Finite Group Databasebeta

← #18009915

Subgroups — #18009915

Order 4736.

262 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 62 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#14558549C211yesmaximal, characteristic, complemented
2C4×#10596957C211yesmaximal, characteristic, complemented
3#14558381C212yesmaximal, complemented
4D4⋊#64438C212yesmaximal, complemented
5#14558078C211yesmaximal, characteristic
6C2×#10596957—21no—
7C4⋊#64438C2212yes—
8C22⋊#64438—21no—
9#11924591—21no—
10C4×#64438—21no—
11C4×#64438C2212yes—
12C2×#10596964—21no—
13#11924535C411yescharacteristic
14#11924532C411yescharacteristic
15#11924522—21no—
16#11924510C411yescharacteristic
17#11924508—21no—
18D4×Dic37C2211yescharacteristic
19#11924498C2211yescharacteristic
20#11924496—21no—
21C2×C4×Dic37C2211yescharacteristic
22#121×C37C411yescharacteristic
23C2×D4×C37—21no—
24C2×D4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28C2×C22⋊D37—21no—
29C22×Dic37—21no—
30C22×Dic37D411yescharacteristic
31C22×Dic37D411yescharacteristic
32#10596964—44no—
33C2×D148C2×C411yescharacteristic
34C2×C4×D37—21no—
35C2×Dic74—21no—
36#10596957—24no—
37C2×#64438—22no—
38C2×#64438—22no—
39C4⋊C4×C37C2×C411yescharacteristic
40C22⋊C4×C37—21no—
41C22⋊Dic37—21no—
42#10596938—21no—
43#10596938—21no—
44C4⋊Dic37C2×C411yescharacteristic
45#10596936—21no—
46C4×Dic37C2×C411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37C2311yescharacteristic
50C23×C37—21no—
51C23×C37C22⋊C411yescharacteristic
52C22×D37—21no—
53D4×C37—22no—
54D4×C37—42no—
55C2×C4×C37—22no—
56C2×C4×C37—21no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22×C411yescharacteristic
59C22⋊D37—42no—
60C22⋊D37—42no—
61C22⋊D37—42no—
62C2×Dic37—22no—
63C2×Dic37—22no—
64C2×Dic37—21no—
65C2×Dic37—42no—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C2×D411yescharacteristic
69C2×Dic37C2×D411yescharacteristic
70D148—22no—
71C4×D37—42no—
72Dic74—42no—
73#64438—24no—
74#64438—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—41no—
83C2×D37—41no—
84C2×D37—41no—
85C4×C37—21no—
86C4×C37—41no—
87C4×C37#13112yes—
88Dic37—21no—
89Dic37—21no—
90Dic37—41no—
91Dic37#10412yes—
92Dic37AGL(1,ℤ/8)12yes—
93#1484—371nomaximal, Sylow
94C2×C37—41no—
95C2×C37—81no—
96C2×C37#40811yescharacteristic
97C2×C37#41811yescharacteristic
98C2×C37C2×#10411yescharacteristic
99D37—81no—
100#532—371no—
101#431—371no—
102C4×M16—371no—
103D4⋊C8—372no—
104D4⋊C8—372no—
105C37#148411yescharacteristic, complemented, Sylow
106C2×#41—741no—
107C2×M16—741no—
108C4⋊Q8—371no—
109#127—371no—
110#124—741no—
111#121—371no—
112#121—741no—
113#121#386611yescharacteristic
114C4×D4—371no—
115C4×D4—371no—
116C4×D4—741no—
117C2×C42—371no—
118C4⋊C8—372no—
119C22⋊C8—741no—
120#97—741no—
121C4×C8—372no—
122C4×C8—741no—
123#41—1484no—
124C2×Q8—741no—
125C2×D4—21no—
126C2×D4—371no—
127C2×D4—741no—
128C2×D4—741no—
129C2×D4—741no—
130C2×D4C2×#386611yescharacteristic
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—741no—
134C22×C4—741no—
135C22×C4C2×#386611yescharacteristic
136M16—744no—
137C2×C8—742no—
138C2×C8—742no—
139C4⋊C4—371no—
140C4⋊C4—741no—
141C4⋊C4C2×#386611yescharacteristic
142C22⋊C4—21no—
143C22⋊C4—741no—
144C22⋊C4—741no—
145C22⋊C4—741no—
146C42—371no—
147C42—371no—
148C42—371no—
149C42—371no—
150C23—21no—
151C23—741no—
152C23C22⋊#386611yescharacteristic
153Q8—1482no—
154D4—22no—
155D4—42no—
156D4—742no—
157D4—1482no—
158D4—1482no—
159D4—1482no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—371no—
165C2×C4—371no—
166C2×C4—742no—
167C2×C4—742no—
168C2×C4—741no—
169C2×C4—1482no—
170C2×C4—1482no—
171C2×C4C22⋊#386611yescharacteristic
172C2×C4C22×#386611yescharacteristic
173C8—744no—
174C8—1482no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—1481no—
182C22—1481no—
183C22—1481no—
184C22C2×C22⋊#386611yescharacteristic
185C4—21no—
186C4—41no—
187C4—372no—
188C4—372no—
189C4—741no—
190C4—741no—
191C4—1481no—
192C4#1192462312yes—
193C2—41no—
194C2—81no—
195C2—2961no—
196C2#1455850611yescharacteristic
197C2#1455852511yescharacteristic
198C2D37⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#121×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558078C2
cosocleC4×Dic37C23
hypercenter#121#3866
hypocenterC37#1484
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #14558549C2semidirect
2. C4×#10596957C2semidirect
3. #14558381C2semidirect
4. D4⋊#64438C2semidirect
105. C37#1484semidirect

Maximal subgroups

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

subgroupindex
#145585492
C4×#105969572
#145583812
D4⋊#644382
#145580782
#148437