Finite Group Databasebeta

← #18010100

Subgroups — #18010100

Order 4736.

246 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558551C212yesmaximal, complemented
2#14558393C212yesmaximal, complemented
3#14558391C212yesmaximal, complemented
4#14558082C211yesmaximal, characteristic
5#11924603C2214yes—
6#11924593—22no—
7C4×#64438—22no—
8C2×#10596966C411yescharacteristic
9C2×#10596964C411yescharacteristic
10#11924534C2211yescharacteristic
11#11924532C2211yescharacteristic
12#11924524C411yescharacteristic
13#11924509—22no—
14#11924496—22no—
15C42×D37C2211yescharacteristic
16#124×C37C411yescharacteristic
17C2×Q8×C37C2×C411yescharacteristic
18C2×D4×C37C2×C411yescharacteristic
19C2×C22⋊D37—21no—
20C2×C22⋊D37—22no—
21C22×Dic37—21no—
22#10596966—42no—
23#10596964—42no—
24C2×D148—21no—
25C2×D148C2×C411yescharacteristic
26C2×C4×D37—21no—
27C2×C4×D37C2×C411yescharacteristic
28C2×C4×D37D412yes—
29C2×Dic74C2×C411yescharacteristic
30C2×#64438—24no—
31C22⋊C4×C37—22no—
32C42×C37C2×C411yescharacteristic
33#10596938—22no—
34#10596936—22no—
35C4×Dic37D412yes—
36C4×Dic37C2311yescharacteristic
37C23×C37—21no—
38C22×D37—21no—
39C22×D37C22⋊C411yescharacteristic
40Q8×C37—41no—
41D4×C37—41no—
42C2×C4×C37—21no—
43C2×C4×C37C22⋊C412yes—
44C2×C4×C37C22×C411yescharacteristic
45C22⋊D37—42no—
46C22⋊D37—44no—
47C2×Dic37—21no—
48C2×Dic37—42no—
49C2×Dic37C22⋊C411yescharacteristic
50C2×Dic37C2×D412yes—
51D148—41no—
52D148—42no—
53C4×D37—22no—
54C4×D37—24no—
55C4×D37—42no—
56Dic74—41no—
57#64438—44no—
58C22×C37—41no—
59C22×C37—42no—
60C22×C37C2×C22⋊C411yescharacteristic
61C2×D37—21no—
62C2×D37—22no—
63C2×D37—41no—
64C2×D37—42no—
65C4×C37—21no—
66C4×C37—22no—
67C4×C37—41no—
68Dic37—41no—
69Dic37#10012yes—
70Dic37#13514yes—
71#1543—371nomaximal, Sylow
72C2×C37—81no—
73C2×C37C2×#10011yescharacteristic
74C2×C37#41612yes—
75D37—41no—
76D37—81no—
77#532—371no—
78#431—372no—
79#333—372no—
80#331—372no—
81C37#154311yescharacteristic, complemented, Sylow
82C2×#41—371no—
83C2×#41—371no—
84C4⋊Q8—371no—
85#127—371no—
86#124—371no—
87#124#386611yescharacteristic
88#121—742no—
89C4×D4—742no—
90C2×C42—371no—
91C4⋊C8—374no—
92C22⋊C8—742no—
93C4×C8—742no—
94#41—1482no—
95#41—1482no—
96C2×Q8—371no—
97C2×Q8C2×#386611yescharacteristic
98C2×D4—371no—
99C2×D4—741no—
100C2×D4—742no—
101C2×D4—741no—
102C2×D4C2×#386611yescharacteristic
103C22×C4—372no—
104C22×C4—371no—
105C22×C4—741no—
106C22×C4—741no—
107C2×C8—744no—
108C4⋊C4—742no—
109C22⋊C4—22no—
110C22⋊C4—742no—
111C42—372no—
112C42—371no—
113C42C2×#386611yescharacteristic
114C23—21no—
115C23—371no—
116C23—741no—
117Q8—41no—
118Q8—1481no—
119D4—41no—
120D4—1481no—
121D4—1482no—
122D4—1484no—
123D4—1482no—
124C2×C4—21no—
125C2×C4—372no—
126C2×C4—371no—
127C2×C4—742no—
128C2×C4—744no—
129C2×C4—741no—
130C2×C4—1482no—
131C2×C4—1482no—
132C2×C4C22⋊#386612yes—
133C2×C4C22×#386611yescharacteristic
134C8—1484no—
135C22—41no—
136C22—42no—
137C22—741no—
138C22—742no—
139C22—1481no—
140C22—1482no—
141C22C2×C22⋊#386611yescharacteristic
142C4—21no—
143C4—22no—
144C4—41no—
145C4—372no—
146C4—374no—
147C4—1481no—
148C2—81no—
149C2—2961no—
150C2—1481no—
151C2D37⋊#10011yescharacteristic
152C2#1455852312yes—
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558082C2
cosocleC4×Dic37C23
hypercenter#124#3866
hypocenterC37#1543
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14558551C2semidirect
2. #14558393C2semidirect
3. #14558391C2semidirect
81. C37#1543semidirect

Maximal subgroups

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

subgroupindex
#145585512
#145583932
#145583912
#145580822
#154337