Finite Group Databasebeta

← #20244255

Subgroups — #20244255

Order 6016.

384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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, complemented
2C2×#13093945C212yesmaximal, complemented
3C2×C8×Dic47C211yesmaximal, characteristic, complemented
4#15689026C212yesmaximal, complemented
5C22×D8×C47C211yesmaximal, characteristic
6C22×C47⋊C8C2211yescharacteristic
7C2×C4⋊Dic47C2212yes—
8C2×C22⋊Dic47—24no—
9C2×C4×Dic47C2211yescharacteristic
10#13093958—22no—
11#13093945—24no—
12C8×Dic47—22no—
13C22×D4×C47C2212yes—
14C2×D8×C47—22no—
15C2×D8×C47—22no—
16C2×D8×C47C414yescomplemented
17C22×C8×C47C2211yescharacteristic
18C24×C47—22no—
19C2×D4×C47—22no—
20C2×D4×C47—22no—
21C2×D4×C47—22no—
22C2×D4×C47—22no—
23C2×D4×C47—22no—
24C2×D4×C47C2×C414yes—
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—22no—
27C22×Dic47D412yes—
28D8×C47—28no—
29C2×C8×C47C2×C412yes—
30C2×C8×C47D412yes—
31C2×C8×C47D412yes—
32C22⋊Dic47—48no—
33C4⋊Dic47—22no—
34C4⋊Dic47—22no—
35C4×Dic47—21no—
36C4×Dic47—21no—
37C2×C47⋊C8—21no—
38C2×C47⋊C8—21no—
39C2×C47⋊C8D412yes—
40C23×C47—24no—
41C23×C47—42no—
42C23×C47—42no—
43C23×C47—44no—
44C23×C47—44no—
45C23×C47C2×D411yescharacteristic
46D4×C47—24no—
47D4×C47—24no—
48D4×C47—42no—
49D4×C47—42no—
50C2×C4×C47C22×C411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47#4111yescharacteristic
55C2×C4×C47#4111yescharacteristic
56C2×Dic47—22no—
57C2×Dic47—22no—
58C2×Dic47—42no—
59C2×Dic47—44no—
60C2×Dic47D814yescomplemented
61C8×C47C22⋊C414yescomplemented
62C47⋊C8—22no—
63C22×C47—44no—
64C22×C47—48no—
65C22×C47—84no—
66C22×C47—82no—
67C22×C47—82no—
68C22×C47C4×D411yescharacteristic
69C22×C47#12111yescharacteristic
70C22×C47#12711yescharacteristic
71C22×C47C2×D812yes—
72C22×C47#13512yes—
73C4×C47C2×C22⋊C411yescharacteristic
74C4×C47C4×D411yescharacteristic
75C4×C47#12111yescharacteristic
76C4×C47#12411yescharacteristic
77Dic47—24no—
78Dic47—82no—
79#1970—471nomaximal, Sylow
80C2×C47—84no—
81C2×C47#39011yescharacteristic
82C2×C47C4×D812yes—
83C2×C47#46612yes—
84C2×C47#49311yescharacteristic
85C2×C47#49511yescharacteristic
86C22×D8D4711yescharacteristic
87C2×#107—471no—
88C2×#102—472no—
89C2×C4×C8—471no—
90#390—472no—
91C47#197011yescharacteristic, complemented, Sylow
92C22×D4C2×D4712yes—
93C2×D8—22no—
94C2×D8—22no—
95C2×D8Dic4714yescomplemented
96C22×C8—471no—
97C22×C8C2×D4711yescharacteristic
98C2×C4⋊C4—472no—
99C2×C22⋊C4—944no—
100C2×C42—471no—
101#107—942no—
102#102—944no—
103C4×C8—942no—
104C24—22no—
105C2×D4—22no—
106C2×D4—22no—
107C2×D4—22no—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4C2×Dic4714yes—
111C22×C4—472no—
112C22×C4—942no—
113C22×C4C22×D4711yescharacteristic
114D8—28no—
115C2×C8—472no—
116C2×C8—941no—
117C2×C8—941no—
118C2×C8C2×Dic4712yes—
119C2×C8C22⋊D4712yes—
120C2×C8C22⋊D4712yes—
121C4⋊C4—942no—
122C4⋊C4—942no—
123C22⋊C4—1888no—
124C42—941no—
125C42—941no—
126C23—24no—
127C23—42no—
128C23—42no—
129C23—44no—
130C23—44no—
131C23D4×D4711yescharacteristic
132D4—24no—
133D4—24no—
134D4—42no—
135D4—42no—
136C2×C4—474no—
137C2×C4—942no—
138C2×C4—942no—
139C2×C4—1882no—
140C2×C4—1884no—
141C2×C4D4×D4711yescharacteristic
142C2×C4#1062535211yescharacteristic
143C2×C4#1062535211yescharacteristic
144C2×C4C22×Dic4711yescharacteristic
145C2×C4C2×C22⋊D4711yescharacteristic
146C2×C4C2×C22⋊D4711yescharacteristic
147C8—942no—
148C8C22⋊Dic4714yescomplemented
149C22—44no—
150C22—48no—
151C22—82no—
152C22—82no—
153C22—84no—
154C22D4×Dic4711yescharacteristic
155C22#1309399511yescharacteristic
156C22#1309402011yescharacteristic
157C22D8×D4712yes—
158C22#1309404312yes—
159C4—944no—
160C4—3762no—
161C4C2×C22⋊Dic4711yescharacteristic
162C4D4×Dic4711yescharacteristic
163C4#1309399511yescharacteristic
164C4#1309401111yescharacteristic
165C2—84no—
166C2#1568902611yescharacteristic
167C2D8×Dic4712yes—
168C2#1568935612yes—
169C2#1568949811yescharacteristic
170C2#1568950611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×D8×C47C2
socleC23×C47C2×D4
hypercenterC22×D8D47
hypocenterC47#1970
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#13093958C2semidirect
2. C2×#13093945C2semidirect
3. C2×C8×Dic47C2semidirect
4. #15689026C2semidirect
16. C2×D8×C47C4semidirect
60. C2×Dic47D8semidirect
61. C8×C47C22⋊C4semidirect
91. C47#1970semidirect
95. C2×D8Dic47semidirect
148. C8C22⋊Dic47semidirect