Finite Group Databasebeta

← #13114142

Subgroups — #13114142

Order 1664.

228 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C13×H(3,𝔽4)C211yesmaximal, characteristic
2#11718721C211yesmaximal, characteristic, complemented
3#11718716C212yesmaximal, complemented
4#11718132C212yesmaximal, complemented
5#11718132C211yesmaximal, characteristic, complemented
6C13×#124—22no—
7C13×#124—21no—
8C13×#124C2212yes—
9C13×#124C2211yescharacteristic
10C13×#120—22no—
11C13×#120—21no—
12C2×#6107—21no—
13C2×#6105—21no—
14#88123C2211yescharacteristic, complemented
15#88075—22no—
16#88072—22no—
17#88043C2212yescomplemented
18#88043C2211yescharacteristic, complemented
19C24×C13—21no—
20C2×Q8×C13D412yes—
21C2×Q8×C13D411yescharacteristic
22C2×D4×C13—21no—
23C2×D4×C13—22no—
24C2×D4×C13D412yes—
25C2×D4×C13D411yescharacteristic
26C2×Dic26—21no—
27C13×C22⋊C4—22no—
28C13×C22⋊C4—21no—
29C13×C22⋊C4—22no—
30C13×C22⋊C4—22no—
31C13×C22⋊C4—22no—
32C42×C13—21no—
33C42×C13C2311yescharacteristic
34#6107—42no—
35#6105—42no—
36C4⋊Dic13—22no—
37C2×#1055—21no—
38C2×#1055—22no—
39#1659—131nomaximal, Sylow
40C23×C13—21no—
41C23×C13—22no—
42C23×C13—81no—
43C23×C13—82no—
44Q8×C13—41no—
45Q8×C13—42no—
46D4×C13—41no—
47D4×C13—42no—
48D4×C13—81no—
49D4×C13—82no—
50C2×C4×C13—21no—
51C2×C4×C13—22no—
52C2×C4×C13C2×D412yes—
53C2×C4×C13C2×D411yescharacteristic
54C2×Dic13—41no—
55Dic26—41no—
56Dic26—41no—
57#1055—22no—
58#1055—42no—
59H(3,𝔽4)D1311yescharacteristic
60#497—131no—
61#489—132no—
62#329—131no—
63#329—132no—
64C22×C13—41no—
65C22×C13—42no—
66C22×C13—42no—
67C22×C13—42no—
68C22×C13—42no—
69C22×C13—84no—
70C22×C13#12011yescharacteristic
71C4×C13—21no—
72C4×C13—22no—
73C4×C13—41no—
74C4×C13—42no—
75Dic13—81no—
76C2×Q16—261no—
77C2×SD16—261no—
78C4⋊Q8—131no—
79#124—22no—
80#124—21no—
81#124C2×D1312yes—
82#124C2×D1311yescharacteristic
83#120—22no—
84#120—21no—
85#103—262no—
86#102—262no—
87#97—132no—
88#97—131no—
89C2×C13—81no—
90C2×C13—82no—
91C2×C13#45311yescharacteristic
92C2×C13#45512yes—
93C24—21no—
94C2×Q8—261no—
95C2×Q8C22⋊D1312yes—
96C2×Q8C22⋊D1311yescharacteristic
97C2×D4—21no—
98C2×D4—22no—
99C2×D4C22⋊D1312yes—
100C2×D4C22⋊D1311yescharacteristic
101Q16—522no—
102SD16—522no—
103C2×C8—261no—
104C2×C8—262no—
105C4⋊C4—262no—
106C22⋊C4—22no—
107C22⋊C4—21no—
108C22⋊C4—22no—
109C22⋊C4—22no—
110C22⋊C4—22no—
111C42—21no—
112C42C22×D1311yescharacteristic
113C13#165911yescharacteristic, complemented, Sylow
114C23—21no—
115C23—22no—
116C23—81no—
117C23—82no—
118Q8—41no—
119Q8—42no—
120Q8—521no—
121Q8—521no—
122D4—41no—
123D4—42no—
124D4—81no—
125D4—82no—
126C2×C4—21no—
127C2×C4—22no—
128C2×C4—521no—
129C2×C4C2×C22⋊D1312yes—
130C2×C4C2×C22⋊D1311yescharacteristic
131C8—262no—
132C8—522no—
133C22—41no—
134C22—42no—
135C22—42no—
136C22—42no—
137C22—42no—
138C22—84no—
139C22#8820711yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—42no—
144C4—1041no—
145C2—81no—
146C2—82no—
147C2#1171890211yescharacteristic
148C2#1171890312yes—
subgroupG/H
centerC22#88207
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
Fitting, prime radicalC13×H(3,𝔽4)C2
socleC22×C13#120
hypercenterH(3,𝔽4)D13
hypocenterC13#1659
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
2. #11718721C2semidirect
3. #11718716C2semidirect
4. #11718132C2semidirect
5. #11718132C2semidirect
14. #88123C22semidirect
17. #88043C22semidirect
18. #88043C22semidirect
113. C13#1659semidirect

Maximal subgroups

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

subgroupindex
C13×H(3,𝔽4)2
#117187212
#117187162
#117181322
#165913