Finite Group Databasebeta

← #20245122

Subgroups — #20245122

Order 6016.

224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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#135×D47C211yesmaximal, characteristic
2M32×D47C211yesmaximal, characteristic, complemented
3#15689158C211yesmaximal, characteristic, complemented
4#15688934C211yesmaximal, characteristic, complemented
5#15688933C211yesmaximal, characteristic, complemented
6#15688932C211yesmaximal, characteristic, complemented
7C47×#360C211yesmaximal, characteristic, complemented
8#41×D47—21no—
9#13094047C411yescharacteristic, complemented
10#13094046C2211yescharacteristic
11#13094045—21no—
12#13094044—21no—
13#13094043C411yescharacteristic, complemented
14Q16×D47C411yescharacteristic, complemented
15SD16×D47—21no—
16D8×D47C411yescharacteristic, complemented
17C2×C8×D47C2211yescharacteristic
18#13093982—21no—
19#13093964C2211yescharacteristic, complemented
20#13093963—21no—
21C16×D47—21no—
22#13093957—21no—
23#13093956C2211yescharacteristic, complemented
24#135×C47C2211yescharacteristic
25M32×C47C2211yescharacteristic, complemented
26#106×C47C2211yescharacteristic, complemented
27#41×C47—21no—
28#10625354—21no—
29Q8×D47—21no—
30#10625352—21no—
31#10625352—41no—
32D4×D47—21no—
33D4×D47—41no—
34#10625350—21no—
35#10625350—41no—
36C2×C4×D47—41no—
37C2×C4×D47D411yescharacteristic
38Q16×C47C2×C411yescharacteristic
39SD16×C47—21no—
40D8×C47C2×C411yescharacteristic
41C2×C8×C47C2311yescharacteristic
42C4⋊C4×C47—21no—
43#10625337—21no—
44#10625336—21no—
45#10625335—21no—
46#10625334—21no—
47(C2×D47)⋊C4—41no—
48C4⋊Dic47—21no—
49C4×Dic47—41no—
50C2×C47⋊C8D411yescharacteristic
51Dic188C2×C411yescharacteristic
52D376C2×C411yescharacteristic
53#10625325—21no—
54C8×D47C2×C411yescharacteristic
55C8×D47C2×C411yescharacteristic
56C8×D47D411yescharacteristic
57C8×D47D411yescharacteristic
58C16×C47—21no—
59C47⋊C16—21no—
60C22×D47—41no—
61C22×D47D811yescharacteristic
62Q8×C47—21no—
63D4×C47—21no—
64D4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47C2×D411yescharacteristic
68C22⋊D47—41no—
69C22⋊D47—41no—
70C22⋊D47—41no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47D811yescharacteristic
74D188—21no—
75D188—41no—
76C4×D47—41no—
77C4×D47—41no—
78C4×D47—41no—
79C4×D47C22⋊C411yescharacteristic
80C4×D47C22⋊C411yescharacteristic
81C4×D47SD1611yescharacteristic
82C4×D47SD1611yescharacteristic
83Dic94—21no—
84Dic94—41no—
85C8×C47C22×C411yescharacteristic
86C8×C47C2×D411yescharacteristic
87C47⋊C8C22⋊C411yescharacteristic
88C47⋊C8C22⋊C411yescharacteristic
89C22×C47—41no—
90C22×C47C2×D811yescharacteristic
91C2×D47—41no—
92C2×D47—41no—
93C2×D47—82no—
94C2×D47#10211yescharacteristic
95C2×D47#10211yescharacteristic
96C4×C47—41no—
97C4×C47—81no—
98C4×C47C2×C22⋊C411yescharacteristic
99C4×C47C2×SD1611yescharacteristic
100Dic47—41no—
101Dic47—81no—
102Dic47#10211yescharacteristic
103Dic47#10211yescharacteristic
104#2145—471nomaximal, Sylow
105C2×C47—21no—
106C2×C47—81no—
107C2×C47C2×#10211yescharacteristic
108D47—21no—
109D47—21no—
110D47—81no—
111C2×#135—471no—
112C2×M32—471no—
113#427—471no—
114#360—471no—
115#360—471no—
116#360—471no—
117#360D4711yescharacteristic, complemented
118C47#214511yescharacteristic, complemented, Sylow
119C2×#41—941no—
120#135—471no—
121#135—471no—
122#135—471no—
123#135—941no—
124#135—941no—
125#135C2×D4711yescharacteristic
126C2×Q16—471no—
127C2×SD16—941no—
128C2×D8—471no—
129C22×C8—471no—
130#117—941no—
131M32—471no—
132M32—941no—
133M32C2×D4711yescharacteristic, complemented
134C2×C16—941no—
135#107—941no—
136#106—471no—
137#106C2×D4711yescharacteristic, complemented
138#41—21no—
139#41—941no—
140#41—941no—
141#41—941no—
142#41—1881no—
143#41—1881no—
144C2×Q8—941no—
145C2×D4—941no—
146C2×D4—1881no—
147C22×C4—471no—
148C22×C4—1881no—
149Q16—471no—
150Q16—941no—
151Q16C4×D4711yescharacteristic
152SD16—21no—
153SD16—941no—
154SD16—941no—
155SD16—941no—
156D8—471no—
157D8—941no—
158D8C4×D4711yescharacteristic
159C2×C8—471no—
160C2×C8—471no—
161C2×C8—471no—
162C2×C8—471no—
163C2×C8—471no—
164C2×C8C22×D4711yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—941no—
167C22⋊C4—1881no—
168C42—1881no—
169C16—21no—
170C16—941no—
171C23—471no—
172C23—1881no—
173Q8—21no—
174Q8—941no—
175Q8—1881no—
176D4—21no—
177D4—41no—
178D4—941no—
179D4—1881no—
180D4—1881no—
181D4—1881no—
182D4—1881no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—471no—
186C2×C4—471no—
187C2×C4—471no—
188C2×C4—471no—
189C2×C4—471no—
190C2×C4—1881no—
191C2×C4—1881no—
192C2×C4—1881no—
193C2×C4—1881no—
194C2×C4—1881no—
195C2×C4D4×D4711yescharacteristic
196C8—471no—
197C8—471no—
198C8C2×C4×D4711yescharacteristic
199C8D4×D4711yescharacteristic
200C22—41no—
201C22—471no—
202C22—471no—
203C22—3762no—
204C22—1881no—
205C22—1881no—
206C22D8×D4711yescharacteristic
207C4—41no—
208C4—81no—
209C4—471no—
210C4—471no—
211C4—3761no—
212C4—1881no—
213C4C22⋊C4×D4711yescharacteristic
214C4SD16×D4711yescharacteristic
215C2—21no—
216C2—81no—
217C2—941no—
218C2—941no—
219C2—3761no—
220C2#102×D4711yescharacteristic
subgroupG/H
centerC2#102×D47
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC47×#360C2
socleC2×C47C2×#102
hypercenter#360D47
hypocenterC47#2145
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. M32×D47C2semidirect
3. #15689158C2semidirect
4. #15688934C2semidirect
5. #15688933C2semidirect
6. #15688932C2semidirect
7. C47×#360C2semidirect
9. #13094047C4semidirect
13. #13094043C4semidirect
14. Q16×D47C4semidirect
16. D8×D47C4semidirect
19. #13093964C22semidirect
23. #13093956C22semidirect
25. M32×C47C22semidirect
26. #106×C47C22semidirect
117. #360D47semidirect
118. C47#2145semidirect
133. M32C2×D47semidirect
137. #106C2×D47semidirect