Finite Group Databasebeta

← #15765645

Subgroups — #15765645

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#13125989C212yesmaximal
2#13123214C211yesmaximal, characteristic
3#13115813C211yesmaximal, characteristic
4#13113520C212yesmaximal
5C13×#1276C211yesmaximal, characteristic
6#11719175C2211yescharacteristic
7C2×#88123C2212yes—
8C13×#431C2212yes—
9C43×C13C2211yescharacteristic
10#11718597—22no—
11#11718590—24no—
12#11718585C2211yescharacteristic
13#11718511—24no—
14#11718383—24no—
15#11718343—22no—
16#11718342—22no—
17#11718115—22no—
18#11718074—24no—
19C22×Dic26—22no—
20C2×C42×C13—22no—
21C2×C42×C13D412yes—
22C2×C42×C13C2311yescharacteristic
23#88180—21no—
24C2×C4⋊Dic13—22no—
25C2×C4⋊Dic13D414yes—
26#88178—22no—
27C2×#6099—21no—
28#88124—21no—
29#88123—22no—
30#88123—22no—
31#88123—22no—
32#88123—22no—
33#88123D412yes—
34C4×Dic26—22no—
35C13×C4⋊C8D414yes—
36C13×C22⋊C8—22no—
37C4×C8×C13—22no—
38#88071—28no—
39#88058—28no—
40#88056—28no—
41C4⋊#1055—22no—
42#10295—131nomaximal, Sylow
43C22×C4×C13—22no—
44C22×C4×C13C2×D411yescharacteristic
45C22×C4×C13C2×D412yes—
46C22×Dic13—24no—
47C2×Dic26—22no—
48C2×Dic26—48no—
49C2×Dic26—42no—
50C2×Dic26—42no—
51C2×C8×C13—24no—
52C42×C13—22no—
53C42×C13—44no—
54C42×C13Q1614yes—
55C42×C13C2×D412yes—
56C42×C13C2×D411yescharacteristic
57C42×C13#4111yescharacteristic
58C22⋊Dic13—41no—
59C4⋊Dic13—22no—
60C4⋊Dic13—24no—
61C4⋊Dic13—24no—
62C4⋊Dic13—22no—
63C4⋊Dic13—42no—
64C4⋊Dic13—42no—
65#6101—42no—
66C4×Dic13—41no—
67#6099—42no—
68C2×#1055—41no—
69#3230—132no—
70#2862—131no—
71#1994—131no—
72#1549—132no—
73#1276D1311yescharacteristic
74C23×C13#12011yescharacteristic
75C2×C4×C13—24no—
76C2×C4×C13—24no—
77C2×C4×C13—44no—
78C2×C4×C13#12012yes—
79C2×C4×C13#12112yes—
80C2×C4×C13#12111yescharacteristic
81C2×C4×C13#12711yescharacteristic
82C2×C4×C13C2×Q1612yes—
83C2×C4×C13#13712yes—
84C2×Dic13—48no—
85C2×Dic13—42no—
86C2×Dic13—44no—
87Dic26—44no—
88Dic26—84no—
89Dic26—84no—
90C8×C13—44no—
91#1055—81no—
92#533—131no—
93C2×C4⋊Q8—132no—
94#500—262no—
95#487—262no—
96#484—264no—
97#477—264no—
98#431C2×D1312yes—
99#423—131no—
100#391—264no—
101#382—262no—
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#45414yes—
111C4×C13#46212yes—
112C4×C13#49411yescharacteristic
113C4×C13#49711yescharacteristic
114Dic13—82no—
115Dic13—84no—
116C22×Q8—262no—
117C2×M16—261no—
118C4⋊Q8—132no—
119C4⋊Q8—262no—
120C4⋊Q8—262no—
121C4⋊Q8—262no—
122C4⋊Q8—262no—
123#125—261no—
124C22⋊Q8—262no—
125C4×Q8—262no—
126#117—261no—
127C2×C4⋊C4—134no—
128C2×C4⋊C4—262no—
129C2×C42—22no—
130C2×C42D5212yes—
131C2×C42C22×D1311yescharacteristic
132#107—268no—
133C4⋊C8—262no—
134C4⋊C8D5214yes—
135#103—268no—
136C22⋊C8—22no—
137C4×C8—22no—
138#95—268no—
139C2×C13—22no—
140C2×C13#200312yes—
141C2×C13#201611yescharacteristic
142C2×Q8—262no—
143C2×Q8—528no—
144C2×Q8—522no—
145C2×Q8—522no—
146C22×C4—22no—
147C22×C4—264no—
148C22×C4C2×D5211yescharacteristic
149C22×C4D4×D1312yes—
150M16—522no—
151C2×C8—24no—
152C2×C8—521no—
153C4⋊C4—264no—
154C4⋊C4—262no—
155C4⋊C4—264no—
156C4⋊C4—262no—
157C4⋊C4—522no—
158C4⋊C4—522no—
159C4⋊C4—522no—
160C22⋊C4—521no—
161C42—22no—
162C42—44no—
163C42—521no—
164C42Dic5214yes—
165C42C2×D5212yes—
166C42D4×D1311yescharacteristic
167C42#613111yescharacteristic
168C13#1029511yescharacteristic, complemented, Sylow
169C23#8813611yescharacteristic
170Q8—524no—
171Q8—1044no—
172Q8—1044no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—528no—
177C2×C4—522no—
178C2×C4—524no—
179C2×C4#8812811yescharacteristic
180C2×C4#8813612yes—
181C2×C4#8814912yes—
182C2×C4#8814911yescharacteristic
183C2×C4C2×Dic5212yes—
184C2×C4#8816312yes—
185C8—44no—
186C8—1041no—
187C22—22no—
188C22#1171833211yescharacteristic
189C22#1171840012yes—
190C4—22no—
191C4—44no—
192C4—1044no—
193C4—1042no—
194C4#1171836011yescharacteristic
195C4#1171837611yescharacteristic
196C4#1171848814yes—
197C4#1171851012yes—
198C2—22no—
199C2#1311586112yes—
200C2#1311593811yescharacteristic
subgroupG/H
centerC22#11718332
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#1276D13
hypocenterC13#10295
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

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
#131259892
#131232142
#131158132
#131135202
C13×#12762
#1029513