Finite Group Databasebeta

← C2×#14557846 #18004467

Subgroups — C2×#14557846 #18004467

Order 4736.

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

normal subgroups only

This group has 512 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
1C2×#11924510C211yesmaximal, characteristic
2#14557846C218yesmaximal, direct product factor
3C2×#11924469C212yesmaximal, complemented
4C2×#11924456C212yesmaximal, complemented
5C2×C22⋊#64436C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C37C211yesmaximal, characteristic, complemented
7C22×D148C2211yescharacteristic
8C22×C22⋊D37—21no—
9C22×#64436C2212yes—
10#11924510—22no—
11#11924510C2214yes—
12C2×C4⋊Dic37C2211yescharacteristic
13C2×#10596938—21no—
14#11924469C2218yescomplemented
15#11924456C2218yescomplemented
16C22⋊#64436C2214yescomplemented
17C23×C4×C37—21no—
18C23×C4×C37C2211yescharacteristic
19C2×C4⋊C4×C37—22no—
20C2×C4⋊C4×C37—21no—
21C2×C4⋊C4×C37C2212yes—
22C2×C4⋊C4×C37C2214yescomplemented
23C24×C37D411yescharacteristic
24C23×D37—21no—
25C22×C4×C37—24no—
26C22×C4×C37—22no—
27C22×C4×C37—24no—
28C22×C4×C37—44no—
29C22×C4×C37D411yescharacteristic
30C22×C4×C37D412yes—
31C22×C4×C37C2312yes—
32C22×C4×C37C2311yescharacteristic
33C2×C22⋊D37—24no—
34C2×C22⋊D37—44no—
35C22×Dic37—21no—
36C2×D148—24no—
37C2×D148—21no—
38C2×D148C2312yes—
39C4⋊C4×C37—22no—
40C4⋊C4×C37—24no—
41C4⋊C4×C37C2314yes—
42#10596938—24no—
43C4⋊Dic37—21no—
44C4⋊Dic37C2312yes—
45C2×#64436—24no—
46C2×#64436C2314yes—
47C23×C37—22no—
48C23×C37—22no—
49C23×C37D814yes—
50C23×C37C2×D412yes—
51C23×C37C2×D411yescharacteristic
52C22×D37—22no—
53C22×D37—42no—
54C22×D37—42no—
55C22×D37—42no—
56C2×C4×C37—22no—
57C2×C4×C37—24no—
58C2×C4×C37—24no—
59C2×C4×C37—24no—
60C2×C4×C37—48no—
61C2×C4×C37—44no—
62C2×C4×C37C2×D412yes—
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37#4114yes—
65C2×C4×C37C2411yescharacteristic
66C22⋊D37—48no—
67C2×Dic37—22no—
68C2×Dic37—42no—
69D148—24no—
70D148—42no—
71#64436—24no—
72C22×C37—22no—
73C22×C37—22no—
74C22×C37—28no—
75C22×C37#12312yes—
76C22×C37C2×D814yes—
77C22×C37C2×D812yes—
78C22×C37#13712yes—
79C22×C37C22×D411yescharacteristic
80C2×D37—42no—
81C2×D37—42no—
82C2×D37—42no—
83C2×D37—84no—
84C4×C37—22no—
85C4×C37—44no—
86C4×C37#12312yes—
87C4×C37C2×#4112yes—
88Dic37—42no—
89C2×#480—371nomaximal, Sylow
90C2×C37—24no—
91C2×C37#48014yescomplemented
92C2×C37C2×#12311yescharacteristic
93C2×C37C22×D811yescharacteristic
94C2×C37C2×#13711yescharacteristic
95D37—82no—
96C2×#121—371no—
97C22×C4⋊C4D3711yescharacteristic, complemented
98#480—378no—
99C2×#107—372no—
100C2×#102—372no—
101C2×C22⋊C8—371no—
102C37C2×#48011yescharacteristic, complemented, Sylow
103C22×D4—371no—
104C22×D4—741no—
105C23×C4—21no—
106C23×C4C2×D3711yescharacteristic
107C22×C8—372no—
108#121—374no—
109#121—742no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—371no—
113C2×C4⋊C4C2×D3712yes—
114C2×C4⋊C4C2×D3714yescomplemented
115C2×C22⋊C4—741no—
116#107—378no—
117#102—378no—
118C22⋊C8—374no—
119C24—741no—
120C24C22⋊D3711yescharacteristic
121C2×D4—372no—
122C2×D4—744no—
123C2×D4—744no—
124C2×D4—741no—
125C2×D4—1484no—
126C22×C4—24no—
127C22×C4—24no—
128C22×C4—22no—
129C22×C4—44no—
130C22×C4—741no—
131C22×C4C22⋊D3712yes—
132C22×C4C22⋊D3711yescharacteristic
133C22×C4C22×D3712yes—
134C22×C4C22×D3711yescharacteristic
135C2×C8—374no—
136C2×C8—744no—
137C4⋊C4—22no—
138C4⋊C4—24no—
139C4⋊C4—372no—
140C4⋊C4—741no—
141C4⋊C4C22×D3714yes—
142C22⋊C4—744no—
143C23—22no—
144C23—22no—
145C23—742no—
146C23—1482no—
147C23—1482no—
148C23—1482no—
149C23#1059693914yes—
150C23C2×C22⋊D3712yes—
151C23C2×C22⋊D3711yescharacteristic
152D4—744no—
153D4—1488no—
154D4—1482no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—48no—
160C2×C4—44no—
161C2×C4—742no—
162C2×C4—1482no—
163C2×C4#1059696214yes—
164C2×C4C2×C22⋊D3712yes—
165C2×C4C2×C22⋊D3711yescharacteristic
166C2×C4C23×D3711yescharacteristic
167C8—744no—
168C22—22no—
169C22—22no—
170C22—28no—
171C22—2964no—
172C22—1482no—
173C22—1482no—
174C22—1482no—
175C22#1192451912yes—
176C22C2×#1059693914yes—
177C22C2×#1059693912yes—
178C22#1192456712yes—
179C22C22×C22⋊D3711yescharacteristic
180C4—22no—
181C4—44no—
182C4—1482no—
183C4#1192451912yes—
184C4C2×#1059696212yes—
185C2—24no—
186C2—2962no—
187C2#1455784614yesdirect product factor
188C2C2×#1192451911yescharacteristic
189C2C22×#1059693911yescharacteristic
190C2C2×#1192456711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC22×C4⋊C4×C37C2
socleC23×C37C2×D4
prime radicalC2×#11924510C2
hypercenterC22×C4⋊C4D37
hypocenterC37C2×#480
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14557846C2direct (N × H)
3. C2×#11924469C2semidirect
4. C2×#11924456C2semidirect
5. C2×C22⋊#64436C2semidirect
6. C22×C4⋊C4×C37C2semidirect
14. #11924469C22semidirect
15. #11924456C22semidirect
16. C22⋊#64436C22semidirect
22. C2×C4⋊C4×C37C22semidirect
91. C2×C37#480semidirect
97. C22×C4⋊C4D37semidirect
102. C37C2×#480semidirect
114. C2×C4⋊C4C2×D37semidirect
187. C2#14557846direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119245102
#145578462
C2×#119244692
C2×#119244562
C2×C22⋊#644362
C22×C4⋊C4×C372
C2×#48037