Finite Group Databasebeta

← #15765581

Subgroups — #15765581

Order 3328.

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

normal subgroups only

This group has 542 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#13125964C212yesmaximal
2#13115664C211yesmaximal, characteristic
3#13113521C212yesmaximal, complemented
4#13112669C211yesmaximal, characteristic, complemented
5C13×#2862C211yesmaximal, characteristic, complemented
6C2×C13×C4⋊Q8C2212yes—
7#11719182C2211yescharacteristic
8C13×#391—24no—
9C13×#382—22no—
10C43×C13C2211yescharacteristic
11#11718749—22no—
12#11718745—24no—
13#11718740—22no—
14#11718629—24no—
15C2×#88045—22no—
16#11718586C2212yes—
17#11718585C2211yescharacteristic
18#11718139—24no—
19C22×Q8×C13—22no—
20C2×#6127—21no—
21C13×C4⋊Q8—22no—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D414yes—
27C2×C42×C13—22no—
28C2×C42×C13D412yes—
29C2×C42×C13C2311yescharacteristic
30#88184—22no—
31C2×#6099—21no—
32#88129—21no—
33#88128D411yescharacteristic
34C4×D52—22no—
35#88123D411yescharacteristic
36C13×#95—28no—
37C22⋊#1055—22no—
38#88049—28no—
39#88048—28no—
40#88045—44no—
41C4⋊#1055—22no—
42C4⋊#1055D414yes—
43C4×#1055—22no—
44#10285—131nomaximal, Sylow
45C2×Q8×C13—48no—
46C2×Q8×C13—42no—
47C2×Q8×C13—42no—
48C22×C4×C13—22no—
49C22×C4×C13—24no—
50C22×C4×C13C2×D412yes—
51C22×C4×C13C2×D411yescharacteristic
52C2×C22⋊D13—41no—
53#6127—42no—
54#6127—42no—
55C2×D52—22no—
56C2×D52—21no—
57C2×C4×D13—41no—
58C2×Dic26—21no—
59C13×C4⋊C4—24no—
60C13×C4⋊C4—24no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—42no—
63C42×C13—22no—
64C42×C13—44no—
65C42×C13SD1614yes—
66C42×C13C2×D411yescharacteristic
67C42×C13C2×D412yes—
68C42×C13#4111yescharacteristic
69#6103—42no—
70C4⋊Dic13—22no—
71#6099—42no—
72C2×#1055—24no—
73C2×#1055—41no—
74#3227—132no—
75#2862D1311yescharacteristic, complemented
76#1962—131no—
77#1549—132no—
78#1276—131no—
79C23×C13#12011yescharacteristic
80C22×D13—41no—
81Q8×C13—84no—
82Q8×C13—84no—
83C2×C4×C13—24no—
84C2×C4×C13—24no—
85C2×C4×C13—44no—
86C2×C4×C13—48no—
87C2×C4×C13—44no—
88C2×C4×C13#12012yes—
89C2×C4×C13#12112yes—
90C2×C4×C13#12111yescharacteristic
91C2×C4×C13#12711yescharacteristic
92C2×C4×C13C2×SD1612yes—
93C2×C4×C13#13712yes—
94C22⋊D13—82no—
95C2×Dic13—41no—
96D52—44no—
97D52—42no—
98C4×D13—81no—
99C4×D13—81no—
100Dic26—42no—
101#1055—44no—
102#1055—81no—
103#532—131no—
104C2×C4⋊Q8C2×D1312yes—
105#498—262no—
106#486—262no—
107#481—264no—
108#476—264no—
109#431—132no—
110#423—131no—
111C2×#104—262no—
112#391—24no—
113#382—22no—
114C43C2×D1311yescharacteristic
115#332—264no—
116C22×C13—22no—
117C22×C13#39211yescharacteristic
118C22×C13#44812yes—
119C2×D13—82no—
120C2×D13—81no—
121C4×C13—22no—
122C4×C13—44no—
123C4×C13—84no—
124C4×C13#45414yes—
125C4×C13#46112yes—
126C4×C13#49211yescharacteristic
127C4×C13#49711yescharacteristic
128Dic13—81no—
129C2×#41—261no—
130C22×Q8—22no—
131C2×M16—261no—
132C4⋊Q8—22no—
133C4⋊Q8—22no—
134C4⋊Q8—22no—
135C4⋊Q8—22no—
136C4⋊Q8—131no—
137#127—131no—
138#124—261no—
139#121—262no—
140C4×D4—262no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4C22⋊D1314yes—
143C2×C42—22no—
144C2×C42C22⋊D1312yes—
145C2×C42C22×D1311yescharacteristic
146#106—268no—
147C4⋊C8—134no—
148C4⋊C8—262no—
149#104—524no—
150#102—268no—
151C22⋊C8—262no—
152C4×C8—262no—
153#95—28no—
154C2×C13—22no—
155C2×C13#200312yes—
156C2×C13#201311yescharacteristic
157D13—161no—
158#41—522no—
159#41—522no—
160C2×Q8—48no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8—261no—
164C2×D4—262no—
165C2×D4—261no—
166C2×D4—521no—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—521no—
170C22×C4C2×C22⋊D1312yes—
171C22×C4C2×C22⋊D1311yescharacteristic
172M16—522no—
173C2×C8—264no—
174C2×C8—521no—
175C4⋊C4—24no—
176C4⋊C4—24no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—262no—
180C22⋊C4—522no—
181C42—22no—
182C42—44no—
183C42#610614yes—
184C42D4×D1311yescharacteristic
185C42D4×D1312yes—
186C42#612911yescharacteristic
187C13#1028511yescharacteristic, complemented, Sylow
188C23—521no—
189C23#8820711yescharacteristic
190Q8—84no—
191Q8—84no—
192Q8—522no—
193D4—524no—
194D4—522no—
195D4—1042no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—48no—
200C2×C4—44no—
201C2×C4—521no—
202C2×C4—1041no—
203C2×C4—1041no—
204C2×C4#8819112yes—
205C2×C4#8819211yescharacteristic
206C2×C4#8819312yes—
207C2×C4#8819411yescharacteristic
208C2×C4C2×#610612yes—
209C2×C4#8819612yes—
210C8—524no—
211C8—1041no—
212C22—22no—
213C22—1041no—
214C22—1042no—
215C22#1171888411yescharacteristic
216C22#1171888812yes—
217C4—22no—
218C4—44no—
219C4—84no—
220C4—1041no—
221C4#1171872314yes—
222C4#1171874412yes—
223C4#1171874611yescharacteristic
224C4#1171874711yescharacteristic
225C2—22no—
226C2—2081no—
227C2#1311585812yes—
228C2#1311591911yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2862C2
socleC22×C13#392
prime radical#11719182C22
hypercenter#2862D13
hypocenterC13#10285
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
3. #13113521C2semidirect
4. #13112669C2semidirect
5. C13×#2862C2semidirect
75. #2862D13semidirect
187. C13#10285semidirect

Maximal subgroups

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

subgroupindex
#131259642
#131156642
#131135212
#131126692
C13×#28622
#1028513