Finite Group Databasebeta

← #20242397

Subgroups — #20242397

Order 6016.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#15689752C211yesmaximal, characteristic
2#15689454C211yesmaximal, characteristic
3#15689451C211yesmaximal, characteristic
4#15689055C211yesmaximal, characteristic
5#15688859C211yesmaximal, characteristic
6#15688848C211yesmaximal, characteristic
7C47×#328C211yesmaximal, characteristic
8#13094023—21no—
9#13094022—21no—
10#13094014—21no—
11#13094014—21no—
12#13094003C2211yescharacteristic
13#13094001—21no—
14#13093980—21no—
15C2×C4⋊Dic47—21no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18#13093956—21no—
19#13093955—21no—
20#13093949—21no—
21#13093948—21no—
22C22⋊(C47⋊C8)C2211yescharacteristic
23C47⋊#95—21no—
24C22⋊Q8×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26#95×C47C2211yescharacteristic
27C2×Q8×C47D411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47D411yescharacteristic
32C22×Dic47D411yescharacteristic
33C2×Dic94—21no—
34C2×Dic94D411yescharacteristic
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47D411yescharacteristic
38C22⋊C4×C47—21no—
39C22⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—42no—
44C4⋊Dic47D411yescharacteristic
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52C4×Dic47—21no—
53C4×Dic47—21no—
54C2×C47⋊C8—21no—
55C23×C47C2×D411yescharacteristic
56Q8×C47—41no—
57C2×C4×C47—22no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47—21no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74C2×Dic47SD1612yes—
75Dic94—41no—
76Dic94—81no—
77C8×C47—41no—
78C47⋊C8—41no—
79C22×C47—21no—
80C22×C47—21no—
81C22×C47#12011yescharacteristic
82C22×C47C2×SD1611yescharacteristic
83C22×C47#13711yescharacteristic
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—42no—
87C4×C47—41no—
88C4×C47—41no—
89Dic47—22no—
90Dic47—41no—
91Dic47—41no—
92Dic47—41no—
93Dic47—81no—
94#1611—471nomaximal, Sylow
95C2×C47—21no—
96C2×C47—21no—
97C2×C47#44811yescharacteristic
98C2×C47#45611yescharacteristic
99C2×C47#45811yescharacteristic
100#544—471no—
101#483—471no—
102#483—471no—
103#398—471no—
104#328—471no—
105#328D4711yescharacteristic
106#324—471no—
107C47#161111yescharacteristic, complemented, Sylow
108C4⋊Q8—941no—
109C4⋊Q8—941no—
110#125—941no—
111#125—941no—
112C22⋊Q8—471no—
113C22⋊Q8—941no—
114C22⋊Q8C2×D4711yescharacteristic
115#117—941no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4—471no—
118C2×C4⋊C4—941no—
119#106—941no—
120#106—941no—
121#103—941no—
122#103—941no—
123C22⋊C8—471no—
124C22⋊C8C2×D4711yescharacteristic
125#95—941no—
126#95C2×D4711yescharacteristic
127C2×Q8—471no—
128C2×Q8—941no—
129C2×Q8D18811yescharacteristic
130C22×C4—21no—
131C22×C4—471no—
132C22×C4—471no—
133C22×C4—941no—
134C22×C4C22×D4711yescharacteristic
135C2×C8—21no—
136C2×C8—941no—
137C4⋊C4—21no—
138C4⋊C4—471no—
139C4⋊C4—941no—
140C4⋊C4—941no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—1882no—
150C4⋊C4D18811yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—941no—
153C42—941no—
154C42—941no—
155C23D4×D4711yescharacteristic
156Q8—41no—
157Q8—3761no—
158Q8—1881no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—472no—
166C2×C4—941no—
167C2×C4—941no—
168C2×C4—941no—
169C2×C4—941no—
170C2×C4—941no—
171C2×C4—1881no—
172C2×C4—1881no—
173C2×C4—1881no—
174C2×C4—1881no—
175C2×C4C2×D18811yescharacteristic
176C2×C4D4×D4711yescharacteristic
177C8—41no—
178C8—1881no—
179C22—21no—
180C22—21no—
181C22#1309399411yescharacteristic
182C22SD16×D4711yescharacteristic
183C22#1309405611yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—942no—
190C4—3761no—
191C4—1881no—
192C4—1881no—
193C4—1881no—
194C2—21no—
195C2—21no—
196C2#1568926311yescharacteristic
197C2#1568930711yescharacteristic
198C2#1568931411yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#328C2
socleC22×C47#120
hypercenter#328D47
hypocenterC47#1611
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
107. C47#1611semidirect