Finite Group Databasebeta

← #17995138

Subgroups — #17995138

Order 4736.

380 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 89 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#14558092C211yesmaximal, characteristic
2C2×#11924451C211yesmaximal, characteristic, complemented
3C2×#11924450C212yesmaximal, complemented
4#14557299C212yesmaximal, complemented
5C37×#518C211yesmaximal, characteristic, complemented
6C22×C22⋊D37C2211yescharacteristic
7#11924519—21no—
8#11924517C412yescomplemented
9#11924508—22no—
10#11924505—21no—
11#11924504C412yescomplemented
12C2×C22⋊Dic37C2212yes—
13C2×C22⋊Dic37C2211yescharacteristic
14#11924451—22no—
15#11924450—24no—
16C22×D4×C37C2211yescharacteristic
17C4×D4×C37—24no—
18#117×C37—21no—
19C2×C22⋊C4×C37—21no—
20C2×C22⋊C4×C37C2212yes—
21C24×C37D411yescharacteristic
22C24×C37C2311yescharacteristic
23C23×D37C2×C411yescharacteristic, complemented
24C2×D4×C37—22no—
25C2×D4×C37—22no—
26C2×D4×C37C2×C412yes—
27C2×D4×C37D412yes—
28C22×C4×C37—22no—
29C22×C4×C37—22no—
30C22×C4×C37D411yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—22no—
34C2×C22⋊D37—22no—
35C2×C22⋊D37—22no—
36C22×Dic37—21no—
37C22×Dic37—22no—
38C22×Dic37C2×C411yescharacteristic, complemented
39C4⋊C4×C37—22no—
40C22⋊C4×C37—22no—
41C22⋊C4×C37—22no—
42C22⋊C4×C37D414yescomplemented
43C42×C37—22no—
44C22⋊Dic37—22no—
45C22⋊Dic37—21no—
46C22⋊Dic37—22no—
47C22⋊Dic37—22no—
48C22⋊Dic37C2×C412yescomplemented
49#10596938—22no—
50#10596936—22no—
51C23×C37—21no—
52C23×C37—21no—
53C23×C37—81no—
54C23×C37—81no—
55C23×C37C22⋊C412yes—
56C23×C37C22×C411yescharacteristic
57C23×C37C2×D411yescharacteristic
58C23×C37C2×D411yescharacteristic
59C23×C37C2×D412yes—
60C23×C37#4112yes—
61C22×D37—21no—
62C22×D37—22no—
63C22×D37—81no—
64D4×C37—24no—
65D4×C37—24no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—24no—
69C2×C4×C37—82no—
70C2×C4×C37—82no—
71C2×C4×C37C22⋊C412yes—
72C22⋊D37—41no—
73C22⋊D37—42no—
74C22⋊D37—41no—
75C22⋊D37—82no—
76C2×Dic37—21no—
77C2×Dic37—22no—
78C2×Dic37—22no—
79C2×Dic37—42no—
80C2×Dic37—81no—
81C2×Dic37—82no—
82C22×C37—22no—
83C22×C37—41no—
84C22×C37—42no—
85C22×C37—42no—
86C22×C37—41no—
87C22×C37—41no—
88C22×C37—42no—
89C22×C37—42no—
90C22×C37—81no—
91C22×C37C2×C22⋊C411yescharacteristic
92C22×C37C4×D412yes—
93C22×C37#12011yescharacteristic
94C22×C37#12112yes—
95C22×C37#12311yescharacteristic
96C2×D37—42no—
97C2×D37—41no—
98C2×D37—82no—
99C4×C37—22no—
100C4×C37—44no—
101Dic37—42no—
102Dic37—41no—
103Dic37—82no—
104#1913—371nomaximal, Sylow
105C2×C37—21no—
106C2×C37—22no—
107C2×C37—21no—
108C2×C37—22no—
109C2×C37—21no—
110C2×C37—42no—
111C2×C37#38611yescharacteristic
112D37—81no—
113#534—371no—
114#518D3711yescharacteristic, complemented
115C2×#99—371no—
116C2×#99—372no—
117#342—372no—
118C37#191311yescharacteristic, complemented, Sylow
119C22×D4—371no—
120C22×D4C2×D3711yescharacteristic
121#123—372no—
122#123—741no—
123#121—742no—
124#120—372no—
125#120—741no—
126C4×D4—24no—
127#117—21no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—371no—
130C2×C22⋊C4—372no—
131C2×C22⋊C4C2×D3712yes—
132#99—742no—
133#99—744no—
134C24—371no—
135C24C22⋊D3711yescharacteristic
136C24C22×D3711yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—742no—
140C2×D4—741no—
141C2×D4—742no—
142C2×D4—742no—
143C2×D4—741no—
144C2×D4C4×D3712yes—
145C2×D4D14812yes—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—371no—
149C22×C4—741no—
150C22×C4—742no—
151C22×C4C22⋊D3711yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—742no—
154C22⋊C4—22no—
155C22⋊C4—22no—
156C22⋊C4—372no—
157C22⋊C4—742no—
158C22⋊C4—741no—
159C22⋊C4—742no—
160C22⋊C4—742no—
161C22⋊C4—742no—
162C22⋊C4C22⋊D3714yescomplemented
163C42—22no—
164C23—21no—
165C23—21no—
166C23—81no—
167C23—81no—
168C23—2961no—
169C23—742no—
170C23—741no—
171C23#1059693812yes—
172C23C2×C4×D3711yescharacteristic
173C23C2×D14811yescharacteristic
174C23#1059696212yes—
175C23C2×C22⋊D3711yescharacteristic
176C23C2×C22⋊D3712yes—
177D4—24no—
178D4—24no—
179D4—2962no—
180D4—1481no—
181D4—1482no—
182D4—1481no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—24no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—2962no—
189C2×C4—2961no—
190C2×C4—742no—
191C2×C4—741no—
192C2×C4—742no—
193C2×C4—1482no—
194C2×C4#1059693812yes—
195C22—22no—
196C22—42no—
197C22—41no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—2962no—
205C22—1482no—
206C22—1481no—
207C22C2×#1059693811yescharacteristic
208C22C4×C22⋊D3712yes—
209C22#1192450511yescharacteristic
210C22#1192451012yes—
211C22#1192451911yescharacteristic
212C4—22no—
213C4—44no—
214C4—2962no—
215C4—1482no—
216C4—1481no—
217C2—21no—
218C2—22no—
219C2—21no—
220C2—21no—
221C2—22no—
222C2—42no—
223C2—2961no—
224C2#1455741211yescharacteristic
subgroupG/H
centerC2#14557412
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#518C2
socleC2×C37#386
prime radical#14558092C2
cosocleC24×C37C23
hypercenter#518D37
hypocenterC37#1913
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C2×#11924451C2semidirect
3. C2×#11924450C2semidirect
4. #14557299C2semidirect
5. C37×#518C2semidirect
8. #11924517C4semidirect
11. #11924504C4semidirect
23. C23×D37C2×C4semidirect
38. C22×Dic37C2×C4semidirect
42. C22⋊C4×C37D4semidirect
48. C22⋊Dic37C2×C4semidirect
114. #518D37semidirect
118. C37#1913semidirect
162. C22⋊C4C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580922
C2×#119244512
C2×#119244502
#145572992
C37×#5182
#191337