Finite Group Databasebeta

← #15765931

Subgroups — #15765931

Order 3328.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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#13115784C212yesmaximal
2#13115637C211yesmaximal, characteristic
3#13112719C211yesmaximal, characteristic
4#13112677C212yesmaximal
5C13×#2551C211yesmaximal, characteristic
6C2×C13×C4⋊Q8—22no—
7C2×#88123C2211yescharacteristic
8C13×#395—22no—
9C13×#389—22no—
10C13×#384C2211yescharacteristic
11C4×C13×C4⋊C4C2212yes—
12C2×#88050—22no—
13C2×C4⋊#1055C2212yes—
14C2×C4×#1055C2211yescharacteristic
15#11718121—22no—
16#11718121—22no—
17C22×Q8×C13—22no—
18C22×Dic26—21no—
19C13×C4⋊Q8—44no—
20C13×C4⋊Q8—44no—
21C2×C13×C4⋊C4—24no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4D412yes—
24C2×C13×C4⋊C4D412yes—
25C2×C13×C4⋊C4D412yes—
26C2×C42×C13—22no—
27C2×C42×C13C2311yescharacteristic
28C2×C4⋊Dic13—22no—
29C22×#1055—21no—
30C22×#1055—22no—
31#88123—22no—
32#88123—21no—
33#88123Q812yescomplemented
34C13×#95—22no—
35C13×#95—22no—
36#88050—44no—
37C4⋊#1055—22no—
38C4⋊#1055—22no—
39C4×#1055—22no—
40#10349—131nomaximal, Sylow
41C2×Q8×C13—48no—
42C2×Q8×C13—82no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13C2×D411yescharacteristic
47C22×C4×C13C2×D412yes—
48C22×Dic13—41no—
49C2×Dic26—22no—
50C2×Dic26—42no—
51C2×Dic26—42no—
52C2×Dic26—41no—
53C13×C4⋊C4—22no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—48no—
57C13×C4⋊C4—42no—
58C13×C4⋊C4—42no—
59C13×C4⋊C4SD1614yes—
60C13×C4⋊C4Q1614yes—
61C42×C13—42no—
62C42×C13—42no—
63C42×C13C2×Q811yescharacteristic
64C42×C13#4112yes—
65C42×C13#4111yescharacteristic
66C4⋊Dic13—24no—
67C4⋊Dic13—42no—
68C2×#1055—22no—
69C2×#1055—41no—
70C2×#1055—41no—
71C2×#1055—42no—
72C2×#1055—42no—
73C2×#1055—42no—
74#2551D1311yescharacteristic
75#1987—132no—
76#1956—131no—
77#1296—131no—
78#1279—132no—
79C23×C13#12011yescharacteristic
80Q8×C13—88no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—24no—
84C2×C4×C13—24no—
85C2×C4×C13—42no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—44no—
90C2×C4×C13—42no—
91C2×C4×C13C22⋊Q811yescharacteristic
92C2×C4×C13C22⋊Q812yes—
93C2×C4×C13#12411yescharacteristic
94C2×C4×C13#12412yes—
95C2×C4×C13C2×SD1612yes—
96C2×C4×C13C2×Q1612yes—
97C2×C4×C13AGL(1,ℤ/8)12yes—
98C2×C4×C13#13712yes—
99C2×Dic13—42no—
100C2×Dic13—81no—
101C2×Dic13—81no—
102Dic26—44no—
103Dic26—82no—
104#1055—42no—
105#1055—82no—
106C2×C4⋊Q8—22no—
107C2×C4⋊Q8—131no—
108C2×C4⋊C8—132no—
109C2×#103—262no—
110C2×C4×C8—131no—
111#395—22no—
112#389—22no—
113#384C2×D1311yescharacteristic
114C4×C4⋊C4C2×D1312yes—
115#340—262no—
116#340—262no—
117C22×C13#39311yescharacteristic
118C22×C13#45012yes—
119C22×C13#45112yes—
120C22×C13#45311yescharacteristic
121C22×C13#45411yescharacteristic
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—44no—
125C4×C13—44no—
126C4×C13—82no—
127C4×C13#47512yes—
128C4×C13#47712yes—
129C4×C13#48712yes—
130C4×C13#48912yes—
131Dic13—82no—
132C22×Q8—22no—
133C22×Q8—261no—
134C22×C8—261no—
135C22×C8—262no—
136C4⋊Q8—44no—
137C4⋊Q8—44no—
138C4⋊Q8—132no—
139C4⋊Q8—262no—
140C4⋊Q8—261no—
141C2×C4⋊C4—24no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—262no—
144C2×C4⋊C4C22⋊D1312yes—
145C2×C4⋊C4C22⋊D1312yes—
146C2×C4⋊C4C22⋊D1312yes—
147C2×C42—22no—
148C2×C42C22×D1311yescharacteristic
149C4⋊C8—262no—
150C4⋊C8—262no—
151#103—524no—
152C4×C8—262no—
153#95—22no—
154#95—22no—
155C2×C13#162911yescharacteristic
156C2×C13#163311yescharacteristic
157C2×C13#163712yes—
158C2×C13#202412yes—
159C2×C13#202711yescharacteristic
160C2×Q8—48no—
161C2×Q8—82no—
162C2×Q8—262no—
163C2×Q8—522no—
164C2×Q8—522no—
165C2×Q8—521no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—521no—
170C22×C4C2×C22⋊D1311yescharacteristic
171C22×C4C2×C22⋊D1312yes—
172C2×C8—262no—
173C2×C8—521no—
174C2×C8—521no—
175C2×C8—522no—
176C2×C8—522no—
177C2×C8—522no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—48no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—264no—
185C4⋊C4—522no—
186C4⋊C4#610514yes—
187C4⋊C4#610714yes—
188C42—42no—
189C42—42no—
190C42Q8×D1311yescharacteristic
191C42#613112yes—
192C42#613111yescharacteristic
193C13#1034911yescharacteristic, complemented, Sylow
194C23#8820711yescharacteristic
195Q8—88no—
196Q8—524no—
197Q8—1042no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—24no—
201C2×C4—24no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—522no—
209C2×C4—1041no—
210C2×C4—1041no—
211C2×C4#8818612yes—
212C2×C4C2×#610512yes—
213C2×C4#8819612yes—
214C2×C4C2×#610712yes—
215C2×C4#8820011yescharacteristic
216C2×C4#8820012yes—
217C2×C4#8820111yescharacteristic
218C2×C4#8820112yes—
219C8—522no—
220C8—1042no—
221C22#1171887912yes—
222C22#1171888912yes—
223C22#1171889211yescharacteristic
224C22#1171890211yescharacteristic
225C22#1171890611yescharacteristic
226C4—21no—
227C4—21no—
228C4—44no—
229C4—44no—
230C4—82no—
231C4—1042no—
232C4#1171875012yes—
233C4#1171875212yes—
234C4#1171875412yes—
235C4#1171875512yes—
236C2#1311395211yescharacteristic
237C2#1311397611yescharacteristic
238C2#1311400112yes—
239C2#1311597412yes—
240C2#1311598911yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2551C2
socle, prime radicalC23×C13#120
hypercenter#2551D13
hypocenterC13#10349
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2551

Complements

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

NH ≅ G/Ntype
33. #88123Q8semidirect
193. C13#10349semidirect

Maximal subgroups

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

subgroupindex
#131157842
#131156372
#131127192
#131126772
C13×#25512
#1034913