Finite Group Databasebeta

← #17993550

Subgroups — #17993550

Order 4736.

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

normal subgroups only

This group has 308 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#14558095C211yesmaximal, characteristic
2#14557674C212yesmaximal, complemented
3#14557445C211yesmaximal, characteristic, complemented
4#14557268C212yesmaximal, complemented
5C37×#323C211yesmaximal, characteristic, complemented
6C22×Dic74C2211yescharacteristic, complemented
7C22×C22⋊D37—21no—
8C2×#10596930—22no—
9#11924520—22no—
10#11924510—21no—
11#11924510C2212yes—
12#11924506—22no—
13C2×C22⋊Dic37—21no—
14#11924461—22no—
15#11924443—21no—
16#11924443C2211yescharacteristic, complemented
17C2×C22⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yescomplemented
19C24×C37D411yescharacteristic
20C23×D37—21no—
21C22×C4×C37D411yescharacteristic
22C22×C4×C37C2311yescharacteristic
23C2×C22⋊D37—22no—
24C2×C22⋊D37—22no—
25C2×C22⋊D37—42no—
26C2×C22⋊D37—42no—
27C22×Dic37—21no—
28C22×Dic37—21no—
29C22×Dic37—21no—
30C2×D148—21no—
31C2×D148D412yes—
32C2×Dic74—22no—
33C2×Dic74—42no—
34C2×C8×C37—22no—
35C22⋊C4×C37—22no—
36C22⋊Dic37—42no—
37#10596938—22no—
38#10596938—22no—
39C4⋊Dic37—21no—
40C4⋊Dic37D412yes—
41#10596930—44no—
42C23×C37—21no—
43C23×C37—21no—
44C23×C37—41no—
45C23×C37—41no—
46C23×C37SD1612yescomplemented
47C23×C37C2×D411yescharacteristic
48C22×D37—22no—
49C22×D37—42no—
50C22×D37—81no—
51C22×D37—81no—
52C2×C4×C37—21no—
53C2×C4×C37—41no—
54C2×C4×C37—41no—
55C2×C4×C37C2×D412yes—
56C22⋊D37—44no—
57C22⋊D37—42no—
58C22⋊D37—42no—
59C2×Dic37—22no—
60C2×Dic37—22no—
61C2×Dic37—41no—
62C2×Dic37—42no—
63C2×Dic37—41no—
64C2×Dic37—41no—
65C2×Dic37—41no—
66C2×Dic37—41no—
67D148—42no—
68D148—81no—
69Dic74—24no—
70Dic74—42no—
71C8×C37—42no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—22no—
75C22×C37—42no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37—81no—
79C22×C37#12011yescharacteristic
80C22×C37C2×SD1611yescharacteristic
81C22×C37AGL(1,ℤ/8)11yescharacteristic
82C2×D37—42no—
83C2×D37—42no—
84C2×D37—42no—
85C2×D37—84no—
86C4×C37—22no—
87C4×C37—41no—
88Dic37—42no—
89Dic37—42no—
90Dic37—81no—
91#1601—371nomaximal, Sylow
92C2×C37—21no—
93C2×C37—21no—
94C2×C37—42no—
95C2×C37#45011yescharacteristic
96C2×C37#45511yescharacteristic
97C2×C37B(4,𝔽2)11yescharacteristic
98D37—82no—
99#534—371no—
100#448—372no—
101#393—371no—
102#327—372no—
103#323D3711yescharacteristic, complemented
104C37#160111yescharacteristic, complemented, Sylow
105C22×Q8—371no—
106C22×D4—741no—
107C2×SD16—742no—
108#123—742no—
109#121—372no—
110#121—741no—
111#120—742no—
112C2×C22⋊C4—741no—
113C2×C22⋊C4C2×D3711yescharacteristic
114#103—742no—
115C22⋊C8C2×D3712yescomplemented
116#95—371no—
117#95—741no—
118C24—741no—
119C24D14811yescharacteristic
120C2×Q8—742no—
121C2×Q8—1482no—
122C2×D4—372no—
123C2×D4—741no—
124C2×D4—742no—
125C2×D4—742no—
126C2×D4—1482no—
127C2×D4—1482no—
128C22×C4—741no—
129C22×C4—741no—
130C22×C4—741no—
131C22×C4D14811yescharacteristic
132C22×C4C22×D3711yescharacteristic
133SD16—1484no—
134C2×C8—22no—
135C4⋊C4—372no—
136C4⋊C4—741no—
137C22⋊C4—22no—
138C22⋊C4—742no—
139C22⋊C4—742no—
140C22⋊C4—1482no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—2961no—
146C23—2961no—
147C23—742no—
148C23—1482no—
149C23#1059693012yescomplemented
150C23C2×D14811yescharacteristic
151Q8—744no—
152Q8—1482no—
153D4—2961no—
154D4—1482no—
155D4—1484no—
156D4—1482no—
157D4—1482no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—742no—
162C2×C4—742no—
163C2×C4—1481no—
164C2×C4—1481no—
165C2×C4—1481no—
166C2×C4—1482no—
167C2×C4—1481no—
168C2×C4—1481no—
169C2×C4D4×D3712yes—
170C8—42no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—81no—
178C22—2964no—
179C22—1482no—
180C22—1482no—
181C22—1482no—
182C22#1192450611yescharacteristic
183C22C2×#1059693011yescharacteristic
184C22#1192456411yescharacteristic
185C4—22no—
186C4—41no—
187C4—2961no—
188C4—1482no—
189C4—1482no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—2962no—
194C2#1455768611yescharacteristic
195C2#1455771311yescharacteristic
196C2#1455772111yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#323C2
socleC22×C37#120
prime radical#14558095C2
hypercenter#323D37
hypocenterC37#1601
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14557674C2semidirect
3. #14557445C2semidirect
4. #14557268C2semidirect
5. C37×#323C2semidirect
6. C22×Dic74C22semidirect
16. #11924443C22semidirect
18. C22⋊C8×C37C22semidirect
46. C23×C37SD16semidirect
103. #323D37semidirect
104. C37#1601semidirect
115. C22⋊C8C2×D37semidirect
149. C23#10596930semidirect

Maximal subgroups

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

subgroupindex
#145580952
#145576742
#145574452
#145572682
C37×#3232
#160137