Finite Group Databasebeta

← #18010623

Subgroups — #18010623

Order 4736.

338 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#10596957C211yesmaximal, characteristic
2C2×#11924597C212yesmaximal, complemented
3#14558503C211yesmaximal, characteristic
4#14558413C212yesmaximal, complemented
5C2×#11924513C211yesmaximal, characteristic
6C2×#10596957—21no—
7C2×#10596957—24no—
8C2×#10596957C2212yes—
9C2×#10596957C2212yes—
10C22×#64438—21no—
11#11924597—24no—
12C22⋊#64438—21no—
13C22⋊#64438—21no—
14C22×Dic74C2211yescharacteristic
15C23×Dic37C2211yescharacteristic
16#11924513—21no—
17#11924513—21no—
18#11924513—21no—
19#11924513—21no—
20C2×C4⋊Dic37C411yescharacteristic
21C2×#10596936C411yescharacteristic
22C2×#10596936C2211yescharacteristic
23C2×C22⋊Dic37C411yescharacteristic
24C2×C22⋊C4×C37C411yescharacteristic
25C24×C37C2×C411yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C22×C4×C37C2×C411yescharacteristic
28C22×Dic37—22no—
29C22×Dic37—22no—
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C22×Dic37C2×C411yescharacteristic
33C22×Dic37D411yescharacteristic
34C22×Dic37D411yescharacteristic
35C22×Dic37D411yescharacteristic
36C22×Dic37D411yescharacteristic
37C22×Dic37C2311yescharacteristic
38C2×Dic74—21no—
39C2×Dic74—21no—
40C2×Dic74—22no—
41C2×Dic74—22no—
42#10596957—24no—
43#10596957—22no—
44#10596957—22no—
45#10596957—22no—
46#10596957D414yes—
47C2×#64438—24no—
48C2×#64438—22no—
49C2×#64438—22no—
50C22⋊C4×C37—21no—
51C22⋊C4×C37—21no—
52C22⋊Dic37—21no—
53C22⋊Dic37—21no—
54C4⋊Dic37—21no—
55C4⋊Dic37—21no—
56#10596936—21no—
57#10596936—21no—
58#10596936—21no—
59#10596936—21no—
60C23×C37—22no—
61C23×C37—22no—
62C23×C37—41no—
63C23×C37C22⋊C411yescharacteristic
64C23×C37C22⋊C411yescharacteristic
65C23×C37C22×C411yescharacteristic
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—22no—
69C2×C4×C37—41no—
70C2×Dic37—22no—
71C2×Dic37—21no—
72C2×Dic37—21no—
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—22no—
80C2×Dic37—41no—
81C2×Dic37C22⋊C411yescharacteristic
82C2×Dic37C22⋊C411yescharacteristic
83C2×Dic37C2×D412yes—
84C2×Dic37C2×D411yescharacteristic
85C2×Dic37C2×D411yescharacteristic
86C2×Dic37#4112yes—
87Dic74—41no—
88Dic74—42no—
89Dic74—41no—
90#64438—24no—
91#64438—42no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37—21no—
96C22×C37—21no—
97C22×C37—21no—
98C22×C37—21no—
99C22×C37—44no—
100C22×C37#10112yescomplemented
101C22×C37C2×C22⋊C411yescharacteristic
102C22×C37C4×D412yes—
103C4×C37—41no—
104C4×C37—41no—
105Dic37—21no—
106Dic37—21no—
107Dic37—41no—
108Dic37—41no—
109Dic37#12011yescharacteristic
110Dic37#12112yes—
111Dic37#12311yescharacteristic
112#1901—371nomaximal, Sylow
113C2×C37—22no—
114C2×C37—22no—
115C2×C37—41no—
116C2×C37#38611yescharacteristic
117C2×C37C2×#10111yescharacteristic
118C2×C37#41311yescharacteristic
119C22×M16—371no—
120C2×C22⋊Q8—371no—
121C2×#101—372no—
122#407—371no—
123#343—372no—
124C37#190111yescharacteristic, complemented, Sylow
125C22×Q8—371no—
126C23×C4—371no—
127C2×M16—372no—
128C2×M16—372no—
129C2×M16—744no—
130C2×M16—741no—
131C22×C8—741no—
132C22⋊Q8—741no—
133C22⋊Q8—741no—
134C22⋊Q8—741no—
135C22⋊Q8—741no—
136C2×C4⋊C4—371no—
137C2×C4⋊C4—371no—
138C2×C4⋊C4—371no—
139C2×C22⋊C4—371no—
140C2×C22⋊C4#386611yescharacteristic
141#101—744no—
142C22⋊C8—741no—
143C22⋊C8—741no—
144C24C2×#386611yescharacteristic
145C2×Q8—742no—
146C2×Q8—741no—
147C2×Q8—741no—
148C2×Q8—742no—
149C22×C4—371no—
150C22×C4—371no—
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—371no—
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—371no—
157C22×C4—742no—
158C22×C4—742no—
159C22×C4C2×#386611yescharacteristic
160C22×C4C2×#386611yescharacteristic
161M16—374no—
162M16—742no—
163M16—744no—
164M16—742no—
165M16—742no—
166C2×C8—742no—
167C2×C8—744no—
168C2×C8—742no—
169C4⋊C4—741no—
170C4⋊C4—741no—
171C4⋊C4—741no—
172C4⋊C4—741no—
173C4⋊C4—741no—
174C4⋊C4—741no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—741no—
178C22⋊C4—741no—
179C23—22no—
180C23—22no—
181C23—41no—
182C23C22⋊#386611yescharacteristic
183C23C22⋊#386611yescharacteristic
184C23C22×#386611yescharacteristic
185Q8—1481no—
186Q8—1482no—
187Q8—1481no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—371no—
193C2×C4—371no—
194C2×C4—372no—
195C2×C4—372no—
196C2×C4—371no—
197C2×C4—371no—
198C2×C4—741no—
199C2×C4—741no—
200C2×C4—742no—
201C2×C4—742no—
202C2×C4—741no—
203C2×C4—741no—
204C2×C4—742no—
205C2×C4—741no—
206C2×C4—741no—
207C2×C4—742no—
208C2×C4—1481no—
209C8—744no—
210C8—1482no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—44no—
219C22#1192459712yescomplemented
220C22C2×C22⋊#386611yescharacteristic
221C22D4×#386612yes—
222C4—41no—
223C4—41no—
224C4—371no—
225C4—372no—
226C4—371no—
227C4—741no—
228C4—741no—
229C4—1481no—
230C4—1481no—
231C2—22no—
232C2—22no—
233C2—41no—
234C2#1455848111yescharacteristic
235C2C2×#1192459711yescharacteristic
236C2#1455852011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC24×C37C2×C4
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1901
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11924597C2semidirect
4. #14558413C2semidirect
100. C22×C37#101semidirect
124. C37#1901semidirect
219. C22#11924597semidirect

Maximal subgroups

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

subgroupindex
C22×#105969572
C2×#119245972
#145585032
#145584132
C2×#119245132
#190137