Finite Group Databasebeta

← #20243386

Subgroups — #20243386

Order 6016.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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×D4×Dic47C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic
4#15688992C211yesmaximal, characteristic, complemented
5#15688886C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic
8C23×Dic47—21no—
9C22×C47⋊C8C2211yescharacteristic
10D4×Dic47—22no—
11D4×Dic47C414yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×Dic47⋊C4—21no—
16C2×C22⋊Dic47—21no—
17C2×C4×Dic47C2211yescharacteristic
18Dic47⋊C8—22no—
19#13093945—22no—
20C22×D4×C47C2211yescharacteristic
21C22×C8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23#102×C47—22no—
24C24×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47C2×C412yes—
29C2×D4×C47D412yes—
30C2×D4×C47Q812yes—
31C22×C4×C47—21no—
32C22×C4×C47C2311yescharacteristic
33C22×Dic47—21no—
34C22×Dic47—24no—
35C22×Dic47—21no—
36C22×Dic47—42no—
37C22×Dic47—42no—
38C22×Dic47D411yescharacteristic
39C22×Dic47D411yescharacteristic
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C2×C8×C47—21no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47—21no—
45C22⋊Dic47—24no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47C2×C412yes—
50Dic47⋊C4—42no—
51Dic47⋊C4—42no—
52C4×Dic47C2×C412yes—
53C4×Dic47D412yes—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C23×C47—22no—
58C23×C47—22no—
59C23×C47—22no—
60C23×C47—41no—
61C23×C47—41no—
62C23×C47—41no—
63C23×C47—41no—
64C23×C47C2×D411yescharacteristic
65D4×C47—22no—
66D4×C47—22no—
67D4×C47—22no—
68D4×C47C4⋊C414yescomplemented
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47C22×C411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×Q811yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47—48no—
84C2×Dic47—41no—
85C2×Dic47—41no—
86C2×Dic47—41no—
87C2×Dic47C22⋊C412yes—
88C2×Dic47C22⋊C412yes—
89C2×Dic47D812yes—
90C2×Dic47SD1612yes—
91C8×C47—41no—
92C47⋊C8—41no—
93C22×C47—24no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47—42no—
97C22×C47—42no—
98C22×C47—42no—
99C22×C47—42no—
100C22×C47C2×C22⋊C411yescharacteristic
101C22×C47#12111yescharacteristic
102C22×C47C22⋊Q811yescharacteristic
103C22×C47C2×D811yescharacteristic
104C22×C47C2×SD1611yescharacteristic
105C22×C47AGL(1,ℤ/8)11yescharacteristic
106C22×C47#13711yescharacteristic
107C4×C47—81no—
108C4×C47C2×C4⋊C411yescharacteristic
109C4×C47#11711yescharacteristic
110C4×C47#12111yescharacteristic
111C4×C47C22⋊Q811yescharacteristic
112Dic47—22no—
113Dic47—42no—
114Dic47—81no—
115Dic47#10214yescomplemented
116#1802—471nomaximal, Sylow
117C2×C47—44no—
118C2×C47#38011yescharacteristic
119C2×C47C2×#10211yescharacteristic
120C2×C47#41711yescharacteristic
121C2×C47#45911yescharacteristic
122C2×C47#46111yescharacteristic
123C2×C47#47411yescharacteristic
124C2×C47#47611yescharacteristic
125C2×C4×D4—471no—
126C2×C4⋊C8—471no—
127C2×#102—471no—
128C2×#102D4711yescharacteristic
129#384—471no—
130#340—471no—
131#340—471no—
132C47#180211yescharacteristic, complemented, Sylow
133C22×D4C2×D4711yescharacteristic
134C23×C4—941no—
135C22×C8—471no—
136C22×C8C2×D4711yescharacteristic
137C4×D4—474no—
138C4×D4—942no—
139C2×C4⋊C4—471no—
140C2×C4⋊C4—471no—
141C2×C4⋊C4—941no—
142C2×C4⋊C4—941no—
143C2×C4⋊C4C2×D4711yescharacteristic
144C2×C22⋊C4—941no—
145C2×C42—471no—
146C4⋊C8—942no—
147#102—22no—
148#102—942no—
149C24—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4Dic9412yes—
154C2×D4C4×D4712yes—
155C2×D4C22⋊D4712yes—
156C22×C4—21no—
157C22×C4—471no—
158C22×C4—471no—
159C22×C4—944no—
160C22×C4—941no—
161C22×C4—941no—
162C22×C4—1882no—
163C22×C4—1882no—
164C22×C4C22×D4711yescharacteristic
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—941no—
169C2×C8—941no—
170C2×C8—941no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—472no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C4⋊C4—941no—
177C4⋊C4—1882no—
178C4⋊C4—1882no—
179C22⋊C4—944no—
180C42—472no—
181C42—472no—
182C23—22no—
183C23—22no—
184C23—22no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23D4×D4711yescharacteristic
190D4—22no—
191D4—22no—
192D4—22no—
193D4Dic47⋊C414yescomplemented
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—472no—
198C2×C4—472no—
199C2×C4—472no—
200C2×C4—472no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—942no—
204C2×C4—1888no—
205C2×C4—1881no—
206C2×C4—1881no—
207C2×C4—1881no—
208C2×C4—1881no—
209C2×C4—1881no—
210C2×C4C2×Dic9411yescharacteristic
211C2×C4C2×C4×D4711yescharacteristic
212C2×C4D4×D4711yescharacteristic
213C2×C4#1062535211yescharacteristic
214C2×C4#1062535211yescharacteristic
215C2×C4C2×C22⋊D4711yescharacteristic
216C8—41no—
217C8—1881no—
218C22—24no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22C22⋊C4×D4711yescharacteristic
226C22#1309399611yescharacteristic
227C22#1309400111yescharacteristic
228C22D8×D4711yescharacteristic
229C22SD16×D4711yescharacteristic
230C22#1309404811yescharacteristic
231C22#1309405311yescharacteristic
232C4—81no—
233C4—474no—
234C4—942no—
235C4—3761no—
236C4—1882no—
237C4C2×Dic47⋊C411yescharacteristic
238C4#1309398011yescharacteristic
239C4#1309399611yescharacteristic
240C4#1309400111yescharacteristic
241C2—44no—
242C2#1568898111yescharacteristic
243C2#102×D4711yescharacteristic
244C2#1568912111yescharacteristic
245C2#1568931611yescharacteristic
246C2#1568932611yescharacteristic
247C2#1568940111yescharacteristic
248C2#1568941111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#1802
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×Dic47⋊C8C2semidirect
4. #15688992C2semidirect
5. #15688886C2semidirect
6. #15688885C2semidirect
11. D4×Dic47C4semidirect
68. D4×C47C4⋊C4semidirect
115. Dic47#102semidirect
132. C47#1802semidirect
193. D4Dic47⋊C4semidirect