Finite Group Databasebeta

← #20243627

Subgroups — #20243627

Order 6016.

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

normal subgroups only

This group has 262 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#15689171C211yesmaximal, characteristic, complemented
3#15689139C211yesmaximal, characteristic
4C2×#13093952C211yesmaximal, characteristic
5#15688894C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C47×#423C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094032—22no—
10#13094030—22no—
11C2×#10625329C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13M16×D47—22no—
14#13093983C2211yescharacteristic
15#13093959—22no—
16#13093952C412yescomplemented
17#13093952C412yescomplemented
18#13093950—22no—
19C2×M16×C47C2211yescharacteristic
20C2×M16×C47C2211yescharacteristic
21C2×C42×C47C2211yescharacteristic
22C4⋊C8×C47—22no—
23C22×C4×C47—21no—
24C22×C4×C47C2311yescharacteristic
25C2×C22⋊D47—21no—
26#10625350—21no—
27#10625350—21no—
28#10625350C2×C412yes—
29#10625350D412yes—
30C2×D188Q811yescharacteristic
31C2×C4×D47—21no—
32C2×Dic94Q811yescharacteristic
33M16×C47—21no—
34M16×C47—21no—
35M16×C47—21no—
36M16×C47—21no—
37C2×C8×C47—21no—
38C2×C8×C47D412yes—
39C42×C47—21no—
40C42×C47C2×C411yescharacteristic
41C42×C47C2×C411yescharacteristic
42C22⋊Dic47—21no—
43C4⋊Dic47—21no—
44C4×Dic47—21no—
45#10625329—21no—
46#10625329—21no—
47#10625329C2×C412yes—
48#10625329D412yes—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51#10625324—24no—
52C8×D47—24no—
53C23×C47#4111yescharacteristic
54C22×D47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—42no—
58C2×C4×C47C22×C411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×Q811yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C22⋊D47—22no—
65C22⋊D47—22no—
66C2×Dic47—21no—
67C2×Dic47—41no—
68D188—21no—
69D188C4⋊C412yes—
70C4×D47—22no—
71C4×D47—22no—
72Dic94—21no—
73Dic94C4⋊C412yes—
74C8×C47—22no—
75C8×C47—41no—
76C47⋊C8—22no—
77C47⋊C8—22no—
78C22×C47—41no—
79C22×C47C4×D411yescharacteristic
80C22×C47C22⋊Q811yescharacteristic
81C22×C47#12311yescharacteristic
82C2×D47—22no—
83C2×D47—81no—
84C4×C47—22no—
85C4×C47—41no—
86C4×C47C2×C4⋊C411yescharacteristic
87C4×C47C4×D411yescharacteristic
88C4×C47#12011yescharacteristic
89C4×C47C22⋊Q811yescharacteristic
90Dic47—22no—
91Dic47—81no—
92#1861—471nomaximal, Sylow
93C2×C47—21no—
94C2×C47—21no—
95C2×C47—21no—
96C2×C47#38511yescharacteristic
97D47—42no—
98#568—471no—
99#430—471no—
100#423D4711yescharacteristic, complemented
101#421—471no—
102C2×#104—471no—
103#344—471no—
104#339—471no—
105C47#186111yescharacteristic, complemented, Sylow
106C2×#41—471no—
107#131—942no—
108#131—942no—
109C2×M16—471no—
110C2×M16—471no—
111C2×M16—942no—
112C2×M16C2×D4711yescharacteristic
113C2×M16C2×D4711yescharacteristic
114#117—471no—
115C2×C42C2×D4711yescharacteristic
116#108—942no—
117C4⋊C8—22no—
118#104—472no—
119#104—472no—
120#104—942no—
121#41—472no—
122#41—472no—
123#41—941no—
124#41—941no—
125C2×Q8—471no—
126C2×D4—471no—
127C2×D4—941no—
128C22×C4—21no—
129C22×C4—941no—
130C22×C4C22×D4711yescharacteristic
131M16—21no—
132M16—21no—
133M16—21no—
134M16—21no—
135M16—472no—
136M16—472no—
137M16—944no—
138M16—941no—
139M16—941no—
140C2×C8—21no—
141C2×C8—944no—
142C2×C8—941no—
143C2×C8—941no—
144C2×C8C22⋊D4712yes—
145C4⋊C4—941no—
146C22⋊C4—941no—
147C42—21no—
148C42—941no—
149C42C4×D4711yescharacteristic
150C42C4×D4711yescharacteristic
151C23—941no—
152C23#1062535011yescharacteristic
153Q8—472no—
154Q8—941no—
155D4—472no—
156D4—942no—
157D4—942no—
158D4—941no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—941no—
163C2×C4—942no—
164C2×C4—942no—
165C2×C4—1881no—
166C2×C4C2×C4×D4711yescharacteristic
167C2×C4D4×D4711yescharacteristic
168C2×C4D4×D4711yescharacteristic
169C2×C4Q8×D4711yescharacteristic
170C2×C4#1062535411yescharacteristic
171C2×C4C2×C22⋊D4711yescharacteristic
172C8—22no—
173C8—41no—
174C8—942no—
175C8—942no—
176C22—41no—
177C22—942no—
178C22—3761no—
179C22C4×C22⋊D4711yescharacteristic
180C22#1309400211yescharacteristic
181C22#1309400911yescharacteristic
182C4—22no—
183C4—41no—
184C4—942no—
185C4—3761no—
186C4C4⋊C4×D4711yescharacteristic
187C4#1309398611yescharacteristic
188C4#1309399211yescharacteristic
189C4#1309400011yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—1882no—
194C2#1568899411yescharacteristic
subgroupG/H
centerC4#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#423C2
socleC2×C47#385
hypercenter#423D47
hypocenterC47#1861
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #15689171C2semidirect
5. #15688894C2semidirect
6. #15688883C2semidirect
7. C47×#423C2semidirect
16. #13093952C4semidirect
17. #13093952C4semidirect
100. #423D47semidirect
105. C47#1861semidirect