Finite Group Databasebeta

← #18010504

Subgroups — #18010504

Order 4736.

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

normal subgroups only

This group has 306 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#14558504C211yesmaximal, characteristic
2C4×C22⋊#3866C211yesmaximal, characteristic
3#14558403C212yesmaximal, complemented
4#14558403C212yesmaximal, complemented
5#117×D37C211yesmaximal, characteristic
6C2×#10596953C2212yes—
7C2×C22⋊#3866—21no—
8C2×C4×#3866C2212yes—
9#11924593—21no—
10C22⋊#64438—21no—
11(C2×#3866)⋊C4—21no—
12C22×C4×D37C2211yescharacteristic
13#11924495C411yescharacteristic, complemented
14#11924494C2211yescharacteristic
15#11924494C2211yescharacteristic
16#11924493—21no—
17#11924492—21no—
18C4⋊C4×D37C411yescharacteristic, complemented
19C4⋊C4×D37C411yescharacteristic, complemented
20C22⋊C4×D37—21no—
21C42×D37—21no—
22#117×C37C411yescharacteristic, complemented
23C23×D37D411yescharacteristic
24C22×#3866—22no—
25C22×C4×C37C2×C411yescharacteristic
26C22×Dic37D411yescharacteristic
27C2×C4×D37—24no—
28C2×C4×D37—21no—
29C2×C4×D37—21no—
30C2×C4×D37C2×C411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37C2311yescharacteristic
34C22⋊#3866—24no—
35C2×#64438—22no—
36C4×#3866—24no—
37#10596953—24no—
38C4⋊C4×C37C2×C411yescharacteristic
39C4⋊C4×C37C2×C411yescharacteristic
40C22⋊C4×C37—21no—
41C42×C37—21no—
42C22⋊Dic37—21no—
43#10596938—21no—
44#10596938—21no—
45C4⋊Dic37C2×C411yescharacteristic
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48#10596936—21no—
49C4×Dic37—21no—
50C4×Dic37—21no—
51C4×Dic37—21no—
52C23×C37C22⋊C411yescharacteristic
53C22×D37—22no—
54C22×D37—22no—
55C22×D37—41no—
56C22×D37C22⋊C411yescharacteristic
57C22×D37C2×D411yescharacteristic
58C2×#3866—24no—
59C2×#3866—42no—
60C2×#3866—42no—
61C2×C4×C37—22no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22×C411yescharacteristic
66C2×Dic37—22no—
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C2×D411yescharacteristic
71C4×D37—22no—
72C4×D37—22no—
73C4×D37—22no—
74C4×D37—42no—
75C4×D37—42no—
76C4×D37#4114yes—
77#64438—42no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37—21no—
81C22×C37C2×C22⋊C411yescharacteristic
82C2×D37—21no—
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—21no—
86C2×D37—44no—
87C2×D37#10412yes—
88C2×D37#12312yes—
89#3866—44no—
90C4×C37—21no—
91C4×C37—41no—
92C4×C37—41no—
93C4×C37#11712yes—
94Dic37—21no—
95Dic37—41no—
96Dic37—41no—
97Dic37#12312yes—
98#1826—371nomaximal, Sylow
99C2×C37—41no—
100C2×C37#38111yescharacteristic
101C2×C37C2×#10411yescharacteristic
102C2×C37#42111yescharacteristic
103D37—22no—
104D37—22no—
105C2×#117—371no—
106#407—371no—
107C4×C22⋊C4—371no—
108#339—372no—
109#339—372no—
110C37#182611yescharacteristic, complemented, Sylow
111C23×C4—371no—
112C2×M16—372no—
113#117—371no—
114#117—371no—
115#117—371no—
116#117—741no—
117#117—741no—
118#117#386611yescharacteristic, complemented
119C2×C4⋊C4—371no—
120C2×C4⋊C4—371no—
121C2×C22⋊C4—741no—
122C2×C22⋊C4—741no—
123C2×C42—372no—
124C2×C42—741no—
125C22⋊C8—741no—
126C22⋊C8—741no—
127#95—741no—
128C24—371no—
129C22×C4—371no—
130C22×C4—371no—
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—371no—
134C22×C4—744no—
135C22×C4—741no—
136C22×C4—741no—
137C22×C4—742no—
138C22×C4C2×#386611yescharacteristic
139M16—744no—
140C2×C8—742no—
141C4⋊C4—371no—
142C4⋊C4—371no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4C2×#386611yescharacteristic
146C4⋊C4C2×#386611yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—741no—
149C22⋊C4—741no—
150C22⋊C4—744no—
151C22⋊C4—741no—
152C42—21no—
153C42—741no—
154C42—741no—
155C42—744no—
156C42—741no—
157C23—371no—
158C23—371no—
159C23—742no—
160C23—742no—
161C23—1481no—
162C23C22⋊#386611yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—371no—
167C2×C4—374no—
168C2×C4—371no—
169C2×C4—742no—
170C2×C4—742no—
171C2×C4—742no—
172C2×C4—742no—
173C2×C4—744no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—1482no—
177C2×C4—1482no—
178C2×C4—1482no—
179C2×C4—1482no—
180C2×C4C22⋊#386611yescharacteristic
181C2×C4C22×#386611yescharacteristic
182C8—1482no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—372no—
187C22—372no—
188C22—741no—
189C22—741no—
190C22—741no—
191C22—741no—
192C22—1484no—
193C22C2×C22⋊#386611yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—372no—
198C4—741no—
199C4—1484no—
200C4—1481no—
201C4—1481no—
202C4#1192461512yes—
203C2—41no—
204C2—742no—
205C2—742no—
206C2#1455847611yescharacteristic
207C2D37⋊#10411yescharacteristic
208C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#117×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenter#117#3866
hypocenterC37#1826
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #14558403C2semidirect
4. #14558403C2semidirect
13. #11924495C4semidirect
18. C4⋊C4×D37C4semidirect
19. C4⋊C4×D37C4semidirect
22. #117×C37C4semidirect
110. C37#1826semidirect
118. #117#3866semidirect

Maximal subgroups

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

subgroupindex
#145585042
C4×C22⋊#38662
#145584032
#117×D372
#182637