Finite Group Databasebeta

← #15758233

Subgroups — #15758233

Order 3328.

404 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 103 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#13125346C211yesmaximal, characteristic
2#13123938C211yesmaximal, characteristic
3#13113258C212yesmaximal
4#13112674C212yesmaximal
5C13×#1526C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7#11719175C2211yescharacteristic
8C4×C13×M16C2212yes—
9#11718740C412yes—
10#11718739C412yes—
11#11718725—22no—
12#11718685—22no—
13Q8×#1055—22no—
14#11718661—22no—
15#11718659—22no—
16#11718586C2212yes—
17C2×C4×#1055C2211yescharacteristic
18C13×#330—22no—
19#11718048—22no—
20#11718048—22no—
21C2×C13×M16—22no—
22C13×C4⋊Q8C2×C412yes—
23C13×#125D412yes—
24C13×C22⋊Q8—22no—
25C4×Q8×C13—22no—
26C13×#117D412yes—
27C2×C42×C13C2311yescharacteristic
28#88180—21no—
29#88178—22no—
30C22×#1055—21no—
31#88124—21no—
32#88123C2×C412yes—
33C4×Dic26—22no—
34C13×#97—22no—
35C4×C8×C13—22no—
36C22⋊#1055—22no—
37#88048—24no—
38#88047—24no—
39C4⋊#1055—24no—
40C4⋊#1055D412yes—
41C4⋊#1055D412yes—
42#88043—22no—
43C4×#1055—22no—
44C4×#1055—22no—
45C4×#1055—21no—
46C4×#1055C2×C411yescharacteristic
47C4×#1055C2×C411yescharacteristic
48#9068—131nomaximal, Sylow
49C2×Q8×C13—22no—
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13#4112yes—
52C2×Dic26—22no—
53C13×M16—24no—
54C13×M16—42no—
55C2×C8×C13—42no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—24no—
58C13×C4⋊C4C22⋊C414yes—
59C13×C22⋊C4—22no—
60C42×C13—22no—
61C42×C13C22×C411yescharacteristic
62C42×C13C2×D412yes—
63C42×C13C2×D411yescharacteristic
64C22⋊Dic13—41no—
65C4⋊Dic13—22no—
66C4⋊Dic13—22no—
67#6101—42no—
68C4×Dic13—41no—
69C2×#1055—24no—
70C2×#1055—21no—
71C2×#1055—21no—
72C2×#1055—22no—
73C2×#1055—22no—
74#3160—131no—
75#2986—131no—
76#1526D1311yescharacteristic
77#1485—132no—
78#1278—132no—
79C23×C13#12311yescharacteristic
80Q8×C13—42no—
81Q8×C13—42no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—24no—
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×C4×C13C4×D412yes—
88C2×C4×C13#12011yescharacteristic
89C2×C4×C13#12112yes—
90C2×Dic13—42no—
91Dic26—42no—
92Dic26—42no—
93C8×C13—44no—
94#1055—22no—
95#1055—22no—
96#1055—42no—
97#1055—42no—
98#533—131no—
99#533C2×D1311yescharacteristic
100#500—132no—
101#499—262no—
102#498—132no—
103#446—262no—
104C8×Q8—262no—
105#433—262no—
106#431—132no—
107#427—262no—
108C4×M16C2×D1312yes—
109C2×C4×C8—131no—
110#330—22no—
111Q8⋊C8—262no—
112Q8⋊C8—262no—
113C22×C13—22no—
114C22×C13—21no—
115C22×C13#38611yescharacteristic
116C4×C13—22no—
117C4×C13—21no—
118C4×C13—44no—
119C4×C13#44312yes—
120C4×C13#44412yes—
121C4×C13#45612yes—
122Dic13—82no—
123C2×M16—22no—
124C22×C8—261no—
125C4⋊Q8—132no—
126C4⋊Q8C4×D1312yes—
127#125—261no—
128#125C22⋊D1312yes—
129C22⋊Q8—22no—
130C22⋊Q8—262no—
131C4×Q8—22no—
132C4×Q8—262no—
133#117—261no—
134#117D5212yes—
135C2×C42C22×D1311yescharacteristic
136#107—264no—
137#106—264no—
138C4⋊C8—132no—
139C4⋊C8—132no—
140C4⋊C8—264no—
141C22⋊C8—262no—
142#97—22no—
143#97—262no—
144C4×C8—22no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8—262no—
148C4×C8—262no—
149C4×C8—261no—
150C2×C13—41no—
151C2×C13#187612yes—
152C2×C13#188611yescharacteristic
153C2×Q8—22no—
154C2×Q8—262no—
155C22×C4C2×D5211yescharacteristic
156C22×C4#612912yes—
157M16—24no—
158M16—42no—
159C2×C8—42no—
160C2×C8—264no—
161C2×C8—261no—
162C2×C8—261no—
163C2×C8—262no—
164C2×C8—262no—
165C4⋊C4—22no—
166C4⋊C4—24no—
167C4⋊C4—262no—
168C4⋊C4—262no—
169C4⋊C4—522no—
170C4⋊C4#610314yes—
171C22⋊C4—22no—
172C22⋊C4—521no—
173C42—22no—
174C42—521no—
175C42C2×C4×D1311yescharacteristic
176C42D4×D1312yes—
177C42C2×C22⋊D1311yescharacteristic
178C13#906811yescharacteristic, complemented, Sylow
179C23#8814011yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—522no—
183Q8—522no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—522no—
189C2×C4#8813512yes—
190C2×C4#8813611yescharacteristic
191C2×C4C2×#610311yescharacteristic
192C2×C4#8819312yes—
193C8—44no—
194C8—262no—
195C8—262no—
196C8—522no—
197C8—522no—
198C22—22no—
199C22—21no—
200C22#1171861911yescharacteristic
201C4—22no—
202C4—21no—
203C4—44no—
204C4—1042no—
205C4#1171841312yes—
206C4#1171848412yes—
207C4#1171848512yes—
208C2—41no—
209C2#1311516112yes—
210C2#1311522711yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1526C2
socleC22×C13#386
prime radicalC23×C13#123
cosocleC2×C42×C13C23
hypercenter#1526D13
hypocenterC13#9068
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
178. C13#9068semidirect

Maximal subgroups

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

subgroupindex
#131253462
#131239382
#131132582
#131126742
C13×#15262
#906813