Finite Group Databasebeta

← #18010050

Subgroups — #18010050

Order 4736.

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

normal subgroups only

This group has 270 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
1C4×#10596957C212yesmaximal, complemented
2#14558389C212yesmaximal, complemented
3#14558388C212yesmaximal, complemented
4#14558079C211yesmaximal, characteristic
5C2×#10596957—22no—
6#11924591C2214yes—
7C4×#64438—22no—
8C2×#10596962C411yescharacteristic
9#11924534C411yescharacteristic
10#11924532C411yescharacteristic
11#11924525C2211yescharacteristic
12#11924523C2211yescharacteristic
13#11924508—22no—
14C4×C22⋊D37—22no—
15C2×C4×Dic37C2211yescharacteristic
16C2×#41×C37C411yescharacteristic
17#41×C37—42no—
18C2×Q8×C37C2×C411yescharacteristic
19C2×D4×C37—21no—
20C2×D4×C37C2×C411yescharacteristic
21C22×C4×C37—21no—
22C22×C4×C37C2×C411yescharacteristic
23C2×C22⋊D37—21no—
24C2×C22⋊D37—22no—
25C22×Dic37D412yes—
26#10596962—42no—
27C2×D148C2×C411yescharacteristic
28C2×C4×D37—21no—
29C2×Dic74C2×C411yescharacteristic
30#10596957—28no—
31C2×#64438—24no—
32C22⋊Dic37—22no—
33#10596938—22no—
34#10596936—22no—
35C4×Dic37C2×C411yescharacteristic
36C4×Dic37D412yes—
37C4×Dic37C2311yescharacteristic
38C23×C37—21no—
39C23×C37C22⋊C411yescharacteristic
40C22×D37—21no—
41Q8×C37—41no—
42D4×C37—41no—
43D4×C37—42no—
44C2×C4×C37—22no—
45C2×C4×C37—21no—
46C2×C4×C37—42no—
47C2×C4×C37C22⋊C411yescharacteristic
48C2×C4×C37C22×C411yescharacteristic
49C22⋊D37—42no—
50C22⋊D37—44no—
51C2×Dic37—24no—
52C2×Dic37—21no—
53C2×Dic37C22⋊C412yes—
54C2×Dic37C2×D412yes—
55D148—41no—
56C4×D37—42no—
57Dic74—41no—
58#64438—28no—
59C22×C37—21no—
60C22×C37—22no—
61C22×C37—41no—
62C22×C37—42no—
63C22×C37C2×C22⋊C411yescharacteristic
64C2×D37—41no—
65C2×D37—42no—
66C4×C37—21no—
67C4×C37—41no—
68C4×C37#10012yes—
69Dic37—22no—
70Dic37—41no—
71Dic37#10414yes—
72#1525—371nomaximal, Sylow
73C2×C37—41no—
74C2×C37—81no—
75C2×C37C2×#10011yescharacteristic
76C2×C37C2×#10412yes—
77D37—81no—
78#532—371no—
79C4×M16—372no—
80#329—372no—
81#329—372no—
82C37#152511yescharacteristic, complemented, Sylow
83C2×#41—371no—
84C2×#41#386611yescharacteristic
85C2×M16—742no—
86C4⋊Q8—371no—
87#127—371no—
88#124—371no—
89#124—371no—
90#121—742no—
91C4×D4—742no—
92C2×C42—371no—
93#97—374no—
94C4×C8—742no—
95#41—42no—
96#41—1482no—
97C2×Q8—371no—
98C2×Q8C2×#386611yescharacteristic
99C2×D4—21no—
100C2×D4—371no—
101C2×D4—742no—
102C2×D4—741no—
103C2×D4C2×#386611yescharacteristic
104C22×C4—21no—
105C22×C4—372no—
106C22×C4—741no—
107C22×C4C2×#386611yescharacteristic
108M16—748no—
109C2×C8—744no—
110C4⋊C4—742no—
111C22⋊C4—742no—
112C22⋊C4—742no—
113C42—372no—
114C42—371no—
115C42—371no—
116C23—21no—
117C23—741no—
118C23C22⋊#386611yescharacteristic
119Q8—41no—
120Q8—1481no—
121D4—41no—
122D4—42no—
123D4—1481no—
124D4—1484no—
125D4—1482no—
126C2×C4—22no—
127C2×C4—21no—
128C2×C4—42no—
129C2×C4—372no—
130C2×C4—372no—
131C2×C4—744no—
132C2×C4—741no—
133C2×C4—1482no—
134C2×C4C22⋊#386611yescharacteristic
135C2×C4C22×#386611yescharacteristic
136C8—748no—
137C22—21no—
138C22—22no—
139C22—41no—
140C22—42no—
141C22—1481no—
142C22—1482no—
143C22C2×C22⋊#386611yescharacteristic
144C4—21no—
145C4—41no—
146C4—374no—
147C4—742no—
148C4—1481no—
149C4#1192459612yes—
150C2—41no—
151C2—81no—
152C2—2961no—
153C2C2×#1192459611yescharacteristic
154C2D37⋊#10412yes—
subgroupG/H
centerC2×C4C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558079C2
cosocleC4×Dic37C23
hypercenterC2×#41#3866
hypocenterC37#1525
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C4×#10596957C2semidirect
2. #14558389C2semidirect
3. #14558388C2semidirect
82. C37#1525semidirect

Maximal subgroups

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

subgroupindex
C4×#105969572
#145583892
#145583882
#145580792
#152537