Finite Group Databasebeta

← #15775495

Subgroups — #15775495

Order 3328.

372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116060C211yesmaximal, characteristic
2#13113872C212yesmaximal
3#13112863C212yesmaximal, complemented
4#13112782C211yesmaximal, characteristic, complemented
5C13×#2571C211yesmaximal, characteristic, complemented
6#11719215C2211yescharacteristic
7C13×#400—21no—
8C13×#400C2212yes—
9C13×#389—22no—
10C13×#384C2211yescharacteristic
11C13×#382—22no—
12C4×C13×C4⋊C4—21no—
13#11718629—22no—
14#11718627—21no—
15C2×#88045—21no—
16#11718122C2211yescharacteristic
17#11718120C2212yes—
18#11718043—22no—
19C2×#6127—21no—
20C2×C13×C4⋊C4—21no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C4⋊C4D412yes—
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13—22no—
28C2×C42×C13D411yescharacteristic
29#88184—22no—
30C2×#6099—21no—
31#88151—41no—
32#88149—41no—
33C13×#95—21no—
34C13×#95—22no—
35C13×#95—22no—
36C13×#95—22no—
37C13×#95D412yes—
38C22⋊#1055—22no—
39#88050—41no—
40#88049—41no—
41#88049—42no—
42#88048—42no—
43#88045—42no—
44#12181—131nomaximal, Sylow
45C22×C4×C13—21no—
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13C2×D411yescharacteristic
50C22×C4×C13C2×D412yes—
51C2×C22⋊D13—41no—
52#6127—41no—
53#6127—41no—
54#6127—41no—
55#6127—41no—
56C2×D52—21no—
57C2×D52—22no—
58C2×C4×D13—41no—
59C2×Dic26—21no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—44no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—81no—
67C42×C13—21no—
68C42×C13—44no—
69C42×C13SD1612yes—
70#6103—42no—
71C4⋊Dic13—22no—
72#6099—41no—
73#6099—41no—
74C2×#1055—42no—
75C2×#1055—41no—
76#2571D1311yescharacteristic, complemented
77#2039—131no—
78#1616—132no—
79#1353—132no—
80#1325—131no—
81C23×C13#12011yescharacteristic
82C22×D13—41no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13C2×SD1611yescharacteristic
99C2×C4×C13#13711yescharacteristic
100C22⋊D13—81no—
101C22⋊D13—81no—
102C2×Dic13—41no—
103D52—41no—
104D52—41no—
105D52—82no—
106C4×D13—81no—
107C4×D13—81no—
108Dic26—41no—
109Dic26—41no—
110#1055—81no—
111#1055—82no—
112#537—131no—
113#481—262no—
114C2×#104—261no—
115#417—261no—
116#400—21no—
117#400C2×D1312yes—
118#389—22no—
119#384C2×D1311yescharacteristic
120#382—22no—
121C4×C4⋊C4—21no—
122#343—131no—
123#327—262no—
124#324—132no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#44811yescharacteristic
128C22×C13#45411yescharacteristic
129C22×C13B(4,𝔽2)11yescharacteristic
130C2×D13—81no—
131C2×D13—81no—
132C2×D13—81no—
133C4×C13—24no—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13—82no—
138C4×C13—81no—
139C4×C13—82no—
140Dic13—81no—
141C2×#41—261no—
142C2×M16—261no—
143C22⋊Q8—521no—
144#121—262no—
145#121—521no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4C22⋊D1311yescharacteristic
151C2×C4⋊C4C22⋊D1312yes—
152C2×C4⋊C4C22×D1311yescharacteristic
153C2×C42—22no—
154C2×C42C22⋊D1311yescharacteristic
155#106—522no—
156#104—522no—
157#103—521no—
158#102—521no—
159#102—522no—
160C22⋊C8—262no—
161#95—21no—
162#95—22no—
163#95—22no—
164#95—22no—
165#95C22⋊D1312yes—
166C2×C13—21no—
167C2×C13—21no—
168C2×C13#159911yescharacteristic
169C2×C13#219811yescharacteristic
170C2×C13#220411yescharacteristic
171D13—161no—
172#41—521no—
173#41—521no—
174#41—521no—
175#41—521no—
176C2×Q8—261no—
177C2×D4—261no—
178C2×D4—262no—
179C2×D4—521no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—21no—
184C22×C4—521no—
185C22×C4C2×C22⋊D1311yescharacteristic
186C22×C4C2×C22⋊D1312yes—
187M16—521no—
188M16—521no—
189C2×C8—522no—
190C2×C8—521no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—44no—
196C4⋊C4—42no—
197C4⋊C4—81no—
198C4⋊C4—262no—
199C22⋊C4—522no—
200C42—21no—
201C42—44no—
202C42#610612yes—
203C13#1218111yescharacteristic, complemented, Sylow
204C23—521no—
205C23#8820711yescharacteristic
206Q8—521no—
207Q8—521no—
208D4—521no—
209D4—521no—
210D4—1042no—
211D4—1041no—
212D4—1041no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—521no—
229C2×C4—1041no—
230C2×C4—1041no—
231C2×C4C2×#610611yescharacteristic
232C2×C4#8819611yescharacteristic
233C8—1041no—
234C8—1042no—
235C22—21no—
236C22—21no—
237C22—1041no—
238C22—1041no—
239C22—1041no—
240C22#1171888811yescharacteristic
241C22#1171890511yescharacteristic
242C22#1171890611yescharacteristic
243C4—24no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—82no—
248C4—81no—
249C4—82no—
250C4—1041no—
251C2—21no—
252C2—21no—
253C2—2081no—
254C2#1311377611yescharacteristic
255C2#1311683211yescharacteristic
256C2#1311686211yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2571C2
socleC22×C13B(4,𝔽2)
prime radical#11719215C22
hypercenter#2571D13
hypocenterC13#12181
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2571

Complements

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

NH ≅ G/Ntype
3. #13112863C2semidirect
4. #13112782C2semidirect
5. C13×#2571C2semidirect
76. #2571D13semidirect
203. C13#12181semidirect

Maximal subgroups

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

subgroupindex
#131160602
#131138722
#131128632
#131127822
C13×#25712
#1218113