Finite Group Databasebeta

← #15777162

Subgroups — #15777162

Order 3328.

214 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 59 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#13117088C211yesmaximal, characteristic, complemented
2#13116917C211yesmaximal, characteristic
3#13116673C211yesmaximal, characteristic
4#13112911C211yesmaximal, characteristic, complemented
5#13112875C211yesmaximal, characteristic, complemented
6#13112874C211yesmaximal, characteristic, complemented
7C13×#2214C211yesmaximal, characteristic
8C13×#510—21no—
9C13×#494C2211yescharacteristic
10C13×#443C2211yescharacteristic
11#11718856—21no—
12C2×#88069—21no—
13C2×#88069—21no—
14#11718801—21no—
15#11718360C2211yescharacteristic
16C13×#364C2211yescharacteristic
17C13×#362—21no—
18#11718153—21no—
19#11718088—21no—
20#11718055C2211yescharacteristic
21#11718055C2211yescharacteristic
22C4×#6090C2211yescharacteristic
23C13×#135D411yescharacteristic
24C2×C13×Q16—21no—
25C2×C13×Q16—21no—
26C13×#131—21no—
27C13×C4⋊Q8—21no—
28C2×Dic52—21no—
29C2×Dic52—21no—
30#88123—21no—
31C13×Q32—41no—
32C13×SD32—41no—
33C13×M32—21no—
34C13×#108D411yescharacteristic
35C13×#104—21no—
36C4×C8×C13C2311yescharacteristic
37#88069—42no—
38#88069—41no—
39#88069—41no—
40#88069—41no—
41#88067—41no—
42#88052—21no—
43#88052—21no—
44#88052—41no—
45C2×#6090—41no—
46C2×#6090D411yescharacteristic
47C2×#6090D411yescharacteristic
48#12437—131nomaximal, Sylow
49C13×#41—21no—
50C2×Q8×C13—41no—
51C2×Dic26—41no—
52C13×Q16—41no—
53C13×Q16—41no—
54C13×Q16—41no—
55C13×Q16—41no—
56C13×Q16D811yescharacteristic
57C13×SD16—21no—
58C13×D8D811yescharacteristic
59C13×M16—21no—
60C13×M16—41no—
61C2×C8×C13—41no—
62C2×C8×C13C2×D411yescharacteristic
63C2×C8×C13C2×D411yescharacteristic
64C13×C4⋊C4—81no—
65C42×C13#4111yescharacteristic
66C4⋊Dic13—81no—
67Dic52—41no—
68Dic52—41no—
69Dic52—41no—
70Dic52—41no—
71C13×C16—41no—
72#6090—21no—
73#6090—41no—
74#6090—41no—
75#6090D811yescharacteristic
76#6090D811yescharacteristic
77#2247—131no—
78#2214—131no—
79#2214D1311yescharacteristic
80#2170—131no—
81#1373—131no—
82#1358—131no—
83#1358—131no—
84Q8×C13—21no—
85Q8×C13—81no—
86Q8×C13—81no—
87D4×C13—21no—
88D4×C13—41no—
89C2×C4×C13—21no—
90C2×C4×C13—41no—
91C2×C4×C13—81no—
92C2×C4×C13#12111yescharacteristic
93C2×Dic13—81no—
94Dic26—81no—
95Dic26—81no—
96C8×C13—41no—
97C8×C13C2×D811yescharacteristic
98C8×C13C2×D811yescharacteristic
99C8×C13#13511yescharacteristic
100C8×C13AGL(1,ℤ/8)11yescharacteristic
101#510—21no—
102#510—261no—
103C2×Q32—261no—
104C2×Q32—261no—
105#504—261no—
106#494—131no—
107#494C2×D1311yescharacteristic
108#443C2×D1311yescharacteristic
109#364—131no—
110#364—131no—
111#364C2×D1311yescharacteristic
112#362—21no—
113#362—261no—
114#350—261no—
115C4×C16—131no—
116C22×C13—41no—
117C22×C13#47211yescharacteristic
118C4×C13—22no—
119C4×C13—41no—
120C4×C13—161no—
121C4×C13#45911yescharacteristic
122C4×C13#46611yescharacteristic
123Dic13—161no—
124#135C22⋊D1311yescharacteristic
125C2×Q16—21no—
126C2×Q16—21no—
127C2×Q16—261no—
128C2×Q16—261no—
129#131—21no—
130C4⋊Q8—21no—
131C4⋊Q8—261no—
132Q32—41no—
133Q32—521no—
134Q32—521no—
135Q32—522no—
136Q32—521no—
137SD32—41no—
138SD32—521no—
139M32—21no—
140M32—261no—
141M32—261no—
142M32—521no—
143C2×C16—131no—
144C2×C16—131no—
145C2×C16—521no—
146#108C22⋊D1311yescharacteristic
147#104—21no—
148C4×C8C22×D1311yescharacteristic
149C2×C13—21no—
150C2×C13—81no—
151C2×C13#166711yescharacteristic
152#41—21no—
153C2×Q8—41no—
154C2×Q8—521no—
155Q16—41no—
156Q16—41no—
157Q16—41no—
158Q16—41no—
159Q16—521no—
160Q16—521no—
161Q16—521no—
162Q16—521no—
163Q16#610411yescharacteristic
164SD16—21no—
165D8#610411yescharacteristic
166M16—21no—
167M16—41no—
168C2×C8—41no—
169C2×C8D4×D1311yescharacteristic
170C2×C8C2×C22⋊D1311yescharacteristic
171C4⋊C4—81no—
172C4⋊C4—1041no—
173C42#612911yescharacteristic
174C16—41no—
175C16—131no—
176C16—131no—
177C16—261no—
178C16—521no—
179C16—521no—
180C13#1243711yescharacteristic, complemented, Sylow
181Q8—21no—
182Q8—81no—
183Q8—81no—
184Q8—1041no—
185Q8—1041no—
186D4—21no—
187D4—41no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—81no—
191C2×C4—1041no—
192C2×C4#8819311yescharacteristic
193C8—41no—
194C8D8×D1311yescharacteristic
195C8#8816511yescharacteristic
196C8C2×#610411yescharacteristic
197C8#8820411yescharacteristic
198C22—41no—
199C22#1171886011yescharacteristic
200C4—22no—
201C4—41no—
202C4—161no—
203C4—2081no—
204C4#1171869911yescharacteristic
205C4#1171881111yescharacteristic
206C2—21no—
207C2—81no—
208C2#1311418911yescharacteristic
subgroupG/H
centerC2#13114189
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2214C2
socleC2×C13#1667
prime radicalC13×#135D4
hypercenter#2214D13
hypocenterC13#12437
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2214

Complements

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

NH ≅ G/Ntype
1. #13117088C2semidirect
4. #13112911C2semidirect
5. #13112875C2semidirect
6. #13112874C2semidirect
180. C13#12437semidirect

Maximal subgroups

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

subgroupindex
#131170882
#131169172
#131166732
#131129112
#131128752
#131128742
C13×#22142
#1243713