Finite Group Databasebeta

← #17993740

Subgroups — #17993740

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#14558248C211yesmaximal, characteristic
2#14557912C211yesmaximal, characteristic, complemented
3#14557820C211yesmaximal, characteristic, complemented
4#14557281C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#476C211yesmaximal, characteristic, complemented
8C2×#10596942—22no—
9#11924536C2211yescharacteristic
10#11924522—22no—
11#11924510—21no—
12#11924507—21no—
13C4×D148C2211yescharacteristic
14#11924495—21no—
15#11924494—21no—
16#11924467—21no—
17C4⋊#64436C2211yescharacteristic
18#11924456—21no—
19C4×#64436C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21C4×D4×C37C2211yescharacteristic
22#106×C37—21no—
23C4⋊C8×C37C2211yescharacteristic
24#102×C37—21no—
25C2×Q8×C37—21no—
26C2×D4×C37D411yescharacteristic
27C22×C4×C37—21no—
28C2×C22⋊D37—22no—
29C2×D148D411yescharacteristic
30C2×C4×D37—21no—
31C2×Dic74D412yes—
32C2×C8×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37D411yescharacteristic
36C22⋊C4×C37—21no—
37C42×C37C2311yescharacteristic
38C22⋊Dic37—22no—
39#10596942—44no—
40#10596938—22no—
41#10596938—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37—21no—
44C4⋊Dic37D411yescharacteristic
45C4×Dic37—22no—
46C2×#64436—21no—
47C2×#64436—21no—
48C23×C37—21no—
49C22×D37—21no—
50Q8×C37—42no—
51D4×C37—21no—
52D4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37—41no—
55C2×C4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C22⋊D37—82no—
61C2×Dic37—21no—
62C2×Dic37—22no—
63D148—21no—
64D148—21no—
65C4×D37—41no—
66C4×D37—41no—
67Dic74—42no—
68C8×C37—41no—
69#64436—22no—
70#64436—41no—
71C22×C37—41no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37#12011yescharacteristic
75C2×D37—41no—
76C2×D37—41no—
77C2×D37—41no—
78C4×C37—21no—
79C4×C37—41no—
80C4×C37—81no—
81C4×C37#13511yescharacteristic
82C4×C37#13511yescharacteristic
83C4×C37#13711yescharacteristic
84C4×C37#13711yescharacteristic
85Dic37—41no—
86Dic37—42no—
87#1634—371nomaximal, Sylow
88C2×C37—81no—
89C2×C37#45211yescharacteristic
90C2×C37#45211yescharacteristic
91C2×C37#45311yescharacteristic
92D37—81no—
93#555—371no—
94#494—371no—
95#476—371no—
96#476D3711yescharacteristic, complemented
97#333—371no—
98D4⋊C8—371no—
99D4⋊C8—371no—
100C37#163411yescharacteristic, complemented, Sylow
101C2×Q16—742no—
102C4⋊Q8—371no—
103C4⋊Q8C2×D3711yescharacteristic
104#124—742no—
105#121—741no—
106#121—741no—
107C4×D4—371no—
108C4×D4C2×D3711yescharacteristic
109#117—741no—
110#117—741no—
111#106—21no—
112#106—741no—
113C4⋊C8—371no—
114C4⋊C8C2×D3711yescharacteristic
115#102—21no—
116#102—741no—
117C4×C8—371no—
118C2×Q8—21no—
119C2×Q8—372no—
120C2×D4—371no—
121C2×D4—742no—
122C2×D4C22⋊D3711yescharacteristic
123C22×C4—21no—
124C22×C4—741no—
125Q16—1484no—
126C2×C8—21no—
127C2×C8—741no—
128C2×C8—741no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—371no—
132C4⋊C4—741no—
133C4⋊C4—741no—
134C4⋊C4C22⋊D3711yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—742no—
137C22⋊C4—742no—
138C22⋊C4—741no—
139C42—742no—
140C42C22×D3711yescharacteristic
141C23—21no—
142C23—741no—
143Q8—42no—
144Q8—1482no—
145D4—21no—
146D4—21no—
147D4—2962no—
148D4—741no—
149D4—741no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—741no—
155C2×C4—742no—
156C2×C4—1481no—
157C2×C4—1481no—
158C2×C4D4×D3711yescharacteristic
159C2×C4D4×D3711yescharacteristic
160C2×C4C2×C22⋊D3711yescharacteristic
161C8—41no—
162C8—742no—
163C8—1481no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—1481no—
168C22—1481no—
169C22—1481no—
170C22#1192450411yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—1482no—
175C4—1481no—
176C4#1192455611yescharacteristic
177C4#1192455711yescharacteristic
178C4#1192456511yescharacteristic
179C4#1192456711yescharacteristic
180C2—81no—
181C2—2961no—
182C2#1455769211yescharacteristic
183C2#1455769311yescharacteristic
184C2#1455769911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#476C2
socleC22×C37#120
prime radical#14558248C2
hypercenter#476D37
hypocenterC37#1634
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #14557912C2semidirect
3. #14557820C2semidirect
4. #14557281C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×#476C2semidirect
96. #476D37semidirect
100. C37#1634semidirect

Maximal subgroups

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

subgroupindex
#145582482
#145579122
#145578202
#145572812
D4⋊#644362
#145572602
C37×#4762
#163437