Finite Group Databasebeta

← #18010008

Subgroups — #18010008

Order 4736.

222 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 56 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#14558555C211yesmaximal, characteristic, complemented
2#14558477C211yesmaximal, characteristic, complemented
3#14558387C212yesmaximal, complemented
4#14558384C212yesmaximal
5#14558062C211yesmaximal, characteristic
6C2×C4⋊#3866—21no—
7C4⋊#64438—21no—
8#11924593C2212yes—
9#11924591—21no—
10(C2×#3866)⋊C4—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—42no—
33C22⋊C4×C37—21no—
34C22⋊C4×C37—21no—
35C42×C37C2×C411yescharacteristic
36C22⋊Dic37—21no—
37C22⋊Dic37—21no—
38#10596938—21no—
39C4⋊Dic37—21no—
40C4⋊Dic37C2×C411yescharacteristic
41C4⋊Dic37C2×C411yescharacteristic
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45C4×Dic37—21no—
46C4×Dic37C2×C411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37D411yescharacteristic
49C23×C37—21no—
50C22×D37C2×D411yescharacteristic
51C2×#3866—42no—
52C2×#3866—42no—
53C2×#3866—42no—
54Q8×C37—41no—
55D4×C37—41no—
56C2×C4×C37—21no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22×C411yescharacteristic
60C22⋊D37—41no—
61C22⋊D37—41no—
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—42no—
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68C4×D37—21no—
69C4×D37—21no—
70C4×D37—41no—
71C4×D37—41no—
72#64438—42no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37—41no—
76C22×C37C2×C22⋊C411yescharacteristic
77C2×D37—21no—
78C2×D37—21no—
79C2×D37AGL(1,ℤ/8)11yescharacteristic
80C2×D37#13711yescharacteristic
81#3866—82no—
82C4×C37—21no—
83C4×C37—21no—
84C4×C37—21no—
85C4×C37—41no—
86Dic37—21no—
87Dic37—21no—
88Dic37—21no—
89Dic37—41no—
90Dic37—41no—
91#1512—371nomaximal, Sylow
92C2×C37—81no—
93C2×C37#41011yescharacteristic
94C2×C37#41711yescharacteristic
95C2×C37#42111yescharacteristic
96D37—21no—
97D37—21no—
98#529—371no—
99#432—371no—
100#382—371no—
101#328—372no—
102#327—372no—
103C37#151211yescharacteristic, complemented, Sylow
104#126—741no—
105#125—371no—
106#124#386611yescharacteristic, complemented
107#123—741no—
108C22⋊Q8—371no—
109#121—371no—
110C4×Q8—371no—
111C4×D4—371no—
112C4×D4—741no—
113#117—741no—
114C2×C4⋊C4—741no—
115C2×C42—371no—
116C4⋊C8—741no—
117C22⋊C8—372no—
118#97—741no—
119#95—372no—
120#95—741no—
121C2×Q8C2×#386611yescharacteristic
122C2×D4—741no—
123C2×D4C2×#386611yescharacteristic
124C22×C4—371no—
125C22×C4—371no—
126C22×C4—371no—
127C22×C4—741no—
128C22×C4—742no—
129C2×C8—742no—
130C4⋊C4—371no—
131C4⋊C4—371no—
132C4⋊C4—741no—
133C4⋊C4—741no—
134C4⋊C4—741no—
135C4⋊C4—741no—
136C4⋊C4—1482no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—741no—
140C22⋊C4—741no—
141C22⋊C4—741no—
142C42—371no—
143C42—371no—
144C42—371no—
145C42—741no—
146C42C2×#386611yescharacteristic
147C23—21no—
148C23—371no—
149Q8—41no—
150D4—41no—
151D4—1481no—
152D4—1481no—
153C2×C4—21no—
154C2×C4—371no—
155C2×C4—371no—
156C2×C4—371no—
157C2×C4—741no—
158C2×C4—741no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—1481no—
162C2×C4—1481no—
163C2×C4—1482no—
164C2×C4—1482no—
165C2×C4—1482no—
166C2×C4—1482no—
167C2×C4C22⋊#386611yescharacteristic
168C2×C4C22⋊#386611yescharacteristic
169C2×C4C22×#386611yescharacteristic
170C8—1482no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—371no—
175C22—371no—
176C22—741no—
177C22—741no—
178C22C2×C22⋊#386611yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—2962no—
184C4—741no—
185C4—741no—
186C4—741no—
187C4—1481no—
188C4—1481no—
189C2—81no—
190C2—741no—
191C2—741no—
192C2#1455851311yescharacteristic
193C2#1455852411yescharacteristic
194C2#1455853011yescharacteristic
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#1512
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. #14558555C2semidirect
2. #14558477C2semidirect
3. #14558387C2semidirect
13. #11924528C4semidirect
17. Q8×Dic37C4semidirect
18. D4×Dic37C4semidirect
22. #124×C37C4semidirect
103. C37#1512semidirect
106. #124#3866semidirect

Maximal subgroups

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

subgroupindex
#145585552
#145584772
#145583872
#145583842
#145580622
#151237