Finite Group Databasebeta

← #15767950

Subgroups — #15767950

Order 3328.

316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115816C211yesmaximal, characteristic
2#13114989C211yesmaximal, characteristic
3#13113608C211yesmaximal, characteristic
4#13113240C211yesmaximal, characteristic
5#13113238C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1570C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88054—22no—
13#11718593C2211yescharacteristic
14#11718586C2211yescharacteristic
15C2×C4⋊#1055C2211yescharacteristic
16C13×#334—22no—
17#11718147—22no—
18#11718076—22no—
19#11718072—22no—
20#11718048—22no—
21C2×C13×M16—21no—
22C22×C8×C13—21no—
23C2×C42×C13C2311yescharacteristic
24#88180—21no—
25#88178—21no—
26#88178—21no—
27C2×C4×Dic13D412yes—
28C22×#1055—21no—
29#88124—21no—
30#88123Q811yescharacteristic
31#88123Q811yescharacteristic
32C4×Dic26—21no—
33C4×Dic26—21no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C4⋊C8—21no—
37C13×C4⋊C8—21no—
38C13×C4⋊C8—21no—
39C13×C22⋊C8—21no—
40C4×C8×C13D412yes—
41#88071—21no—
42#88071—21no—
43C22⋊#1055—21no—
44#88054—44no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48C4×#1055D412yes—
49#10670—131nomaximal, Sylow
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13#4111yescharacteristic
52C22×C4×C13#4111yescharacteristic
53C22×Dic13—22no—
54C2×Dic26—21no—
55C2×Dic26—21no—
56C13×M16—42no—
57C2×C8×C13—22no—
58C2×C8×C13—41no—
59C2×C8×C13—41no—
60C2×C8×C13—42no—
61C42×C13C2×D411yescharacteristic
62C42×C13C2×D411yescharacteristic
63C42×C13C2×Q811yescharacteristic
64C42×C13#4111yescharacteristic
65C22⋊Dic13—41no—
66C4⋊Dic13—21no—
67C4⋊Dic13—21no—
68C4⋊Dic13—21no—
69C4⋊Dic13—21no—
70#6101—41no—
71#6101—41no—
72C4×Dic13—22no—
73C4×Dic13—41no—
74C4×Dic13SD1614yes—
75C2×#1055—22no—
76C2×#1055—41no—
77C2×#1055—42no—
78#1995—131no—
79#1843—131no—
80#1570—131no—
81#1570D1311yescharacteristic
82#1481—131no—
83#1481—131no—
84#1274—131no—
85C23×C13#12311yescharacteristic
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13C22⋊Q811yescharacteristic
89C2×C4×C13C22⋊Q811yescharacteristic
90C2×C4×C13C22⋊Q811yescharacteristic
91C2×C4×C13#12311yescharacteristic
92C2×C4×C13#12311yescharacteristic
93C2×C4×C13#12711yescharacteristic
94C2×C4×C13C2×SD1612yes—
95C2×C4×C13#13712yes—
96C2×Dic13—24no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—41no—
100C2×Dic13—41no—
101Dic26—42no—
102Dic26—42no—
103C8×C13—42no—
104C8×C13—81no—
105C8×C13—81no—
106#1055—42no—
107#1055—81no—
108#533—131no—
109#431—131no—
110#431C2×D1311yescharacteristic
111#423C2×D1311yescharacteristic
112C2×C4⋊C8—131no—
113C2×C4⋊C8—262no—
114C2×C4⋊C8C2×D1311yescharacteristic
115#376—131no—
116#339—262no—
117#334—22no—
118#334—262no—
119Q8⋊C8—262no—
120Q8⋊C8—262no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13#39911yescharacteristic
124C22×C13#48312yes—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13#47512yes—
130C4×C13#49211yescharacteristic
131C4×C13#49711yescharacteristic
132Dic13—44no—
133Dic13—81no—
134Dic13—81no—
135C2×M16—21no—
136C22×C8—21no—
137C22×C8—261no—
138C4⋊Q8—131no—
139C4⋊Q8—131no—
140#125—261no—
141C22⋊Q8—261no—
142C22⋊Q8—261no—
143C4×Q8—261no—
144C4×Q8—261no—
145#117—261no—
146C2×C42—132no—
147C2×C42C22×D1311yescharacteristic
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—21no—
151C4⋊C8—21no—
152C4⋊C8—21no—
153C4⋊C8—261no—
154C4⋊C8—261no—
155C4⋊C8—261no—
156C4⋊C8—524no—
157C22⋊C8—21no—
158C22⋊C8—261no—
159C4×C8—132no—
160C4×C8C22⋊D1312yes—
161#95—261no—
162#95—261no—
163C2×C13—22no—
164C2×C13#209611yescharacteristic
165C2×C13#209811yescharacteristic
166C2×C13#209811yescharacteristic
167C2×Q8—261no—
168C2×Q8—261no—
169C22×C4—262no—
170C22×C4#612711yescharacteristic
171C22×C4D4×D1311yescharacteristic
172C22×C4#613111yescharacteristic
173M16—42no—
174C2×C8—22no—
175C2×C8—42no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—262no—
179C2×C8—522no—
180C2×C8—521no—
181C4⋊C4—261no—
182C4⋊C4—261no—
183C4⋊C4—261no—
184C4⋊C4—261no—
185C4⋊C4—521no—
186C4⋊C4—521no—
187C22⋊C4—521no—
188C42—134no—
189C42—262no—
190C42—521no—
191C42#612711yescharacteristic
192C42D4×D1311yescharacteristic
193C42Q8×D1311yescharacteristic
194C42C2×C22⋊D1311yescharacteristic
195C13#1067011yescharacteristic, complemented, Sylow
196C23#8814811yescharacteristic
197Q8—522no—
198Q8—522no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—264no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4—521no—
205C2×C4—521no—
206C2×C4#8814811yescharacteristic
207C2×C4#8815011yescharacteristic
208C2×C4#8815011yescharacteristic
209C2×C4SD16×D1312yes—
210C2×C4#8816912yes—
211C2×C4#8818311yescharacteristic
212C2×C4#8819411yescharacteristic
213C2×C4#8820011yescharacteristic
214C8—42no—
215C8—81no—
216C8—81no—
217C8—522no—
218C8—1041no—
219C22—21no—
220C22—21no—
221C22#1171852312yes—
222C22#1171865311yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—524no—
228C4—1041no—
229C4—1041no—
230C4#1171851512yes—
231C4#1171882811yescharacteristic
232C4#1171883611yescharacteristic
233C2—22no—
234C2#1311637611yescharacteristic
235C2#1311638811yescharacteristic
236C2#1311639211yescharacteristic
subgroupG/H
centerC2×C4#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1570C2
socleC22×C13#399
prime radicalC23×C13#123
hypercenter#1570D13
hypocenterC13#10670
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
195. C13#10670semidirect

Maximal subgroups

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

subgroupindex
#131158162
#131149892
#131136082
#131132402
#131132382
#131126642
C13×#15702
#1067013