Finite Group Databasebeta

← C2×#15689306 #20252730

Subgroups — C2×#15689306 #20252730

Order 6016.

708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13094054C212yesmaximal, complemented
2C2×#13094022C211yesmaximal, characteristic, complemented
3#15689306C218yesmaximal, direct product factor
4C2×#13093951C212yesmaximal, complemented
5C2×#13093943C211yesmaximal, characteristic, complemented
6C2×2−1+4×C47C211yesmaximal, characteristic
7C22×Dic94C2211yescharacteristic
8#13094054—24no—
9#13094054C2218yescomplemented
10C2×#10625337—22no—
11C2×#10625335—22no—
12C2×#10625329C2212yes—
13#13094022—22no—
14#13094022C2214yescomplemented
15C2×Dic47⋊C4—22no—
16C2×C4×Dic47C2211yescharacteristic
17#13093951C2218yescomplemented
18#13093943C2214yescomplemented
192−1+4×C47—24no—
202−1+4×C47—22no—
212−1+4×C47C2214yes—
22C2×#41×C47—22no—
23C2×#41×C47—22no—
24C2×#41×C47C2212yes—
25C22×Q8×C47—22no—
26C22×Q8×C47C2211yescharacteristic
27#41×C47—28no—
28#41×C47—28no—
29#41×C47—28no—
30#41×C47—28no—
31#41×C47—22no—
32#41×C47—22no—
33#41×C47D414yes—
34#41×C47C2314yes—
35C2×Q8×C47—22no—
36C2×Q8×C47—28no—
37C2×Q8×C47—28no—
38C2×Q8×C47—22no—
39C2×Q8×C47—22no—
40C2×Q8×C47D412yes—
41C2×Q8×C47D412yes—
42C2×Q8×C47C2312yes—
43C2×D4×C47—22no—
44C2×D4×C47—22no—
45C2×D4×C47D412yes—
46C22×C4×C47—24no—
47C22×C4×C47—22no—
48C22×C4×C47D412yes—
49C22×C4×C47C2311yescharacteristic
50C22×Dic47—21no—
51C22×Dic47—21no—
52C2×Dic94—22no—
53C2×Dic94—22no—
54C2×Dic94—21no—
55C2×Dic94C2312yes—
56#10625337—28no—
57#10625335—28no—
58Dic47⋊C4—28no—
59C4×Dic47—21no—
60C4×Dic47C2312yes—
61#10625329—22no—
62#10625329C2314yes—
63C2×C47⋊C8—22no—
64C23×C47—22no—
65C23×C47C2×D411yescharacteristic
66Q8×C47—28no—
67Q8×C47—22no—
68Q8×C47—24no—
69Q8×C47—24no—
70Q8×C47C2×D414yes—
71D4×C47—28no—
72D4×C47—24no—
73D4×C47—24no—
74D4×C47—22no—
75D4×C47C2×D414yes—
76C2×C4×C47—216no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—24no—
81C2×C4×C47—24no—
82C2×C4×C47C2×D414yes—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D412yes—
85C2×C4×C47C2×D412yes—
86C2×C4×C47C2411yescharacteristic
87C2×Dic47—24no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—41no—
91C2×Dic47—41no—
92Dic94—24no—
93Dic94—42no—
94C47⋊C8—24no—
95C22×C47—22no—
96C22×C47—24no—
97C22×C47—44no—
98C22×C47#12011yescharacteristic
99C22×C47#12011yescharacteristic
100C22×C47C22×D411yescharacteristic
101C4×C47—24no—
102C4×C47—24no—
103C4×C47#12012yes—
104C4×C47C22×D412yes—
105Dic47—24no—
106Dic47—42no—
107C2×#456—471nomaximal, Sylow
108C2×C47—21no—
109C2×C47—21no—
110C2×C47—44no—
111C2×C47#45612yescomplemented
112C2×C47C2×#12011yescharacteristic
113C2×2−1+4D4711yescharacteristic
114C2×#137—472no—
115C2×C4⋊Q8—471no—
116#456—478no—
117C2×#104—472no—
118C2×#101—471no—
119C47C2×#45611yescharacteristic, complemented, Sylow
1202−1+4—24no—
1212−1+4—22no—
1222−1+4C2×D4714yes—
123C2×#41—22no—
124C2×#41—22no—
125C2×#41C2×D4712yes—
126C22×Q8—22no—
127C22×Q8—471no—
128C22×Q8C2×D4711yescharacteristic
129#137—478no—
130#137—944no—
131C2×Q16—942no—
132C2×SD16—942no—
133C2×M16—472no—
134C4⋊Q8—474no—
135C4⋊Q8—942no—
136C2×C4⋊C4—942no—
137C2×C42—471no—
138#104—478no—
139#101—474no—
140#41—28no—
141#41—28no—
142#41—28no—
143#41—28no—
144#41—22no—
145#41—22no—
146#41C22⋊D4714yes—
147#41C22×D4714yes—
148C2×Q8—22no—
149C2×Q8—28no—
150C2×Q8—28no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—472no—
154C2×Q8—941no—
155C2×Q8—942no—
156C2×Q8—942no—
157C2×Q8C22⋊D4712yes—
158C2×Q8C22⋊D4712yes—
159C2×Q8C22×D4712yes—
160C2×D4—22no—
161C2×D4—22no—
162C2×D4C22⋊D4712yes—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—941no—
166C22×C4—941no—
167C22×C4C22⋊D4712yes—
168C22×C4C22×D4711yescharacteristic
169Q16—948no—
170SD16—948no—
171M16—474no—
172M16—942no—
173C2×C8—942no—
174C4⋊C4—948no—
175C42—472no—
176C42—941no—
177C23—22no—
178C23C2×C22⋊D4711yescharacteristic
179Q8—28no—
180Q8—22no—
181Q8—24no—
182Q8—24no—
183Q8—944no—
184Q8—1882no—
185Q8C2×C22⋊D4714yes—
186D4—28no—
187D4—24no—
188D4—24no—
189D4—22no—
190D4C2×C22⋊D4714yes—
191C2×C4—216no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—944no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—1881no—
201C2×C4—1881no—
202C2×C4C2×C22⋊D4714yes—
203C2×C4C2×C22⋊D4711yescharacteristic
204C2×C4C2×C22⋊D4712yes—
205C2×C4C2×C22⋊D4712yes—
206C2×C4C23×D4711yescharacteristic
207C8—944no—
208C22—22no—
209C22—24no—
210C22—44no—
211C22#1309399311yescharacteristic
212C22#1309399311yescharacteristic
213C22C22×C22⋊D4711yescharacteristic
214C4—24no—
215C4—24no—
216C4—944no—
217C4—1882no—
218C4#1309399312yes—
219C4C22×C22⋊D4712yes—
220C2—21no—
221C2—21no—
222C2—44no—
223C2#1568930612yesdirect product factor
224C2C2×#1309399311yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×2−1+4×C47C2
socleC22×C47#120
hypercenterC2×2−1+4D47
hypocenterC47C2×#456
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#13094054C2semidirect
2. C2×#13094022C2semidirect
3. #15689306C2direct (N × H)
4. C2×#13093951C2semidirect
5. C2×#13093943C2semidirect
9. #13094054C22semidirect
14. #13094022C22semidirect
17. #13093951C22semidirect
18. #13093943C22semidirect
111. C2×C47#456semidirect
119. C47C2×#456semidirect
223. C2#15689306direct (N × H)