Finite Group Databasebeta

← #15767951

Subgroups — #15767951

Order 3328.

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

normal subgroups only

This group has 316 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#13115818C211yesmaximal, characteristic
2#13114989C211yesmaximal, characteristic
3#13113607C211yesmaximal, characteristic
4#13113606C211yesmaximal, characteristic
5#13113239C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1481C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×#88054—22no—
12#11718593C2211yescharacteristic
13#11718586C2211yescharacteristic
14#11718585C2211yescharacteristic
15C2×C4⋊#1055C2211yescharacteristic
16C13×Q8⋊C8—22no—
17Q8⋊#1055—22no—
18#11718124—22no—
19#11718072—22no—
20#11718049—22no—
21C22×C8×C13—21no—
22C13×C4⋊Q8Q811yescharacteristic
23C13×C4⋊Q8Q811yescharacteristic
24C13×#125—21no—
25C13×C22⋊Q8—21no—
26C13×C22⋊Q8—21no—
27C4×Q8×C13—21no—
28C4×Q8×C13—21no—
29C13×#117—21no—
30C2×C42×C13C2311yescharacteristic
31C2×C4×Dic13D412yes—
32C2×#6099—21no—
33C22×#1055—21no—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C4⋊C8—21no—
37C13×C22⋊C8—21no—
38C4×C8×C13D412yes—
39#88071—21no—
40#88071—21no—
41C22⋊#1055—21no—
42#88054—44no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48C4×#1055D412yes—
49#10670—131nomaximal, Sylow
50C2×Q8×C13—21no—
51C2×Q8×C13—21no—
52C22×C4×C13C2×D411yescharacteristic
53C22×C4×C13#4111yescharacteristic
54C22×C4×C13#4111yescharacteristic
55C22×Dic13—22no—
56C2×C8×C13—22no—
57C2×C8×C13—41no—
58C2×C8×C13—42no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—21no—
61C13×C4⋊C4—21no—
62C13×C4⋊C4—21no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C22⋊C4—41no—
66C42×C13—41no—
67C42×C13C2×D411yescharacteristic
68C42×C13C2×D411yescharacteristic
69C42×C13C2×Q811yescharacteristic
70C42×C13#4111yescharacteristic
71C4×Dic13—22no—
72C4×Dic13SD1614yes—
73#6099—42no—
74C2×#1055—22no—
75C2×#1055—41no—
76C2×#1055—41no—
77C2×#1055—42no—
78#1995—131no—
79#1843—131no—
80#1570—131no—
81#1570—131no—
82#1481—131no—
83#1481D1311yescharacteristic
84#1274—131no—
85C23×C13#12311yescharacteristic
86Q8×C13—42no—
87Q8×C13—42no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13C22⋊Q811yescharacteristic
93C2×C4×C13C22⋊Q811yescharacteristic
94C2×C4×C13C22⋊Q811yescharacteristic
95C2×C4×C13#12311yescharacteristic
96C2×C4×C13#12311yescharacteristic
97C2×C4×C13#12711yescharacteristic
98C2×C4×C13C2×SD1612yes—
99C2×C4×C13#13712yes—
100C2×Dic13—24no—
101C2×Dic13—42no—
102C2×Dic13—42no—
103C8×C13—42no—
104C8×C13—81no—
105#1055—42no—
106#1055—81no—
107#1055—81no—
108#533C2×D1311yescharacteristic
109#431—131no—
110#431C2×D1311yescharacteristic
111#423—131no—
112C2×C4⋊C8—131no—
113C2×C4⋊C8—262no—
114C2×C4⋊C8C2×D1311yescharacteristic
115#376—131no—
116#339—262no—
117#334—262no—
118#334—262no—
119Q8⋊C8—22no—
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—81no—
130C4×C13—81no—
131C4×C13#47512yes—
132C4×C13#49211yescharacteristic
133C4×C13#49711yescharacteristic
134Dic13—44no—
135C2×M16—261no—
136C22×C8—21no—
137C22×C8—261no—
138C4⋊Q8Dic2611yescharacteristic
139C4⋊Q8Dic2611yescharacteristic
140#125—21no—
141C22⋊Q8—21no—
142C22⋊Q8—21no—
143C4×Q8—21no—
144C4×Q8—21no—
145#117—21no—
146C2×C42—132no—
147C2×C42C22×D1311yescharacteristic
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—21no—
151C4⋊C8—261no—
152C4⋊C8—261no—
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—21no—
168C2×Q8—21no—
169C22×C4—262no—
170C22×C4#612711yescharacteristic
171C22×C4D4×D1311yescharacteristic
172C22×C4#612911yescharacteristic
173M16—522no—
174C2×C8—22no—
175C2×C8—42no—
176C2×C8—41no—
177C2×C8—262no—
178C2×C8—522no—
179C2×C8—521no—
180C2×C8—521no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C22⋊C4—41no—
188C42—41no—
189C42—134no—
190C42—262no—
191C42C2×Dic2611yescharacteristic
192C42D4×D1311yescharacteristic
193C42#612911yescharacteristic
194C42C2×C22⋊D1311yescharacteristic
195C13#1067011yescharacteristic, complemented, Sylow
196C23#8813711yescharacteristic
197Q8—42no—
198Q8—42no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—264no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4#8813211yescharacteristic
207C2×C4#8813211yescharacteristic
208C2×C4#8813711yescharacteristic
209C2×C4SD16×D1312yes—
210C2×C4#8817212yes—
211C2×C4#8817811yescharacteristic
212C2×C4#8818911yescharacteristic
213C2×C4#8819411yescharacteristic
214C8—42no—
215C8—81no—
216C8—522no—
217C8—1041no—
218C8—1041no—
219C22—21no—
220C22—21no—
221C22#1171846612yes—
222C22#1171861011yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—81no—
228C4—81no—
229C4—524no—
230C4#1171845212yes—
231C4#1171883611yescharacteristic
232C4#1171885111yescharacteristic
233C2—22no—
234C2#1311637711yescharacteristic
235C2#1311638911yescharacteristic
236C2#1311639111yescharacteristic
subgroupG/H
centerC2×C4#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1481C2
socleC22×C13#399
prime radicalC23×C13#123
hypercenter#1481D13
hypocenterC13#10670
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

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
#131158182
#131149892
#131136072
#131136062
#131132392
#131126642
C13×#14812
#1067013