Finite Group Databasebeta

← C4×#14519838 #21461571

Subgroups — C4×#14519838 #21461571

Order 7808.

296 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 96 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
2C4×#11758217C212yesmaximal
3#16840642C212yesmaximal
4C2×C4×Dic122C211yesmaximal, characteristic
5C2×#11758217C2214yes—
6#14519838C418yesdirect product factor
7#14519832—22no—
8C4×#92420—22no—
9C22×Dic122C2211yescharacteristic
10C4×Dic122—22no—
11C4×Dic122—22no—
12C2×C4⋊Dic61C411yescharacteristic
13C2×#11758196C411yescharacteristic
14C2×#11758196C2211yescharacteristic
15C2×C4×Dic61C411yescharacteristic
16C2×C4×Dic61C2211yescharacteristic
17C2×C42×C61C411yescharacteristic
18C22×C4×C61C2×C411yescharacteristic
19C22×C4×C61C2×C411yescharacteristic
20C22×C4×C61C2×C411yescharacteristic
21C22×Dic61C2×C411yescharacteristic
22C22×Dic61C2×C411yescharacteristic
23C22×Dic61C2×C411yescharacteristic
24C22×Dic61C2311yescharacteristic
25C2×Dic122—22no—
26C2×Dic122—22no—
27C2×Dic122C2×C414yes—
28#11758217—24no—
29#11758217C2×C418yes—
30C2×#92420—24no—
31C42×C61—21no—
32C42×C61—21no—
33C4⋊Dic61—22no—
34#11758196—22no—
35#11758196—22no—
36C4×Dic61—21no—
37C4×Dic61—21no—
38C4×Dic61D412yes—
39C4×Dic61D412yes—
40C23×C61C22×C411yescharacteristic
41C2×C4×C61—21no—
42C2×C4×C61—21no—
43C2×C4×C61—22no—
44C2×C4×C61—21no—
45C2×C4×C61—41no—
46C2×C4×C61C4212yes—
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×Dic61—21no—
50C2×Dic61—21no—
51C2×Dic61—21no—
52C2×Dic61—41no—
53C2×Dic61—41no—
54C2×Dic61C4212yes—
55C2×Dic61C22⋊C412yes—
56C2×Dic61C22×C412yes—
57C2×Dic61C2×D412yes—
58C2×Dic61#4112yes—
59Dic122—28no—
60#92420—28no—
61C22×C61—21no—
62C22×C61—21no—
63C22×C61C2×C4211yescharacteristic
64C22×C61C2×C22⋊C411yescharacteristic
65C22×C61#11711yescharacteristic
66C4×C61—22no—
67C4×C61—21no—
68C4×C61—41no—
69C4×C61#10112yescomplemented
70Dic61—22no—
71Dic61—22no—
72Dic61—41no—
73Dic61C4×D414yes—
74C4×#101—611nomaximal, Sylow
75C2×C61—21no—
76C2×C61—21no—
77C2×C61C4×C22⋊C411yescharacteristic
78C2×C61C2×#10111yescharacteristic
79C2×C61#41311yescharacteristic
80C2×C4×Q8—611no—
81C2×#101—612no—
82C4×M16—612no—
83#343—612no—
84C61C4×#10111yescharacteristic, complemented, Sylow
85C22×Q8—611no—
86C2×M16—614no—
87C4×Q8—1222no—
88C4×Q8—1222no—
89C2×C4⋊C4—611no—
90C2×C4⋊C4—611no—
91C2×C4⋊C4—611no—
92C2×C42—611no—
93C2×C42—611no—
94C2×C42#692311yescharacteristic
95#101—618no—
96#97—1222no—
97C4×C8—1222no—
98C2×Q8—614no—
99C2×Q8—1222no—
100C2×Q8—1222no—
101C22×C4—611no—
102C22×C4—611no—
103C22×C4—611no—
104C22×C4—611no—
105C22×C4C2×#692311yescharacteristic
106C22×C4C2×#692311yescharacteristic
107C22×C4C2×#692311yescharacteristic
108M16—618no—
109M16—1224no—
110C2×C8—1224no—
111C4⋊C4—1222no—
112C4⋊C4—1222no—
113C4⋊C4—1222no—
114C42—21no—
115C42—21no—
116C42—612no—
117C42—612no—
118C42—1221no—
119C42—1221no—
120C23C22×#692311yescharacteristic
121Q8—1228no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—22no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—612no—
128C2×C4—612no—
129C2×C4—612no—
130C2×C4—612no—
131C2×C4—612no—
132C2×C4—1221no—
133C2×C4—1221no—
134C2×C4—1221no—
135C2×C4—2441no—
136C2×C4—2441no—
137C2×C4C4×#692312yes—
138C2×C4C22⋊#692311yescharacteristic
139C2×C4C22⋊#692311yescharacteristic
140C8—1228no—
141C22—21no—
142C22—21no—
143C22C2×C4×#692311yescharacteristic
144C22C2×C22⋊#692311yescharacteristic
145C22#1451985611yescharacteristic
146C4—21no—
147C4—22no—
148C4—41no—
149C4—614no—
150C4—1222no—
151C4—1222no—
152C4—2441no—
153C4#1451983812yesdirect product factor
154C2—21no—
155C2—21no—
156C2C4×C22⋊#692311yescharacteristic
157C2C2×#1451983811yescharacteristic
158C2#1684074811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC22×C61C2×C42
FrattiniC23C22×#6923
FittingC2×C42×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C42#6923
hypocenterC61C4×#101
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
6. #14519838C4direct (N × H)
69. C4×C61#101semidirect
84. C61C4×#101semidirect
153. C4#14519838direct (N × H)