Finite Group Databasebeta

← #17993928

Subgroups — #17993928

Order 4736.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#14558287C211yesmaximal, characteristic
2#14557901C211yesmaximal, characteristic, complemented
3#14557895C211yesmaximal, characteristic
4#14557275C211yesmaximal, characteristic, complemented
5#14557274C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic
7C37×#501C211yesmaximal, characteristic, complemented
8#11924535—21no—
9#11924531—21no—
10#11924531—21no—
11#11924528C2211yescharacteristic
12#11924524C2211yescharacteristic
13#11924521—21no—
14#11924516—21no—
15#11924514—21no—
16#11924460—21no—
17#11924460—21no—
18#11924459—21no—
19#11924456—21no—
20#11924447C2211yescharacteristic
21#11924447C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23#125×C37C2211yescharacteristic
24#107×C37—21no—
25#106×C37—21no—
26#97×C37C2211yescharacteristic
27C2×Q8×C37—21no—
28C2×D148D411yescharacteristic
29C2×C4×D37—21no—
30C2×Dic74—21no—
31C2×Dic74D411yescharacteristic
32C2×C8×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D411yescharacteristic
38C4⋊C4×C37D411yescharacteristic
39C42×C37C2311yescharacteristic
40#10596938—21no—
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37D411yescharacteristic
47C4⋊Dic37D411yescharacteristic
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51C4×Dic37—21no—
52C2×#64436—21no—
53C2×#64436—21no—
54C22×D37—21no—
55Q8×C37—42no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—41no—
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—21no—
65D148—41no—
66C4×D37—81no—
67Dic74—41no—
68Dic74—81no—
69C8×C37—22no—
70#64436—41no—
71#64436—41no—
72C22×C37#12011yescharacteristic
73C2×D37—41no—
74C2×D37—41no—
75C2×D37—41no—
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—21no—
79C4×C37—41no—
80C4×C37—41no—
81C4×C37—81no—
82Dic37—41no—
83Dic37—41no—
84Dic37—41no—
85#1664—371nomaximal, Sylow
86C2×C37#45411yescharacteristic
87C2×C37#45511yescharacteristic
88C2×C37#45611yescharacteristic
89D37—81no—
90#563—371no—
91#501D3711yescharacteristic, complemented
92#491—371no—
93#489—371no—
94#330—371no—
95#330—371no—
96#329—371no—
97C37#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—741no—
99C4⋊Q8C2×D3711yescharacteristic
100#126—741no—
101#126—741no—
102#125—371no—
103#125C2×D3711yescharacteristic
104#124—371no—
105#123—741no—
106C22⋊Q8—741no—
107C22⋊Q8—741no—
108#107—21no—
109#106—21no—
110#103—741no—
111#103—741no—
112#103—741no—
113#102—741no—
114#97—371no—
115#97—371no—
116#97C2×D3711yescharacteristic
117C2×Q8—21no—
118C2×Q8—371no—
119C2×Q8—741no—
120C2×D4—371no—
121C22×C4—741no—
122C2×C8—21no—
123C2×C8—741no—
124C2×C8—741no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—371no—
130C4⋊C4—371no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C4⋊C4C22⋊D3711yescharacteristic
136C4⋊C4C22⋊D3711yescharacteristic
137C22⋊C4—741no—
138C22⋊C4—741no—
139C22⋊C4—741no—
140C22⋊C4—741no—
141C22⋊C4—741no—
142C42—741no—
143C42C22×D3711yescharacteristic
144C23—741no—
145Q8—42no—
146Q8—2961no—
147Q8—1481no—
148D4—1481no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—2961no—
153C2×C4—741no—
154C2×C4—741no—
155C2×C4—741no—
156C2×C4D4×D3711yescharacteristic
157C2×C4D4×D3711yescharacteristic
158C2×C4C2×C22⋊D3711yescharacteristic
159C8—22no—
160C8—1481no—
161C8—1481no—
162C22—1481no—
163C22—1481no—
164C22—1481no—
165C22#1192450411yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—1481no—
173C4—1481no—
174C4—1481no—
175C2—2961no—
176C2#1455770411yescharacteristic
177C2#1455770911yescharacteristic
178C2#1455771511yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#501C2
socleC22×C37#120
prime radicalC2×D148D4
hypercenter#501D37
hypocenterC37#1664
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #14557901C2semidirect
4. #14557275C2semidirect
5. #14557274C2semidirect
7. C37×#501C2semidirect
91. #501D37semidirect
97. C37#1664semidirect

Maximal subgroups

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

subgroupindex
#145582872
#145579012
#145578952
#145572752
#145572742
#145572722
C37×#5012
#166437