Finite Group Databasebeta

← #18010105

Subgroups — #18010105

Order 4736.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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#14558550C211yesmaximal, characteristic
2#14558536C211yesmaximal, characteristic
3#14558392C214yesmaximal, complemented
4C2×#11924535C211yesmaximal, characteristic
5C2×#10596957—21no—
6#11924603C2212yes—
7#11924603C2212yes—
8C4⋊#64438—21no—
9C22⋊#64438—21no—
10C4×#64438—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—42no—
28C2×Dic74—42no—
29#10596957—42no—
30C2×#64438—22no—
31C2×#64438—22no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C412yes—
34C4⋊Dic37—21no—
35C4⋊Dic37C2×C412yes—
36#10596936—22no—
37#10596936—22no—
38C4×Dic37C2×C411yescharacteristic
39C4×Dic37D411yescharacteristic
40C4×Dic37D411yescharacteristic
41C4×Dic37C2311yescharacteristic
42C23×C37C22⋊C411yescharacteristic
43C2×C4×C37—22no—
44C2×C4×C37—22no—
45C2×C4×C37—42no—
46C2×C4×C37C22⋊C411yescharacteristic
47C2×C4×C37C22×C411yescharacteristic
48C2×Dic37—22no—
49C2×Dic37—22no—
50C2×Dic37—42no—
51C2×Dic37C22⋊C411yescharacteristic
52C2×Dic37C22⋊C411yescharacteristic
53C2×Dic37D812yes—
54C2×Dic37SD1612yes—
55C2×Dic37C2×D411yescharacteristic
56C2×Dic37C2×D411yescharacteristic
57Dic74—44no—
58Dic74—42no—
59Dic74—42no—
60#64438—42no—
61#64438—42no—
62C22×C37—21no—
63C22×C37—21no—
64C22×C37#10212yes—
65C22×C37C2×C22⋊C411yescharacteristic
66C4×C37—21no—
67C4×C37—42no—
68C4×C37#10112yes—
69Dic37—21no—
70Dic37—42no—
71Dic37#10212yes—
72Dic37C2×D811yescharacteristic
73Dic37C2×SD1611yescharacteristic
74Dic37#13712yes—
75#1546—371nomaximal, Sylow
76C2×C37—22no—
77C2×C37C2×#10111yescharacteristic
78C2×C37C2×#10211yescharacteristic
79C2×C37#41911yescharacteristic
80C2×C4⋊Q8—371no—
81#431—371no—
82#423—371no—
83#332—374no—
84C37#154611yescharacteristic, complemented, Sylow
85C22×Q8—741no—
86C2×M16—741no—
87C4⋊Q8—372no—
88C4⋊Q8—372no—
89C4⋊Q8—741no—
90C4⋊Q8—741no—
91C2×C4⋊C4—371no—
92C2×C4⋊C4—741no—
93C2×C4⋊C4#386611yescharacteristic
94C2×C42—371no—
95C4⋊C8—372no—
96C4⋊C8—372no—
97C4⋊C8—741no—
98C22⋊C8—741no—
99C4×C8—741no—
100C2×Q8—742no—
101C2×Q8—742no—
102C2×Q8—1482no—
103C2×Q8—1482no—
104C22×C4—21no—
105C22×C4—371no—
106C22×C4—371no—
107C22×C4—741no—
108C22×C4C2×#386611yescharacteristic
109M16—1482no—
110C2×C8—742no—
111C2×C8—742no—
112C4⋊C4—21no—
113C4⋊C4—372no—
114C4⋊C4—742no—
115C4⋊C4—742no—
116C4⋊C4—741no—
117C4⋊C4C2×#386612yes—
118C42—371no—
119C42—371no—
120C42—371no—
121C42—371no—
122C23C22⋊#386611yescharacteristic
123Q8—1482no—
124Q8—1484no—
125Q8—1482no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—42no—
129C2×C4—372no—
130C2×C4—372no—
131C2×C4—371no—
132C2×C4—371no—
133C2×C4—371no—
134C2×C4—371no—
135C2×C4—742no—
136C2×C4—742no—
137C2×C4—1482no—
138C2×C4C22⋊#386611yescharacteristic
139C2×C4C22×#386611yescharacteristic
140C8—1482no—
141C8—1482no—
142C22—21no—
143C22—21no—
144C22#1192459812yes—
145C22C2×C22⋊#386611yescharacteristic
146C4—21no—
147C4—42no—
148C4—371no—
149C4—372no—
150C4—371no—
151C4—372no—
152C4—741no—
153C4—1482no—
154C4#1192459712yes—
155C2—22no—
156C2C2×#1192459711yescharacteristic
157C2C2×#1192459811yescharacteristic
158C2#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#1546
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
84. C37#1546semidirect

Maximal subgroups

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

subgroupindex
#145585502
#145585362
#145583922
C2×#119245352
#154637