Finite Group Databasebeta

← #15752220

Subgroups — #15752220

Order 3328.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#13121868C211yesmaximal, characteristic
2#13116400C212yesmaximal
3#13116374C211yesmaximal, characteristic
4#13112658C212yesmaximal
5C13×#1272C211yesmaximal, characteristic
6C2×#88198—21no—
7C13×#391C2211yescharacteristic
8C2×#88075—21no—
9#11718644—21no—
10C2×#88047—21no—
11#11718596C2211yescharacteristic
12#11718589C2212yes—
13#11718317—22no—
14#11718314—22no—
15C13×#336C2212yes—
16#11718143—22no—
17#11718143—22no—
18#11718116C2211yescharacteristic
19C22×Q8×C13D411yescharacteristic
20C22×Dic26—21no—
21C22×C8×C13—22no—
22C2×C13×C4⋊C4D411yescharacteristic
23C2×C42×C13C2311yescharacteristic
24#88198—42no—
25#88198—42no—
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13—22no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13D412yes—
30C2×C4⋊Dic13D412yes—
31C2×#6101—22no—
32C2×#6101—22no—
33C2×C4×Dic13—21no—
34C22×#1055—21no—
35C13×#95—22no—
36#88075—42no—
37#88071—21no—
38#88071—22no—
39#88071—22no—
40#88047—42no—
41#7829—131nomaximal, Sylow
42C2×Q8×C13—21no—
43C2×Q8×C13—41no—
44C2×Q8×C13—41no—
45C2×Q8×C13SD1612yes—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C2×D411yescharacteristic
49C22×C4×C13C2×D412yes—
50C22×Dic13—22no—
51C22×Dic13—22no—
52C22×Dic13—41no—
53C2×Dic26—42no—
54C2×Dic26—81no—
55C2×Dic26—81no—
56C2×C8×C13—42no—
57C2×C8×C13—42no—
58C2×C8×C13—42no—
59C13×C4⋊C4—41no—
60C42×C13—41no—
61C4⋊Dic13—22no—
62C4⋊Dic13—42no—
63C4⋊Dic13—41no—
64C4⋊Dic13—44no—
65C4⋊Dic13—41no—
66C4⋊Dic13—81no—
67C4⋊Dic13Q1614yes—
68#6101—44no—
69#6101—42no—
70#6101—42no—
71C4×Dic13—42no—
72C2×#1055—22no—
73C2×#1055—41no—
74C2×#1055—41no—
75#2734—131no—
76#2100—132no—
77#2095—131no—
78#1272D1311yescharacteristic
79#1271—132no—
80C23×C13#12011yescharacteristic
81Q8×C13—42no—
82Q8×C13—81no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—42no—
92C2×C4×C13C2×SD1611yescharacteristic
93C2×C4×C13C2×Q1612yes—
94C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C13#13712yes—
96C2×Dic13—24no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—42no—
102C2×Dic13—81no—
103C2×Dic13—82no—
104Dic26—84no—
105C8×C13—82no—
106#1055—42no—
107C2×C4⋊Q8—261no—
108C2×#107—261no—
109C2×#103—261no—
110#398—261no—
111#395—262no—
112#391C2×D1311yescharacteristic
113#389—132no—
114#387—262no—
115#384—131no—
116#340—262no—
117#340—262no—
118#336—131no—
119#336C2×D1312yes—
120C22×C13#45011yescharacteristic
121C22×C13#45112yes—
122C22×C13#45311yescharacteristic
123C22×C13#45412yes—
124C22×C13#45811yescharacteristic
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—22no—
128C4×C13—22no—
129C4×C13—42no—
130C4×C13—81no—
131Dic13—44no—
132Dic13—82no—
133Dic13—161no—
134C22×Q8—261no—
135C22×Q8D5211yescharacteristic
136C22×C8—22no—
137C22×C8—261no—
138C4⋊Q8—522no—
139C4⋊Q8—522no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4—132no—
142C2×C4⋊C4—262no—
143C2×C4⋊C4—262no—
144C2×C4⋊C4—261no—
145C2×C4⋊C4—262no—
146C2×C4⋊C4—261no—
147C2×C4⋊C4D5211yescharacteristic
148C2×C42—261no—
149C2×C42C22×D1311yescharacteristic
150#107—522no—
151#103—522no—
152#95—22no—
153#95—261no—
154#95—262no—
155#95—262no—
156C2×C13#161311yescharacteristic
157C2×C13#161712yes—
158C2×C13#163311yescharacteristic
159C2×C13#163712yes—
160C2×C13#165711yescharacteristic
161C2×Q8—21no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—522no—
165C2×Q8—1041no—
166C2×Q8—1041no—
167C2×Q8#609512yes—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—262no—
171C22×C4—262no—
172C22×C4—521no—
173C22×C4C2×D5211yescharacteristic
174C22×C4D4×D1312yes—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—262no—
179C2×C8—521no—
180C2×C8—521no—
181C4⋊C4—41no—
182C4⋊C4—134no—
183C4⋊C4—262no—
184C4⋊C4—522no—
185C4⋊C4—524no—
186C4⋊C4—521no—
187C4⋊C4—521no—
188C4⋊C4—524no—
189C4⋊C4—522no—
190C4⋊C4—522no—
191C4⋊C4—1041no—
192C42—41no—
193C42—522no—
194C13#782911yescharacteristic, complemented, Sylow
195C23#8813611yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—1044no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—264no—
209C2×C4—522no—
210C2×C4—522no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4—522no—
214C2×C4—1041no—
215C2×C4—1042no—
216C2×C4C2×#609511yescharacteristic
217C2×C4#8816211yescharacteristic
218C2×C4#8816912yes—
219C2×C4Q16×D1312yes—
220C8—82no—
221C8—522no—
222C22#1171839211yescharacteristic
223C22#1171840311yescharacteristic
224C22#1171840811yescharacteristic
225C22#1171846912yes—
226C22#1171848812yes—
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—81no—
233C4—524no—
234C4—1042no—
235C4—2081no—
236C2#1311385811yescharacteristic
237C2#1311387912yes—
238C2#1311397711yescharacteristic
239C2#1311400312yes—
240C2#1311413511yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socle, prime radicalC23×C13#120
hypercenter#1272D13
hypocenterC13#7829
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
194. C13#7829semidirect

Maximal subgroups

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

subgroupindex
#131218682
#131164002
#131163742
#131126582
C13×#12722
#782913