Finite Group Databasebeta

← #18010115

Subgroups — #18010115

Order 4736.

252 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 62 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
2C2×#11924603C211yesmaximal, characteristic, complemented
3#14558393C212yesmaximal, complemented
4#14558391C212yesmaximal, complemented
5#14558079C211yesmaximal, characteristic
6C22×#64438—21no—
7#11924603—21no—
8#11924603C2212yes—
9#11924603C2212yes—
10C22⋊#64438—21no—
11#11924591—21no—
12C2×#10596962C411yescharacteristic
13#11924534C2211yescharacteristic
14#11924532C2211yescharacteristic
15#11924525C411yescharacteristic
16#11924523C411yescharacteristic
17#11924508—21no—
18#11924508—21no—
19C4×C22⋊D37—21no—
20C4×C22⋊D37—21no—
21C2×C4×Dic37C2211yescharacteristic
22C2×#41×C37C411yescharacteristic
23#41×C37—42no—
24C2×Q8×C37C2×C411yescharacteristic
25C2×D4×C37—21no—
26C2×D4×C37C2×C411yescharacteristic
27C22×C4×C37—21no—
28C22×C4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C22×Dic37D411yescharacteristic
33C22×Dic37D411yescharacteristic
34#10596962—42no—
35C2×D148C2×C411yescharacteristic
36C2×C4×D37—21no—
37C2×Dic74C2×C411yescharacteristic
38C2×#64438—22no—
39C2×#64438—22no—
40C2×#64438—42no—
41C22⋊Dic37—21no—
42C22⋊Dic37—21no—
43#10596938—21no—
44#10596938—21no—
45#10596936—21no—
46#10596936—21no—
47C4×Dic37C2×C411yescharacteristic
48C4×Dic37D411yescharacteristic
49C4×Dic37D411yescharacteristic
50C4×Dic37C2311yescharacteristic
51C23×C37—21no—
52C23×C37C22⋊C411yescharacteristic
53C22×D37—21no—
54Q8×C37—41no—
55D4×C37—41no—
56D4×C37—42no—
57C2×C4×C37—22no—
58C2×C4×C37—21no—
59C2×C4×C37—42no—
60C2×C4×C37C22⋊C411yescharacteristic
61C2×C4×C37C22×C411yescharacteristic
62C22⋊D37—42no—
63C22⋊D37—42no—
64C22⋊D37—41no—
65C22⋊D37—41no—
66C2×Dic37—22no—
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37C22⋊C411yescharacteristic
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C2×D411yescharacteristic
73C2×Dic37C2×D411yescharacteristic
74D148—41no—
75C4×D37—42no—
76Dic74—41no—
77#64438—42no—
78#64438—42no—
79C22×C37—21no—
80C22×C37—21no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37#10012yes—
85C22×C37C2×C22⋊C411yescharacteristic
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—41no—
89C4×C37—21no—
90C4×C37—21no—
91C4×C37—41no—
92Dic37—21no—
93Dic37—21no—
94Dic37—41no—
95Dic37#13512yes—
96Dic37AGL(1,ℤ/8)11yescharacteristic
97Dic37#13711yescharacteristic
98#1551—371nomaximal, Sylow
99C2×C37—22no—
100C2×C37—81no—
101C2×C37C2×#10011yescharacteristic
102C2×C37#41611yescharacteristic
103C2×C37#41711yescharacteristic
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#386611yescharacteristic
113C22×C8—741no—
114C4⋊Q8—371no—
115#127—371no—
116#124—371no—
117#124—371no—
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—42no—
129#41—1482no—
130C2×Q8—371no—
131C2×Q8C2×#386611yescharacteristic
132C2×D4—21no—
133C2×D4—371no—
134C2×D4—741no—
135C2×D4—741no—
136C2×D4—741no—
137C2×D4C2×#386611yescharacteristic
138C22×C4—21no—
139C22×C4—371no—
140C22×C4—371no—
141C22×C4—741no—
142C22×C4C2×#386611yescharacteristic
143C2×C8—742no—
144C2×C8—742no—
145C2×C8—1482no—
146C4⋊C4—741no—
147C4⋊C4—741no—
148C22⋊C4—741no—
149C22⋊C4—741no—
150C22⋊C4—741no—
151C22⋊C4—741no—
152C42—371no—
153C42—371no—
154C42—371no—
155C42—371no—
156C23—21no—
157C23—741no—
158C23C22⋊#386611yescharacteristic
159Q8—41no—
160Q8—1481no—
161D4—41no—
162D4—42no—
163D4—1481no—
164D4—1482no—
165D4—1481no—
166D4—1481no—
167D4—1482no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—371no—
172C2×C4—371no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—741no—
176C2×C4—742no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—1482no—
180C2×C4C22⋊#386611yescharacteristic
181C2×C4C22×#386611yescharacteristic
182C8—1482no—
183C8—1482no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—1481no—
190C22—1481no—
191C22—1481no—
192C22#1192459612yes—
193C22C2×C22⋊#386611yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—372no—
198C4—371no—
199C4—371no—
200C4—741no—
201C4—741no—
202C4—1481no—
203C2—22no—
204C2—81no—
205C2—2961no—
206C2C2×#1192459611yescharacteristic
207C2#1455852311yescharacteristic
208C2#1455852411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×#41×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558079C2
cosocleC4×Dic37C23
hypercenterC2×#41#3866
hypocenterC37#1551
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14558553C2semidirect
2. C2×#11924603C2semidirect
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
#145585532
C2×#119246032
#145583932
#145583912
#145580792
#155137