Finite Group Databasebeta

← C22×D4×#90673 #28407548

Subgroups — C22×D4×#90673 #28407548

Order 14464.

2528 conjugacy classes of subgroups; only the 850 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 850 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
1C24×#90673C212yesmaximal, complemented
2C2×D4×#90673C2124yesmaximal, direct product factor
3C22×C4⋊#90673C211yesmaximal, characteristic, complemented
4C22×C22⋊#90673C212yesmaximal, complemented
5C22×C4×#90673C211yesmaximal, characteristic, complemented
6C22×D4×D113C211yesmaximal, characteristic
7C23×#90673—216no—
8C23×#90673C2211yescharacteristic
9C23×#90673C2212yes—
10C23×#90673C2211yescharacteristic
11C23×#90673C22124yescomplemented
12D4×#90673C22164yesdirect product factor
13C2×C4⋊#90673C22112yescomplemented
14C2×C22⋊#90673C22124yescomplemented
15C2×C4×#90673C22112yescomplemented
16C24×D113C2212yes—
17C22×D452C411yescharacteristic, complemented
18C22×C22⋊D113C412yescomplemented
19C2×D4×D113C4112yescomplemented
20C2×D4×D113C22112yes—
21C22×C4×D113C2211yescharacteristic
22C22×D4×C113C411yescharacteristic, complemented
23C22×#90673—28no—
24C22×#90673—24no—
25C22×#90673—296no—
26C22×#90673D418yesdirect product factor
27C22×#90673C2316yes—
28C22×#90673C23112yes—
29C22×#90673C2316yes—
30C22×#90673C23132yescomplemented
31C4⋊#90673C23116yescomplemented
32C22⋊#90673C23132yescomplemented
33C4×#90673C23116yescomplemented
34C23×D113—28no—
35C23×D113—28no—
36C23×D113C2×C4112yescomplemented
37C23×D113C2×C412yescomplemented
38C23×D113C23112yes—
39C23×D113C2311yescharacteristic
40C2×D452C2×C4112yescomplemented
41C2×C22⋊D113C2×C4124yescomplemented
42D4×D113C2×C4148yescomplemented
43D4×D113C23116yes—
44C22×Dic113C2×C411yescharacteristic, complemented
45C2×C4×D113C2×C416yescomplemented
46C2×C4×D113C2316yes—
47C24×C113C2×C412yescomplemented
48C2×D4×C113C2×C4112yescomplemented
49C22×C4×C113C2×C411yescharacteristic, complemented
50C23×C113—28no—
51C23×C113C22×C411yescharacteristic
52C23×C113C22×C4112yescomplemented
53C22×D113—28no—
54C22×D113—248no—
55C22×D113—224no—
56C22×D113—224no—
57C22×D113C22×C413yes—
58C22×D113C22×C4124yescomplemented
59C22×D113C22×C4112yescomplemented
60C22×D113C2×D414yes—
61C22×D113#4114yes—
62C22×D113C2418yes—
63C22×D113C2413yes—
64C2×#90673—224no—
65C2×#90673—212no—
66C2×#90673—264no—
67C2×#90673C2×D4124yesdirect product factor
68C2×#90673C2414yes—
69C2×#90673C2418yes—
70C2×#90673C2414yes—
71D4×C113C22×C4116yescomplemented
72C2×C4×C113C22×C416yescomplemented
73C22⋊D113C22×C4132yescomplemented
74C2×Dic113C22×C416yescomplemented
75D452C22×C4116yescomplemented
76C4×D113C22×C4112yescomplemented
77C4×D113C2414yes—
78C22×C113—224no—
79C22×C113C4×D414yescomplemented
80C22×C113C23×C413yes—
81C22×C113C23×C418yescomplemented
82C2×D113—224no—
83C2×D113—248no—
84C2×D113—28no—
85C2×D113—28no—
86C2×D113C4×D4112yescomplemented
87C2×D113C23×C413yes—
88C2×D113C23×C418yescomplemented
89C2×D113C22×D416yes—
90C2×D113C2×#4116yes—
91C2×D113C2511yescharacteristic
92#90673—28no—
93#90673—24no—
94#90673C22×D418yesdirect product factor
95C4×C113C23×C414yescomplemented
96Dic113C23×C414yescomplemented
97C2×C113—28no—
98C2×C113C2×C4×D416yescomplemented
99C2×C113C24×C411yescharacteristic
100D113—28no—
101D113C2×C4×D416yescomplemented
102D113C23×D411yescharacteristic
103D113C22×#4111yescharacteristic
104C22×C4×D4—1131nomaximal, Sylow
105C113C22×C4×D411yescharacteristic, complemented, Sylow
106C23×D4—1131no—
107C24×C4—1132no—
108C2×C4×D4—11324no—
109C22×C4⋊C4—1131no—
110C22×C22⋊C4—1132no—
111C22×C42—1131no—
112C25—1132no—
113C22×D4—1132no—
114C22×D4—11312no—
115C22×D4—11312no—
116C22×D4—1131no—
117C22×D4#9067311yescharacteristic, direct product factor
118C23×C4—1131no—
119C23×C4—1131no—
120C23×C4—1131no—
121C23×C4—1132no—
122C23×C4—11324no—
123C23×C4—22616no—
124C4×D4—11364no—
125C2×C4⋊C4—11312no—
126C2×C22⋊C4—11324no—
127C2×C42—11312no—
128C24—1131no—
129C24—1132no—
130C24—11312no—
131C24—11312no—
132C24—2268no—
133C24—2268no—
134C24C2×#9067312yescomplemented
135C2×D4—11324no—
136C2×D4—11316no—
137C2×D4—11348no—
138C2×D4—11312no—
139C2×D4C2×#90673112yesdirect product factor
140C22×C4—1136no—
141C22×C4—1138no—
142C22×C4—1131no—
143C22×C4—1136no—
144C22×C4—1136no—
145C22×C4—1136no—
146C22×C4—11312no—
147C22×C4—11332no—
148C22×C4—22696no—
149C22×C4—2268no—
150C22×C4—2264no—
151C22×C4C2×#9067311yescharacteristic, complemented
152C4⋊C4—11316no—
153C22⋊C4—11332no—
154C42—11316no—
155C23—28no—
156C23—1134no—
157C23—1134no—
158C23—1133no—
159C23—1133no—
160C23—11312no—
161C23—1138no—
162C23—11324no—
163C23—22624no—
164C23—22624no—
165C23—22648no—
166C23—2268no—
167C23C22×#9067311yescharacteristic
168C23C22×#90673112yescomplemented
169D4—11332no—
170D4—11316no—
171D4C22×#90673116yesdirect product factor
172C2×C4—1134no—
173C2×C4—11324no—
174C2×C4—1136no—
175C2×C4—1134no—
176C2×C4—11312no—
177C2×C4—1134no—
178C2×C4—1138no—
179C2×C4—22664no—
180C2×C4—22624no—
181C2×C4—22612no—
182C2×C4C22×#9067316yescomplemented
183C22—224no—
184C22—1136no—
185C22—1136no—
186C22—11312no—
187C22—1131no—
188C22—1133no—
189C22—1138no—
190C22—2268no—
191C22—2268no—
192C22—22648no—
193C22—22624no—
194C22D4×#9067314yesdirect product factor
195C22C23×#9067313yes—
196C22C23×#9067318yescomplemented
197C4—1138no—
198C4—1134no—
199C4—2268no—
200C4—2264no—
201C4C23×#9067314yescomplemented
202C2—28no—
203C2—1131no—
204C2—1131no—
205C2—1136no—
206C2—2268no—
207C2C2×D4×#9067316yesdirect product factor
208C2C24×#9067311yescharacteristic
subgroupG/H
centerC23C22×#90673
commutatorC2×C113C24×C4
FrattiniC2C24×#90673
FittingC22×D4×C113C4
socleC23×C113C22×C4
prime radicalC22×D4×D113C2
cosocleC2×D113C25
hypercenterC22×D4#90673
hypocenterC113C22×C4×D4
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C24×#90673C2semidirect
2. C2×D4×#90673C2direct (N × H)
3. C22×C4⋊#90673C2semidirect
4. C22×C22⋊#90673C2semidirect
5. C22×C4×#90673C2semidirect
11. C23×#90673C22semidirect
12. D4×#90673C22direct (N × H)
13. C2×C4⋊#90673C22semidirect
14. C2×C22⋊#90673C22semidirect
15. C2×C4×#90673C22semidirect
17. C22×D452C4semidirect
18. C22×C22⋊D113C4semidirect
19. C2×D4×D113C4semidirect
22. C22×D4×C113C4semidirect
26. C22×#90673D4direct (N × H)
30. C22×#90673C23semidirect
31. C4⋊#90673C23semidirect
32. C22⋊#90673C23semidirect
33. C4×#90673C23semidirect
36. C23×D113C2×C4semidirect
37. C23×D113C2×C4semidirect
40. C2×D452C2×C4semidirect
41. C2×C22⋊D113C2×C4semidirect
42. D4×D113C2×C4semidirect
44. C22×Dic113C2×C4semidirect
45. C2×C4×D113C2×C4semidirect
47. C24×C113C2×C4semidirect
48. C2×D4×C113C2×C4semidirect
49. C22×C4×C113C2×C4semidirect
52. C23×C113C22×C4semidirect
58. C22×D113C22×C4semidirect
59. C22×D113C22×C4semidirect
67. C2×#90673C2×D4direct (N × H)
71. D4×C113C22×C4semidirect
72. C2×C4×C113C22×C4semidirect
73. C22⋊D113C22×C4semidirect
74. C2×Dic113C22×C4semidirect
75. D452C22×C4semidirect
76. C4×D113C22×C4semidirect
79. C22×C113C4×D4semidirect
81. C22×C113C23×C4semidirect
86. C2×D113C4×D4semidirect
88. C2×D113C23×C4semidirect
94. #90673C22×D4direct (N × H)
95. C4×C113C23×C4semidirect
96. Dic113C23×C4semidirect
98. C2×C113C2×C4×D4semidirect
101. D113C2×C4×D4semidirect
105. C113C22×C4×D4semidirect
117. C22×D4#90673direct (N × H)
134. C24C2×#90673semidirect
139. C2×D4C2×#90673direct (N × H)
151. C22×C4C2×#90673semidirect
168. C23C22×#90673semidirect
171. D4C22×#90673direct (N × H)
182. C2×C4C22×#90673semidirect
194. C22D4×#90673direct (N × H)
196. C22C23×#90673semidirect
201. C4C23×#90673semidirect
207. C2C2×D4×#90673direct (N × H)

Maximal subgroups

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

subgroupindex
C24×#906732
C2×D4×#906732
C22×C4⋊#906732
C22×C22⋊#906732
C22×C4×#906732
C22×D4×D1132
C22×C4×D4113