Finite Group Databasebeta

← #20244726

Subgroups — #20244726

Order 6016.

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

normal subgroups only

This group has 250 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×#13094016C211yesmaximal, characteristic
2C2×#13093957C211yesmaximal, characteristic
3C2×#13093955C211yesmaximal, characteristic
4#15688885C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688878C211yesmaximal, characteristic
7C47×#389C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094016—22no—
11#13094016—22no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×Dic47⋊C4—21no—
16#13093957—22no—
17#13093955—22no—
18C2×C4⋊C4×C47—21no—
19C2×C4⋊C4×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic
21C2×C42×C47C2211yescharacteristic
22#95×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—21no—
29C22×Dic47—21no—
30C4⋊C4×C47—21no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—42no—
34C4⋊C4×C47Q812yes—
35C42×C47—21no—
36C42×C47—21no—
37C4⋊Dic47—21no—
38C4⋊Dic47—21no—
39C4⋊Dic47D412yes—
40C4⋊Dic47D412yes—
41Dic47⋊C4—24no—
42Dic47⋊C4—24no—
43C2×C47⋊C8—21no—
44C2×C47⋊C8—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8Q812yes—
48C2×C47⋊C8Q812yes—
49C23×C47C2×D411yescharacteristic
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—22no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×Q811yescharacteristic
65C2×C4×C47C2×Q811yescharacteristic
66C2×C4×C47C2×Q811yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74C47⋊C8—22no—
75C47⋊C8—22no—
76C22×C47#12011yescharacteristic
77C22×C47C22⋊Q811yescharacteristic
78C22×C47C4⋊Q811yescharacteristic
79C22×C47#13511yescharacteristic
80C22×C47#13511yescharacteristic
81C22×C47AGL(1,ℤ/8)11yescharacteristic
82C22×C47#13711yescharacteristic
83C4×C47—41no—
84C4×C47—41no—
85C4×C47—42no—
86C4×C47—81no—
87C4×C47C22⋊Q811yescharacteristic
88C4×C47C22⋊Q811yescharacteristic
89C4×C47C4⋊Q811yescharacteristic
90C4×C47C4⋊Q811yescharacteristic
91Dic47—42no—
92Dic47—42no—
93#2059—471nomaximal, Sylow
94C2×C47#39511yescharacteristic
95C2×C47#44911yescharacteristic
96C2×C47#45211yescharacteristic
97C2×C47#47811yescharacteristic
98C2×C47#47911yescharacteristic
99C2×C47#49911yescharacteristic
100C2×C47#50111yescharacteristic
101C2×#125—471no—
102C2×#107—471no—
103C2×#106—471no—
104#389D4711yescharacteristic
105#340—471no—
106#340—471no—
107#336—471no—
108C47#205911yescharacteristic, complemented, Sylow
109C22×C8—471no—
110C22×C8—471no—
111#125—942no—
112#125—942no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—471no—
115C2×C4⋊C4—471no—
116C2×C4⋊C4—941no—
117C2×C4⋊C4—941no—
118C2×C4⋊C4C2×D4711yescharacteristic
119C2×C4⋊C4C2×D4711yescharacteristic
120C2×C42C2×D4711yescharacteristic
121#107—942no—
122#106—942no—
123#95—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—941no—
127C22×C4—941no—
128C22×C4C22⋊D4711yescharacteristic
129C22×C4C22⋊D4711yescharacteristic
130C22×C4C22×D4711yescharacteristic
131C2×C8—472no—
132C2×C8—472no—
133C2×C8—941no—
134C2×C8—941no—
135C2×C8—941no—
136C2×C8—941no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—42no—
141C4⋊C4—472no—
142C4⋊C4—472no—
143C4⋊C4—944no—
144C4⋊C4—944no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C4⋊C4Dic9412yes—
148C42—21no—
149C42—21no—
150C23C2×C22⋊D4711yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—942no—
164C2×C4—942no—
165C2×C4—1881no—
166C2×C4—1881no—
167C2×C4—1881no—
168C2×C4—1881no—
169C2×C4C2×Dic9411yescharacteristic
170C2×C4#1062535011yescharacteristic
171C2×C4D4×D4711yescharacteristic
172C2×C4D4×D4711yescharacteristic
173C2×C4Q8×D4711yescharacteristic
174C2×C4Q8×D4711yescharacteristic
175C8—942no—
176C8—942no—
177C22#1309399211yescharacteristic
178C22#1309400311yescharacteristic
179C22#1309402211yescharacteristic
180C22#1309404411yescharacteristic
181C22#1309404411yescharacteristic
182C22#1309405011yescharacteristic
183C22#1309405511yescharacteristic
184C4—41no—
185C4—41no—
186C4—42no—
187C4—81no—
188C4—1882no—
189C4—1882no—
190C4#1309400211yescharacteristic
191C4#1309400211yescharacteristic
192C4#1309402311yescharacteristic
193C4#1309402311yescharacteristic
194C2#1568904311yescharacteristic
195C2#1568926611yescharacteristic
196C2#1568928311yescharacteristic
197C2#1568942311yescharacteristic
198C2#1568943011yescharacteristic
199C2#1568952211yescharacteristic
200C2#1568952911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#389C2
socleC23×C47C2×D4
hypercenter#389D47
hypocenterC47#2059
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
108. C47#2059semidirect