Finite Group Databasebeta

← #18010855

Subgroups — #18010855

Order 4736.

266 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 54 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#14558519C211yesmaximal, characteristic, complemented
2#14558512C211yesmaximal, characteristic, complemented
3#14558433C214yesmaximal, complemented
4#14558100C211yesmaximal, characteristic
5D37⋊M16—21no—
6#11924615—21no—
7#11924597—21no—
8#11924596C2212yes—
9#11924595—21no—
10#11924594C2212yes—
11C2×#10596962C2211yescharacteristic
12#11924532—21no—
13#11924523—21no—
14#11924507—21no—
15#11924507—21no—
16#11924505C412yescomplemented
17#11924505C2212yes—
18#11924495C411yescharacteristic, complemented
19C22×D4×C37C411yescharacteristic, complemented
20C24×C37C2×C412yes—
21C2×D4×C37—21no—
22C2×D4×C37—21no—
23C2×D4×C37—41no—
24C2×D4×C37—41no—
25C22×C4×C37C2×C411yescharacteristic
26C2×C22⋊D37—22no—
27C2×C22⋊D37—22no—
28C2×C22⋊D37C2×C411yescharacteristic
29C2×C22⋊D37C2311yescharacteristic
30#10596962—41no—
31#10596962—41no—
32C2×D148D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×Dic74D411yescharacteristic
36C22⋊#3866—22no—
37#10596957—22no—
38C4⋊#3866—41no—
39C4×#3866—41no—
40#10596953—41no—
41D37⋊C8—41no—
42C22⋊Dic37—22no—
43C22⋊Dic37—22no—
44C22⋊Dic37C2×C412yes—
45C4⋊Dic37—21no—
46C4×Dic37—21no—
47C23×C37—22no—
48C23×C37—42no—
49C23×C37—82no—
50C23×C37C22×C411yescharacteristic
51C22×D37C22⋊C411yescharacteristic
52C22×D37C2×D411yescharacteristic
53C2×#3866—42no—
54D4×C37—42no—
55D4×C37—41no—
56D4×C37—41no—
57C2×C4×C37—21no—
58C2×C4×C37—21no—
59C2×C4×C37C22⋊C411yescharacteristic
60C2×C4×C37C22⋊C411yescharacteristic
61C22⋊D37—41no—
62C22⋊D37—41no—
63C22⋊D37—82no—
64C22⋊D37—82no—
65C2×Dic37—22no—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68D148—41no—
69C4×D37—21no—
70C4×D37—21no—
71C4×D37—21no—
72C4×D37—21no—
73Dic74—41no—
74#64438—42no—
75C22×C37—21no—
76C22×C37—41no—
77C22×C37—42no—
78C22×C37—42no—
79C22×C37—42no—
80C22×C37—84no—
81C22×C37C2×C22⋊C411yescharacteristic
82C2×D37—21no—
83C2×D37—21no—
84C2×D37—41no—
85C2×D37—41no—
86#3866—82no—
87C4×C37—21no—
88C4×C37#9911yescharacteristic
89C4×C37#9911yescharacteristic
90Dic37—21no—
91Dic37—21no—
92Dic37—42no—
93#2122—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—41no—
96C2×C37—82no—
97C2×C37C2×#9911yescharacteristic
98D37—41no—
99D37—41no—
100#535—371no—
101#413—371no—
102#410—371no—
103AΣL(1,𝔽16)—374no—
104C37#212211yescharacteristic, complemented, Sylow
105C2×#41—371no—
106C22×D4#386611yescharacteristic, complemented
107C2×M16—741no—
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—741no—
117#100—372no—
118#99—372no—
119#99—741no—
120C24C2×#386612yes—
121#41—1481no—
122#41—1481no—
123C2×Q8—371no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—41no—
127C2×D4—41no—
128C2×D4—371no—
129C2×D4—371no—
130C2×D4—371no—
131C2×D4—742no—
132C2×D4—742no—
133C22×C4—371no—
134C22×C4—371no—
135C22×C4C2×#386611yescharacteristic
136M16—742no—
137M16—1481no—
138C2×C8—1481no—
139C4⋊C4—741no—
140C4⋊C4—1481no—
141C22⋊C4—372no—
142C22⋊C4—742no—
143C22⋊C4—742no—
144C22⋊C4—742no—
145C42—741no—
146C42—1481no—
147C23—22no—
148C23—42no—
149C23—82no—
150C23—371no—
151C23—371no—
152C23C22×#386611yescharacteristic
153Q8—1481no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—2962no—
158D4—2962no—
159D4—1481no—
160D4—1481no—
161D4—1481no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—371no—
165C2×C4—371no—
166C2×C4—741no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4—741no—
170C2×C4—742no—
171C2×C4—1482no—
172C2×C4C22⋊#386611yescharacteristic
173C2×C4C22⋊#386611yescharacteristic
174C8—1482no—
175C22—21no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—84no—
181C22—741no—
182C22—741no—
183C22—1481no—
184C22—1481no—
185C22C2×C22⋊#386611yescharacteristic
186C4—21no—
187C4—2962no—
188C4—741no—
189C4—741no—
190C4—1482no—
191C4#1192459411yescharacteristic
192C4#1192459411yescharacteristic
193C2—21no—
194C2—41no—
195C2—82no—
196C2—1481no—
197C2—1481no—
198C2C2×#1192459411yescharacteristic
subgroupG/H
centerC2C2×#11924594
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC22×D4×C37C4
socleC2×C37C2×#99
prime radical#14558100C2
cosocleC2×C22⋊D37C23
hypercenterC22×D4#3866
hypocenterC37#2122
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #14558519C2semidirect
2. #14558512C2semidirect
3. #14558433C2semidirect
16. #11924505C4semidirect
18. #11924495C4semidirect
19. C22×D4×C37C4semidirect
104. C37#2122semidirect
106. C22×D4#3866semidirect

Maximal subgroups

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

subgroupindex
#145585192
#145585122
#145584332
#145581002
#212237