Finite Group Databasebeta

← #20243520

Subgroups — #20243520

Order 6016.

224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13093934C211yesmaximal, characteristic
2#15688992C211yesmaximal, characteristic
3#15688988C211yesmaximal, characteristic
4#15688886C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—21no—
12C2×Dic47⋊C4—21no—
13C2×C4×Dic47C2211yescharacteristic
14#13093934C414yescomplemented
15C47⋊#95—21no—
16C47⋊#95—21no—
17C22×C8×C47C2211yescharacteristic
18C2×C4⋊C4×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20C22×C4×C47—21no—
21C22×C4×C47—21no—
22C22×C4×C47C2311yescharacteristic
23C22×Dic47—21no—
24C22×Dic47—21no—
25C22×Dic47D411yescharacteristic
26C22×Dic47D411yescharacteristic
27C2×C8×C47—21no—
28C2×C8×C47—21no—
29C2×C8×C47C2×C412yes—
30C4⋊C4×C47—21no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊Dic47—21no—
35C4⋊Dic47—21no—
36C4⋊Dic47—21no—
37C4⋊Dic47—21no—
38Dic47⋊C4—42no—
39Dic47⋊C4—42no—
40C4×Dic47C2×C412yes—
41C4×Dic47Q812yes—
42C2×C47⋊C8—21no—
43C2×C47⋊C8—21no—
44C2×C47⋊C8C2×C412yes—
45C23×C47C2×D411yescharacteristic
46C2×C4×C47—41no—
47C2×C4×C47—41no—
48C2×C4×C47—41no—
49C2×C4×C47—41no—
50C2×C4×C47—41no—
51C2×C4×C47—41no—
52C2×C4×C47C22×C411yescharacteristic
53C2×C4×C47C2×Q811yescharacteristic
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×Dic47C4⋊C412yes—
69C2×Dic47C4⋊C412yes—
70C8×C47—22no—
71C47⋊C8—22no—
72C22×C47C2×C4⋊C411yescharacteristic
73C22×C47#12411yescharacteristic
74C22×C47#12411yescharacteristic
75C22×C47AGL(1,ℤ/8)11yescharacteristic
76C22×C47AGL(1,ℤ/8)11yescharacteristic
77C22×C47#13711yescharacteristic
78C22×C47#13711yescharacteristic
79C4×C47—81no—
80C4×C47—81no—
81C4×C47#11711yescharacteristic
82C4×C47#11711yescharacteristic
83C4×C47#12511yescharacteristic
84C4×C47#12511yescharacteristic
85Dic47—22no—
86Dic47—22no—
87Dic47—81no—
88Dic47—81no—
89#1836—471nomaximal, Sylow
90C2×C47#38211yescharacteristic
91C2×C47#42811yescharacteristic
92C2×C47#42811yescharacteristic
93C2×C47#48911yescharacteristic
94C2×C47#48911yescharacteristic
95C2×C47#49011yescharacteristic
96C2×C47#49111yescharacteristic
97C2×#97—471no—
98#384—471no—
99#382—471no—
100#340—471no—
101#340—471no—
102#340—471no—
103#340D4711yescharacteristic
104C47#183611yescharacteristic, 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⋊C4C2×D4711yescharacteristic
112C2×C4⋊C4C2×D4711yescharacteristic
113C2×C42—471no—
114#97—474no—
115#95—941no—
116#95—941no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—471no—
120C22×C4—471no—
121C22×C4—941no—
122C22×C4—941no—
123C22×C4C22×D4711yescharacteristic
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—472no—
127C2×C8—941no—
128C2×C8—941no—
129C2×C8C4×D4712yes—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—941no—
135C4⋊C4—941no—
136C4⋊C4—941no—
137C4⋊C4—941no—
138C4⋊C4—1882no—
139C4⋊C4—1882no—
140C42—472no—
141C42—472no—
142C23D4×D4711yescharacteristic
143C2×C4—41no—
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×C4×D4711yescharacteristic
162C2×C4#1062535011yescharacteristic
163C2×C4#1062535011yescharacteristic
164C2×C4#1062535211yescharacteristic
165C2×C4#1062535211yescharacteristic
166C2×C4Q8×D4711yescharacteristic
167C8—22no—
168C8—942no—
169C22C4⋊C4×D4711yescharacteristic
170C22#1309401011yescharacteristic
171C22#1309401011yescharacteristic
172C22#1309404811yescharacteristic
173C22#1309405111yescharacteristic
174C22#1309405311yescharacteristic
175C22#1309405611yescharacteristic
176C4—81no—
177C4—81no—
178C4—942no—
179C4—942no—
180C4—3761no—
181C4—3761no—
182C4#1309398011yescharacteristic
183C4#1309398111yescharacteristic
184C4#1309401411yescharacteristic
185C4#1309401411yescharacteristic
186C2#1568898711yescharacteristic
187C2#1568916211yescharacteristic
188C2#1568916411yescharacteristic
189C2#1568948111yescharacteristic
190C2#1568948411yescharacteristic
191C2#1568948611yescharacteristic
192C2#1568949011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#1836
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
14. #13093934C4semidirect
104. C47#1836semidirect