Finite Group Databasebeta

← #18010507

Subgroups — #18010507

Order 4736.

296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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×#11924594C212yesmaximal
2#14558410C214yesmaximal, complemented
3#14558006C211yesmaximal, characteristic
4C2×C22⋊#3866C2214yes—
5#11924594—22no—
6#11924594—22no—
7C22×C22⋊D37C2211yescharacteristic
8C4×C22⋊D37—22no—
9#11924496—22no—
10#11924492C412yescomplemented
11C2×C22⋊Dic37C411yescharacteristic, complemented
12C22⋊C4×D37C2212yes—
13C2×C22⋊C4×C37C411yescharacteristic, complemented
14C24×C37C2×C411yescharacteristic
15C23×D37C2311yescharacteristic
16C22×#3866—24no—
17C22×C4×C37—21no—
18C2×C22⋊D37—24no—
19C2×C22⋊D37D412yes—
20C2×C22⋊D37D412yes—
21C22×Dic37—21no—
22C22×Dic37C2×C411yescharacteristic
23C2×C4×D37—22no—
24C22⋊#3866—24no—
25C22⋊#3866—24no—
26C22⋊C4×C37—21no—
27C22⋊C4×C37C2×C412yes—
28C22⋊Dic37—21no—
29C22⋊Dic37C2×C412yes—
30#10596938—22no—
31#10596936—22no—
32C4×Dic37—22no—
33C23×C37—22no—
34C23×C37—81no—
35C23×C37C22⋊C411yescharacteristic
36C23×C37C22⋊C411yescharacteristic
37C23×C37C22×C411yescharacteristic
38C22×D37—81no—
39C22×D37C2×D412yes—
40C22×D37#4114yes—
41C2×#3866—44no—
42C2×#3866—84no—
43C2×C4×C37—22no—
44C2×C4×C37—81no—
45C22⋊D37—24no—
46C22⋊D37—24no—
47C2×Dic37—22no—
48C2×Dic37—22no—
49C2×Dic37—81no—
50C2×Dic37C22⋊C412yes—
51C4×D37—82no—
52C22×C37—21no—
53C22×C37—21no—
54C22×C37—41no—
55C22×C37—41no—
56C22×C37—41no—
57C22×C37—82no—
58C22×C37C2×C22⋊C411yescharacteristic
59C22×C37#11712yes—
60C2×D37—42no—
61C2×D37—44no—
62C2×D37#12314yes—
63#3866—84no—
64C4×C37—42no—
65Dic37—22no—
66Dic37—42no—
67#1828—371nomaximal, Sylow
68C2×C37—21no—
69C2×C37—22no—
70C2×C37—41no—
71C2×C37—41no—
72C2×C37#38111yescharacteristic
73D37—24no—
74#518—371no—
75C2×#99—372no—
76#342—374no—
77C37#182811yescharacteristic, complemented, Sylow
78C22×D4—371no—
79C4×D4—742no—
80C4×D4—742no—
81#117—372no—
82C2×C22⋊C4—371no—
83C2×C22⋊C4—372no—
84C2×C22⋊C4—374no—
85C2×C22⋊C4#386611yescharacteristic, complemented
86#99—742no—
87#99—742no—
88C24—371no—
89C24C2×#386611yescharacteristic
90C2×D4—372no—
91C2×D4—372no—
92C2×D4—744no—
93C22×C4—21no—
94C22×C4—371no—
95C22×C4—742no—
96C22×C4—741no—
97C22×C4—744no—
98C4⋊C4—742no—
99C22⋊C4—21no—
100C22⋊C4—372no—
101C22⋊C4—742no—
102C22⋊C4—741no—
103C22⋊C4—744no—
104C22⋊C4—744no—
105C22⋊C4C2×#386612yes—
106C42—742no—
107C23—22no—
108C23—81no—
109C23—372no—
110C23—374no—
111C23—2961no—
112C23C22⋊#386611yescharacteristic
113C23C22⋊#386611yescharacteristic
114C23C22×#386611yescharacteristic
115D4—744no—
116D4—744no—
117C2×C4—22no—
118C2×C4—81no—
119C2×C4—372no—
120C2×C4—2962no—
121C2×C4—2964no—
122C2×C4—2961no—
123C2×C4—742no—
124C2×C4—742no—
125C2×C4—1484no—
126C22—21no—
127C22—21no—
128C22—41no—
129C22—41no—
130C22—41no—
131C22—82no—
132C22—374no—
133C22—1482no—
134C22—1484no—
135C22C2×C22⋊#386611yescharacteristic
136C22#1192461512yes—
137C4—42no—
138C4—2964no—
139C4—742no—
140C4—1482no—
141C2—21no—
142C2—22no—
143C2—41no—
144C2—41no—
145C2—744no—
146C2#1455847611yescharacteristic
subgroupG/H
centerC2#14558476
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC2×C37#381
prime radicalC22×C22⋊D37C22
cosocleC23×D37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1828
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14558410C2semidirect
10. #11924492C4semidirect
11. C2×C22⋊Dic37C4semidirect
13. C2×C22⋊C4×C37C4semidirect
77. C37#1828semidirect
85. C2×C22⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245942
#145584102
#145580062
#182837