Finite Group Databasebeta

← #15775665

Subgroups — #15775665

Order 3328.

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

normal subgroups only

This group has 388 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#13116003C211yesmaximal, characteristic
2#13113826C212yesmaximal
3#13112836C212yesmaximal
4#13112766C211yesmaximal, characteristic
5C13×#2817C211yesmaximal, characteristic
6C2×C13×C22⋊Q8—21no—
7#11719188C2211yescharacteristic
8C13×#400—22no—
9C13×#397—21no—
10C13×#397C2212yes—
11C13×#395—22no—
12C13×#381C2211yescharacteristic
13#11718872—21no—
14#11718632—22no—
15#11718119—21no—
16#11718118C2211yescharacteristic
17#11718117C2212yes—
18#11718044—22no—
19C22×Q8×C13—21no—
20C23×C4×C13D411yescharacteristic
21C13×C22⋊Q8—42no—
22C13×C22⋊Q8—42no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4D412yes—
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4D411yescharacteristic
29C2×C13×C22⋊C4C2311yescharacteristic
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13—21no—
32#88178—22no—
33#88132—42no—
34C13×#95—22no—
35C13×#95—21no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95D412yes—
39#88071—42no—
40C22⋊#1055—22no—
41#88050—42no—
42#88048—42no—
43#12207—131nomaximal, Sylow
44C24×C13C2×D411yescharacteristic
45C2×Q8×C13—42no—
46C2×Q8×C13—81no—
47C2×Q8×C13—81no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13SD1612yes—
56C22×C4×C13C2×D412yes—
57C22×Dic13—22no—
58C22×Dic13—41no—
59C2×Dic26—22no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C13×C4⋊C4—44no—
63C13×C4⋊C4—81no—
64C13×C22⋊C4—41no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—41no—
68C22⋊Dic13—41no—
69C22⋊Dic13—41no—
70C22⋊Dic13—41no—
71C22⋊Dic13—41no—
72C4⋊Dic13—22no—
73#6101—42no—
74C2×#1055—42no—
75#2817D1311yescharacteristic
76#2030—131no—
77#1608—132no—
78#1344—132no—
79#1317—131no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—42no—
83C23×C13#12011yescharacteristic
84C23×C13C2×SD1611yescharacteristic
85C23×C13AGL(1,ℤ/8)11yescharacteristic
86Q8×C13—84no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—44no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—41no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—81no—
101C2×Dic13—42no—
102C2×Dic13—82no—
103C2×Dic13—81no—
104C2×Dic13—82no—
105Dic26—82no—
106#1055—82no—
107#543—131no—
108C2×C22⋊Q8—21no—
109#483—262no—
110#400—22no—
111#397—21no—
112#397C2×D1312yes—
113#395—22no—
114#381—261no—
115#381C2×D1311yescharacteristic
116#342—131no—
117#342—261no—
118#328—262no—
119#323—132no—
120C22×C13—22no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—42no—
126C22×C13—81no—
127C22×C13#45011yescharacteristic
128C22×C13#45511yescharacteristic
129C22×C13B(4,𝔽2)11yescharacteristic
130C4×C13—42no—
131C4×C13—42no—
132C4×C13—82no—
133C4×C13—81no—
134C4×C13—82no—
135Dic13—82no—
136Dic13—161no—
137C22×Q8—21no—
138C23×C4C22⋊D1311yescharacteristic
139C22⋊Q8—42no—
140C22⋊Q8—42no—
141C22⋊Q8—262no—
142C22⋊Q8—522no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4C22⋊D1312yes—
147C2×C22⋊C4—22no—
148C2×C22⋊C4—261no—
149C2×C22⋊C4—261no—
150C2×C22⋊C4C22⋊D1311yescharacteristic
151C2×C22⋊C4C22×D1311yescharacteristic
152#106—522no—
153#103—522no—
154C22⋊C8—262no—
155#95—22no—
156#95—21no—
157#95—22no—
158#95—22no—
159#95—522no—
160#95C22⋊D1312yes—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13—41no—
164C2×C13—41no—
165C2×C13#160111yescharacteristic
166C2×C13#220112yes—
167C24C2×C22⋊D1311yescharacteristic
168C2×Q8—42no—
169C2×Q8—81no—
170C2×Q8—81no—
171C2×Q8—262no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—262no—
180C22×C4—521no—
181C22×C4#610512yes—
182C22×C4C2×C22⋊D1312yes—
183C2×C8—522no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—44no—
187C4⋊C4—81no—
188C4⋊C4—262no—
189C4⋊C4—522no—
190C22⋊C4—41no—
191C22⋊C4—42no—
192C22⋊C4—42no—
193C22⋊C4—41no—
194C22⋊C4—521no—
195C22⋊C4—521no—
196C22⋊C4—521no—
197C22⋊C4—521no—
198C13#1220711yescharacteristic, complemented, Sylow
199C23—21no—
200C23—21no—
201C23—42no—
202C23#8818611yescharacteristic
203C23C2×#610511yescharacteristic
204C23#8820711yescharacteristic
205Q8—84no—
206Q8—1042no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—81no—
221C2×C4—522no—
222C2×C4—1042no—
223C2×C4—1041no—
224C2×C4—1042no—
225C8—1042no—
226C22—22no—
227C22—21no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—81no—
233C22#1171887911yescharacteristic
234C22#1171890311yescharacteristic
235C22#1171890511yescharacteristic
236C4—42no—
237C4—42no—
238C4—82no—
239C4—81no—
240C4—82no—
241C4—1042no—
242C4—2081no—
243C2—21no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2#1311378811yescharacteristic
248C2#1311684912yes—
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2817C2
socleC22×C13B(4,𝔽2)
prime radicalC24×C13C2×D4
hypercenter#2817D13
hypocenterC13#12207
LCSG ▷ C2×C13×C22⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2817

Complements

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

NH ≅ G/Ntype
198. C13#12207semidirect

Maximal subgroups

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

subgroupindex
#131160032
#131138262
#131128362
#131127662
C13×#28172
#1220713