22no—
80C4×C251C22×D418yescomplemented
81Dic251—28no—
82C2×C251—48no—
83C2×C251D4214yescomplemented
84C2×C251C23×D412yes—
85C2×C251C2×H(5,𝔽2)11yescharacteristic
86D251—216no—
87C251C2×D4211yescharacteristic, complemented, Sylow
88C2×D42—2511nomaximal, Sylow
89C23×D4—2514no—
90D42—25116no—
91C2×#127D25111yescharacteristic, complemented
92C2×#121—2514no—
93C2×#120—2514no—
94C2×C4×D4—2512no—
95C25—2514no—
96C22×D4—50232no—
97C22×D4—2518no—
98C22×D4—25132no—
99C22×D4—2512no—
100C22×D4C2×D25114yescomplemented
101C22×D4C2×D25112yescomplemented
102C23×C4—2514no—
103#127C2×D25118yescomplemented
104#121—25132no—
105#120—25132no—
106C4×D4—25116no—
107C2×C4⋊C4—2512no—
108C2×C22⋊C4—2514no—
109C2×C22⋊C4—2514no—
110C2×C42C2×D25111yescharacteristic, complemented
111C24—10048no—
112C24—50232no—
113C24—25116no—
114C24—2514no—
115C24C22×D25114yes—
116C2×D4—216no—
117C2×D4—44no—
118C2×D4—502128no—
119C2×D4—50232no—
120C2×D4—25132no—
121C2×D4—25116no—
122C2×D4—2518no—
123C2×D4C22×D251116yescomplemented
124C2×D4C22×D25118yescomplemented
125C22×C4—50216no—
126C22×C4—2514no—
127C22×C4—25116no—
128C22×C4C22×D25111yescharacteristic
129C22×C4C22×D25112yes—
130C4⋊C4—2518no—
131C22⋊C4—25116no—
132C22⋊C4—25116no—
133C42C22×D25114yescomplemented
134C23—216no—
135C23—28no—
136C23—100416no—
137C23—100464no—
138C23—50264no—
139C23—5028no—
140C23—5028no—
141C23—25116no—
142C23—2518no—
143C23C23×D25118yes—
144C23C23×D25111yescharacteristic
145D4—232no—
146D4—48no—
147D4—50264no—
148D4—25132no—
149C2×C4—22no—
150C2×C4—5028no—
151C2×C4—50232no—
152C2×C4—2518no—
153C2×C4D4×D25118yescomplemented
154C2×C4C23×D25112yes—
155C2×C4C23×D25114yes—
156C22—216no—
157C22—28no—
158C22—416no—
159C22—100464no—
160C22—5028no—
161C22—5028no—
162C22—50232no—
163C22—25116no—
164C22C2×D4×D25114yes—
165C22#2254876012yes—
166C22C24×D25111yescharacteristic
167C4—22no—
168C4—5028no—
169C4C2×D4×D25118yescomplemented
170C2—48no—
171C2—50216no—
172C2#3063232214yesdirect product factor
173C2C22×D4×D25112yes—
174C2C2×#2254876011yescharacteristic
subgroupG/H
centerC23C23×D251
commutator, cosocleC22×C251C25
FrattiniC22C24×D251
FittingC2×#127×C251C2
socleC23×C251C24
hypercenterC2×#127D251
hypocenterC251C2×D42
LCSG ▷ C22×C251 ▷ C251
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D251C2semidirect
2. #30632322C2direct (N × H)
3. C2×#22548686C2semidirect
4. C2×#22548683C2semidirect
5. C2×C4×D1004C2semidirect
6. C2×#127×C251C2semidirect
7. C24×D251C22semidirect
9. C22×C22⋊D251C22semidirect
11. C2×D4×D251C22semidirect
12. C22×C4×D251C22semidirect
13. #22548686C22semidirect
14. #22548683C22semidirect
15. C4×D1004C22semidirect
16. C2×C4⋊Dic251C22semidirect
17. C2×C22⋊Dic251C22semidirect
18. C2×(C2×D251)⋊C4C22semidirect
19. C22×D4×C251C22semidirect
20. C22×D4×C251C22semidirect
21. #127×C251C22semidirect
22. C2×C42×C251C22semidirect
26. C23×D251C23semidirect
27. C2×D1004D4semidirect
30. C2×C22⋊D251C23semidirect
34. C2×C4×D251C23semidirect
35. C4⋊Dic251C23semidirect
36. C22⋊Dic251C23semidirect
37. (C2×D251)⋊C4C23semidirect
41. C2×D4×C251C23semidirect
42. C2×D4×C251C23semidirect
45. C42×C251C23semidirect
51. C22×D251C2×D4semidirect
53. D1004C2×D4semidirect
65. C2×C4×C251C2×D4semidirect
78. C2×D251C22×D4semidirect
80. C4×C251C22×D4semidirect
83. C2×C251D42semidirect
87. C251C2×D42semidirect
91. C2×#127D251semidirect
100. C22×D4C2×D251semidirect
101. C22×D4C2×D251semidirect
103. #127C2×D251semidirect
110. C2×C42C2×D251semidirect
123. C2×D4C22×D251semidirect
124. C2×D4C22×D251semidirect
133. C42C22×D251semidirect
153. C2×C4D4×D251semidirect
169. C4C2×D4×D251semidirect
172. C2#30632322direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D2512
#306323222
C2×#225486862
C2×#225486832
C2×C4×D10042
C2×#127×C2512
C2×D42251