Finite Group Databasebeta

← #15766053

Subgroups — #15766053

Order 3328.

416 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 97 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#13118129C211yesmaximal, characteristic
2#13115817C211yesmaximal, characteristic
3#13113336C212yesmaximal
4#13112738C212yesmaximal
5C13×#1274C211yesmaximal, characteristic
6#11719175C2211yescharacteristic
7C2×C4×Dic26—21no—
8C13×#431C2212yes—
9C13×#376C2211yescharacteristic
10C4×C4⋊Dic13—21no—
11C4×C4⋊Dic13C2212yes—
12#11718585C2211yescharacteristic
13#11718322—22no—
14#11718317—22no—
15#11718115—21no—
16#11718115—21no—
17#11718059—22no—
18#11718059—22no—
19C22×Dic26—21no—
20C2×C42×C13D411yescharacteristic
21C2×C42×C13D411yescharacteristic
22C2×C42×C13C2311yescharacteristic
23#88180—21no—
24C2×C4⋊Dic13—21no—
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13—22no—
27#88178—22no—
28C2×#6101—22no—
29C2×C4×Dic13—22no—
30C2×#6099—21no—
31#88124—21no—
32#88123Q812yescomplemented
33C4×Dic26—22no—
34C4×Dic26—42no—
35C4×Dic26—42no—
36C13×C4⋊C8—22no—
37C13×C22⋊C8—22no—
38C4×C8×C13—22no—
39C13×#95—22no—
40#88071—21no—
41#88071—21no—
42#88071D412yes—
43#88071D412yes—
44C4⋊#1055—22no—
45#10371—131nomaximal, Sylow
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C2×D411yescharacteristic
49C22×C4×C13C2×D412yes—
50C22×Dic13—22no—
51C22×Dic13—22no—
52C2×Dic26—22no—
53C2×Dic26—44no—
54C2×Dic26—42no—
55C2×C8×C13—42no—
56C42×C13—21no—
57C42×C13—21no—
58C42×C13SD1612yes—
59C42×C13Q1612yes—
60C42×C13C2×Q811yescharacteristic
61C42×C13#4112yes—
62C42×C13#4111yescharacteristic
63C22⋊Dic13—41no—
64C4⋊Dic13—22no—
65C4⋊Dic13—22no—
66C4⋊Dic13—44no—
67C4⋊Dic13—44no—
68C4⋊Dic13—42no—
69#6101—44no—
70#6101—42no—
71C4×Dic13—41no—
72C4×Dic13—42no—
73C4×Dic13—42no—
74#6099—41no—
75#6099—41no—
76C2×#1055—41no—
77#2399—131no—
78#1995—131no—
79#1503—132no—
80#1303—132no—
81#1274D1311yescharacteristic
82C23×C13#12011yescharacteristic
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13C22⋊Q812yes—
89C2×C4×C13C22⋊Q811yescharacteristic
90C2×C4×C13#12412yes—
91C2×C4×C13#12411yescharacteristic
92C2×C4×C13C2×SD1611yescharacteristic
93C2×C4×C13C2×Q1611yescharacteristic
94C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C13#13711yescharacteristic
96C2×Dic13—24no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103Dic26—48no—
104Dic26—82no—
105C8×C13—82no—
106#1055—81no—
107#533—131no—
108C2×C4×Q8—261no—
109#431C2×D1312yes—
110#423—131no—
111#398—262no—
112#395—262no—
113C4×C4⋊C4—132no—
114C4×C4⋊C4—261no—
115#376C2×D1311yescharacteristic
116#339—261no—
117#339—261no—
118#328—262no—
119#328—262no—
120C22×C13—22no—
121C22×C13#39311yescharacteristic
122C22×C13#45011yescharacteristic
123C22×C13#45111yescharacteristic
124C4×C13—22no—
125C4×C13—22no—
126C4×C13—42no—
127C4×C13—42no—
128C4×C13#47511yescharacteristic
129C4×C13#47711yescharacteristic
130C4×C13#48711yescharacteristic
131C4×C13#48911yescharacteristic
132Dic13—44no—
133Dic13—82no—
134Dic13—82no—
135C22×Q8—261no—
136C2×M16—261no—
137C4⋊Q8—132no—
138#125—261no—
139C22⋊Q8—262no—
140C4×Q8—262no—
141C4×Q8—522no—
142C4×Q8—522no—
143#117—261no—
144C2×C4⋊C4—262no—
145C2×C4⋊C4—261no—
146C2×C4⋊C4—262no—
147C2×C4⋊C4—262no—
148C2×C42—262no—
149C2×C42D5211yescharacteristic
150C2×C42D5211yescharacteristic
151C2×C42C22×D1311yescharacteristic
152C4⋊C8—22no—
153C4⋊C8—262no—
154C22⋊C8—22no—
155C4×C8—22no—
156#95—22no—
157#95—132no—
158#95—132no—
159#95—261no—
160#95—261no—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13#202411yescharacteristic
164C2×C13#203112yes—
165C2×Q8—262no—
166C2×Q8—522no—
167C2×Q8—524no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—262no—
171C22×C4—262no—
172C22×C4C2×D5211yescharacteristic
173C22×C4D4×D1312yes—
174M16—521no—
175M16—521no—
176C2×C8—42no—
177C2×C8—521no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4—524no—
181C4⋊C4—522no—
182C4⋊C4—524no—
183C4⋊C4—524no—
184C4⋊C4—522no—
185C22⋊C4—521no—
186C42—21no—
187C42—21no—
188C42—521no—
189C42—522no—
190C42—522no—
191C42#609512yes—
192C42Dic5212yes—
193C42#612712yes—
194C42#612911yescharacteristic
195C42Q8×D1311yescharacteristic
196C13#1037111yescharacteristic, complemented, Sylow
197C23#8813611yescharacteristic
198Q8—528no—
199Q8—1042no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—264no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—522no—
211C2×C4—522no—
212C2×C4#8812911yescharacteristic
213C2×C4#8813912yes—
214C2×C4#8815012yes—
215C2×C4#8815111yescharacteristic
216C2×C4C2×#609511yescharacteristic
217C2×C4C2×Dic5211yescharacteristic
218C2×C4#8816211yescharacteristic
219C2×C4#8816311yescharacteristic
220C8—82no—
221C8—1041no—
222C22—22no—
223C22#1171833411yescharacteristic
224C22#1171839211yescharacteristic
225C22#1171840011yescharacteristic
226C4—22no—
227C4—22no—
228C4—42no—
229C4—42no—
230C4—524no—
231C4—1042no—
232C4—1042no—
233C4#1171834211yescharacteristic
234C4#1171837511yescharacteristic
235C4#1171851111yescharacteristic
236C4#1171851211yescharacteristic
237C2—21no—
238C2—21no—
239C2#1311597811yescharacteristic
240C2#1311600712yes—
subgroupG/H
centerC2×C4#88129
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1274C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1274D13
hypocenterC13#10371
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
32. #88123Q8semidirect
196. C13#10371semidirect

Maximal subgroups

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

subgroupindex
#131181292
#131158172
#131133362
#131127382
C13×#12742
#1037113