Finite Group Databasebeta

← #17993797

Subgroups — #17993797

Order 4736.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558203C211yesmaximal, characteristic
2#14557879C211yesmaximal, characteristic, complemented
3#14557819C211yesmaximal, characteristic, complemented
4#14557739C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#331C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9C2×#10596930—21no—
10#11924536C2211yescharacteristic
11#11924532—21no—
12#11924508—22no—
13#11924507—21no—
14C4×Dic74C2211yescharacteristic
15C4×D148C2211yescharacteristic
16D4×Dic37—21no—
17#11924468—21no—
18#11924461—21no—
19#11924461—21no—
20#11924457—22no—
21C4×#64436C2211yescharacteristic
22#127×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37D412yes—
28C2×C22⋊D37—22no—
29C2×C22⋊D37—22no—
30C22×Dic37—22no—
31#10596964—42no—
32#10596964—42no—
33C2×D148D411yescharacteristic
34C2×C4×D37—21no—
35C2×Dic74—21no—
36C2×Dic74D411yescharacteristic
37C2×C8×C37—21no—
38C2×C8×C37—21no—
39C42×C37C2311yescharacteristic
40C22⋊Dic37—22no—
41#10596938—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37—21no—
44C4⋊Dic37D411yescharacteristic
45C4⋊Dic37D411yescharacteristic
46#10596936—21no—
47C4×Dic37—21no—
48C2×#64436—21no—
49#10596930—42no—
50C23×C37—22no—
51C22×D37—21no—
52D4×C37—42no—
53D4×C37—41no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C22⋊D37—44no—
61C22⋊D37—82no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—21no—
65C2×Dic37—44no—
66C2×Dic37—41no—
67D148—21no—
68D148—21no—
69C4×D37—41no—
70C4×D37—41no—
71Dic74—21no—
72Dic74—41no—
73Dic74—41no—
74Dic74SD1612yescomplemented
75C8×C37—41no—
76C8×C37—41no—
77#64436—41no—
78C22×C37—42no—
79C22×C37—42no—
80C22×C37—42no—
81C22×C37#12011yescharacteristic
82C2×D37—41no—
83C2×D37—41no—
84C2×D37—41no—
85C4×C37—21no—
86C4×C37C2×SD1611yescharacteristic
87C4×C37#13511yescharacteristic
88C4×C37AGL(1,ℤ/8)11yescharacteristic
89C4×C37AGL(1,ℤ/8)11yescharacteristic
90Dic37—22no—
91Dic37—41no—
92Dic37—41no—
93Dic37—81no—
94#1642—371nomaximal, Sylow
95C2×C37—82no—
96C2×C37#44911yescharacteristic
97C2×C37#45011yescharacteristic
98C2×C37#45511yescharacteristic
99D37—81no—
100#550—371no—
101#486—371no—
102#475—371no—
103#461—371no—
104#331D3711yescharacteristic, complemented
105Q8⋊C8—371no—
106D4⋊C8—371no—
107C37#164211yescharacteristic, complemented, Sylow
108C2×#41—741no—
109C2×SD16—741no—
110C4⋊Q8—371no—
111#127—741no—
112#127C2×D3711yescharacteristic
113#121—741no—
114#121—742no—
115C4×Q8—371no—
116C4×D4—371no—
117C4×D4—741no—
118#106—741no—
119C4⋊C8C2×D3711yescharacteristic
120C4⋊C8C2×D3711yescharacteristic
121#103—741no—
122#103—741no—
123#102—742no—
124C4×C8—371no—
125#41—1482no—
126#41—1482no—
127C2×Q8—371no—
128C2×Q8—741no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—371no—
132C2×D4—742no—
133C2×D4—742no—
134C2×D4D14812yes—
135C22×C4—742no—
136C22×C4—741no—
137SD16—1482no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—741no—
141C4⋊C4—371no—
142C4⋊C4—371no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4—741no—
146C22⋊C4—742no—
147C22⋊C4—741no—
148C42—741no—
149C42C22×D3711yescharacteristic
150C23—22no—
151C23—741no—
152Q8—372no—
153Q8—741no—
154Q8—1481no—
155Q8—1481no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—2962no—
162D4—741no—
163D4—741no—
164D4—1484no—
165C2×C4—741no—
166C2×C4—741no—
167C2×C4—741no—
168C2×C4—1481no—
169C2×C4—1484no—
170C2×C4—1481no—
171C2×C4—1481no—
172C2×C4C2×D14811yescharacteristic
173C2×C4D4×D3711yescharacteristic
174C2×C4D4×D3711yescharacteristic
175C8—41no—
176C8—41no—
177C8—1481no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—1481no—
182C22—1481no—
183C22—1481no—
184C22#1192450611yescharacteristic
185C4—21no—
186C4—2961no—
187C4—742no—
188C4—1481no—
189C4—1481no—
190C4SD16×D3711yescharacteristic
191C4#1192455711yescharacteristic
192C4#1192456011yescharacteristic
193C4#1192456011yescharacteristic
194C2—82no—
195C2—2961no—
196C2#1455767911yescharacteristic
197C2#1455768511yescharacteristic
198C2#1455771311yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#331C2
socleC22×C37#120
prime radical#14558203C2
hypercenter#331D37
hypocenterC37#1642
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #14557879C2semidirect
3. #14557819C2semidirect
4. #14557739C2semidirect
5. #14557263C2semidirect
6. #14557260C2semidirect
7. C37×#331C2semidirect
74. Dic74SD16semidirect
104. #331D37semidirect
107. C37#1642semidirect

Maximal subgroups

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

subgroupindex
#145582032
#145578792
#145578192
#145577392
#145572632
#145572602
C37×#3312
#164237