Finite Group Databasebeta

← #20276256

Subgroups — #20276256

Order 6784.

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

normal subgroups only

This group has 254 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×#13133149C211yesmaximal, characteristic
2C2×#13133148C211yesmaximal, characteristic
3C2×#13133141C211yesmaximal, characteristic
4#16810530C211yesmaximal, characteristic
5#16810492C211yesmaximal, characteristic
6#16810377C211yesmaximal, characteristic
7C2×#103×C53C211yesmaximal, characteristic
8C22×#88322C2211yescharacteristic
9C2×C4⋊Dic53C2211yescharacteristic
10C2×C4⋊Dic53C2211yescharacteristic
11C2×#11719919—22no—
12C2×C4×Dic53C2211yescharacteristic
13#13133149—22no—
14#13133148—22no—
15#13133141—22no—
16#13133124—22no—
17C22×Q8×C53C2211yescharacteristic
18C22×C8×C53C2211yescharacteristic
19C2×C4⋊C4×C53C2211yescharacteristic
20#103×C53—22no—
21C2×Q8×C53—21no—
22C2×Q8×C53—21no—
23C2×Q8×C53—21no—
24C2×Q8×C53—21no—
25C2×Q8×C53—21no—
26C2×Q8×C53Q812yes—
27C22×C4×C53—21no—
28C22×C4×C53—21no—
29C22×C4×C53C2311yescharacteristic
30C22×Dic53—21no—
31C22×Dic53—21no—
32C22×Dic53D412yes—
33C2×C8×C53—21no—
34C2×C8×C53—21no—
35C2×C8×C53D412yes—
36C4⋊C4×C53—21no—
37C4⋊C4×C53—21no—
38C4⋊Dic53—21no—
39C4⋊Dic53—21no—
40C4⋊Dic53—21no—
41C4⋊Dic53—21no—
42#11719919—44no—
43C4×Dic53—21no—
44C4×Dic53—21no—
45C2×#88322—21no—
46C2×#88322—21no—
47C2×#88322D412yes—
48C23×C53C2×D411yescharacteristic
49Q8×C53—22no—
50Q8×C53—22no—
51Q8×C53—41no—
52Q8×C53—41no—
53C2×C4×C53—22no—
54C2×C4×C53—41no—
55C2×C4×C53—41no—
56C2×C4×C53—41no—
57C2×C4×C53—42no—
58C2×C4×C53C2×D411yescharacteristic
59C2×C4×C53C2×D411yescharacteristic
60C2×C4×C53C2×Q811yescharacteristic
61C2×C4×C53#4111yescharacteristic
62C2×C4×C53#4111yescharacteristic
63C2×C4×C53#4111yescharacteristic
64C2×Dic53—22no—
65C2×Dic53—22no—
66C2×Dic53—41no—
67C2×Dic53—41no—
68C2×Dic53—42no—
69C2×Dic53—42no—
70C2×Dic53SD1614yes—
71C8×C53—22no—
72#88322—22no—
73C22×C53C22⋊Q811yescharacteristic
74C22×C53#12311yescharacteristic
75C22×C53#12711yescharacteristic
76C22×C53C2×SD1612yes—
77C22×C53#13712yes—
78C4×C53—42no—
79C4×C53—81no—
80C4×C53C22⋊Q811yescharacteristic
81C4×C53C22⋊Q811yescharacteristic
82C4×C53#12311yescharacteristic
83C4×C53#12311yescharacteristic
84Dic53—24no—
85Dic53—81no—
86Dic53—81no—
87#2096—531nomaximal, Sylow
88C2×C53#39911yescharacteristic
89C2×C53#47512yes—
90C2×C53#48312yes—
91C2×C53#49211yescharacteristic
92C2×C53#49711yescharacteristic
93C2×#106—531no—
94C2×#106—531no—
95C2×#103—531no—
96C2×#103D5311yescharacteristic
97#391—531no—
98#384—531no—
99#336—531no—
100C53#209611yescharacteristic, complemented, Sylow
101C22×Q8C2×D5311yescharacteristic
102C22×C8—531no—
103C22×C8C2×D5311yescharacteristic
104C2×C4⋊C4—531no—
105C2×C4⋊C4—531no—
106C2×C4⋊C4—1062no—
107C2×C4⋊C4C2×D5311yescharacteristic
108C2×C42—531no—
109#106—1062no—
110#106—1062no—
111#103—22no—
112#103—1062no—
113#95—1062no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8Dic10612yes—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—532no—
123C22×C4—1061no—
124C22×C4—1061no—
125C22×C4C22×D5311yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—532no—
129C2×C8—1061no—
130C2×C8—1061no—
131C2×C8C22⋊D5312yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—1061no—
135C4⋊C4—1061no—
136C4⋊C4—1061no—
137C4⋊C4—1061no—
138C4⋊C4—2124no—
139C42—1061no—
140C42—1061no—
141C23D4×D5311yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—41no—
145Q8—41no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—42no—
151C2×C4—534no—
152C2×C4—1062no—
153C2×C4—1062no—
154C2×C4—2121no—
155C2×C4—2121no—
156C2×C4—2122no—
157C2×C4—2122no—
158C2×C4C2×Dic10611yescharacteristic
159C2×C4#1171994511yescharacteristic
160C2×C4D4×D5311yescharacteristic
161C2×C4#1171994711yescharacteristic
162C2×C4#1171994711yescharacteristic
163C2×C4C2×C22⋊D5311yescharacteristic
164C8—22no—
165C8—1062no—
166C22#1313319411yescharacteristic
167C22#1313319911yescharacteristic
168C22#1313321311yescharacteristic
169C22SD16×D5312yes—
170C22#1313324912yes—
171C4—42no—
172C4—81no—
173C4—1064no—
174C4—4241no—
175C4—4241no—
176C4#1313319411yescharacteristic
177C4#1313319611yescharacteristic
178C4#1313319811yescharacteristic
179C4#1313319911yescharacteristic
180C2#1681055911yescharacteristic
181C2#1681090612yes—
182C2#1681095212yes—
183C2#1681099411yescharacteristic
184C2#1681101611yescharacteristic
subgroupG/H
centerC23D4×D53
commutatorC22×C4×C53C23
FrattiniC22×C4C22×D53
FittingC2×#103×C53C2
socleC23×C53C2×D4
hypercenterC2×#103D53
hypocenterC53#2096
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
100. C53#2096semidirect