Finite Group Databasebeta

← #20244924

Subgroups — #20244924

Order 6016.

254 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13093958C211yesmaximal, characteristic
2C2×#13093957C211yesmaximal, characteristic
3C2×#13093948C211yesmaximal, characteristic
4#15689030C211yesmaximal, characteristic
5#15688992C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C2×#103×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—22no—
12C2×C4×Dic47C2211yescharacteristic
13#13093958—22no—
14#13093957—22no—
15#13093948—22no—
16C47⋊#95—22no—
17C22×Q8×C47C2211yescharacteristic
18C22×C8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20#103×C47—22no—
21C2×Q8×C47—21no—
22C2×Q8×C47—21no—
23C2×Q8×C47—21no—
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47Q812yes—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47—21no—
32C22×Dic47D412yes—
33C2×C8×C47—21no—
34C2×C8×C47—21no—
35C2×C8×C47D412yes—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊Dic47—21no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42Dic47⋊C4—44no—
43C4×Dic47—21no—
44C4×Dic47—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8D412yes—
48C23×C47C2×D411yescharacteristic
49Q8×C47—22no—
50Q8×C47—22no—
51Q8×C47—41no—
52Q8×C47—41no—
53C2×C4×C47—22no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—42no—
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×Q811yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×Dic47—22no—
65C2×Dic47—22no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68C2×Dic47—42no—
69C2×Dic47—42no—
70C2×Dic47Q1614yes—
71C8×C47—22no—
72C47⋊C8—22no—
73C22×C47C22⋊Q811yescharacteristic
74C22×C47#12311yescharacteristic
75C22×C47#12711yescharacteristic
76C22×C47C2×Q1612yes—
77C22×C47AGL(1,ℤ/8)12yes—
78C4×C47—42no—
79C4×C47—81no—
80C4×C47C22⋊Q811yescharacteristic
81C4×C47C22⋊Q811yescharacteristic
82C4×C47#12311yescharacteristic
83C4×C47#12311yescharacteristic
84Dic47—24no—
85Dic47—81no—
86Dic47—81no—
87#2095—471nomaximal, Sylow
88C2×C47#39911yescharacteristic
89C2×C47#47712yes—
90C2×C47#48412yes—
91C2×C47#49411yescharacteristic
92C2×C47#49611yescharacteristic
93C2×#107—471no—
94C2×#107—471no—
95C2×#103—471no—
96C2×#103D4711yescharacteristic
97#391—471no—
98#384—471no—
99#336—471no—
100C47#209511yescharacteristic, complemented, Sylow
101C22×Q8C2×D4711yescharacteristic
102C22×C8—471no—
103C22×C8C2×D4711yescharacteristic
104C2×C4⋊C4—471no—
105C2×C4⋊C4—471no—
106C2×C4⋊C4—942no—
107C2×C4⋊C4C2×D4711yescharacteristic
108C2×C42—471no—
109#107—942no—
110#107—942no—
111#103—22no—
112#103—942no—
113#95—942no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8Dic9412yes—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—472no—
123C22×C4—941no—
124C22×C4—941no—
125C22×C4C22×D4711yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—472no—
129C2×C8—941no—
130C2×C8—941no—
131C2×C8C22⋊D4712yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—941no—
135C4⋊C4—941no—
136C4⋊C4—941no—
137C4⋊C4—941no—
138C4⋊C4—1884no—
139C42—941no—
140C42—941no—
141C23D4×D4711yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—41no—
145Q8—41no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—42no—
151C2×C4—474no—
152C2×C4—942no—
153C2×C4—942no—
154C2×C4—1881no—
155C2×C4—1881no—
156C2×C4—1882no—
157C2×C4—1882no—
158C2×C4C2×Dic9411yescharacteristic
159C2×C4#1062535011yescharacteristic
160C2×C4D4×D4711yescharacteristic
161C2×C4#1062535211yescharacteristic
162C2×C4#1062535211yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C8—22no—
165C8—942no—
166C22#1309400111yescharacteristic
167C22#1309400611yescharacteristic
168C22#1309402011yescharacteristic
169C22Q16×D4712yes—
170C22#1309405112yes—
171C4—42no—
172C4—81no—
173C4—944no—
174C4—3761no—
175C4—3761no—
176C4#1309400111yescharacteristic
177C4#1309400311yescharacteristic
178C4#1309400511yescharacteristic
179C4#1309400611yescharacteristic
180C2#1568905911yescharacteristic
181C2#1568941612yes—
182C2#1568945712yes—
183C2#1568950111yescharacteristic
184C2#1568950911yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#2095
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
100. C47#2095semidirect