Finite Group Databasebeta

← #15775974

Subgroups — #15775974

Order 3328.

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

normal subgroups only

This group has 442 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#13116181C211yesmaximal, characteristic
2#13113809C212yesmaximal
3#13112866C212yesmaximal
4#13112782C211yesmaximal, characteristic
5C13×#2551C211yesmaximal, characteristic
6C2×C13×C4⋊Q8—22no—
7#11719205C2211yescharacteristic
8C13×#395—21no—
9C13×#395C2212yes—
10C13×#389—22no—
11C13×#384C2211yescharacteristic
12C4×C13×C4⋊C4—21no—
13#11718889—22no—
14#11718625—21no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C22×Q8×C13—21no—
20C22×Q8×C13D412yes—
21C13×C4⋊Q8—48no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C42×C13—22no—
30C2×C42×C13D411yescharacteristic
31C2×#6107—42no—
32#88180—21no—
33#88178—22no—
34C2×#6099—21no—
35#88144—41no—
36#88142—41no—
37C13×#95—21no—
38C13×#95—22no—
39C13×#95D412yes—
40#88075—42no—
41C22⋊#1055—22no—
42#88048—41no—
43#88047—41no—
44#12256—131nomaximal, Sylow
45C2×Q8×C13—44no—
46C2×Q8×C13—44no—
47C2×Q8×C13—42no—
48C2×Q8×C13—81no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13C2×D411yescharacteristic
54C22×C4×C13C2×D412yes—
55C2×Dic26—22no—
56C13×C4⋊C4—24no—
57C13×C4⋊C4—24no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—44no—
61C13×C4⋊C4—44no—
62C13×C4⋊C4—44no—
63C42×C13—21no—
64C42×C13—44no—
65C42×C13Q1612yescomplemented
66C22⋊Dic13—41no—
67#6107—84no—
68C4⋊Dic13—22no—
69C4⋊Dic13—21no—
70C4⋊Dic13—21no—
71#6101—42no—
72C4×Dic13—41no—
73#6099—22no—
74#6099—41no—
75C2×#1055—41no—
76C2×#1055—42no—
77#2551D1311yescharacteristic
78#2060—131no—
79#1605—132no—
80#1354—132no—
81#1325—131no—
82C23×C13#12011yescharacteristic
83Q8×C13—44no—
84Q8×C13—82no—
85Q8×C13—84no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—24no—
92C2×C4×C13—24no—
93C2×C4×C13—22no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13C2×Q1611yescharacteristic
102C2×C4×C13#13711yescharacteristic
103C2×Dic13—41no—
104C2×Dic13—41no—
105Dic26—82no—
106#1055—42no—
107#1055—82no—
108#544—131no—
109C2×C4⋊Q8—22no—
110#451—262no—
111#428—261no—
112#395—21no—
113#395C2×D1312yes—
114#389—22no—
115#384C2×D1311yescharacteristic
116C4×C4⋊C4—21no—
117#343—131no—
118#339—261no—
119#328—262no—
120#324—132no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#45111yescharacteristic
124C22×C13#45611yescharacteristic
125C22×C13B(4,𝔽2)11yescharacteristic
126C4×C13—24no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13—44no—
130C4×C13—42no—
131C4×C13—44no—
132C4×C13—81no—
133Dic13—81no—
134Dic13—81no—
135C22×Q8—21no—
136C22×Q8C22⋊D1312yes—
137C2×Q16—522no—
138C2×M16—261no—
139C4⋊Q8—48no—
140C4⋊Q8—521no—
141#125—521no—
142C22⋊Q8—262no—
143#117—261no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4C22⋊D1311yescharacteristic
150C2×C4⋊C4C22×D1311yescharacteristic
151C2×C42—22no—
152C2×C42C22⋊D1311yescharacteristic
153#107—521no—
154#106—521no—
155#103—522no—
156C22⋊C8—262no—
157#95—21no—
158#95—22no—
159#95C22⋊D1312yes—
160C2×C13—21no—
161C2×C13—21no—
162C2×C13#160511yescharacteristic
163C2×C13#219611yescharacteristic
164C2×C13#220511yescharacteristic
165C2×Q8—44no—
166C2×Q8—44no—
167C2×Q8—42no—
168C2×Q8—81no—
169C2×Q8—262no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4C2×C22⋊D1311yescharacteristic
175C22×C4C2×C22⋊D1312yes—
176Q16—1044no—
177M16—262no—
178M16—521no—
179C2×C8—521no—
180C2×C8—522no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—44no—
186C4⋊C4—44no—
187C4⋊C4—44no—
188C4⋊C4—262no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4—522no—
192C22⋊C4—521no—
193C42—21no—
194C42—44no—
195C42—521no—
196C42#610712yescomplemented
197C13#1225611yescharacteristic, complemented, Sylow
198C23#8820711yescharacteristic
199Q8—44no—
200Q8—82no—
201Q8—84no—
202Q8—1042no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—24no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—521no—
219C2×C4—521no—
220C2×C4#8819611yescharacteristic
221C2×C4C2×#610711yescharacteristic
222C8—522no—
223C8—1042no—
224C22—21no—
225C22—21no—
226C22#1171888911yescharacteristic
227C22#1171890511yescharacteristic
228C22#1171890711yescharacteristic
229C4—24no—
230C4—21no—
231C4—21no—
232C4—44no—
233C4—42no—
234C4—44no—
235C4—81no—
236C4—1041no—
237C4—1041no—
238C2—21no—
239C2—21no—
240C2#1311381011yescharacteristic
241C2#1311682011yescharacteristic
242C2#1311686611yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2551C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2551D13
hypocenterC13#12256
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2551

Complements

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

NH ≅ G/Ntype
65. C42×C13Q16semidirect
196. C42#6107semidirect
197. C13#12256semidirect

Maximal subgroups

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

subgroupindex
#131161812
#131138092
#131128662
#131127822
C13×#25512
#1225613