Finite Group Databasebeta

← #20246719

Subgroups — #20246719

Order 6016.

864 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 185 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×#13094005C212yesmaximal, complemented
2C22×Dic47⋊C4C211yesmaximal, characteristic, complemented
3#15689042C212yesmaximal, complemented
4#15689037C212yesmaximal, complemented
5#15689003C212yesmaximal, complemented
6#15688996C214yesmaximal, complemented
7#15688986C211yesmaximal, characteristic, complemented
8C22×#41×C47C211yesmaximal, characteristic
9C23×Dic47C2211yescharacteristic
10C23×Dic47C2211yescharacteristic
11#13094005—28no—
12C2×Dic47⋊C4—24no—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2214yes—
15C2×Dic47⋊C4C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2214yes—
18C2×C22⋊Dic47C2214yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2214yes—
22C2×#41×C47—28no—
23C2×#41×C47—24no—
24C22×Q8×C47C2211yescharacteristic
25C22×D4×C47C2211yescharacteristic
26C22×D4×C47C2212yes—
27C23×C4×C47C2212yes—
28C23×C4×C47C2211yescharacteristic
29C24×C47C2312yes—
30C24×C47C2311yescharacteristic
31#41×C47—232no—
32C2×Q8×C47—24no—
33C2×Q8×C47—22no—
34C2×D4×C47—24no—
35C2×D4×C47—24no—
36C2×D4×C47—24no—
37C2×D4×C47—22no—
38C2×D4×C47D418yes—
39C22×C4×C47—24no—
40C22×C4×C47—24no—
41C22×C4×C47—24no—
42C22×C4×C47—24no—
43C22×C4×C47D414yes—
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2312yes—
46C22×C4×C47C2311yescharacteristic
47C22×Dic47—22no—
48C22×Dic47—24no—
49C22×Dic47—22no—
50C22×Dic47—24no—
51C22×Dic47C2314yes—
52C22×Dic47C2312yes—
53C22×Dic47C2312yes—
54C22⋊Dic47—24no—
55C22⋊Dic47—28no—
56C22⋊Dic47—28no—
57Dic47⋊C4—24no—
58Dic47⋊C4—24no—
59Dic47⋊C4—28no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—22no—
63C23×C47—22no—
64C23×C47—24no—
65C23×C47—24no—
66C23×C47C2×D414yes—
67C23×C47C2×D414yes—
68C23×C47C2×D412yes—
69C23×C47C2411yescharacteristic
70Q8×C47—28no—
71D4×C47—28no—
72D4×C47—216no—
73C2×C4×C47—216no—
74C2×C4×C47—28no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2×D414yes—
81C2×C4×C47C2×D412yes—
82C2×Dic47—28no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—24no—
87C2×Dic47—24no—
88C2×Dic47—24no—
89C2×Dic47—24no—
90C2×Dic47—44no—
91C2×Dic47#4114yescomplemented
92C22×C47—22no—
93C22×C47—22no—
94C22×C47—28no—
95C22×C47—24no—
96C22×C47—28no—
97C22×C47—42no—
98C22×C47—42no—
99C22×C47—44no—
100C22×C47#12014yes—
101C22×C47C22×D411yescharacteristic
102C22×C47C22×D412yes—
103C22×C47C2×#4112yes—
104C22×C472−1+412yes—
105C4×C47—22no—
106C4×C47—24no—
107C4×C47—22no—
108Dic47—24no—
109Dic47—42no—
110Dic47—44no—
111#2406—471nomaximal, Sylow
112C2×C47—24no—
113C2×C47—44no—
114C2×C47C2×#12011yescharacteristic
115C2×C47#52511yescharacteristic
116C2×C47#53611yescharacteristic
117C2×C47#54714yes—
118C22×#41D4711yescharacteristic
119C2×#123—472no—
120C22×C4⋊C4—471no—
121#395—472no—
122#394—472no—
123#386—472no—
124#385—474no—
125#381—471no—
126C47#240611yescharacteristic, complemented, Sylow
127C2×#41—28no—
128C2×#41—24no—
129C22×Q8C2×D4711yescharacteristic
130C22×D4C2×D4711yescharacteristic
131C22×D4C2×D4712yes—
132C23×C4—471no—
133C23×C4—471no—
134C23×C4C2×D4712yes—
135C23×C4C2×D4711yescharacteristic
136#123—948no—
137C2×C4⋊C4—472no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—474no—
140C2×C4⋊C4—944no—
141C2×C22⋊C4—472no—
142C2×C22⋊C4—474no—
143C2×C22⋊C4—474no—
144#95—472no—
145#95—472no—
146#95—474no—
147C24C22×D4712yes—
148C24C22×D4711yescharacteristic
149#41—232no—
150C2×Q8—24no—
151C2×Q8—22no—
152C2×D4—24no—
153C2×D4—24no—
154C2×D4—24no—
155C2×D4—22no—
156C2×D4C22⋊D4718yes—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—24no—
161C22×C4—472no—
162C22×C4—474no—
163C22×C4—472no—
164C22×C4—944no—
165C22×C4—942no—
166C22×C4—942no—
167C22×C4—944no—
168C22×C4C22⋊D4714yes—
169C22×C4C22×D4711yescharacteristic
170C22×C4C22×D4712yes—
171C22×C4C22×D4711yescharacteristic
172C4⋊C4—944no—
173C4⋊C4—944no—
174C4⋊C4—948no—
175C22⋊C4—948no—
176C22⋊C4—944no—
177C22⋊C4—948no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—24no—
183C23—24no—
184C23C2×C22⋊D4714yes—
185C23C2×C22⋊D4714yes—
186C23C2×C22⋊D4712yes—
187C23C23×D4711yescharacteristic
188Q8—28no—
189D4—28no—
190D4—216no—
191C2×C4—216no—
192C2×C4—28no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—474no—
198C2×C4—948no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—944no—
202C2×C4—944no—
203C2×C4—942no—
204C2×C4—944no—
205C2×C4—944no—
206C2×C4—1884no—
207C2×C4C2×C22⋊D4712yes—
208C2×C4C2×C22⋊D4714yes—
209C2×C4C2×C22⋊D4712yes—
210C22—28no—
211C22—22no—
212C22—22no—
213C22—28no—
214C22—24no—
215C22—44no—
216C22—42no—
217C22—42no—
218C22#1309399314yes—
219C22C22×C22⋊D4712yes—
220C22C22×C22⋊D4711yescharacteristic
221C22#41×D4712yes—
222C22#1309407112yes—
223C4—22no—
224C4—24no—
225C4—22no—
226C4—944no—
227C4—1884no—
228C4—1882no—
229C2—24no—
230C2—44no—
231C2C2×#1309399311yescharacteristic
232C2#1568963011yescharacteristic
233C2#1568969411yescharacteristic
234C2#1568977214yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×#41×C47C2
hypercenterC22×#41D47
hypocenterC47#2406
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13094005C2semidirect
2. C22×Dic47⋊C4C2semidirect
3. #15689042C2semidirect
4. #15689037C2semidirect
5. #15689003C2semidirect
6. #15688996C2semidirect
7. #15688986C2semidirect
91. C2×Dic47#41semidirect
126. C47#2406semidirect