Finite Group Databasebeta

← #13116124

Subgroups — #13116124

Order 1664.

266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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
1#11719453C211yesmaximal, characteristic
2C2×#88065C212yesmaximal, complemented
3#11718793C212yesmaximal, complemented
4#11718779C211yesmaximal, characteristic, complemented
5C13×#338C211yesmaximal, characteristic, complemented
6C2×#6127C2212yes—
7C2×C13×M16C2212yes—
8C2×C13×M16C2211yescharacteristic
9C2×C4×Dic13C2211yescharacteristic
10C2×#6099C2211yescharacteristic
11#88163—22no—
12#88162—22no—
13#88158—22no—
14#88065—22no—
15#88065—22no—
16#88064—22no—
17#88063—22no—
18#88054—22no—
19C22×C4×C13C2311yescharacteristic
20C2×C22⋊D13—22no—
21C22×Dic13—21no—
22#6127—22no—
23#6127—22no—
24#6127—22no—
25#6127—22no—
26C2×D52D412yes—
27C2×C4×D13—22no—
28C2×Dic26D412yes—
29C13×M16—22no—
30C13×M16—22no—
31C13×M16—22no—
32C2×C8×C13—22no—
33C2×C8×C13D412yes—
34C4×Dic13—21no—
35C4×Dic13D411yescharacteristic
36C4×Dic13D411yescharacteristic
37#6099—22no—
38C2×#1055—21no—
39Dic52—22no—
40D104—22no—
41#6095—24no—
42#2050—131nomaximal, Sylow
43C23×C13#4111yescharacteristic
44C22×D13—22no—
45C2×C4×C13C2×D412yes—
46C2×C4×C13C2×D411yescharacteristic
47C2×C4×C13C2×D411yescharacteristic
48C2×C4×C13#4112yes—
49C22⋊D13—42no—
50C22⋊D13—42no—
51C2×Dic13—21no—
52C2×Dic13—21no—
53C2×Dic13—22no—
54C2×Dic13—42no—
55D52—22no—
56D52—22no—
57C4×D13—42no—
58C4×D13—42no—
59Dic26—22no—
60Dic26—22no—
61C8×C13—22no—
62C8×C13—42no—
63#1055—41no—
64#575—131no—
65#423—131no—
66C2×#104—132no—
67#413—132no—
68#338D1311yescharacteristic, complemented
69C22×C13—41no—
70C22×C13#12111yescharacteristic
71C22×C13#12312yes—
72C2×D13—42no—
73C2×D13—82no—
74C4×C13#12011yescharacteristic
75C4×C13#12112yes—
76C4×C13#12411yescharacteristic
77Dic13—22no—
78Dic13—41no—
79Dic13—42no—
80C2×#41—132no—
81#137—262no—
82AGL(1,ℤ/8)—262no—
83#135—262no—
84C2×M16—131no—
85C2×M16C2×D1312yes—
86C2×M16C2×D1311yescharacteristic
87C2×C42—131no—
88C4⋊C8—262no—
89#104—262no—
90#104—262no—
91#101—262no—
92#100—262no—
93C2×C13—21no—
94C2×C13—22no—
95C2×C13#39411yescharacteristic
96D13—82no—
97#41—262no—
98#41—262no—
99#41—262no—
100#41—262no—
101C2×Q8—132no—
102C2×D4—132no—
103C2×D4—262no—
104C22×C4—261no—
105C22×C4—262no—
106C22×C4C22×D1311yescharacteristic
107Q16—262no—
108SD16—264no—
109D8—262no—
110M16—22no—
111M16—22no—
112M16—22no—
113M16—262no—
114C2×C8—22no—
115C2×C8—261no—
116C2×C8D5212yes—
117C42—131no—
118C42—131no—
119C42—261no—
120C13#205011yescharacteristic, complemented, Sylow
121C23—262no—
122C23#613111yescharacteristic
123Q8—262no—
124Q8—262no—
125D4—262no—
126D4—262no—
127D4—522no—
128D4—522no—
129C2×C4—261no—
130C2×C4—262no—
131C2×C4—261no—
132C2×C4—522no—
133C2×C4—522no—
134C2×C4—522no—
135C2×C4C2×D5211yescharacteristic
136C2×C4#612712yes—
137C2×C4D4×D1312yes—
138C2×C4D4×D1311yescharacteristic
139C8—22no—
140C8—42no—
141C8—521no—
142C22—41no—
143C22—522no—
144C22—1042no—
145C22#8814812yes—
146C22#8814911yescharacteristic
147C4—262no—
148C4—521no—
149C4—522no—
150C4#8812911yescharacteristic
151C4#8813611yescharacteristic
152C4#8813812yes—
153C2—21no—
154C2—22no—
155C2—1042no—
156C2#1171833311yescharacteristic
subgroupG/H
centerC4#88129
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#338C2
socleC2×C13#394
prime radical#11719453C2
hypercenter#338D13
hypocenterC13#2050
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #338

Complements

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

NH ≅ G/Ntype
2. C2×#88065C2semidirect
3. #11718793C2semidirect
4. #11718779C2semidirect
5. C13×#338C2semidirect
68. #338D13semidirect
120. C13#2050semidirect

Maximal subgroups

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

subgroupindex
#117194532
C2×#880652
#117187932
#117187792
C13×#3382
#205013