Finite Group Databasebeta

← #18010125

Subgroups — #18010125

Order 4736.

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

normal subgroups only

This group has 228 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
1#14558553C211yesmaximal, characteristic
2#14558553C211yesmaximal, characteristic
3#14558392C214yesmaximal, complemented
4C2×#11924535C211yesmaximal, characteristic
5#11924603C2212yes—
6#11924603C2212yes—
7C22⋊#64438—21no—
8C22⋊#64438—21no—
9#11924591—21no—
10#11924591—21no—
11C22×Dic74—21no—
12#11924535—21no—
13#11924535—21no—
14#11924535C412yes—
15#11924535C2212yes—
16C2×C4⋊Dic37C411yescharacteristic
17C2×#10596936—21no—
18C2×C4×Dic37C2211yescharacteristic
19C2×C4⋊C4×C37C411yescharacteristic
20C22×C4×C37—21no—
21C22×C4×C37C2×C411yescharacteristic
22C22×Dic37—21no—
23C22×Dic37D411yescharacteristic
24C22×Dic37D411yescharacteristic
25C2×Dic74—22no—
26C2×Dic74—22no—
27C2×Dic74—44no—
28C2×#64438—22no—
29C2×#64438—22no—
30C4⋊C4×C37—21no—
31C4⋊C4×C37C2×C412yes—
32C4⋊Dic37—21no—
33C4⋊Dic37C2×C412yes—
34#10596936—22no—
35#10596936—22no—
36C4×Dic37C2×C411yescharacteristic
37C4×Dic37D411yescharacteristic
38C4×Dic37D411yescharacteristic
39C4×Dic37C2311yescharacteristic
40C23×C37C22⋊C411yescharacteristic
41C2×C4×C37—22no—
42C2×C4×C37—22no—
43C2×C4×C37—42no—
44C2×C4×C37C22⋊C411yescharacteristic
45C2×C4×C37C22×C411yescharacteristic
46C2×Dic37—22no—
47C2×Dic37—22no—
48C2×Dic37—22no—
49C2×Dic37—42no—
50C2×Dic37C22⋊C411yescharacteristic
51C2×Dic37C22⋊C411yescharacteristic
52C2×Dic37C2×D411yescharacteristic
53C2×Dic37C2×D411yescharacteristic
54Dic74—44no—
55Dic74—44no—
56#64438—42no—
57#64438—42no—
58C22×C37—21no—
59C22×C37—21no—
60C22×C37#10112yes—
61C22×C37C2×C22⋊C411yescharacteristic
62C4×C37—21no—
63C4×C37—21no—
64C4×C37—42no—
65Dic37—21no—
66Dic37—21no—
67Dic37—42no—
68Dic37AGL(1,ℤ/8)12yes—
69Dic37#13712yes—
70#1556—371nomaximal, Sylow
71C2×C37—22no—
72C2×C37C2×#10111yescharacteristic
73C2×C37#41811yescharacteristic
74C2×C37#41911yescharacteristic
75C2×C4⋊Q8—371no—
76#432—371no—
77#432—371no—
78#332—374no—
79C37#155611yescharacteristic, complemented, Sylow
80C22×Q8—741no—
81C4⋊Q8—372no—
82C4⋊Q8—372no—
83C4⋊Q8—741no—
84C4⋊Q8—741no—
85C2×C4⋊C4—371no—
86C2×C4⋊C4—741no—
87C2×C4⋊C4#386611yescharacteristic
88C2×C42—371no—
89C4⋊C8—372no—
90C4⋊C8—372no—
91C22⋊C8—741no—
92C22⋊C8—741no—
93#97—741no—
94#97—741no—
95C2×Q8—742no—
96C2×Q8—742no—
97C2×Q8—1484no—
98C22×C4—21no—
99C22×C4—371no—
100C22×C4—371no—
101C22×C4—741no—
102C22×C4C2×#386611yescharacteristic
103C2×C8—742no—
104C2×C8—742no—
105C4⋊C4—21no—
106C4⋊C4—372no—
107C4⋊C4—742no—
108C4⋊C4—742no—
109C4⋊C4—741no—
110C4⋊C4C2×#386612yes—
111C42—371no—
112C42—371no—
113C42—371no—
114C42—371no—
115C23C22⋊#386611yescharacteristic
116Q8—1484no—
117Q8—1484no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—42no—
121C2×C4—371no—
122C2×C4—371no—
123C2×C4—371no—
124C2×C4—371no—
125C2×C4—742no—
126C2×C4—742no—
127C2×C4—742no—
128C2×C4—1482no—
129C2×C4C22⋊#386611yescharacteristic
130C2×C4C22×#386611yescharacteristic
131C8—1482no—
132C8—1482no—
133C22—21no—
134C22—21no—
135C22#1192459712yes—
136C22C2×C22⋊#386611yescharacteristic
137C4—21no—
138C4—21no—
139C4—42no—
140C4—372no—
141C4—372no—
142C4—741no—
143C4—741no—
144C4—1482no—
145C2—22no—
146C2C2×#1192459711yescharacteristic
147C2#1455852511yescharacteristic
148C2#1455852611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×C37C22⋊C4
cosocleC4×Dic37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1556
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14558392C2semidirect
79. C37#1556semidirect

Maximal subgroups

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

subgroupindex
#145585532
#145583922
C2×#119245352
#155637