Finite Group Databasebeta

← C2×#20292631 #28344961

Subgroups — C2×#20292631 #28344961

Order 13696.

1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 1008 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
1C23×D428C211yesmaximal, characteristic
2C22×#13133802C211yesmaximal, characteristic, complemented
3#20292631C218yesmaximal, direct product factor
4C2×#16812029C214yesmaximal, complemented
5C2×#117×C107C211yesmaximal, characteristic, complemented
6C24×D107—21no—
7C22×D428—24no—
8C22×D428—21no—
9C22×D428—22no—
10C22×D428C418yescomplemented
11C22×D428C2212yes—
12C22×D428C2214yes—
13C2×#13133802—24no—
14C2×#13133802C2214yescomplemented
15C22×C107⋊C8C2212yescomplemented
16#16812029C22116yescomplemented
17C23×C4×C107C2211yescharacteristic
18#117×C107—22no—
19#117×C107C2214yescomplemented
20C2×C4⋊C4×C107C2212yescomplemented
21C2×C22⋊C4×C107—21no—
22C2×C42×C107—21no—
23C23×D107—28no—
24C23×D107—24no—
25C23×D107—22no—
26C23×D107—48no—
27C2×D428—216no—
28C2×D428—28no—
29C2×D428—22no—
30C2×D428—24no—
31C2×D428—24no—
32C2×D428—28no—
33C2×D428C2×C418yes—
34C2×D428C2×C4116yescomplemented
35C2×D428C2314yes—
36#13133802—28no—
37C2×C107⋊C8—24no—
38C2×C107⋊C8C2314yescomplemented
39C24×C107D411yescharacteristic
40C22×C4×C107—22no—
41C22×C4×C107C2×C414yes—
42C22×C4×C107D414yes—
43C22×C4×C107D411yescharacteristic
44C22×C4×C107D412yes—
45C22×C4×C107C2311yescharacteristic
46C22×C4×C107C2312yes—
47C4⋊C4×C107—22no—
48C4⋊C4×C107C2314yescomplemented
49C22⋊C4×C107—24no—
50C42×C107—24no—
51C23×C107—24no—
52C23×C107C22⋊C414yes—
53C23×C107C2×D412yes—
54C23×C107C2×D411yescharacteristic
55C22×D107—28no—
56C22×D107—216no—
57C22×D107—24no—
58C22×D107—416no—
59C22×D107—432no—
60C22×D107—48no—
61C2×C4×C107—24no—
62C2×C4×C107—44no—
63C2×C4×C107C22⋊C418yes—
64C2×C4×C107C22⋊C414yes—
65C2×C4×C107C22×C412yes—
66C2×C4×C107C22×C414yes—
67C2×C4×C107C2×D412yes—
68C2×C4×C107C2×D411yescharacteristic
69C2×C4×C107C2×D412yes—
70C2×C4×C107C2×D414yes—
71C2×C4×C107C2411yescharacteristic
72D428—28no—
73D428—216no—
74D428—24no—
75D428C22×C418yes—
76C107⋊C8—24no—
77C22×C107—24no—
78C22×C107—28no—
79C22×C107C2×C22⋊C414yes—
80C22×C107C2×C22⋊C412yes—
81C22×C107AGL(1,ℤ/8)14yes—
82C22×C107C22×D411yescharacteristic
83C2×D107—28no—
84C2×D107—432no—
85C2×D107—48no—
86C2×D107—416no—
87C4×C107—44no—
88C4×C107C2×C22⋊C412yes—
89C4×C107C2×C22⋊C414yes—
90C4×C107C23×C411yescharacteristic
91C4×C107C22×D411yescharacteristic
92C2×C107—24no—
93C2×C107#41814yescomplemented
94C2×C107C22×C22⋊C411yescharacteristic
95C2×C107C2×AGL(1,ℤ/8)12yes—
96D107—48no—
97C2×#418—1071nomaximal, Sylow
98C107C2×#41811yescharacteristic, complemented, Sylow
99C23×D4—1071no—
100C22×M16—1071no—
101C2×#117D10711yescharacteristic, complemented
102#418—1078no—
103C2×#102—1074no—
104C25—2141no—
105C22×D4—1078no—
106C22×D4—1072no—
107C22×D4—1074no—
108C22×D4—2144no—
109C22×D4—2142no—
110C22×D4—2141no—
111C23×C4C2×D10711yescharacteristic
112C2×M16—1074no—
113C2×M16—2144no—
114C22×C8—1072no—
115#117—22no—
116#117C2×D10714yescomplemented
117C2×C4⋊C4C2×D10712yescomplemented
118C2×C22⋊C4—21no—
119C2×C42—21no—
120#102—10716no—
121C24—4288no—
122C24—2148no—
123C24—2144no—
124C24—2142no—
125C24C22⋊D10711yescharacteristic
126C2×D4—1078no—
127C2×D4—10716no—
128C2×D4—1074no—
129C2×D4—21416no—
130C2×D4—2148no—
131C2×D4—2144no—
132C2×D4—2142no—
133C2×D4—2144no—
134C2×D4—2148no—
135C22×C4—22no—
136C22×C4C4×D10714yes—
137C22×C4D42814yes—
138C22×C4C22⋊D10712yes—
139C22×C4C22⋊D10711yescharacteristic
140C22×C4C22×D10712yes—
141C22×C4C22×D10711yescharacteristic
142M16—2148no—
143C2×C8—1074no—
144C2×C8—2144no—
145C4⋊C4—22no—
146C4⋊C4C22×D10714yescomplemented
147C22⋊C4—24no—
148C42—24no—
149C23—24no—
150C23—42832no—
151C23—42816no—
152C23—4288no—
153C23—21416no—
154C23—2148no—
155C23—2144no—
156C23(C2×D107)⋊C414yes—
157C23C2×C22⋊D10712yes—
158C23C2×C22⋊D10711yescharacteristic
159D4—1078no—
160D4—2148no—
161D4—21416no—
162D4—2144no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4(C2×D107)⋊C418yes—
166C2×C4(C2×D107)⋊C414yes—
167C2×C4C2×C4×D10714yes—
168C2×C4C2×C4×D10712yes—
169C2×C4C2×C22⋊D10712yes—
170C2×C4C2×C22⋊D10711yescharacteristic
171C2×C4C2×D42812yes—
172C2×C4C2×D42814yes—
173C2×C4C23×D10711yescharacteristic
174C8—2144no—
175C22—28no—
176C22—24no—
177C22—42832no—
178C22—42816no—
179C22—4288no—
180C22—2148no—
181C22C2×(C2×D107)⋊C414yes—
182C22C2×(C2×D107)⋊C412yes—
183C22#1681213414yes—
184C22C22×C22⋊D10711yescharacteristic
185C4—44no—
186C4C2×(C2×D107)⋊C414yes—
187C4C2×(C2×D107)⋊C412yes—
188C4C22×C4×D10711yescharacteristic
189C4C22×D42811yescharacteristic
190C2—24no—
191C2—4288no—
192C2#2029263114yesdirect product factor
193C2C22×(C2×D107)⋊C411yescharacteristic
194C2C2×#1681213412yes—
subgroupG/H
centerC23C2×C22⋊D107
commutatorC4×C107C23×C4
FrattiniC2×C4C23×D107
FittingC2×#117×C107C2
socleC23×C107C2×D4
prime radicalC23×D428C2
cosocleC2×C4×C107C24
hypercenterC2×#117D107
hypocenterC107C2×#418
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C22×#13133802C2semidirect
3. #20292631C2direct (N × H)
4. C2×#16812029C2semidirect
5. C2×#117×C107C2semidirect
10. C22×D428C4semidirect
14. C2×#13133802C22semidirect
15. C22×C107⋊C8C22semidirect
16. #16812029C22semidirect
19. #117×C107C22semidirect
20. C2×C4⋊C4×C107C22semidirect
34. C2×D428C2×C4semidirect
38. C2×C107⋊C8C23semidirect
48. C4⋊C4×C107C23semidirect
93. C2×C107#418semidirect
98. C107C2×#418semidirect
101. C2×#117D107semidirect
116. #117C2×D107semidirect
117. C2×C4⋊C4C2×D107semidirect
146. C4⋊C4C22×D107semidirect
192. C2#20292631direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4282
C22×#131338022
#202926312
C2×#168120292
C2×#117×C1072
C2×#418107