Finite Group Databasebeta

← #20243907

Subgroups — #20243907

Order 6016.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689889C211yesmaximal, characteristic
2#15689697C211yesmaximal, characteristic
3#15689132C211yesmaximal, characteristic, complemented
4#15689096C211yesmaximal, characteristic
5#15688880C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#419C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094032—22no—
10#13094030—22no—
11C2×#10625329C2211yescharacteristic
12M16×D47—22no—
13#13094022C412yescomplemented
14#13094013C412yescomplemented
15#13094007—22no—
16#13094000—22no—
17#13093983C2211yescharacteristic
18#13093983C2211yescharacteristic
19#13093948—22no—
20#13093938—22no—
21C22×Q8×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23#117×C47C2211yescharacteristic
24#103×C47—22no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47C2×C412yes—
31C22×C4×C47—21no—
32C22×C4×C47C2311yescharacteristic
33C2×C22⋊D47D412yes—
34#10625350—21no—
35#10625350—21no—
36#10625350—21no—
37#10625350—21no—
38C2×D188C2×C411yescharacteristic
39C2×C4×D47D412yes—
40C2×Dic94C2×C411yescharacteristic
41M16×C47—21no—
42M16×C47—21no—
43C2×C8×C47D412yes—
44C4⋊C4×C47—21no—
45C22⋊C4×C47—21no—
46C42×C47—21no—
47C22⋊Dic47—21no—
48C22⋊Dic47—21no—
49(C2×D47)⋊C4—24no—
50C4⋊Dic47—21no—
51C4⋊Dic47—21no—
52Dic47⋊C4—24no—
53C4×Dic47—21no—
54C4×Dic47C2×C412yes—
55#10625329—21no—
56#10625329—21no—
57C2×C47⋊C8D412yes—
58#10625324—24no—
59C8×D47—24no—
60C23×C47C2×D411yescharacteristic
61C22×D47C22⋊C412yes—
62Q8×C47—22no—
63Q8×C47—22no—
64Q8×C47—41no—
65Q8×C47—41no—
66C2×C4×C47—22no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47C22×C411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C22⋊D47—22no—
77C22⋊D47—22no—
78C2×Dic47—22no—
79C2×Dic47—41no—
80C2×Dic47C22⋊C412yes—
81D188—21no—
82D188—21no—
83C4×D47—22no—
84C4×D47—22no—
85Dic94—21no—
86Dic94—21no—
87C8×C47—22no—
88C47⋊C8—22no—
89C22×C47—41no—
90C22×C47C2×C22⋊C411yescharacteristic
91C22×C47#12111yescharacteristic
92C22×C47#12111yescharacteristic
93C2×D47—22no—
94C2×D47—42no—
95C4×C47—42no—
96C4×C47—81no—
97C4×C47C4×D411yescharacteristic
98C4×C47C4×D411yescharacteristic
99C4×C47#12011yescharacteristic
100C4×C47#12311yescharacteristic
101Dic47—22no—
102Dic47—42no—
103Dic47—81no—
104#1909—471nomaximal, Sylow
105C2×C47—21no—
106C2×C47—21no—
107C2×C47—21no—
108C2×C47#38611yescharacteristic
109D47—42no—
110#568—471no—
111#536—471no—
112#419—471no—
113#419D4711yescharacteristic, complemented
114#410—471no—
115H(3,ℤ/4)—471no—
116H(3,ℤ/4)—471no—
117C47#190911yescharacteristic, complemented, Sylow
118C2×#41—471no—
119C22×Q8C2×D4711yescharacteristic
120#131—942no—
121#131—942no—
122C2×M16—471no—
123C2×M16—942no—
124C2×M16C2×D4711yescharacteristic
125C4⋊Q8—472no—
126#124—472no—
127#123—942no—
128C22⋊Q8—942no—
129#117—471no—
130#117—471no—
131#117C2×D4711yescharacteristic
132#103—22no—
133#103—942no—
134#99—942no—
135#41—941no—
136#41—941no—
137#41—941no—
138#41—941no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—471no—
145C2×Q8C4×D4712yes—
146C2×D4—472no—
147C2×D4—471no—
148C22×C4—21no—
149C22×C4—472no—
150C22×C4C22×D4711yescharacteristic
151M16—21no—
152M16—21no—
153M16—944no—
154M16—941no—
155M16—941no—
156C2×C8—472no—
157C2×C8—944no—
158C2×C8C22⋊D4712yes—
159C4⋊C4—21no—
160C4⋊C4—944no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C22⋊C4—21no—
164C22⋊C4—944no—
165C22⋊C4—941no—
166C22⋊C4—941no—
167C42—21no—
168C42—472no—
169C42—941no—
170C23—472no—
171C23D4×D4711yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—941no—
177Q8—941no—
178D4—942no—
179D4—942no—
180D4—941no—
181D4—941no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—472no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—1881no—
191C2×C4C2×C4×D4711yescharacteristic
192C2×C4#1062535011yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C2×C4D4×D4711yescharacteristic
195C2×C4#1062535211yescharacteristic
196C2×C4C2×C22⋊D4711yescharacteristic
197C8—22no—
198C8—942no—
199C22—41no—
200C22—942no—
201C22—1882no—
202C22C22⋊C4×D4711yescharacteristic
203C22#1309399511yescharacteristic
204C22#1309399711yescharacteristic
205C4—42no—
206C4—81no—
207C4—942no—
208C4—3761no—
209C4—1882no—
210C4(C22⋊D47)⋊C411yescharacteristic
211C4C4×C22⋊D4711yescharacteristic
212C4#1309399211yescharacteristic
213C4#1309400611yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—1882no—
218C2#1568899911yescharacteristic
subgroupG/H
centerC2#15688999
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#419C2
socleC2×C47#386
hypercenter#419D47
hypocenterC47#1909
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #15689132C2semidirect
5. #15688880C2semidirect
6. #15688879C2semidirect
7. C47×#419C2semidirect
13. #13094022C4semidirect
14. #13094013C4semidirect
113. #419D47semidirect
117. C47#1909semidirect