Finite Group Databasebeta

← #15777169

Subgroups — #15777169

Order 3328.

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

normal subgroups only

This group has 224 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#13117092C211yesmaximal, characteristic, complemented
2#13116917C211yesmaximal, characteristic, complemented
3#13116912C211yesmaximal, characteristic
4#13112912C211yesmaximal, characteristic, complemented
5#13112874C211yesmaximal, characteristic, complemented
6#13112872C211yesmaximal, characteristic, complemented
7C13×#2170C211yesmaximal, characteristic, complemented
8C13×#504—21no—
9C13×#443C2211yescharacteristic
10#11718856—21no—
11#11718854—21no—
12C2×#88040—21no—
13C2×#88040—21no—
14#11718360C2211yescharacteristic
15#11718356C2211yescharacteristic
16C13×#364C2211yescharacteristic
17C13×#350—21no—
18C4×C13×C16C2211yescharacteristic
19#11718088—21no—
20#11718087—21no—
21#11718055C2211yescharacteristic
22#11718055C2211yescharacteristic
23C13×#135D411yescharacteristic
24C13×#131—21no—
25C2×Dic52—21no—
26C2×Dic52—21no—
27C2×D104—21no—
28C2×D104—21no—
29#88128—21no—
30#88123—21no—
31C13×M32—21no—
32C13×M32—41no—
33C2×C13×C16—41no—
34C2×C13×C16D411yescharacteristic
35C2×C13×C16D411yescharacteristic
36C13×#108D411yescharacteristic
37C13×#104—21no—
38C4×C8×C13C2311yescharacteristic
39#88069—41no—
40#88068—41no—
41#88067—41no—
42#88066—41no—
43#88052—21no—
44#88052—21no—
45#88040—42no—
46#88040—41no—
47#88040—41no—
48#12438—131nomaximal, Sylow
49C13×#41—21no—
50C2×D52—41no—
51C2×D52—81no—
52C2×Dic26—41no—
53C13×Q16D811yescharacteristic
54C13×SD16—21no—
55C13×D8D811yescharacteristic
56C13×M16—21no—
57C13×M16—41no—
58C2×C8×C13—41no—
59C2×C8×C13C2×D411yescharacteristic
60C2×C8×C13C2×D411yescharacteristic
61C42×C13#4111yescharacteristic
62C4⋊Dic13—81no—
63Dic52—41no—
64Dic52—41no—
65Dic52—41no—
66Dic52—41no—
67D104—41no—
68D104—41no—
69D104—41no—
70D104—41no—
71C13×C16—21no—
72C13×C16—41no—
73C13×C16D811yescharacteristic
74C13×C16D811yescharacteristic
75#6090—41no—
76#6090—41no—
77#2248—131no—
78#2214—131no—
79#2213—131no—
80#2170D1311yescharacteristic, complemented
81#1373—131no—
82#1358—131no—
83#1357—131no—
84C22×D13—81no—
85Q8×C13—21no—
86D4×C13—21no—
87D4×C13—41no—
88C2×C4×C13—21no—
89C2×C4×C13—41no—
90C2×C4×C13#12111yescharacteristic
91C2×Dic13—81no—
92D52—81no—
93D52—81no—
94D52—162no—
95Dic26—81no—
96Dic26—81no—
97C8×C13—41no—
98C8×C13C2×D811yescharacteristic
99C8×C13C2×D811yescharacteristic
100C8×C13#13511yescharacteristic
101C8×C13AGL(1,ℤ/8)11yescharacteristic
102#510—261no—
103#509—261no—
104C2×SD32—261no—
105C2×SD32—261no—
106#504—21no—
107#494—131no—
108#493—131no—
109#443C2×D1311yescharacteristic
110#364—131no—
111#364—131no—
112#364C2×D1311yescharacteristic
113#362—261no—
114#361—261no—
115#350—21no—
116C4×C16C2×D1311yescharacteristic
117C22×C13—41no—
118C22×C13#47211yescharacteristic
119C2×D13—162no—
120C2×D13—161no—
121C4×C13—22no—
122C4×C13—41no—
123C4×C13#45911yescharacteristic
124C4×C13#46611yescharacteristic
125Dic13—161no—
126#135D5211yescharacteristic
127C2×Q16—261no—
128C2×Q16—261no—
129C2×D8—261no—
130C2×D8—261no—
131#131—21no—
132C4⋊Q8—261no—
133#127—261no—
134Q32—521no—
135SD32—522no—
136SD32—521no—
137SD32—521no—
138SD32—521no—
139SD32—521no—
140D16—521no—
141M32—21no—
142M32—41no—
143M32—261no—
144M32—261no—
145C2×C16—41no—
146C2×C16C22⋊D1311yescharacteristic
147C2×C16C22⋊D1311yescharacteristic
148#108D5211yescharacteristic
149#104—21no—
150C4×C8C22×D1311yescharacteristic
151C2×C13—21no—
152C2×C13—81no—
153C2×C13#166711yescharacteristic
154D13—321no—
155#41—21no—
156C2×Q8—521no—
157C2×D4—521no—
158C2×D4—1041no—
159Q16—521no—
160Q16—521no—
161Q16—521no—
162Q16—521no—
163Q16D10411yescharacteristic
164SD16—21no—
165D8—521no—
166D8—521no—
167D8—521no—
168D8—521no—
169D8D10411yescharacteristic
170M16—21no—
171M16—41no—
172C2×C8—41no—
173C2×C8C2×D5211yescharacteristic
174C2×C8C2×C22⋊D1311yescharacteristic
175C4⋊C4—1041no—
176C42#612711yescharacteristic
177C16—21no—
178C16—41no—
179C16—521no—
180C16—521no—
181C16#610411yescharacteristic
182C16#610411yescharacteristic
183C13#1243811yescharacteristic, complemented, Sylow
184C23—1041no—
185Q8—21no—
186Q8—1041no—
187Q8—1041no—
188D4—21no—
189D4—41no—
190D4—1041no—
191D4—1041no—
192D4—2082no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—1041no—
196C2×C4#8818411yescharacteristic
197C8—41no—
198C8C2×D10411yescharacteristic
199C8#8815811yescharacteristic
200C8C2×#610411yescharacteristic
201C8#8820311yescharacteristic
202C22—41no—
203C22—2082no—
204C22—2081no—
205C22#1171880311yescharacteristic
206C4—22no—
207C4—41no—
208C4—2081no—
209C4#1171867611yescharacteristic
210C4#1171877611yescharacteristic
211C2—21no—
212C2—81no—
213C2—4161no—
214C2#1311419111yescharacteristic
subgroupG/H
centerC2#13114191
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2170C2
socleC2×C13#1667
prime radical#13116912C2
hypercenter#2170D13
hypocenterC13#12438
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2170

Complements

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

NH ≅ G/Ntype
1. #13117092C2semidirect
2. #13116917C2semidirect
4. #13112912C2semidirect
5. #13112874C2semidirect
6. #13112872C2semidirect
7. C13×#2170C2semidirect
80. #2170D13semidirect
183. C13#12438semidirect

Maximal subgroups

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

subgroupindex
#131170922
#131169172
#131169122
#131129122
#131128742
#131128722
C13×#21702
#1243813