Finite Group Databasebeta

← #487×D47 #20253696

Subgroups — #487×D47 #20253696

Order 6016.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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⋊Q8×D47C211yesmaximal, characteristic
2C4⋊Q8×D47C211yesmaximal, characteristic
3#15689475C211yesmaximal, characteristic, complemented
4#15689474C211yesmaximal, characteristic, complemented
5#15689473C211yesmaximal, characteristic, complemented
6#15689472C214yesmaximal, complemented
7#103×D47C214yesmaximal
8C4×C8×D47C211yesmaximal, characteristic
9C47×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D47—21no—
11C2×Q8×D47C2212yes—
12C2×C8×D47C2212yes—
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094023—21no—
16#13094023—21no—
17#13094023—21no—
18#13094023C2212yes—
19#13094022—21no—
20#13094022C2212yes—
21C4⋊C4×D47—21no—
22C4⋊C4×D47—21no—
23C4⋊C4×D47—21no—
24C4⋊C4×D47C2212yes—
25C42×D47C2211yescharacteristic
26#13093949C2214yes—
27#13093948C2214yes—
28#13093947C2214yes—
29C4×C47⋊C8C2211yescharacteristic
30C8×Dic47C2212yes—
31C4⋊Q8×C47C2211yescharacteristic
32C4⋊Q8×C47C2211yescharacteristic
33#103×C47C2214yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×Q8×C47C2312yes—
37Q8×D47—28no—
38Q8×D47—44no—
39C2×C4×D47—22no—
40C2×C4×D47—22no—
41C2×C4×D47D411yescharacteristic
42C2×C4×D47D411yescharacteristic
43C2×C4×D47C2311yescharacteristic
44C2×Dic94—21no—
45C2×Dic94—22no—
46C2×Dic94—22no—
47C2×Dic94C2312yes—
48C2×C8×C47C2312yes—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2312yes—
53C42×C47C2311yescharacteristic
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47C2312yes—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47D411yescharacteristic
63C4×Dic47D411yescharacteristic
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8C2312yes—
66C8×D47—24no—
67C22×D47C2×D411yescharacteristic
68Q8×C47—24no—
69Q8×C47—42no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47C2×D411yescharacteristic
78C2×Dic47C2×D411yescharacteristic
79C2×Dic47C2×D411yescharacteristic
80C4×D47—44no—
81C4×D47—44no—
82C4×D47SD1614yes—
83C4×D47Q1614yes—
84C4×D47#4114yes—
85Dic94—24no—
86Dic94—42no—
87Dic94—44no—
88Dic94—44no—
89C8×C47—22no—
90C47⋊C8—22no—
91C22×C47C22×D411yescharacteristic
92C2×D47#12412yes—
93C2×D47C2×SD1612yes—
94C2×D47C2×Q1612yes—
95C4×C47—42no—
96C4×C47—42no—
97C4×C47C2×SD1612yes—
98C4×C47C2×Q1612yes—
99C4×C47C2×#4112yes—
100Dic47—42no—
101Dic47—42no—
102Dic47#12412yes—
103Dic47C2×SD1612yes—
104Dic47C2×Q1612yes—
105C2×#487—471nomaximal, Sylow
106C2×C47C2×#12411yescharacteristic
107C2×C47C22×SD1611yescharacteristic
108C2×C47C22×Q1611yescharacteristic
109D47#48714yesdirect product factor
110C2×C4⋊Q8—471no—
111C2×C4⋊Q8—471no—
112#487—471no—
113#487—471no—
114#487—474no—
115#487—471no—
116#487D4711yescharacteristic, direct product factor
117C2×#103—474no—
118C2×C4×C8—471no—
119C47C2×#48711yescharacteristic, complemented, Sylow
120C22×Q8—472no—
121C22×Q8—941no—
122C22×C8—472no—
123C4⋊Q8—472no—
124C4⋊Q8—472no—
125C4⋊Q8—471no—
126C4⋊Q8—471no—
127C4⋊Q8—941no—
128C4⋊Q8—941no—
129C4⋊Q8—941no—
130C4⋊Q8—941no—
131C4⋊Q8C2×D4711yescharacteristic
132C4⋊Q8C2×D4711yescharacteristic
133C2×C4⋊C4—472no—
134C2×C4⋊C4—941no—
135C2×C4⋊C4—941no—
136C2×C4⋊C4—941no—
137C2×C42—471no—
138#103—474no—
139#103—474no—
140#103—474no—
141#103C2×D4714yes—
142C4×C8—472no—
143C4×C8—471no—
144C4×C8C2×D4711yescharacteristic
145C2×Q8—21no—
146C2×Q8—472no—
147C2×Q8—942no—
148C2×Q8—942no—
149C2×Q8—948no—
150C2×Q8—941no—
151C2×Q8—1884no—
152C2×Q8C22×D4712yes—
153C22×C4—471no—
154C22×C4—471no—
155C22×C4—471no—
156C22×C4—942no—
157C22×C4—942no—
158C2×C8—472no—
159C2×C8—944no—
160C2×C8C22×D4712yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—472no—
165C4⋊C4—942no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—941no—
170C4⋊C4—941no—
171C4⋊C4—941no—
172C4⋊C4C22×D4712yes—
173C42—471no—
174C42—471no—
175C42—471no—
176C42C22×D4711yescharacteristic
177C23—471no—
178Q8—24no—
179Q8—42no—
180Q8—944no—
181Q8—1884no—
182Q8—1884no—
183Q8—1882no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—471no—
187C2×C4—471no—
188C2×C4—471no—
189C2×C4—474no—
190C2×C4—474no—
191C2×C4—474no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—1884no—
195C2×C4—1884no—
196C2×C4D4×D4711yescharacteristic
197C2×C4D4×D4711yescharacteristic
198C2×C4C23×D4711yescharacteristic
199C8—22no—
200C8—942no—
201C22—472no—
202C22—472no—
203C22—472no—
204C22C2×D4×D4711yescharacteristic
205C4—42no—
206C4—42no—
207C4—472no—
208C4—472no—
209C4—472no—
210C4—1882no—
211C4—1882no—
212C4SD16×D4712yes—
213C4Q16×D4712yes—
214C4#41×D4712yes—
215C2—474no—
216C2#124×D4711yescharacteristic
217C2C2×SD16×D4711yescharacteristic
218C2C2×Q16×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#487C2
socleC22×C47C22×D4
hypercenter#487D47
hypocenterC47C2×#487
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #15689475C2semidirect
4. #15689474C2semidirect
5. #15689473C2semidirect
6. #15689472C2semidirect
9. C47×#487C2semidirect
109. D47#487direct (N × H)
116. #487D47direct (N × H)
119. C47C2×#487semidirect