Finite Group Databasebeta

← C2×#15688913 #20245024

Subgroups — C2×#15688913 #20245024

Order 6016.

278 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 77 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×#13093941C211yesmaximal, characteristic
2C2×#13093939C211yesmaximal, characteristic
3#15688913C214yesmaximal, direct product factor
4C2×#123×C47C211yesmaximal, characteristic
5C2×#10625329—21no—
6C2×C22⋊Dic47—21no—
7#13093941—21no—
8#13093941C2212yes—
9#13093939—21no—
10#13093939C2212yes—
11C22×D4×C47C2211yescharacteristic
12C23×C4×C47C411yescharacteristic, complemented
13#123×C47—21no—
14#123×C47—21no—
15#123×C47C412yescomplemented
16#123×C47C2212yes—
17C2×C4⋊C4×C47—21no—
18C2×C22⋊C4×C47—21no—
19C2×C22⋊C4×C47C411yescharacteristic, complemented
20C24×C47C2×C411yescharacteristic
21C24×C47D411yescharacteristic
22C2×D4×C47—41no—
23C2×D4×C47—41no—
24C2×D4×C47C2×C411yescharacteristic
25C2×D4×C47D411yescharacteristic
26C2×D4×C47D411yescharacteristic
27C2×D4×C47C2311yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47—21no—
31C22×C4×C47—41no—
32C22×C4×C47—41no—
33C22×C4×C47C2×C412yescomplemented
34C22×C4×C47D411yescharacteristic
35C22×Dic47—41no—
36C4⋊C4×C47—22no—
37C4⋊C4×C47—22no—
38C22⋊C4×C47—22no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—22no—
41C22⋊C4×C47C2×C412yescomplemented
42C22⋊Dic47—22no—
43C22⋊Dic47—41no—
44#10625329—22no—
45#10625329—41no—
46C2×C47⋊C8—41no—
47C23×C47—21no—
48C23×C47—21no—
49C23×C47—21no—
50C23×C47—21no—
51C23×C47—42no—
52C23×C47—42no—
53C23×C47C22⋊C411yescharacteristic
54C23×C47C22⋊C411yescharacteristic
55C23×C47C22⋊C411yescharacteristic
56C23×C47C22×C411yescharacteristic
57C23×C47C2×D411yescharacteristic
58D4×C47—41no—
59D4×C47—41no—
60D4×C47—41no—
61D4×C47—41no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—42no—
67C2×C4×C47—42no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—42no—
71C2×C4×C47C22⋊C411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×Dic47—42no—
74C2×Dic47—82no—
75C47⋊C8—42no—
76C22×C47—22no—
77C22×C47—21no—
78C22×C47—21no—
79C22×C47—21no—
80C22×C47—21no—
81C22×C47—41no—
82C22×C47—41no—
83C22×C47—41no—
84C22×C47—41no—
85C22×C47—42no—
86C22×C47—42no—
87C22×C47—42no—
88C22×C47—81no—
89C22×C47#9911yescharacteristic
90C22×C47#9911yescharacteristic
91C22×C47C2×C22⋊C411yescharacteristic
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—42no—
95C4×C47—42no—
96Dic47—82no—
97C2×#352—471nomaximal, Sylow
98C2×C47—21no—
99C2×C47—21no—
100C2×C47—41no—
101C2×C47—41no—
102C2×C47—41no—
103C2×C47—41no—
104C2×C47#35212yescomplemented
105C2×C47C2×#9911yescharacteristic
106C2×#123D4711yescharacteristic
107C2×#100—471no—
108C2×#99—471no—
109#352—474no—
110C47C2×#35211yescharacteristic, complemented, Sylow
111C22×D4C2×D4711yescharacteristic
112C23×C4Dic4711yescharacteristic, complemented
113C2×M16—941no—
114#123—21no—
115#123—21no—
116#123Dic4712yescomplemented
117#123C2×D4712yes—
118C2×C4⋊C4—21no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—941no—
121C2×C22⋊C4Dic4711yescharacteristic, complemented
122#100—472no—
123#100—941no—
124#99—472no—
125#99—941no—
126C24C2×Dic4711yescharacteristic
127C24C22⋊D4711yescharacteristic
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C2×Dic4711yescharacteristic
131C2×D4C22⋊D4711yescharacteristic
132C2×D4C22⋊D4711yescharacteristic
133C2×D4C22×D4711yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—1881no—
140C22×C4C2×Dic4712yescomplemented
141C22×C4C22⋊D4711yescharacteristic
142M16—942no—
143M16—1881no—
144C2×C8—1881no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—21no—
149C22⋊C4—22no—
150C22⋊C4—942no—
151C22⋊C4—1881no—
152C22⋊C4C2×Dic4712yescomplemented
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23—42no—
158C23—42no—
159C23C22⋊Dic4711yescharacteristic
160C23C22⋊Dic4711yescharacteristic
161C23C22⋊Dic4711yescharacteristic
162C23C22×Dic4711yescharacteristic
163C23C2×C22⋊D4711yescharacteristic
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—3762no—
178C2×C4—1882no—
179C2×C4C22⋊Dic4711yescharacteristic
180C2×C4C2×C22⋊D4711yescharacteristic
181C8—1882no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22#1309393911yescharacteristic
196C22#1309393911yescharacteristic
197C22C2×C22⋊Dic4711yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—42no—
202C4—3762no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—41no—
208C2—41no—
209C2#1568891312yesdirect product factor
210C2C2×#1309393911yescharacteristic
subgroupG/H
centerC22#13093939
commutatorC23×C47C22×C4
FrattiniC2×D4C22×D47
FittingC2×#123×C47C2
socleC22×C47#99
hypercenterC2×#123D47
hypocenterC47C2×#352
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. #15688913C2direct (N × H)
12. C23×C4×C47C4semidirect
15. #123×C47C4semidirect
19. C2×C22⋊C4×C47C4semidirect
33. C22×C4×C47C2×C4semidirect
41. C22⋊C4×C47C2×C4semidirect
104. C2×C47#352semidirect
110. C47C2×#352semidirect
112. C23×C4Dic47semidirect
116. #123Dic47semidirect
121. C2×C22⋊C4Dic47semidirect
140. C22×C4C2×Dic47semidirect
152. C22⋊C4C2×Dic47semidirect
209. C2#15688913direct (N × H)