Finite Group Databasebeta

← C2×#14521655 #16859072

Subgroups — C2×#14521655 #16859072

Order 3968.

1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.

normal subgroups only

This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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#14521655C2116yesmaximal, direct product factor
2C2×#11758451C211yesmaximal, characteristic, complemented
3C2×#11758471C214yesmaximal, complemented
4C2×#11758472C214yesmaximal, complemented
5C2×#11758472C212yesmaximal, complemented
6C2×#11758470C212yesmaximal, complemented
7C2×#11758449C211yesmaximal, characteristic, complemented
8C2×C31×#125C211yesmaximal, characteristic, complemented
9C22×D124C2212yes—
10C22×D124C2214yes—
11C22×D124C2214yes—
12C22×C4×D31C2211yescharacteristic
13C22×C4×D31C2214yes—
14C31×#125C2218yescomplemented
15C2×C4⋊C4×C31C2212yes—
16C2×C4⋊C4×C31C2214yes—
17C2×C42×C31C2211yescharacteristic
18C2×(C2×D31)⋊C4C2212yes—
19C2×(C2×D31)⋊C4C2214yes—
20C2×(C2×D31)⋊C4C2214yes—
21C2×Dic31⋊C4C2212yes—
22C2×C4×Dic31C2211yescharacteristic
23#11758472C22132yescomplemented
24#11758472C22116yescomplemented
25#11758471C22132yescomplemented
26#11758470C22116yescomplemented
27#11758451C2218yescomplemented
28#11758449C2218yescomplemented
29C23×D31C2311yescharacteristic
30C23×D31C2314yes—
31C22×C4×C31C2312yes—
32C22×C4×C31C2314yes—
33C22×C4×C31C2311yescharacteristic
34C22×Dic31C2312yes—
35C22×Dic31C2311yescharacteristic
36C2×D124—28no—
37C2×D124—48no—
38C2×D124—48no—
39C2×D124C2318yes—
40C2×D124C23116yes—
41C2×D124C23116yes—
42C2×C4×D31—24no—
43C2×C4×D31—48no—
44C2×C4×D31C2314yes—
45C2×C4×D31C23116yes—
46C4⋊C4×C31C2318yes—
47C4⋊C4×C31C23116yes—
48C42×C31C2314yes—
49(C2×D31)⋊C4C2318yes—
50(C2×D31)⋊C4C23116yes—
51(C2×D31)⋊C4C23116yes—
52Dic31⋊C4C2318yes—
53C4×Dic31C2314yes—
54C23×C31C2411yescharacteristic
55C22×D31—22no—
56C22×D31—28no—
57C22×D31—28no—
58C22×D31—24no—
59C22×D31—28no—
60C22×D31C2412yes—
61C22×D31C2418yes—
62C2×C4×C31—28no—
63C2×C4×C31—24no—
64C2×C4×C31#4114yes—
65C2×C4×C31C2414yes—
66C2×C4×C31C2418yes—
67C2×C4×C31C2412yes—
68C2×Dic31—22no—
69C2×Dic31—24no—
70C2×Dic31C2414yes—
71C2×Dic31C2412yes—
72D124—216no—
73D124—416no—
74D124—416no—
75C4×D31—28no—
76C4×D31—416no—
77C2×#540—311nomaximal, Sylow
78C22×C31C2×#4112yes—
79C22×C31H(5,𝔽2)14yes—
80C22×C31C2511yescharacteristic
81C2×D31—22no—
82C2×D31—28no—
83C2×D31—28no—
84C2×D31—24no—
85C2×D31—28no—
86C2×D31—44no—
87C2×D31—416no—
88C4×C31—28no—
89C4×C31—24no—
90C4×C31C2×#4114yes—
91Dic31—22no—
92Dic31—24no—
93#540—3116no—
94C2×#127—311no—
95C2×#125D3111yescharacteristic, complemented
96C2×#123—314no—
97C2×#121—314no—
98C2×#121—312no—
99C2×C4×D4—312no—
100C2×#117—311no—
101C2×C31#54014yescomplemented
102C2×C31C22×#4111yescharacteristic
103C2×C31C2×H(5,𝔽2)12yes—
104D31—42no—
105D31—48no—
106C22×D4—312no—
107C22×D4—314no—
108C22×D4—314no—
109C23×C4—311no—
110C23×C4—314no—
111#127—318no—
112#125C2×D3118yescomplemented
113#123—3132no—
114#121—3132no—
115#121—3116no—
116C4×D4—3116no—
117#117—318no—
118C2×C4⋊C4—312no—
119C2×C4⋊C4C2×D3112yes—
120C2×C4⋊C4C2×D3114yes—
121C2×C22⋊C4—312no—
122C2×C22⋊C4—314no—
123C2×C22⋊C4—314no—
124C2×C42—311no—
125C2×C42C2×D3111yescharacteristic
126C31C2×#54011yescharacteristic, complemented, Sylow
127C24—311no—
128C24—314no—
129C2×D4—318no—
130C2×D4—3116no—
131C2×D4—3116no—
132C2×D4—628no—
133C2×D4—1248no—
134C2×D4—1248no—
135C22×C4—312no—
136C22×C4—311no—
137C22×C4—314no—
138C22×C4—3116no—
139C22×C4—624no—
140C22×C4—1248no—
141C22×C4C22×D3112yes—
142C22×C4C22×D3114yes—
143C22×C4C22×D3111yescharacteristic
144C4⋊C4—318no—
145C4⋊C4C22×D3118yes—
146C4⋊C4C22×D31116yes—
147C22⋊C4—318no—
148C22⋊C4—3116no—
149C22⋊C4—3116no—
150C42—314no—
151C42C22×D3114yes—
152C23—312no—
153C23—318no—
154C23—622no—
155C23—628no—
156C23—628no—
157C23—624no—
158C23—628no—
159C23C23×D3111yescharacteristic
160D4—6216no—
161D4—12416no—
162D4—12416no—
163C2×C4—28no—
164C2×C4—24no—
165C2×C4—314no—
166C2×C4—312no—
167C2×C4—622no—
168C2×C4—624no—
169C2×C4—628no—
170C2×C4—12416no—
171C2×C4#9249914yes—
172C2×C4C23×D3114yes—
173C2×C4C23×D3118yes—
174C2×C4C23×D3112yes—
175C22—622no—
176C22—628no—
177C22—628no—
178C22—624no—
179C22—628no—
180C22—1244no—
181C22—12416no—
182C22C2×#9249912yes—
183C22#1175856614yes—
184C22C24×D3111yescharacteristic
185C4—28no—
186C4—24no—
187C4—622no—
188C4—624no—
189C4C2×#9249914yes—
190C2—1242no—
191C2—1248no—
192C2#1452165514yesdirect product factor
193C2C22×#9249911yescharacteristic
194C2C2×#1175856612yes—
subgroupG/H
centerC23C23×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC2×C31×#125C2
socleC23×C31C24
hypercenterC2×#125D31
hypocenterC31C2×#540
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #14521655C2direct (N × H)
2. C2×#11758451C2semidirect
3. C2×#11758471C2semidirect
4. C2×#11758472C2semidirect
5. C2×#11758472C2semidirect
6. C2×#11758470C2semidirect
7. C2×#11758449C2semidirect
8. C2×C31×#125C2semidirect
14. C31×#125C22semidirect
23. #11758472C22semidirect
24. #11758472C22semidirect
25. #11758471C22semidirect
26. #11758470C22semidirect
27. #11758451C22semidirect
28. #11758449C22semidirect
95. C2×#125D31semidirect
101. C2×C31#540semidirect
112. #125C2×D31semidirect
126. C31C2×#540semidirect
192. C2#14521655direct (N × H)

Maximal subgroups

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

subgroupindex
#145216552
C2×#117584512
C2×#117584712
C2×#117584722
C2×#117584702
C2×#117584492
C2×C31×#1252
C2×#54031