Finite Group Databasebeta

← C2×#28409072 #44408317

Subgroups — C2×#28409072 #44408317

Order 29056.

536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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×#16813868C211yesmaximal, characteristic
2C2×#20300247C211yesmaximal, characteristic
3#28409072C218yesmaximal, direct product factor
4C2×#20300221C212yesmaximal, complemented
5C2×#20300219C212yesmaximal, complemented
6C22×C4⋊C4×C227C211yesmaximal, characteristic
7C2×#16813868C418yescomplemented
8C2×#16813868C2214yes—
9C22×C227⋊C8C2212yes—
10#20300247—22no—
11#20300247C2214yes—
12C2×C4⋊Dic227C2211yescharacteristic
13C2×C4⋊Dic227C2211yescharacteristic
14C2×C22⋊Dic227—21no—
15C2×C4×Dic227—21no—
16#20300221C2218yescomplemented
17#20300219C2218yescomplemented
18C23×C4×C227—21no—
19C23×C4×C227C2211yescharacteristic
20C2×C4⋊C4×C227—21no—
21C2×C4⋊C4×C227—22no—
22C2×C4⋊C4×C227C2212yes—
23C2×C4⋊C4×C227C2214yes—
24C22×Dic227—21no—
25C22×Dic227—21no—
26#16813868C2×C4116yescomplemented
27C2×C227⋊C8C2×C418yescomplemented
28C2×C227⋊C8C2314yes—
29C4⋊Dic227—21no—
30C4⋊Dic227—21no—
31C4⋊Dic227C2312yes—
32C4⋊Dic227C2312yes—
33C22⋊Dic227—24no—
34C4×Dic227—24no—
35C24×C227D411yescharacteristic
36C22×C4×C227—24no—
37C22×C4×C227—22no—
38C22×C4×C227—44no—
39C22×C4×C227C2×C414yes—
40C22×C4×C227D411yescharacteristic
41C22×C4×C227D412yes—
42C22×C4×C227Q814yes—
43C22×C4×C227C2311yescharacteristic
44C22×C4×C227C2312yes—
45C4⋊C4×C227—24no—
46C4⋊C4×C227—22no—
47C4⋊C4×C227C2314yes—
48C2×Dic227—22no—
49C2×Dic227—22no—
50C2×Dic227—42no—
51C2×Dic227—42no—
52C227⋊C8C22×C418yescomplemented
53C23×C227—22no—
54C23×C227—22no—
55C23×C227C4⋊C414yes—
56C23×C227C2×D412yes—
57C23×C227C2×D411yescharacteristic
58C2×C4×C227—24no—
59C2×C4×C227—48no—
60C2×C4×C227—44no—
61C2×C4×C227C4⋊C418yes—
62C2×C4×C227C4⋊C414yes—
63C2×C4×C227C22×C412yes—
64C2×C4×C227C22×C414yes—
65C2×C4×C227C2×D412yes—
66C2×C4×C227C2×D411yescharacteristic
67C2×C4×C227C2×Q814yes—
68C2×C4×C227C2×Q812yes—
69C2×C4×C227C2411yescharacteristic
70C22×C227—22no—
71C22×C227—22no—
72C22×C227—28no—
73C22×C227C2×C4⋊C414yes—
74C22×C227C2×C4⋊C412yes—
75C22×C227AGL(1,ℤ/8)12yes—
76C22×C227#13712yes—
77C22×C227C22×D411yescharacteristic
78C4×C227—44no—
79C4×C227C2×C4⋊C412yes—
80C4×C227C2×C4⋊C414yes—
81C4×C227C23×C411yescharacteristic
82C4×C227C22×Q811yescharacteristic
83Dic227—42no—
84Dic227—42no—
85C2×C227—24no—
86C2×C227#42814yescomplemented
87C2×C227C22×C4⋊C411yescharacteristic
88C2×C227C2×AGL(1,ℤ/8)11yescharacteristic
89C2×C227C2×#13711yescharacteristic
90C227C2×#42811yescharacteristic, complemented, Sylow
91C2×#428—2271nomaximal, Sylow
92C22×M16—2271no—
93C2×#117—2271no—
94C22×C4⋊C4D22711yescharacteristic
95#428—2278no—
96C2×#107—2272no—
97C2×#106—2272no—
98C23×C4—21no—
99C23×C4C2×D22711yescharacteristic
100C2×M16—2278no—
101C2×M16—2274no—
102C22×C8—2272no—
103#117—4542no—
104#117—2274no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—2271no—
108C2×C4⋊C4—2271no—
109C2×C4⋊C4C2×D22712yes—
110C2×C4⋊C4C2×D22714yes—
111C2×C22⋊C4—4541no—
112C2×C42—4541no—
113#107—2278no—
114#106—2278no—
115C24C22⋊D22711yescharacteristic
116C22×C4—24no—
117C22×C4—22no—
118C22×C4—44no—
119C22×C4—4541no—
120C22×C4—4541no—
121C22×C4C4×D22714yes—
122C22×C4C22⋊D22712yes—
123C22×C4C22⋊D22711yescharacteristic
124C22×C4Dic45414yes—
125C22×C4C22×D22712yes—
126C22×C4C22×D22711yescharacteristic
127M16—22716no—
128C2×C8—2278no—
129C2×C8—2274no—
130C4⋊C4—24no—
131C4⋊C4—22no—
132C4⋊C4—4541no—
133C4⋊C4—4541no—
134C4⋊C4—2272no—
135C4⋊C4—2272no—
136C4⋊C4C22×D22714yes—
137C22⋊C4—4544no—
138C42—4544no—
139C23—22no—
140C23—22no—
141C23Dic227⋊C414yes—
142C23C2×C22⋊D22712yes—
143C23C2×C22⋊D22711yescharacteristic
144C2×C4—24no—
145C2×C4—48no—
146C2×C4—44no—
147C2×C4—9082no—
148C2×C4—9082no—
149C2×C4—4542no—
150C2×C4—4542no—
151C2×C4Dic227⋊C418yes—
152C2×C4Dic227⋊C414yes—
153C2×C4C2×C4×D22712yes—
154C2×C4C2×C4×D22714yes—
155C2×C4C2×C22⋊D22712yes—
156C2×C4C2×C22⋊D22711yescharacteristic
157C2×C4C2×Dic45414yes—
158C2×C4C2×Dic45412yes—
159C2×C4C23×D22711yescharacteristic
160C8—2278no—
161C22—22no—
162C22—22no—
163C22—28no—
164C22C2×Dic227⋊C414yes—
165C22C2×Dic227⋊C412yes—
166C22#2030031412yes—
167C22#2030031912yes—
168C22C22×C22⋊D22711yescharacteristic
169C4—44no—
170C4—9082no—
171C4—9082no—
172C4C2×Dic227⋊C412yes—
173C4C2×Dic227⋊C414yes—
174C4C22×C4×D22711yescharacteristic
175C4C22×Dic45411yescharacteristic
176C2—24no—
177C2#2840907214yesdirect product factor
178C2C22×Dic227⋊C411yescharacteristic
179C2C2×#2030031411yescharacteristic
180C2C2×#2030031911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC22×C4⋊C4×C227C2
socleC23×C227C2×D4
prime radicalC24×C227D4
cosocleC2×C4×C227C24
hypercenterC22×C4⋊C4D227
hypocenterC227C2×#428
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #28409072C2direct (N × H)
4. C2×#20300221C2semidirect
5. C2×#20300219C2semidirect
7. C2×#16813868C4semidirect
16. #20300221C22semidirect
17. #20300219C22semidirect
26. #16813868C2×C4semidirect
27. C2×C227⋊C8C2×C4semidirect
52. C227⋊C8C22×C4semidirect
86. C2×C227#428semidirect
90. C227C2×#428semidirect
177. C2#28409072direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168138682
C2×#203002472
#284090722
C2×#203002212
C2×#203002192
C22×C4⋊C4×C2272
C2×#428227