Finite Group Databasebeta

← #20282891

Subgroups — #20282891

Order 6784.

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

normal subgroups only

This group has 332 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
1C53⋊#401C212yesmaximal
2#16810565C212yesmaximal
3#16810564C212yesmaximal
4#16810562C211yesmaximal, characteristic
5#16810557C212yesmaximal
6#16810553C211yesmaximal, characteristic
7#16810542C212yesmaximal
8#16810507C212yesmaximal
9C53×#391C211yesmaximal, characteristic
10C2×C4⋊Dic53C2211yescharacteristic
11C2×C4⋊Dic53C2211yescharacteristic
12C2×#11719919C2212yes—
13C2×#11719919C2212yes—
14C2×#11719919C2212yes—
15C2×#11719919C2212yes—
16#13133124C2212yes—
17#13133124C2212yes—
18#13133124C2212yes—
19#13133124C2212yes—
20#13133124C2212yes—
21#13133124C2212yes—
22#13133124C2212yes—
23#13133124C2211yescharacteristic
24#13133124C2212yes—
25#13133124C2211yescharacteristic
26C22×Q8×C53C2211yescharacteristic
27C2×C4⋊C4×C53C2211yescharacteristic
28C2×C42×C53C2211yescharacteristic
29#95×C53C2212yes—
30#95×C53C2212yes—
31C2×Q8×C53—22no—
32C2×Q8×C53—41no—
33C2×Q8×C53—41no—
34C22×C4×C53C2312yes—
35C22×C4×C53C2311yescharacteristic
36C22×C4×C53C2311yescharacteristic
37C22×C4×C53C2312yes—
38C22×C4×C53C2311yescharacteristic
39C22×Dic53C2312yes—
40C22×Dic53C2312yes—
41C22×Dic53C2312yes—
42C22×Dic53C2312yes—
43C4⋊C4×C53—41no—
44C42×C53—41no—
45C4⋊Dic53—41no—
46C4⋊Dic53—41no—
47#11719919—24no—
48#11719919—42no—
49#11719919—42no—
50#11719919—42no—
51C23×C53C2411yescharacteristic
52Q8×C53—44no—
53C2×C4×C53—21no—
54C2×C4×C53—21no—
55C2×C4×C53—22no—
56C2×C4×C53—22no—
57C2×C4×C53—22no—
58C2×C4×C53—22no—
59C2×C4×C53—21no—
60C2×C4×C53—21no—
61C2×C4×C53—22no—
62C2×C4×C53—22no—
63C2×C4×C53—22no—
64C2×C4×C53—22no—
65C2×C4×C53#4112yes—
66C2×Dic53—22no—
67C2×Dic53—22no—
68C2×Dic53—22no—
69C2×Dic53—22no—
70C2×Dic53—22no—
71C2×Dic53—22no—
72C2×Dic53—22no—
73C2×Dic53—22no—
74C2×Dic53—22no—
75C2×Dic53—22no—
76C2×Dic53—24no—
77C22×C53C2×#4111yescharacteristic
78C22×C53H(5,𝔽2)11yescharacteristic
79C22×C53H(5,𝔽2)11yescharacteristic
80C22×C532−1+412yes—
81C22×C532−1+412yes—
82C4×C53—22no—
83C4×C53—42no—
84C4×C53—41no—
85C4×C53—41no—
86C4×C53—42no—
87Dic53—42no—
88Dic53—42no—
89Dic53—42no—
90Dic53—42no—
91#2833—531nomaximal, Sylow
92C2×C53#53811yescharacteristic
93C2×C53#54112yes—
94C2×C53#56311yescharacteristic
95C2×C53#56311yescharacteristic
96C2×C53#56312yes—
97#401—532no—
98#400—531no—
99#400—532no—
100#400—532no—
101#398—531no—
102#398—532no—
103#395—532no—
104#391D5311yescharacteristic
105#387—532no—
106C53#283311yescharacteristic, complemented, Sylow
107C22×Q8C2×D5311yescharacteristic
108C2×C4⋊C4—532no—
109C2×C4⋊C4—532no—
110C2×C4⋊C4—532no—
111C2×C4⋊C4—532no—
112C2×C4⋊C4—531no—
113C2×C4⋊C4—531no—
114C2×C4⋊C4C2×D5311yescharacteristic
115C2×C42C2×D5311yescharacteristic
116#95—532no—
117#95—532no—
118#95—532no—
119#95—532no—
120#95—532no—
121#95—532no—
122#95—532no—
123#95—532no—
124#95—531no—
125#95—531no—
126#95C2×D5312yes—
127#95C2×D5312yes—
128C2×Q8—22no—
129C2×Q8—41no—
130C2×Q8—41no—
131C22×C4—532no—
132C22×C4—532no—
133C22×C4—532no—
134C22×C4—532no—
135C22×C4C22×D5312yes—
136C22×C4C22×D5311yescharacteristic
137C22×C4C22×D5311yescharacteristic
138C22×C4C22×D5312yes—
139C22×C4C22×D5311yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—1064no—
142C4⋊C4—2122no—
143C4⋊C4—2122no—
144C4⋊C4—2122no—
145C4⋊C4—2121no—
146C4⋊C4—2121no—
147C42—41no—
148C23C23×D5311yescharacteristic
149Q8—44no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—1062no—
163C2×C4—1062no—
164C2×C4—1062no—
165C2×C4—1062no—
166C2×C4—1062no—
167C2×C4—1062no—
168C2×C4—1062no—
169C2×C4—1062no—
170C2×C4—1064no—
171C2×C4—1062no—
172C2×C4—1062no—
173C2×C4#1171994512yes—
174C22C2×#1171994511yescharacteristic
175C22#1313326211yescharacteristic
176C22#1313326211yescharacteristic
177C22#1313326412yes—
178C22#1313326512yes—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—42no—
183C4—42no—
184C4—2122no—
185C4—2122no—
186C4—2122no—
187C4—2122no—
188C2#1681121111yescharacteristic
189C2#1681123112yes—
190C2#1681137211yescharacteristic
191C2#1681137311yescharacteristic
192C2#1681137412yes—
subgroupG/H
center, FrattiniC23C23×D53
commutator, socleC23×C53C24
FittingC53×#391C2
hypercenter#391D53
hypocenterC53#2833
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
106. C53#2833semidirect