Finite Group Databasebeta

← #15765655

Subgroups — #15765655

Order 3328.

528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 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#13125784C212yesmaximal
2#13115813C211yesmaximal, characteristic
3#13113517C212yesmaximal
4#13112669C211yesmaximal, characteristic
5C13×#2862C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2212yes—
7#11719175C2211yescharacteristic
8C13×#391—24no—
9C13×#382—22no—
10C43×C13C2211yescharacteristic
11#11718889—24no—
12#11718753—22no—
13#11718751—24no—
14#11718742—22no—
15#11718586C2212yes—
16#11718585C2211yescharacteristic
17#11718138—24no—
18#11718115—22no—
19C22×Q8×C13D414yes—
20C13×C4⋊Q8—22no—
21C13×C4⋊Q8—22no—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C42×C13—22no—
27C2×C42×C13D412yes—
28C2×C42×C13C2311yescharacteristic
29C2×#6107—28no—
30#88180—21no—
31#88178—22no—
32C2×#6099—21no—
33#88124—21no—
34#88123D412yes—
35C4×Dic26—22no—
36C13×#95—28no—
37#88075—28no—
38C22⋊#1055—22no—
39C4⋊#1055—22no—
40C4⋊#1055D414yes—
41C4×#1055—22no—
42#10297—131nomaximal, Sylow
43C2×Q8×C13—24no—
44C2×Q8×C13—24no—
45C2×Q8×C13—48no—
46C22×C4×C13—22no—
47C22×C4×C13—24no—
48C22×C4×C13C2×D412yes—
49C22×C4×C13C2×D411yescharacteristic
50C2×Dic26—22no—
51C13×C4⋊C4—42no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C42×C13—22no—
56C42×C13—44no—
57C42×C13Q1614yescomplemented
58C42×C13C2×D411yescharacteristic
59C42×C13C2×D412yes—
60C42×C13#4111yescharacteristic
61C22⋊Dic13—41no—
62#6107—88no—
63C4⋊Dic13—22no—
64C4⋊Dic13—22no—
65#6101—42no—
66C4×Dic13—41no—
67#6099—42no—
68C2×#1055—24no—
69C2×#1055—41no—
70#3209—132no—
71#2862D1311yescharacteristic
72#1994—131no—
73#1548—132no—
74#1276—131no—
75C23×C13#12011yescharacteristic
76Q8×C13—48no—
77Q8×C13—84no—
78C2×C4×C13—24no—
79C2×C4×C13—24no—
80C2×C4×C13—44no—
81C2×C4×C13—48no—
82C2×C4×C13—44no—
83C2×C4×C13#12012yes—
84C2×C4×C13#12112yes—
85C2×C4×C13#12111yescharacteristic
86C2×C4×C13#12711yescharacteristic
87C2×C4×C13C2×Q1612yes—
88C2×C4×C13#13712yes—
89C2×Dic13—42no—
90Dic26—44no—
91#1055—44no—
92#1055—81no—
93#533—131no—
94C2×C4⋊Q8C2×D1312yes—
95#494—262no—
96#487—262no—
97#462—264no—
98#451—264no—
99#431—132no—
100#423—131no—
101#391—24no—
102#382—22no—
103C43C2×D1311yescharacteristic
104#339—262no—
105#333—264no—
106C22×C13—22no—
107C22×C13#39211yescharacteristic
108C22×C13#45112yes—
109C4×C13—22no—
110C4×C13—44no—
111C4×C13—84no—
112C4×C13#45514yes—
113C4×C13#46212yes—
114C4×C13#49411yescharacteristic
115C4×C13#49711yescharacteristic
116Dic13—82no—
117C22×Q8C22⋊D1314yes—
118C2×Q16—268no—
119C2×M16—261no—
120C4⋊Q8—22no—
121C4⋊Q8—22no—
122C4⋊Q8—22no—
123C4⋊Q8—22no—
124C4⋊Q8—132no—
125#125—261no—
126C22⋊Q8—262no—
127C4×Q8—262no—
128#117—261no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C42—22no—
132C2×C42C22⋊D1312yes—
133C2×C42C22×D1311yescharacteristic
134C4⋊C8—134no—
135C4⋊C8—262no—
136#103—268no—
137C22⋊C8—262no—
138C4×C8—262no—
139#95—28no—
140C2×C13—22no—
141C2×C13#200412yes—
142C2×C13#201611yescharacteristic
143C2×Q8—24no—
144C2×Q8—24no—
145C2×Q8—48no—
146C2×Q8—262no—
147C22×C4—22no—
148C22×C4—24no—
149C22×C4C2×C22⋊D1312yes—
150C22×C4C2×C22⋊D1311yescharacteristic
151Q16—1048no—
152M16—522no—
153C2×C8—264no—
154C2×C8—521no—
155C4⋊C4—42no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—262no—
160C4⋊C4—262no—
161C4⋊C4—522no—
162C22⋊C4—521no—
163C42—22no—
164C42—44no—
165C42—521no—
166C42#610714yescomplemented
167C42D4×D1311yescharacteristic
168C42D4×D1312yes—
169C42#612911yescharacteristic
170C13#1029711yescharacteristic, complemented, Sylow
171C23#8820711yescharacteristic
172Q8—48no—
173Q8—84no—
174Q8—524no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—48no—
179C2×C4—44no—
180C2×C4—522no—
181C2×C4#8819112yes—
182C2×C4#8819211yescharacteristic
183C2×C4#8819312yes—
184C2×C4#8819411yescharacteristic
185C2×C4#8819612yes—
186C2×C4C2×#610712yes—
187C8—524no—
188C8—1041no—
189C22—22no—
190C22#1171888411yescharacteristic
191C22#1171888912yes—
192C4—22no—
193C4—44no—
194C4—84no—
195C4—1042no—
196C4#1171872214yes—
197C4#1171874711yescharacteristic
198C4#1171875112yes—
199C4#1171875311yescharacteristic
200C2—22no—
201C2#1311586512yes—
202C2#1311593611yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2862C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#2862D13
hypocenterC13#10297
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

Complements

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

NH ≅ G/Ntype
57. C42×C13Q16semidirect
166. C42#6107semidirect
170. C13#10297semidirect

Maximal subgroups

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

subgroupindex
#131257842
#131158132
#131135172
#131126692
C13×#28622
#1029713