Finite Group Databasebeta

← D37⋊#323 #18009822

Subgroups — D37⋊#323 #18009822

Order 4736.

456 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D37⋊(C22⋊C8)C212yesmaximal, complemented
2#14558377C212yesmaximal, complemented
3#14558376C212yesmaximal, complemented
4C2×C22⋊C4×D37C211yesmaximal, characteristic
5C2×D37⋊C8—22no—
6#11924593—22no—
7C22⋊#64438C2214yescomplemented
8C24×D37C411yescharacteristic
9C22×C4×D37C411yescharacteristic
10C22×C4×D37C2211yescharacteristic
11C2×C22⋊Dic37C2211yescharacteristic
12C2×#10596938C411yescharacteristic
13C2×#10596938C2211yescharacteristic
14C22⋊C4×D37—22no—
15C22⋊C4×D37—22no—
16C2×C22⋊C4×C37C411yescharacteristic
17C24×C37C2×C411yescharacteristic
18C23×D37—21no—
19C23×D37—21no—
20C23×D37—22no—
21C23×D37—42no—
22C23×D37—42no—
23C23×D37C814yescomplemented
24C23×D37C2×C411yescharacteristic
25C23×D37C2×C411yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C22×C4×C37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C22×Dic37C2311yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37—21no—
32C2×C4×D37—42no—
33C2×C4×D37—42no—
34C2×C4×D37D412yes—
35C2×C4×D37D412yes—
36C2×#64438—24no—
37D37⋊C8—44no—
38C22⋊C4×C37—22no—
39C22⋊Dic37—22no—
40#10596938—22no—
41#10596938—22no—
42C23×C37—21no—
43C23×C37—21no—
44C23×C37—41no—
45C23×C37—41no—
46C23×C37C2×C812yescomplemented
47C23×C37C22×C411yescharacteristic
48C22×D37—22no—
49C22×D37—22no—
50C22×D37—21no—
51C22×D37—21no—
52C22×D37—24no—
53C22×D37—24no—
54C22×D37—42no—
55C22×D37—42no—
56C22×D37—48no—
57C22×D37—48no—
58C22×D37—42no—
59C22×D37—42no—
60C22×D37—41no—
61C22×D37—41no—
62C22×D37C22⋊C411yescharacteristic
63C22×D37C22⋊C411yescharacteristic
64C22×D37C2×C812yes—
65C22×D37C2×C812yescomplemented
66C22×D37M1612yes—
67C2×C4×C37—21no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37C22⋊C412yes—
71C2×Dic37—21no—
72C2×Dic37—41no—
73C2×Dic37—41no—
74C2×Dic37C2×D412yes—
75C4×D37—24no—
76C4×D37—42no—
77C4×D37—42no—
78C4×D37—42no—
79#64438—44no—
80C22×C37—21no—
81C22×C37—21no—
82C22×C37—22no—
83C22×C37—42no—
84C22×C37—42no—
85C22×C37—41no—
86C22×C37—41no—
87C22×C37C2×C22⋊C411yescharacteristic
88C22×C37C22×C811yescharacteristic
89C22×C37C2×M1611yescharacteristic
90C2×D37—21no—
91C2×D37—21no—
92C2×D37—24no—
93C2×D37—24no—
94C2×D37—22no—
95C2×D37—48no—
96C2×D37—42no—
97C2×D37—41no—
98C2×D37—41no—
99C2×D37—48no—
100C2×D37—42no—
101C2×D37C22⋊C812yes—
102C2×D37C22⋊C812yes—
103C2×D37#9912yes—
104C2×D37#10012yes—
105C4×C37—22no—
106C4×C37—41no—
107Dic37—22no—
108Dic37—41no—
109C2×#323—371nomaximal, Sylow
110C2×C37—21no—
111C2×C37—21no—
112C2×C37—42no—
113C2×C37C2×C22⋊C811yescharacteristic
114C2×C37C2×#9911yescharacteristic
115C2×C37C2×#10011yescharacteristic
116D37—22no—
117D37—42no—
118D37#32314yescomplemented
119C22×C22⋊C4—371no—
120C2×C22⋊C8—372no—
121#323—372no—
122#323—372no—
123C37C2×#32311yescharacteristic, complemented, Sylow
124C25—371no—
125C23×C4—371no—
126C23×C4—371no—
127C22×C8—742no—
128C2×C22⋊C4—371no—
129C2×C22⋊C4—371no—
130C2×C22⋊C4—371no—
131C2×C22⋊C4—742no—
132C2×C22⋊C4—742no—
133C2×C22⋊C4#386611yescharacteristic
134C22⋊C8—374no—
135C22⋊C8—742no—
136C24—371no—
137C24—374no—
138C24—371no—
139C24—741no—
140C24—741no—
141C24—742no—
142C24—1482no—
143C24—1482no—
144C24C2×#386611yescharacteristic
145C22×C4—371no—
146C22×C4—372no—
147C22×C4—372no—
148C22×C4—371no—
149C22×C4—741no—
150C22×C4—741no—
151C22×C4—1482no—
152C22×C4—1482no—
153C22×C4C2×#386611yescharacteristic
154C22×C4C2×#386611yescharacteristic
155C2×C8—744no—
156C2×C8—1484no—
157C22⋊C4—22no—
158C22⋊C4—742no—
159C22⋊C4—742no—
160C22⋊C4—742no—
161C23—21no—
162C23—21no—
163C23—41no—
164C23—41no—
165C23—371no—
166C23—371no—
167C23—372no—
168C23—372no—
169C23—372no—
170C23—742no—
171C23—742no—
172C23—744no—
173C23—744no—
174C23—741no—
175C23—741no—
176C23—1481no—
177C23—1481no—
178C23—1482no—
179C23—1482no—
180C23—1488no—
181C23—1488no—
182C23—1482no—
183C23—1482no—
184C23D37⋊C812yescomplemented
185C23C22×#386611yescharacteristic
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—372no—
190C2×C4—744no—
191C2×C4—741no—
192C2×C4—1482no—
193C2×C4—1482no—
194C2×C4—1482no—
195C2×C4—1481no—
196C2×C4—1481no—
197C2×C4C22⋊#386612yes—
198C8—1484no—
199C22—21no—
200C22—21no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—372no—
207C22—372no—
208C22—372no—
209C22—372no—
210C22—744no—
211C22—744no—
212C22—741no—
213C22—741no—
214C22—742no—
215C22—1482no—
216C22—1482no—
217C22—1488no—
218C22—1488no—
219C22—1481no—
220C22—1481no—
221C22C2×C22⋊#386611yescharacteristic
222C22C2×D37⋊C811yescharacteristic
223C22D37⋊M1611yescharacteristic
224C4—22no—
225C4—41no—
226C4—742no—
227C4—1481no—
228C2—21no—
229C2—21no—
230C2—42no—
231C2—374no—
232C2—742no—
233C2—1482no—
234C2D37⋊(C22⋊C8)11yescharacteristic
235C2D37⋊#9911yescharacteristic
236C2D37⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC22×C37C22×C8
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC24×D37C4
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37C2×#323
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. D37⋊(C22⋊C8)C2semidirect
2. #14558377C2semidirect
3. #14558376C2semidirect
7. C22⋊#64438C22semidirect
23. C23×D37C8semidirect
46. C23×C37C2×C8semidirect
65. C22×D37C2×C8semidirect
118. D37#323semidirect
123. C37C2×#323semidirect
184. C23D37⋊C8semidirect

Maximal subgroups

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

subgroupindex
D37⋊(C22⋊C8)2
#145583772
#145583762
C2×C22⋊C4×D372
C2×#32337