Finite Group Databasebeta

← #20243387

Subgroups — #20243387

Order 6016.

372 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13093986C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
3C2×#13093946C211yesmaximal, characteristic
4C2×#13093944C211yesmaximal, characteristic
5#15688992C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C47×#340C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C4×D47—21no—
10C22×C47⋊C8C2211yescharacteristic
11#13093986—22no—
12#13093986C414yescomplemented
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×Dic47⋊C4—21no—
16C2×(C2×D47)⋊C4—21no—
17C2×C4×Dic47C2211yescharacteristic
18Dic47⋊C8—22no—
19#13093946—22no—
20#13093944—22no—
21C22×C8×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24C23×D47—21no—
25C22×C4×C47—21no—
26C22×C4×C47—21no—
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—21no—
29C22×Dic47D411yescharacteristic
30C22×Dic47D411yescharacteristic
31C2×D188—21no—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188C2×C412yes—
35C2×D188D412yes—
36C2×D188Q812yes—
37C2×C4×D47—24no—
38C2×C4×D47—42no—
39C2×C4×D47—42no—
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C2×C8×C47—21no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47—21no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47C2×C412yes—
47(C2×D47)⋊C4—24no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50Dic47⋊C4—42no—
51Dic47⋊C4—42no—
52C4×Dic47C2×C412yes—
53C4×Dic47D412yes—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C23×C47C2×D411yescharacteristic
58C22×D47—22no—
59C22×D47—22no—
60C22×D47—22no—
61C22×D47—41no—
62C22×D47—41no—
63C22×D47—41no—
64C22×D47—41no—
65C2×C4×C47—22no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×Q811yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47C22⋊C412yes—
83C2×Dic47C22⋊C412yes—
84C2×Dic47D812yes—
85C2×Dic47SD1612yes—
86D188—22no—
87D188—22no—
88D188—22no—
89D188C4⋊C414yescomplemented
90C4×D47—48no—
91C8×C47—41no—
92C47⋊C8—41no—
93C22×C47C2×C22⋊C411yescharacteristic
94C22×C47#12111yescharacteristic
95C22×C47C22⋊Q811yescharacteristic
96C22×C47C2×D811yescharacteristic
97C22×C47C2×SD1611yescharacteristic
98C22×C47AGL(1,ℤ/8)11yescharacteristic
99C22×C47#13711yescharacteristic
100C2×D47—24no—
101C2×D47—42no—
102C2×D47—42no—
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—42no—
107C4×C47—42no—
108C4×C47—81no—
109C4×C47C2×C4⋊C411yescharacteristic
110C4×C47#11711yescharacteristic
111C4×C47#12111yescharacteristic
112C4×C47C22⋊Q811yescharacteristic
113Dic47—22no—
114Dic47—81no—
115Dic47#10214yescomplemented
116#1802—471nomaximal, Sylow
117C2×C47#38011yescharacteristic
118C2×C47C2×#10211yescharacteristic
119C2×C47#41711yescharacteristic
120C2×C47#45911yescharacteristic
121C2×C47#46111yescharacteristic
122C2×C47#47411yescharacteristic
123C2×C47#47611yescharacteristic
124D47—44no—
125C2×C4×D4—471no—
126C2×C4⋊C8—471no—
127C2×#102—471no—
128C2×#102—471no—
129#384—471no—
130#340—471no—
131#340D4711yescharacteristic, complemented
132C47#180211yescharacteristic, complemented, Sylow
133C22×D4—471no—
134C23×C4—941no—
135C22×C8—471no—
136C22×C8C2×D4711yescharacteristic
137C4×D4—474no—
138C4×D4—942no—
139C2×C4⋊C4—471no—
140C2×C4⋊C4—941no—
141C2×C4⋊C4—941no—
142C2×C4⋊C4C2×D4711yescharacteristic
143C2×C4⋊C4C2×D4711yescharacteristic
144C2×C22⋊C4—941no—
145C2×C42—471no—
146C4⋊C8—942no—
147#102—942no—
148#102—942no—
149C24—941no—
150C2×D4—472no—
151C2×D4—472no—
152C2×D4—472no—
153C2×D4—941no—
154C2×D4—941no—
155C2×D4—941no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—471no—
159C22×C4—471no—
160C22×C4—944no—
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—21no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C4⋊C4—1882no—
177C4⋊C4—1882no—
178C4⋊C4C4×D4712yes—
179C22⋊C4—944no—
180C42—472no—
181C42—472no—
182C23—942no—
183C23—942no—
184C23—942no—
185C23—1881no—
186C23—1881no—
187C23—1881no—
188C23—1881no—
189C23D4×D4711yescharacteristic
190D4—474no—
191D4—942no—
192D4—942no—
193D4—942no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—472no—
201C2×C4—472no—
202C2×C4—472no—
203C2×C4—472no—
204C2×C4—941no—
205C2×C4—941no—
206C2×C4—1888no—
207C2×C4—1881no—
208C2×C4—1881no—
209C2×C4—1881no—
210C2×C4C2×C4×D4711yescharacteristic
211C2×C4#1062535011yescharacteristic
212C2×C4#1062535011yescharacteristic
213C2×C4D4×D4711yescharacteristic
214C2×C4D4×D4711yescharacteristic
215C2×C4Q8×D4711yescharacteristic
216C8—41no—
217C8—1881no—
218C22—944no—
219C22—1882no—
220C22—1882no—
221C22—1882no—
222C22—1882no—
223C22—1882no—
224C22—1882no—
225C22C22⋊C4×D4711yescharacteristic
226C22#1309399711yescharacteristic
227C22#1309400211yescharacteristic
228C22D8×D4711yescharacteristic
229C22SD16×D4711yescharacteristic
230C22#1309405111yescharacteristic
231C22#1309405611yescharacteristic
232C4—42no—
233C4—81no—
234C4—474no—
235C4—942no—
236C4—3761no—
237C4C4⋊C4×D4711yescharacteristic
238C4#1309398111yescharacteristic
239C4#1309399711yescharacteristic
240C4#1309400211yescharacteristic
241C2—1884no—
242C2#1568898211yescharacteristic
243C2#102×D4711yescharacteristic
244C2#1568912311yescharacteristic
245C2#1568931711yescharacteristic
246C2#1568932711yescharacteristic
247C2#1568940211yescharacteristic
248C2#1568941211yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#1802
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×Dic47⋊C8C2semidirect
5. #15688992C2semidirect
6. #15688885C2semidirect
7. C47×#340C2semidirect
12. #13093986C4semidirect
89. D188C4⋊C4semidirect
115. Dic47#102semidirect
131. #340D47semidirect
132. C47#1802semidirect