Finite Group Databasebeta

← #15766049

Subgroups — #15766049

Order 3328.

416 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 101 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#13115817C211yesmaximal, characteristic
2#13113334C212yesmaximal
3#13112739C212yesmaximal
4#13112665C211yesmaximal, characteristic
5C13×#2399C211yesmaximal, characteristic
6C2×C4×Q8×C13—21no—
7#11719175C2211yescharacteristic
8C13×#398—22no—
9C13×#395—22no—
10C4×C13×C4⋊C4—21no—
11C4×C13×C4⋊C4C2212yes—
12C13×#376C2211yescharacteristic
13#11718586C2212yes—
14#11718585C2211yescharacteristic
15#11718115—21no—
16#11718115—21no—
17#11718044—22no—
18#11718044—22no—
19C22×Q8×C13—21no—
20C4×Q8×C13—42no—
21C4×Q8×C13—42no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—22no—
26C2×C42×C13—22no—
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13C2311yescharacteristic
30#88180—21no—
31#88178—22no—
32C2×#6099—21no—
33#88124—21no—
34#88123Q812yescomplemented
35C4×Dic26—22no—
36C13×#95—21no—
37C13×#95—21no—
38C13×#95—22no—
39C13×#95D412yes—
40C13×#95D412yes—
41C22⋊#1055—22no—
42C4⋊#1055—22no—
43C4⋊#1055—22no—
44C4×#1055—22no—
45#10371—131nomaximal, Sylow
46C2×Q8×C13—42no—
47C2×Q8×C13—44no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13C2×D412yes—
53C22×C4×C13C2×D411yescharacteristic
54C2×Dic26—22no—
55C13×C4⋊C4—44no—
56C13×C4⋊C4—44no—
57C13×C4⋊C4—44no—
58C13×C4⋊C4—42no—
59C42×C13—21no—
60C42×C13—21no—
61C42×C13—42no—
62C42×C13—42no—
63C42×C13SD1612yes—
64C42×C13Q1612yes—
65C42×C13C2×Q811yescharacteristic
66C42×C13#4112yes—
67C42×C13#4111yescharacteristic
68C22⋊Dic13—41no—
69C4⋊Dic13—22no—
70C4⋊Dic13—22no—
71#6101—42no—
72C4×Dic13—41no—
73#6099—41no—
74#6099—41no—
75C2×#1055—42no—
76C2×#1055—41no—
77#2399D1311yescharacteristic
78#1995—131no—
79#1503—132no—
80#1303—132no—
81#1274—131no—
82C23×C13#12011yescharacteristic
83Q8×C13—48no—
84C2×C4×C13—24no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13C22⋊Q812yes—
96C2×C4×C13C22⋊Q811yescharacteristic
97C2×C4×C13#12412yes—
98C2×C4×C13#12411yescharacteristic
99C2×C4×C13C2×SD1611yescharacteristic
100C2×C4×C13C2×Q1611yescharacteristic
101C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C13#13711yescharacteristic
103C2×Dic13—42no—
104Dic26—82no—
105#1055—82no—
106#1055—81no—
107#533—131no—
108C2×C4×Q8—21no—
109#431—132no—
110#423—131no—
111#398—22no—
112#395—22no—
113C4×C4⋊C4—21no—
114C4×C4⋊C4C2×D1312yes—
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—44no—
128C4×C13—42no—
129C4×C13—82no—
130C4×C13#47511yescharacteristic
131C4×C13#47711yescharacteristic
132C4×C13#48711yescharacteristic
133C4×C13#48911yescharacteristic
134Dic13—82no—
135C22×Q8—21no—
136C2×M16—261no—
137C4⋊Q8—132no—
138#125—261no—
139C22⋊Q8—262no—
140C4×Q8—42no—
141C4×Q8—42no—
142C4×Q8—262no—
143#117—261no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C42—22no—
149C2×C42C22⋊D1311yescharacteristic
150C2×C42C22⋊D1311yescharacteristic
151C2×C42C22×D1311yescharacteristic
152C4⋊C8—262no—
153C4⋊C8—262no—
154C22⋊C8—262no—
155C4×C8—262no—
156#95—21no—
157#95—21no—
158#95—22no—
159#95C22⋊D1312yes—
160#95C22⋊D1312yes—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13#202411yescharacteristic
164C2×C13#203112yes—
165C2×Q8—42no—
166C2×Q8—44no—
167C2×Q8—262no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4C2×C22⋊D1312yes—
173C22×C4C2×C22⋊D1311yescharacteristic
174M16—521no—
175M16—521no—
176C2×C8—522no—
177C2×C8—521no—
178C4⋊C4—44no—
179C4⋊C4—42no—
180C4⋊C4—44no—
181C4⋊C4—44no—
182C4⋊C4—262no—
183C4⋊C4—262no—
184C4⋊C4—522no—
185C22⋊C4—521no—
186C42—21no—
187C42—21no—
188C42—42no—
189C42—42no—
190C42—521no—
191C42#610512yes—
192C42#610712yes—
193C42Q8×D1311yescharacteristic
194C42#613111yescharacteristic
195C42#613112yes—
196C13#1037111yescharacteristic, complemented, Sylow
197C23#8820711yescharacteristic
198Q8—48no—
199Q8—1042no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—522no—
212C2×C4#8818611yescharacteristic
213C2×C4C2×#610511yescharacteristic
214C2×C4#8819611yescharacteristic
215C2×C4C2×#610711yescharacteristic
216C2×C4#8820012yes—
217C2×C4#8820011yescharacteristic
218C2×C4#8820112yes—
219C2×C4#8820111yescharacteristic
220C8—1042no—
221C8—1041no—
222C22—22no—
223C22#1171887911yescharacteristic
224C22#1171888911yescharacteristic
225C22#1171889211yescharacteristic
226C4—22no—
227C4—22no—
228C4—42no—
229C4—44no—
230C4—42no—
231C4—82no—
232C4—1042no—
233C4#1171875011yescharacteristic
234C4#1171875211yescharacteristic
235C4#1171875411yescharacteristic
236C4#1171875511yescharacteristic
237C2—21no—
238C2—21no—
239C2#1311597411yescharacteristic
240C2#1311600512yes—
subgroupG/H
centerC2×C4#88201
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2399C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#2399D13
hypocenterC13#10371
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
34. #88123Q8semidirect
196. C13#10371semidirect

Maximal subgroups

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

subgroupindex
#131158172
#131133342
#131127392
#131126652
C13×#23992
#1037113