Finite Group Databasebeta

← C2×#17986561 #22601643

Subgroups — C2×#17986561 #22601643

Order 9088.

1984 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1984 conjugacy classes of subgroups — too many to draw. Only its 565 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×C22⋊D71C212yesmaximal, complemented
2#17986561C2116yesmaximal, direct product factor
3C2×#14556112C214yesmaximal, complemented
4C2×#14556102C214yesmaximal, complemented
5C2×#14556098C214yesmaximal, complemented
6C22×C22⋊C4×C71C211yesmaximal, characteristic, complemented
7C24×D71C2212yescomplemented
8C22×D284C2214yescomplemented
9C22×C22⋊D71—216no—
10C22×C22⋊D71C2214yes—
11C22×C22⋊D71C2214yescomplemented
12C22×C22⋊D71C22116yescomplemented
13C23×Dic71C2212yescomplemented
14#14556112C22132yescomplemented
15#14556102C22132yescomplemented
16#14556098C22132yescomplemented
17C2×C4⋊Dic71C2214yescomplemented
18C2×(C2×D71)⋊C4C2218yescomplemented
19C25×C71C2211yescharacteristic
20C23×C4×C71C2212yescomplemented
21C2×C22⋊C4×C71C2214yescomplemented
22C2×C22⋊C4×C71C2218yescomplemented
23C23×D71—28no—
24C23×D71—48no—
25C23×D71C2314yes—
26C23×D71C2318yescomplemented
27C2×D284—48no—
28C2×D284C23116yescomplemented
29C2×C22⋊D71—216no—
30C2×C22⋊D71—216no—
31C2×C22⋊D71—264no—
32C2×C22⋊D71C23116yes—
33C2×C22⋊D71C23116yescomplemented
34C22×Dic71—28no—
35C22×Dic71C2314yes—
36C22×Dic71C2318yescomplemented
37C4⋊Dic71C23116yescomplemented
38(C2×D71)⋊C4C23132yescomplemented
39C24×C71—44no—
40C24×C71D418yescomplemented
41C24×C71C2312yes—
42C24×C71C2311yescharacteristic
43C24×C71C2314yes—
44C22×C4×C71—44no—
45C22×C4×C71C2314yes—
46C22×C4×C71C2318yescomplemented
47C22⋊C4×C71C23116yescomplemented
48C23×C71—24no—
49C23×C71—28no—
50C23×C71—416no—
51C23×C71—48no—
52C23×C71C2×D418yes—
53C23×C71C2×D414yes—
54C23×C71C2×D4116yescomplemented
55C23×C71C2414yes—
56C23×C71C2412yes—
57C23×C71C2411yescharacteristic
58C22×D71—28no—
59C22×D71—216no—
60C22×D71—216no—
61C22×D71—416no—
62C22×D71—432no—
63C22×D71C2418yes—
64C2×C4×C71—28no—
65C2×C4×C71—48no—
66C2×C4×C71C2418yes—
67C22⋊D71—232no—
68C22⋊D71—232no—
69C2×Dic71—28no—
70C2×Dic71—216no—
71C2×Dic71C2418yes—
72D284—416no—
73C22×C71—216no—
74C22×C71—28no—
75C22×C71—24no—
76C22×C71—28no—
77C22×C71—416no—
78C22×C71C22×D418yes—
79C22×C71C22×D414yes—
80C22×C71C22×D412yes—
81C22×C71H(5,𝔽2)14yes—
82C22×C71C2511yescharacteristic
83C2×D71—28no—
84C2×D71—216no—
85C2×D71—432no—
86C2×D71—416no—
87C4×C71—28no—
88Dic71—28no—
89C2×C71—28no—
90C2×C71—24no—
91C2×C71#53414yescomplemented
92C2×C71C23×D411yescharacteristic
93C2×C71C2×H(5,𝔽2)12yes—
94D71—48no—
95C2×#534—711nomaximal, Sylow
96C71C2×#53411yescharacteristic, complemented, Sylow
97C23×D4—712no—
98#534—7116no—
99C2×#123—714no—
100C2×#121—714no—
101C2×#120—714no—
102C22×C22⋊C4D7111yescharacteristic, complemented
103C25—712no—
104C25C2×D7111yescharacteristic
105C22×D4—714no—
106C22×D4—714no—
107C22×D4—7116no—
108C22×D4—714no—
109C22×D4—14216no—
110C23×C4—712no—
111C23×C4C2×D7112yescomplemented
112#123—7132no—
113#121—7132no—
114#120—7132no—
115C2×C4⋊C4—714no—
116C2×C22⋊C4—718no—
117C2×C22⋊C4C2×D7114yescomplemented
118C2×C22⋊C4C2×D7118yescomplemented
119C24—44no—
120C24—2848no—
121C24—718no—
122C24—714no—
123C24—1428no—
124C24D28418yescomplemented
125C24C22×D7112yes—
126C24C22×D7111yescharacteristic
127C24C22×D7114yes—
128C2×D4—2848no—
129C2×D4—7116no—
130C2×D4—7116no—
131C2×D4—7116no—
132C2×D4—14216no—
133C2×D4—14216no—
134C2×D4—14264no—
135C22×C4—44no—
136C22×C4—718no—
137C22×C4—714no—
138C22×C4—1428no—
139C22×C4C22×D7114yes—
140C22×C4C22×D7118yescomplemented
141C4⋊C4—7116no—
142C22⋊C4—7132no—
143C22⋊C4C22×D71116yescomplemented
144C23—24no—
145C23—28no—
146C23—416no—
147C23—48no—
148C23—28432no—
149C23—28416no—
150C23—718no—
151C23—14216no—
152C23—1428no—
153C23—14216no—
154C23C2×D28418yes—
155C23C2×D28414yes—
156C23C2×D284116yescomplemented
157C23C23×D7114yes—
158C23C23×D7112yes—
159C23C23×D7111yescharacteristic
160D4—28416no—
161D4—14232no—
162D4—14232no—
163C2×C4—28no—
164C2×C4—48no—
165C2×C4—718no—
166C2×C4—14216no—
167C2×C4—1428no—
168C2×C4C23×D7118yes—
169C22—216no—
170C22—28no—
171C22—24no—
172C22—28no—
173C22—416no—
174C22—28432no—
175C22—28416no—
176C22—1428no—
177C22—14216no—
178C22C22×D28418yes—
179C22C22×D28414yes—
180C22C22×D28412yes—
181C22#1455617314yes—
182C22C24×D7111yescharacteristic
183C4—28no—
184C4—1428no—
185C2—28no—
186C2—24no—
187C2—2848no—
188C2#1798656114yesdirect product factor
189C2C23×D28411yescharacteristic
190C2C2×#1455617312yes—
subgroupG/H
centerC23C23×D71
commutatorC22×C71C25
FrattiniC22C24×D71
FittingC22×C22⋊C4×C71C2
socleC23×C71C24
hypercenterC22×C22⋊C4D71
hypocenterC71C2×#534
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D71C2semidirect
2. #17986561C2direct (N × H)
3. C2×#14556112C2semidirect
4. C2×#14556102C2semidirect
5. C2×#14556098C2semidirect
6. C22×C22⋊C4×C71C2semidirect
7. C24×D71C22semidirect
8. C22×D284C22semidirect
11. C22×C22⋊D71C22semidirect
12. C22×C22⋊D71C22semidirect
13. C23×Dic71C22semidirect
14. #14556112C22semidirect
15. #14556102C22semidirect
16. #14556098C22semidirect
17. C2×C4⋊Dic71C22semidirect
18. C2×(C2×D71)⋊C4C22semidirect
20. C23×C4×C71C22semidirect
21. C2×C22⋊C4×C71C22semidirect
22. C2×C22⋊C4×C71C22semidirect
26. C23×D71C23semidirect
28. C2×D284C23semidirect
33. C2×C22⋊D71C23semidirect
36. C22×Dic71C23semidirect
37. C4⋊Dic71C23semidirect
38. (C2×D71)⋊C4C23semidirect
40. C24×C71D4semidirect
46. C22×C4×C71C23semidirect
47. C22⋊C4×C71C23semidirect
54. C23×C71C2×D4semidirect
91. C2×C71#534semidirect
96. C71C2×#534semidirect
102. C22×C22⋊C4D71semidirect
111. C23×C4C2×D71semidirect
117. C2×C22⋊C4C2×D71semidirect
118. C2×C22⋊C4C2×D71semidirect
124. C24D284semidirect
140. C22×C4C22×D71semidirect
143. C22⋊C4C22×D71semidirect
156. C23C2×D284semidirect
188. C2#17986561direct (N × H)