Finite Group Databasebeta

← #15765643

Subgroups — #15765643

Order 3328.

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

normal subgroups only

This group has 504 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#13125987C212yesmaximal
2#13115813C211yesmaximal, characteristic
3#13113521C212yesmaximal
4#13112669C211yesmaximal, characteristic
5C13×#2862C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2212yes—
7#11719175C2211yescharacteristic
8C13×#391—24no—
9C13×#382—22no—
10C43×C13C2211yescharacteristic
11#11718754—22no—
12#11718752—24no—
13#11718739—22no—
14#11718631—24no—
15#11718586C2212yes—
16#11718585C2211yescharacteristic
17#11718139—24no—
18#11718115—22no—
19C22×Q8×C13—22no—
20C13×C4⋊Q8—22no—
21C13×C4⋊Q8—22no—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—22no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4D414yes—
26C2×C42×C13—22no—
27C2×C42×C13D412yes—
28C2×C42×C13C2311yescharacteristic
29#88180—21no—
30#88178—22no—
31C2×#6099—21no—
32#88124—21no—
33#88123D412yes—
34C4×Dic26—22no—
35C13×#95—28no—
36C22⋊#1055—22no—
37#88050—28no—
38#88047—28no—
39C4⋊#1055—22no—
40C4⋊#1055D414yes—
41C4×#1055—22no—
42#10295—131nomaximal, Sylow
43C2×Q8×C13—48no—
44C2×Q8×C13—42no—
45C2×Q8×C13—42no—
46C22×C4×C13—22no—
47C22×C4×C13—24no—
48C22×C4×C13C2×D412yes—
49C22×C4×C13C2×D411yescharacteristic
50C2×Dic26—22no—
51C13×C4⋊C4—24no—
52C13×C4⋊C4—24no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C42×C13—22no—
56C42×C13—44no—
57C42×C13Q1614yes—
58C42×C13C2×D411yescharacteristic
59C42×C13C2×D412yes—
60C42×C13#4111yescharacteristic
61C22⋊Dic13—41no—
62C4⋊Dic13—22no—
63C4⋊Dic13—22no—
64#6101—42no—
65C4×Dic13—41no—
66#6099—42no—
67C2×#1055—24no—
68C2×#1055—41no—
69#3230—132no—
70#2862D1311yescharacteristic
71#1994—131no—
72#1549—132no—
73#1276—131no—
74C23×C13#12011yescharacteristic
75Q8×C13—84no—
76Q8×C13—84no—
77C2×C4×C13—24no—
78C2×C4×C13—24no—
79C2×C4×C13—44no—
80C2×C4×C13—48no—
81C2×C4×C13—44no—
82C2×C4×C13#12012yes—
83C2×C4×C13#12112yes—
84C2×C4×C13#12111yescharacteristic
85C2×C4×C13#12711yescharacteristic
86C2×C4×C13C2×Q1612yes—
87C2×C4×C13#13712yes—
88C2×Dic13—42no—
89Dic26—44no—
90#1055—44no—
91#1055—81no—
92#533—131no—
93C2×C4⋊Q8C2×D1312yes—
94#500—262no—
95#487—262no—
96#484—264no—
97#477—264no—
98#431—132no—
99#423—131no—
100#391—24no—
101#382—22no—
102C43C2×D1311yescharacteristic
103#339—262no—
104#332—264no—
105C22×C13—22no—
106C22×C13#39211yescharacteristic
107C22×C13#45112yes—
108C4×C13—22no—
109C4×C13—44no—
110C4×C13—84no—
111C4×C13#45414yes—
112C4×C13#46212yes—
113C4×C13#49411yescharacteristic
114C4×C13#49711yescharacteristic
115Dic13—82no—
116C22×Q8—22no—
117C2×M16—261no—
118C4⋊Q8—22no—
119C4⋊Q8—22no—
120C4⋊Q8—22no—
121C4⋊Q8—22no—
122C4⋊Q8—132no—
123#125—261no—
124C22⋊Q8—262no—
125C4×Q8—262no—
126#117—261no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4C22⋊D1314yes—
129C2×C42—22no—
130C2×C42C22⋊D1312yes—
131C2×C42C22×D1311yescharacteristic
132#107—268no—
133C4⋊C8—134no—
134C4⋊C8—262no—
135#103—268no—
136C22⋊C8—262no—
137C4×C8—262no—
138#95—28no—
139C2×C13—22no—
140C2×C13#200312yes—
141C2×C13#201611yescharacteristic
142C2×Q8—48no—
143C2×Q8—42no—
144C2×Q8—42no—
145C2×Q8—262no—
146C22×C4—22no—
147C22×C4—24no—
148C22×C4C2×C22⋊D1312yes—
149C22×C4C2×C22⋊D1311yescharacteristic
150M16—522no—
151C2×C8—264no—
152C2×C8—521no—
153C4⋊C4—24no—
154C4⋊C4—24no—
155C4⋊C4—42no—
156C4⋊C4—42no—
157C4⋊C4—262no—
158C4⋊C4—262no—
159C4⋊C4—522no—
160C22⋊C4—521no—
161C42—22no—
162C42—44no—
163C42—521no—
164C42#610714yes—
165C42D4×D1311yescharacteristic
166C42D4×D1312yes—
167C42#612911yescharacteristic
168C13#1029511yescharacteristic, complemented, Sylow
169C23#8820711yescharacteristic
170Q8—84no—
171Q8—84no—
172Q8—524no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—522no—
179C2×C4#8819112yes—
180C2×C4#8819211yescharacteristic
181C2×C4#8819312yes—
182C2×C4#8819411yescharacteristic
183C2×C4#8819612yes—
184C2×C4C2×#610712yes—
185C8—524no—
186C8—1041no—
187C22—22no—
188C22#1171888411yescharacteristic
189C22#1171888912yes—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—1042no—
194C4#1171872314yes—
195C4#1171874711yescharacteristic
196C4#1171875112yes—
197C4#1171875311yescharacteristic
198C2—22no—
199C2#1311585812yes—
200C2#1311593611yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2862C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#2862D13
hypocenterC13#10295
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
168. C13#10295semidirect

Maximal subgroups

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

subgroupindex
#131259872
#131158132
#131135212
#131126692
C13×#28622
#1029513