Finite Group Databasebeta

← #18009997

Subgroups — #18009997

Order 4736.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558556C211yesmaximal, characteristic, complemented
2C4×C4⋊#3866C211yesmaximal, characteristic, complemented
3#14558387C212yesmaximal, complemented
4#14558384C212yesmaximal
5#14558062C211yesmaximal, characteristic
6C2×C4⋊#3866—21no—
7C2×C4×#3866—21no—
8#11924603—21no—
9#11924593C2212yes—
10#11924591—21no—
11(C2×#3866)⋊C4C2212yes—
12#11924529—21no—
13#11924528C411yescharacteristic, complemented
14#11924518—21no—
15#11924512C2211yescharacteristic
16#11924507C2211yescharacteristic
17Q8×Dic37C411yescharacteristic, complemented
18D4×Dic37C411yescharacteristic, complemented
19#11924496—21no—
20#11924492—21no—
21C42×D37C2211yescharacteristic
22#124×C37C411yescharacteristic, complemented
23C22×#3866—22no—
24C2×Q8×C37C2×C411yescharacteristic
25C2×D4×C37C2×C411yescharacteristic
26C2×C22⋊D37—21no—
27C22×Dic37—21no—
28C2×C4×D37D411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×C4×D37C2311yescharacteristic
31C2×#64438—22no—
32C4⋊#3866—24no—
33C4×#3866—42no—
34C22⋊C4×C37—21no—
35C22⋊C4×C37—21no—
36C42×C37C2×C411yescharacteristic
37C22⋊Dic37—21no—
38C22⋊Dic37—21no—
39#10596938—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37C2×C411yescharacteristic
42C4⋊Dic37C2×C411yescharacteristic
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46C4×Dic37—21no—
47C4×Dic37C2×C411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C23×C37—21no—
51C22×D37C2×D411yescharacteristic
52C2×#3866—24no—
53C2×#3866—42no—
54C2×#3866—42no—
55Q8×C37—41no—
56D4×C37—41no—
57C2×C4×C37—21no—
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22⋊C411yescharacteristic
60C2×C4×C37C22×C411yescharacteristic
61C22⋊D37—41no—
62C22⋊D37—41no—
63C2×Dic37—21no—
64C2×Dic37—21no—
65C2×Dic37—42no—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C2×D411yescharacteristic
69C4×D37—21no—
70C4×D37—21no—
71C4×D37—22no—
72C4×D37—41no—
73#64438—42no—
74C22×C37—41no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37C2×C22⋊C411yescharacteristic
78C2×D37—21no—
79C2×D37—21no—
80C2×D37AGL(1,ℤ/8)11yescharacteristic
81C2×D37#13711yescharacteristic
82#3866—44no—
83C4×C37—21no—
84C4×C37—21no—
85C4×C37—21no—
86C4×C37—41no—
87Dic37—21no—
88Dic37—21no—
89Dic37—41no—
90Dic37—41no—
91Dic37#10412yes—
92#1509—371nomaximal, Sylow
93C2×C37—81no—
94C2×C37#41011yescharacteristic
95C2×C37#41711yescharacteristic
96C2×C37C2×#10411yescharacteristic
97D37—21no—
98D37—21no—
99#529—371no—
100#432—371no—
101C4×C4⋊C4—371no—
102#328—372no—
103#327—372no—
104C37#150911yescharacteristic, complemented, Sylow
105#126—741no—
106#125—371no—
107#124#386611yescharacteristic, complemented
108#123—741no—
109C22⋊Q8—371no—
110#121—371no—
111C4×Q8—371no—
112C4×D4—371no—
113C4×D4—741no—
114#117—741no—
115C2×C4⋊C4—741no—
116C2×C42—371no—
117C2×C42—741no—
118C4⋊C8—741no—
119C22⋊C8—372no—
120#97—741no—
121#95—372no—
122C2×Q8C2×#386611yescharacteristic
123C2×D4—741no—
124C2×D4C2×#386611yescharacteristic
125C22×C4—371no—
126C22×C4—371no—
127C22×C4—371no—
128C22×C4—741no—
129C22×C4—742no—
130C2×C8—742no—
131C4⋊C4—371no—
132C4⋊C4—371no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C4⋊C4—744no—
136C4⋊C4—741no—
137C4⋊C4—741no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—741no—
141C22⋊C4—741no—
142C22⋊C4—741no—
143C42—371no—
144C42—371no—
145C42—371no—
146C42—741no—
147C42—1482no—
148C42C2×#386611yescharacteristic
149C23—21no—
150C23—371no—
151Q8—41no—
152D4—41no—
153D4—1481no—
154D4—1481no—
155C2×C4—21no—
156C2×C4—371no—
157C2×C4—371no—
158C2×C4—371no—
159C2×C4—742no—
160C2×C4—741no—
161C2×C4—741no—
162C2×C4—744no—
163C2×C4—741no—
164C2×C4—741no—
165C2×C4—1481no—
166C2×C4—1482no—
167C2×C4—1482no—
168C2×C4—1482no—
169C2×C4C22⋊#386611yescharacteristic
170C2×C4C22⋊#386611yescharacteristic
171C2×C4C22×#386611yescharacteristic
172C8—1482no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—371no—
177C22—371no—
178C22—741no—
179C22—741no—
180C22C2×C22⋊#386611yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—372no—
186C4—741no—
187C4—741no—
188C4—1484no—
189C4—1481no—
190C4—1481no—
191C2—81no—
192C2—741no—
193C2—741no—
194C2#1455851311yescharacteristic
195C2#1455852411yescharacteristic
196C2D37⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC22×C37C2×C22⋊C4
prime radical#11924507C22
cosocleC2×C4×D37C23
hypercenter#124#3866
hypocenterC37#1509
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14558556C2semidirect
2. C4×C4⋊#3866C2semidirect
3. #14558387C2semidirect
13. #11924528C4semidirect
17. Q8×Dic37C4semidirect
18. D4×Dic37C4semidirect
22. #124×C37C4semidirect
104. C37#1509semidirect
107. #124#3866semidirect

Maximal subgroups

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

subgroupindex
#145585562
C4×C4⋊#38662
#145583872
#145583842
#145580622
#150937