Finite Group Databasebeta

← #15775766

Subgroups — #15775766

Order 3328.

336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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#13122824C211yesmaximal, characteristic
2#13113878C212yesmaximal
3#13112862C212yesmaximal
4#13112770C211yesmaximal, characteristic
5C13×#2028C211yesmaximal, characteristic
6C13×#544C2211yescharacteristic
7C13×#419—21no—
8C13×#391C2211yescharacteristic
9#11718891—21no—
10#11718705—22no—
11#11718647C2212yes—
12#11718589—21no—
13#11718322—22no—
14#11718316—22no—
15C13×#343C2211yescharacteristic
16C13×#339—21no—
17#11718130—22no—
18#11718120C2212yes—
19C22×Q8×C13D411yescharacteristic
20C2×C13×M16—21no—
21C13×C4⋊Q8—41no—
22C13×#125—41no—
23C13×C22⋊Q8—22no—
24C13×#117—21no—
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C42×C13D411yescharacteristic
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13D412yes—
31C2×#6101—22no—
32C2×C4×Dic13—21no—
33C13×#103—41no—
34C13×#103—41no—
35C13×#95—22no—
36#88075—42no—
37#88071—22no—
38#88071—22no—
39#88071—22no—
40#88071D412yes—
41C22⋊#1055—22no—
42#88047—42no—
43#12225—131nomaximal, Sylow
44C2×Q8×C13—21no—
45C2×Q8×C13—22no—
46C2×Q8×C13—41no—
47C2×Q8×C13—41no—
48C2×Q8×C13Q1612yes—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13C2×D412yes—
52C22×C4×C13C2×D411yescharacteristic
53C22×Dic13—22no—
54C22×Dic13—22no—
55C13×M16—41no—
56C13×M16—41no—
57C2×C8×C13—41no—
58C13×C4⋊C4—21no—
59C13×C4⋊C4—21no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—42no—
63C13×C22⋊C4—41no—
64C42×C13—41no—
65C42×C13—41no—
66C4⋊Dic13—42no—
67C4⋊Dic13—42no—
68C4⋊Dic13—81no—
69C4⋊Dic13—81no—
70#6101—44no—
71C4×Dic13—81no—
72C2×#1055—42no—
73#2809—131no—
74#2028D1311yescharacteristic
75#1617—132no—
76#1353—132no—
77#1319—131no—
78C23×C13#12011yescharacteristic
79Q8×C13—42no—
80Q8×C13—81no—
81Q8×C13—82no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13C2×Q1611yescharacteristic
95C2×C4×C13#13711yescharacteristic
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C8×C13—81no—
103#1055—82no—
104#544C2×D1311yescharacteristic
105#484—262no—
106#419—21no—
107#400—132no—
108#398—262no—
109#391—261no—
110#391C2×D1311yescharacteristic
111#389—261no—
112#387—262no—
113#343C2×D1311yescharacteristic
114#339—21no—
115#328—262no—
116#324—132no—
117C22×C13—21no—
118C22×C13—21no—
119C22×C13#45111yescharacteristic
120C22×C13#45511yescharacteristic
121C22×C13B(4,𝔽2)11yescharacteristic
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—42no—
125C4×C13—42no—
126C4×C13—42no—
127C4×C13—81no—
128C4×C13—81no—
129Dic13—82no—
130Dic13—82no—
131C22×Q8C22⋊D1311yescharacteristic
132C2×M16—21no—
133C4⋊Q8—41no—
134#125—41no—
135C22⋊Q8—22no—
136#117—21no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—262no—
139C2×C4⋊C4—261no—
140C2×C4⋊C4—261no—
141C2×C4⋊C4—261no—
142C2×C4⋊C4C22×D1311yescharacteristic
143C2×C42—261no—
144C2×C42C22⋊D1311yescharacteristic
145#107—522no—
146#103—41no—
147#103—41no—
148#103—522no—
149C22⋊C8—262no—
150#95—22no—
151#95—132no—
152#95—262no—
153#95—262no—
154#95—262no—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#160211yescharacteristic
158C2×C13#220111yescharacteristic
159C2×C13#220411yescharacteristic
160C2×Q8—21no—
161C2×Q8—22no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8#610712yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—262no—
168C22×C4—262no—
169C22×C4D4×D1312yes—
170C22×C4C2×C22⋊D1311yescharacteristic
171M16—41no—
172M16—41no—
173C2×C8—41no—
174C2×C8—522no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—22no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C4⋊C4—522no—
181C4⋊C4—524no—
182C4⋊C4—522no—
183C4⋊C4—1041no—
184C4⋊C4—1041no—
185C22⋊C4—41no—
186C42—41no—
187C42—41no—
188C42—1041no—
189C13#1222511yescharacteristic, complemented, Sylow
190C23#8819111yescharacteristic
191Q8—42no—
192Q8—81no—
193Q8—82no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4—522no—
209C2×C4—522no—
210C2×C4—522no—
211C2×C4—522no—
212C2×C4C2×#610711yescharacteristic
213C2×C4#8820511yescharacteristic
214C8—81no—
215C8—1042no—
216C22—21no—
217C22—21no—
218C22#1171869311yescharacteristic
219C22#1171871111yescharacteristic
220C22#1171872211yescharacteristic
221C4—21no—
222C4—21no—
223C4—42no—
224C4—42no—
225C4—42no—
226C4—81no—
227C4—81no—
228C4—1042no—
229C4—1042no—
230C2—21no—
231C2—21no—
232C2#1311379211yescharacteristic
233C2#1311684811yescharacteristic
234C2#1311686111yescharacteristic
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2028C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2028D13
hypocenterC13#12225
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2028

Complements

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

NH ≅ G/Ntype
189. C13#12225semidirect

Maximal subgroups

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

subgroupindex
#131228242
#131138782
#131128622
#131127702
C13×#20282
#1222513