Finite Group Databasebeta

← #17992942

Subgroups — #17992942

Order 4736.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#11924519C211yesmaximal, characteristic
2#14557497C211yesmaximal, characteristic, complemented
3#14557258C212yesmaximal, complemented
4#14557256C212yesmaximal, complemented
5C2×C22⋊C8×C37C211yesmaximal, characteristic, complemented
6C22×C22⋊D37C411yescharacteristic
7C2×#10596934—21no—
8#11924519—21no—
9#11924519—21no—
10#11924519—21no—
11#11924519—21no—
12C2×#10596936C411yescharacteristic
13C2×#10596936C2211yescharacteristic
14C2×C22⋊Dic37C411yescharacteristic
15C2×#10596938C411yescharacteristic
16C2×#10596938C2211yescharacteristic
17C22⋊#64436—21no—
18C22⋊#64436C2212yes—
19C23×C4×C37C2211yescharacteristic
20C22×C8×C37—21no—
21C22⋊C8×C37—21no—
22C22⋊C8×C37C2212yes—
23C24×C37C2×C411yescharacteristic
24C23×D37C2×C411yescharacteristic
25C22×C4×C37—42no—
26C22×C4×C37C2×C411yescharacteristic
27C22×C4×C37D411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×C4×C37D411yescharacteristic
30C22×C4×C37D411yescharacteristic
31C22×C4×C37C2311yescharacteristic
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C2×C22⋊D37—42no—
35C22×Dic37C2×C411yescharacteristic
36C22×Dic37C2×C411yescharacteristic
37C22×Dic37C2×C411yescharacteristic
38C2×C8×C37—22no—
39C2×C8×C37—42no—
40C22⋊Dic37—21no—
41C22⋊Dic37—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46#10596936—21no—
47#10596936—21no—
48#10596936—21no—
49#10596936—21no—
50#10596934—42no—
51C2×#64436—22no—
52C23×C37—22no—
53C23×C37—22no—
54C23×C37—41no—
55C23×C37C22⋊C411yescharacteristic
56C23×C37C22⋊C411yescharacteristic
57C23×C37C22×C411yescharacteristic
58C22×D37—21no—
59C22×D37—22no—
60C22×D37—41no—
61C22×D37—41no—
62C2×C4×C37—22no—
63C2×C4×C37—22no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37C22⋊C411yescharacteristic
69C2×C4×C37C22⋊C411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C22⋊D37—42no—
73C22⋊D37—42no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—22no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C8×C37—42no—
81#64436—42no—
82C22×C37—21no—
83C22×C37—21no—
84C22×C37—21no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37—44no—
90C22×C37#9912yes—
91C22×C37C2×C22⋊C411yescharacteristic
92C22×C37#13112yes—
93C2×D37—41no—
94C2×D37—41no—
95C2×D37—41no—
96C2×D37—82no—
97C4×C37—21no—
98C4×C37—21no—
99C4×C37—21no—
100C4×C37—21no—
101Dic37—41no—
102Dic37—41no—
103Dic37—41no—
104#1468—371nomaximal, Sylow
105C2×C37—22no—
106C2×C37—22no—
107C2×C37—41no—
108C2×C37#40811yescharacteristic
109C2×C37C2×#9911yescharacteristic
110C2×C37#41311yescharacteristic
111D37—81no—
112C2×#123—371no—
113#407—371no—
114C2×C22⋊C8D3711yescharacteristic, complemented
115#324—372no—
116#323—372no—
117C37#146811yescharacteristic, complemented, Sylow
118C22×D4—371no—
119C23×C4C2×D3711yescharacteristic
120C2×M16—741no—
121C22×C8—21no—
122#123—741no—
123#123—741no—
124#123—741no—
125#123—741no—
126C2×C4⋊C4—371no—
127C2×C4⋊C4—371no—
128C2×C22⋊C4—371no—
129C2×C22⋊C4—371no—
130C2×C22⋊C4—371no—
131C22⋊C8—21no—
132C22⋊C8—372no—
133C22⋊C8—741no—
134C22⋊C8C2×D3712yes—
135C24—371no—
136C24C4×D3711yescharacteristic
137C2×D4—741no—
138C2×D4—741no—
139C2×D4—1482no—
140C22×C4—42no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4C4×D3711yescharacteristic
145C22×C4D14811yescharacteristic
146C22×C4D14811yescharacteristic
147C22×C4C22⋊D3711yescharacteristic
148C22×C4C22⋊D3711yescharacteristic
149C22×C4C22×D3711yescharacteristic
150M16—1482no—
151C2×C8—22no—
152C2×C8—42no—
153C2×C8—742no—
154C4⋊C4—741no—
155C4⋊C4—741no—
156C4⋊C4—741no—
157C4⋊C4—741no—
158C22⋊C4—741no—
159C22⋊C4—741no—
160C22⋊C4—741no—
161C22⋊C4—741no—
162C22⋊C4—741no—
163C22⋊C4—741no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—742no—
168C23—741no—
169C23—1481no—
170C23—1481no—
171C23#1059693811yescharacteristic
172C23#1059693811yescharacteristic
173C23C2×C4×D3711yescharacteristic
174D4—1482no—
175D4—1482no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—742no—
186C2×C4—1481no—
187C2×C4—1481no—
188C2×C4#1059693811yescharacteristic
189C2×C4#1059693811yescharacteristic
190C2×C4C2×D14811yescharacteristic
191C2×C4C2×C22⋊D3711yescharacteristic
192C8—42no—
193C8—1482no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—2962no—
203C22—1481no—
204C22—1481no—
205C22—1481no—
206C22#1192445012yes—
207C22C2×#1059693811yescharacteristic
208C22#1192454212yes—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—1481no—
214C4—1481no—
215C4—1481no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—2961no—
220C2#1455749911yescharacteristic
221C2C2×#1192445011yescharacteristic
222C2#1455751511yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×C22⋊C8×C37C2
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C4
cosocleC22×C4×C37C23
hypercenterC2×C22⋊C8D37
hypocenterC37#1468
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #14557497C2semidirect
3. #14557258C2semidirect
4. #14557256C2semidirect
5. C2×C22⋊C8×C37C2semidirect
114. C2×C22⋊C8D37semidirect
117. C37#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#119245192
#145574972
#145572582
#145572562
C2×C22⋊C8×C372
#146837