Finite Group Databasebeta

← #20254452

Subgroups — #20254452

Order 6016.

388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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#15689729C211yesmaximal, characteristic, complemented
2#15689693C211yesmaximal, characteristic, complemented
3#15689513C211yesmaximal, characteristic, complemented
4#15689496C211yesmaximal, characteristic, complemented
5#15689493C211yesmaximal, characteristic, complemented
6#15689337C212yesmaximal, complemented
7#15689327C212yesmaximal, complemented
8#15689269C212yesmaximal, complemented
9#15689263C212yesmaximal, complemented
10#15689182C211yesmaximal, characteristic, complemented
11C47×#488C211yesmaximal, characteristic, complemented
12C2×#10625352C2211yescharacteristic
13C2×Q8×D47C2211yescharacteristic
14C2×#10625325C2212yes—
15C2×#10625325C2212yes—
16C2×#10625336C2212yes—
17C2×#10625334C2212yes—
18#13094024C2211yescharacteristic
19#13094022C2211yescharacteristic
20#13094021C2211yescharacteristic
21#13094011C2211yescharacteristic
22#13094009—22no—
23#13094006—22no—
24#13094001—22no—
25#13093999—22no—
26#13093999C2212yes—
27#13093986C2212yes—
28#13093981C2211yescharacteristic
29Dic47⋊C8C2212yes—
30#13093947C2212yes—
31#13093947C2212yes—
32(C2×D47)⋊C8C2212yes—
33#13093935C2211yescharacteristic
34#125×C47C2211yescharacteristic
35#124×C47C2211yescharacteristic
36#103×C47C2212yes—
37#102×C47C2212yes—
38C4×C8×C47C2211yescharacteristic
39C2×Q8×C47C2311yescharacteristic
40C2×D4×C47C2311yescharacteristic
41C2×C22⋊D47—21no—
42C22×Dic47—21no—
43Q8×D47—42no—
44#10625352—42no—
45C2×D188—22no—
46C2×D188—22no—
47C2×D188C2312yes—
48C2×C4×D47—21no—
49C2×C4×D47—22no—
50C2×C4×D47C2311yescharacteristic
51C2×Dic94—21no—
52C2×Dic94C2311yescharacteristic
53C2×Dic94C2311yescharacteristic
54C2×C8×C47C2312yes—
55C4⋊C4×C47—22no—
56C4⋊C4×C47C2312yes—
57C22⋊C4×C47—22no—
58C42×C47C2311yescharacteristic
59C22⋊Dic47—22no—
60#10625336—42no—
61#10625334—42no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4D412yes—
65C4⋊Dic47—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4D412yes—
68C4×Dic47C2311yescharacteristic
69C2×C47⋊C8C2312yes—
70#10625325—42no—
71#10625325—42no—
72C23×C47—21no—
73C22×D47—22no—
74C22×D47C2×D411yescharacteristic
75Q8×C47—22no—
76D4×C47—22no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2411yescharacteristic
81C22⋊D47—42no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—42no—
85C2×Dic47C2×D412yes—
86C2×Dic47C2×D411yescharacteristic
87D188—22no—
88D188—22no—
89D188—82no—
90D188—82no—
91C4×D47—22no—
92C4×D47—42no—
93C4×D47—82no—
94Dic94—22no—
95Dic94—22no—
96Dic94—42no—
97C8×C47—22no—
98C47⋊C8—22no—
99C22×C47—41no—
100C22×C47—42no—
101C22×C47C22×D411yescharacteristic
102C2×D47—21no—
103C2×D47—22no—
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—42no—
107C4×C47—22no—
108C4×C47—41no—
109C4×C47—42no—
110C4×C47H(5,𝔽2)12yes—
111Dic47—21no—
112Dic47—22no—
113Dic47—41no—
114Dic47—41no—
115#3221—471nomaximal, Sylow
116C2×C47—81no—
117C2×C47#53511yescharacteristic
118C2×C47#57712yes—
119D47—41no—
120D47—82no—
121#540—471no—
122#536—471no—
123#496—471no—
124#492—471no—
125#491—471no—
126#488D4711yescharacteristic, complemented
127#463—472no—
128#461—472no—
129#449—472no—
130#448—472no—
131#433—471no—
132C47#322111yescharacteristic, complemented, Sylow
133C2×#41—471no—
134C22×Q8—471no—
135C2×SD16—472no—
136C2×SD16—472no—
137C2×SD16—472no—
138C2×D8—472no—
139C4⋊Q8—471no—
140C4⋊Q8—471no—
141#127—471no—
142#125C2×D4711yescharacteristic
143#124—471no—
144#124C2×D4711yescharacteristic
145#123—942no—
146#123—942no—
147C22⋊Q8—942no—
148#121—472no—
149#121—942no—
150C4×D4—472no—
151#117—471no—
152C4⋊C8—472no—
153#103—472no—
154#103—472no—
155#103C2×D4712yes—
156#102C2×D4712yes—
157C22⋊C8—472no—
158#97—471no—
159C4×C8C2×D4711yescharacteristic
160#41—1882no—
161C2×Q8—471no—
162C2×Q8—471no—
163C2×Q8—941no—
164C2×Q8—1882no—
165C2×Q8C22×D4711yescharacteristic
166C2×D4—472no—
167C2×D4—942no—
168C2×D4—941no—
169C2×D4—942no—
170C2×D4C22×D4711yescharacteristic
171C22×C4—471no—
172C22×C4—942no—
173C22×C4—941no—
174C22×C4—941no—
175SD16—1882no—
176SD16—1882no—
177SD16—1882no—
178D8—1882no—
179C2×C8—472no—
180C2×C8C22×D4712yes—
181C4⋊C4—22no—
182C4⋊C4—472no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4C22×D4712yes—
186C22⋊C4—22no—
187C22⋊C4—472no—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C42—471no—
192C42C22×D4711yescharacteristic
193C23—21no—
194C23—471no—
195C23—942no—
196Q8—22no—
197Q8—942no—
198Q8—942no—
199Q8—1882no—
200D4—22no—
201D4—942no—
202D4—942no—
203D4—3762no—
204D4—3762no—
205D4—1882no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—472no—
209C2×C4—471no—
210C2×C4—942no—
211C2×C4—941no—
212C2×C4—941no—
213C2×C4—3762no—
214C2×C4—1882no—
215C2×C4—1882no—
216C2×C4D4×D4712yes—
217C2×C4C23×D4711yescharacteristic
218C8—22no—
219C8—942no—
220C22—42no—
221C22—41no—
222C22—942no—
223C22—941no—
224C22—1882no—
225C22—1882no—
226C22—1882no—
227C22C2×D4×D4711yescharacteristic
228C4—22no—
229C4—42no—
230C4—41no—
231C4—942no—
232C4—941no—
233C4—1881no—
234C4—1881no—
235C4#1309407012yes—
236C2—81no—
237C2—3762no—
238C2—1881no—
239C2#1568969111yescharacteristic
240C2#1568993012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#488C2
socleC22×C47C22×D4
hypercenter#488D47
hypocenterC47#3221
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #15689729C2semidirect
2. #15689693C2semidirect
3. #15689513C2semidirect
4. #15689496C2semidirect
5. #15689493C2semidirect
6. #15689337C2semidirect
7. #15689327C2semidirect
8. #15689269C2semidirect
9. #15689263C2semidirect
10. #15689182C2semidirect
11. C47×#488C2semidirect
126. #488D47semidirect
132. C47#3221semidirect