Finite Group Databasebeta

← #15763789

Subgroups — #15763789

Order 3328.

528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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#13124875C212yesmaximal
2#13115817C211yesmaximal, characteristic
3#13113265C212yesmaximal
4#13112665C211yesmaximal, characteristic
5C13×#2399C211yesmaximal, characteristic
6C2×C4×Q8×C13C2212yes—
7#11719175C2211yescharacteristic
8C13×#398—22no—
9C13×#395—22no—
10C4×C13×C4⋊C4—22no—
11C13×#376C2211yescharacteristic
12#11718889—22no—
13#11718692—22no—
14C4×#6107—24no—
15#11718682—22no—
16#11718631—22no—
17#11718586C2212yes—
18#11718585C2211yescharacteristic
19Q8⋊#1055—24no—
20#11718115—22no—
21C22×Q8×C13D412yes—
22C4×Q8×C13—22no—
23C4×Q8×C13—22no—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C2×C13×C4⋊C4—24no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4D412yes—
29C2×C42×C13—22no—
30C2×C42×C13D412yes—
31C2×C42×C13C2311yescharacteristic
32C2×#6107—24no—
33#88180—21no—
34#88178—22no—
35C2×#6099—21no—
36#88124—21no—
37#88123D412yes—
38C4×Dic26—22no—
39C13×#95—22no—
40C13×#95—22no—
41C13×#95—22no—
42#88075—24no—
43C22⋊#1055—22no—
44#88050—24no—
45#88047—24no—
46C4⋊#1055—22no—
47C4⋊#1055—22no—
48C4×#1055D414yes—
49#10017—131nomaximal, Sylow
50C2×Q8×C13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—44no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13C2×D412yes—
57C22×C4×C13C2×D411yescharacteristic
58C2×Dic26—22no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—48no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C42×C13—22no—
65C42×C13—42no—
66C42×C13—42no—
67C42×C13Q1614yescomplemented
68C42×C13C2×D411yescharacteristic
69C42×C13C2×D412yes—
70C42×C13#4111yescharacteristic
71C22⋊Dic13—41no—
72#6107—48no—
73C4⋊Dic13—22no—
74C4⋊Dic13—22no—
75#6101—42no—
76C4×Dic13—41no—
77#6099—42no—
78C2×#1055—24no—
79C2×#1055—41no—
80#3104—132no—
81#2399D1311yescharacteristic
82#1995—131no—
83#1487—132no—
84#1274—131no—
85C23×C13#12011yescharacteristic
86Q8×C13—24no—
87Q8×C13—24no—
88Q8×C13—42no—
89Q8×C13—42no—
90C2×C4×C13—24no—
91C2×C4×C13—24no—
92C2×C4×C13—42no—
93C2×C4×C13—44no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—44no—
97C2×C4×C13—42no—
98C2×C4×C13#12012yes—
99C2×C4×C13#12112yes—
100C2×C4×C13#12111yescharacteristic
101C2×C4×C13#12711yescharacteristic
102C2×C4×C13C2×Q1612yes—
103C2×C4×C13#13712yes—
104C2×Dic13—42no—
105Dic26—44no—
106#1055—44no—
107#1055—81no—
108#533—131no—
109C2×C4×Q8C2×D1312yes—
110#484—262no—
111#477—262no—
112#462—262no—
113#451—262no—
114C4×Q16—264no—
115#431—132no—
116#423—131no—
117#398—22no—
118#395—22no—
119C4×C4⋊C4—22no—
120#376C2×D1311yescharacteristic
121#339—262no—
122Q8⋊C8—264no—
123C22×C13—22no—
124C22×C13#39211yescharacteristic
125C22×C13#45112yes—
126C4×C13—22no—
127C4×C13—22no—
128C4×C13—44no—
129C4×C13—44no—
130C4×C13—82no—
131C4×C13#46212yes—
132C4×C13#49411yescharacteristic
133C4×C13#49711yescharacteristic
134Dic13—82no—
135C22×Q8C22⋊D1312yes—
136C2×Q16—264no—
137C2×M16—261no—
138C4⋊Q8—132no—
139#125—261no—
140C22⋊Q8—262no—
141C4×Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—262no—
146#117—261no—
147C2×C4⋊C4—24no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4C22⋊D1312yes—
150C2×C42—22no—
151C2×C42C22⋊D1312yes—
152C2×C42C22×D1311yescharacteristic
153#107—264no—
154C4⋊C8—262no—
155C4⋊C8—262no—
156#103—264no—
157#103—264no—
158C22⋊C8—262no—
159C4×C8—134no—
160#95—22no—
161#95—22no—
162#95—22no—
163C2×C13—22no—
164C2×C13#201012yes—
165C2×C13#201611yescharacteristic
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—44no—
169C2×Q8—262no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4C2×C22⋊D1312yes—
174C22×C4C2×C22⋊D1311yescharacteristic
175Q16—528no—
176M16—522no—
177C2×C8—264no—
178C2×C8—521no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—48no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—262no—
185C4⋊C4—262no—
186C4⋊C4—522no—
187C22⋊C4—521no—
188C42—22no—
189C42—42no—
190C42—42no—
191C42—521no—
192C42#610714yescomplemented
193C42D4×D1311yescharacteristic
194C42D4×D1312yes—
195C42#612911yescharacteristic
196C13#1001711yescharacteristic, complemented, Sylow
197C23#8820711yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—42no—
201Q8—42no—
202Q8—524no—
203C2×C4—24no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—522no—
212C2×C4#8819112yes—
213C2×C4#8819211yescharacteristic
214C2×C4#8819312yes—
215C2×C4#8819411yescharacteristic
216C2×C4#8819612yes—
217C2×C4C2×#610712yes—
218C8—524no—
219C8—1041no—
220C22—22no—
221C22#1171888411yescharacteristic
222C22#1171888912yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—44no—
227C4—82no—
228C4—1042no—
229C4#1171874711yescharacteristic
230C4#1171875112yes—
231C4#1171875311yescharacteristic
232C2—22no—
233C2#1311590112yes—
234C2#1311593611yescharacteristic
subgroupG/H
centerC2×C4#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2399C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#2399D13
hypocenterC13#10017
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
67. C42×C13Q16semidirect
192. C42#6107semidirect
196. C13#10017semidirect

Maximal subgroups

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

subgroupindex
#131248752
#131158172
#131132652
#131126652
C13×#23992
#1001713