Finite Group Databasebeta

← C2×#14521790 #16859829

Subgroups — C2×#14521790 #16859829

Order 3968.

1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 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
1#14521790C2116yesmaximal, direct product factor
2C2×#11758451C211yesmaximal, characteristic, complemented
3C2×#11758453C211yesmaximal, characteristic, complemented
4C2×#11758471C213yesmaximal, complemented
5C2×#11758472C213yesmaximal, complemented
6C2×#11758461C213yesmaximal, complemented
7C2×#11758459C213yesmaximal, complemented
8C2×C31×#126C211yesmaximal, characteristic, complemented
9C24×D31C2211yescharacteristic
10C22×C22⋊D31C2213yes—
11C22×D124C2213yes—
12C22×D124C2213yes—
13C22×D124C2213yescomplemented
14C22×C4×D31C2213yescomplemented
15C31×#126C2218yescomplemented
16C2×C4⋊C4×C31C2213yescomplemented
17C2×C22⋊C4×C31C2213yes—
18C2×C42×C31C2211yescharacteristic, complemented
19C2×(C2×D31)⋊C4C2213yes—
20C2×(C2×D31)⋊C4C2213yes—
21C2×(C2×D31)⋊C4C2213yescomplemented
22C2×Dic31⋊C4C2213yescomplemented
23#11758472C22124yescomplemented
24#11758471C22124yescomplemented
25#11758461C22124yescomplemented
26#11758459C22124yescomplemented
27#11758453C2218yescomplemented
28#11758451C2218yescomplemented
29C24×C31C2311yescharacteristic
30C23×D31—46no—
31C23×D31C2311yescharacteristic
32C23×D31C2311yescharacteristic
33C23×D31C2313yes—
34C23×D31C2314yes—
35C22×C4×C31C2313yes—
36C22×C4×C31C2313yes—
37C2×C22⋊D31—46no—
38C2×C22⋊D31C23112yes—
39C22×Dic31C2313yes—
40C2×D124—46no—
41C2×D124—46no—
42C2×D124—46no—
43C2×D124C23112yes—
44C2×D124C23112yes—
45C2×D124C23112yescomplemented
46C2×C4×D31—46no—
47C2×C4×D31C23112yescomplemented
48C4⋊C4×C31C23112yescomplemented
49C22⋊C4×C31C23112yes—
50C42×C31C2314yescomplemented
51(C2×D31)⋊C4C23112yes—
52(C2×D31)⋊C4C23112yes—
53(C2×D31)⋊C4C23112yescomplemented
54Dic31⋊C4C23112yescomplemented
55C23×C31—26no—
56C23×C31C2412yes—
57C23×C31C2411yescharacteristic
58C22×D31—26no—
59C22×D31—26no—
60C22×D31—26no—
61C22×D31—26no—
62C22×D31—26no—
63C22×D31—412no—
64C22×D31—416no—
65C22×D31C2412yes—
66C22×D31C2412yes—
67C22×D31C2416yes—
68C2×C4×C31—26no—
69C2×C4×C31—26no—
70C2×C4×C31C2416yes—
71C2×C4×C31C2416yes—
72C22⋊D31—412no—
73C2×Dic31—26no—
74C2×Dic31C2416yes—
75D124—412no—
76D124—412no—
77D124—412no—
78C4×D31—412no—
79C2×#560—311nomaximal, Sylow
80C22×C31—26no—
81C22×C31—44no—
82C22×C31H(5,𝔽2)16yes—
83C22×C31C2511yescharacteristic
84C2×D31—26no—
85C2×D31—26no—
86C2×D31—26no—
87C2×D31—26no—
88C2×D31—26no—
89C2×D31—416no—
90C2×D31—412no—
91C2×D31—44no—
92C2×D31—44no—
93C4×C31—26no—
94C4×C31—26no—
95Dic31—26no—
96#560—3116no—
97C2×#127—311no—
98C2×#126—311no—
99C2×#126D3111yescharacteristic, complemented
100C2×#123—313no—
101C2×#121—313no—
102C2×#121—313no—
103C2×#120—313no—
104C2×C31—42no—
105C2×C31#56014yescomplemented
106C2×C31C2×H(5,𝔽2)13yes—
107D31—46no—
108D31—42no—
109D31—42no—
110C25—311no—
111C22×D4—313no—
112C22×D4—313no—
113C22×D4—313no—
114C22×D4—313no—
115C23×C4—313no—
116#127—318no—
117#126—318no—
118#126C2×D3118yescomplemented
119#123—3124no—
120#121—3124no—
121#121—3124no—
122#120—3124no—
123C2×C4⋊C4—313no—
124C2×C4⋊C4C2×D3113yescomplemented
125C2×C22⋊C4—313no—
126C2×C22⋊C4—313no—
127C2×C22⋊C4—313no—
128C2×C22⋊C4C2×D3113yes—
129C2×C42C2×D3111yescharacteristic, complemented
130C31C2×#56011yescharacteristic, complemented, Sylow
131C24—311no—
132C24—311no—
133C24—313no—
134C24—314no—
135C24—1246no—
136C24C22×D3111yescharacteristic
137C2×D4—3112no—
138C2×D4—3112no—
139C2×D4—3112no—
140C2×D4—3112no—
141C2×D4—1246no—
142C2×D4—1246no—
143C2×D4—1246no—
144C2×D4—1246no—
145C22×C4—313no—
146C22×C4—3112no—
147C22×C4—1246no—
148C22×C4C22×D3113yes—
149C22×C4C22×D3113yes—
150C4⋊C4—3112no—
151C4⋊C4C22×D31112yescomplemented
152C22⋊C4—3112no—
153C22⋊C4—3112no—
154C22⋊C4—3112no—
155C22⋊C4C22×D31112yes—
156C42C22×D3114yescomplemented
157C23—26no—
158C23—312no—
159C23—312no—
160C23—316no—
161C23—626no—
162C23—626no—
163C23—626no—
164C23—626no—
165C23—626no—
166C23—12412no—
167C23—12416no—
168C23C23×D3112yes—
169C23C23×D3111yescharacteristic
170D4—12412no—
171D4—12412no—
172D4—12412no—
173D4—12412no—
174C2×C4—26no—
175C2×C4—26no—
176C2×C4—316no—
177C2×C4—626no—
178C2×C4—12412no—
179C2×C4C23×D3116yes—
180C2×C4C23×D3116yes—
181C22—26no—
182C22—44no—
183C22—626no—
184C22—626no—
185C22—626no—
186C22—626no—
187C22—626no—
188C22—12416no—
189C22—1244no—
190C22—1244no—
191C22—12412no—
192C22#1175856616yes—
193C22C24×D3111yescharacteristic
194C4—26no—
195C4—26no—
196C4—626no—
197C2—42no—
198C2—1242no—
199C2—1242no—
200C2—1246no—
201C2#1452179014yesdirect product factor
202C2C2×#1175856613yes—
subgroupG/H
centerC23C23×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC2×C31×#126C2
socleC23×C31C24
hypercenterC2×#126D31
hypocenterC31C2×#560
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #14521790C2direct (N × H)
2. C2×#11758451C2semidirect
3. C2×#11758453C2semidirect
4. C2×#11758471C2semidirect
5. C2×#11758472C2semidirect
6. C2×#11758461C2semidirect
7. C2×#11758459C2semidirect
8. C2×C31×#126C2semidirect
13. C22×D124C22semidirect
14. C22×C4×D31C22semidirect
15. C31×#126C22semidirect
16. C2×C4⋊C4×C31C22semidirect
18. C2×C42×C31C22semidirect
21. C2×(C2×D31)⋊C4C22semidirect
22. C2×Dic31⋊C4C22semidirect
23. #11758472C22semidirect
24. #11758471C22semidirect
25. #11758461C22semidirect
26. #11758459C22semidirect
27. #11758453C22semidirect
28. #11758451C22semidirect
45. C2×D124C23semidirect
47. C2×C4×D31C23semidirect
48. C4⋊C4×C31C23semidirect
50. C42×C31C23semidirect
53. (C2×D31)⋊C4C23semidirect
54. Dic31⋊C4C23semidirect
99. C2×#126D31semidirect
105. C2×C31#560semidirect
118. #126C2×D31semidirect
124. C2×C4⋊C4C2×D31semidirect
129. C2×C42C2×D31semidirect
130. C31C2×#560semidirect
151. C4⋊C4C22×D31semidirect
156. C42C22×D31semidirect
201. C2#14521790direct (N × H)

Maximal subgroups

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

subgroupindex
#145217902
C2×#117584512
C2×#117584532
C2×#117584712
C2×#117584722
C2×#117584612
C2×#117584592
C2×C31×#1262
C2×#56031