Finite Group Databasebeta

← D37⋊(D4⋊C8) #18009882

Subgroups — D37⋊(D4⋊C8) #18009882

Order 4736.

344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 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⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×D37⋊C8C211yesmaximal, characteristic, complemented
3#14558381C212yesmaximal, complemented
4D4⋊#64438C212yesmaximal, complemented
5C4×D4×D37C211yesmaximal, characteristic
6C2×D37⋊C8—21no—
7C2×D37⋊C8—21no—
8#11924603—21no—
9C4⋊#64438C2212yescomplemented
10C4×#64438—21no—
11C4×#64438C2212yescomplemented
12C2×D4×D37C411yescharacteristic
13C22×C4×D37—21no—
14C4×D148C411yescharacteristic
15D4×Dic37C2211yescharacteristic
16#11924498C2211yescharacteristic
17C4×C22⋊D37—21no—
18#11924496—21no—
19C4⋊C4×D37C411yescharacteristic
20C22⋊C4×D37—21no—
21C42×D37C2211yescharacteristic
22C4×D4×C37C411yescharacteristic
23C23×D37—21no—
24C2×D4×C37C2×C411yescharacteristic
25C22×C4×C37—21no—
26C2×C22⋊D37—21no—
27C22×Dic37—21no—
28D4×D37—22no—
29D4×D37C814yescomplemented
30C2×D148C2×C411yescharacteristic
31C2×C4×D37—21no—
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—42no—
35C2×C4×D37—42no—
36C2×C4×D37C2×C411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C4×D37D411yescharacteristic
39C2×#64438—22no—
40C2×#64438—22no—
41D37⋊C8—24no—
42D37⋊C8—42no—
43C4⋊C4×C37C2×C411yescharacteristic
44C22⋊C4×C37—21no—
45C42×C37C2×C411yescharacteristic
46C22⋊Dic37—21no—
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37C2×C411yescharacteristic
50#10596936—21no—
51C4×Dic37D411yescharacteristic
52C4×Dic37D411yescharacteristic
53C4×Dic37C2311yescharacteristic
54C23×C37—21no—
55C22×D37—21no—
56C22×D37—24no—
57C22×D37—42no—
58C22×D37—42no—
59C22×D37C22⋊C411yescharacteristic
60D4×C37—21no—
61D4×C37C2×C812yescomplemented
62C2×C4×C37—21no—
63C2×C4×C37—42no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22×C411yescharacteristic
67C22⋊D37—24no—
68C2×Dic37—21no—
69C2×Dic37—41no—
70C2×Dic37—41no—
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C2×D411yescharacteristic
73C2×Dic37C2×D411yescharacteristic
74D148—21no—
75D148C2×C812yescomplemented
76C4×D37—22no—
77C4×D37—42no—
78C4×D37—42no—
79C4×D37—41no—
80C4×D37—41no—
81C4×D37C2×C812yes—
82C4×D37M1612yes—
83C4×D37D812yes—
84C4×D37SD1612yes—
85#64438—24no—
86#64438—42no—
87C22×C37—22no—
88C22×C37—41no—
89C22×C37—41no—
90C22×C37C2×C22⋊C411yescharacteristic
91C2×D37—22no—
92C2×D37—41no—
93C2×D37—41no—
94C2×D37—48no—
95C2×D37C22⋊C812yes—
96C2×D37#10212yes—
97C2×D37#10412yes—
98C4×C37—21no—
99C4×C37—41no—
100C4×C37#10212yes—
101C4×C37C22×C811yescharacteristic
102C4×C37C2×M1611yescharacteristic
103Dic37—21no—
104Dic37—41no—
105Dic37C22⋊C812yes—
106Dic37C2×D811yescharacteristic
107Dic37C2×SD1611yescharacteristic
108C2×D4⋊C8—371nomaximal, Sylow
109C2×C37—42no—
110C2×C37C2×C22⋊C811yescharacteristic
111C2×C37C2×#10211yescharacteristic
112C2×C37C2×#10411yescharacteristic
113D37—42no—
114D37D4⋊C814yescomplemented
115C2×C4×D4—371no—
116C2×C4⋊C8—371no—
117C2×C4×C8—371no—
118D4⋊C8—372no—
119D4⋊C8—372no—
120C37C2×D4⋊C811yescharacteristic, complemented, Sylow
121C22×D4—371no—
122C23×C4—741no—
123C22×C8—741no—
124C22×C8—741no—
125C4×D4—371no—
126C4×D4—371no—
127C4×D4—371no—
128C4×D4—741no—
129C4×D4—741no—
130C4×D4#386611yescharacteristic
131C2×C4⋊C4—371no—
132C2×C22⋊C4—741no—
133C2×C42—371no—
134C4⋊C8—372no—
135C4⋊C8—741no—
136C4×C8—372no—
137C4×C8—741no—
138C24—741no—
139C2×D4—374no—
140C2×D4—371no—
141C2×D4—742no—
142C2×D4—741no—
143C2×D4C2×#386611yescharacteristic
144C22×C4—21no—
145C22×C4—371no—
146C22×C4—371no—
147C22×C4—371no—
148C22×C4—741no—
149C22×C4—741no—
150C22×C4—741no—
151C22×C4—741no—
152C22×C4—1482no—
153C22×C4—1482no—
154C2×C8—742no—
155C2×C8—744no—
156C2×C8—742no—
157C2×C8—1482no—
158C4⋊C4—371no—
159C4⋊C4—741no—
160C4⋊C4C2×#386611yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—741no—
163C22⋊C4—741no—
164C22⋊C4—741no—
165C42—371no—
166C42—371no—
167C42—371no—
168C42C2×#386611yescharacteristic
169C23—21no—
170C23—371no—
171C23—744no—
172C23—741no—
173C23—1482no—
174C23—1482no—
175D4—21no—
176D4—372no—
177D4—744no—
178D4—741no—
179D4D37⋊C812yescomplemented
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—371no—
183C2×C4—371no—
184C2×C4—372no—
185C2×C4—372no—
186C2×C4—372no—
187C2×C4—372no—
188C2×C4—371no—
189C2×C4—742no—
190C2×C4—741no—
191C2×C4—1481no—
192C2×C4—1481no—
193C2×C4—1482no—
194C2×C4—1481no—
195C2×C4—1481no—
196C2×C4—1482no—
197C2×C4C22⋊#386611yescharacteristic
198C2×C4C22⋊#386611yescharacteristic
199C2×C4C22×#386611yescharacteristic
200C8—744no—
201C8—1482no—
202C22—22no—
203C22—41no—
204C22—41no—
205C22—372no—
206C22—372no—
207C22—372no—
208C22—742no—
209C22—1488no—
210C22—1481no—
211C22—1481no—
212C22C2×C22⋊#386611yescharacteristic
213C4—21no—
214C4—41no—
215C4—372no—
216C4—371no—
217C4—371no—
218C4—741no—
219C4—1481no—
220C4#1192459812yes—
221C4C2×D37⋊C811yescharacteristic
222C4D37⋊M1611yescharacteristic
223C2—42no—
224C2—374no—
225C2—1482no—
226C2D37⋊(C22⋊C8)11yescharacteristic
227C2C2×#1192459811yescharacteristic
228C2D37⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#3866
commutatorC4×C37C22×C8
FrattiniC2×C4C22×#3866
FittingC4×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×D4×D37C4
cosocleC4×Dic37C23
hypercenterC4×D4#3866
hypocenterC37C2×D4⋊C8
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D37⋊(C4⋊C8)C2semidirect
2. C4×D37⋊C8C2semidirect
3. #14558381C2semidirect
4. D4⋊#64438C2semidirect
9. C4⋊#64438C22semidirect
11. C4×#64438C22semidirect
29. D4×D37C8semidirect
61. D4×C37C2×C8semidirect
75. D148C2×C8semidirect
114. D37D4⋊C8semidirect
120. C37C2×D4⋊C8semidirect
179. D4D37⋊C8semidirect

Maximal subgroups

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

subgroupindex
D37⋊(C4⋊C8)2
C4×D37⋊C82
#145583812
D4⋊#644382
C4×D4×D372
C2×D4⋊C837