Finite Group Databasebeta

← #16777945

Subgroups — #16777945

Order 3328.

198 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 36 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#13129779C211yesmaximal, characteristic
2#13129714C211yesmaximal, characteristic
3#13116178C211yesmaximal, characteristic
4C13×#544C411yescharacteristic
5C2×#88112—21no—
6#11718656—21no—
7#11718637C2211yescharacteristic
8#11718285—21no—
9#11718124—21no—
10#11718122C411yescharacteristic
11C22×#1057—41no—
12C13×C4⋊Q8—41no—
13C13×#125—41no—
14C13×C22⋊Q8—41no—
15C13×#117—21no—
16C2×C13×C4⋊C4C2×C411yescharacteristic
17C2×C4⋊Dic13D411yescharacteristic
18C2×#6101—41no—
19C2×C4×Dic13D411yescharacteristic
20C2×#6099—21no—
21C22⋊#1057—41no—
22#88112—22no—
23#88112—41no—
24#88048—41no—
25#88047—41no—
26#7443—131nomaximal, Sylow
27C2×Q8×C13—41no—
28C22×C4×C13—21no—
29C22×C4×C13C22⋊C411yescharacteristic
30C22×Dic13—21no—
31C22×Dic13—21no—
32C2×#1057—42no—
33C2×#1057—81no—
34C2×#1057—81no—
35C2×#1057—81no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4—21no—
38C13×C4⋊C4—41no—
39C13×C4⋊C4—41no—
40C13×C4⋊C4—42no—
41C13×C22⋊C4—41no—
42C42×C13—41no—
43C4⋊Dic13—41no—
44#6101—81no—
45#6101—81no—
46C4×Dic13—21no—
47C4×Dic13SD1611yescharacteristic
48C4×Dic13Q1611yescharacteristic
49#6099—22no—
50#6099—41no—
51C2×#1055—41no—
52#2060—131no—
53#1325—131no—
54#1296—131no—
55C23×C13#9911yescharacteristic
56Q8×C13—161no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—41no—
60C2×C4×C13—41no—
61C2×C4×C13—41no—
62C2×C4×C13—81no—
63C2×C4×C13#10311yescharacteristic
64C2×C4×C13#10411yescharacteristic
65C2×Dic13—21no—
66C2×Dic13—21no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—21no—
71C2×Dic13—41no—
72C2×Dic13—81no—
73#1057—82no—
74#1057—161no—
75#1055—42no—
76#544#26111yescharacteristic
77#428—261no—
78C2×C4⋊C8—261no—
79#384—131no—
80#343—131no—
81#339—261no—
82#324—261no—
83C22×C13—21no—
84C22×C13—21no—
85C22×C13#32811yescharacteristic
86C22×C13AΣL(1,𝔽16)11yescharacteristic
87C22×C13#35611yescharacteristic
88C4×C13—21no—
89C4×C13—21no—
90C4×C13—81no—
91C4×C13—81no—
92C4×C13—81no—
93Dic13—21no—
94Dic13—21no—
95Dic13—21no—
96Dic13—21no—
97Dic13—81no—
98C2×M16—261no—
99C22×C8—521no—
100C4⋊Q8—41no—
101#125—41no—
102C22⋊Q8—41no—
103#117—21no—
104C2×C4⋊C4—131no—
105C2×C4⋊C4—521no—
106C2×C4⋊C4C2×#26111yescharacteristic
107C2×C42—131no—
108#107—521no—
109#106—521no—
110C4⋊C8—262no—
111C4⋊C8—521no—
112C22⋊C8—521no—
113C2×C13—21no—
114C2×C13—21no—
115C2×C13#135411yescharacteristic
116C2×C13#140211yescharacteristic
117C2×C13#140511yescharacteristic
118C2×Q8—41no—
119C22×C4—21no—
120C22×C4—261no—
121C22×C4—261no—
122C22×C4C22⋊#26111yescharacteristic
123M16—262no—
124M16—521no—
125C2×C8—521no—
126C2×C8—522no—
127C2×C8—1041no—
128C2×C8—1041no—
129C2×C8—1041no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—41no—
133C4⋊C4—41no—
134C4⋊C4—42no—
135C4⋊C4—521no—
136C4⋊C4—1041no—
137C4⋊C4—1041no—
138C22⋊C4—41no—
139C42—41no—
140C42—131no—
141C42—131no—
142C42—261no—
143C13#744311yescharacteristic, complemented, Sylow
144C23#8811911yescharacteristic
145Q8—161no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—81no—
152C2×C4—261no—
153C2×C4—261no—
154C2×C4—261no—
155C2×C4—261no—
156C2×C4—261no—
157C2×C4—261no—
158C2×C4—521no—
159C2×C4—1041no—
160C2×C4#8811711yescharacteristic
161C2×C4#8811811yescharacteristic
162C8—522no—
163C8—1042no—
164C8—2081no—
165C22—21no—
166C22—21no—
167C22#1171829811yescharacteristic
168C22#1171830111yescharacteristic
169C22#1171830611yescharacteristic
170C4—21no—
171C4—21no—
172C4—81no—
173C4—81no—
174C4—81no—
175C4—261no—
176C4—261no—
177C4—261no—
178C4—261no—
179C4—1041no—
180C2—21no—
181C2—21no—
182C2#1312983711yescharacteristic
183C2#1312995511yescharacteristic
184C2#1312996111yescharacteristic
subgroupG/H
centerC22#11718306
commutatorC2×C13×C4⋊C4C2×C4
FrattiniC2×C4⋊C4C2×#261
FittingC13×#544C4
socleC22×C13AΣL(1,𝔽16)
prime radicalC23×C13#99
cosocle#11718637C22
hypercenter#544#261
hypocenterC13#7443
LCSG ▷ C2×C13×C4⋊C4 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #544

Complements

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

NH ≅ G/Ntype
143. C13#7443semidirect

Maximal subgroups

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

subgroupindex
#131297792
#131297142
#131161782
#744313