Finite Group Databasebeta

← #20243790

Subgroups — #20243790

Order 6016.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#13094012C211yesmaximal, characteristic
2#15689600C211yesmaximal, characteristic, complemented
3#15689129C211yesmaximal, characteristic
4#15689127C211yesmaximal, characteristic
5C2×#13093942C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C47×#339C211yesmaximal, characteristic, complemented
8C22×Dic94C2211yescharacteristic
9C22×D188C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13094012—22no—
12#13094012C414yescomplemented
13C4×Dic94—22no—
14#13093989—22no—
15#13093983C2211yescharacteristic
16#13093980—22no—
17C2×(C2×D47)⋊C4—22no—
18#13093946—22no—
19#13093944—22no—
20#13093942—22no—
21C2×M16×C47C2211yescharacteristic
22#117×C47C2211yescharacteristic
23C2×C42×C47C2211yescharacteristic
24C23×D47—21no—
25C22×C4×C47—21no—
26C22×C4×C47C2311yescharacteristic
27C22×Dic47D412yes—
28C2×D188—21no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188—21no—
32C2×D188—21no—
33C2×D188C2×C412yes—
34C2×Dic94—21no—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94C2×C412yes—
39C2×Dic94D412yes—
40M16×C47—21no—
41M16×C47—21no—
42C2×C8×C47—21no—
43C4⋊C4×C47D412yes—
44C22⋊C4×C47—21no—
45C42×C47—21no—
46C42×C47—21no—
47C42×C47C2×C412yes—
48C22⋊Dic47—21no—
49(C2×D47)⋊C4—28no—
50C4⋊Dic47D412yes—
51Dic47⋊C4—24no—
52C4×Dic47—24no—
53C4×Dic47—21no—
54#10625329—21no—
55#10625329—21no—
56C2×C47⋊C8—21no—
57C23×C47C2×D411yescharacteristic
58C22×D47—22no—
59C22×D47—44no—
60C22×D47—41no—
61C22×D47—41no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—42no—
65C2×C4×C47C22×C411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47C22⋊C414yes—
75D188—22no—
76D188—22no—
77D188—41no—
78D188—41no—
79Dic94—22no—
80Dic94—22no—
81Dic94—22no—
82Dic94—22no—
83C8×C47—41no—
84C47⋊C8—41no—
85C22×C47—22no—
86C22×C47C2×C22⋊C411yescharacteristic
87C22×C47#12011yescharacteristic
88C22×C47#12311yescharacteristic
89C2×D47—44no—
90C2×D47—42no—
91C2×D47—82no—
92C2×D47—82no—
93C4×C47—42no—
94C4×C47—42no—
95C4×C47C4×D411yescharacteristic
96C4×C47C4×D411yescharacteristic
97C4×C47#12111yescharacteristic
98C4×C47#12111yescharacteristic
99Dic47—24no—
100Dic47—42no—
101#1888—471nomaximal, Sylow
102C2×C47—21no—
103C2×C47—21no—
104C2×C47#38611yescharacteristic
105C2×C47#45412yes—
106D47—82no—
107C2×#124—471no—
108#519—471no—
109#418—471no—
110#418—471no—
111C2×#101—471no—
112#339—471no—
113#339D4711yescharacteristic, complemented
114C47#188811yescharacteristic, complemented, Sylow
115C22×Q8—471no—
116C22×D4—471no—
117C2×M16—471no—
118C2×M16C2×D4711yescharacteristic
119#124—474no—
120#124—942no—
121C4×Q8—942no—
122C4×Q8—942no—
123#117—471no—
124#117—942no—
125#117C2×D4711yescharacteristic
126C2×C22⋊C4—942no—
127C2×C42C2×D4711yescharacteristic
128#102—942no—
129#102—942no—
130#101—942no—
131C24—941no—
132C2×Q8—472no—
133C2×Q8—472no—
134C2×Q8—941no—
135C2×Q8—941no—
136C2×Q8—941no—
137C2×Q8—941no—
138C2×D4—472no—
139C2×D4—941no—
140C2×D4—941no—
141C2×D4—941no—
142C2×D4—941no—
143C2×D4—941no—
144C22×C4—21no—
145C22×C4—472no—
146C22×C4C22×D4711yescharacteristic
147M16—21no—
148M16—21no—
149M16—941no—
150M16—941no—
151C2×C8—21no—
152C2×C8—941no—
153C4⋊C4—472no—
154C4⋊C4—944no—
155C4⋊C4D18812yes—
156C22⋊C4—21no—
157C22⋊C4—948no—
158C22⋊C4—941no—
159C42—21no—
160C42—21no—
161C42—944no—
162C42—941no—
163C42C4×D4712yes—
164C23—942no—
165C23—1884no—
166C23—1881no—
167C23—1881no—
168C23D4×D4711yescharacteristic
169Q8—942no—
170Q8—942no—
171Q8—942no—
172Q8—942no—
173D4—942no—
174D4—942no—
175D4—1881no—
176D4—1881no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—474no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4C2×C4×D4711yescharacteristic
185C2×C4C2×D18811yescharacteristic
186C2×C4#1062535011yescharacteristic
187C2×C4D4×D4711yescharacteristic
188C2×C4D4×D4711yescharacteristic
189C2×C4#1062535411yescharacteristic
190C8—41no—
191C8—1881no—
192C22—22no—
193C22—3762no—
194C22—3762no—
195C22—1884no—
196C22—1882no—
197C22C22⋊C4×D4711yescharacteristic
198C22#1309399411yescharacteristic
199C22#1309400911yescharacteristic
200C4—42no—
201C4—42no—
202C4—944no—
203C4—1882no—
204C4#1309398611yescharacteristic
205C4C4×D18811yescharacteristic
206C4#1309399711yescharacteristic
207C4#1309399911yescharacteristic
208C2—21no—
209C2—21no—
210C2—3762no—
211C2#1568900111yescharacteristic
212C2#1568929712yes—
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47#120
hypercenter#339D47
hypocenterC47#1888
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #15689600C2semidirect
5. C2×#13093942C2semidirect
6. #15688883C2semidirect
7. C47×#339C2semidirect
12. #13094012C4semidirect
113. #339D47semidirect
114. C47#1888semidirect