Finite Group Databasebeta

← #18010116

Subgroups — #18010116

Order 4736.

252 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 60 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
2D37⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#14558393C212yesmaximal, complemented
4#14558391C212yesmaximal, complemented
5#14558082C211yesmaximal, characteristic
6C2×D37⋊C8—21no—
7#11924603C2212yes—
8#11924603C2212yes—
9C4⋊#64438—21no—
10#11924593—21no—
11#11924591—21no—
12C2×#10596966C411yescharacteristic
13C2×#10596964C411yescharacteristic
14#11924534C2211yescharacteristic
15#11924532C2211yescharacteristic
16#11924524C411yescharacteristic
17#11924509—21no—
18#11924509—21no—
19#11924496—21no—
20#11924496—21no—
21C42×D37C2211yescharacteristic
22#124×C37C411yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24C2×D4×C37C2×C411yescharacteristic
25C2×C22⋊D37—21no—
26C2×C22⋊D37—21no—
27C2×C22⋊D37—21no—
28C22×Dic37—21no—
29#10596966—42no—
30#10596964—42no—
31C2×D148—21no—
32C2×D148C2×C411yescharacteristic
33C2×C4×D37—21no—
34C2×C4×D37C2×C411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×Dic74C2×C411yescharacteristic
38C2×#64438—22no—
39C2×#64438—22no—
40D37⋊C8—42no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37—21no—
43C42×C37C2×C411yescharacteristic
44#10596938—21no—
45#10596938—21no—
46#10596936—21no—
47#10596936—21no—
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37C2311yescharacteristic
51C23×C37—21no—
52C22×D37—21no—
53C22×D37C22⋊C411yescharacteristic
54Q8×C37—41no—
55D4×C37—41no—
56C2×C4×C37—21no—
57C2×C4×C37C22⋊C411yescharacteristic
58C2×C4×C37C22⋊C411yescharacteristic
59C2×C4×C37C22×C411yescharacteristic
60C22⋊D37—42no—
61C22⋊D37—42no—
62C22⋊D37—41no—
63C22⋊D37—41no—
64C2×Dic37—21no—
65C2×Dic37—42no—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68C2×Dic37C2×D411yescharacteristic
69D148—41no—
70D148—42no—
71C4×D37—22no—
72C4×D37—22no—
73C4×D37—21no—
74C4×D37—21no—
75C4×D37—42no—
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#10012yes—
89C4×C37—21no—
90C4×C37—21no—
91C4×C37—21no—
92C4×C37—41no—
93Dic37—21no—
94Dic37—41no—
95Dic37#13512yes—
96Dic37AGL(1,ℤ/8)11yescharacteristic
97Dic37#13711yescharacteristic
98#1551—371nomaximal, Sylow
99C2×C37—81no—
100C2×C37C2×#10011yescharacteristic
101C2×C37#41611yescharacteristic
102C2×C37#41711yescharacteristic
103D37—22no—
104D37—81no—
105#532—371no—
106#432—371no—
107C2×C4⋊C8—371no—
108#333—372no—
109#331—372no—
110C37#155111yescharacteristic, complemented, Sylow
111C2×#41—371no—
112C2×#41—371no—
113C22×C8—741no—
114C4⋊Q8—371no—
115#127—371no—
116#124—371no—
117#124#386611yescharacteristic
118#121—741no—
119#121—741no—
120C4×D4—741no—
121C4×D4—741no—
122C2×C42—371no—
123C4⋊C8—372no—
124C4⋊C8—372no—
125C4⋊C8—741no—
126C22⋊C8—741no—
127#97—741no—
128#41—1482no—
129#41—1482no—
130C2×Q8—371no—
131C2×Q8C2×#386611yescharacteristic
132C2×D4—371no—
133C2×D4—741no—
134C2×D4—741no—
135C2×D4—741no—
136C2×D4—741no—
137C2×D4C2×#386611yescharacteristic
138C22×C4—371no—
139C22×C4—371no—
140C22×C4—371no—
141C22×C4—741no—
142C22×C4—741no—
143C2×C8—742no—
144C2×C8—742no—
145C2×C8—1482no—
146C4⋊C4—741no—
147C4⋊C4—741no—
148C22⋊C4—21no—
149C22⋊C4—21no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C42—371no—
153C42—371no—
154C42—371no—
155C42C2×#386611yescharacteristic
156C23—21no—
157C23—371no—
158C23—741no—
159Q8—41no—
160Q8—1481no—
161D4—41no—
162D4—1481no—
163D4—1482no—
164D4—1482no—
165D4—1481no—
166D4—1481no—
167D4—1482no—
168C2×C4—21no—
169C2×C4—371no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—741no—
173C2×C4—742no—
174C2×C4—741no—
175C2×C4—742no—
176C2×C4—741no—
177C2×C4—1482no—
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—21no—
197C4—41no—
198C4—372no—
199C4—371no—
200C4—371no—
201C4—741no—
202C4—1481no—
203C2—81no—
204C2—2961no—
205C2—742no—
206C2D37⋊#10011yescharacteristic
207C2#1455852311yescharacteristic
208C2#1455852411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558082C2
cosocleC4×Dic37C23
hypercenter#124#3866
hypocenterC37#1551
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. D37⋊(C4⋊C8)C2semidirect
3. #14558393C2semidirect
4. #14558391C2semidirect
110. C37#1551semidirect

Maximal subgroups

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

subgroupindex
#145585562
D37⋊(C4⋊C8)2
#145583932
#145583912
#145580822
#155137