Finite Group Databasebeta

← C2×#14583081 #19143936

Subgroups — C2×#14583081 #19143936

Order 5504.

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×#13063373C211yesmaximal, characteristic
2C2×#13063356C212yesmaximal, complemented
3#14583081C218yesmaximal, direct product factor
4C2×#13063253C212yesmaximal, complemented
5C2×#13063244C211yesmaximal, characteristic, complemented
6C2×C4⋊Q8×C43C211yesmaximal, characteristic, complemented
7#13063373—22no—
8#13063373—24no—
9#13063373C2214yes—
10C2×#10621902—22no—
11C2×#10621898—22no—
12C2×#10621898C2212yes—
13C2×Q8×D43—22no—
14#13063356—24no—
15#13063356C2218yescomplemented
16C2×#10621885—22no—
17C2×#10621884—22no—
18C2×#10621877C2212yes—
19#13063253C2218yescomplemented
20#13063244C2214yescomplemented
21C22×Q8×C43C2211yescharacteristic
22C22×Q8×C43C2211yescharacteristic
23C4⋊Q8×C43—22no—
24C4⋊Q8×C43C2214yescomplemented
25C2×C4⋊C4×C43—22no—
26C2×C42×C43C2211yescharacteristic
27C2×Q8×C43—22no—
28C2×Q8×C43—22no—
29C2×Q8×C43—21no—
30C2×Q8×C43—22no—
31C2×Q8×C43—22no—
32C2×Q8×C43D412yes—
33C2×Q8×C43C2312yes—
34C2×Q8×C43C2312yes—
35C22×C4×C43—21no—
36C22×C4×C43—21no—
37C22×C4×C43D412yes—
38C22×C4×C43C2311yescharacteristic
39C2×C22⋊D43—22no—
40#10621902—28no—
41#10621902—28no—
42Q8×D43—28no—
43Q8×D43—28no—
44#10621898—28no—
45#10621898—28no—
46#10621898—22no—
47#10621898—22no—
48#10621898D414yes—
49#10621898C2314yes—
50C2×D172—22no—
51C2×D172D412yes—
52C2×C4×D43—24no—
53C2×C4×D43—22no—
54C2×Dic86—22no—
55C2×Dic86D412yes—
56C4⋊C4×C43—28no—
57C42×C43—21no—
58C42×C43C2312yes—
59#10621885—28no—
60#10621884—28no—
61#10621877—22no—
62#10621877C2314yes—
63C2×C43⋊C8—22no—
64C23×C43C2×D411yescharacteristic
65C22×D43—22no—
66Q8×C43—24no—
67Q8×C43—24no—
68Q8×C43—24no—
69Q8×C43—42no—
70C2×C4×C43—24no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43C2×D412yes—
78C2×C4×C43C2×D412yes—
79C2×C4×C43C2×D414yes—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2411yescharacteristic
82C22⋊D43—24no—
83C22⋊D43—24no—
84C2×Dic43—22no—
85D172—28no—
86D172—22no—
87D172C2×D414yes—
88C4×D43—216no—
89C4×D43—24no—
90C4×D43—24no—
91Dic86—28no—
92Dic86—22no—
93Dic86C2×D414yes—
94C43⋊C8—24no—
95C22×C43—22no—
96C22×C43#12011yescharacteristic
97C22×C43#12011yescharacteristic
98C22×C43C22×D411yescharacteristic
99C2×D43—24no—
100C2×D43—44no—
101C4×C43—24no—
102C4×C43—24no—
103C4×C43—42no—
104C4×C43#12012yes—
105C4×C43C22×D412yes—
106Dic43—24no—
107C2×#456—431nomaximal, Sylow
108C2×C43—21no—
109C2×C43—21no—
110C2×C43#45612yescomplemented
111C2×C43C2×#12011yescharacteristic
112D43—44no—
113C2×2−1+4—431no—
114C2×#137—432no—
115C2×C4⋊Q8D4311yescharacteristic, complemented
116#456—438no—
117C2×#104—432no—
118C2×#101—431no—
119C43C2×#45611yescharacteristic, complemented, Sylow
1202−1+4—434no—
1212−1+4—864no—
1222−1+4—862no—
123C2×#41—432no—
124C2×#41—862no—
125C2×#41—862no—
126C22×Q8—862no—
127C22×Q8C2×D4311yescharacteristic
128C22×Q8C2×D4311yescharacteristic
129#137—438no—
130#137—864no—
131C2×Q16—862no—
132C2×SD16—862no—
133C2×M16—432no—
134C4⋊Q8—22no—
135C4⋊Q8C2×D4314yescomplemented
136C2×C4⋊C4—22no—
137C2×C42C2×D4311yescharacteristic
138#104—438no—
139#101—434no—
140#41—434no—
141#41—434no—
142#41—868no—
143#41—868no—
144#41—868no—
145#41—862no—
146#41—862no—
147#41—868no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—432no—
154C2×Q8—862no—
155C2×Q8—868no—
156C2×Q8—868no—
157C2×Q8C22⋊D4312yes—
158C2×Q8C22×D4312yes—
159C2×Q8C22×D4312yes—
160C2×D4—432no—
161C2×D4—862no—
162C2×D4—862no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—864no—
166C22×C4—862no—
167C22×C4C22⋊D4312yes—
168C22×C4C22×D4311yescharacteristic
169Q16—868no—
170SD16—868no—
171M16—434no—
172M16—862no—
173C2×C8—862no—
174C4⋊C4—28no—
175C42—21no—
176C42C22×D4312yes—
177C23—862no—
178C23C2×C22⋊D4311yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—24no—
182Q8—42no—
183Q8—434no—
184Q8—868no—
185Q8—862no—
186D4—434no—
187D4—868no—
188D4—864no—
189D4—864no—
190D4—862no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—8616no—
199C2×C4—862no—
200C2×C4—864no—
201C2×C4—864no—
202C2×C4D4×D4312yes—
203C2×C4D4×D4312yes—
204C2×C4C2×C22⋊D4314yes—
205C2×C4C2×C22⋊D4311yescharacteristic
206C2×C4C23×D4311yescharacteristic
207C8—864no—
208C22—22no—
209C22—864no—
210C22—1724no—
211C22#1306329311yescharacteristic
212C22#1306329311yescharacteristic
213C22C22×C22⋊D4311yescharacteristic
214C4—24no—
215C4—24no—
216C4—42no—
217C4—864no—
218C4#1306329312yes—
219C4C2×D4×D4312yes—
220C2—21no—
221C2—21no—
222C2—1724no—
223C2#1458308112yesdirect product factor
224C2C2×#1306329311yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×C4⋊Q8×C43C2
socleC22×C43#120
hypercenterC2×C4⋊Q8D43
hypocenterC43C2×#456
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#13063356C2semidirect
3. #14583081C2direct (N × H)
4. C2×#13063253C2semidirect
5. C2×#13063244C2semidirect
6. C2×C4⋊Q8×C43C2semidirect
15. #13063356C22semidirect
19. #13063253C22semidirect
20. #13063244C22semidirect
24. C4⋊Q8×C43C22semidirect
110. C2×C43#456semidirect
115. C2×C4⋊Q8D43semidirect
119. C43C2×#456semidirect
135. C4⋊Q8C2×D43semidirect
223. C2#14583081direct (N × H)