Finite Group Databasebeta

← C2×#16840671 #21462106

Subgroups — C2×#16840671 #21462106

Order 7808.

260 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 58 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×#14519838C212yesmaximal, complemented
2#16840671C214yesmaximal, direct product factor
3C2×#14519765C211yesmaximal, characteristic
4C2×#11758217—22no—
5#14519838—22no—
6#14519838C2214yescomplemented
7C22×Dic122C2211yescharacteristic
8C22×D244C411yescharacteristic
9#14519765—22no—
10#14519765C412yes—
11#14519765C2212yes—
12C2×#11758198—22no—
13C2×C42×C61C411yescharacteristic
14C23×D61—21no—
15C22×C4×C61—21no—
16C22×C4×C61C2×C411yescharacteristic
17C22×Dic61D412yes—
18C2×D244—21no—
19C2×D244—41no—
20C2×D244—41no—
21C2×D244C2×C412yes—
22C2×Dic122—41no—
23C2×Dic122—41no—
24C2×Dic122C2×C411yescharacteristic
25C2×Dic122D412yes—
26C2×Dic122C2311yescharacteristic
27#11758217—24no—
28#11758217—42no—
29C2×#92420—42no—
30C42×C61—21no—
31C42×C61C2×C412yes—
32#11758198—24no—
33#11758198—24no—
34C23×C61C22⋊C411yescharacteristic
35C22×D61—22no—
36C22×D61—44no—
37C22×D61—41no—
38C22×D61—41no—
39C2×C4×C61—21no—
40C2×C4×C61—21no—
41C2×C4×C61—22no—
42C2×C4×C61—42no—
43C2×C4×C61C22⋊C411yescharacteristic
44C2×C4×C61C22×C411yescharacteristic
45C2×Dic61—22no—
46C2×Dic61—22no—
47C2×Dic61C22⋊C412yes—
48C2×Dic61C2×D412yes—
49D244—42no—
50D244—42no—
51Dic122—41no—
52Dic122—42no—
53Dic122—41no—
54#92420—44no—
55C22×C61—22no—
56C22×C61#9911yescharacteristic
57C22×C61#9911yescharacteristic
58C22×C61C2×C22⋊C411yescharacteristic
59C2×D61—44no—
60C2×D61—42no—
61C2×D61—82no—
62C2×D61—82no—
63C4×C61—21no—
64C4×C61—21no—
65C4×C61—42no—
66Dic61—22no—
67Dic61—22no—
68C2×#355—611nomaximal, Sylow
69C2×C61—21no—
70C2×C61—21no—
71C2×C61#35512yescomplemented
72C2×C61C2×#9911yescharacteristic
73D61—82no—
74C2×#124—611no—
75C2×#101—612no—
76#355—614no—
77C61C2×#35511yescharacteristic, complemented, Sylow
78C22×Q8—611no—
79C22×D4—611no—
80C2×M16—1222no—
81#124—612no—
82#124—612no—
83#124—1222no—
84C2×C22⋊C4—1222no—
85C2×C42#692311yescharacteristic
86#101—614no—
87#101—1222no—
88C24—1221no—
89C2×Q8—612no—
90C2×Q8—611no—
91C2×Q8—611no—
92C2×Q8—2441no—
93C2×Q8—2441no—
94C2×D4—612no—
95C2×D4—1221no—
96C2×D4—2441no—
97C2×D4—2441no—
98C22×C4—21no—
99C22×C4—612no—
100C22×C4C2×#692311yescharacteristic
101M16—1224no—
102M16—2442no—
103C2×C8—2442no—
104C22⋊C4—1224no—
105C22⋊C4—1224no—
106C42—21no—
107C42C2×#692312yes—
108C23—1222no—
109C23—2444no—
110C23—2441no—
111C23—2441no—
112C23C22⋊#692311yescharacteristic
113Q8—2442no—
114Q8—2441no—
115Q8—2441no—
116D4—2442no—
117D4—2442no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—22no—
121C2×C4—42no—
122C2×C4—612no—
123C2×C4—612no—
124C2×C4—1222no—
125C2×C4—1222no—
126C2×C4C22⋊#692311yescharacteristic
127C2×C4C22×#692311yescharacteristic
128C8—2444no—
129C22—22no—
130C22—4882no—
131C22—4882no—
132C22—2444no—
133C22—2442no—
134C22#1451983611yescharacteristic
135C22#1451983611yescharacteristic
136C22C2×C22⋊#692311yescharacteristic
137C4—21no—
138C4—21no—
139C4—42no—
140C4—1222no—
141C4—1222no—
142C2—21no—
143C2—21no—
144C2—4882no—
145C2#1684067112yesdirect product factor
146C2C2×#1451983611yescharacteristic
subgroupG/H
centerC22#14519836
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×C42×C61C4
socleC22×C61#99
hypercenterC2×C42#6923
hypocenterC61C2×#355
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#14519838C2semidirect
2. #16840671C2direct (N × H)
6. #14519838C22semidirect
71. C2×C61#355semidirect
77. C61C2×#355semidirect
145. C2#16840671direct (N × H)