Finite Group Databasebeta

← #15767946

Subgroups — #15767946

Order 3328.

296 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 91 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#13114955C211yesmaximal, characteristic
3#13113611C211yesmaximal, characteristic
4#13113606C211yesmaximal, characteristic
5#13113239C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1481C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11#11718593C2211yescharacteristic
12#11718586C2211yescharacteristic
13#11718585C2211yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15C13×Q8⋊C8—22no—
16#11718142—22no—
17Q8⋊#1055—22no—
18#11718124—22no—
19#11718072—22no—
20#11718050—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—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46C4⋊#1055—21no—
47C4×#1055D412yes—
48#10669—131nomaximal, Sylow
49C2×Q8×C13—21no—
50C2×Q8×C13—21no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13#4111yescharacteristic
53C22×C4×C13#4111yescharacteristic
54C22×Dic13—22no—
55C2×C8×C13—22no—
56C2×C8×C13—41no—
57C2×C8×C13—42no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—21no—
61C13×C4⋊C4—21no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C22⋊C4—41no—
65C42×C13—41no—
66C42×C13C2×D411yescharacteristic
67C42×C13C2×D411yescharacteristic
68C42×C13C2×Q811yescharacteristic
69C42×C13#4111yescharacteristic
70C4×Dic13—22no—
71C4×Dic13—22no—
72#6099—42no—
73C2×#1055—22no—
74C2×#1055—41no—
75C2×#1055—41no—
76C2×#1055—42no—
77#1995—131no—
78#1832—131no—
79#1571—131no—
80#1570—131no—
81#1481—131no—
82#1481D1311yescharacteristic
83#1274—131no—
84C23×C13#12311yescharacteristic
85Q8×C13—42no—
86Q8×C13—42no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13C22⋊Q811yescharacteristic
92C2×C4×C13C22⋊Q811yescharacteristic
93C2×C4×C13C22⋊Q811yescharacteristic
94C2×C4×C13#12311yescharacteristic
95C2×C4×C13#12311yescharacteristic
96C2×C4×C13#12711yescharacteristic
97C2×C4×C13#13512yes—
98C2×C4×C13#13712yes—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C8×C13—42no—
103C8×C13—81no—
104#1055—42no—
105#1055—81no—
106#1055—81no—
107#533C2×D1311yescharacteristic
108#431—131no—
109#431C2×D1311yescharacteristic
110#423—131no—
111C2×C4⋊C8—131no—
112C2×C4⋊C8C2×D1311yescharacteristic
113#376—131no—
114#339—262no—
115#336—262no—
116#335—262no—
117#334—262no—
118Q8⋊C8—22no—
119Q8⋊C8—262no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13#39911yescharacteristic
123C22×C13#48512yes—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13—81no—
129C4×C13—81no—
130C4×C13#47912yes—
131C4×C13#49511yescharacteristic
132C4×C13#49711yescharacteristic
133Dic13—82no—
134C2×M16—261no—
135C22×C8—21no—
136C22×C8—261no—
137C4⋊Q8Dic2611yescharacteristic
138C4⋊Q8Dic2611yescharacteristic
139#125—21no—
140C22⋊Q8—21no—
141C22⋊Q8—21no—
142C4×Q8—21no—
143C4×Q8—21no—
144#117—21no—
145C2×C42—132no—
146C2×C42C22×D1311yescharacteristic
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—261no—
151C4⋊C8—261no—
152C4⋊C8—261no—
153C4⋊C8—261no—
154C4⋊C8—261no—
155C22⋊C8—21no—
156C22⋊C8—261no—
157C4×C8—132no—
158C4×C8C22⋊D1312yes—
159#95—261no—
160#95—261no—
161C2×C13—22no—
162C2×C13#209711yescharacteristic
163C2×C13#209811yescharacteristic
164C2×C13#209811yescharacteristic
165C2×Q8—21no—
166C2×Q8—21no—
167C22×C4—262no—
168C22×C4#612711yescharacteristic
169C22×C4D4×D1311yescharacteristic
170C22×C4#612911yescharacteristic
171M16—522no—
172C2×C8—22no—
173C2×C8—42no—
174C2×C8—41no—
175C2×C8—262no—
176C2×C8—522no—
177C2×C8—521no—
178C2×C8—521no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C22⋊C4—41no—
186C42—41no—
187C42—262no—
188C42—262no—
189C42C2×Dic2611yescharacteristic
190C42D4×D1311yescharacteristic
191C42#612911yescharacteristic
192C42C2×C22⋊D1311yescharacteristic
193C13#1066911yescharacteristic, complemented, Sylow
194C23#8813711yescharacteristic
195Q8—42no—
196Q8—42no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—522no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4#8813211yescharacteristic
205C2×C4#8813211yescharacteristic
206C2×C4#8813711yescharacteristic
207C2×C4#8816912yes—
208C2×C4#8817312yes—
209C2×C4#8817811yescharacteristic
210C2×C4#8818911yescharacteristic
211C2×C4#8819411yescharacteristic
212C8—42no—
213C8—81no—
214C8—522no—
215C8—1041no—
216C8—1041no—
217C22—21no—
218C22—21no—
219C22#1171847512yes—
220C22#1171861011yescharacteristic
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—81no—
226C4—81no—
227C4—1042no—
228C4#1171845712yes—
229C4#1171882811yescharacteristic
230C4#1171885211yescharacteristic
231C2—22no—
232C2#1311638211yescharacteristic
233C2#1311638911yescharacteristic
234C2#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#10669
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
193. C13#10669semidirect

Maximal subgroups

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

subgroupindex
#131158182
#131149552
#131136112
#131136062
#131132392
#131126642
C13×#14812
#1066913