Finite Group Databasebeta

← C2×#16840080 #21455718

Subgroups — C2×#16840080 #21455718

Order 7808.

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

normal subgroups only

This group has 512 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×#14519751C211yesmaximal, characteristic
2#16840080C218yesmaximal, direct product factor
3C2×#14519708C212yesmaximal, complemented
4C2×#14519697C212yesmaximal, complemented
5C2×C22⋊#92418C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C61C211yesmaximal, characteristic, complemented
7C22×D244C2211yescharacteristic
8C22×C22⋊D61—21no—
9C22×#92418C2212yes—
10#14519751—22no—
11#14519751C2214yes—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758198—21no—
14#14519708C2218yescomplemented
15#14519697C2218yescomplemented
16C22⋊#92418C2214yescomplemented
17C23×C4×C61—21no—
18C23×C4×C61C2211yescharacteristic
19C2×C4⋊C4×C61—22no—
20C2×C4⋊C4×C61—21no—
21C2×C4⋊C4×C61C2212yes—
22C2×C4⋊C4×C61C2214yescomplemented
23C24×C61D411yescharacteristic
24C23×D61—21no—
25C22×C4×C61—24no—
26C22×C4×C61—22no—
27C22×C4×C61—24no—
28C22×C4×C61—44no—
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D412yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—24no—
34C2×C22⋊D61—44no—
35C22×Dic61—21no—
36C2×D244—24no—
37C2×D244—21no—
38C2×D244C2312yes—
39C4⋊C4×C61—22no—
40C4⋊C4×C61—24no—
41C4⋊C4×C61C2314yes—
42#11758198—24no—
43C4⋊Dic61—21no—
44C4⋊Dic61C2312yes—
45C2×#92418—24no—
46C2×#92418C2314yes—
47C23×C61—22no—
48C23×C61—22no—
49C23×C61SD1614yes—
50C23×C61C2×D412yes—
51C23×C61C2×D411yescharacteristic
52C22×D61—22no—
53C22×D61—42no—
54C22×D61—42no—
55C22×D61—42no—
56C2×C4×C61—22no—
57C2×C4×C61—24no—
58C2×C4×C61—24no—
59C2×C4×C61—24no—
60C2×C4×C61—48no—
61C2×C4×C61—44no—
62C2×C4×C61C2×D412yes—
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61#4114yes—
65C2×C4×C61C2411yescharacteristic
66C22⋊D61—48no—
67C2×Dic61—22no—
68C2×Dic61—42no—
69D244—24no—
70D244—42no—
71#92418—24no—
72C22×C61—22no—
73C22×C61—22no—
74C22×C61—28no—
75C22×C61#12312yes—
76C22×C61C2×SD1614yes—
77C22×C61C2×SD1612yes—
78C22×C61AGL(1,ℤ/8)12yes—
79C22×C61C22×D411yescharacteristic
80C2×D61—42no—
81C2×D61—42no—
82C2×D61—42no—
83C2×D61—84no—
84C4×C61—22no—
85C4×C61—44no—
86C4×C61#12312yes—
87C4×C61C2×#4112yes—
88Dic61—42no—
89C2×#481—611nomaximal, Sylow
90C2×C61—24no—
91C2×C61#48114yescomplemented
92C2×C61C2×#12311yescharacteristic
93C2×C61C22×SD1611yescharacteristic
94C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
95D61—82no—
96C2×#121—611no—
97C22×C4⋊C4D6111yescharacteristic, complemented
98#481—618no—
99C2×#106—612no—
100C2×#102—612no—
101C2×C22⋊C8—611no—
102C61C2×#48111yescharacteristic, complemented, Sylow
103C22×D4—611no—
104C22×D4—1221no—
105C23×C4—21no—
106C23×C4C2×D6111yescharacteristic
107C22×C8—612no—
108#121—614no—
109#121—1222no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4C2×D6112yes—
114C2×C4⋊C4C2×D6114yescomplemented
115C2×C22⋊C4—1221no—
116#106—618no—
117#102—618no—
118C22⋊C8—614no—
119C24—1221no—
120C24C22⋊D6111yescharacteristic
121C2×D4—612no—
122C2×D4—1224no—
123C2×D4—1224no—
124C2×D4—1221no—
125C2×D4—2444no—
126C22×C4—24no—
127C22×C4—24no—
128C22×C4—22no—
129C22×C4—44no—
130C22×C4—1221no—
131C22×C4C22⋊D6112yes—
132C22×C4C22⋊D6111yescharacteristic
133C22×C4C22×D6112yes—
134C22×C4C22×D6111yescharacteristic
135C2×C8—614no—
136C2×C8—1224no—
137C4⋊C4—22no—
138C4⋊C4—24no—
139C4⋊C4—612no—
140C4⋊C4—1221no—
141C4⋊C4C22×D6114yes—
142C22⋊C4—1224no—
143C23—22no—
144C23—22no—
145C23—1222no—
146C23—2442no—
147C23—2442no—
148C23—2442no—
149C23#1175820114yes—
150C23C2×C22⋊D6112yes—
151C23C2×C22⋊D6111yescharacteristic
152D4—1224no—
153D4—2448no—
154D4—2442no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—48no—
160C2×C4—44no—
161C2×C4—1222no—
162C2×C4—2442no—
163C2×C4#1175822214yes—
164C2×C4C2×C22⋊D6112yes—
165C2×C4C2×C22⋊D6111yescharacteristic
166C2×C4C23×D6111yescharacteristic
167C8—1224no—
168C22—22no—
169C22—22no—
170C22—28no—
171C22—4884no—
172C22—2442no—
173C22—2442no—
174C22—2442no—
175C22#1451976012yes—
176C22C2×#1175820114yes—
177C22C2×#1175820112yes—
178C22#1451980312yes—
179C22C22×C22⋊D6111yescharacteristic
180C4—22no—
181C4—44no—
182C4—2442no—
183C4#1451976012yes—
184C4C2×#1175822212yes—
185C2—24no—
186C2—4882no—
187C2#1684008014yesdirect product factor
188C2C2×#1451976011yescharacteristic
189C2C22×#1175820111yescharacteristic
190C2C2×#1451980311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×C4⋊C4×C61C2
socleC23×C61C2×D4
hypercenterC22×C4⋊C4D61
hypocenterC61C2×#481
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #16840080C2direct (N × H)
3. C2×#14519708C2semidirect
4. C2×#14519697C2semidirect
5. C2×C22⋊#92418C2semidirect
6. C22×C4⋊C4×C61C2semidirect
14. #14519708C22semidirect
15. #14519697C22semidirect
16. C22⋊#92418C22semidirect
22. C2×C4⋊C4×C61C22semidirect
91. C2×C61#481semidirect
97. C22×C4⋊C4D61semidirect
102. C61C2×#481semidirect
114. C2×C4⋊C4C2×D61semidirect
187. C2#16840080direct (N × H)