Finite Group Databasebeta

← #20244949

Subgroups — #20244949

Order 6016.

214 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 83 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#15689022C211yesmaximal, characteristic
2#15688992C211yesmaximal, characteristic
3#15688886C211yesmaximal, characteristic
4#15688885C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C2×C4⋊Dic47—21no—
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13C2×Dic47⋊C4—21no—
14C2×C4×Dic47C2211yescharacteristic
15C47⋊#95—21no—
16C22×C8×C47C2211yescharacteristic
17C2×C4⋊C4×C47C2211yescharacteristic
18C2×C4⋊C4×C47C2211yescharacteristic
19C22×C4×C47—21no—
20C22×C4×C47—21no—
21C22×C4×C47C2311yescharacteristic
22C22×Dic47—21no—
23C22×Dic47—21no—
24C22×Dic47D411yescharacteristic
25C22×Dic47D411yescharacteristic
26C2×C8×C47—21no—
27C2×C8×C47—21no—
28C2×C8×C47—21no—
29C4⋊C4×C47—21no—
30C4⋊C4×C47—21no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47Q812yes—
33C4⋊Dic47—21no—
34C4⋊Dic47—21no—
35C4⋊Dic47—21no—
36C4⋊Dic47—21no—
37C4⋊Dic47—42no—
38Dic47⋊C4—42no—
39Dic47⋊C4—42no—
40C4×Dic47—21no—
41C4×Dic47—21no—
42C2×C47⋊C8—21no—
43C2×C47⋊C8—21no—
44C2×C47⋊C8—21no—
45C23×C47C2×D411yescharacteristic
46C2×C4×C47—22no—
47C2×C4×C47—41no—
48C2×C4×C47—41no—
49C2×C4×C47—41no—
50C2×C4×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47C2×Q811yescharacteristic
53C2×C4×C47#4111yescharacteristic
54C2×C4×C47#4111yescharacteristic
55C2×C4×C47#4111yescharacteristic
56C2×C4×C47#4111yescharacteristic
57C2×C4×C47#4111yescharacteristic
58C2×Dic47—21no—
59C2×Dic47—21no—
60C2×Dic47—21no—
61C2×Dic47—21no—
62C2×Dic47—41no—
63C2×Dic47—41no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68C2×Dic47D812yes—
69C2×Dic47SD1612yes—
70C8×C47—41no—
71C47⋊C8—41no—
72C22×C47C22⋊Q811yescharacteristic
73C22×C47#12311yescharacteristic
74C22×C47#12411yescharacteristic
75C22×C47C2×D811yescharacteristic
76C22×C47C2×SD1611yescharacteristic
77C22×C47#13711yescharacteristic
78C22×C47#13711yescharacteristic
79C4×C47—42no—
80C4×C47—81no—
81C4×C47#12511yescharacteristic
82C4×C47#12511yescharacteristic
83C4×C47#12611yescharacteristic
84C4×C47#12611yescharacteristic
85Dic47—22no—
86Dic47—22no—
87Dic47—81no—
88Dic47—81no—
89#2099—471nomaximal, Sylow
90C2×C47#40011yescharacteristic
91C2×C47#47411yescharacteristic
92C2×C47#47511yescharacteristic
93C2×C47#48011yescharacteristic
94C2×C47#48311yescharacteristic
95C2×C47#48611yescharacteristic
96C2×C47#49111yescharacteristic
97#389—471no—
98#384—471no—
99#340—471no—
100#340—471no—
101#340—471no—
102#340D4711yescharacteristic
103#336—471no—
104C47#209911yescharacteristic, complemented, Sylow
105C22×C8—471no—
106C22×C8C2×D4711yescharacteristic
107C2×C4⋊C4—471no—
108C2×C4⋊C4—471no—
109C2×C4⋊C4—941no—
110C2×C4⋊C4—941no—
111C2×C4⋊C4—941no—
112C2×C4⋊C4C2×D4711yescharacteristic
113C2×C4⋊C4C2×D4711yescharacteristic
114C2×C42—471no—
115#95—941no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—471no—
119C22×C4—471no—
120C22×C4—941no—
121C22×C4—941no—
122C22×C4C22×D4711yescharacteristic
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—941no—
127C2×C8—941no—
128C2×C8—941no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—941no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4—941no—
136C4⋊C4—1882no—
137C4⋊C4—1882no—
138C4⋊C4—1882no—
139C4⋊C4Dic9412yes—
140C42—941no—
141C42—941no—
142C23D4×D4711yescharacteristic
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—472no—
150C2×C4—472no—
151C2×C4—941no—
152C2×C4—941no—
153C2×C4—941no—
154C2×C4—941no—
155C2×C4—1881no—
156C2×C4—1881no—
157C2×C4—1881no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4—1881no—
161C2×C4C2×Dic9411yescharacteristic
162C2×C4#1062535011yescharacteristic
163C2×C4#1062535011yescharacteristic
164C2×C4#1062535211yescharacteristic
165C2×C4#1062535211yescharacteristic
166C2×C4#1062535411yescharacteristic
167C8—41no—
168C8—1881no—
169C22#1309400111yescharacteristic
170C22#1309400911yescharacteristic
171C22#1309401011yescharacteristic
172C22D8×D4711yescharacteristic
173C22SD16×D4711yescharacteristic
174C22#1309405311yescharacteristic
175C22#1309405611yescharacteristic
176C4—42no—
177C4—81no—
178C4—942no—
179C4—942no—
180C4—3761no—
181C4—3761no—
182C4#1309401511yescharacteristic
183C4#1309401611yescharacteristic
184C4#1309401711yescharacteristic
185C4#1309401911yescharacteristic
186C2#1568906511yescharacteristic
187C2#1568940111yescharacteristic
188C2#1568940611yescharacteristic
189C2#1568943811yescharacteristic
190C2#1568945511yescharacteristic
191C2#1568946811yescharacteristic
192C2#1568949011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#2099
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
104. C47#2099semidirect