Finite Group Databasebeta

← #20255252

Subgroups — #20255252

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#15689776C211yesmaximal, characteristic
3#15689452C212yesmaximal, complemented
4#15689405C211yesmaximal, characteristic, complemented
5#15689355C212yesmaximal, complemented
6#15689325C211yesmaximal, characteristic, complemented
7#15689263C212yesmaximal, complemented
8C4×#10625325C211yesmaximal, characteristic, complemented
9C8×D188C211yesmaximal, characteristic, complemented
10#103×D47C212yesmaximal, complemented
11C47×#487C211yesmaximal, characteristic, complemented
12C2×#10625354—21no—
13C2×Q8×D47C2212yes—
14C2×#10625325C2211yescharacteristic
15C2×#10625336C2212yes—
16C2×C8×D47C2212yes—
17#13094023—21no—
18#13094009—22no—
19#13094002—22no—
20#13094000—21no—
21#13094000C2212yes—
22#13093999C2212yes—
23C4×Dic94C2211yescharacteristic
24C4×D188C2211yescharacteristic
25C4×D188C2211yescharacteristic
26#13093986—21no—
27C4⋊C4×D47C2212yes—
28#13093956C2211yescharacteristic
29#13093955C2212yes—
30C4⋊(C47⋊C8)C2211yescharacteristic
31#13093949C2211yescharacteristic
32#13093948C2212yes—
33#13093947C2212yes—
34#13093946C2211yescharacteristic
35(C2×D47)⋊C8C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4⋊Q8×C47C2211yescharacteristic
38#103×C47C2212yes—
39#103×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47C2312yes—
43#10625354—44no—
44Q8×D47—24no—
45Q8×D47—42no—
46C2×D188—22no—
47C2×D188D411yescharacteristic
48C2×D188C2311yescharacteristic
49C2×C4×D47—22no—
50C2×C4×D47—22no—
51C2×C4×D47—21no—
52C2×C4×D47C2312yes—
53C2×Dic94—22no—
54C2×Dic94C2311yescharacteristic
55C2×C8×C47C2311yescharacteristic
56C2×C8×C47C2311yescharacteristic
57C4⋊C4×C47—21no—
58C4⋊C4×C47—21no—
59C4⋊C4×C47—21no—
60C4⋊C4×C47C2312yes—
61C42×C47C2311yescharacteristic
62#10625336—42no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—21no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4D412yes—
67C4⋊Dic47D411yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71Dic47⋊C4—22no—
72Dic47⋊C4—22no—
73C4×Dic47—21no—
74C2×C47⋊C8C2312yes—
75#10625325—22no—
76C8×D47—42no—
77C22×D47—21no—
78C22×D47C2×D412yes—
79Q8×C47—22no—
80Q8×C47—22no—
81Q8×C47—42no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2411yescharacteristic
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47C2×D412yes—
91D188—21no—
92D188—21no—
93D188—44no—
94D188SD1614yescomplemented
95C4×D47—22no—
96C4×D47—22no—
97C4×D47—44no—
98C4×D47—44no—
99C4×D47—42no—
100Dic94—21no—
101Dic94—44no—
102Dic94#4112yescomplemented
103C8×C47—21no—
104C8×C47—21no—
105C47⋊C8—22no—
106C22×C47C22×D411yescharacteristic
107C2×D47—22no—
108C2×D47—22no—
109C2×D47—41no—
110C2×D47—41no—
111C2×D47—41no—
112C2×D47C2×SD1614yes—
113C4×C47—21no—
114C4×C47—42no—
115C4×C47—42no—
116C4×C47C2×SD1612yes—
117C4×C47C2×#4111yescharacteristic
118C4×C47H(5,𝔽2)11yescharacteristic
119Dic47—22no—
120Dic47—22no—
121Dic47—41no—
122Dic47—41no—
123#3298—471nomaximal, Sylow
124C2×C47#54611yescharacteristic
125C2×C47C22×SD1611yescharacteristic
126C2×C47#57811yescharacteristic
127D47—24no—
128D47—81no—
129D4×Q8—471no—
130#547—471no—
131#487D4711yescharacteristic, complemented
132#483—472no—
133#475—471no—
134#465—472no—
135#461—471no—
136#448—472no—
137C4×SD16—471no—
138C8×D4—471no—
139C2×#103—472no—
140C47#329811yescharacteristic, complemented, Sylow
141C2×#41—941no—
142C22×Q8—472no—
143C2×SD16—472no—
144C2×SD16—471no—
145C22×C8—472no—
146C4⋊Q8—941no—
147C4⋊Q8C2×D4711yescharacteristic
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—471no—
157C4×D4—941no—
158C2×C4⋊C4—472no—
159#106—471no—
160#106—472no—
161C4⋊C8—471no—
162#103—472no—
163#103—471no—
164#103—472no—
165#103C2×D4712yes—
166#103C2×D4712yes—
167#102—471no—
168C22⋊C8—472no—
169C4×C8C2×D4711yescharacteristic
170#41—1884no—
171C2×Q8—21no—
172C2×Q8—471no—
173C2×Q8—942no—
174C2×Q8—944no—
175C2×Q8—1882no—
176C2×Q8C22×D4712yes—
177C2×D4—471no—
178C2×D4—471no—
179C2×D4—942no—
180C22×C4—472no—
181C22×C4—942no—
182C22×C4—942no—
183C22×C4—941no—
184SD16—942no—
185SD16—1882no—
186C2×C8—472no—
187C2×C8—1882no—
188C2×C8C22×D4711yescharacteristic
189C2×C8C22×D4711yescharacteristic
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—471no—
194C4⋊C4—471no—
195C4⋊C4—471no—
196C4⋊C4—942no—
197C4⋊C4—942no—
198C4⋊C4—941no—
199C4⋊C4C22×D4712yes—
200C22⋊C4—472no—
201C22⋊C4—942no—
202C22⋊C4—942no—
203C22⋊C4—941no—
204C42—941no—
205C42C22×D4711yescharacteristic
206C23—472no—
207C23—941no—
208Q8—22no—
209Q8—22no—
210Q8—42no—
211Q8—472no—
212Q8—941no—
213Q8—1884no—
214D4—474no—
215D4—941no—
216D4—941no—
217D4—1884no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—472no—
221C2×C4—941no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—941no—
225C2×C4—941no—
226C2×C4—1884no—
227C2×C4—1884no—
228C2×C4—1882no—
229C2×C4D4×D4711yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4C23×D4711yescharacteristic
232C8—21no—
233C8—21no—
234C8—942no—
235C22—474no—
236C22—942no—
237C22—942no—
238C22—1881no—
239C22—1881no—
240C22—1881no—
241C22C2×D4×D4711yescharacteristic
242C4—21no—
243C4—42no—
244C4—42no—
245C4—942no—
246C4—942no—
247C4—1881no—
248C4—1881no—
249C4SD16×D4712yes—
250C4#41×D4711yescharacteristic
251C4#1309407011yescharacteristic
252C2—944no—
253C2—3761no—
254C2#1568976611yescharacteristic
255C2C2×SD16×D4711yescharacteristic
256C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#487C2
socleC22×C47C22×D4
hypercenter#487D47
hypocenterC47#3298
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
1. #15689788C2semidirect
3. #15689452C2semidirect
4. #15689405C2semidirect
5. #15689355C2semidirect
6. #15689325C2semidirect
7. #15689263C2semidirect
8. C4×#10625325C2semidirect
9. C8×D188C2semidirect
10. #103×D47C2semidirect
11. C47×#487C2semidirect
94. D188SD16semidirect
102. Dic94#41semidirect
131. #487D47semidirect
140. C47#3298semidirect