Finite Group Databasebeta

← #18010093

Subgroups — #18010093

Order 4736.

256 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 68 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#14558551C211yesmaximal, characteristic, complemented
2D37⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#14558392C212yesmaximal, complemented
4#14558391C212yesmaximal, complemented
5#14558080C211yesmaximal, characteristic
6C2×D37⋊C8—21no—
7#11924603C2212yes—
8#11924603C2212yes—
9C4⋊#64438—21no—
10#11924593—21no—
11C4×#64438—21no—
12C2×#10596962—21no—
13#11924535C2211yescharacteristic
14#11924532C2211yescharacteristic
15#11924522—21no—
16#11924511C411yescharacteristic
17#11924509—21no—
18#11924507C411yescharacteristic
19C4×D148C411yescharacteristic
20C4×C22⋊D37—21no—
21C42×D37C2211yescharacteristic
22C4×D4×C37C411yescharacteristic
23C2×D4×C37C2×C411yescharacteristic
24C22×C4×C37—21no—
25C2×C22⋊D37—21no—
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28#10596962—42no—
29#10596962—42no—
30C2×D148—21no—
31C2×D148C2×C411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37C2×C411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×Dic74—21no—
37C2×#64438—22no—
38C2×#64438—22no—
39D37⋊C8—42no—
40C4⋊C4×C37C2×C411yescharacteristic
41C22⋊C4×C37—21no—
42C42×C37C2×C411yescharacteristic
43C22⋊Dic37—21no—
44#10596938—21no—
45#10596938—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37C2311yescharacteristic
51C23×C37—21no—
52C22×D37—21no—
53C22×D37C22⋊C411yescharacteristic
54D4×C37—41no—
55C2×C4×C37—21no—
56C2×C4×C37—42no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22×C411yescharacteristic
60C22⋊D37—42no—
61C22⋊D37—41no—
62C22⋊D37—41no—
63C22⋊D37—42no—
64C2×Dic37—21no—
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C2×D411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68D148—41no—
69D148—42no—
70C4×D37—22no—
71C4×D37—41no—
72C4×D37—42no—
73C4×D37D812yes—
74C4×D37SD1612yes—
75Dic74—41no—
76Dic74—41no—
77#64438—42no—
78#64438—42no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37—41no—
82C22×C37C2×C22⋊C411yescharacteristic
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—41no—
86C2×D37—41no—
87C2×D37—41no—
88C2×D37#10212yes—
89C4×C37—21no—
90C4×C37—21no—
91C4×C37—41no—
92C4×C37#10212yes—
93Dic37—21no—
94Dic37—41no—
95Dic37C2×D811yescharacteristic
96Dic37C2×SD1611yescharacteristic
97Dic37#13512yes—
98#1540—371nomaximal, Sylow
99C2×C37—81no—
100C2×C37#41311yescharacteristic
101C2×C37C2×#10211yescharacteristic
102C2×C37#41611yescharacteristic
103D37—22no—
104D37—81no—
105#532—371no—
106#431—371no—
107C2×C4⋊C8—371no—
108#332—372no—
109#331—372no—
110C37#154011yescharacteristic, complemented, Sylow
111C2×#41—741no—
112C22×C8—741no—
113C4⋊Q8—371no—
114#127—371no—
115#124—741no—
116#121—371no—
117#121—371no—
118#121—741no—
119C4×D4—371no—
120C4×D4—741no—
121C4×D4#386611yescharacteristic
122C2×C42—371no—
123C4⋊C8—372no—
124C4⋊C8—372no—
125C4⋊C8—741no—
126C22⋊C8—741no—
127C4×C8—741no—
128#41—1482no—
129#41—1482no—
130C2×Q8—741no—
131C2×D4—371no—
132C2×D4—741no—
133C2×D4—741no—
134C2×D4—741no—
135C2×D4—741no—
136C2×D4C2×#386611yescharacteristic
137C22×C4—21no—
138C22×C4—371no—
139C22×C4—371no—
140C22×C4—371no—
141C22×C4—741no—
142C2×C8—742no—
143C2×C8—742no—
144C2×C8—1482no—
145C4⋊C4—371no—
146C4⋊C4—741no—
147C4⋊C4C2×#386611yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—741no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C42—371no—
153C42—371no—
154C42—371no—
155C42C2×#386611yescharacteristic
156C23—21no—
157C23—371no—
158C23—741no—
159Q8—1481no—
160Q8—1481no—
161D4—41no—
162D4—1481no—
163D4—1482no—
164D4—1481no—
165D4—1481no—
166D4—1482no—
167D4—1482no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—372no—
173C2×C4—372no—
174C2×C4—371no—
175C2×C4—742no—
176C2×C4—741no—
177C2×C4—1481no—
178C2×C4—1482no—
179C2×C4C22⋊#386611yescharacteristic
180C2×C4C22⋊#386611yescharacteristic
181C2×C4C22×#386611yescharacteristic
182C8—1482no—
183C8—1482no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—372no—
188C22—741no—
189C22—741no—
190C22—1481no—
191C22—1481no—
192C22—1481no—
193C22C2×C22⋊#386611yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—371no—
198C4—371no—
199C4—372no—
200C4—741no—
201C4—1481no—
202C4#1192459812yes—
203C2—81no—
204C2—2961no—
205C2—742no—
206C2#1455851911yescharacteristic
207C2C2×#1192459811yescharacteristic
208C2#1455852311yescharacteristic
subgroupG/H
centerC2×C4C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558080C2
cosocleC4×Dic37C23
hypercenterC4×D4#3866
hypocenterC37#1540
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14558551C2semidirect
2. D37⋊(C4⋊C8)C2semidirect
3. #14558392C2semidirect
4. #14558391C2semidirect
110. C37#1540semidirect

Maximal subgroups

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

subgroupindex
#145585512
D37⋊(C4⋊C8)2
#145583922
#145583912
#145580802
#154037