Finite Group Databasebeta

← C2×#14558401 #18010267

Subgroups — C2×#14558401 #18010267

Order 4736.

404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 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×#11924615C212yesmaximal
2#14558401C214yesmaximal, direct product factor
3C22×#10596929C211yesmaximal, characteristic
4#11924615—22no—
5#11924615—22no—
6#11924615C414yescomplemented
7#11924615C2214yes—
8C2×C4⋊#3866—22no—
9C2×C22⋊#3866—22no—
10C2×C4×#3866C414yescomplemented
11C22×C4×D37C2211yescharacteristic
12C2×#10596929—22no—
13C2×#10596929—22no—
14C2×#10596929C412yescomplemented
15C2×#10596929C2212yes—
16C22×#64436C411yescharacteristic, complemented
17C22×C8×C37C411yescharacteristic, complemented
18C23×D37D411yescharacteristic
19C22×#3866—24no—
20C22×C4×C37C2×C411yescharacteristic
21C22×Dic37Q811yescharacteristic
22C2×C4×D37C2×C411yescharacteristic
23C2×C4×D37C2×C412yes—
24C2×C4×D37C2×C412yes—
25C2×C4×D37D411yescharacteristic
26C2×C4×D37D412yes—
27C2×C4×D37D412yes—
28C2×C4×D37Q811yescharacteristic
29C2×C4×D37C2311yescharacteristic
30C22⋊#3866—24no—
31C22⋊#3866—24no—
32C4⋊#3866—24no—
33C4⋊#3866—24no—
34C4×#3866—24no—
35C4×#3866C2×C418yescomplemented
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C2×C8×C37C2×C412yescomplemented
39C2×#64436—21no—
40C2×#64436—21no—
41C2×#64436C2×C412yescomplemented
42#10596929—24no—
43#10596929—24no—
44C23×C37C4⋊C411yescharacteristic
45C22×D37—42no—
46C22×D37C22⋊C412yes—
47C22×D37C22⋊C412yes—
48C22×D37C4⋊C411yescharacteristic
49C22×D37C2×D411yescharacteristic
50C2×#3866—28no—
51C2×#3866—48no—
52C2×C4×C37C4211yescharacteristic
53C2×C4×C37C4211yescharacteristic
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C4⋊C411yescharacteristic
57C2×C4×C37C22×C411yescharacteristic
58C2×Dic37C4⋊C411yescharacteristic
59C2×Dic37C4⋊C412yes—
60C2×Dic37C4⋊C412yes—
61C2×Dic37C2×Q811yescharacteristic
62C4×D37C4212yes—
63C4×D37C22⋊C412yes—
64C4×D37C22⋊C412yes—
65C4×D37C22⋊C412yes—
66C4×D37C4⋊C412yes—
67C4×D37C4⋊C412yes—
68C4×D37C22×C412yes—
69C4×D37C2×D412yes—
70C8×C37—22no—
71#64436—22no—
72C22×C37—22no—
73C22×C37#9511yescharacteristic
74C22×C37#9511yescharacteristic
75C22×C37C2×C4⋊C411yescharacteristic
76C2×D37—24no—
77C2×D37—42no—
78C2×D37—41no—
79C2×D37—41no—
80C2×D37#9512yes—
81C2×D37C2×C22⋊C412yes—
82#3866—48no—
83C4×C37#9511yescharacteristic
84C4×C37#9511yescharacteristic
85C4×C37C2×C4211yescharacteristic
86C4×C37C2×C22⋊C411yescharacteristic
87Dic37#9512yes—
88Dic37C2×C4⋊C412yes—
89C2×H(3,ℤ/4)—371nomaximal, Sylow
90C2×C37—21no—
91C2×C37—21no—
92C2×C37H(3,ℤ/4)12yescomplemented
93C2×C37C2×#9511yescharacteristic
94D37—22no—
95D37—22no—
96C22×M16—371no—
97C2×#117—372no—
98H(3,ℤ/4)—374no—
99C37C2×H(3,ℤ/4)11yescharacteristic, complemented, Sylow
100C23×C4—371no—
101C2×M16—372no—
102C2×M16—372no—
103C2×M16—742no—
104C2×M16—742no—
105C22×C8—371no—
106C22×C8#386611yescharacteristic, complemented
107#117—374no—
108#117—374no—
109#117—742no—
110#117—742no—
111C2×C4⋊C4—742no—
112C2×C22⋊C4—742no—
113C2×C42—374no—
114C24—371no—
115C22×C4—371no—
116C22×C4—372no—
117C22×C4—372no—
118C22×C4—371no—
119C22×C4—371no—
120C22×C4—372no—
121C22×C4—372no—
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—744no—
125C22×C4C2×#386611yescharacteristic
126M16—744no—
127M16—744no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—372no—
131C2×C8—741no—
132C2×C8—741no—
133C2×C8C2×#386612yescomplemented
134C4⋊C4—744no—
135C4⋊C4—744no—
136C22⋊C4—744no—
137C22⋊C4—744no—
138C42—378no—
139C42—744no—
140C23—372no—
141C23—372no—
142C23—371no—
143C23—371no—
144C23—1482no—
145C23C4⋊#386611yescharacteristic
146C2×C4—372no—
147C2×C4—372no—
148C2×C4—371no—
149C2×C4—371no—
150C2×C4—372no—
151C2×C4—372no—
152C2×C4—372no—
153C2×C4—372no—
154C2×C4—372no—
155C2×C4—372no—
156C2×C4—372no—
157C2×C4—372no—
158C2×C4—748no—
159C2×C4—1488no—
160C2×C4C4×#386611yescharacteristic
161C2×C4C4×#386611yescharacteristic
162C2×C4C4⋊#386611yescharacteristic
163C2×C4C22⋊#386611yescharacteristic
164C2×C4C22⋊#386611yescharacteristic
165C2×C4C22×#386611yescharacteristic
166C8—22no—
167C8—742no—
168C22—22no—
169C22—372no—
170C22—372no—
171C22—744no—
172C22—1482no—
173C22—1481no—
174C22—1481no—
175C22(C2×#3866)⋊C411yescharacteristic
176C22(C2×#3866)⋊C411yescharacteristic
177C22C2×C4⋊#386611yescharacteristic
178C4—372no—
179C4—372no—
180C4—1488no—
181C4(C2×#3866)⋊C411yescharacteristic
182C4(C2×#3866)⋊C411yescharacteristic
183C4C2×C4×#386611yescharacteristic
184C4C2×C22⋊#386611yescharacteristic
185C2—21no—
186C2—21no—
187C2—742no—
188C2—742no—
189C2#1455840112yesdirect product factor
190C2C2×(C2×#3866)⋊C411yescharacteristic
subgroupG/H
centerC2×C4C4×#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
FittingC22×C8×C37C4
socleC22×C37#95
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenterC22×C8#3866
hypocenterC37C2×H(3,ℤ/4)
LCSG ▷ C4×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #14558401C2direct (N × H)
6. #11924615C4semidirect
10. C2×C4×#3866C4semidirect
14. C2×#10596929C4semidirect
16. C22×#64436C4semidirect
17. C22×C8×C37C4semidirect
35. C4×#3866C2×C4semidirect
38. C2×C8×C37C2×C4semidirect
41. C2×#64436C2×C4semidirect
92. C2×C37H(3,ℤ/4)semidirect
99. C37C2×H(3,ℤ/4)semidirect
106. C22×C8#3866semidirect
133. C2×C8C2×#3866semidirect
189. C2#14558401direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119246152
#145584012
C22×#105969292
C2×H(3,ℤ/4)37