Finite Group Databasebeta

← #20242503

Subgroups — #20242503

Order 6016.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D188C211yesmaximal, characteristic
2#15689497C211yesmaximal, characteristic, complemented
3#15689410C211yesmaximal, characteristic, complemented
4#15688866C211yesmaximal, characteristic, complemented
5D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×#476C211yesmaximal, characteristic, complemented
8C22×D188—21no—
9C2×D4×D47—21no—
10C2×#10625336—22no—
11#13094021C2211yescharacteristic
12#13093999—21no—
13#13093998—21no—
14#13093994—22no—
15C4×D188C2211yescharacteristic
16#13093955—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic, complemented
18#13093944—21no—
19C4×C47⋊C8C2211yescharacteristic, complemented
20C4⋊Q8×C47C2211yescharacteristic, complemented
21C4×D4×C47C2211yescharacteristic
22#106×C47—21no—
23C4⋊C8×C47C2211yescharacteristic, complemented
24#102×C47—21no—
25C23×D47—22no—
26C2×Q8×C47—21no—
27C2×D4×C47D411yescharacteristic
28C22×C4×C47—21no—
29C2×C22⋊D47—22no—
30D4×D47—42no—
31D4×D47—42no—
32C2×D188—22no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188—42no—
36C2×D188—42no—
37C2×D188D411yescharacteristic
38C2×D188D412yes—
39C2×C4×D47—21no—
40C2×C8×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47D411yescharacteristic
44C22⋊C4×C47—21no—
45C42×C47C2311yescharacteristic
46#10625336—44no—
47(C2×D47)⋊C4—22no—
48(C2×D47)⋊C4—21no—
49C4⋊Dic47D411yescharacteristic
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C23×C47—21no—
53C22×D47—21no—
54C22×D47—22no—
55C22×D47—44no—
56C22×D47—44no—
57C22×D47—82no—
58Q8×C47—42no—
59D4×C47—21no—
60D4×C47SD1612yescomplemented
61C2×C4×C47—21no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C22⋊D47—44no—
69C2×Dic47—21no—
70D188—21no—
71D188—42no—
72D188—44no—
73D188—41no—
74D188—41no—
75D188—41no—
76D188—41no—
77D188SD1612yescomplemented
78C4×D47—41no—
79C4×D47—41no—
80C8×C47—41no—
81C47⋊C8—22no—
82C47⋊C8—41no—
83C22×C47—22no—
84C22×C47—41no—
85C22×C47—41no—
86C22×C47#12011yescharacteristic
87C2×D47—22no—
88C2×D47—41no—
89C2×D47—41no—
90C2×D47—42no—
91C2×D47—42no—
92C2×D47—42no—
93C2×D47—88no—
94C4×C47—21no—
95C4×C47—41no—
96C4×C47—81no—
97C4×C47C2×SD1611yescharacteristic
98C4×C47C2×SD1611yescharacteristic
99C4×C47AGL(1,ℤ/8)11yescharacteristic
100C4×C47AGL(1,ℤ/8)11yescharacteristic
101Dic47—41no—
102#1629—471nomaximal, Sylow
103C2×C47—42no—
104C2×C47#45011yescharacteristic
105C2×C47#45011yescharacteristic
106C2×C47#45311yescharacteristic
107D47—42no—
108D47—82no—
109D42—471no—
110#492—471no—
111#476—471no—
112#476D4711yescharacteristic, complemented
113#331—471no—
114D4⋊C8—471no—
115D4⋊C8—471no—
116C47#162911yescharacteristic, complemented, Sylow
117C22×D4—941no—
118C22×D4—941no—
119C2×SD16—942no—
120C4⋊Q8C2×D4711yescharacteristic, complemented
121#127—471no—
122#121—941no—
123#121—941no—
124#120—942no—
125C4×D4—471no—
126C4×D4C2×D4711yescharacteristic
127#106—21no—
128#106—941no—
129C4⋊C8—471no—
130C4⋊C8C2×D4711yescharacteristic, complemented
131#102—21no—
132#102—941no—
133C4×C8—471no—
134C24—942no—
135C2×Q8—21no—
136C2×D4—471no—
137C2×D4—472no—
138C2×D4—942no—
139C2×D4—942no—
140C2×D4—941no—
141C2×D4—941no—
142C2×D4—1882no—
143C2×D4—1882no—
144C2×D4—1882no—
145C2×D4—1882no—
146C2×D4C22⋊D4711yescharacteristic
147C22×C4—21no—
148C22×C4—941no—
149SD16—1884no—
150C2×C8—21no—
151C2×C8—941no—
152C2×C8—941no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—471no—
156C4⋊C4C22⋊D4711yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—942no—
159C22⋊C4—941no—
160C42C22×D4711yescharacteristic
161C23—21no—
162C23—941no—
163C23—942no—
164C23—3762no—
165C23—1884no—
166C23—1884no—
167Q8—42no—
168D4—21no—
169D4—472no—
170D4—941no—
171D4—1882no—
172D4—1884no—
173D4—1884no—
174D4—1881no—
175D4—1881no—
176D4—1881no—
177D4—1881no—
178D4#1062533612yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—941no—
184C2×C4—1881no—
185C2×C4—1881no—
186C2×C4D4×D4711yescharacteristic
187C2×C4D4×D4711yescharacteristic
188C2×C4C2×C22⋊D4711yescharacteristic
189C8—41no—
190C8—942no—
191C8—1881no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—942no—
196C22—3768no—
197C22—1882no—
198C22—1882no—
199C22—1882no—
200C22—1881no—
201C22—1881no—
202C22#1309399211yescharacteristic
203C4—21no—
204C4—41no—
205C4—81no—
206C4—1881no—
207C4SD16×D4711yescharacteristic
208C4C2×#1062533611yescharacteristic
209C4#1309404911yescharacteristic
210C4#1309405111yescharacteristic
211C2—42no—
212C2—3762no—
213C2—1882no—
214C2#1568927211yescharacteristic
215C2#1568927311yescharacteristic
216C2#1568928911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#476C2
socleC22×C47#120
hypercenter#476D47
hypocenterC47#1629
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #15689497C2semidirect
3. #15689410C2semidirect
4. #15688866C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×#476C2semidirect
17. C4⋊(C47⋊C8)C22semidirect
19. C4×C47⋊C8C22semidirect
20. C4⋊Q8×C47C22semidirect
23. C4⋊C8×C47C22semidirect
60. D4×C47SD16semidirect
77. D188SD16semidirect
112. #476D47semidirect
116. C47#1629semidirect
120. C4⋊Q8C2×D47semidirect
130. C4⋊C8C2×D47semidirect
178. D4#10625336semidirect