Finite Group Databasebeta

← #13115939

Subgroups — #13115939

Order 1664.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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×#575C211yesmaximal, characteristic, complemented
2#11719527C212yesmaximal, complemented
3#11718895C212yesmaximal, complemented
4#11718790C211yesmaximal, characteristic, complemented
5#11718152C211yesmaximal, characteristic, complemented
6C2×C13×#41C2212yes—
7C2×#6127C2211yescharacteristic
8C13×#137—22no—
9C13×AGL(1,ℤ/8)—22no—
10C13×#135—22no—
11C2×C13×M16C2211yescharacteristic
12#88205—22no—
13#88204—24no—
14#88203—22no—
15#88196—22no—
16#88186—22no—
17C2×#6099C2212yes—
18C22×#1055C2211yescharacteristic
19C22⋊#1055—24no—
20#88060—22no—
21C13×#41—22no—
22C13×#41—22no—
23C13×#41—22no—
24C13×#41—22no—
25C2×Q8×C13D412yes—
26C2×D4×C13—22no—
27C2×D4×C13D412yes—
28C22×C4×C13—22no—
29C22×C4×C13C2311yescharacteristic
30C2×C22⋊D13—21no—
31#6127—22no—
32#6127—22no—
33C2×D52D411yescharacteristic
34C2×C4×D13—21no—
35C2×Dic26D411yescharacteristic
36C13×Q16—22no—
37C13×SD16—24no—
38C13×D8—22no—
39C13×M16—22no—
40C2×C8×C13D412yes—
41#6107—24no—
42#6106—24no—
43#6105—24no—
44#6104—24no—
45#6099—22no—
46#6099—22no—
47C2×#1055—22no—
48C2×#1055—21no—
49C2×#1055D414yes—
50#2017—131nomaximal, Sylow
51C23×C13—22no—
52C23×C13#4111yescharacteristic
53C22×D13—21no—
54Q8×C13—22no—
55Q8×C13—22no—
56D4×C13—22no—
57D4×C13—22no—
58D4×C13—42no—
59D4×C13—42no—
60C2×C4×C13—22no—
61C2×C4×C13—42no—
62C2×C4×C13—42no—
63C2×C4×C13C2×D411yescharacteristic
64C2×C4×C13C2×D412yes—
65C2×C4×C13C2×D412yes—
66C2×C4×C13C2×D411yescharacteristic
67C22⋊D13—42no—
68C2×Dic13—21no—
69D52—22no—
70C4×D13—41no—
71C4×D13—41no—
72Dic26—22no—
73C8×C13—22no—
74#1055—24no—
75#1055—41no—
76#575—132no—
77#575D1311yescharacteristic, complemented
78#408—132no—
79#408—131no—
80#338—131no—
81C22×C13—41no—
82C22×C13—44no—
83C22×C13—42no—
84C22×C13#12111yescharacteristic
85C22×C13#12112yes—
86C2×D13—42no—
87C2×D13—41no—
88C4×C13—42no—
89C4×C13#12012yes—
90C4×C13#12011yescharacteristic
91C4×C13#12711yescharacteristic
92Dic13—41no—
93C2×#41—131no—
94C2×#41C2×D1312yes—
95#137—22no—
96#137—262no—
97#137—262no—
98AGL(1,ℤ/8)—22no—
99AGL(1,ℤ/8)—262no—
100AGL(1,ℤ/8)—262no—
101#135—22no—
102#135—264no—
103C2×M16—132no—
104C2×M16C2×D1311yescharacteristic
105C22×C8—131no—
106C22⋊C8—264no—
107C22⋊C8—262no—
108C2×C13—21no—
109C2×C13—22no—
110C2×C13—82no—
111C2×C13#39211yescharacteristic
112D13—81no—
113#41—22no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—262no—
118#41—262no—
119C2×Q8—131no—
120C2×Q8C22⋊D1312yes—
121C2×D4—22no—
122C2×D4—131no—
123C2×D4—261no—
124C2×D4C22⋊D1312yes—
125C22×C4—22no—
126C22×C4—261no—
127C22×C4C22×D1311yescharacteristic
128Q16—22no—
129Q16—264no—
130SD16—24no—
131SD16—264no—
132SD16—264no—
133D8—22no—
134D8—264no—
135M16—22no—
136M16—262no—
137M16—262no—
138C2×C8—134no—
139C2×C8—262no—
140C2×C8—261no—
141C2×C8C22⋊D1312yes—
142C13#201711yescharacteristic, complemented, Sylow
143C23—22no—
144C23—261no—
145C23#612911yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—262no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—262no—
154D4—522no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—261no—
159C2×C4—521no—
160C2×C4—521no—
161C2×C4D4×D1311yescharacteristic
162C2×C4D4×D1312yes—
163C2×C4C2×C22⋊D1312yes—
164C2×C4C2×C22⋊D1311yescharacteristic
165C8—22no—
166C8—264no—
167C8—521no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—522no—
172C22—521no—
173C22#8819211yescharacteristic
174C22#8819312yes—
175C4—42no—
176C4—521no—
177C4#8819112yes—
178C4#8819411yescharacteristic
179C4#8820711yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—1041no—
184C2#1171888411yescharacteristic
subgroupG/H
centerC4#88194
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#575C2
socleC2×C13#392
hypercenter#575D13
hypocenterC13#2017
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C13×#575C2semidirect
2. #11719527C2semidirect
3. #11718895C2semidirect
4. #11718790C2semidirect
5. #11718152C2semidirect
77. #575D13semidirect
142. C13#2017semidirect

Maximal subgroups

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

subgroupindex
C13×#5752
#117195272
#117188952
#117187902
#117181522
#201713