Finite Group Databasebeta

← C2×#16811526 #20290965

Subgroups — C2×#16811526 #20290965

Order 6784.

278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 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×#13133277C211yesmaximal, characteristic
2C2×#13133275C211yesmaximal, characteristic
3#16811526C214yesmaximal, direct product factor
4C2×#13133201C211yesmaximal, characteristic
5C2×#11719940—21no—
6C2×C22⋊#6157—21no—
7#13133277—21no—
8#13133277C2212yes—
9#13133275—21no—
10#13133275C2212yes—
11C22×C22⋊D53C2211yescharacteristic
12C23×Dic53C411yescharacteristic, complemented
13#13133201—21no—
14#13133201—21no—
15#13133201C412yescomplemented
16#13133201C2212yes—
17C2×C4⋊Dic53—21no—
18C2×#11719921—21no—
19C2×C22⋊C4×C53C411yescharacteristic, complemented
20C24×C53C2×C411yescharacteristic
21C23×D53D411yescharacteristic
22C22×#6157—41no—
23C22×C4×C53—21no—
24C2×C22⋊D53—41no—
25C2×C22⋊D53—41no—
26C2×C22⋊D53C2×C411yescharacteristic
27C2×C22⋊D53D411yescharacteristic
28C2×C22⋊D53D411yescharacteristic
29C2×C22⋊D53C2311yescharacteristic
30C22×Dic53—21no—
31C22×Dic53—21no—
32C22×Dic53—41no—
33C22×Dic53—41no—
34C22×Dic53C2×C412yescomplemented
35C22×Dic53D411yescharacteristic
36C22⋊#6157—22no—
37C22⋊#6157—41no—
38#11719940—22no—
39#11719940—41no—
40C2×#88324—41no—
41C22⋊C4×C53—21no—
42C22⋊C4×C53C2×C412yescomplemented
43#11719921—22no—
44#11719921—22no—
45C4⋊Dic53—22no—
46C4⋊Dic53—22no—
47C23×C53—21no—
48C23×C53—21no—
49C23×C53—42no—
50C23×C53C22⋊C411yescharacteristic
51C23×C53C22⋊C411yescharacteristic
52C23×C53C22×C411yescharacteristic
53C22×D53—21no—
54C22×D53—21no—
55C22×D53—42no—
56C22×D53C22⋊C411yescharacteristic
57C22×D53C2×D411yescharacteristic
58C2×#6157—42no—
59C2×#6157—82no—
60C2×C4×C53—22no—
61C2×C4×C53—42no—
62C22⋊D53—41no—
63C22⋊D53—41no—
64C22⋊D53—41no—
65C22⋊D53—41no—
66C2×Dic53—21no—
67C2×Dic53—21no—
68C2×Dic53—22no—
69C2×Dic53—42no—
70C2×Dic53—41no—
71C2×Dic53—41no—
72C2×Dic53—42no—
73C2×Dic53C22⋊C411yescharacteristic
74C2×Dic53C2×D411yescharacteristic
75#88324—42no—
76C22×C53—22no—
77C22×C53—21no—
78C22×C53—21no—
79C22×C53—41no—
80C22×C53—41no—
81C22×C53—42no—
82C22×C53—42no—
83C22×C53#9911yescharacteristic
84C22×C53#9911yescharacteristic
85C22×C53C2×C22⋊C411yescharacteristic
86C2×D53—21no—
87C2×D53—21no—
88C2×D53—42no—
89C2×D53—41no—
90C2×D53—41no—
91C2×D53—81no—
92#6157—82no—
93C4×C53—42no—
94Dic53—21no—
95Dic53—21no—
96Dic53—42no—
97C2×#352—531nomaximal, Sylow
98C2×C53—21no—
99C2×C53—21no—
100C2×C53—41no—
101C2×C53—41no—
102C2×C53#35212yescomplemented
103C2×C53C2×#9911yescharacteristic
104D53—41no—
105D53—41no—
106C2×#123—531no—
107C2×#100—531no—
108C2×#99—531no—
109#352—534no—
110C53C2×#35211yescharacteristic, complemented, Sylow
111C22×D4—531no—
112C23×C4—531no—
113C2×M16—1061no—
114#123—532no—
115#123—532no—
116#123—1061no—
117#123—1061no—
118C2×C4⋊C4—1061no—
119C2×C22⋊C4—1061no—
120C2×C22⋊C4—1061no—
121C2×C22⋊C4#615711yescharacteristic, complemented
122#100—532no—
123#100—1061no—
124#99—532no—
125#99—1061no—
126C24—531no—
127C24C2×#615711yescharacteristic
128C2×D4—531no—
129C2×D4—531no—
130C2×D4—531no—
131C2×D4—531no—
132C2×D4—2121no—
133C2×D4—2121no—
134C22×C4—21no—
135C22×C4—531no—
136C22×C4—532no—
137C22×C4—1061no—
138C22×C4—1061no—
139C22×C4—2121no—
140C22×C4—2121no—
141C22×C4—2121no—
142M16—1062no—
143M16—2121no—
144C2×C8—2121no—
145C4⋊C4—1062no—
146C4⋊C4—1062no—
147C22⋊C4—21no—
148C22⋊C4—1062no—
149C22⋊C4—1062no—
150C22⋊C4—1062no—
151C22⋊C4—2121no—
152C22⋊C4C2×#615712yescomplemented
153C23—21no—
154C23—21no—
155C23—42no—
156C23—531no—
157C23—531no—
158C23—1061no—
159C23—1061no—
160C23—2122no—
161C23C22⋊#615711yescharacteristic
162C23C22⋊#615711yescharacteristic
163C23C22×#615711yescharacteristic
164D4—2121no—
165D4—2121no—
166D4—2121no—
167D4—2121no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—531no—
171C2×C4—531no—
172C2×C4—1061no—
173C2×C4—1061no—
174C2×C4—1062no—
175C2×C4—4242no—
176C2×C4—2122no—
177C2×C4—2122no—
178C2×C4—2121no—
179C2×C4—2121no—
180C2×C4—2122no—
181C8—2122no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—1061no—
190C22—1061no—
191C22—4241no—
192C22—2121no—
193C22—2121no—
194C22—2122no—
195C22#1313327611yescharacteristic
196C22#1313327611yescharacteristic
197C22C2×C22⋊#615711yescharacteristic
198C4—42no—
199C4—1061no—
200C4—1061no—
201C4—4242no—
202C4—2122no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—2121no—
208C2—2121no—
209C2#1681152612yesdirect product factor
210C2C2×#1313327611yescharacteristic
subgroupG/H
centerC22#13133276
commutatorC23×C53C22×C4
FrattiniC23C22×#6157
FittingC2×C22⋊C4×C53C4
socleC22×C53#99
hypercenterC2×C22⋊C4#6157
hypocenterC53C2×#352
LCSG ▷ C23×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #16811526C2direct (N × H)
12. C23×Dic53C4semidirect
15. #13133201C4semidirect
19. C2×C22⋊C4×C53C4semidirect
34. C22×Dic53C2×C4semidirect
42. C22⋊C4×C53C2×C4semidirect
102. C2×C53#352semidirect
110. C53C2×#352semidirect
121. C2×C22⋊C4#6157semidirect
152. C22⋊C4C2×#6157semidirect
209. C2#16811526direct (N × H)