Finite Group Databasebeta

← C2×#14271560 #16829990

Subgroups — C2×#14271560 #16829990

Order 3712.

424 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 181 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×#11745250C212yesmaximal
2#14271560C218yesmaximal, direct product factor
3C2×#11745165C211yesmaximal, characteristic
4C2×#11745156C212yesmaximal
5C2×C8×Dic29C211yesmaximal, characteristic
6C2×C29×#106C211yesmaximal, characteristic
7C22×Dic58—22no—
8C22×C8×C29C2211yescharacteristic
9C2×C4⋊C4×C29C2212yes—
10C2×C4⋊Dic29C2212yes—
11C2×#90779—22no—
12C2×C4×Dic29C2211yescharacteristic
13C22×#6597C2211yescharacteristic
14#11745250—24no—
15#11745250C2218yes—
16C29×#106C2214yes—
17#11745165C2214yes—
18C8×Dic29C2214yes—
19#11745156C2218yes—
20C22×C4×C29—22no—
21C22×C4×C29C2311yescharacteristic
22C22×Dic29—22no—
23C22×Dic29D412yes—
24C2×Dic58—28no—
25C2×Dic58—48no—
26C2×C8×C29Q814yescomplemented
27C2×C8×C29C2312yes—
28C4⋊C4×C29—22no—
29C4⋊C4×C29C2314yes—
30C4⋊Dic29—22no—
31C4⋊Dic29C2314yes—
32#90779—28no—
33C4×Dic29D412yes—
34C4×Dic29C2312yes—
35C2×#6597Q814yescomplemented
36C2×#6597C2312yes—
37C23×C29C2×D411yescharacteristic
38C2×C4×C29—24no—
39C2×C4×C29—44no—
40C2×C4×C29C2×D411yescharacteristic
41C2×C4×C29C2×Q812yes—
42C2×C4×C29C2×Q812yes—
43C2×C4×C29C2411yescharacteristic
44C2×Dic29—24no—
45C2×Dic29—44no—
46C2×Dic29SD1618yes—
47C2×Dic29C2×D414yes—
48Dic58—416no—
49C8×C29C2×Q814yescomplemented
50#6597C2×Q814yescomplemented
51C2×#498—291nomaximal, Sylow
52C22×C29C4⋊Q812yes—
53C22×C29C2×SD1614yes—
54C22×C29C22×D411yescharacteristic
55C4×C29—44no—
56C4×C29C4⋊Q812yes—
57C4×C29C22×Q811yescharacteristic
58C4×C29C22×Q811yescharacteristic
59Dic29—44no—
60Dic29C2×SD1618yes—
61C2×C4⋊Q8—292no—
62#498—298no—
63C2×#106—291no—
64C2×#106—292no—
65C2×#106D2911yescharacteristic
66C2×C4×C8—291no—
67C2×C29#49814yescomplemented
68C2×C29C2×C4⋊Q811yescharacteristic
69C2×C29C22×SD1612yes—
70C22×Q8—582no—
71C22×C8—291no—
72C22×C8C2×D2911yescharacteristic
73C4⋊Q8—298no—
74C4⋊Q8—584no—
75C2×C4⋊C4—292no—
76C2×C4⋊C4—582no—
77C2×C4⋊C4C2×D2912yes—
78C2×C42—291no—
79#106—294no—
80#106—298no—
81#106C2×D2914yes—
82C4×C8—294no—
83C29C2×#49811yescharacteristic, complemented, Sylow
84C2×Q8—588no—
85C2×Q8—1168no—
86C22×C4—22no—
87C22×C4—292no—
88C22×C4—582no—
89C22×C4C22×D2911yescharacteristic
90C2×C8—294no—
91C2×C8—292no—
92C2×C8Dic5814yescomplemented
93C2×C8C22×D2912yes—
94C4⋊C4—22no—
95C4⋊C4—294no—
96C4⋊C4—588no—
97C4⋊C4—582no—
98C4⋊C4C22×D2914yes—
99C42—292no—
100C42—292no—
101C23D4×D2911yescharacteristic
102Q8—11616no—
103C2×C4—24no—
104C2×C4—44no—
105C2×C4—294no—
106C2×C4—298no—
107C2×C4—584no—
108C2×C4—1164no—
109C2×C4C2×Dic5812yes—
110C2×C4D4×D2911yescharacteristic
111C2×C4Q8×D2912yes—
112C2×C4C23×D2911yescharacteristic
113C8—294no—
114C8C2×Dic5814yescomplemented
115C22#1174525012yes—
116C22SD16×D2914yes—
117C22C2×D4×D2911yescharacteristic
118C4—44no—
119C4—298no—
120C4—1164no—
121C4#1174525012yes—
122C4C22×Dic5811yescharacteristic
123C4C2×Q8×D2911yescharacteristic
124C2#1427156014yesdirect product factor
125C2C2×#1174525011yescharacteristic
126C2C2×SD16×D2912yes—
subgroupG/H
centerC23D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#106C2
socle, prime radicalC23×C29C2×D4
hypercenterC2×#106D29
hypocenterC29C2×#498
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. #14271560C2direct (N × H)
26. C2×C8×C29Q8semidirect
35. C2×#6597Q8semidirect
49. C8×C29C2×Q8semidirect
50. #6597C2×Q8semidirect
67. C2×C29#498semidirect
83. C29C2×#498semidirect
92. C2×C8Dic58semidirect
114. C8C2×Dic58semidirect
124. C2#14271560direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117452502
#142715602
C2×#117451652
C2×#117451562
C2×C8×Dic292
C2×C29×#1062
C2×#49829