Finite Group Databasebeta

← #20243445

Subgroups — #20243445

Order 6016.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13094031C211yesmaximal, characteristic
2C2×#13093959C211yesmaximal, characteristic, complemented
3C2×#13093955C211yesmaximal, characteristic, complemented
4#15689124C211yesmaximal, characteristic
5#15688892C211yesmaximal, characteristic, complemented
6#15688891C211yesmaximal, characteristic, complemented
7C47×#417C211yesmaximal, characteristic
8#13094031—22no—
9#13094031C414yescomplemented
10C2×#10625329—21no—
11C2×#10625329C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13C22×C47⋊C8—21no—
14C22×C47⋊C8C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16#13093959—22no—
17#13093955—21no—
18#13093955—21no—
19#13093948—21no—
20#13093945—21no—
21C2×#41×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#103×C47—21no—
25#102×C47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47C2×C412yes—
29#41×C47Q812yes—
30C2×Q8×C47D411yescharacteristic
31C2×D4×C47—21no—
32C2×D4×C47D411yescharacteristic
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37M16×C47—21no—
38M16×C47—21no—
39C2×C8×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—21no—
44#10625329—21no—
45#10625329—24no—
46#10625329—21no—
47#10625329—21no—
48#10625329C2×C412yes—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—24no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8C2×C412yes—
53C2×C47⋊C8D411yescharacteristic
54C2×C47⋊C8D411yescharacteristic
55C2×C47⋊C8D412yes—
56C23×C47—21no—
57C23×C47#4111yescharacteristic
58Q8×C47—21no—
59Q8×C47C4⋊C412yes—
60D4×C47—22no—
61D4×C47—22no—
62D4×C47—21no—
63D4×C47C4⋊C412yes—
64C2×C4×C47—21no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—41no—
68C2×C4×C47—81no—
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×Q811yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×Dic47—41no—
76C2×Dic47—81no—
77C8×C47—41no—
78C47⋊C8—22no—
79C47⋊C8—41no—
80C47⋊C8C22⋊C412yes—
81C47⋊C8C22⋊C412yes—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47—22no—
85C22×C47—41no—
86C22×C47—41no—
87C22×C47#11711yescharacteristic
88C22×C47#12111yescharacteristic
89C22×C47C22⋊Q811yescharacteristic
90C4×C47—22no—
91C4×C47—81no—
92C4×C47C2×C22⋊C411yescharacteristic
93C4×C47C2×C4⋊C411yescharacteristic
94C4×C47#12111yescharacteristic
95C4×C47C22⋊Q811yescharacteristic
96Dic47—81no—
97#1815—471nomaximal, Sylow
98C2×C47—21no—
99C2×C47—21no—
100C2×C47—42no—
101C2×C47#38011yescharacteristic
102C2×C47#47111yescharacteristic
103C2×C47#47111yescharacteristic
104C2×#131—471no—
105C2×#108—471no—
106C2×#106—471no—
107#417—471no—
108#417D4711yescharacteristic
109#343—471no—
110#343—471no—
111C47#181511yescharacteristic, complemented, Sylow
112C2×#41C2×D4711yescharacteristic
113#131—474no—
114#131—942no—
115C2×M16—471no—
116C2×M16—471no—
117C2×M16—941no—
118C2×M16C2×D4711yescharacteristic
119C22×C8—471no—
120C22×C8—941no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4C2×D4711yescharacteristic
123#108—942no—
124#106—941no—
125#106—941no—
126#103—21no—
127#103—941no—
128#102—21no—
129#102—941no—
130#41—21no—
131#41—21no—
132#41Dic9412yes—
133#41C4×D4712yes—
134C2×Q8C22⋊D4711yescharacteristic
135C2×D4—21no—
136C2×D4C22⋊D4711yescharacteristic
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—941no—
140C22×C4C22×D4711yescharacteristic
141M16—21no—
142M16—21no—
143M16—472no—
144M16—944no—
145M16—941no—
146M16—941no—
147M16—941no—
148C2×C8—21no—
149C2×C8—472no—
150C2×C8—471no—
151C2×C8—471no—
152C2×C8—472no—
153C2×C8—944no—
154C2×C8—941no—
155C2×C8—941no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—941no—
159C4⋊C4—941no—
160C23—21no—
161C23#1062535211yescharacteristic
162Q8—21no—
163Q8Dic47⋊C412yes—
164D4—22no—
165D4—22no—
166D4—21no—
167D4Dic47⋊C412yes—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—3761no—
174C2×C4—1881no—
175C2×C4C2×Dic9411yescharacteristic
176C2×C4C2×C4×D4711yescharacteristic
177C2×C4D4×D4711yescharacteristic
178C2×C4D4×D4711yescharacteristic
179C2×C4#1062535211yescharacteristic
180C2×C4C2×C22⋊D4711yescharacteristic
181C8—41no—
182C8—472no—
183C8—472no—
184C8—942no—
185C8—1881no—
186C22—21no—
187C22—21no—
188C22—22no—
189C22—41no—
190C22—41no—
191C22#1309398011yescharacteristic
192C22#1309399611yescharacteristic
193C22#1309400111yescharacteristic
194C4—22no—
195C4—81no—
196C4—3761no—
197C4C22⋊C4×D4711yescharacteristic
198C4C2×Dic47⋊C411yescharacteristic
199C4#1309399611yescharacteristic
200C4#1309400111yescharacteristic
201C2—21no—
202C2—21no—
203C2—42no—
204C2#1568898111yescharacteristic
205C2#1568938411yescharacteristic
206C2#1568938811yescharacteristic
subgroupG/H
centerC22#13093996
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#417C2
socleC22×C47#121
hypercenter#417D47
hypocenterC47#1815
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#13093959C2semidirect
3. C2×#13093955C2semidirect
5. #15688892C2semidirect
6. #15688891C2semidirect
9. #13094031C4semidirect
111. C47#1815semidirect