Finite Group Databasebeta

← #15765273

Subgroups — #15765273

Order 3328.

560 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#11718682C212yesmaximal
2#13115637C211yesmaximal, characteristic
3C2×Q8⋊#1055C212yesmaximal
4#13112719C211yesmaximal, characteristic
5C13×#2582C211yesmaximal, characteristic
6C2×C4×Q8×C13C2212yes—
7C2×#88123C2211yescharacteristic
8C13×#398—22no—
9C13×#391—22no—
10C13×#389—22no—
11C13×#384C2211yescharacteristic
12C2×#88075—22no—
13#11718682—24no—
14#11718682—24no—
15C2×#88050—22no—
16C2×#88047—22no—
17C2×C4⋊#1055C2212yes—
18C2×C4×#1055C2211yescharacteristic
19Q8⋊#1055—24no—
20C22×Q8×C13D412yes—
21C22×Dic26—21no—
22C4×Q8×C13—22no—
23C4×Q8×C13—22no—
24C4×Q8×C13—22no—
25C4×Q8×C13—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4D412yes—
31C2×C42×C13—22no—
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—22no—
34C22×#1055—21no—
35C22×#1055—22no—
36#88123—22no—
37#88123—21no—
38#88123D412yes—
39C13×#95—24no—
40C13×#95—22no—
41#88075—28no—
42#88050—44no—
43#88047—28no—
44C4⋊#1055—22no—
45C4⋊#1055D414yes—
46C4×#1055—22no—
47#10237—131nomaximal, Sylow
48C2×Q8×C13—22no—
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—22no—
52C2×Q8×C13—22no—
53C2×Q8×C13Q1614yes—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D412yes—
59C22×Dic13—41no—
60C2×Dic26—22no—
61C2×Dic26—42no—
62C2×Dic26—42no—
63C2×Dic26—41no—
64C13×C4⋊C4—22no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—82no—
72C42×C13—42no—
73C42×C13—42no—
74C42×C13C2×D411yescharacteristic
75C42×C13C2×D412yes—
76C42×C13#4111yescharacteristic
77C4⋊Dic13—24no—
78C4⋊Dic13—42no—
79C2×#1055—22no—
80C2×#1055—24no—
81C2×#1055—41no—
82C2×#1055—41no—
83C2×#1055—42no—
84C2×#1055—42no—
85C2×#477—132no—
86#2582D1311yescharacteristic
87#1956—131no—
88C2×Q8⋊C8—132no—
89#1296—131no—
90C23×C13#12011yescharacteristic
91Q8×C13—24no—
92Q8×C13—24no—
93Q8×C13—42no—
94Q8×C13—42no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—24no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—44no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13#12012yes—
106C2×C4×C13#12111yescharacteristic
107C2×C4×C13#12112yes—
108C2×C4×C13#12711yescharacteristic
109C2×C4×C13C2×Q1612yes—
110C2×C4×C13#13512yes—
111C2×C4×C13#13712yes—
112C2×C4×C13#13712yes—
113C2×Dic13—42no—
114C2×Dic13—81no—
115C2×Dic13—81no—
116Dic26—44no—
117Dic26—82no—
118#1055—42no—
119#1055—44no—
120C2×C4⋊Q8—131no—
121C2×C4×Q8C2×D1312yes—
122#477—264no—
123#477—264no—
124C2×#107—262no—
125C2×C4⋊C8—132no—
126C2×#103—262no—
127C2×#103—262no—
128C2×C4×C8—131no—
129#398—22no—
130#391—22no—
131#389—22no—
132#384C2×D1311yescharacteristic
133Q8⋊C8—264no—
134C22×C13#39211yescharacteristic
135C22×C13#45112yes—
136C22×C13#45212yes—
137C22×C13#45311yescharacteristic
138C22×C13#45411yescharacteristic
139C4×C13—21no—
140C4×C13—21no—
141C4×C13—44no—
142C4×C13—82no—
143C4×C13—82no—
144C4×C13#45112yes—
145C4×C13#45212yes—
146C4×C13#46712yes—
147C4×C13#47012yes—
148Dic13—82no—
149C22×Q8—261no—
150C22×Q8C22⋊D1312yes—
151C22×C8—261no—
152C22×C8—262no—
153C4⋊Q8—132no—
154C4⋊Q8—262no—
155C4⋊Q8—261no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—262no—
164C2×C4⋊C4C22⋊D1312yes—
165C2×C4⋊C4C22⋊D1312yes—
166C2×C42—22no—
167C2×C42C22×D1311yescharacteristic
168#107—268no—
169C4⋊C8—134no—
170C4⋊C8—262no—
171#103—268no—
172#103—524no—
173C4×C8—262no—
174#95—24no—
175#95—22no—
176C2×C13#163011yescharacteristic
177C2×C13#163311yescharacteristic
178C2×C13#163612yes—
179C2×C13#200112yes—
180C2×C13#200611yescharacteristic
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—262no—
187C2×Q8—522no—
188C2×Q8—522no—
189C2×Q8—521no—
190C2×Q8#610714yes—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—521no—
195C22×C4C2×C22⋊D1311yescharacteristic
196C22×C4C2×C22⋊D1312yes—
197C2×C8—262no—
198C2×C8—264no—
199C2×C8—521no—
200C2×C8—521no—
201C2×C8—522no—
202C2×C8—522no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—82no—
211C4⋊C4—264no—
212C4⋊C4—522no—
213C42—42no—
214C42—42no—
215C42D4×D1311yescharacteristic
216C42D4×D1312yes—
217C42#612911yescharacteristic
218C13#1023711yescharacteristic, complemented, Sylow
219C23#8820711yescharacteristic
220Q8—24no—
221Q8—24no—
222Q8—42no—
223Q8—42no—
224Q8—524no—
225Q8—1042no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—24no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—522no—
237C2×C4—1041no—
238C2×C4—1041no—
239C2×C4#8819112yes—
240C2×C4#8819211yescharacteristic
241C2×C4#8819312yes—
242C2×C4#8819411yescharacteristic
243C2×C4#8819612yes—
244C2×C4C2×#610712yes—
245C2×C4#8820412yes—
246C2×C4#8820512yes—
247C8—522no—
248C8—524no—
249C22#1171888411yescharacteristic
250C22#1171888912yes—
251C22#1171890012yes—
252C22#1171890211yescharacteristic
253C22#1171890611yescharacteristic
254C4—21no—
255C4—21no—
256C4—44no—
257C4—82no—
258C4—82no—
259C4—1042no—
260C4#1171870812yes—
261C4#1171871112yes—
262C4#1171871212yes—
263C4#1171871312yes—
264C2#1311395711yescharacteristic
265C2#1311397611yescharacteristic
266C2#1311399412yes—
267C2#1311584412yes—
268C2#1311587811yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2582C2
socle, prime radicalC23×C13#120
hypercenter#2582D13
hypocenterC13#10237
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2582

Complements

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

NH ≅ G/Ntype
218. C13#10237semidirect

Maximal subgroups

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

subgroupindex
C2×#117186822
#131156372
C2×Q8⋊#10552
#131127192
C13×#25822
#1023713