Finite Group Databasebeta

← C2×#16840062 #21455576

Subgroups — C2×#16840062 #21455576

Order 7808.

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

normal subgroups only

This group has 448 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×#14519769C211yesmaximal, characteristic, complemented
2#16840062C218yesmaximal, direct product factor
3C2×#14519710C211yesmaximal, characteristic, complemented
4C2×#14519708C211yesmaximal, characteristic, complemented
5C2×C4⋊#92418C211yesmaximal, characteristic, complemented
6C2×#14519698C211yesmaximal, characteristic
7C2×#14519698C211yesmaximal, characteristic
8C2×C4×D4×C61C211yesmaximal, characteristic
9C22×#92418C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11#14519769—22no—
12#14519769C2214yescomplemented
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196—21no—
16C2×#11758196—21no—
17#14519710C2214yescomplemented
18#14519708C2214yescomplemented
19C4⋊#92418C2214yescomplemented
20#14519698C2214yes—
21#14519698C2214yes—
22C22×D4×C61C2211yescharacteristic
23C23×C4×C61—21no—
24C4×D4×C61—22no—
25C4×D4×C61C2214yes—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C22⋊C4×C61—21no—
28C2×C42×C61C2211yescharacteristic
29C24×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61—22no—
32C2×D4×C61Q814yes—
33C2×D4×C61C2312yes—
34C22×C4×C61—21no—
35C22×C4×C61—24no—
36C22×C4×C61—44no—
37C22×C4×C61D411yescharacteristic
38C22×C4×C61D411yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×Dic61—21no—
41C22×Dic61—21no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61C2312yes—
44C22⋊C4×C61—24no—
45C42×C61D412yes—
46C42×C61C2312yes—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61C2312yes—
50C4⋊Dic61C2312yes—
51#11758196—24no—
52#11758196—24no—
53C2×#92418—22no—
54C2×#92418—22no—
55C2×#92418C2312yes—
56C2×#92418C2312yes—
57C23×C61—24no—
58C23×C61—22no—
59C23×C61—42no—
60C23×C61—42no—
61C23×C61C2×D411yescharacteristic
62D4×C61—24no—
63D4×C61—22no—
64D4×C61C2×Q814yes—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—48no—
69C2×C4×C61—42no—
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×Q812yes—
74C2×C4×C61#4112yes—
75C2×C4×C61C2411yescharacteristic
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—42no—
79C2×Dic61—42no—
80#92418—22no—
81#92418—22no—
82C22×C61—24no—
83C22×C61—42no—
84C22×C61—42no—
85C22×C61—48no—
86C22×C61C22⋊Q812yes—
87C22×C61#13512yes—
88C22×C61AGL(1,ℤ/8)12yes—
89C22×C61C22×D411yescharacteristic
90C4×C61—22no—
91C4×C61—22no—
92C4×C61—42no—
93C4×C61C22⋊Q812yes—
94C4×C61C22×Q811yescharacteristic
95C4×C61C2×#4111yescharacteristic
96Dic61—42no—
97Dic61—42no—
98C2×#478—611nomaximal, Sylow
99C2×C61—44no—
100C2×C61#47814yescomplemented
101C2×C61C2×C22⋊Q811yescharacteristic
102C2×C61C2×#13511yescharacteristic
103C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
104C2×#125—611no—
105C2×C4×D4D6111yescharacteristic
106#478—618no—
107C2×#107—611no—
108C2×#106—611no—
109C2×C4⋊C8—611no—
110C2×#102—611no—
111C2×#102—611no—
112C61C2×#47811yescharacteristic, complemented, Sylow
113C22×D4C2×D6111yescharacteristic
114C23×C4—21no—
115C22×C8—611no—
116C22×C8—611no—
117#125—614no—
118#125—1222no—
119C4×D4—22no—
120C4×D4C2×D6114yes—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—611no—
123C2×C4⋊C4—1221no—
124C2×C4⋊C4—1221no—
125C2×C4⋊C4C2×D6111yescharacteristic
126C2×C22⋊C4—21no—
127C2×C42C2×D6111yescharacteristic
128#107—614no—
129#106—614no—
130C4⋊C8—614no—
131#102—614no—
132#102—614no—
133C24—21no—
134C2×D4—22no—
135C2×D4—21no—
136C2×D4Dic12214yes—
137C2×D4C22×D6112yes—
138C22×C4—21no—
139C22×C4—24no—
140C22×C4—44no—
141C22×C4—1221no—
142C22×C4—1221no—
143C22×C4C22⋊D6111yescharacteristic
144C22×C4C22⋊D6111yescharacteristic
145C22×C4C22×D6111yescharacteristic
146C2×C8—612no—
147C2×C8—612no—
148C2×C8—1222no—
149C2×C8—1222no—
150C4⋊C4—21no—
151C4⋊C4—612no—
152C4⋊C4—612no—
153C4⋊C4—1221no—
154C4⋊C4—1221no—
155C4⋊C4—1224no—
156C4⋊C4—1224no—
157C4⋊C4C22×D6112yes—
158C22⋊C4—24no—
159C42C22⋊D6112yes—
160C42C22×D6112yes—
161C23—22no—
162C23—24no—
163C23—42no—
164C23—42no—
165C23C2×C22⋊D6111yescharacteristic
166D4—22no—
167D4—24no—
168D4C2×Dic12214yes—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—48no—
173C2×C4—42no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—2442no—
177C2×C4—2442no—
178C2×C4C2×Dic12212yes—
179C2×C4#1175822212yes—
180C2×C4C2×C22⋊D6112yes—
181C2×C4C2×C22⋊D6112yes—
182C2×C4C2×C22⋊D6111yescharacteristic
183C2×C4C23×D6111yescharacteristic
184C8—1222no—
185C8—1222no—
186C22—24no—
187C22—42no—
188C22—42no—
189C22—48no—
190C22#1451975612yes—
191C22#1451979712yes—
192C22#1451980312yes—
193C22C22×C22⋊D6111yescharacteristic
194C4—22no—
195C4—22no—
196C4—42no—
197C4—2442no—
198C4—2442no—
199C4#1451975612yes—
200C4C22×Dic12211yescharacteristic
201C4C2×#1175822211yescharacteristic
202C2—44no—
203C2#1684006214yesdirect product factor
204C2C2×#1451975611yescharacteristic
205C2C2×#1451979711yescharacteristic
206C2C2×#1451980311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×C4×D4×C61C2
socleC23×C61C2×D4
hypercenterC2×C4×D4D61
hypocenterC61C2×#478
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519769C2semidirect
2. #16840062C2direct (N × H)
3. C2×#14519710C2semidirect
4. C2×#14519708C2semidirect
5. C2×C4⋊#92418C2semidirect
12. #14519769C22semidirect
17. #14519710C22semidirect
18. #14519708C22semidirect
19. C4⋊#92418C22semidirect
100. C2×C61#478semidirect
112. C61C2×#478semidirect
203. C2#16840062direct (N × H)