Finite Group Databasebeta

← #20255256

Subgroups — #20255256

Order 6016.

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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#15689788C211yesmaximal, characteristic, complemented
2#15689778C211yesmaximal, characteristic
3#15689473C211yesmaximal, characteristic, complemented
4#15689452C212yesmaximal, complemented
5#15689409C211yesmaximal, characteristic, complemented
6#15689349C212yesmaximal, complemented
7#15689260C212yesmaximal, complemented
8C4×#10625335C211yesmaximal, characteristic, complemented
9#15689188C211yesmaximal, characteristic, complemented
10#103×D47C212yesmaximal, complemented
11C47×#461C211yesmaximal, characteristic, complemented
12C2×#10625350—21no—
13C2×Q8×D47C2212yes—
14C2×#10625335C2211yescharacteristic
15C2×C8×D47C2212yes—
16#13094024C2211yescharacteristic
17#13094023—21no—
18#13094006—22no—
19#13094003—21no—
20#13094002—22no—
21#13094000C2212yes—
22#13093995C2212yes—
23C4×Dic94C2211yescharacteristic
24C4×D188C2211yescharacteristic
25#13093986—21no—
26C4⋊C4×D47C2212yes—
27#13093956C2212yes—
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—
47#10625350—44no—
48C2×D188D411yescharacteristic
49C2×C4×D47—22no—
50C2×C4×D47—22no—
51C2×C4×D47C2312yes—
52C2×Dic94—21no—
53C2×Dic94—22no—
54C2×Dic94C2311yescharacteristic
55SD16×C47—42no—
56C2×C8×C47C2312yes—
57C4⋊C4×C47—21no—
58C4⋊C4×C47—21no—
59C4⋊C4×C47C2311yescharacteristic
60C22⋊C4×C47—21no—
61C42×C47C2311yescharacteristic
62C22⋊Dic47—22no—
63#10625335—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4D412yes—
66C4⋊Dic47—21no—
67C4⋊Dic47D411yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69C4⋊Dic47C2312yes—
70Dic47⋊C4—21no—
71Dic47⋊C4—22no—
72Dic47⋊C4—22no—
73C4×Dic47—21no—
74C2×C47⋊C8C2311yescharacteristic
75C2×C47⋊C8C2311yescharacteristic
76C8×D47—42no—
77C23×C47—21no—
78C22×D47C2×D412yes—
79Q8×C47—22no—
80Q8×C47—22no—
81D4×C47—21no—
82D4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47—42no—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2411yescharacteristic
89C22⋊D47—44no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47C2×D412yes—
94D188SD1614yescomplemented
95C4×D47—22no—
96C4×D47—22no—
97C4×D47—44no—
98C4×D47—44no—
99Dic94—21no—
100Dic94—44no—
101Dic94—42no—
102Dic94#4112yescomplemented
103C8×C47—22no—
104C47⋊C8—21no—
105C47⋊C8—21no—
106C22×C47—41no—
107C22×C47—41no—
108C22×C47—41no—
109C22×C47C22×D411yescharacteristic
110C2×D47—22no—
111C2×D47—22no—
112C2×D47C2×SD1614yes—
113C4×C47—21no—
114C4×C47—42no—
115C4×C47—41no—
116C4×C47C2×SD1612yes—
117C4×C47C2×#4111yescharacteristic
118C4×C47H(5,𝔽2)11yescharacteristic
119Dic47—22no—
120Dic47—22no—
121Dic47—42no—
122Dic47—41no—
123#3298—471nomaximal, Sylow
124C2×C47—81no—
125C2×C47#54611yescharacteristic
126C2×C47C22×SD1611yescharacteristic
127C2×C47#57811yescharacteristic
128D47—24no—
129D4×Q8—471no—
130#547—471no—
131#487—471no—
132#483—472no—
133#475—471no—
134#465—472no—
135#461D4711yescharacteristic, complemented
136#448—472no—
137C4×SD16—471no—
138C8×D4—471no—
139C2×#103—472no—
140C47#329811yescharacteristic, complemented, Sylow
141C2×#41—941no—
142C22×Q8—472no—
143C2×SD16—471no—
144C2×SD16C2×D4712yes—
145C22×C8—472no—
146C4⋊Q8—471no—
147C4⋊Q8—941no—
148C4⋊Q8C2×D4711yescharacteristic
149#123—942no—
150C22⋊Q8—472no—
151C22⋊Q8—942no—
152C22⋊Q8—941no—
153#121—472no—
154C4×Q8—471no—
155C4×D4—471no—
156C4×D4—941no—
157C4×D4C2×D4711yescharacteristic
158C2×C4⋊C4—472no—
159#106—472no—
160#106—471no—
161C4⋊C8C2×D4711yescharacteristic
162#103—472no—
163#103—472no—
164#103—472no—
165#103—471no—
166#103C2×D4712yes—
167#102—471no—
168C22⋊C8—472no—
169C4×C8—471no—
170#41—1884no—
171C2×Q8—471no—
172C2×Q8—942no—
173C2×Q8—941no—
174C2×Q8—944no—
175C2×Q8—1882no—
176C2×Q8C22×D4712yes—
177C2×D4—471no—
178C2×D4—942no—
179C2×D4C22×D4711yescharacteristic
180C22×C4—21no—
181C22×C4—472no—
182C22×C4—942no—
183C22×C4—942no—
184SD16—42no—
185SD16—942no—
186C2×C8—471no—
187C2×C8—471no—
188C2×C8—1882no—
189C2×C8C22×D4712yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—471no—
193C4⋊C4—471no—
194C4⋊C4—472no—
195C4⋊C4—942no—
196C4⋊C4—942no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C4⋊C4C22×D4711yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—472no—
202C22⋊C4—942no—
203C22⋊C4—942no—
204C42—941no—
205C42C22×D4711yescharacteristic
206C23—21no—
207C23—472no—
208Q8—22no—
209Q8—22no—
210Q8—472no—
211Q8—941no—
212Q8—1884no—
213Q8—1882no—
214D4—21no—
215D4—21no—
216D4—474no—
217D4—1884no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—472no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—941no—
226C2×C4—942no—
227C2×C4—1884no—
228C2×C4—1884no—
229C2×C4D4×D4711yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4C23×D4711yescharacteristic
232C8—22no—
233C8—941no—
234C8—941no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—474no—
239C22—942no—
240C22—942no—
241C22C2×D4×D4711yescharacteristic
242C4—21no—
243C4—42no—
244C4—41no—
245C4—942no—
246C4—942no—
247C4—1882no—
248C4—1881no—
249C4SD16×D4712yes—
250C4#41×D4711yescharacteristic
251C4#1309406911yescharacteristic
252C2—81no—
253C2—944no—
254C2#1568977011yescharacteristic
255C2C2×SD16×D4711yescharacteristic
256C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3298
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
1. #15689788C2semidirect
3. #15689473C2semidirect
4. #15689452C2semidirect
5. #15689409C2semidirect
6. #15689349C2semidirect
7. #15689260C2semidirect
8. C4×#10625335C2semidirect
9. #15689188C2semidirect
10. #103×D47C2semidirect
11. C47×#461C2semidirect
94. D188SD16semidirect
102. Dic94#41semidirect
135. #461D47semidirect
140. C47#3298semidirect