Finite Group Databasebeta

← #20244800

Subgroups — #20244800

Order 6016.

238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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×#13093949C211yesmaximal, characteristic
2C2×#13093947C211yesmaximal, characteristic
3#15689028C211yesmaximal, characteristic
4#15688992C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—21no—
12C2×Dic47⋊C4—21no—
13C2×C4×Dic47C2211yescharacteristic
14#13093949—22no—
15#13093947—22no—
16C47⋊#95—21no—
17C47⋊#95—21no—
18C22×C8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic
21C22×C4×C47—21no—
22C22×C4×C47—21no—
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—21no—
25C22×Dic47—21no—
26C22×Dic47D411yescharacteristic
27C22×Dic47D411yescharacteristic
28C2×Dic94—21no—
29C2×Dic94—21no—
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×Dic94—21no—
33C2×Dic94D412yes—
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C2×C8×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43Dic47⋊C4—42no—
44Dic47⋊C4—42no—
45C4×Dic47—21no—
46C4×Dic47—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C23×C47C2×D411yescharacteristic
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47#4111yescharacteristic
59C2×C4×C47#4111yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×Dic47—21no—
64C2×Dic47—21no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—22no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47SD1612yes—
74C2×Dic47Q1612yes—
75Dic94—22no—
76Dic94—22no—
77Dic94—41no—
78Dic94—41no—
79C8×C47—41no—
80C47⋊C8—41no—
81C22×C47#12111yescharacteristic
82C22×C47#12311yescharacteristic
83C22×C47#12411yescharacteristic
84C22×C47C2×SD1611yescharacteristic
85C22×C47C2×Q1611yescharacteristic
86C22×C47AGL(1,ℤ/8)11yescharacteristic
87C22×C47#13711yescharacteristic
88C4×C47—81no—
89C4×C47—81no—
90C4×C47#12311yescharacteristic
91C4×C47#12311yescharacteristic
92C4×C47#12611yescharacteristic
93C4×C47#12611yescharacteristic
94Dic47—22no—
95Dic47—22no—
96Dic47—42no—
97Dic47—81no—
98#2072—471nomaximal, Sylow
99C2×C47#39711yescharacteristic
100C2×C47#46011yescharacteristic
101C2×C47#46211yescharacteristic
102C2×C47#48311yescharacteristic
103C2×C47#48411yescharacteristic
104C2×C47#48711yescharacteristic
105C2×C47#48911yescharacteristic
106C2×#103—471no—
107C2×#103—471no—
108#391—471no—
109#384—471no—
110#340—471no—
111#340D4711yescharacteristic
112#336—471no—
113C47#207211yescharacteristic, complemented, Sylow
114C22×Q8—471no—
115C22×C8—471no—
116C22×C8C2×D4711yescharacteristic
117C2×C4⋊C4—471no—
118C2×C4⋊C4—941no—
119C2×C4⋊C4—941no—
120C2×C4⋊C4C2×D4711yescharacteristic
121C2×C4⋊C4C2×D4711yescharacteristic
122C2×C42—471no—
123#103—942no—
124#103—942no—
125#95—941no—
126#95—941no—
127C2×Q8—472no—
128C2×Q8—941no—
129C2×Q8—941no—
130C2×Q8—941no—
131C2×Q8—941no—
132C2×Q8—941no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—471no—
136C22×C4—471no—
137C22×C4—941no—
138C22×C4—941no—
139C22×C4C22×D4711yescharacteristic
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—941no—
144C2×C8—941no—
145C2×C8—941no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—941no—
151C4⋊C4—941no—
152C4⋊C4—1882no—
153C4⋊C4—1882no—
154C42—941no—
155C42—941no—
156C23D4×D4711yescharacteristic
157Q8—942no—
158Q8—942no—
159Q8—1881no—
160Q8—1881no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—472no—
168C2×C4—472no—
169C2×C4—941no—
170C2×C4—941no—
171C2×C4—941no—
172C2×C4—941no—
173C2×C4—942no—
174C2×C4—1881no—
175C2×C4—1881no—
176C2×C4—1881no—
177C2×C4—1881no—
178C2×C4—1881no—
179C2×C4#1062535011yescharacteristic
180C2×C4#1062535011yescharacteristic
181C2×C4#1062535011yescharacteristic
182C2×C4D4×D4711yescharacteristic
183C2×C4#1062535211yescharacteristic
184C2×C4#1062535411yescharacteristic
185C8—41no—
186C8—1881no—
187C22#1309399711yescharacteristic
188C22#1309400911yescharacteristic
189C22#1309401011yescharacteristic
190C22SD16×D4711yescharacteristic
191C22Q16×D4711yescharacteristic
192C22#1309404811yescharacteristic
193C22#1309405311yescharacteristic
194C4—81no—
195C4—81no—
196C4—942no—
197C4—942no—
198C4—3761no—
199C4—1882no—
200C4#1309400611yescharacteristic
201C4#1309400911yescharacteristic
202C4#1309401811yescharacteristic
203C4#1309401911yescharacteristic
204C2#1568905211yescharacteristic
205C2#1568932211yescharacteristic
206C2#1568933211yescharacteristic
207C2#1568945511yescharacteristic
208C2#1568946011yescharacteristic
209C2#1568947211yescharacteristic
210C2#1568948111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2072
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
113. C47#2072semidirect