Finite Group Databasebeta

← #15777167

Subgroups — #15777167

Order 3328.

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

normal subgroups only

This group has 224 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#13117091C211yesmaximal, characteristic, complemented
2#13116917C211yesmaximal, characteristic, complemented
3#13116673C211yesmaximal, characteristic, complemented
4#13112911C211yesmaximal, characteristic, complemented
5#13112874C211yesmaximal, characteristic, complemented
6#13112873C211yesmaximal, characteristic, complemented
7C13×#2213C211yesmaximal, characteristic
8C13×#509—21no—
9C13×#493C2211yescharacteristic
10C13×#443C2211yescharacteristic
11#11718856—21no—
12C2×#88067—21no—
13C2×#88067—21no—
14#11718801—21no—
15#11718360C2211yescharacteristic
16C13×#364C2211yescharacteristic
17C13×#361—21no—
18#11718153—21no—
19#11718088—21no—
20#11718055C2211yescharacteristic
21#11718055C2211yescharacteristic
22C4×#6090C2211yescharacteristic
23C13×#135D411yescharacteristic
24C2×C13×D8—21no—
25C2×C13×D8—21no—
26C13×#131—21no—
27C13×#127—21no—
28C2×Dic52—21no—
29C2×Dic52—21no—
30#88123—21no—
31C13×SD32—41no—
32C13×D16—41no—
33C13×M32—21no—
34C13×#108D411yescharacteristic
35C13×#104—21no—
36C4×C8×C13C2311yescharacteristic
37#88069—41no—
38#88067—42no—
39#88067—41no—
40#88067—41no—
41#88067—41no—
42#88052—21no—
43#88052—21no—
44#88052—41no—
45C2×#6090—41no—
46C2×#6090D411yescharacteristic
47C2×#6090D411yescharacteristic
48#12438—131nomaximal, Sylow
49C13×#41—21no—
50C2×D4×C13—41no—
51C2×D4×C13—81no—
52C2×Dic26—41no—
53C13×Q16D811yescharacteristic
54C13×SD16—21no—
55C13×D8—41no—
56C13×D8—41no—
57C13×D8—41no—
58C13×D8—41no—
59C13×D8D811yescharacteristic
60C13×M16—21no—
61C13×M16—41no—
62C2×C8×C13—41no—
63C2×C8×C13C2×D411yescharacteristic
64C2×C8×C13C2×D411yescharacteristic
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#2248—131no—
78#2214—131no—
79#2213D1311yescharacteristic
80#2170—131no—
81#1373—131no—
82#1358—131no—
83#1357—131no—
84C23×C13—81no—
85Q8×C13—21no—
86D4×C13—21no—
87D4×C13—41no—
88D4×C13—81no—
89D4×C13—81no—
90D4×C13—162no—
91C2×C4×C13—21no—
92C2×C4×C13—41no—
93C2×C4×C13#12111yescharacteristic
94C2×Dic13—81no—
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—21no—
104C2×SD32—261no—
105C2×SD32—261no—
106#504—261no—
107#494—131no—
108#493C2×D1311yescharacteristic
109#443C2×D1311yescharacteristic
110#364—131no—
111#364—131no—
112#364C2×D1311yescharacteristic
113#362—261no—
114#361—21no—
115#350—261no—
116C4×C16—131no—
117C22×C13—41no—
118C22×C13—162no—
119C22×C13—161no—
120C22×C13#47211yescharacteristic
121C4×C13—22no—
122C4×C13—41no—
123C4×C13#45911yescharacteristic
124C4×C13#46611yescharacteristic
125Dic13—161no—
126#135C22⋊D1311yescharacteristic
127C2×Q16—261no—
128C2×Q16—261no—
129C2×D8—21no—
130C2×D8—21no—
131#131—21no—
132C4⋊Q8—261no—
133#127—21no—
134Q32—521no—
135SD32—41no—
136SD32—521no—
137SD32—521no—
138SD32—522no—
139SD32—521no—
140D16—41no—
141M32—21no—
142M32—261no—
143M32—261no—
144M32—521no—
145C2×C16—131no—
146C2×C16—131no—
147C2×C16—521no—
148#108C22⋊D1311yescharacteristic
149#104—21no—
150C4×C8C22×D1311yescharacteristic
151C2×C13—21no—
152C2×C13—81no—
153C2×C13—321no—
154C2×C13#166711yescharacteristic
155#41—21no—
156C2×Q8—521no—
157C2×D4—41no—
158C2×D4—81no—
159Q16—521no—
160Q16—521no—
161Q16—521no—
162Q16—521no—
163Q16#610411yescharacteristic
164SD16—21no—
165D8—41no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8#610411yescharacteristic
170M16—21no—
171M16—41no—
172C2×C8—41no—
173C2×C8D4×D1311yescharacteristic
174C2×C8C2×C22⋊D1311yescharacteristic
175C4⋊C4—1041no—
176C42#612911yescharacteristic
177C16—41no—
178C16—131no—
179C16—131no—
180C16—261no—
181C16—521no—
182C16—521no—
183C13#1243811yescharacteristic, complemented, Sylow
184C23—81no—
185Q8—21no—
186Q8—1041no—
187Q8—1041no—
188D4—21no—
189D4—41no—
190D4—81no—
191D4—81no—
192D4—162no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—1041no—
196C2×C4#8819311yescharacteristic
197C8—41no—
198C8D8×D1311yescharacteristic
199C8#8816511yescharacteristic
200C8C2×#610411yescharacteristic
201C8#8820411yescharacteristic
202C22—41no—
203C22—162no—
204C22—161no—
205C22#1171886011yescharacteristic
206C4—22no—
207C4—41no—
208C4—2081no—
209C4#1171869911yescharacteristic
210C4#1171881111yescharacteristic
211C2—21no—
212C2—81no—
213C2—321no—
214C2#1311418911yescharacteristic
subgroupG/H
centerC2#13114189
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
Fitting, prime radicalC13×#2213C2
socleC2×C13#1667
hypercenter#2213D13
hypocenterC13#12438
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #13117091C2semidirect
2. #13116917C2semidirect
3. #13116673C2semidirect
4. #13112911C2semidirect
5. #13112874C2semidirect
6. #13112873C2semidirect
183. C13#12438semidirect

Maximal subgroups

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

subgroupindex
#131170912
#131169172
#131166732
#131129112
#131128742
#131128732
C13×#22132
#1243813