Finite Group Databasebeta

← D53⋊#324 #20289944

Subgroups — D53⋊#324 #20289944

Order 6784.

328 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D53⋊(C22⋊C8)C212yesmaximal
2#16811469C212yesmaximal, complemented
3#16811468C212yesmaximal, complemented
4C2×C4⋊C4×D53C211yesmaximal, characteristic
5C2×D53⋊C8—22no—
6#13133274—22no—
7C22⋊#88324C2214yes—
8C22×C4×D53C411yescharacteristic
9C22×C4×D53C411yescharacteristic
10C22×C4×D53C2211yescharacteristic
11C2×C4⋊Dic53C2211yescharacteristic
12C2×#11719919C411yescharacteristic
13C2×#11719919C2211yescharacteristic
14C4⋊C4×D53—22no—
15C4⋊C4×D53—22no—
16C2×C4⋊C4×C53C411yescharacteristic
17C23×D53C2×C411yescharacteristic
18C22×C4×C53C2×C411yescharacteristic
19C22×C4×C53C2×C411yescharacteristic
20C22×C4×C53C2×C411yescharacteristic
21C22×Dic53C2×C411yescharacteristic
22C22×Dic53C2×C411yescharacteristic
23C22×Dic53C2311yescharacteristic
24C2×C4×D53—21no—
25C2×C4×D53—21no—
26C2×C4×D53—22no—
27C2×C4×D53—21no—
28C2×C4×D53—21no—
29C2×C4×D53—42no—
30C2×C4×D53—42no—
31C2×C4×D53C814yescomplemented
32C2×C4×D53D412yes—
33C2×C4×D53D412yes—
34C2×#88324—24no—
35D53⋊C8—44no—
36C4⋊C4×C53—22no—
37C4⋊Dic53—22no—
38#11719919—22no—
39#11719919—22no—
40C23×C53C22×C411yescharacteristic
41C22×D53—22no—
42C22×D53—22no—
43C22×D53C22⋊C411yescharacteristic
44C22×D53C22⋊C411yescharacteristic
45C22×D53C2×C812yes—
46C22×D53M1612yes—
47C2×C4×C53—21no—
48C2×C4×C53—21no—
49C2×C4×C53—21no—
50C2×C4×C53—41no—
51C2×C4×C53—41no—
52C2×C4×C53C22⋊C412yes—
53C2×C4×C53C2×C812yescomplemented
54C2×Dic53—21no—
55C2×Dic53—21no—
56C2×Dic53—21no—
57C2×Dic53—41no—
58C2×Dic53—41no—
59C2×Dic53C2×C812yescomplemented
60C2×Dic53C2×D412yes—
61C4×D53—24no—
62C4×D53—24no—
63C4×D53—24no—
64C4×D53—42no—
65C4×D53—42no—
66C4×D53—42no—
67#88324—44no—
68C22×C53—21no—
69C22×C53—21no—
70C22×C53C2×C22⋊C411yescharacteristic
71C22×C53C22×C811yescharacteristic
72C22×C53C2×M1611yescharacteristic
73C2×D53—21no—
74C2×D53—21no—
75C2×D53—24no—
76C2×D53—24no—
77C2×D53C22⋊C812yes—
78C2×D53C22⋊C812yes—
79C2×D53#9912yes—
80C2×D53#10112yes—
81C4×C53—22no—
82C4×C53—22no—
83C4×C53—41no—
84Dic53—22no—
85Dic53—22no—
86Dic53—41no—
87C2×#324—531nomaximal, Sylow
88C2×C53—21no—
89C2×C53—21no—
90C2×C53C2×C22⋊C811yescharacteristic
91C2×C53C2×#9911yescharacteristic
92C2×C53C2×#10111yescharacteristic
93D53—22no—
94D53#32414yescomplemented
95C22×C4⋊C4—531no—
96C2×C22⋊C8—532no—
97#324—532no—
98#324—532no—
99C53C2×#32411yescharacteristic, complemented, Sylow
100C23×C4—531no—
101C23×C4—531no—
102C23×C4—531no—
103C22×C8—1062no—
104C2×C4⋊C4—531no—
105C2×C4⋊C4—531no—
106C2×C4⋊C4—531no—
107C2×C4⋊C4—1062no—
108C2×C4⋊C4—1062no—
109C2×C4⋊C4#615711yescharacteristic
110C22⋊C8—534no—
111C22⋊C8—1062no—
112C24—531no—
113C22×C4—531no—
114C22×C4—531no—
115C22×C4—532no—
116C22×C4—534no—
117C22×C4—532no—
118C22×C4—531no—
119C22×C4—1061no—
120C22×C4—1061no—
121C22×C4—1062no—
122C22×C4—1061no—
123C22×C4—1061no—
124C22×C4—2122no—
125C22×C4—2122no—
126C22×C4C2×#615711yescharacteristic
127C22×C4C2×#615711yescharacteristic
128C22×C4C2×#615711yescharacteristic
129C2×C8—1064no—
130C2×C8—2124no—
131C4⋊C4—22no—
132C4⋊C4—1062no—
133C4⋊C4—1062no—
134C4⋊C4—1062no—
135C23—531no—
136C23—531no—
137C23—532no—
138C23—532no—
139C23—1062no—
140C23—1062no—
141C23C22×#615711yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—532no—
148C2×C4—532no—
149C2×C4—1064no—
150C2×C4—1064no—
151C2×C4—1064no—
152C2×C4—1061no—
153C2×C4—1061no—
154C2×C4—1061no—
155C2×C4—2122no—
156C2×C4—2122no—
157C2×C4—2122no—
158C2×C4—2121no—
159C2×C4—2121no—
160C2×C4D53⋊C812yescomplemented
161C2×C4C22⋊#615712yes—
162C8—2124no—
163C22—21no—
164C22—21no—
165C22—532no—
166C22—532no—
167C22—532no—
168C22—532no—
169C22—1064no—
170C22—1064no—
171C22—1061no—
172C22—1061no—
173C22C2×C22⋊#615711yescharacteristic
174C22C2×D53⋊C811yescharacteristic
175C22D53⋊M1611yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—1062no—
180C4—1062no—
181C4—2121no—
182C2—21no—
183C2—21no—
184C2—534no—
185C2—1062no—
186C2D53⋊(C22⋊C8)11yescharacteristic
187C2D53⋊#9911yescharacteristic
188C2D53⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6157
commutatorC22×C53C22×C8
FrattiniC23C22×#6157
FittingC2×C4⋊C4×C53C4
socleC22×C53C2×C22⋊C4
hypercenterC2×C4⋊C4#6157
hypocenterC53C2×#324
LCSG ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #16811469C2semidirect
3. #16811468C2semidirect
31. C2×C4×D53C8semidirect
53. C2×C4×C53C2×C8semidirect
59. C2×Dic53C2×C8semidirect
94. D53#324semidirect
99. C53C2×#324semidirect
160. C2×C4D53⋊C8semidirect