Finite Group Databasebeta

← C4×#14556514 #22609754

Subgroups — C4×#14556514 #22609754

Order 9344.

332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×Dic146C211yesmaximal, characteristic
2C2×#14556514C212yesmaximal
3C2×C4×#10596831C211yesmaximal, characteristic
4#17988349C212yesmaximal
5C4×C4⋊C4×C73C211yesmaximal, characteristic
6C22×Dic146C2211yescharacteristic
7C22×#10596831C2212yes—
8C4×Dic146—22no—
9C4×Dic146C414yescomplemented
10C2×C4⋊Dic73C2211yescharacteristic
11C2×#11924007—21no—
12C2×C4×Dic73—21no—
13#14556514C418yesdirect product factor
14C4×#10596831—22no—
15C2×C4⋊C4×C73C2212yes—
16C2×C42×C73—21no—
17C2×C42×C73C2211yescharacteristic
18#95×C73—21no—
19C2×Dic146—21no—
20C2×Dic146—22no—
21C2×Dic146C2×C414yes—
22C2×Dic146C2×C412yes—
23C22×Dic73—21no—
24C22×Dic73—21no—
25C2×#10596831—22no—
26C2×#10596831—22no—
27C2×#10596831C2×C414yes—
28C4⋊Dic73—21no—
29C4⋊Dic73C2×C412yes—
30#11924007—24no—
31C4×Dic73—24no—
32C22×C4×C73—22no—
33C22×C4×C73D411yescharacteristic
34C22×C4×C73D411yescharacteristic
35C22×C4×C73C2311yescharacteristic
36C4⋊C4×C73—22no—
37C4⋊C4×C73C2×C414yes—
38C42×C73—42no—
39C42×C73C2×C412yes—
40C42×C73D412yes—
41C23×C73C2×D411yescharacteristic
42C2×C4×C73—22no—
43C2×C4×C73—24no—
44C2×C4×C73—42no—
45C2×C4×C73—42no—
46C2×C4×C73C22⋊C412yes—
47C2×C4×C73C22⋊C412yes—
48C2×C4×C73SD1612yes—
49C2×C4×C73Q1612yes—
50C2×C4×C73C22×C411yescharacteristic
51C2×C4×C73C22×C412yes—
52C2×C4×C73C2×D411yescharacteristic
53C2×C4×C73#4112yes—
54C2×Dic73—22no—
55C2×Dic73—24no—
56C2×Dic73—22no—
57C2×Dic73—42no—
58Dic146—22no—
59Dic146—24no—
60Dic146C4214yescomplemented
61#10596831—24no—
62C22×C73C2×C22⋊C411yescharacteristic
63C22×C73C4×D412yes—
64C22×C73C2×SD1611yescharacteristic
65C22×C73C2×Q1611yescharacteristic
66C22×C73#13512yes—
67C4×C73—22no—
68C4×C73—44no—
69C4×C73#10314yescomplemented
70C4×C73C2×C4211yescharacteristic
71C4×C73#11711yescharacteristic
72C4×C73C4×D412yes—
73Dic73—24no—
74Dic73—42no—
75C2×C73C4×C22⋊C411yescharacteristic
76C2×C73C2×#10311yescharacteristic
77C2×C73#41611yescharacteristic
78C2×C73C4×SD1612yes—
79C2×C73C4×Q1612yes—
80C4×#103—731nomaximal, Sylow
81C73C4×#10311yescharacteristic, complemented, Sylow
82C2×C4×Q8—731no—
83C2×#103—732no—
84C2×C4×C8—731no—
85C4×C4⋊C4D7311yescharacteristic
86#340—732no—
87C22×Q8—731no—
88C22×C8—732no—
89C4×Q8—734no—
90C4×Q8—1462no—
91C2×C4⋊C4—731no—
92C2×C4⋊C4—1461no—
93C2×C4⋊C4C2×D7312yes—
94C2×C42—21no—
95C2×C42—1461no—
96C2×C42C2×D7311yescharacteristic
97#103—738no—
98C4×C8—1462no—
99#95—21no—
100C2×Q8—734no—
101C2×Q8—732no—
102C2×Q8—1461no—
103C2×Q8—1462no—
104C22×C4—22no—
105C22×C4—1461no—
106C22×C4—1461no—
107C22×C4C22⋊D7311yescharacteristic
108C22×C4C22⋊D7311yescharacteristic
109C22×C4C22×D7311yescharacteristic
110C2×C8—734no—
111C2×C8—1462no—
112C2×C8—1462no—
113C4⋊C4—22no—
114C4⋊C4—732no—
115C4⋊C4—1464no—
116C4⋊C4—1461no—
117C4⋊C4C4×D7314yes—
118C42—42no—
119C42—1464no—
120C42C4×D7312yes—
121C42D29212yes—
122C23C2×C22⋊D7311yescharacteristic
123Q8—734no—
124Q8—1462no—
125Q8—1464no—
126C2×C4—22no—
127C2×C4—24no—
128C2×C4—42no—
129C2×C4—42no—
130C2×C4—2922no—
131C2×C4—1462no—
132C2×C4—1462no—
133C2×C4—1464no—
134C2×C4#1192400512yes—
135C2×C4#1192400512yes—
136C2×C4#1192401612yes—
137C2×C4#1192401812yes—
138C2×C4C2×C4×D7311yescharacteristic
139C2×C4C2×C4×D7312yes—
140C2×C4C2×D29211yescharacteristic
141C2×C4#1192402812yes—
142C8—1464no—
143C22C2×#1192400511yescharacteristic
144C22C4×C22⋊D7312yes—
145C22C2×#1192401611yescharacteristic
146C22C2×#1192401811yescharacteristic
147C22#1455661112yes—
148C4—22no—
149C4—44no—
150C4—2922no—
151C4—1464no—
152C4#1455651414yesdirect product factor
153C4C42×D7311yescharacteristic
154C4#1455654811yescharacteristic
155C4C4×D29212yes—
156C2C4×#1192400511yescharacteristic
157C2C2×#1455651411yescharacteristic
158C2#1798858111yescharacteristic
159C2C4×#1192401612yes—
160C2C4×#1192401812yes—
subgroupG/H
centerC22×C4C22⋊D73
commutatorC4×C73C2×C42
FrattiniC22×C4C22×D73
FittingC4×C4⋊C4×C73C2
socleC23×C73C2×D4
hypercenterC4×C4⋊C4D73
hypocenterC73C4×#103
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. C4×Dic146C4semidirect
13. #14556514C4direct (N × H)
60. Dic146C42semidirect
69. C4×C73#103semidirect
81. C73C4×#103semidirect
152. C4#14556514direct (N × H)