Finite Group Databasebeta

← C2×#15689305 #20252729

Subgroups — C2×#15689305 #20252729

Order 6016.

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

normal subgroups only

This group has 708 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×#13094072C211yesmaximal, characteristic
2C2×#13094055C212yesmaximal, complemented
3#15689305C218yesmaximal, direct product factor
4C2×#13093952C212yesmaximal, complemented
5C2×#13093943C211yesmaximal, characteristic, complemented
6C2×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
7#13094072—22no—
8#13094072—24no—
9#13094072C2214yes—
10C2×#10625354—22no—
11C2×#10625350—22no—
12C2×#10625350C2212yes—
13C2×Q8×D47—22no—
14#13094055—24no—
15#13094055C2218yescomplemented
16C2×#10625337—22no—
17C2×#10625336—22no—
18C2×#10625329C2212yes—
19#13093952C2218yescomplemented
20#13093943C2214yescomplemented
21C22×Q8×C47C2211yescharacteristic
22C22×Q8×C47C2211yescharacteristic
23C4⋊Q8×C47—22no—
24C4⋊Q8×C47C2214yescomplemented
25C2×C4⋊C4×C47—22no—
26C2×C42×C47C2211yescharacteristic
27C2×Q8×C47—22no—
28C2×Q8×C47—22no—
29C2×Q8×C47—21no—
30C2×Q8×C47—22no—
31C2×Q8×C47—22no—
32C2×Q8×C47D412yes—
33C2×Q8×C47C2312yes—
34C2×Q8×C47C2312yes—
35C22×C4×C47—21no—
36C22×C4×C47—21no—
37C22×C4×C47D412yes—
38C22×C4×C47C2311yescharacteristic
39C2×C22⋊D47—22no—
40#10625354—28no—
41#10625354—28no—
42Q8×D47—28no—
43Q8×D47—28no—
44#10625350—28no—
45#10625350—28no—
46#10625350—22no—
47#10625350—22no—
48#10625350D414yes—
49#10625350C2314yes—
50C2×D188—22no—
51C2×D188D412yes—
52C2×C4×D47—24no—
53C2×C4×D47—22no—
54C2×Dic94—22no—
55C2×Dic94D412yes—
56C4⋊C4×C47—28no—
57C42×C47—21no—
58C42×C47C2312yes—
59#10625337—28no—
60#10625336—28no—
61#10625329—22no—
62#10625329C2314yes—
63C2×C47⋊C8—22no—
64C23×C47C2×D411yescharacteristic
65C22×D47—22no—
66Q8×C47—24no—
67Q8×C47—24no—
68Q8×C47—24no—
69Q8×C47—42no—
70C2×C4×C47—24no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×D414yes—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2411yescharacteristic
82C22⋊D47—24no—
83C22⋊D47—24no—
84C2×Dic47—22no—
85D188—28no—
86D188—22no—
87D188C2×D414yes—
88C4×D47—216no—
89C4×D47—24no—
90C4×D47—24no—
91Dic94—28no—
92Dic94—22no—
93Dic94C2×D414yes—
94C47⋊C8—24no—
95C22×C47—22no—
96C22×C47#12011yescharacteristic
97C22×C47#12011yescharacteristic
98C22×C47C22×D411yescharacteristic
99C2×D47—24no—
100C2×D47—44no—
101C4×C47—24no—
102C4×C47—24no—
103C4×C47—42no—
104C4×C47#12012yes—
105C4×C47C22×D412yes—
106Dic47—24no—
107C2×#456—471nomaximal, Sylow
108C2×C47—21no—
109C2×C47—21no—
110C2×C47#45612yescomplemented
111C2×C47C2×#12011yescharacteristic
112D47—44no—
113C2×2−1+4—471no—
114C2×#137—472no—
115C2×C4⋊Q8D4711yescharacteristic, complemented
116#456—478no—
117C2×#104—472no—
118C2×#101—471no—
119C47C2×#45611yescharacteristic, complemented, Sylow
1202−1+4—474no—
1212−1+4—944no—
1222−1+4—942no—
123C2×#41—472no—
124C2×#41—942no—
125C2×#41—942no—
126C22×Q8—942no—
127C22×Q8C2×D4711yescharacteristic
128C22×Q8C2×D4711yescharacteristic
129#137—478no—
130#137—944no—
131C2×Q16—942no—
132C2×SD16—942no—
133C2×M16—472no—
134C4⋊Q8—22no—
135C4⋊Q8C2×D4714yescomplemented
136C2×C4⋊C4—22no—
137C2×C42C2×D4711yescharacteristic
138#104—478no—
139#101—474no—
140#41—474no—
141#41—474no—
142#41—948no—
143#41—948no—
144#41—948no—
145#41—942no—
146#41—942no—
147#41—948no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—472no—
154C2×Q8—942no—
155C2×Q8—948no—
156C2×Q8—948no—
157C2×Q8C22⋊D4712yes—
158C2×Q8C22×D4712yes—
159C2×Q8C22×D4712yes—
160C2×D4—472no—
161C2×D4—942no—
162C2×D4—942no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—944no—
166C22×C4—942no—
167C22×C4C22⋊D4712yes—
168C22×C4C22×D4711yescharacteristic
169Q16—948no—
170SD16—948no—
171M16—474no—
172M16—942no—
173C2×C8—942no—
174C4⋊C4—28no—
175C42—21no—
176C42C22×D4712yes—
177C23—942no—
178C23C2×C22⋊D4711yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—24no—
182Q8—42no—
183Q8—474no—
184Q8—948no—
185Q8—942no—
186D4—474no—
187D4—948no—
188D4—944no—
189D4—944no—
190D4—942no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—9416no—
199C2×C4—942no—
200C2×C4—944no—
201C2×C4—944no—
202C2×C4D4×D4712yes—
203C2×C4D4×D4712yes—
204C2×C4C2×C22⋊D4714yes—
205C2×C4C2×C22⋊D4711yescharacteristic
206C2×C4C23×D4711yescharacteristic
207C8—944no—
208C22—22no—
209C22—944no—
210C22—1884no—
211C22#1309399211yescharacteristic
212C22#1309399211yescharacteristic
213C22C22×C22⋊D4711yescharacteristic
214C4—24no—
215C4—24no—
216C4—42no—
217C4—944no—
218C4#1309399212yes—
219C4C2×D4×D4712yes—
220C2—21no—
221C2—21no—
222C2—1884no—
223C2#1568930512yesdirect product factor
224C2C2×#1309399211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C4⋊Q8×C47C2
socleC22×C47#120
hypercenterC2×C4⋊Q8D47
hypocenterC47C2×#456
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#13094055C2semidirect
3. #15689305C2direct (N × H)
4. C2×#13093952C2semidirect
5. C2×#13093943C2semidirect
6. C2×C4⋊Q8×C47C2semidirect
15. #13094055C22semidirect
19. #13093952C22semidirect
20. #13093943C22semidirect
24. C4⋊Q8×C47C22semidirect
110. C2×C47#456semidirect
115. C2×C4⋊Q8D47semidirect
119. C47C2×#456semidirect
135. C4⋊Q8C2×D47semidirect
223. C2#15689305direct (N × H)