Finite Group Databasebeta

← #15765583

Subgroups — #15765583

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#13125966C212yesmaximal
2#13123214C211yesmaximal, characteristic, complemented
3#13115664C211yesmaximal, characteristic
4#13113520C212yesmaximal, complemented
5C13×#1276C211yesmaximal, characteristic, complemented
6#11719182C2211yescharacteristic
7C2×#88123C2212yes—
8C13×#431C2212yes—
9C43×C13C2211yescharacteristic
10#11718597—22no—
11#11718590—24no—
12C2×#88045—22no—
13#11718585C2211yescharacteristic
14#11718503—24no—
15#11718396—24no—
16#11718355—22no—
17#11718341—22no—
18#11718074—24no—
19C2×#6127—21no—
20C22×Dic26—22no—
21C2×C42×C13—22no—
22C2×C42×C13D412yes—
23C2×C42×C13C2311yescharacteristic
24#88184—22no—
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13D414yes—
27C2×#6099—21no—
28#88129—21no—
29#88128D411yescharacteristic
30C4×D52—22no—
31#88123—22no—
32#88123—22no—
33#88123—22no—
34#88123—22no—
35#88123D411yescharacteristic
36C13×C4⋊C8D414yes—
37C13×C22⋊C8—22no—
38C4×C8×C13—22no—
39#88071—28no—
40#88061—28no—
41#88057—28no—
42#88045—44no—
43C4⋊#1055—22no—
44#10285—131nomaximal, Sylow
45C22×C4×C13—22no—
46C22×C4×C13C2×D411yescharacteristic
47C22×C4×C13C2×D412yes—
48C2×C22⋊D13—41no—
49C22×Dic13—24no—
50#6127—42no—
51#6127—42no—
52C2×D52—22no—
53C2×D52—21no—
54C2×C4×D13—41no—
55C2×Dic26—21no—
56C2×Dic26—48no—
57C2×Dic26—42no—
58C2×Dic26—42no—
59C2×C8×C13—24no—
60C42×C13—22no—
61C42×C13—44no—
62C42×C13SD1614yes—
63C42×C13C2×D412yes—
64C42×C13C2×D411yescharacteristic
65C42×C13#4111yescharacteristic
66#6103—42no—
67C4⋊Dic13—24no—
68C4⋊Dic13—22no—
69C4⋊Dic13—24no—
70C4⋊Dic13—42no—
71C4⋊Dic13—42no—
72#6099—42no—
73C2×#1055—41no—
74#3227—132no—
75#2862—131no—
76#1962—131no—
77#1549—132no—
78#1276D1311yescharacteristic, complemented
79C23×C13#12011yescharacteristic
80C22×D13—41no—
81C2×C4×C13—24no—
82C2×C4×C13—24no—
83C2×C4×C13—44no—
84C2×C4×C13#12012yes—
85C2×C4×C13#12112yes—
86C2×C4×C13#12111yescharacteristic
87C2×C4×C13#12711yescharacteristic
88C2×C4×C13C2×SD1612yes—
89C2×C4×C13#13712yes—
90C22⋊D13—82no—
91C2×Dic13—48no—
92C2×Dic13—44no—
93C2×Dic13—41no—
94D52—44no—
95D52—42no—
96C4×D13—81no—
97C4×D13—81no—
98Dic26—42no—
99Dic26—84no—
100Dic26—84no—
101C8×C13—44no—
102#1055—81no—
103#532—131no—
104C2×C4⋊Q8—132no—
105#498—262no—
106#486—262no—
107#481—264no—
108#476—264no—
109#431C2×D1312yes—
110#423—131no—
111C2×#104—262no—
112#391—264no—
113#382—262no—
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#45414yes—
124C4×C13#46112yes—
125C4×C13#49211yescharacteristic
126C4×C13#49711yescharacteristic
127Dic13—84no—
128Dic13—81no—
129C2×#41—261no—
130C22×Q8—262no—
131C2×M16—261no—
132C4⋊Q8—131no—
133C4⋊Q8—262no—
134C4⋊Q8—262no—
135C4⋊Q8—262no—
136C4⋊Q8—262no—
137#127—131no—
138#124—261no—
139#121—262no—
140C4×D4—262no—
141C2×C4⋊C4—134no—
142C2×C4⋊C4—262no—
143C2×C42—22no—
144C2×C42D5212yes—
145C2×C42C22×D1311yescharacteristic
146#106—268no—
147C4⋊C8—262no—
148C4⋊C8D5214yes—
149#104—524no—
150#102—268no—
151C22⋊C8—22no—
152C4×C8—22no—
153#95—268no—
154C2×C13—22no—
155C2×C13#200312yes—
156C2×C13#201311yescharacteristic
157D13—161no—
158#41—522no—
159#41—522no—
160C2×Q8—261no—
161C2×Q8—528no—
162C2×Q8—522no—
163C2×Q8—522no—
164C2×D4—262no—
165C2×D4—261no—
166C2×D4—521no—
167C22×C4—22no—
168C22×C4—264no—
169C22×C4—521no—
170C22×C4C2×D5211yescharacteristic
171C22×C4D4×D1312yes—
172M16—522no—
173C2×C8—24no—
174C2×C8—521no—
175C4⋊C4—264no—
176C4⋊C4—262no—
177C4⋊C4—264no—
178C4⋊C4—522no—
179C4⋊C4—522no—
180C22⋊C4—522no—
181C42—22no—
182C42—44no—
183C42#609514yes—
184C42C2×D5212yes—
185C42D4×D1311yescharacteristic
186C42#613111yescharacteristic
187C13#1028511yescharacteristic, complemented, Sylow
188C23—521no—
189C23#8813611yescharacteristic
190Q8—522no—
191Q8—1044no—
192Q8—1044no—
193D4—524no—
194D4—522no—
195D4—1042no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—528no—
200C2×C4—521no—
201C2×C4—524no—
202C2×C4—1041no—
203C2×C4—1041no—
204C2×C4#8812811yescharacteristic
205C2×C4#8813612yes—
206C2×C4#8814912yes—
207C2×C4#8814911yescharacteristic
208C2×C4C2×#609512yes—
209C2×C4#8816312yes—
210C8—44no—
211C8—1041no—
212C22—22no—
213C22—1041no—
214C22—1042no—
215C22#1171833211yescharacteristic
216C22#1171839912yes—
217C4—22no—
218C4—44no—
219C4—1041no—
220C4—1044no—
221C4#1171835411yescharacteristic
222C4#1171837611yescharacteristic
223C4#1171848814yes—
224C4#1171850212yes—
225C2—22no—
226C2—2081no—
227C2#1311586112yes—
228C2#1311592111yescharacteristic
subgroupG/H
centerC22#11718332
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1276C2
socleC22×C13#392
prime radical#11719182C22
hypercenter#1276D13
hypocenterC13#10285
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
2. #13123214C2semidirect
4. #13113520C2semidirect
5. C13×#1276C2semidirect
78. #1276D13semidirect
187. C13#10285semidirect

Maximal subgroups

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

subgroupindex
#131259662
#131232142
#131156642
#131135202
C13×#12762
#1028513