Finite Group Databasebeta

← D53⋊#352 #20290964

Subgroups — D53⋊#352 #20290964

Order 6784.

278 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 54 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⋊#100C211yesmaximal, characteristic
2D53⋊#99C211yesmaximal, characteristic
3#16811526C212yesmaximal, complemented
4#16811525C212yesmaximal, complemented
5#123×D53C211yesmaximal, characteristic
6D53⋊M16—21no—
7C2×C22⋊#6157—21no—
8#13133277—21no—
9#13133277C2212yes—
10#13133276—21no—
11#13133275C2212yes—
12C2×D4×D53C2211yescharacteristic
13C22×C4×D53C411yescharacteristic, complemented
14#13133202—21no—
15#13133201C2211yescharacteristic
16#13133200C2211yescharacteristic
17#13133199—21no—
18#13133198C411yescharacteristic, complemented
19C4⋊C4×D53—21no—
20C22⋊C4×D53—21no—
21C22⋊C4×D53C411yescharacteristic, complemented
22#123×C53C411yescharacteristic, complemented
23C23×D53C2×C411yescharacteristic
24C23×D53D411yescharacteristic
25C22×#6157—41no—
26C2×D4×C53C2×C411yescharacteristic
27C22×C4×C53C2×C411yescharacteristic, complemented
28C2×C22⋊D53D411yescharacteristic
29C2×C22⋊D53C2311yescharacteristic
30C22×Dic53C2×C411yescharacteristic, complemented
31D4×D53—41no—
32D4×D53—41no—
33C2×D212D411yescharacteristic
34C2×C4×D53—21no—
35C2×C4×D53—21no—
36C2×C4×D53—21no—
37C2×C4×D53—41no—
38C2×C4×D53—41no—
39C2×C4×D53D411yescharacteristic
40C22⋊#6157—22no—
41C22⋊#6157—41no—
42#11719940—22no—
43#11719936—41no—
44D53⋊C8—41no—
45C4⋊C4×C53—21no—
46C22⋊C4×C53—21no—
47C22⋊C4×C53C2×C411yescharacteristic, complemented
48C22⋊Dic53—21no—
49C22⋊Dic53C2×C411yescharacteristic, complemented
50#11719921—21no—
51#11719921—21no—
52#11719921—21no—
53C4⋊Dic53—21no—
54#11719919—21no—
55#11719919—21no—
56C23×C53C22⋊C411yescharacteristic
57C23×C53C22×C411yescharacteristic
58C22×D53—21no—
59C22×D53—21no—
60C22×D53—21no—
61C22×D53—21no—
62C22×D53—42no—
63C22×D53—42no—
64C22×D53C22⋊C411yescharacteristic
65C22×D53C22⋊C411yescharacteristic
66C22×D53C2×D411yescharacteristic
67C2×#6157—42no—
68C2×#6157—82no—
69D4×C53—41no—
70C2×C4×C53—21no—
71C2×C4×C53—21no—
72C2×C4×C53—41no—
73C2×C4×C53C22⋊C411yescharacteristic
74C22⋊D53—41no—
75C22⋊D53—41no—
76C2×Dic53—21no—
77C2×Dic53—21no—
78C2×Dic53—41no—
79C2×Dic53C2×D411yescharacteristic
80D212—41no—
81C4×D53—21no—
82C4×D53—21no—
83C4×D53—42no—
84C4×D53—42no—
85C4×D53—41no—
86C4×D53—41no—
87#88324—42no—
88C22×C53—21no—
89C22×C53—21no—
90C22×C53—41no—
91C22×C53—41no—
92C22×C53C2×C22⋊C411yescharacteristic
93C2×D53—22no—
94C2×D53—21no—
95C2×D53—21no—
96C2×D53—42no—
97C2×D53—42no—
98C2×D53—42no—
99C2×D53—41no—
100C2×D53—41no—
101C2×D53—81no—
102C2×D53#9911yescharacteristic
103C2×D53#9911yescharacteristic
104#6157—82no—
105C4×C53—21no—
106C4×C53—41no—
107C4×C53—41no—
108Dic53—21no—
109Dic53—41no—
110Dic53—41no—
111C2×#352—531nomaximal, Sylow
112C2×C53—21no—
113C2×C53—41no—
114C2×C53—41no—
115C2×C53C2×#9911yescharacteristic
116D53—21no—
117D53—41no—
118D53—41no—
119D53#35212yescomplemented
120C2×#123—531no—
121C2×#100—531no—
122C2×#99—531no—
123#352—532no—
124#352—532no—
125C53C2×#35211yescharacteristic, complemented, Sylow
126C22×D4—531no—
127C23×C4—531no—
128C2×M16—1061no—
129#123—531no—
130#123—531no—
131#123—531no—
132#123—1061no—
133#123—1061no—
134#123#615711yescharacteristic, complemented
135C2×C4⋊C4—1061no—
136C2×C22⋊C4—531no—
137C2×C22⋊C4—1061no—
138C2×C22⋊C4—1061no—
139#100—532no—
140#100—1061no—
141#99—532no—
142#99—1061no—
143C24—531no—
144C24—531no—
145C2×D4—531no—
146C2×D4—531no—
147C2×D4—531no—
148C2×D4—2121no—
149C2×D4—2121no—
150C2×D4C2×#615711yescharacteristic
151C22×C4—531no—
152C22×C4—531no—
153C22×C4—1061no—
154C22×C4—1061no—
155C22×C4—1061no—
156C22×C4—2121no—
157C22×C4—2121no—
158C22×C4—2121no—
159C22×C4C2×#615711yescharacteristic, complemented
160M16—1062no—
161M16—2121no—
162C2×C8—2121no—
163C4⋊C4—21no—
164C4⋊C4—1061no—
165C4⋊C4—1061no—
166C4⋊C4—1061no—
167C22⋊C4—21no—
168C22⋊C4—531no—
169C22⋊C4—1061no—
170C22⋊C4—1061no—
171C22⋊C4—1061no—
172C22⋊C4—1061no—
173C22⋊C4—1062no—
174C22⋊C4—2121no—
175C22⋊C4C2×#615711yescharacteristic, complemented
176C23—531no—
177C23—531no—
178C23—531no—
179C23—1061no—
180C23—1061no—
181C23—1061no—
182C23—1061no—
183C23—2122no—
184C23—2122no—
185C23C22⋊#615711yescharacteristic
186C23C22×#615711yescharacteristic
187D4—41no—
188D4—2121no—
189D4—2121no—
190D4—2121no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—531no—
195C2×C4—1061no—
196C2×C4—1061no—
197C2×C4—1061no—
198C2×C4—1061no—
199C2×C4—4242no—
200C2×C4—2121no—
201C2×C4—2121no—
202C2×C4—2122no—
203C2×C4—2122no—
204C2×C4—2122no—
205C2×C4—2121no—
206C2×C4C22⋊#615711yescharacteristic
207C8—2122no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—531no—
213C22—531no—
214C22—1062no—
215C22—1061no—
216C22—1061no—
217C22—4241no—
218C22—2121no—
219C22—2121no—
220C22—2122no—
221C22—2122no—
222C22—2122no—
223C22C2×C22⋊#615711yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—1061no—
228C4—4242no—
229C4—2121no—
230C4—2121no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—532no—
235C2—1061no—
236C2—2121no—
237C2—2121no—
238C2D53⋊#9911yescharacteristic
subgroupG/H
centerC2D53⋊#99
commutatorC23×C53C22×C4
FrattiniC23C22×#6157
Fitting#123×C53C4
socleC2×C53C2×#99
hypercenter#123#6157
hypocenterC53C2×#352
LCSG ▷ C23×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #16811526C2semidirect
4. #16811525C2semidirect
13. C22×C4×D53C4semidirect
18. #13133198C4semidirect
21. C22⋊C4×D53C4semidirect
22. #123×C53C4semidirect
27. C22×C4×C53C2×C4semidirect
30. C22×Dic53C2×C4semidirect
47. C22⋊C4×C53C2×C4semidirect
49. C22⋊Dic53C2×C4semidirect
119. D53#352semidirect
125. C53C2×#352semidirect
134. #123#6157semidirect
159. C22×C4C2×#6157semidirect
175. C22⋊C4C2×#6157semidirect