Finite Group Databasebeta

← #15783739

Subgroups — #15783739

Order 3328.

216 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 51 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#13117151C211yesmaximal, characteristic, complemented
2#13117149C211yesmaximal, characteristic, complemented
3#13117084C211yesmaximal, characteristic, complemented
4#13116716C211yesmaximal, characteristic, complemented
5#13113033C211yesmaximal, characteristic, complemented
6#13113025C211yesmaximal, characteristic, complemented
7C13×#1419C211yesmaximal, characteristic, complemented
8C2×C13×D16C2211yescharacteristic
9#11718812—21no—
10C2×#88066—21no—
11#11718565C2211yescharacteristic
12C2×D208C2211yescharacteristic
13#11718556—21no—
14C13×M64C2211yescharacteristic
15C13×#368C2211yescharacteristic
16#11718112—21no—
17#11718111—21no—
18C16×Dic13C2211yescharacteristic
19#11718091C2211yescharacteristic
20#11718089—21no—
21#11718041—21no—
22D416—21no—
23C2×C13×D8—21no—
24#88194—41no—
25C2×#6104—41no—
26#88161—41no—
27#88158—21no—
28C2×D104—21no—
29C13×D16—21no—
30C13×D16—21no—
31C2×C13×C16C2311yescharacteristic
32C13×#108—21no—
33#88066—42no—
34#88065—41no—
35C8×Dic13D411yescharacteristic
36C2×#6090D411yescharacteristic
37Dic104D411yescharacteristic, complemented
38#88040—21no—
39D208—21no—
40D208—21no—
41D208D411yescharacteristic, complemented
42C13×C32—21no—
43#88034—21no—
44#13692—131nomaximal, Sylow
45C2×D4×C13—41no—
46C2×C22⋊D13—82no—
47#6127—41no—
48C2×D52—41no—
49C13×D8—41no—
50C13×D8—41no—
51C13×M16—41no—
52C2×C8×C13C2×D411yescharacteristic
53#6104—81no—
54#6104—81no—
55C4×Dic13D811yescharacteristic
56C2×#1055D811yescharacteristic
57Dic52—21no—
58D104—21no—
59D104—41no—
60D104—41no—
61#6095—41no—
62#6094—81no—
63C8×D13—81no—
64C13×C16C2×D411yescharacteristic
65C13×C16#4111yescharacteristic
66#6090—21no—
67#2263—131no—
68#2263—131no—
69#2246—131no—
70#2178—131no—
71#1422—131no—
72#1419—131no—
73#1419D1311yescharacteristic, complemented
74C23×C13—81no—
75C22×D13—81no—
76D4×C13—81no—
77D4×C13—81no—
78C2×C4×C13C2×D811yescharacteristic
79C22⋊D13—81no—
80C22⋊D13—164no—
81C2×Dic13—21no—
82D52—41no—
83D52—81no—
84D52—81no—
85C4×D13—81no—
86Dic26—41no—
87C8×C13—81no—
88C8×C13#12111yescharacteristic
89C8×C13AGL(1,ℤ/8)11yescharacteristic
90#1055D1611yescharacteristic
91#1055D1611yescharacteristic
92#508—131no—
93C2×D16—131no—
94C2×D16—261no—
95C2×D16C2×D1311yescharacteristic
96#493—261no—
97#443—261no—
98SD64—261no—
99SD64—261no—
100D32—261no—
101D32—261no—
102M64—131no—
103M64C2×D1311yescharacteristic
104#368C2×D1311yescharacteristic
105#359—261no—
106C4×C16—131no—
107C22×C13—162no—
108C22×C13—161no—
109C22×C13#50911yescharacteristic
110C2×D13—81no—
111C2×D13—162no—
112C2×D13—161no—
113C4×C13#45911yescharacteristic
114C4×C13C2×D1611yescharacteristic
115Dic13—22no—
116Dic13—81no—
117#135—261no—
118C2×D8—21no—
119C2×D8—261no—
120C2×D8—521no—
121#131—521no—
122#127—521no—
123Q32—131no—
124SD32—261no—
125D16—21no—
126D16—21no—
127D16—131no—
128D16—261no—
129D16—261no—
130D16—522no—
131C2×C16—131no—
132C2×C16C22×D1311yescharacteristic
133#108—21no—
134#104—521no—
135C4×C8—131no—
136C32—21no—
137C32—261no—
138C2×C13—21no—
139C2×C13—321no—
140C2×C13#220611yescharacteristic
141D13—161no—
142D13—321no—
143#41—521no—
144C2×D4—41no—
145C2×D4—521no—
146C2×D4—1042no—
147Q16—261no—
148SD16—521no—
149D8—41no—
150D8—41no—
151D8—261no—
152D8—521no—
153D8—521no—
154D8—1041no—
155D8—1041no—
156M16—41no—
157M16—1041no—
158C2×C8—131no—
159C2×C8—1041no—
160C2×C8D4×D1311yescharacteristic
161C42—131no—
162C16—261no—
163C16#612711yescharacteristic
164C16D4×D1311yescharacteristic
165C13#1369211yescharacteristic, complemented, Sylow
166C23—81no—
167C23—1041no—
168Q8—521no—
169D4—81no—
170D4—81no—
171D4—521no—
172D4—1041no—
173D4—1041no—
174D4—1041no—
175D4—2084no—
176C2×C4—261no—
177C2×C4—1041no—
178C2×C4D8×D1311yescharacteristic
179C8—81no—
180C8—131no—
181C8—131no—
182C8#8813811yescharacteristic
183C8#8816811yescharacteristic
184C22—162no—
185C22—161no—
186C22—1041no—
187C22—2082no—
188C22—2081no—
189C22#1171857511yescharacteristic
190C4—262no—
191C4—1041no—
192C4#1171844711yescharacteristic
193C4D13×D1611yescharacteristic
194C2—21no—
195C2—321no—
196C2—4161no—
197C2—2081no—
198C2#1311687011yescharacteristic
subgroupG/H
centerC2#13116870
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#1419C2
socleC2×C13#2206
hypercenter#1419D13
hypocenterC13#13692
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
1. #13117151C2semidirect
2. #13117149C2semidirect
3. #13117084C2semidirect
4. #13116716C2semidirect
5. #13113033C2semidirect
6. #13113025C2semidirect
7. C13×#1419C2semidirect
37. Dic104D4semidirect
41. D208D4semidirect
73. #1419D13semidirect
165. C13#13692semidirect

Maximal subgroups

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

subgroupindex
#131171512
#131171492
#131170842
#131167162
#131130332
#131130252
C13×#14192
#1369213