Finite Group Databasebeta

← #15752116

Subgroups — #15752116

Order 3328.

398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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#13116379C211yesmaximal, characteristic
2#13116244C212yesmaximal
3#13112662C212yesmaximal
4#13112662C211yesmaximal, characteristic
5C13×#2811C211yesmaximal, characteristic
6C13×#395—21no—
7C13×#395—22no—
8C13×#391—22no—
9C13×#391—21no—
10C13×#391C2212yes—
11C13×#391C2211yescharacteristic
12C2×#88075—22no—
13C2×#88075—21no—
14C2×#88048—21no—
15#11718596C2211yescharacteristic
16#11718121—22no—
17#11718116C2212yes—
18#11718116C2211yescharacteristic
19C22×Q8×C13—21no—
20C22×Q8×C13D412yes—
21C22×Q8×C13D411yescharacteristic
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C4⋊C4D412yes—
26C2×C42×C13—21no—
27C2×C42×C13C2311yescharacteristic
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—22no—
30C22×#1055—21no—
31C22×#1055—22no—
32C13×#95—21no—
33C13×#95—22no—
34C13×#95—22no—
35C13×#95—22no—
36C13×#95—22no—
37#88075—42no—
38#88075—44no—
39#88048—42no—
40#7812—131nomaximal, Sylow
41C2×Q8×C13—22no—
42C2×Q8×C13—21no—
43C2×Q8×C13—41no—
44C2×Q8×C13—42no—
45C2×Q8×C13—42no—
46C2×Q8×C13—41no—
47C2×Q8×C13—81no—
48C2×Q8×C13—82no—
49C2×Q8×C13SD1614yes—
50C2×Q8×C13Q1612yes—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—22no—
55C22×C4×C13C2×D412yes—
56C22×C4×C13C2×D411yescharacteristic
57C22×Dic13—41no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—81no—
61C13×C4⋊C4—82no—
62C42×C13—41no—
63C42×C13—81no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66C4⋊Dic13—42no—
67C4⋊Dic13—42no—
68C2×#1055—22no—
69C2×#1055—41no—
70C2×#1055—41no—
71C2×#1055—42no—
72C2×#1055—42no—
73C2×#1055—42no—
74#2811D1311yescharacteristic
75#2096—131no—
76#2072—132no—
77#1272—131no—
78#1272—132no—
79C23×C13#12011yescharacteristic
80Q8×C13—44no—
81Q8×C13—42no—
82Q8×C13—82no—
83Q8×C13—81no—
84Q8×C13—84no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—24no—
90C2×C4×C13—22no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13C2×SD1612yes—
101C2×C4×C13C2×Q1611yescharacteristic
102C2×C4×C13#13712yes—
103C2×C4×C13#13711yescharacteristic
104C2×Dic13—82no—
105C2×Dic13—81no—
106#1055—42no—
107#1055—82no—
108C2×#106—261no—
109C2×#103—262no—
110C2×#103—261no—
111#395—22no—
112#395—21no—
113#391—22no—
114#391—21no—
115#391C2×D1312yes—
116#391C2×D1311yescharacteristic
117#384—131no—
118#340—262no—
119#336—132no—
120#336—131no—
121C22×C13#44812yes—
122C22×C13#45111yescharacteristic
123C22×C13#45311yescharacteristic
124C22×C13#45512yes—
125C22×C13#45811yescharacteristic
126C4×C13—22no—
127C4×C13—22no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—44no—
131C4×C13—42no—
132C4×C13—81no—
133C4×C13—82no—
134Dic13—161no—
135C22×Q8—21no—
136C22×Q8C22⋊D1312yes—
137C22×Q8C22⋊D1311yescharacteristic
138C22×C8—261no—
139C22×C8—262no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—262no—
143C2×C4⋊C4—261no—
144C2×C4⋊C4C22⋊D1312yes—
145C2×C4⋊C4C22⋊D1311yescharacteristic
146C2×C42—21no—
147C2×C42C22×D1311yescharacteristic
148#106—522no—
149#103—522no—
150#103—524no—
151#95—21no—
152#95—22no—
153#95—22no—
154#95—22no—
155#95—22no—
156C2×C13#160812yes—
157C2×C13#161411yescharacteristic
158C2×C13#162311yescharacteristic
159C2×C13#164512yes—
160C2×C13#165911yescharacteristic
161C2×Q8—22no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—41no—
167C2×Q8—81no—
168C2×Q8—82no—
169C2×Q8#610614yes—
170C2×Q8#610712yes—
171C22×C4—22no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—521no—
176C22×C4C2×C22⋊D1312yes—
177C22×C4C2×C22⋊D1311yescharacteristic
178C2×C8—262no—
179C2×C8—521no—
180C2×C8—521no—
181C2×C8—522no—
182C2×C8—522no—
183C2×C8—522no—
184C4⋊C4—41no—
185C4⋊C4—42no—
186C4⋊C4—81no—
187C4⋊C4—82no—
188C4⋊C4—521no—
189C4⋊C4—521no—
190C4⋊C4—522no—
191C4⋊C4—522no—
192C42—41no—
193C42—81no—
194C13#781211yescharacteristic, complemented, Sylow
195C23#8820711yescharacteristic
196Q8—44no—
197Q8—42no—
198Q8—81no—
199Q8—82no—
200Q8—84no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—1042no—
217C2×C4—1041no—
218C2×C4C2×#610612yes—
219C2×C4#8819612yes—
220C2×C4#8819611yescharacteristic
221C2×C4C2×#610711yescharacteristic
222C8—522no—
223C8—1042no—
224C22#1171888812yes—
225C22#1171888911yescharacteristic
226C22#1171890211yescharacteristic
227C22#1171890312yes—
228C22#1171890411yescharacteristic
229C4—21no—
230C4—21no—
231C4—22no—
232C4—22no—
233C4—42no—
234C4—44no—
235C4—81no—
236C4—82no—
237C4—2081no—
238C2#1311382712yes—
239C2#1311386111yescharacteristic
240C2#1311391411yescharacteristic
241C2#1311405712yes—
242C2#1311414211yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2811C2
socle, prime radicalC23×C13#120
hypercenter#2811D13
hypocenterC13#7812
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2811

Complements

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

NH ≅ G/Ntype
194. C13#7812semidirect

Maximal subgroups

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

subgroupindex
#131163792
#131162442
#131126622
C13×#28112
#781213