Finite Group Databasebeta

← #15783791

Subgroups — #15783791

Order 3328.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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#13117129C211yesmaximal, characteristic, complemented
2#13116958C211yesmaximal, characteristic, complemented
3#13116953C211yesmaximal, characteristic
4#13113040C211yesmaximal, characteristic, complemented
5#13113029C211yesmaximal, characteristic, complemented
6#13113026C211yesmaximal, characteristic, complemented
7C2×C13×SD64C211yesmaximal, characteristic, complemented
8C2×C13×Q32C2211yescharacteristic
9C2×C13×D16C2211yescharacteristic
10#11718853—21no—
11#11718821—21no—
12#11718562C2211yescharacteristic
13C13×SD64—21no—
14C13×SD64—21no—
15C2×C13×C32C2211yescharacteristic
16#11718157—21no—
17#11718155—21no—
18#11718098C2211yescharacteristic
19#11718098C2211yescharacteristic
20#11718091C2211yescharacteristic
21#11718039—21no—
22D13×C32—21no—
23C2×C13×Q16—21no—
24C2×C13×D8—21no—
25#88196—41no—
26#88186—41no—
27#88155D411yescharacteristic
28C13×Q32—21no—
29C13×Q32—21no—
30C13×D16—21no—
31C13×D16—21no—
32C2×C13×C16C2311yescharacteristic
33#88076—41no—
34#88073—41no—
35#88059—21no—
36#88059—21no—
37#88052D411yescharacteristic
38#88038—21no—
39C16×D13—21no—
40C13×C32D411yescharacteristic
41C13×C32D411yescharacteristic
42#88034—21no—
43#13702—131nomaximal, Sylow
44C2×Q8×C13—41no—
45C2×D4×C13—41no—
46#6127D811yescharacteristic
47C13×Q16—41no—
48C13×Q16—41no—
49C13×D8—41no—
50C13×D8—41no—
51C2×C8×C13C2×D411yescharacteristic
52#6107—81no—
53#6106—81no—
54#6105—81no—
55#6104—81no—
56#6099—41no—
57#6099—41no—
58#6099D811yescharacteristic
59#6094—21no—
60C8×D13—21no—
61C13×C16C2×D411yescharacteristic
62C13×C16#4111yescharacteristic
63#6090—21no—
64C2×SD64D1311yescharacteristic, complemented
65#2258—131no—
66#2222—131no—
67#2221—131no—
68#1425—131no—
69#1420—131no—
70#1419—131no—
71C23×C13—81no—
72Q8×C13—81no—
73Q8×C13—81no—
74D4×C13—81no—
75D4×C13—81no—
76C2×C4×C13—81no—
77C2×C4×C13C2×D811yescharacteristic
78C22⋊D13—21no—
79D52D1611yescharacteristic
80C4×D13—21no—
81Dic26D1611yescharacteristic
82C8×C13#12111yescharacteristic
83C8×C13#13511yescharacteristic
84#1055—21no—
85#1055—81no—
86#1055—81no—
87C2×Q32C2×D1311yescharacteristic
88C2×D16C2×D1311yescharacteristic
89#504—131no—
90#473—261no—
91#472—261no—
92SD64—21no—
93SD64—21no—
94M64—131no—
95M64—261no—
96C2×C32—261no—
97C2×C32C2×D1311yescharacteristic
98#368—131no—
99#368—131no—
100#362—261no—
101#361—261no—
102C22×C13—161no—
103C22×C13—321no—
104C22×C13#50811yescharacteristic
105C2×D13—21no—
106C4×C13—161no—
107C4×C13#46611yescharacteristic
108C4×C13C2×D1611yescharacteristic
109Dic13—21no—
110#137—521no—
111AGL(1,ℤ/8)—521no—
112C2×Q16—21no—
113C2×D8—21no—
114#131—131no—
115Q32—21no—
116Q32—21no—
117D16—21no—
118D16—21no—
119M32—131no—
120M32—261no—
121C2×C16—261no—
122C2×C16C22×D1311yescharacteristic
123#108—261no—
124#108—261no—
125#101—521no—
126#100—521no—
127C32—261no—
128C32C22⋊D1311yescharacteristic
129C32C22⋊D1311yescharacteristic
130C2×C13—21no—
131C2×C13—321no—
132C2×C13#221511yescharacteristic
133D13—41no—
134#41—131no—
135C2×Q8—41no—
136C2×D4—41no—
137Q16—41no—
138Q16—41no—
139Q16—1041no—
140SD16—1041no—
141SD16—1041no—
142D8—41no—
143D8—41no—
144D8—1041no—
145M16—131no—
146M16—261no—
147M16—521no—
148M16—521no—
149C2×C8—261no—
150C2×C8D4×D1311yescharacteristic
151C16—261no—
152C16#612911yescharacteristic
153C16C2×C22⋊D1311yescharacteristic
154C13#1370211yescharacteristic, complemented, Sylow
155C23—81no—
156Q8—81no—
157Q8—81no—
158Q8—131no—
159D4—81no—
160D4—81no—
161D4—131no—
162D4—261no—
163C2×C4—81no—
164C2×C4—261no—
165C2×C4D8×D1311yescharacteristic
166C8—261no—
167C8—1041no—
168C8—1041no—
169C8#8816611yescharacteristic
170C8#8819211yescharacteristic
171C22—161no—
172C22—261no—
173C22—321no—
174C22#1171857311yescharacteristic
175C4—161no—
176C4—261no—
177C4D13×D1611yescharacteristic
178C4#1171881811yescharacteristic
179C2—21no—
180C2—321no—
181C2—521no—
182C2#1311691911yescharacteristic
subgroupG/H
centerC2#13116919
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC2×C13×SD64C2
socleC2×C13#2215
prime radical#13116953C2
hypercenterC2×SD64D13
hypocenterC13#13702
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. #13117129C2semidirect
2. #13116958C2semidirect
4. #13113040C2semidirect
5. #13113029C2semidirect
6. #13113026C2semidirect
7. C2×C13×SD64C2semidirect
64. C2×SD64D13semidirect
154. C13#13702semidirect

Maximal subgroups

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

subgroupindex
#131171292
#131169582
#131169532
#131130402
#131130292
#131130262
C2×C13×SD642
#1370213