Finite Group Databasebeta

← D4⋊C8×D47 #20241759

Subgroups — D4⋊C8×D47 #20241759

Order 6016.

344 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C4×D4×D47C211yesmaximal, characteristic
2C4⋊C8×D47C211yesmaximal, characteristic, complemented
3C4×C8×D47C211yesmaximal, characteristic, complemented
4#15688852C211yesmaximal, characteristic, complemented
5D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×D4×D47C411yescharacteristic
9C22×C4×D47—21no—
10C2×C8×D47—21no—
11C2×C8×D47—21no—
12C4×D188C2211yescharacteristic
13D4×Dic47C411yescharacteristic
14#13093986C411yescharacteristic
15C4×C22⋊D47—21no—
16(C22⋊D47)⋊C4—21no—
17C4⋊C4×D47C411yescharacteristic
18C22⋊C4×D47—21no—
19C42×D47C2211yescharacteristic
20C4⋊(C47⋊C8)C2211yescharacteristic, complemented
21Dic47⋊C8—21no—
22C4×C47⋊C8C2211yescharacteristic, complemented
23C8×Dic47—21no—
24C4×D4×C47C2211yescharacteristic
25C4⋊C8×C47C2211yescharacteristic, complemented
26C4×C8×C47C2211yescharacteristic, complemented
27C23×D47—21no—
28C2×D4×C47C2×C411yescharacteristic
29C22×C4×C47—21no—
30C2×C22⋊D47—21no—
31C22×Dic47—21no—
32D4×D47—22no—
33D4×D47C814yescomplemented
34C2×D188C2×C411yescharacteristic
35C2×C4×D47—21no—
36C2×C4×D47—21no—
37C2×C4×D47—21no—
38C2×C4×D47—42no—
39C2×C4×D47—42no—
40C2×C4×D47C2×C411yescharacteristic
41C2×C4×D47D411yescharacteristic
42C2×C4×D47D411yescharacteristic
43C2×C8×C47—21no—
44C2×C8×C47—21no—
45C4⋊C4×C47C2×C411yescharacteristic
46C22⋊C4×C47—21no—
47C42×C47C2311yescharacteristic
48C22⋊Dic47—21no—
49(C2×D47)⋊C4—21no—
50(C2×D47)⋊C4—21no—
51C4⋊Dic47C2×C411yescharacteristic
52Dic47⋊C4—21no—
53C4×Dic47C2×C411yescharacteristic
54C4×Dic47D411yescharacteristic
55C4×Dic47D411yescharacteristic
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C8×D47—24no—
59C8×D47—42no—
60C23×C47—21no—
61C22×D47—21no—
62C22×D47—24no—
63C22×D47—42no—
64C22×D47—42no—
65C22×D47C22⋊C411yescharacteristic
66D4×C47—21no—
67D4×C47C2×C812yescomplemented
68C2×C4×C47—21no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C22⋊D47—24no—
75C2×Dic47—21no—
76C2×Dic47—42no—
77C2×Dic47C22⋊C411yescharacteristic
78C2×Dic47C22⋊C411yescharacteristic
79C2×Dic47C22⋊C411yescharacteristic
80D188—21no—
81D188C2×C812yescomplemented
82C4×D47—22no—
83C4×D47—42no—
84C4×D47—41no—
85C4×D47—41no—
86C4×D47—42no—
87C4×D47C2×C812yes—
88C4×D47M1612yes—
89C4×D47D812yes—
90C4×D47SD1612yes—
91C8×C47—22no—
92C8×C47—41no—
93C47⋊C8—22no—
94C47⋊C8—41no—
95C22×C47—22no—
96C22×C47—41no—
97C22×C47—41no—
98C22×C47C2×C22⋊C411yescharacteristic
99C2×D47—22no—
100C2×D47—41no—
101C2×D47—41no—
102C2×D47—48no—
103C2×D47C22⋊C812yes—
104C2×D47#10212yes—
105C2×D47#10412yes—
106C4×C47—21no—
107C4×C47—41no—
108C4×C47C22×C811yescharacteristic
109C4×C47C2×M1611yescharacteristic
110C4×C47C2×D811yescharacteristic
111C4×C47C2×SD1611yescharacteristic
112Dic47—21no—
113Dic47—41no—
114Dic47C22⋊C812yes—
115Dic47#10212yes—
116C2×D4⋊C8—471nomaximal, Sylow
117C2×C47—42no—
118C2×C47C2×C22⋊C811yescharacteristic
119C2×C47C2×#10211yescharacteristic
120C2×C47C2×#10411yescharacteristic
121D47—42no—
122D47D4⋊C814yesdirect product factor
123C2×C4×D4—471no—
124C2×C4⋊C8—471no—
125C2×C4×C8—471no—
126D4⋊C8—471no—
127D4⋊C8—471no—
128D4⋊C8—471no—
129D4⋊C8D4711yescharacteristic, direct product factor
130C47C2×D4⋊C811yescharacteristic, complemented, Sylow
131C22×D4—471no—
132C23×C4—941no—
133C22×C8—941no—
134C22×C8—941no—
135C4×D4—471no—
136C4×D4—471no—
137C4×D4—471no—
138C4×D4—941no—
139C4×D4—941no—
140C4×D4C2×D4711yescharacteristic
141C2×C4⋊C4—471no—
142C2×C22⋊C4—941no—
143C2×C42—471no—
144C4⋊C8—471no—
145C4⋊C8—941no—
146C4⋊C8C2×D4711yescharacteristic, complemented
147C4×C8—471no—
148C4×C8—941no—
149C4×C8C2×D4711yescharacteristic, complemented
150C24—941no—
151C2×D4—474no—
152C2×D4—471no—
153C2×D4—942no—
154C2×D4—941no—
155C2×D4C4×D4711yescharacteristic
156C22×C4—21no—
157C22×C4—471no—
158C22×C4—471no—
159C22×C4—471no—
160C22×C4—941no—
161C22×C4—941no—
162C22×C4—941no—
163C22×C4—941no—
164C22×C4—1882no—
165C22×C4—1882no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—944no—
169C2×C8—941no—
170C2×C8—941no—
171C2×C8—1882no—
172C4⋊C4—471no—
173C4⋊C4—941no—
174C4⋊C4C4×D4711yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—941no—
177C22⋊C4—941no—
178C22⋊C4—941no—
179C42—471no—
180C42—471no—
181C42—471no—
182C42C22×D4711yescharacteristic
183C23—21no—
184C23—471no—
185C23—944no—
186C23—941no—
187C23—1882no—
188C23—1882no—
189D4—21no—
190D4—472no—
191D4—944no—
192D4—941no—
193D4C8×D4712yescomplemented
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—471no—
198C2×C4—471no—
199C2×C4—472no—
200C2×C4—472no—
201C2×C4—472no—
202C2×C4—472no—
203C2×C4—471no—
204C2×C4—942no—
205C2×C4—941no—
206C2×C4—1882no—
207C2×C4—1882no—
208C2×C4—1882no—
209C2×C4—1881no—
210C2×C4—1881no—
211C2×C4C2×C4×D4711yescharacteristic
212C2×C4D4×D4711yescharacteristic
213C2×C4D4×D4711yescharacteristic
214C8—22no—
215C8—41no—
216C8—942no—
217C8—1881no—
218C22—22no—
219C22—41no—
220C22—41no—
221C22—472no—
222C22—472no—
223C22—472no—
224C22—942no—
225C22—1888no—
226C22—1881no—
227C22—1881no—
228C22C22⋊C4×D4711yescharacteristic
229C4—21no—
230C4—41no—
231C4—472no—
232C4—472no—
233C4—941no—
234C4—1881no—
235C4C2×C8×D4711yescharacteristic
236C4M16×D4711yescharacteristic
237C4D8×D4711yescharacteristic
238C4SD16×D4711yescharacteristic
239C2—42no—
240C2—474no—
241C2—1882no—
242C2C22⋊C8×D4711yescharacteristic
243C2#102×D4711yescharacteristic
244C2#104×D4711yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC4×C47C22×C8
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47C2×C22⋊C4
hypercenterD4⋊C8D47
hypocenterC47C2×D4⋊C8
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×D47C2semidirect
3. C4×C8×D47C2semidirect
4. #15688852C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×D4⋊C8C2semidirect
20. C4⋊(C47⋊C8)C22semidirect
22. C4×C47⋊C8C22semidirect
25. C4⋊C8×C47C22semidirect
26. C4×C8×C47C22semidirect
33. D4×D47C8semidirect
67. D4×C47C2×C8semidirect
81. D188C2×C8semidirect
122. D47D4⋊C8direct (N × H)
129. D4⋊C8D47direct (N × H)
130. C47C2×D4⋊C8semidirect
146. C4⋊C8C2×D47semidirect
149. C4×C8C2×D47semidirect
193. D4C8×D47semidirect