Finite Group Databasebeta

← #17993780

Subgroups — #17993780

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#14557881C211yesmaximal, characteristic
3#14557815C211yesmaximal, characteristic, complemented
4#14557276C211yesmaximal, characteristic
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557263C211yesmaximal, characteristic, complemented
7C37×#462C211yesmaximal, characteristic, complemented
8#11924533C2211yescharacteristic
9#11924525—21no—
10#11924524—21no—
11#11924521—22no—
12C4×Dic74C2211yescharacteristic
13C4×D148—21no—
14#11924498—21no—
15#11924467—21no—
16C4⋊#64436C2211yescharacteristic
17#11924459—21no—
18#11924456—22no—
19C4×#64436C2211yescharacteristic
20C2×Q16×C37—21no—
21C4⋊Q8×C37C2211yescharacteristic
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#103×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37D411yescharacteristic
27C2×D148—21no—
28C2×D148—21no—
29C2×D148D412yes—
30C2×C4×D37—22no—
31C2×Dic74D411yescharacteristic
32Q16×C37—42no—
33C2×C8×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D411yescharacteristic
38C42×C37—21no—
39C42×C37C2311yescharacteristic
40#10596938—22no—
41#10596938—22no—
42#10596938—22no—
43C4⋊Dic37D411yescharacteristic
44#10596936—21no—
45C4×Dic37—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48C22×D37—22no—
49Q8×C37—21no—
50Q8×C37—21no—
51Q8×C37—41no—
52Q8×C37—41no—
53C2×C4×C37—21no—
54C2×C4×C37—21no—
55C2×C4×C37—41no—
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37—21no—
61D148—42no—
62D148—41no—
63D148—41no—
64D148—41no—
65D148—41no—
66C4×D37—82no—
67Dic74—21no—
68Dic74—21no—
69C8×C37—41no—
70#64436—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—81no—
80C4×C37#13511yescharacteristic
81C4×C37#13511yescharacteristic
82C4×C37AGL(1,ℤ/8)11yescharacteristic
83C4×C37#13711yescharacteristic
84Dic37—41no—
85Dic37—41no—
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#462D3711yescharacteristic, complemented
95#331—371no—
96Q8⋊C8—371no—
97Q8⋊C8—371no—
98C37#164011yescharacteristic, complemented, Sylow
99C2×Q16—21no—
100C4⋊Q8C2×D3711yescharacteristic
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—21no—
113#103—741no—
114#102—742no—
115C4×C8—371no—
116C2×Q8—21no—
117C2×Q8—371no—
118C2×Q8C22⋊D3711yescharacteristic
119C2×D4—372no—
120C2×D4—741no—
121C2×D4—741no—
122C22×C4—742no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—741no—
126C2×C8—741no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—371no—
131C4⋊C4—741no—
132C4⋊C4C22⋊D3711yescharacteristic
133C22⋊C4—742no—
134C22⋊C4—742no—
135C22⋊C4—742no—
136C42—21no—
137C42—741no—
138C42C22×D3711yescharacteristic
139C23—742no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—741no—
145Q8—741no—
146D4—1482no—
147D4—1481no—
148D4—1481no—
149D4—1481no—
150D4—1481no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—2962no—
155C2×C4—741no—
156C2×C4—741no—
157C2×C4D4×D3711yescharacteristic
158C2×C4D4×D3711yescharacteristic
159C2×C4C2×C22⋊D3711yescharacteristic
160C8—41no—
161C8—1481no—
162C8—1481no—
163C22—1482no—
164C22—1482no—
165C22—1482no—
166C22#1192450411yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—1481no—
172C4—1481no—
173C4#1192455611yescharacteristic
174C4#1192455911yescharacteristic
175C4#1192456211yescharacteristic
176C4#1192456811yescharacteristic
177C2—2962no—
178C2#1455767611yescharacteristic
179C2#1455769411yescharacteristic
180C2#1455770911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#462C2
socleC22×C37#120
prime radical#11924533C22
hypercenter#462D37
hypocenterC37#1640
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #14557815C2semidirect
5. Q8⋊#64436C2semidirect
6. #14557263C2semidirect
7. C37×#462C2semidirect
94. #462D37semidirect
98. C37#1640semidirect

Maximal subgroups

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

subgroupindex
#145582682
#145578812
#145578152
#145572762
Q8⋊#644362
#145572632
C37×#4622
#164037