Finite Group Databasebeta

← #15775330

Subgroups — #15775330

Order 3328.

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

normal subgroups only

This group has 424 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#13120209C211yesmaximal, characteristic, complemented
2#13113839C212yesmaximal
3#13112841C212yesmaximal, complemented
4#13112782C211yesmaximal, characteristic, complemented
5C13×#2039C211yesmaximal, characteristic
6C13×#537C2211yescharacteristic
7C2×C4×Dic26—21no—
8C2×C13×#104—21no—
9C13×#417—21no—
10C13×#384C2211yescharacteristic
11#11718694—22no—
12#11718646—22no—
13#11718644—21no—
14#11718644C2212yes—
15#11718635—22no—
16C13×#343C2211yescharacteristic
17#11718129—22no—
18#11718120C2212yes—
19C2×C13×#41—21no—
20C22×Dic26—21no—
21C2×C13×M16—21no—
22C13×C22⋊Q8—41no—
23C13×#121—22no—
24C13×#121—41no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4C2311yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13D412yes—
32C2×#6101—22no—
33C2×C4×Dic13—22no—
34C4×Dic26—42no—
35C4×Dic26—42no—
36C13×#104—42no—
37C13×#103—41no—
38C13×#102—41no—
39#88072—42no—
40#88071—21no—
41#88071—22no—
42#88071—22no—
43#88071D412yes—
44C22⋊#1055—22no—
45#88047—42no—
46#12153—131nomaximal, Sylow
47C13×#41—41no—
48C13×#41—41no—
49C13×#41—41no—
50C13×#41—41no—
51C2×Q8×C13—21no—
52C2×D4×C13—21no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—41no—
58C22×C4×C13C2×D412yes—
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—22no—
61C22×Dic13—22no—
62C2×Dic26—24no—
63C2×Dic26—42no—
64C2×Dic26—42no—
65C13×M16—41no—
66C13×M16—41no—
67C2×C8×C13—41no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—44no—
72C13×C22⋊C4—42no—
73C42×C13—21no—
74C42×C13D812yes—
75C4⋊Dic13—42no—
76C4⋊Dic13—42no—
77C4⋊Dic13—81no—
78#6101—42no—
79#6101—42no—
80C4×Dic13—44no—
81C2×#1055—42no—
82#2582—131no—
83#2039D1311yescharacteristic
84#1610—132no—
85#1346—132no—
86#1325—131no—
87C23×C13—41no—
88C23×C13#12011yescharacteristic
89Q8×C13—41no—
90Q8×C13—41no—
91D4×C13—41no—
92D4×C13—41no—
93D4×C13—82no—
94D4×C13—81no—
95D4×C13—81no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—81no—
107C2×C4×C13—81no—
108C2×C4×C13C2×D811yescharacteristic
109C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
110C2×Dic13—24no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116Dic26—48no—
117C8×C13—81no—
118#1055—82no—
119#537C2×D1311yescharacteristic
120C2×C4×Q8—261no—
121#480—262no—
122C2×#104—21no—
123#417—21no—
124#398—132no—
125#398—261no—
126#391—262no—
127#389—262no—
128#384C2×D1311yescharacteristic
129#343C2×D1311yescharacteristic
130#327—262no—
131#324—132no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—81no—
135C22×C13—81no—
136C22×C13—81no—
137C22×C13#44711yescharacteristic
138C22×C13#45411yescharacteristic
139C22×C13B(4,𝔽2)11yescharacteristic
140C4×C13—24no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—42no—
144C4×C13—81no—
145C4×C13—81no—
146Dic13—44no—
147Dic13—82no—
148C2×#41—21no—
149C22×Q8—261no—
150C2×M16—21no—
151C22⋊Q8—41no—
152#121—22no—
153#121—41no—
154C4×Q8—522no—
155C4×Q8—522no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—132no—
158C2×C4⋊C4—261no—
159C2×C4⋊C4—262no—
160C2×C4⋊C4—261no—
161C2×C4⋊C4C22⋊D1311yescharacteristic
162C2×C4⋊C4C22×D1311yescharacteristic
163C2×C42—262no—
164C2×C42C22⋊D1311yescharacteristic
165#107—522no—
166#104—42no—
167#103—41no—
168#102—41no—
169#102—522no—
170C22⋊C8—262no—
171#95—132no—
172#95—262no—
173#95—261no—
174#95—262no—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13—161no—
178C2×C13#159811yescharacteristic
179C2×C13#219811yescharacteristic
180C2×C13#220511yescharacteristic
181#41—41no—
182#41—41no—
183#41—41no—
184#41—41no—
185C2×Q8—21no—
186C2×Q8—264no—
187C2×Q8—522no—
188C2×Q8—522no—
189C2×D4—21no—
190C2×D4—22no—
191C2×D4—41no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—41no—
195C22×C4—262no—
196C22×C4—262no—
197C22×C4D4×D1312yes—
198C22×C4C2×C22⋊D1311yescharacteristic
199M16—41no—
200M16—41no—
201C2×C8—41no—
202C2×C8—522no—
203C4⋊C4—22no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—44no—
207C4⋊C4—522no—
208C4⋊C4—522no—
209C4⋊C4—522no—
210C4⋊C4—522no—
211C4⋊C4—1041no—
212C22⋊C4—42no—
213C42—21no—
214C42—524no—
215C42#610412yes—
216C13#1215311yescharacteristic, complemented, Sylow
217C23—41no—
218C23#8819111yescharacteristic
219Q8—41no—
220Q8—41no—
221Q8—528no—
222D4—41no—
223D4—41no—
224D4—82no—
225D4—81no—
226D4—81no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—264no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4—522no—
245C2×C4C2×#610411yescharacteristic
246C2×C4#8820311yescharacteristic
247C8—81no—
248C8—1042no—
249C22—21no—
250C22—21no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22#1171869311yescharacteristic
255C22#1171869711yescharacteristic
256C22#1171872311yescharacteristic
257C4—24no—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—81no—
262C4—81no—
263C4—524no—
264C4—1042no—
265C2—21no—
266C2—21no—
267C2—161no—
268C2#1311377011yescharacteristic
269C2#1311683111yescharacteristic
270C2#1311686511yescharacteristic
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2039C2
socleC22×C13B(4,𝔽2)
prime radicalC13×#537C22
hypercenter#2039D13
hypocenterC13#12153
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #13120209C2semidirect
3. #13112841C2semidirect
4. #13112782C2semidirect
216. C13#12153semidirect

Maximal subgroups

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

subgroupindex
#131202092
#131138392
#131128412
#131127822
C13×#20392
#1215313