Finite Group Databasebeta

← #18010283

Subgroups — #18010283

Order 4736.

448 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 138 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×D37⋊M16C211yesmaximal, characteristic
2C2×#11924615C211yesmaximal, characteristic
3#14558406C214yesmaximal, complemented
4C2×C4⋊C4×D37C211yesmaximal, characteristic
5C2×#10596953—21no—
6D37⋊M16—22no—
7D37⋊M16C414yescomplemented
8C2×#10596957—21no—
9C2×D37⋊C8C2212yes—
10#11924615—22no—
11#11924615C414yescomplemented
12C2×C4⋊#3866C2212yes—
13C2×C22⋊#3866—21no—
14C2×C4×#3866—21no—
15C22×C4×D37—21no—
16C22×C4×D37C2211yescharacteristic
17C2×C4⋊Dic37C411yescharacteristic, complemented
18C2×#10596936—21no—
19C4⋊C4×D37—21no—
20C4⋊C4×D37—21no—
21C4⋊C4×D37C412yescomplemented
22C4⋊C4×D37C2212yes—
23C2×C4⋊C4×C37C411yescharacteristic, complemented
24C23×D37D411yescharacteristic
25C22×#3866—22no—
26C22×C4×C37—21no—
27C22×C4×C37C2×C411yescharacteristic
28C22×Dic37—21no—
29C22×Dic37D411yescharacteristic
30C2×C4×D37—22no—
31C2×C4×D37—22no—
32C2×C4×D37—44no—
33C2×C4×D37C2×C411yescharacteristic
34C2×C4×D37C2×C412yes—
35C2×C4×D37C2×C412yes—
36C2×C4×D37D411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C4×D37D412yes—
39C2×C4×D37Q812yes—
40C2×C4×D37C2311yescharacteristic
41C22⋊#3866—24no—
42#10596957—24no—
43C2×#64438—22no—
44C4⋊#3866—22no—
45C4⋊#3866C2×C414yescomplemented
46C4×#3866—24no—
47#10596953—24no—
48D37⋊C8—22no—
49D37⋊C8C2×C414yescomplemented
50C4⋊C4×C37—21no—
51C4⋊C4×C37C2×C412yes—
52C4⋊Dic37—21no—
53C4⋊Dic37C2×C412yes—
54#10596936—22no—
55#10596936—22no—
56C23×C37C22⋊C411yescharacteristic
57C22×D37—22no—
58C22×D37—22no—
59C22×D37C22⋊C411yescharacteristic
60C22×D37C22⋊C412yes—
61C22×D37C4⋊C412yes—
62C22×D37C2×D411yescharacteristic
63C2×#3866—24no—
64C2×#3866—42no—
65C2×#3866—42no—
66C2×C4×C37—22no—
67C2×C4×C37—42no—
68C2×C4×C37C4212yes—
69C2×C4×C37C22⋊C411yescharacteristic
70C2×C4×C37C4⋊C412yes—
71C2×C4×C37C22×C411yescharacteristic
72C2×Dic37—22no—
73C2×Dic37—42no—
74C2×Dic37C22⋊C411yescharacteristic
75C2×Dic37C22⋊C412yes—
76C2×Dic37C4⋊C412yes—
77C2×Dic37C2×D411yescharacteristic
78C4×D37—44no—
79C4×D37—44no—
80C4×D37C4212yes—
81C4×D37C22⋊C412yes—
82C4×D37C22⋊C412yes—
83C4×D37C4⋊C412yes—
84C4×D37C4⋊C412yes—
85C4×D37C4⋊C412yes—
86C4×D37C22×C411yescharacteristic
87C4×D37C22×C411yescharacteristic
88C4×D37C2×D411yescharacteristic
89C4×D37C2×Q811yescharacteristic
90#64438—24no—
91C22×C37—21no—
92C22×C37—21no—
93C22×C37#9512yes—
94C22×C37C2×C22⋊C411yescharacteristic
95C2×D37—21no—
96C2×D37—21no—
97C2×D37—24no—
98C2×D37—24no—
99C2×D37#9512yes—
100C2×D37C2×C22⋊C411yescharacteristic
101C2×D37C2×C4⋊C411yescharacteristic
102C2×D37AGL(1,ℤ/8)12yes—
103C2×D37#13712yes—
104#3866—44no—
105C4×C37—42no—
106C4×C37#9512yes—
107C4×C37C2×C4211yescharacteristic
108C4×C37C2×C4⋊C411yescharacteristic
109Dic37—42no—
110Dic37#9512yes—
111Dic37C2×C22⋊C411yescharacteristic
112Dic37C2×C4⋊C411yescharacteristic
113#1736—371nomaximal, Sylow
114C2×C37—22no—
115C2×C37C2×#9511yescharacteristic
116C2×C37#41811yescharacteristic
117C2×C37#41911yescharacteristic
118D37—22no—
119D37#41712yes—
120D37#42812yes—
121C22×M16—371no—
122C2×#117—371no—
123C22×C4⋊C4—371no—
124#340—374no—
125C37#173611yescharacteristic, complemented, Sylow
126C23×C4—371no—
127C23×C4—741no—
128C2×M16—374no—
129C2×M16—741no—
130C2×M16—742no—
131C2×M16—741no—
132C22×C8—372no—
133#117—374no—
134#117—742no—
135C2×C4⋊C4—372no—
136C2×C4⋊C4—371no—
137C2×C4⋊C4—372no—
138C2×C4⋊C4—372no—
139C2×C4⋊C4—741no—
140C2×C4⋊C4—741no—
141C2×C4⋊C4—741no—
142C2×C4⋊C4#386611yescharacteristic, complemented
143C2×C22⋊C4—741no—
144C2×C42—741no—
145C24—371no—
146C22×C4—21no—
147C22×C4—371no—
148C22×C4—372no—
149C22×C4—372no—
150C22×C4—372no—
151C22×C4—372no—
152C22×C4—371no—
153C22×C4—371no—
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—742no—
157C22×C4—742no—
158C22×C4—742no—
159C22×C4—741no—
160C22×C4—1484no—
161C22×C4C2×#386611yescharacteristic
162M16—744no—
163M16—744no—
164C2×C8—374no—
165C2×C8—742no—
166C2×C8—742no—
167C4⋊C4—21no—
168C4⋊C4—374no—
169C4⋊C4—372no—
170C4⋊C4—742no—
171C4⋊C4—742no—
172C4⋊C4—742no—
173C4⋊C4—741no—
174C4⋊C4C2×#386612yes—
175C22⋊C4—744no—
176C42—744no—
177C23—371no—
178C23—372no—
179C23—372no—
180C23—371no—
181C23—742no—
182C23—742no—
183C23C22⋊#386611yescharacteristic
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—372no—
187C2×C4—372no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—372no—
191C2×C4—372no—
192C2×C4—372no—
193C2×C4—372no—
194C2×C4—371no—
195C2×C4—371no—
196C2×C4—372no—
197C2×C4—371no—
198C2×C4—372no—
199C2×C4—371no—
200C2×C4—744no—
201C2×C4—742no—
202C2×C4—1484no—
203C2×C4—1484no—
204C2×C4—1482no—
205C2×C4—1482no—
206C2×C4—1482no—
207C2×C4C4×#386612yes—
208C2×C4C4⋊#386612yes—
209C2×C4C22⋊#386611yescharacteristic
210C2×C4C22×#386611yescharacteristic
211C8—744no—
212C22—21no—
213C22—21no—
214C22—371no—
215C22—371no—
216C22—372no—
217C22—372no—
218C22—372no—
219C22—744no—
220C22—744no—
221C22—741no—
222C22—741no—
223C22(C2×#3866)⋊C412yes—
224C22C2×C22⋊#386611yescharacteristic
225C4—42no—
226C4—371no—
227C4—372no—
228C4—371no—
229C4—1484no—
230C4—1482no—
231C4(C2×#3866)⋊C412yes—
232C4C2×C4×#386611yescharacteristic
233C4C2×C4⋊#386611yescharacteristic
234C2—22no—
235C2—372no—
236C2—372no—
237C2—742no—
238C2C2×(C2×#3866)⋊C411yescharacteristic
239C2#1455852511yescharacteristic
240C2#1455852611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC4×C37C2×C42
FrattiniC2×C4C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1736
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14558406C2semidirect
7. D37⋊M16C4semidirect
11. #11924615C4semidirect
17. C2×C4⋊Dic37C4semidirect
21. C4⋊C4×D37C4semidirect
23. C2×C4⋊C4×C37C4semidirect
45. C4⋊#3866C2×C4semidirect
49. D37⋊C8C2×C4semidirect
125. C37#1736semidirect
142. C2×C4⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
C2×D37⋊M162
C2×#119246152
#145584062
C2×C4⋊C4×D372
#173637