Finite Group Databasebeta

← #18010134

Subgroups — #18010134

Order 4736.

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

normal subgroups only

This group has 254 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#14558538C212yesmaximal, complemented
2#14558393C212yesmaximal, complemented
3#14558391C212yesmaximal, complemented
4#14558082C211yesmaximal, characteristic
5C2×#10596953—22no—
6#11924603—22no—
7#11924603C2214yes—
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—
31#10596953—44no—
32C22⋊C4×C37—22no—
33C42×C37C2×C411yescharacteristic
34#10596938—22no—
35#10596936—22no—
36C4×Dic37D412yes—
37C4×Dic37C2311yescharacteristic
38C23×C37—21no—
39C22×D37—21no—
40C22×D37C22⋊C411yescharacteristic
41Q8×C37—41no—
42D4×C37—41no—
43C2×C4×C37—21no—
44C2×C4×C37C22⋊C412yes—
45C2×C4×C37C22×C411yescharacteristic
46C22⋊D37—42no—
47C22⋊D37—42no—
48C22⋊D37—42no—
49C2×Dic37—21no—
50C2×Dic37—42no—
51C2×Dic37C22⋊C411yescharacteristic
52C2×Dic37C2×D412yes—
53D148—41no—
54D148—42no—
55C4×D37—22no—
56C4×D37—22no—
57C4×D37—22no—
58C4×D37—42no—
59Dic74—41no—
60#64438—44no—
61C22×C37—41no—
62C22×C37—42no—
63C22×C37C2×C22⋊C411yescharacteristic
64C2×D37—21no—
65C2×D37—22no—
66C2×D37—41no—
67C2×D37—42no—
68C4×C37—21no—
69C4×C37—22no—
70C4×C37—41no—
71Dic37—41no—
72Dic37#10012yes—
73Dic37AGL(1,ℤ/8)12yes—
74Dic37#13712yes—
75#1560—371nomaximal, Sylow
76C2×C37—81no—
77C2×C37C2×#10011yescharacteristic
78C2×C37#41712yes—
79D37—41no—
80D37—81no—
81#532—371no—
82#423—372no—
83#333—372no—
84#331—372no—
85C37#156011yescharacteristic, complemented, Sylow
86C2×#41—371no—
87C2×#41—371no—
88C2×M16—742no—
89C4⋊Q8—371no—
90#127—371no—
91#124—371no—
92#124#386611yescharacteristic
93#121—742no—
94C4×D4—742no—
95C2×C42—371no—
96C4⋊C8—374no—
97C4⋊C8—742no—
98#41—1482no—
99#41—1482no—
100C2×Q8—371no—
101C2×Q8C2×#386611yescharacteristic
102C2×D4—371no—
103C2×D4—741no—
104C2×D4—742no—
105C2×D4—741no—
106C2×D4C2×#386611yescharacteristic
107C22×C4—372no—
108C22×C4—371no—
109C22×C4—741no—
110C22×C4—741no—
111M16—1484no—
112C2×C8—744no—
113C4⋊C4—742no—
114C22⋊C4—22no—
115C22⋊C4—742no—
116C42—372no—
117C42—371no—
118C42C2×#386611yescharacteristic
119C23—21no—
120C23—371no—
121C23—741no—
122Q8—41no—
123Q8—1481no—
124D4—41no—
125D4—1481no—
126D4—1482no—
127D4—1482no—
128D4—1482no—
129D4—1482no—
130C2×C4—21no—
131C2×C4—372no—
132C2×C4—371no—
133C2×C4—742no—
134C2×C4—742no—
135C2×C4—742no—
136C2×C4—741no—
137C2×C4—1482no—
138C2×C4—1482no—
139C2×C4C22⋊#386612yes—
140C2×C4C22×#386611yescharacteristic
141C8—1484no—
142C22—41no—
143C22—42no—
144C22—741no—
145C22—742no—
146C22—1481no—
147C22—1482no—
148C22C2×C22⋊#386611yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—372no—
153C4—372no—
154C4—372no—
155C4—1481no—
156C2—81no—
157C2—2961no—
158C2—1481no—
159C2D37⋊#10011yescharacteristic
160C2#1455852412yes—
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#1560
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. #14558538C2semidirect
2. #14558393C2semidirect
3. #14558391C2semidirect
85. C37#1560semidirect

Maximal subgroups

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

subgroupindex
#145585382
#145583932
#145583912
#145580822
#156037