Finite Group Databasebeta

← #17996247

Subgroups — #17996247

Order 4736.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#14558097C211yesmaximal, characteristic
2#14557507C211yesmaximal, characteristic, complemented
3#14557321C214yesmaximal, complemented
4C37×#413C211yesmaximal, characteristic, complemented
5C22×D148C411yescharacteristic, complemented
6#11924532—21no—
7#11924525—21no—
8#11924510—21no—
9#11924510—21no—
10#11924504C412yescomplemented
11#11924504C2212yes—
12#11924495—21no—
13#11924495C411yescharacteristic, complemented
14#11924451—21no—
15#11924451C2212yes—
16C2×#41×C37C2211yescharacteristic
17C2×M16×C37—21no—
18#101×C37—21no—
19#100×C37C2212yes—
20C23×D37C2×C412yes—
21#41×C37—41no—
22#41×C37—41no—
23C2×Q8×C37D411yescharacteristic
24C2×D4×C37C2×C411yescharacteristic
25C2×D4×C37D411yescharacteristic
26C2×D4×C37C2311yescharacteristic
27C22×C4×C37C2×C411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×C4×C37D411yescharacteristic
30C2×C22⋊D37—22no—
31C2×C22⋊D37—22no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148—41no—
35C2×D148—41no—
36M16×C37—22no—
37M16×C37—41no—
38C2×C8×C37—41no—
39C22⋊Dic37—22no—
40C22⋊Dic37C2×C412yes—
41#10596938—22no—
42#10596938—22no—
43C4⋊Dic37—21no—
44C4⋊Dic37—41no—
45C4×Dic37—21no—
46C4×Dic37—41no—
47C23×C37C22⋊C411yescharacteristic
48C23×C37C22×C411yescharacteristic
49C23×C37C2×D411yescharacteristic
50C22×D37—22no—
51C22×D37—42no—
52C22×D37—82no—
53Q8×C37—41no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57C2×C4×C37—21no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37C22⋊C411yescharacteristic
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C22⋊D37—82no—
68C22⋊D37—82no—
69C2×Dic37—22no—
70C2×Dic37—42no—
71D148—42no—
72D148—41no—
73D148—41no—
74C8×C37—42no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37C2×C22⋊C411yescharacteristic
82C2×D37—42no—
83C2×D37—42no—
84C2×D37—42no—
85C2×D37—84no—
86C4×C37—21no—
87C4×C37—21no—
88C4×C37—21no—
89C4×C37#9911yescharacteristic
90C4×C37#9911yescharacteristic
91Dic37—42no—
92Dic37—82no—
93#2122—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—41no—
96C2×C37—41no—
97C2×C37—41no—
98C2×C37C2×#9911yescharacteristic
99D37—82no—
100#535—371no—
101#413D3711yescharacteristic, complemented
102#410—371no—
103AΣL(1,𝔽16)—374no—
104C37#212211yescharacteristic, complemented, Sylow
105C2×#41C2×D3711yescharacteristic
106C22×D4—371no—
107C2×M16—21no—
108#127—741no—
109#124—741no—
110#121—741no—
111#121—741no—
112#120—372no—
113#120—372no—
114#117—371no—
115#117—741no—
116#101—21no—
117#100C2×D3712yes—
118#99—372no—
119#99—741no—
120C24—372no—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D3711yescharacteristic
124C2×D4—742no—
125C2×D4—742no—
126C2×D4—741no—
127C2×D4—741no—
128C2×D4—1481no—
129C2×D4—1481no—
130C2×D4C4×D3711yescharacteristic
131C2×D4D14811yescharacteristic
132C2×D4C22×D3711yescharacteristic
133C22×C4C4×D3711yescharacteristic
134C22×C4D14811yescharacteristic
135C22×C4C22⋊D3711yescharacteristic
136M16—22no—
137M16—41no—
138C2×C8—41no—
139C4⋊C4—741no—
140C4⋊C4—1481no—
141C22⋊C4—372no—
142C22⋊C4—742no—
143C22⋊C4—742no—
144C22⋊C4—742no—
145C42—741no—
146C42—1481no—
147C23—2962no—
148C23—742no—
149C23—1482no—
150C23#1059693811yescharacteristic
151C23C2×C4×D3711yescharacteristic
152C23C2×D14811yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—2962no—
158D4—2962no—
159D4—1482no—
160D4—1481no—
161D4—1481no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—742no—
169C2×C4—1482no—
170C2×C4#1059693811yescharacteristic
171C2×C4#1059693811yescharacteristic
172C2×C4#1059693811yescharacteristic
173C2×C4C2×C22⋊D3711yescharacteristic
174C8—42no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2964no—
182C22—1482no—
183C22—1482no—
184C22—1482no—
185C22C2×#1059693811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—2962no—
190C4—1482no—
191C4#1192445011yescharacteristic
192C4#1192445011yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—2962no—
198C2C2×#1192445011yescharacteristic
subgroupG/H
centerC2C2×#11924450
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#413C2
socleC2×C37C2×#99
prime radical#14558097C2
cosocleC2×D4×C37C23
hypercenter#413D37
hypocenterC37#2122
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14557507C2semidirect
3. #14557321C2semidirect
4. C37×#413C2semidirect
5. C22×D148C4semidirect
10. #11924504C4semidirect
13. #11924495C4semidirect
101. #413D37semidirect
104. C37#2122semidirect

Maximal subgroups

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

subgroupindex
#145580972
#145575072
#145573212
C37×#4132
#212237