Finite Group Databasebeta

← #18010120

Subgroups — #18010120

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#14558553C211yesmaximal, characteristic, complemented
2#14558550C211yesmaximal, characteristic, complemented
3#14558392C212yesmaximal, complemented
4#14558391C212yesmaximal, complemented
5#14558078C211yesmaximal, characteristic
6#11924603C2212yes—
7#11924603C2212yes—
8C22⋊#64438—21no—
9C22⋊#64438—21no—
10#11924591—21no—
11C4×#64438—21no—
12C2×#10596964—21no—
13#11924535C2211yescharacteristic
14#11924532C2211yescharacteristic
15#11924522—21no—
16#11924510C411yescharacteristic
17#11924508—21no—
18D4×Dic37C411yescharacteristic
19#11924498C411yescharacteristic
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—
36C2×#64438—22no—
37C2×#64438—22no—
38C4⋊C4×C37C2×C411yescharacteristic
39C22⋊C4×C37—21no—
40C22⋊Dic37—21no—
41#10596938—21no—
42#10596938—21no—
43C4⋊Dic37C2×C411yescharacteristic
44#10596936—21no—
45C4×Dic37C2×C411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37C2311yescharacteristic
49C23×C37—21no—
50C23×C37C22⋊C411yescharacteristic
51C22×D37—21no—
52D4×C37—41no—
53D4×C37—42no—
54C2×C4×C37—21no—
55C2×C4×C37—41no—
56C2×C4×C37C22⋊C411yescharacteristic
57C2×C4×C37C22×C411yescharacteristic
58C22⋊D37—42no—
59C22⋊D37—42no—
60C22⋊D37—42no—
61C2×Dic37—22no—
62C2×Dic37—22no—
63C2×Dic37—21no—
64C2×Dic37—42no—
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68C2×Dic37C2×D411yescharacteristic
69D148—41no—
70C4×D37—42no—
71Dic74—42no—
72#64438—42no—
73#64438—42no—
74C22×C37—21no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37C2×C22⋊C411yescharacteristic
81C2×D37—41no—
82C2×D37—41no—
83C2×D37—41no—
84C4×C37—21no—
85C4×C37—21no—
86C4×C37—41no—
87Dic37—21no—
88Dic37—21no—
89Dic37—41no—
90Dic37#13512yes—
91Dic37AGL(1,ℤ/8)12yes—
92#1553—371nomaximal, Sylow
93C2×C37—41no—
94C2×C37—81no—
95C2×C37#41311yescharacteristic
96C2×C37#41611yescharacteristic
97C2×C37#41811yescharacteristic
98D37—81no—
99#532—371no—
100#432—371no—
101#431—371no—
102#332—372no—
103#331—372no—
104C37#155311yescharacteristic, complemented, Sylow
105C2×#41—741no—
106C4⋊Q8—371no—
107#127—371no—
108#124—741no—
109#121—371no—
110#121—741no—
111#121#386611yescharacteristic
112C4×D4—371no—
113C4×D4—371no—
114C4×D4—741no—
115C2×C42—371no—
116C4⋊C8—372no—
117C4⋊C8—372no—
118C22⋊C8—741no—
119C22⋊C8—741no—
120#97—741no—
121C4×C8—741no—
122#41—1484no—
123C2×Q8—741no—
124C2×D4—21no—
125C2×D4—371no—
126C2×D4—741no—
127C2×D4—741no—
128C2×D4—741no—
129C2×D4C2×#386611yescharacteristic
130C22×C4—371no—
131C22×C4—371no—
132C22×C4—741no—
133C22×C4—741no—
134C22×C4C2×#386611yescharacteristic
135C2×C8—742no—
136C2×C8—742no—
137C4⋊C4—371no—
138C4⋊C4—741no—
139C4⋊C4C2×#386611yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—741no—
142C22⋊C4—741no—
143C22⋊C4—741no—
144C42—371no—
145C42—371no—
146C42—371no—
147C42—371no—
148C23—21no—
149C23—741no—
150C23C22⋊#386611yescharacteristic
151Q8—1482no—
152D4—41no—
153D4—42no—
154D4—1481no—
155D4—1482no—
156D4—1482no—
157D4—1482no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—371no—
161C2×C4—371no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—742no—
165C2×C4—742no—
166C2×C4—741no—
167C2×C4—1482no—
168C2×C4—1482no—
169C2×C4C22⋊#386611yescharacteristic
170C2×C4C22×#386611yescharacteristic
171C8—1482no—
172C8—1482no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—1481no—
180C22—1481no—
181C22—1481no—
182C22C2×C22⋊#386611yescharacteristic
183C4—21no—
184C4—21no—
185C4—41no—
186C4—372no—
187C4—372no—
188C4—741no—
189C4—741no—
190C4—1481no—
191C2—41no—
192C2—81no—
193C2—2961no—
194C2#1455852011yescharacteristic
195C2#1455852311yescharacteristic
196C2#1455852511yescharacteristic
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#1553
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #14558553C2semidirect
2. #14558550C2semidirect
3. #14558392C2semidirect
4. #14558391C2semidirect
104. C37#1553semidirect

Maximal subgroups

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

subgroupindex
#145585532
#145585502
#145583922
#145583912
#145580782
#155337