Finite Group Databasebeta

← #15775698

Subgroups — #15775698

Order 3328.

380 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 59 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#13121868C211yesmaximal, characteristic
2#13113844C212yesmaximal
3#13112841C212yesmaximal
4#13112770C211yesmaximal, characteristic
5C13×#2028C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C2×#88198—21no—
8C13×#419—21no—
9C13×#391C2211yescharacteristic
10#11718704—22no—
11#11718644C2212yes—
12#11718589—21no—
13#11718317—22no—
14#11718314—22no—
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17#11718130—22no—
18#11718120C2212yes—
19C22×Q8×C13D411yescharacteristic
20C22×Dic26—21no—
21C2×C13×M16—21no—
22C13×C4⋊Q8—41no—
23C13×#125—41no—
24C13×C22⋊Q8—22no—
25C13×#117—21no—
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13D411yescharacteristic
28#88198—42no—
29#88198—42no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13D412yes—
33C2×#6101—22no—
34C2×#6101—22no—
35C2×C4×Dic13—21no—
36C13×#103—41no—
37C13×#103—41no—
38C13×#95—22no—
39#88075—42no—
40#88071—22no—
41#88071—22no—
42#88071D412yes—
43C22⋊#1055—22no—
44#88048—42no—
45#12213—131nomaximal, Sylow
46C2×Q8×C13—21no—
47C2×Q8×C13—22no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13SD1612yes—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13C2×D412yes—
54C22×C4×C13C2×D411yescharacteristic
55C22×Dic13—22no—
56C22×Dic13—22no—
57C2×Dic26—42no—
58C2×Dic26—81no—
59C2×Dic26—81no—
60C13×M16—41no—
61C13×M16—41no—
62C2×C8×C13—41no—
63C13×C4⋊C4—21no—
64C13×C4⋊C4—21no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—42no—
68C13×C22⋊C4—41no—
69C42×C13—41no—
70C42×C13—41no—
71C4⋊Dic13—24no—
72C4⋊Dic13—42no—
73C4⋊Dic13—81no—
74#6101—44no—
75#6101—42no—
76#6101—42no—
77C4×Dic13—42no—
78C2×#1055—42no—
79#2734—131no—
80#2028D1311yescharacteristic
81#1611—132no—
82#1346—132no—
83#1319—131no—
84C23×C13#12011yescharacteristic
85Q8×C13—42no—
86Q8×C13—81no—
87Q8×C13—82no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13C2×SD1611yescharacteristic
101C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
102C2×Dic13—24no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108Dic26—84no—
109C8×C13—81no—
110#1055—82no—
111#544C2×D1311yescharacteristic
112C2×C4⋊Q8—261no—
113#483—262no—
114#419—21no—
115#398—132no—
116#395—262no—
117#391C2×D1311yescharacteristic
118#389—261no—
119#387—262no—
120#343C2×D1311yescharacteristic
121#339—21no—
122#328—262no—
123#324—132no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13#45011yescharacteristic
127C22×C13#45511yescharacteristic
128C22×C13B(4,𝔽2)11yescharacteristic
129C4×C13—21no—
130C4×C13—21no—
131C4×C13—42no—
132C4×C13—42no—
133C4×C13—42no—
134C4×C13—81no—
135C4×C13—81no—
136Dic13—44no—
137Dic13—82no—
138C22×Q8—261no—
139C22×Q8C22⋊D1311yescharacteristic
140C2×M16—21no—
141C4⋊Q8—41no—
142C4⋊Q8—522no—
143C4⋊Q8—522no—
144#125—41no—
145C22⋊Q8—22no—
146#117—21no—
147C2×C4⋊C4—132no—
148C2×C4⋊C4—261no—
149C2×C4⋊C4—262no—
150C2×C4⋊C4—262no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4C22×D1311yescharacteristic
153C2×C42—261no—
154C2×C42C22⋊D1311yescharacteristic
155#106—522no—
156#103—41no—
157#103—41no—
158#103—522no—
159C22⋊C8—262no—
160#95—22no—
161#95—132no—
162#95—262no—
163#95—262no—
164C2×C13—21no—
165C2×C13—21no—
166C2×C13#160111yescharacteristic
167C2×C13#220111yescharacteristic
168C2×C13#220511yescharacteristic
169C2×Q8—21no—
170C2×Q8—22no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—522no—
174C2×Q8—1041no—
175C2×Q8—1041no—
176C2×Q8#610612yes—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—262no—
180C22×C4—262no—
181C22×C4D4×D1312yes—
182C22×C4C2×C22⋊D1311yescharacteristic
183M16—41no—
184M16—41no—
185C2×C8—41no—
186C2×C8—522no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—22no—
190C4⋊C4—41no—
191C4⋊C4—42no—
192C4⋊C4—264no—
193C4⋊C4—522no—
194C4⋊C4—524no—
195C4⋊C4—522no—
196C4⋊C4—522no—
197C4⋊C4—1041no—
198C22⋊C4—41no—
199C42—41no—
200C42—41no—
201C42—522no—
202C13#1221311yescharacteristic, complemented, Sylow
203C23#8819111yescharacteristic
204Q8—42no—
205Q8—81no—
206Q8—82no—
207Q8—1044no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—264no—
221C2×C4—522no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—522no—
226C2×C4C2×#610611yescharacteristic
227C2×C4#8820311yescharacteristic
228C8—81no—
229C8—1042no—
230C22—21no—
231C22—21no—
232C22#1171869311yescharacteristic
233C22#1171870711yescharacteristic
234C22#1171872211yescharacteristic
235C4—21no—
236C4—21no—
237C4—42no—
238C4—42no—
239C4—42no—
240C4—81no—
241C4—81no—
242C4—524no—
243C4—1042no—
244C2—21no—
245C2—21no—
246C2#1311378711yescharacteristic
247C2#1311684811yescharacteristic
248C2#1311686511yescharacteristic
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2028C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2028D13
hypocenterC13#12213
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2028

Complements

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

NH ≅ G/Ntype
202. C13#12213semidirect

Maximal subgroups

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

subgroupindex
#131218682
#131138442
#131128412
#131127702
C13×#20282
#1221313