Finite Group Databasebeta

← #17993112

Subgroups — #17993112

Order 4736.

346 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 85 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#14557497C211yesmaximal, characteristic, complemented
2C4×C22⋊Dic37C211yesmaximal, characteristic, complemented
3#14557267C214yesmaximal, complemented
4C2×#121×C37C211yesmaximal, characteristic
5C2×#10596934—21no—
6C2×C22⋊Dic37—21no—
7C2×C4×Dic37—21no—
8C22⋊#64436—21no—
9C22⋊#64436C2212yescomplemented
10#11924443C2212yescomplemented
11C22×D4×C37—21no—
12C22×D4×C37C411yescharacteristic, complemented
13C23×C4×C37C2211yescharacteristic
14#121×C37—21no—
15#121×C37—21no—
16#121×C37C412yescomplemented
17#121×C37C2212yes—
18C2×C4⋊C4×C37C411yescharacteristic, complemented
19C2×C22⋊C4×C37—21no—
20C24×C37—21no—
21C24×C37D411yescharacteristic
22C2×D4×C37—22no—
23C2×D4×C37—22no—
24C2×D4×C37—21no—
25C2×D4×C37—42no—
26C2×D4×C37—44no—
27C2×D4×C37C2×C412yes—
28C22×C4×C37—21no—
29C22×C4×C37—42no—
30C22×C4×C37C2×C411yescharacteristic
31C22×C4×C37C2×C411yescharacteristic
32C22×C4×C37D411yescharacteristic
33C22×C4×C37D411yescharacteristic
34C22×C4×C37D411yescharacteristic
35C22×C4×C37C2311yescharacteristic
36C22×Dic37—22no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37C2×C412yes—
39C22⋊C4×C37—22no—
40C22⋊C4×C37—22no—
41C22⋊Dic37—24no—
42C4×Dic37—42no—
43#10596934—42no—
44C2×#64436—22no—
45C23×C37—22no—
46C23×C37—22no—
47C23×C37—22no—
48C23×C37—41no—
49C23×C37—42no—
50C23×C37—42no—
51C23×C37—42no—
52C23×C37C22⋊C411yescharacteristic
53C23×C37C22⋊C411yescharacteristic
54C23×C37C2×D411yescharacteristic
55D4×C37—42no—
56D4×C37—44no—
57D4×C37—44no—
58D4×C37—42no—
59C2×C4×C37—22no—
60C2×C4×C37—22no—
61C2×C4×C37—22no—
62C2×C4×C37—22no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—42no—
67C2×C4×C37C22⋊C411yescharacteristic
68C2×C4×C37C22⋊C411yescharacteristic
69C2×C4×C37C22×C411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×Dic37—24no—
72C2×Dic37—42no—
73C2×Dic37—42no—
74#64436—42no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37—21no—
81C22×C37—21no—
82C22×C37—44no—
83C22×C37—42no—
84C22×C37—42no—
85C22×C37—42no—
86C22×C37—84no—
87C22×C37#10412yes—
88C22×C37C2×C22⋊C411yescharacteristic
89C22×C37AGL(1,ℤ/8)12yes—
90C4×C37—21no—
91C4×C37—21no—
92C4×C37—21no—
93C4×C37—42no—
94C4×C37#9912yes—
95Dic37—44no—
96#1507—371nomaximal, Sylow
97C2×C37—22no—
98C2×C37—22no—
99C2×C37—41no—
100C2×C37—82no—
101C2×C37C2×#9911yescharacteristic
102C2×C37#41811yescharacteristic
103C2×C37C2×#10411yescharacteristic
104C2×#121D3711yescharacteristic
105#407—371no—
106C4×C22⋊C4—371no—
107#327—374no—
108C37#150711yescharacteristic, complemented, Sylow
109C22×D4—21no—
110C22×D4Dic3711yescharacteristic, complemented
111C23×C4C2×D3711yescharacteristic
112C2×M16—741no—
113#121—21no—
114#121—21no—
115#121Dic3712yescomplemented
116#121C2×D3712yes—
117C2×C4⋊C4Dic3711yescharacteristic, complemented
118C2×C22⋊C4—21no—
119C2×C22⋊C4—741no—
120C2×C42—741no—
121C22⋊C8—372no—
122C22⋊C8—741no—
123#95—372no—
124C24—21no—
125C24C22⋊D3711yescharacteristic
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—21no—
129C2×D4—42no—
130C2×D4—44no—
131C2×D4C2×Dic3712yes—
132C22×C4—21no—
133C22×C4—42no—
134C22×C4—742no—
135C22×C4C2×Dic3711yescharacteristic
136C22×C4C2×Dic3711yescharacteristic
137C22×C4C22⋊D3711yescharacteristic
138C22×C4C22⋊D3711yescharacteristic
139C22×C4C22⋊D3711yescharacteristic
140C22×C4C22×D3711yescharacteristic
141M16—1482no—
142C2×C8—742no—
143C4⋊C4—21no—
144C4⋊C4C2×Dic3712yes—
145C22⋊C4—22no—
146C22⋊C4—22no—
147C22⋊C4—744no—
148C42—1482no—
149C23—22no—
150C23—22no—
151C23—22no—
152C23—41no—
153C23—42no—
154C23—42no—
155C23—42no—
156C23C22⋊Dic3711yescharacteristic
157C23C22⋊Dic3711yescharacteristic
158C23C2×C22⋊D3711yescharacteristic
159D4—42no—
160D4—44no—
161D4—44no—
162D4—42no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—42no—
171C2×C4—744no—
172C2×C4—1482no—
173C2×C4—1482no—
174C2×C4C22⋊Dic3711yescharacteristic
175C2×C4C22⋊Dic3711yescharacteristic
176C2×C4C22×Dic3711yescharacteristic
177C2×C4C2×C22⋊D3711yescharacteristic
178C8—1482no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—44no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—84no—
191C22#1192446312yes—
192C22C2×C22⋊Dic3711yescharacteristic
193C22#1192456212yes—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—1484no—
199C4#1192445112yes—
200C2—22no—
201C2—22no—
202C2—41no—
203C2—82no—
204C2C2×#1192445111yescharacteristic
205C2#1455753811yescharacteristic
206C2C2×#1192446311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC2×#121×C37C2
socleC22×C37C2×C22⋊C4
cosocleC22×C4×C37C23
hypercenterC2×#121D37
hypocenterC37#1507
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #14557497C2semidirect
2. C4×C22⋊Dic37C2semidirect
3. #14557267C2semidirect
9. C22⋊#64436C22semidirect
10. #11924443C22semidirect
12. C22×D4×C37C4semidirect
16. #121×C37C4semidirect
18. C2×C4⋊C4×C37C4semidirect
108. C37#1507semidirect
110. C22×D4Dic37semidirect
115. #121Dic37semidirect
117. C2×C4⋊C4Dic37semidirect

Maximal subgroups

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

subgroupindex
#145574972
C4×C22⋊Dic372
#145572672
C2×#121×C372
#150737