Finite Group Databasebeta

← C2×#14521286 #16855280

Subgroups — C2×#14521286 #16855280

Order 3968.

616 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 165 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×D248C211yesmaximal, characteristic, complemented
2C22×C8×D31C211yesmaximal, characteristic, complemented
3C2×#11758472C212yesmaximal, complemented
4#14521286C218yesmaximal, direct product factor
5C2×#11758397C212yesmaximal, complemented
6C2×C31×#107C211yesmaximal, characteristic, complemented
7C22×D124—22no—
8C22×D124C2212yes—
9C22×C4×D31C2211yescharacteristic
10C22×C8×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2212yes—
12C2×(C2×D31)⋊C4—22no—
13C22×C31⋊C8C2211yescharacteristic
14C2×D248—24no—
15C2×D248C2214yescomplemented
16C2×C8×D31—24no—
17C2×C8×D31C2214yescomplemented
18#11758472—24no—
19#11758472C2218yescomplemented
20C31×#107C2214yescomplemented
21#11758397C2218yescomplemented
22C23×D31—22no—
23C23×D31D411yescharacteristic
24C22×C4×C31—22no—
25C22×C4×C31C2311yescharacteristic
26C22×Dic31D411yescharacteristic
27C2×D124—24no—
28C2×D124—24no—
29C2×D124—28no—
30C2×D124—22no—
31C2×D124—48no—
32C2×D124C2314yes—
33C2×C4×D31—22no—
34C2×C4×D31—22no—
35C2×C4×D31D412yes—
36C2×C4×D31C2312yes—
37C2×C8×C31D414yescomplemented
38C2×C8×C31C2312yes—
39C4⋊C4×C31—22no—
40C4⋊C4×C31C2314yes—
41(C2×D31)⋊C4—28no—
42C2×C31⋊C8—22no—
43C2×C31⋊C8C2312yes—
44D248—28no—
45C8×D31—28no—
46C23×C31C2×D411yescharacteristic
47C22×D31—22no—
48C22×D31—22no—
49C22×D31—24no—
50C22×D31—44no—
51C22×D31—44no—
52C22×D31—44no—
53C22×D31D814yescomplemented
54C22×D31C2×D412yes—
55C2×C4×C31—24no—
56C2×C4×C31—44no—
57C2×C4×C31C2×D412yes—
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31#4112yes—
60C2×C4×C31C2411yescharacteristic
61C2×Dic31—22no—
62C2×Dic31C2×D412yes—
63D124—24no—
64D124—24no—
65D124—416no—
66D124—44no—
67C4×D31—24no—
68C4×D31—22no—
69C4×D31—22no—
70C8×C31C2×D414yescomplemented
71C31⋊C8—22no—
72C2×#466—311nomaximal, Sylow
73C22×C31#12112yes—
74C22×C31C2×D812yes—
75C22×C31#13512yes—
76C22×C31C22×D411yescharacteristic
77C2×D31—22no—
78C2×D31—22no—
79C2×D31—28no—
80C2×D31—44no—
81C2×D31—44no—
82C2×D31—44no—
83C2×D31—88no—
84C2×D31C2×D814yescomplemented
85C4×C31—44no—
86C4×C31#12112yes—
87C4×C31C22×D411yescharacteristic
88C4×C31C2×#4111yescharacteristic
89Dic31—22no—
90C22×D8—311no—
91C23×C8—311no—
92C2×#121—312no—
93#466—318no—
94C2×#107D3111yescharacteristic, complemented
95C2×#102—312no—
96C2×C31#46614yescomplemented
97C2×C31C2×#12111yescharacteristic
98C2×C31C22×D811yescharacteristic
99C2×C31C2×#13511yescharacteristic
100D31—24no—
101D31—84no—
102C22×D4—312no—
103C22×D4—622no—
104C23×C4—311no—
105C2×D8—314no—
106C2×D8—624no—
107C22×C8—311no—
108C22×C8—314no—
109C22×C8—624no—
110C22×C8C2×D3111yescharacteristic
111#121—318no—
112#121—624no—
113C2×C4⋊C4C2×D3112yes—
114C2×C22⋊C4—622no—
115#107C2×D3114yescomplemented
116#102—318no—
117C31C2×#46611yescharacteristic, complemented, Sylow
118C24—311no—
119C24—622no—
120C2×D4—314no—
121C2×D4—628no—
122C2×D4—624no—
123C2×D4—622no—
124C2×D4—624no—
125C2×D4—1248no—
126C22×C4—22no—
127C22×C4—311no—
128C22×C4—312no—
129C22×C4—312no—
130C22×C4—622no—
131C22×C4—622no—
132C22×C4C22×D3111yescharacteristic
133D8—628no—
134C2×C8—312no—
135C2×C8—622no—
136C2×C8—628no—
137C2×C8D12414yescomplemented
138C2×C8C22×D3112yes—
139C4⋊C4—22no—
140C4⋊C4C22×D3114yes—
141C22⋊C4—628no—
142C23—314no—
143C23—312no—
144C23—622no—
145C23—622no—
146C23—624no—
147C23—1244no—
148C23—1244no—
149C23—1244no—
150C23D4×D3111yescharacteristic
151D4—624no—
152D4—624no—
153D4—12416no—
154D4—1244no—
155C2×C4—24no—
156C2×C4—44no—
157C2×C4—312no—
158C2×C4—622no—
159C2×C4—624no—
160C2×C4—622no—
161C2×C4—622no—
162C2×C4C2×D12412yes—
163C2×C4D4×D3111yescharacteristic
164C2×C4#9249912yes—
165C2×C4C23×D3111yescharacteristic
166C8—622no—
167C8C2×D12414yescomplemented
168C22—314no—
169C22—628no—
170C22—622no—
171C22—622no—
172C22—1244no—
173C22—1244no—
174C22—1244no—
175C22—2488no—
176C22#1175847212yes—
177C22D8×D3112yes—
178C22#1175849612yes—
179C22C2×D4×D3111yescharacteristic
180C4—44no—
181C4—622no—
182C4#1175847212yes—
183C4C22×D12411yescharacteristic
184C4C2×#9249911yescharacteristic
185C2—624no—
186C2—2484no—
187C2#1452128614yesdirect product factor
188C2C2×#1175847211yescharacteristic
189C2C2×D8×D3111yescharacteristic
190C2C2×#1175849611yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#107C2
socleC23×C31C2×D4
hypercenterC2×#107D31
hypocenterC31C2×#466
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×D248C2semidirect
2. C22×C8×D31C2semidirect
3. C2×#11758472C2semidirect
4. #14521286C2direct (N × H)
5. C2×#11758397C2semidirect
6. C2×C31×#107C2semidirect
15. C2×D248C22semidirect
17. C2×C8×D31C22semidirect
19. #11758472C22semidirect
20. C31×#107C22semidirect
21. #11758397C22semidirect
37. C2×C8×C31D4semidirect
53. C22×D31D8semidirect
70. C8×C31C2×D4semidirect
84. C2×D31C2×D8semidirect
94. C2×#107D31semidirect
96. C2×C31#466semidirect
115. #107C2×D31semidirect
117. C31C2×#466semidirect
137. C2×C8D124semidirect
167. C8C2×D124semidirect
187. C2#14521286direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D2482
C22×C8×D312
C2×#117584722
#145212862
C2×#117583972
C2×C31×#1072
C2×#46631