Finite Group Databasebeta

← #16777884

Subgroups — #16777884

Order 3328.

190 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 32 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#13129783C211yesmaximal, characteristic, complemented
2#13129742C211yesmaximal, characteristic, complemented
3#13116120C211yesmaximal, characteristic
4C13×#575C411yescharacteristic
5#11719130—21no—
6#11718898—21no—
7C2×#88077—21no—
8#11718779C2211yescharacteristic
9#11718284—21no—
10#11718152C411yescharacteristic
11C2×C13×#41—21no—
12C13×#137—41no—
13C13×AGL(1,ℤ/8)—41no—
14C13×#135—41no—
15C2×C13×M16C2×C411yescharacteristic
16C2×C4×Dic13D411yescharacteristic
17C2×#6099—21no—
18C2×#6099D411yescharacteristic
19C22⋊#1057—22no—
20#88110—41no—
21C4⋊#1057—41no—
22#88106—41no—
23#88077—41no—
24#88077—41no—
25#88076—41no—
26#88073—41no—
27#88054—41no—
28#7415—131nomaximal, Sylow
29C13×#41—41no—
30C13×#41—41no—
31C13×#41—41no—
32C13×#41—41no—
33C2×Q8×C13—21no—
34C2×D4×C13—21no—
35C2×D4×C13—41no—
36C22×C4×C13—41no—
37C22×C4×C13C22⋊C411yescharacteristic
38C22×Dic13—21no—
39C2×#1057—42no—
40C13×Q16—41no—
41C13×SD16—42no—
42C13×D8—41no—
43C13×M16—41no—
44C2×C8×C13—21no—
45C4×Dic13—21no—
46C4×Dic13D811yescharacteristic
47C4×Dic13SD1611yescharacteristic
48#6099—41no—
49#6099—41no—
50#6099—41no—
51C2×#1055—21no—
52C2×#1055—41no—
53#6092—81no—
54#2050—131no—
55#1327—131no—
56#1307—131no—
57C23×C13—41no—
58C23×C13#10411yescharacteristic
59Q8×C13—41no—
60Q8×C13—41no—
61D4×C13—41no—
62D4×C13—41no—
63D4×C13—81no—
64D4×C13—81no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—41no—
68C2×C4×C13—81no—
69C2×C4×C13—81no—
70C2×C4×C13#9911yescharacteristic
71C2×C4×C13#10211yescharacteristic
72C2×Dic13—21no—
73C2×Dic13—21no—
74C2×Dic13—81no—
75#1057—82no—
76C8×C13—41no—
77#1055—41no—
78#1055—81no—
79#575#26111yescharacteristic
80#432—261no—
81#423—131no—
82C2×#104—261no—
83#413—261no—
84#349—261no—
85#338—131no—
86C22×C13—21no—
87C22×C13—41no—
88C22×C13—81no—
89C22×C13—161no—
90C22×C13#32711yescharacteristic
91C4×C13—21no—
92C4×C13—81no—
93C4×C13AΣL(1,𝔽16)11yescharacteristic
94C4×C13#35511yescharacteristic
95Dic13—41no—
96Dic13—41no—
97C2×#41—21no—
98#137—41no—
99AGL(1,ℤ/8)—41no—
100#135—41no—
101C2×M16—131no—
102C2×M16—261no—
103C2×M16C2×#26111yescharacteristic
104C2×C42—131no—
105M32—521no—
106C4⋊C8—521no—
107C4⋊C8—521no—
108#104—521no—
109#104—521no—
110#101—521no—
111#100—521no—
112C22⋊C8—262no—
113#97—521no—
114C2×C13—21no—
115C2×C13—41no—
116C2×C13—161no—
117C2×C13#134511yescharacteristic
118#41—41no—
119#41—41no—
120#41—41no—
121#41—41no—
122C2×Q8—21no—
123C2×D4—21no—
124C2×D4—41no—
125C22×C4—41no—
126C22×C4—261no—
127C22×C4C22⋊#26111yescharacteristic
128Q16—41no—
129SD16—42no—
130D8—41no—
131M16—41no—
132M16—521no—
133M16—521no—
134M16—521no—
135C2×C8—21no—
136C2×C8—261no—
137C2×C8—521no—
138C2×C8—522no—
139C42—131no—
140C42—131no—
141C42—261no—
142C16—1041no—
143C13#741511yescharacteristic, complemented, Sylow
144C23—41no—
145C23#8811611yescharacteristic
146Q8—41no—
147Q8—41no—
148D4—41no—
149D4—41no—
150D4—81no—
151D4—81no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—261no—
158C2×C4—261no—
159C2×C4—1041no—
160C2×C4#8811511yescharacteristic
161C2×C4#8811911yescharacteristic
162C8—41no—
163C8—521no—
164C8—1041no—
165C8—1042no—
166C22—21no—
167C22—41no—
168C22—81no—
169C22—161no—
170C22#1171829211yescharacteristic
171C4—21no—
172C4—81no—
173C4—521no—
174C4—521no—
175C4#1171829511yescharacteristic
176C4#1171830611yescharacteristic
177C2—21no—
178C2—41no—
179C2—161no—
180C2#1312981811yescharacteristic
subgroupG/H
centerC2#13129818
commutatorC2×C13×M16C2×C4
FrattiniC2×M16C2×#261
Fitting, prime radicalC13×#575C4
socleC2×C13#1345
cosocle#11718779C22
hypercenter#575#261
hypocenterC13#7415
LCSG ▷ C2×C13×M16 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #13129783C2semidirect
2. #13129742C2semidirect
143. C13#7415semidirect

Maximal subgroups

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

subgroupindex
#131297832
#131297422
#131161202
#741513