Finite Group Databasebeta

← #17993719

Subgroups — #17993719

Order 4736.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558268C211yesmaximal, characteristic
2#14557906C211yesmaximal, characteristic
3#14557829C211yesmaximal, characteristic, complemented
4#14557828C211yesmaximal, characteristic, complemented
5#14557276C211yesmaximal, characteristic
6#14557265C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596930—22no—
9#11924536C2211yescharacteristic
10#11924533C2211yescharacteristic
11#11924525—21no—
12#11924524—21no—
13#11924521—22no—
14C4×Dic74C2211yescharacteristic
15C4×D148—21no—
16#11924498—21no—
17#11924470—21no—
18#11924469—21no—
19C4⋊#64436C2211yescharacteristic
20#11924461—21no—
21#11924460—21no—
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37D411yescharacteristic
26C2×D148—21no—
27C2×D148—21no—
28C2×D148D412yes—
29C2×C4×D37—22no—
30C2×Dic74—21no—
31C2×Dic74D411yescharacteristic
32C2×C8×C37—21no—
33C2×C8×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37D411yescharacteristic
36C42×C37—21no—
37C42×C37C2311yescharacteristic
38#10596938—22no—
39#10596938—22no—
40#10596938—22no—
41C4⋊Dic37—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37D411yescharacteristic
44#10596936—21no—
45C4×Dic37—21no—
46C2×#64436—21no—
47#10596930—44no—
48C22×D37—22no—
49Q8×C37—21no—
50Q8×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37—21no—
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×C4×C37C2×D411yescharacteristic
56C2×Dic37—21no—
57C2×Dic37—21no—
58C2×Dic37—41no—
59D148—42no—
60D148—41no—
61D148—41no—
62D148—41no—
63D148—41no—
64C4×D37—82no—
65Dic74—21no—
66Dic74—21no—
67Dic74—42no—
68C8×C37—22no—
69C8×C37—41no—
70#64436—41no—
71C22×C37#12011yescharacteristic
72C2×D37—42no—
73C2×D37—42no—
74C2×D37—42no—
75C4×C37—21no—
76C4×C37—41no—
77C4×C37—41no—
78C4×C37#13511yescharacteristic
79C4×C37#13511yescharacteristic
80C4×C37#13711yescharacteristic
81C4×C37#13711yescharacteristic
82Dic37—41no—
83Dic37—41no—
84Dic37—81no—
85#1630—371nomaximal, Sylow
86C2×C37#45211yescharacteristic
87C2×C37#45211yescharacteristic
88C2×C37#45311yescharacteristic
89D37—82no—
90#559—371no—
91#492—371no—
92#477—371no—
93#477—371no—
94#331—371no—
95Q8⋊C8—371no—
96Q8⋊C8D3711yescharacteristic, complemented
97C37#163011yescharacteristic, complemented, Sylow
98C2×SD16—742no—
99C4⋊Q8—371no—
100#127—371no—
101#124—741no—
102#124—741no—
103#123—742no—
104C4×Q8—371no—
105C4×Q8C2×D3711yescharacteristic
106C4×D4—741no—
107C4×D4—741no—
108#107—741no—
109#107—741no—
110C4⋊C8—371no—
111C4⋊C8C2×D3711yescharacteristic
112#103—741no—
113#103—741no—
114C4×C8C2×D3711yescharacteristic
115C2×Q8—371no—
116C2×Q8—741no—
117C2×Q8D14811yescharacteristic
118C2×D4—372no—
119C2×D4—741no—
120C2×D4—741no—
121C22×C4—742no—
122SD16—1484no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—741no—
126C4⋊C4—21no—
127C4⋊C4—371no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C4⋊C4D14811yescharacteristic
132C22⋊C4—742no—
133C22⋊C4—742no—
134C22⋊C4—742no—
135C42—21no—
136C42—741no—
137C42C22×D3711yescharacteristic
138C23—742no—
139Q8—21no—
140Q8—21no—
141Q8—741no—
142Q8—741no—
143Q8—1482no—
144D4—1482no—
145D4—1481no—
146D4—1481no—
147D4—1481no—
148D4—1481no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—2962no—
152C2×C4—741no—
153C2×C4—741no—
154C2×C4—1481no—
155C2×C4C2×D14811yescharacteristic
156C2×C4D4×D3711yescharacteristic
157C2×C4D4×D3711yescharacteristic
158C8—22no—
159C8—41no—
160C8—1481no—
161C22—1482no—
162C22—1482no—
163C22—1482no—
164C22#1192450611yescharacteristic
165C4—21no—
166C4—41no—
167C4—41no—
168C4—2961no—
169C4—1481no—
170C4—1481no—
171C4#1192455711yescharacteristic
172C4#1192455811yescharacteristic
173C4#1192456811yescharacteristic
174C4#1192456911yescharacteristic
175C2—2962no—
176C2#1455769711yescharacteristic
177C2#1455769811yescharacteristic
178C2#1455770211yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37#120
prime radical#11924533C22
hypercenterQ8⋊C8D37
hypocenterC37#1630
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #14557829C2semidirect
4. #14557828C2semidirect
6. #14557265C2semidirect
7. C37×Q8⋊C8C2semidirect
96. Q8⋊C8D37semidirect
97. C37#1630semidirect

Maximal subgroups

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

subgroupindex
#145582682
#145579062
#145578292
#145578282
#145572762
#145572652
C37×Q8⋊C82
#163037