Finite Group Databasebeta

← #18010068

Subgroups — #18010068

Order 4736.

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

normal subgroups only

This group has 212 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#14558553C211yesmaximal, characteristic
2C2×#11924591C211yesmaximal, characteristic
3#14558390C212yesmaximal, complemented
4#14558390C212yesmaximal, complemented
5#14558086C211yesmaximal, characteristic
6C22×#64438—21no—
7#11924603—21no—
8C22⋊#64438—21no—
9#11924591—21no—
10#11924591C2212yes—
11#11924591C2212yes—
12#11924535C411yescharacteristic
13#11924535C411yescharacteristic
14#11924527C2211yescharacteristic
15#11924527C2211yescharacteristic
16#11924513—21no—
17#11924513—21no—
18C4×Dic74—21no—
19C4×Dic74—21no—
20#11924495C411yescharacteristic
21C2×C4×Dic37C2211yescharacteristic
22#117×C37C411yescharacteristic
23C22×C4×C37C2×C411yescharacteristic
24C22×Dic37D411yescharacteristic
25C22×Dic37D411yescharacteristic
26C2×Dic74—21no—
27C2×Dic74—21no—
28C2×#64438—24no—
29C2×#64438—22no—
30C2×#64438—22no—
31C4⋊C4×C37C2×C411yescharacteristic
32C4⋊C4×C37C2×C411yescharacteristic
33C22⋊C4×C37—21no—
34C42×C37—21no—
35C22⋊Dic37—21no—
36C4⋊Dic37—21no—
37C4⋊Dic37—21no—
38C4⋊Dic37C2×C411yescharacteristic
39C4⋊Dic37C2×C411yescharacteristic
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44C4×Dic37—21no—
45C4×Dic37C2×C411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37C2311yescharacteristic
49C23×C37C22⋊C411yescharacteristic
50C2×C4×C37—22no—
51C2×C4×C37—21no—
52C2×C4×C37—21no—
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22×C411yescharacteristic
55C2×Dic37—22no—
56C2×Dic37—21no—
57C2×Dic37—21no—
58C2×Dic37—41no—
59C2×Dic37C22⋊C411yescharacteristic
60C2×Dic37C22⋊C411yescharacteristic
61C2×Dic37C2×D411yescharacteristic
62C2×Dic37C2×D411yescharacteristic
63Dic74—42no—
64Dic74—42no—
65#64438—24no—
66#64438—42no—
67C22×C37—21no—
68C22×C37—21no—
69C22×C37#10112yes—
70C22×C37C2×C22⋊C411yescharacteristic
71C4×C37—21no—
72C4×C37—21no—
73C4×C37—41no—
74C4×C37—41no—
75Dic37—21no—
76Dic37—21no—
77Dic37—21no—
78Dic37—41no—
79Dic37—41no—
80Dic37#10412yes—
81#1531—371nomaximal, Sylow
82C2×C37—22no—
83C2×C37C2×#10111yescharacteristic
84C2×C37C2×#10411yescharacteristic
85C2×C37#42111yescharacteristic
86#533—371no—
87#432—371no—
88C2×#97—371no—
89#330—372no—
90#330—372no—
91C37#153111yescharacteristic, complemented, Sylow
92C22×C8—741no—
93C4⋊Q8—371no—
94C4⋊Q8—371no—
95#125—371no—
96#125—371no—
97C22⋊Q8—741no—
98C22⋊Q8—741no—
99C4×Q8—741no—
100C4×Q8—741no—
101#117—371no—
102#117#386611yescharacteristic
103C2×C42—371no—
104C4⋊C8—741no—
105C22⋊C8—741no—
106#97—372no—
107#97—372no—
108#97—741no—
109C2×Q8—741no—
110C2×Q8—741no—
111C22×C4—371no—
112C22×C4—371no—
113C22×C4C2×#386611yescharacteristic
114C2×C8—742no—
115C2×C8—744no—
116C2×C8—742no—
117C4⋊C4—371no—
118C4⋊C4—371no—
119C4⋊C4—741no—
120C4⋊C4—741no—
121C4⋊C4—741no—
122C4⋊C4—741no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4C2×#386611yescharacteristic
126C4⋊C4C2×#386611yescharacteristic
127C22⋊C4—21no—
128C22⋊C4—741no—
129C42—21no—
130C42—371no—
131C42—371no—
132C42—371no—
133C42—371no—
134C42—741no—
135C23C22⋊#386611yescharacteristic
136Q8—1482no—
137Q8—1482no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—371no—
142C2×C4—371no—
143C2×C4—371no—
144C2×C4—371no—
145C2×C4—742no—
146C2×C4—741no—
147C2×C4—741no—
148C2×C4—1481no—
149C2×C4C22⋊#386611yescharacteristic
150C2×C4C22×#386611yescharacteristic
151C8—744no—
152C8—1482no—
153C22—21no—
154C22—21no—
155C22#1192459712yes—
156C22C2×C22⋊#386611yescharacteristic
157C4—21no—
158C4—21no—
159C4—41no—
160C4—41no—
161C4—372no—
162C4—741no—
163C4—741no—
164C4—741no—
165C4—1481no—
166C4—1481no—
167C2—22no—
168C2C2×#1192459711yescharacteristic
169C2D37⋊#10411yescharacteristic
170C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#117×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×C37C22⋊C4
cosocleC4×Dic37C23
hypercenter#117#3866
hypocenterC37#1531
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #14558390C2semidirect
4. #14558390C2semidirect
91. C37#1531semidirect

Maximal subgroups

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

subgroupindex
#145585532
C2×#119245912
#145583902
#145580862
#153137