Finite Group Databasebeta

← #17996266

Subgroups — #17996266

Order 4736.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558096C211yesmaximal, characteristic
2#14557505C212yesmaximal, complemented
3#14557326C211yesmaximal, characteristic, complemented
4#14557325C212yesmaximal, complemented
5C37×#353C211yesmaximal, characteristic, complemented
6C2×#10596964C2211yescharacteristic
7C2×D4×D37C411yescharacteristic, complemented
8#11924532C2211yescharacteristic
9#11924524C411yescharacteristic, complemented
10#11924523C411yescharacteristic, complemented
11#11924508—22no—
12#11924504—22no—
13#11924493C411yescharacteristic, complemented
14#11924492—22no—
15#11924451C2212yescomplemented
16#11924450—22no—
17#127×C37C2211yescharacteristic
18#99×C37C2212yescomplemented
19C23×D37—21no—
20C2×D4×C37—22no—
21C2×D4×C37C2×C411yescharacteristic
22C2×D4×C37C2311yescharacteristic
23C2×C22⋊D37—22no—
24C2×C22⋊D37—21no—
25C2×C22⋊D37D412yes—
26C22×Dic37D412yes—
27#10596964—42no—
28D4×D37—42no—
29C2×D148C2×C411yescharacteristic
30C2×C4×D37C2×C411yescharacteristic
31C2×Dic74C2×C411yescharacteristic
32C22⋊C4×C37—22no—
33C42×C37C2×C411yescharacteristic
34C22⋊Dic37—22no—
35C22⋊Dic37—22no—
36#10596938—21no—
37#10596938—22no—
38#10596936—21no—
39#10596936—42no—
40C4×Dic37—42no—
41C4×Dic37C2×C411yescharacteristic
42C23×C37—21no—
43C23×C37C2×D412yes—
44C22×D37—21no—
45C22×D37—42no—
46C22×D37—82no—
47C22×D37C22⋊C411yescharacteristic
48D4×C37—41no—
49D4×C37—41no—
50D4×C37—82no—
51C2×C4×C37—21no—
52C2×C4×C37—42no—
53C2×C4×C37C22×C411yescharacteristic
54C22⋊D37—42no—
55C22⋊D37—42no—
56C22⋊D37—82no—
57C2×Dic37—22no—
58C2×Dic37—22no—
59C2×Dic37—21no—
60C2×Dic37—42no—
61C2×Dic37C22⋊C412yes—
62C2×Dic37C22⋊C411yescharacteristic
63D148—41no—
64C4×D37—22no—
65Dic74—41no—
66C22×C37—22no—
67C22×C37—42no—
68C22×C37—42no—
69C22×C37—41no—
70C22×C37C2×C22⋊C411yescharacteristic
71C2×D37—21no—
72C2×D37—41no—
73C2×D37—42no—
74C2×D37—41no—
75C2×D37—84no—
76C4×C37—21no—
77C4×C37—41no—
78C4×C37—82no—
79Dic37—22no—
80Dic37—41no—
81Dic37—82no—
82Dic37#9912yes—
83#2128—371nomaximal, Sylow
84C2×C37—21no—
85C2×C37—42no—
86C2×C37—81no—
87C2×C37C2×#9911yescharacteristic
88D37—41no—
89D37—81no—
90#535—371no—
91#410—372no—
92#353—371no—
93#353—372no—
94#353D3711yescharacteristic, complemented
95C37#212811yescharacteristic, complemented, Sylow
96C2×#41—371no—
97C22×D4—371no—
98#127—371no—
99#127C2×D3711yescharacteristic
100#124—371no—
101#124—371no—
102#121—742no—
103#120—742no—
104#117—371no—
105#117—742no—
106#99—372no—
107#99—742no—
108#99C2×D3712yescomplemented
109C24—741no—
110#41—1482no—
111C2×Q8—371no—
112C2×D4—22no—
113C2×D4—372no—
114C2×D4—371no—
115C2×D4—741no—
116C2×D4—742no—
117C2×D4—1482no—
118C2×D4C4×D3711yescharacteristic
119C2×D4C22×D3711yescharacteristic
120C22×C4—372no—
121C22×C4—371no—
122C4⋊C4—741no—
123C4⋊C4—1482no—
124C22⋊C4—22no—
125C22⋊C4—742no—
126C22⋊C4—741no—
127C22⋊C4—742no—
128C22⋊C4—742no—
129C42—371no—
130C42—1482no—
131C42C4×D3711yescharacteristic
132C23—21no—
133C23—371no—
134C23—2962no—
135C23—741no—
136C23—1482no—
137C23D4×D3712yes—
138Q8—1481no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—2962no—
143D4—1481no—
144D4—1482no—
145D4—1482no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—371no—
149C2×C4—372no—
150C2×C4—742no—
151C2×C4—742no—
152C2×C4—742no—
153C2×C4—741no—
154C2×C4—1482no—
155C2×C4C2×C4×D3711yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—2964no—
161C22—741no—
162C22—1482no—
163C22—1481no—
164C22—1481no—
165C22C22⋊C4×D3711yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—372no—
170C4—2962no—
171C4—742no—
172C4—1481no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—2961no—
177C2—1481no—
178C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#353C2
socleC2×C37C2×#99
prime radical#14558096C2
cosocleC2×D4×C37C23
hypercenter#353D37
hypocenterC37#2128
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #14557505C2semidirect
3. #14557326C2semidirect
4. #14557325C2semidirect
5. C37×#353C2semidirect
7. C2×D4×D37C4semidirect
9. #11924524C4semidirect
10. #11924523C4semidirect
13. #11924493C4semidirect
15. #11924451C22semidirect
18. #99×C37C22semidirect
94. #353D37semidirect
95. C37#2128semidirect
108. #99C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580962
#145575052
#145573262
#145573252
C37×#3532
#212837