Finite Group Databasebeta

← #15774437

Subgroups — #15774437

Order 3328.

292 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 79 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#13125486C211yesmaximal, characteristic
2#13116602C211yesmaximal, characteristic, complemented
3#13112896C212yesmaximal, complemented
4#13112872C212yesmaximal, complemented
5C13×#2166C211yesmaximal, characteristic, complemented
6#11719240C412yes—
7C13×#405C2211yescharacteristic
8#11718796—21no—
9#11718776—21no—
10C2×#88052—21no—
11#11718374C412yes—
12#11718372—21no—
13#11718356C2211yescharacteristic
14C4×D104—21no—
15#11718344C2211yescharacteristic
16C13×#364C2212yes—
17C13×#349—21no—
18C13×#347—21no—
19#11718055—21no—
20#11718055C2212yes—
21C2×C13×M16D411yescharacteristic
22C22×C8×C13D411yescharacteristic
23C13×#117C2×C411yescharacteristic
24#88184—22no—
25C2×D104—21no—
26C2×D104—21no—
27#88148—42no—
28#88138—42no—
29#88128C2×C412yes—
30C4×D52—22no—
31#88124C2×C412yes—
32C13×M32—22no—
33C13×#97C2×C411yescharacteristic
34C13×#97D411yescharacteristic
35C4×C8×C13D411yescharacteristic
36C4×C8×C13C2311yescharacteristic
37#88061—22no—
38#88061—22no—
39#88058—21no—
40#88057—21no—
41#88052—22no—
42#88052—41no—
43C2×#6090—41no—
44#11989—131nomaximal, Sylow
45C22×C4×C13C22⋊C411yescharacteristic
46C2×C22⋊D13—42no—
47C2×D52—22no—
48C2×D52—42no—
49C2×C4×D13—42no—
50C13×M16—22no—
51C2×C8×C13—21no—
52C2×C8×C13—21no—
53C2×C8×C13C22⋊C411yescharacteristic
54C2×C8×C13C22⋊C411yescharacteristic
55C2×C8×C13C2×D411yescharacteristic
56C2×C8×C13C2×D411yescharacteristic
57C13×C4⋊C4—21no—
58C13×C22⋊C4—21no—
59C42×C13C22⋊C411yescharacteristic
60C42×C13C22×C411yescharacteristic
61#6103—42no—
62#6103—42no—
63C4⋊Dic13—22no—
64#6101—42no—
65D104—42no—
66D104—41no—
67D104—41no—
68C13×C16—42no—
69#6090—42no—
70#3176—131no—
71#2166D1311yescharacteristic, complemented
72#2153—131no—
73#1366—132no—
74#1357—132no—
75C23×C13#10011yescharacteristic
76C22×D13—42no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13#10011yescharacteristic
82C2×C4×C13C2×C22⋊C411yescharacteristic
83C22⋊D13—162no—
84C2×Dic13—42no—
85D52—42no—
86D52—42no—
87D52—162no—
88C4×D13—162no—
89C8×C13—21no—
90C8×C13—21no—
91C8×C13#13512yes—
92C8×C13AGL(1,ℤ/8)11yescharacteristic
93C8×C13#13711yescharacteristic
94#540—132no—
95C2×M32—261no—
96#499—131no—
97#493—131no—
98#490—132no—
99#469—261no—
100#466—261no—
101#442—261no—
102C4×D8—261no—
103#405C2×D1311yescharacteristic
104#364—132no—
105#364—261no—
106#364C2×D1312yes—
107#349—21no—
108#347—21no—
109C22×C13—21no—
110C22×C13—41no—
111C22×C13C2×#10011yescharacteristic
112C2×D13—82no—
113C2×D13—82no—
114C2×D13—82no—
115C4×C13—21no—
116C4×C13—41no—
117C4×C13—41no—
118C4×C13#41611yescharacteristic
119C4×C13#41711yescharacteristic
120Dic13—82no—
121C2×D8—261no—
122C2×D8—261no—
123C2×M16C22⋊D1311yescharacteristic
124C22×C8D5211yescharacteristic
125#127—132no—
126#125—132no—
127#123—522no—
128#121—262no—
129#121—522no—
130C4×D4—262no—
131#117C4×D1311yescharacteristic
132M32—22no—
133M32—262no—
134M32—521no—
135C2×C16—521no—
136#107—261no—
137#106—261no—
138#102—262no—
139#102—262no—
140#97C4×D1311yescharacteristic
141#97C22⋊D1311yescharacteristic
142C4×C8D5211yescharacteristic
143C4×C8C22×D1311yescharacteristic
144C2×C13—21no—
145C2×C13—41no—
146C2×C13#155111yescharacteristic
147D13—162no—
148C2×D4—262no—
149C2×D4—522no—
150C2×D4—522no—
151C22×C4—522no—
152C22×C4#610311yescharacteristic
153D8—521no—
154D8—521no—
155D8—522no—
156M16—22no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8#610311yescharacteristic
160C2×C8#610311yescharacteristic
161C2×C8C2×D5211yescharacteristic
162C2×C8C2×C22⋊D1311yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—262no—
165C4⋊C4—522no—
166C22⋊C4—21no—
167C22⋊C4—522no—
168C22⋊C4—522no—
169C42#610311yescharacteristic
170C42C2×C4×D1311yescharacteristic
171C16—42no—
172C16—522no—
173C13#1198911yescharacteristic, complemented, Sylow
174C23—522no—
175C23#8806311yescharacteristic
176D4—522no—
177D4—522no—
178D4—2082no—
179D4—2082no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—522no—
185C2×C4—2082no—
186C2×C4#8806311yescharacteristic
187C2×C4C2×#610311yescharacteristic
188C8—21no—
189C8—21no—
190C8#8816211yescharacteristic
191C8#8816311yescharacteristic
192C8#8820412yes—
193C22—21no—
194C22—41no—
195C22—1042no—
196C22—1042no—
197C22—1042no—
198C22C2×#8806311yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—1042no—
203C4#1171866311yescharacteristic
204C4#1171879411yescharacteristic
205C2—21no—
206C2—41no—
207C2—2082no—
208C2#1311353211yescharacteristic
subgroupG/H
centerC2#13113532
commutatorC42×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#2166C2
socleC2×C13#1551
prime radical#13125486C2
cosocleC4×C8×C13C23
hypercenter#2166D13
hypocenterC13#11989
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #13116602C2semidirect
3. #13112896C2semidirect
4. #13112872C2semidirect
5. C13×#2166C2semidirect
71. #2166D13semidirect
173. C13#11989semidirect

Maximal subgroups

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

subgroupindex
#131254862
#131166022
#131128962
#131128722
C13×#21662
#1198913