Finite Group Databasebeta

← #17993785

Subgroups — #17993785

Order 4736.

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

normal subgroups only

This group has 212 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#14557880C211yesmaximal, characteristic
3#14557818C211yesmaximal, characteristic, complemented
4#14557744C211yesmaximal, characteristic, complemented
5#14557276C211yesmaximal, characteristic
6#14557265C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Dic148—21no—
9#11924536C2211yescharacteristic
10#11924533C2211yescharacteristic
11#11924525—21no—
12#11924524—21no—
13#11924521—22no—
14C4×Dic74C2211yescharacteristic
15C4×D148—21no—
16#11924498—21no—
17#11924467—21no—
18C4⋊#64436C2211yescharacteristic
19#11924461—21no—
20#11924460—21no—
21#11924458—22no—
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—
47Dic148—42no—
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—41no—
68Dic74—41no—
69C8×C37—41no—
70C8×C37—41no—
71#64436—41no—
72C22×C37#12011yescharacteristic
73C2×D37—42no—
74C2×D37—42no—
75C2×D37—42no—
76C4×C37—21no—
77C4×C37—41no—
78C4×C37—41no—
79C4×C37#13511yescharacteristic
80C4×C37#13511yescharacteristic
81C4×C37AGL(1,ℤ/8)11yescharacteristic
82C4×C37#13711yescharacteristic
83Dic37—41no—
84Dic37—41no—
85Dic37—81no—
86#1640—371nomaximal, Sylow
87C2×C37#44911yescharacteristic
88C2×C37#45211yescharacteristic
89C2×C37#45511yescharacteristic
90D37—82no—
91#559—371no—
92#486—371no—
93#475—371no—
94#462—371no—
95#331—371no—
96Q8⋊C8—371no—
97Q8⋊C8D3711yescharacteristic, complemented
98C37#164011yescharacteristic, complemented, Sylow
99C2×Q16—741no—
100C4⋊Q8—371no—
101#127—371no—
102#124—741no—
103#124—741no—
104#123—742no—
105C4×Q8—371no—
106C4×Q8C2×D3711yescharacteristic
107C4×D4—741no—
108C4×D4—741no—
109#106—741no—
110C4⋊C8—371no—
111C4⋊C8C2×D3711yescharacteristic
112#103—741no—
113#103—741no—
114#102—742no—
115C4×C8C2×D3711yescharacteristic
116C2×Q8—371no—
117C2×Q8—741no—
118C2×Q8D14811yescharacteristic
119C2×D4—372no—
120C2×D4—741no—
121C2×D4—741no—
122C22×C4—742no—
123Q16—1482no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—741no—
127C4⋊C4—21no—
128C4⋊C4—371no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C4⋊C4—741no—
132C4⋊C4D14811yescharacteristic
133C22⋊C4—742no—
134C22⋊C4—742no—
135C22⋊C4—742no—
136C42—21no—
137C42—741no—
138C42C22×D3711yescharacteristic
139C23—742no—
140Q8—21no—
141Q8—21no—
142Q8—741no—
143Q8—741no—
144Q8—1481no—
145Q8—1481no—
146D4—1482no—
147D4—1481no—
148D4—1481no—
149D4—1481no—
150D4—1481no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—2962no—
154C2×C4—741no—
155C2×C4—741no—
156C2×C4—1481no—
157C2×C4C2×D14811yescharacteristic
158C2×C4D4×D3711yescharacteristic
159C2×C4D4×D3711yescharacteristic
160C8—41no—
161C8—41no—
162C8—1481no—
163C22—1482no—
164C22—1482no—
165C22—1482no—
166C22#1192450611yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—2961no—
171C4—1481no—
172C4—1481no—
173C4#1192455811yescharacteristic
174C4#1192455911yescharacteristic
175C4#1192456311yescharacteristic
176C4#1192456911yescharacteristic
177C2—2962no—
178C2#1455768111yescharacteristic
179C2#1455769711yescharacteristic
180C2#1455771211yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37#120
prime radical#11924533C22
hypercenterQ8⋊C8D37
hypocenterC37#1640
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. #14557818C2semidirect
4. #14557744C2semidirect
6. #14557265C2semidirect
7. C37×Q8⋊C8C2semidirect
97. Q8⋊C8D37semidirect
98. C37#1640semidirect

Maximal subgroups

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

subgroupindex
#145582682
#145578802
#145578182
#145577442
#145572762
#145572652
C37×Q8⋊C82
#164037