Finite Group Databasebeta

← #20244731

Subgroups — #20244731

Order 6016.

246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689751C211yesmaximal, characteristic
2#15689163C211yesmaximal, characteristic
3#15688992C211yesmaximal, characteristic
4#15688891C211yesmaximal, characteristic
5#15688884C211yesmaximal, characteristic
6#15688882C211yesmaximal, characteristic
7C47×#428C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9#13094024—21no—
10#13094023—21no—
11#13094016—21no—
12#13094015—21no—
13#13094001—22no—
14#13093983C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×Dic47⋊C4—22no—
17C2×C4×Dic47C2211yescharacteristic
18#13093957—21no—
19#13093955—21no—
20C2×M16×C47C2211yescharacteristic
21#117×C47C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23#107×C47—21no—
24#106×C47—21no—
25C22×C4×C47—21no—
26C22×C4×C47C2311yescharacteristic
27C22×Dic47—21no—
28C22×Dic47D412yes—
29C2×Dic94—22no—
30M16×C47—21no—
31M16×C47Q812yescomplemented
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47D411yescharacteristic
36C4⋊C4×C47D411yescharacteristic
37C22⋊C4×C47—21no—
38C42×C47—21no—
39C22⋊Dic47—21no—
40C4⋊Dic47—22no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47D411yescharacteristic
44C4⋊Dic47D411yescharacteristic
45Dic47⋊C4—22no—
46Dic47⋊C4—22no—
47Dic47⋊C4—44no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50C4×Dic47Q812yescomplemented
51#10625329—21no—
52#10625329Q812yescomplemented
53C2×C47⋊C8—21no—
54C23×C47C2×D411yescharacteristic
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—42no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×Q811yescharacteristic
62C2×C4×C47C2×Q811yescharacteristic
63C2×C4×C47C2×Q811yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×Dic47—22no—
66C2×Dic47—22no—
67C2×Dic47—22no—
68C2×Dic47—21no—
69C2×Dic47—21no—
70C2×Dic47—22no—
71C2×Dic47—42no—
72Dic94—82no—
73C8×C47—22no—
74C47⋊C8—22no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47#12011yescharacteristic
78C22×C47C22⋊Q811yescharacteristic
79C22×C47C4⋊Q811yescharacteristic
80C4×C47—41no—
81C4×C47—41no—
82C4×C47—81no—
83C4×C47C22⋊Q811yescharacteristic
84C4×C47C22⋊Q811yescharacteristic
85C4×C47C4⋊Q811yescharacteristic
86C4×C47C4⋊Q811yescharacteristic
87Dic47—24no—
88Dic47—41no—
89Dic47—42no—
90Dic47—41no—
91#2060—471nomaximal, Sylow
92C2×C47—21no—
93C2×C47—21no—
94C2×C47#39511yescharacteristic
95C2×C47#45311yescharacteristic
96C2×C47#45611yescharacteristic
97#544—471no—
98#428—471no—
99#428D4711yescharacteristic
100#384—471no—
101#343—471no—
102#339—471no—
103#339—471no—
104C47#206011yescharacteristic, complemented, Sylow
105C2×M16—471no—
106C2×M16C2×D4711yescharacteristic
107C4⋊Q8—941no—
108C4⋊Q8—941no—
109#125—941no—
110#125—941no—
111C22⋊Q8—942no—
112#117—471no—
113#117C2×D4711yescharacteristic
114C2×C4⋊C4—471no—
115C2×C4⋊C4—942no—
116C2×C4⋊C4C2×D4711yescharacteristic
117C2×C42—471no—
118#107—21no—
119#107—941no—
120#106—21no—
121#106—941no—
122C2×Q8—942no—
123C22×C4—21no—
124C22×C4—472no—
125C22×C4—941no—
126C22×C4C22×D4711yescharacteristic
127M16—21no—
128M16—472no—
129M16—941no—
130M16Dic9412yescomplemented
131C2×C8—21no—
132C2×C8—941no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—471no—
136C4⋊C4—471no—
137C4⋊C4—942no—
138C4⋊C4—942no—
139C4⋊C4—942no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—1884no—
143C4⋊C4C22⋊D4711yescharacteristic
144C4⋊C4C22⋊D4711yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—941no—
147C42—21no—
148C42—472no—
149C42—941no—
150C42—941no—
151C23D4×D4711yescharacteristic
152Q8—3762no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—942no—
158C2×C4—942no—
159C2×C4—942no—
160C2×C4—941no—
161C2×C4—941no—
162C2×C4—942no—
163C2×C4—1882no—
164C2×C4C2×Dic9411yescharacteristic
165C2×C4#1062535011yescharacteristic
166C2×C4D4×D4711yescharacteristic
167C2×C4Q8×D4711yescharacteristic
168C2×C4Q8×D4711yescharacteristic
169C2×C4C2×C22⋊D4711yescharacteristic
170C8—22no—
171C8—942no—
172C22—21no—
173C22—21no—
174C22#1309399211yescharacteristic
175C22#1309400211yescharacteristic
176C22#1309402311yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—944no—
181C4—1882no—
182C4—1881no—
183C4—1881no—
184C4#1309400211yescharacteristic
185C4#1309400311yescharacteristic
186C4#1309402211yescharacteristic
187C4#1309402311yescharacteristic
188C2—21no—
189C2—21no—
190C2#1568904311yescharacteristic
191C2#1568928911yescharacteristic
192C2#1568930411yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#428C2
socleC22×C47#120
hypercenter#428D47
hypocenterC47#2060
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
31. M16×C47Q8semidirect
50. C4×Dic47Q8semidirect
52. #10625329Q8semidirect
104. C47#2060semidirect
130. M16Dic94semidirect