Finite Group Databasebeta

← #15767947

Subgroups — #15767947

Order 3328.

296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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#13113610C211yesmaximal, characteristic
3#13113606C211yesmaximal, characteristic
4#13113238C211yesmaximal, characteristic
5#13113238C211yesmaximal, characteristic
6#13112665C211yesmaximal, characteristic
7C13×#1832C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#376C2211yescharacteristic
12#11718586C2211yescharacteristic
13#11718586C2211yescharacteristic
14#11718585C2211yescharacteristic
15C13×#336—22no—
16#11718115—22no—
17#11718076—22no—
18#11718076—22no—
19#11718072—22no—
20#11718071—22no—
21C22×C8×C13—21no—
22C22×C8×C13—21no—
23C2×C42×C13D412yes—
24C2×C42×C13C2311yescharacteristic
25#88180—21no—
26#88178—21no—
27#88178—21no—
28C2×#6099—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×#95—21no—
39C13×#95—21no—
40C22⋊#1055—21no—
41C22⋊#1055—21no—
42C4⋊#1055—21no—
43C4⋊#1055—21no—
44C4⋊#1055—21no—
45C4⋊#1055—21no—
46C4×#1055D412yes—
47C4×#1055D412yes—
48#10669—131nomaximal, Sylow
49C22×C4×C13—22no—
50C22×C4×C13C2×D411yescharacteristic
51C22×C4×C13#4111yescharacteristic
52C22×C4×C13#4111yescharacteristic
53C2×Dic26—21no—
54C2×Dic26—21no—
55C2×C8×C13—41no—
56C2×C8×C13—41no—
57C2×C8×C13—42no—
58C2×C8×C13—42no—
59C42×C13—22no—
60C42×C13—22no—
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—41no—
73#6099—42no—
74C2×#1055—22no—
75C2×#1055—22no—
76C2×#1055—41no—
77#1995—131no—
78#1832D1311yescharacteristic
79#1571—131no—
80#1570—131no—
81#1481—131no—
82#1481—131no—
83#1274—131no—
84C23×C13#12311yescharacteristic
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13C22⋊Q811yescharacteristic
91C2×C4×C13C22⋊Q811yescharacteristic
92C2×C4×C13C22⋊Q811yescharacteristic
93C2×C4×C13#12311yescharacteristic
94C2×C4×C13#12311yescharacteristic
95C2×C4×C13#12711yescharacteristic
96C2×C4×C13#13512yes—
97C2×C4×C13#13712yes—
98C2×Dic13—41no—
99C2×Dic13—41no—
100Dic26—42no—
101Dic26—42no—
102C8×C13—81no—
103C8×C13—81no—
104#1055—42no—
105#1055—42no—
106#1055—81no—
107#533—131no—
108#431—131no—
109#431—131no—
110#423—131no—
111C2×C4⋊C8C2×D1311yescharacteristic
112C2×C4⋊C8C2×D1311yescharacteristic
113#376C2×D1311yescharacteristic
114#339—262no—
115#336—22no—
116#335—262no—
117#334—262no—
118Q8⋊C8—262no—
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—82no—
129C4×C13#47912yes—
130C4×C13#49511yescharacteristic
131C4×C13#49711yescharacteristic
132Dic13—81no—
133Dic13—81no—
134C2×M16—261no—
135C22×C8—21no—
136C22×C8—21no—
137C4⋊Q8—131no—
138C4⋊Q8—131no—
139#125—261no—
140C22⋊Q8—261no—
141C22⋊Q8—261no—
142C4×Q8—261no—
143C4×Q8—261no—
144#117—261no—
145C2×C42C22⋊D1312yes—
146C2×C42C22×D1311yescharacteristic
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—21no—
151C4⋊C8—261no—
152C4⋊C8—261no—
153C4⋊C8—261no—
154C4⋊C8—261no—
155C22⋊C8—261no—
156C22⋊C8—261no—
157C4×C8—132no—
158C4×C8—132no—
159#95—21no—
160#95—21no—
161C2×C13—22no—
162C2×C13#209711yescharacteristic
163C2×C13#209811yescharacteristic
164C2×C13#209811yescharacteristic
165C2×Q8—261no—
166C2×Q8—261no—
167C22×C4—22no—
168C22×C4#612711yescharacteristic
169C22×C4#612711yescharacteristic
170C22×C4C2×C22⋊D1311yescharacteristic
171M16—522no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—262no—
177C2×C8—262no—
178C2×C8—521no—
179C4⋊C4—261no—
180C4⋊C4—261no—
181C4⋊C4—261no—
182C4⋊C4—261no—
183C4⋊C4—521no—
184C4⋊C4—521no—
185C22⋊C4—521no—
186C42—22no—
187C42—22no—
188C42—521no—
189C42D4×D1311yescharacteristic
190C42D4×D1311yescharacteristic
191C42Q8×D1311yescharacteristic
192C42#613111yescharacteristic
193C13#1066911yescharacteristic, complemented, Sylow
194C23#8818311yescharacteristic
195Q8—522no—
196Q8—522no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—521no—
203C2×C4—521no—
204C2×C4#8814811yescharacteristic
205C2×C4#8814811yescharacteristic
206C2×C4#8815011yescharacteristic
207C2×C4#8815011yescharacteristic
208C2×C4#8819411yescharacteristic
209C2×C4#8820011yescharacteristic
210C2×C4#8820412yes—
211C2×C4#8820512yes—
212C8—81no—
213C8—81no—
214C8—522no—
215C8—522no—
216C8—1041no—
217C22—21no—
218C22—21no—
219C22#1171865311yescharacteristic
220C22#1171865712yes—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—82no—
226C4—1041no—
227C4—1041no—
228C4#1171872011yescharacteristic
229C4#1171872111yescharacteristic
230C4#1171872412yes—
231C2—22no—
232C2#1311638711yescharacteristic
233C2#1311639211yescharacteristic
234C2#1311639211yescharacteristic
subgroupG/H
centerC2×C4#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1832C2
socleC22×C13#399
prime radicalC23×C13#123
hypercenter#1832D13
hypocenterC13#10669
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1832

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
#131158172
#131136102
#131136062
#131132382
#131126652
C13×#18322
#1066913