Finite Group Databasebeta

← #20255685

Subgroups — #20255685

Order 6016.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#15689838C211yesmaximal, characteristic
2#15689788C211yesmaximal, characteristic, complemented
3#15689473C211yesmaximal, characteristic, complemented
4#15689463C212yesmaximal, complemented
5#15689419C211yesmaximal, characteristic, complemented
6#15689366C212yesmaximal, complemented
7#15689260C212yesmaximal, complemented
8C4×#10625335C211yesmaximal, characteristic, complemented
9#15689200C211yesmaximal, characteristic, complemented
10#15689130C212yesmaximal, complemented
11C47×#461C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2212yes—
13C2×#10625335C2211yescharacteristic
14C2×#10625324C2212yes—
15#13094024C2211yescharacteristic
16#13094023—21no—
17#13094010—22no—
18#13094002—22no—
19#13094000C2212yes—
20#13093998—21no—
21#13093995C2212yes—
22C4×Dic94C2211yescharacteristic
23C4×D188C2211yescharacteristic
24#13093986—21no—
25#13093983—21no—
26#13093982C2212yes—
27#13093958C2212yes—
28#13093955C2211yescharacteristic
29#13093949C2212yes—
30#13093948C2212yes—
31#13093948C2212yes—
32#13093947C2211yescharacteristic
33#13093945C2211yescharacteristic
34(C2×D47)⋊C8C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C2×SD16×C47C2212yes—
37C4⋊Q8×C47C2211yescharacteristic
38C4×D4×C47C2211yescharacteristic
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47C2312yes—
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C2×C22⋊D47—22no—
45Q8×D47—24no—
46Q8×D47—42no—
47C2×D188D411yescharacteristic
48C2×C4×D47—22no—
49C2×C4×D47C2312yes—
50C2×Dic94—22no—
51C2×Dic94—21no—
52C2×Dic94C2311yescharacteristic
53SD16×C47—42no—
54C2×C8×C47C2312yes—
55C4⋊C4×C47—21no—
56C4⋊C4×C47—21no—
57C4⋊C4×C47C2311yescharacteristic
58C22⋊C4×C47—21no—
59C42×C47C2311yescharacteristic
60C22⋊Dic47—22no—
61#10625335—22no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4D412yes—
65C4⋊Dic47—21no—
66C4⋊Dic47D411yescharacteristic
67C4⋊Dic47C2311yescharacteristic
68C4⋊Dic47C2312yes—
69Dic47⋊C4—21no—
70Dic47⋊C4—22no—
71C4×Dic47—21no—
72C4×Dic47—22no—
73C2×C47⋊C8C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75#10625324—42no—
76C23×C47—21no—
77C22×D47C2×D412yes—
78Q8×C47—22no—
79Q8×C47—22no—
80D4×C47—21no—
81D4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—42no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C22⋊D47—82no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—22no—
92C2×Dic47C2×D412yes—
93D188—22no—
94C4×D47—22no—
95C4×D47—22no—
96C4×D47—44no—
97Dic94—21no—
98Dic94—44no—
99Dic94—81no—
100Dic94#4112yes—
101C8×C47—22no—
102C47⋊C8—21no—
103C47⋊C8—21no—
104C22×C47—41no—
105C22×C47—41no—
106C22×C47—41no—
107C22×C47C22×D411yescharacteristic
108C2×D47—22no—
109C2×D47—22no—
110C2×D47—22no—
111C4×C47—21no—
112C4×C47—42no—
113C4×C47—41no—
114C4×C47#13712yes—
115C4×C47C2×#4111yescharacteristic
116C4×C47H(5,𝔽2)11yescharacteristic
117Dic47—22no—
118Dic47—22no—
119Dic47—42no—
120Dic47—41no—
121#3329—471nomaximal, Sylow
122C2×C47—81no—
123C2×C47#54611yescharacteristic
124C2×C47C2×#13711yescharacteristic
125C2×C47#57711yescharacteristic
126D47—42no—
127#555—471no—
128D4×Q8—471no—
129#487—471no—
130#485—472no—
131#477—471no—
132#468—472no—
133#461D4711yescharacteristic, complemented
134#448—472no—
135C4×SD16—471no—
136#436—471no—
137#419—472no—
138C47#332911yescharacteristic, complemented, Sylow
139C22×Q8—472no—
140C2×SD16—471no—
141C2×SD16C2×D4712yes—
142C2×M16—472no—
143C4⋊Q8—471no—
144C4⋊Q8—941no—
145C4⋊Q8C2×D4711yescharacteristic
146#124—942no—
147C22⋊Q8—472no—
148C22⋊Q8—942no—
149#121—472no—
150#121—941no—
151C4×Q8—471no—
152C4×D4—471no—
153C4×D4—941no—
154C4×D4C2×D4711yescharacteristic
155#117—472no—
156#117—941no—
157#107—472no—
158#106—471no—
159C4⋊C8C2×D4711yescharacteristic
160#103—472no—
161#103—472no—
162#103—472no—
163#103—471no—
164#103C2×D4712yes—
165#102—471no—
166C22⋊C8—472no—
167C4×C8—471no—
168C2×Q8—471no—
169C2×Q8—942no—
170C2×Q8—941no—
171C2×Q8—944no—
172C2×Q8—1882no—
173C2×Q8C22×D4712yes—
174C2×D4—471no—
175C2×D4—942no—
176C2×D4C22×D4711yescharacteristic
177C22×C4—21no—
178C22×C4—472no—
179C22×C4—942no—
180SD16—42no—
181SD16—942no—
182M16—1882no—
183C2×C8—471no—
184C2×C8—471no—
185C2×C8C22×D4712yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—471no—
189C4⋊C4—471no—
190C4⋊C4—472no—
191C4⋊C4—942no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4C22×D4711yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—472no—
197C22⋊C4—942no—
198C22⋊C4—942no—
199C22⋊C4—942no—
200C42—942no—
201C42—941no—
202C42C22×D4711yescharacteristic
203C23—21no—
204C23—472no—
205Q8—22no—
206Q8—22no—
207Q8—472no—
208Q8—941no—
209Q8—3761no—
210Q8—1884no—
211D4—21no—
212D4—21no—
213D4—942no—
214D4—3762no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—472no—
219C2×C4—941no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—1884no—
225C2×C4D4×D4711yescharacteristic
226C2×C4D4×D4711yescharacteristic
227C2×C4C23×D4711yescharacteristic
228C8—22no—
229C8—941no—
230C8—941no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—942no—
235C22—942no—
236C22—942no—
237C22C2×D4×D4711yescharacteristic
238C4—21no—
239C4—42no—
240C4—41no—
241C4—942no—
242C4—942no—
243C4—1882no—
244C4—1881no—
245C4#1309405312yes—
246C4#41×D4711yescharacteristic
247C4#1309406911yescharacteristic
248C2—81no—
249C2—1882no—
250C2#1568977011yescharacteristic
251C2C2×#1309405311yescharacteristic
252C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3329
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #15689788C2semidirect
3. #15689473C2semidirect
4. #15689463C2semidirect
5. #15689419C2semidirect
6. #15689366C2semidirect
7. #15689260C2semidirect
8. C4×#10625335C2semidirect
9. #15689200C2semidirect
10. #15689130C2semidirect
11. C47×#461C2semidirect
133. #461D47semidirect
138. C47#3329semidirect