Finite Group Databasebeta

← C2×#15689461 #20253277

Subgroups — C2×#15689461 #20253277

Order 6016.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13093983C211yesmaximal, characteristic
2#15689461C218yesmaximal, direct product factor
3C2×#13093957C211yesmaximal, characteristic, complemented
4C2×#13093955C211yesmaximal, characteristic, complemented
5C2×#13093948C211yesmaximal, characteristic, complemented
6C2×#13093948C211yesmaximal, characteristic, complemented
7C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic
8C2×C22⋊Q8×C47C211yesmaximal, characteristic
9C22×C47⋊C8C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11#13093983—22no—
12#13093983C2214yes—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C22⋊Dic47—21no—
16C2×C4×Dic47—21no—
17#13093957C2214yescomplemented
18#13093955C2214yescomplemented
19#13093948C2214yescomplemented
20#13093948C2214yescomplemented
21C22⋊(C47⋊C8)C2214yes—
22C22×Q8×C47C2211yescharacteristic
23C23×C4×C47C2211yescharacteristic
24C22⋊Q8×C47—22no—
25C22⋊Q8×C47C2214yes—
26C2×C4⋊C4×C47—21no—
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47—21no—
29C24×C47D411yescharacteristic
30C2×Q8×C47—21no—
31C2×Q8×C47—22no—
32C2×Q8×C47—22no—
33C2×Q8×C47C2312yes—
34C22×C4×C47—22no—
35C22×C4×C47—22no—
36C22×C4×C47—21no—
37C22×C4×C47—21no—
38C22×C4×C47D411yescharacteristic
39C22×C4×C47D412yes—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×Dic47—21no—
43C22×Dic47—21no—
44C4⋊C4×C47—24no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47C2312yes—
47C22⋊C4×C47—24no—
48C22⋊Dic47—24no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47C2312yes—
52C4⋊Dic47C2312yes—
53C4×Dic47—24no—
54C2×C47⋊C8—22no—
55C2×C47⋊C8—22no—
56C2×C47⋊C8C2312yes—
57C2×C47⋊C8C2312yes—
58C23×C47—22no—
59C23×C47—22no—
60C23×C47—22no—
61C23×C47C2×D412yes—
62C23×C47C2×D411yescharacteristic
63Q8×C47—22no—
64Q8×C47—22no—
65Q8×C47—42no—
66C2×C4×C47—22no—
67C2×C4×C47—24no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47#4112yes—
77C2×C4×C47#4112yes—
78C2×C4×C47C2411yescharacteristic
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—42no—
82C2×Dic47—42no—
83C47⋊C8—22no—
84C47⋊C8—22no—
85C22×C47—22no—
86C22×C47—22no—
87C22×C47—22no—
88C22×C47—44no—
89C22×C47#12312yes—
90C22×C47#13512yes—
91C22×C47#13712yes—
92C22×C47C22×D411yescharacteristic
93C4×C47—22no—
94C4×C47—42no—
95C4×C47—42no—
96C4×C47#12312yes—
97C4×C47C2×#4111yescharacteristic
98C4×C47C2×#4111yescharacteristic
99Dic47—42no—
100Dic47—42no—
101C2×#485—471nomaximal, Sylow
102C2×C47—42no—
103C2×C47#48514yescomplemented
104C2×C47C2×#12311yescharacteristic
105C2×C47C2×#13511yescharacteristic
106C2×C47C2×#13711yescharacteristic
107C2×C22⋊Q8D4711yescharacteristic
108C2×#117—471no—
109#485—478no—
110C2×#107—471no—
111C2×#106—471no—
112C2×#103—471no—
113C2×#103—471no—
114C2×C22⋊C8—471no—
115C47C2×#48511yescharacteristic, complemented, Sylow
116C22×Q8C2×D4711yescharacteristic
117C23×C4C2×D4711yescharacteristic
118C22×C8—471no—
119C22×C8—471no—
120C22⋊Q8—22no—
121C22⋊Q8C2×D4714yes—
122#117—474no—
123#117—942no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—471no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C22⋊C4—21no—
129C2×C22⋊C4—941no—
130C2×C42—941no—
131#107—474no—
132#106—474no—
133#103—474no—
134#103—474no—
135C22⋊C8—474no—
136C24C22⋊D4711yescharacteristic
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8C22×D4712yes—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—941no—
146C22×C4—941no—
147C22×C4C22⋊D4712yes—
148C22×C4C22⋊D4711yescharacteristic
149C22×C4C22×D4712yes—
150C22×C4C22×D4711yescharacteristic
151C2×C8—472no—
152C2×C8—472no—
153C2×C8—942no—
154C2×C8—942no—
155C4⋊C4—24no—
156C4⋊C4—21no—
157C4⋊C4—472no—
158C4⋊C4—472no—
159C4⋊C4—941no—
160C4⋊C4—941no—
161C4⋊C4C22×D4712yes—
162C22⋊C4—24no—
163C22⋊C4—944no—
164C42—944no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23C2×C22⋊D4712yes—
169C23C2×C22⋊D4711yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—42no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—1882no—
184C2×C4—1882no—
185C2×C4#1062535212yes—
186C2×C4#1062535212yes—
187C2×C4C2×C22⋊D4712yes—
188C2×C4C2×C22⋊D4711yescharacteristic
189C2×C4C23×D4711yescharacteristic
190C8—942no—
191C8—942no—
192C22—22no—
193C22—22no—
194C22—22no—
195C22—44no—
196C22#1309400512yes—
197C22#1309404412yes—
198C22#1309405512yes—
199C22C22×C22⋊D4711yescharacteristic
200C4—22no—
201C4—42no—
202C4—42no—
203C4—1882no—
204C4—1882no—
205C4#1309400512yes—
206C4C2×#1062535211yescharacteristic
207C4C2×#1062535211yescharacteristic
208C2—42no—
209C2#1568946114yesdirect product factor
210C2C2×#1309400511yescharacteristic
211C2C2×#1309404411yescharacteristic
212C2C2×#1309405511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C22⋊Q8×C47C2
socleC23×C47C2×D4
hypercenterC2×C22⋊Q8D47
hypocenterC47C2×#485
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689461C2direct (N × H)
3. C2×#13093957C2semidirect
4. C2×#13093955C2semidirect
5. C2×#13093948C2semidirect
6. C2×#13093948C2semidirect
17. #13093957C22semidirect
18. #13093955C22semidirect
19. #13093948C22semidirect
20. #13093948C22semidirect
103. C2×C47#485semidirect
115. C47C2×#485semidirect
209. C2#15689461direct (N × H)