Finite Group Databasebeta

← #20244524

Subgroups — #20244524

Order 6016.

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

normal subgroups only

This group has 326 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×#13094024C211yesmaximal, characteristic, complemented
2C2×#13093945C212yesmaximal
3#15688885C212yesmaximal, complemented
4#15688878C211yesmaximal, characteristic, complemented
5C47×#390C211yesmaximal, characteristic
6C22×Dic94—21no—
7C22×C47⋊C8C2212yes—
8#13094024—24no—
9C2×C4⋊Dic47—21no—
10C2×C4⋊Dic47C2212yes—
11#13093945—24no—
12C22×D4×C47C2211yescharacteristic
13C2×C4⋊C4×C47C2211yescharacteristic
14C2×C22⋊C4×C47—21no—
15C2×C22⋊C4×C47—21no—
16C2×C42×C47C2211yescharacteristic
17C24×C47—21no—
18C2×D4×C47—22no—
19C2×D4×C47—22no—
20C2×D4×C47—21no—
21C2×D4×C47Q812yescomplemented
22C22×C4×C47—21no—
23C22×C4×C47D411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—22no—
27C2×Dic94—24no—
28C2×Dic94—42no—
29C2×Dic94—42no—
30C4⋊C4×C47—22no—
31C22⋊C4×C47—42no—
32C22⋊C4×C47—42no—
33C42×C47—22no—
34C4⋊Dic47—24no—
35C4⋊Dic47—22no—
36C4⋊Dic47D414yes—
37C2×C47⋊C8—22no—
38C2×C47⋊C8—22no—
39C2×C47⋊C8—22no—
40C23×C47—22no—
41C23×C47—41no—
42C23×C47—41no—
43C23×C47—41no—
44C23×C47—41no—
45C23×C47—41no—
46C23×C47—41no—
47C23×C47C2×D411yescharacteristic
48D4×C47—24no—
49D4×C47—42no—
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47D812yes—
58C2×C4×C47SD1612yes—
59C2×C4×C47C2×D412yes—
60C2×C4×C47C2×Q811yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×C4×C47#4112yes—
63C2×Dic47—24no—
64C2×Dic47—42no—
65C2×Dic47—42no—
66Dic94—48no—
67C47⋊C8—42no—
68C22×C47—42no—
69C22×C47—42no—
70C22×C47—42no—
71C22×C47—81no—
72C22×C47—81no—
73C22×C47—81no—
74C22×C47—81no—
75C22×C47#12011yescharacteristic
76C22×C47C22⋊Q811yescharacteristic
77C22×C47#12411yescharacteristic
78C22×C47C2×D811yescharacteristic
79C22×C47C2×SD1611yescharacteristic
80C22×C47AGL(1,ℤ/8)11yescharacteristic
81C22×C47#13711yescharacteristic
82C4×C47—22no—
83C4×C47—22no—
84C4×C47—81no—
85C4×C47C22⋊Q812yes—
86C4×C47#12412yes—
87Dic47—44no—
88#2023—471nomaximal, Sylow
89C2×C47—82no—
90C2×C47#39311yescharacteristic
91C2×C47#44711yescharacteristic
92C2×C47#44811yescharacteristic
93C2×C47#47411yescharacteristic
94C2×C47#47611yescharacteristic
95C2×C47#48611yescharacteristic
96C2×C47#48911yescharacteristic
97C2×C4⋊Q8—471no—
98C2×#102—472no—
99#390D4711yescharacteristic
100#340—472no—
101#336—471no—
102C47#202311yescharacteristic, complemented, Sylow
103C22×Q8—941no—
104C22×D4C2×D4711yescharacteristic
105C22×C8—472no—
106C4⋊Q8—944no—
107C2×C4⋊C4—472no—
108C2×C4⋊C4—941no—
109C2×C4⋊C4C2×D4711yescharacteristic
110C2×C22⋊C4—21no—
111C2×C22⋊C4—21no—
112C2×C42C2×D4711yescharacteristic
113#102—944no—
114C24—21no—
115C2×Q8—944no—
116C2×Q8—1882no—
117C2×Q8—1882no—
118C2×D4—21no—
119C2×D4—22no—
120C2×D4—22no—
121C2×D4Dic9412yescomplemented
122C22×C4—21no—
123C22×C4—942no—
124C22×C4C22⋊D4711yescharacteristic
125C22×C4C22⋊D4711yescharacteristic
126C22×C4C22×D4711yescharacteristic
127C2×C8—942no—
128C2×C8—942no—
129C2×C8—942no—
130C4⋊C4—22no—
131C4⋊C4—474no—
132C4⋊C4—944no—
133C4⋊C4—942no—
134C22⋊C4—42no—
135C22⋊C4—42no—
136C42—22no—
137C23—22no—
138C23—41no—
139C23—41no—
140C23—41no—
141C23—41no—
142C23—41no—
143C23—41no—
144C23C2×C22⋊D4711yescharacteristic
145Q8—1888no—
146D4—24no—
147D4—42no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—944no—
156C2×C4—1882no—
157C2×C4—1882no—
158C2×C4#1062533412yes—
159C2×C4#1062533512yes—
160C2×C4C2×Dic9411yescharacteristic
161C2×C4#1062535011yescharacteristic
162C2×C4D4×D4712yes—
163C2×C4#1062535212yes—
164C8—1882no—
165C22—42no—
166C22—42no—
167C22—42no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22#1309399211yescharacteristic
173C22#1309400311yescharacteristic
174C22#1309401111yescharacteristic
175C22C2×#1062533411yescharacteristic
176C22C2×#1062533511yescharacteristic
177C22#1309404911yescharacteristic
178C22#1309405411yescharacteristic
179C4—22no—
180C4—22no—
181C4—81no—
182C4—1884no—
183C4#1309400112yes—
184C4#1309401012yes—
185C2—82no—
186C2#1568903511yescharacteristic
187C2#1568925611yescharacteristic
188C2#1568926111yescharacteristic
189C2#1568940311yescharacteristic
190C2#1568941311yescharacteristic
191C2#1568946911yescharacteristic
192C2#1568948211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#390C2
socleC23×C47C2×D4
hypercenter#390D47
hypocenterC47#2023
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13094024C2semidirect
3. #15688885C2semidirect
4. #15688878C2semidirect
21. C2×D4×C47Q8semidirect
102. C47#2023semidirect
121. C2×D4Dic94semidirect