Finite Group Databasebeta

← #15775331

Subgroups — #15775331

Order 3328.

424 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116060C211yesmaximal, characteristic
2#13113838C212yesmaximal
3#13112842C212yesmaximal, complemented
4#13112782C211yesmaximal, characteristic, complemented
5C13×#2582C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13—21no—
7#11719215C2211yescharacteristic
8C13×#398—21no—
9C13×#398C2212yes—
10C13×#391—22no—
11C13×#389—22no—
12C13×#384C2211yescharacteristic
13#11718628—22no—
14#11718627—21no—
15C2×#88045—21no—
16#11718122C2211yescharacteristic
17#11718120C2212yes—
18#11718043—22no—
19C22×Q8×C13—21no—
20C2×#6127—21no—
21C4×Q8×C13—42no—
22C4×Q8×C13—42no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D412yes—
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C42×C13—22no—
31C2×C42×C13D411yescharacteristic
32#88184—22no—
33C2×#6099—21no—
34#88151—41no—
35#88149—41no—
36C13×#95—22no—
37C13×#95—21no—
38C13×#95—22no—
39C13×#95D412yes—
40C22⋊#1055—22no—
41#88050—41no—
42#88049—41no—
43#88049—42no—
44#88047—42no—
45#88045—42no—
46#12153—131nomaximal, Sylow
47C2×Q8×C13—24no—
48C2×Q8×C13—42no—
49C2×Q8×C13—42no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13C2×D412yes—
56C2×C22⋊D13—41no—
57#6127—41no—
58#6127—41no—
59#6127—41no—
60#6127—41no—
61C2×D52—21no—
62C2×D52—22no—
63C2×C4×D13—41no—
64C2×Dic26—21no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—44no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C13×C4⋊C4—81no—
73C42×C13—21no—
74C42×C13—44no—
75C42×C13D812yes—
76#6103—42no—
77C4⋊Dic13—22no—
78#6099—41no—
79#6099—41no—
80C2×#1055—42no—
81C2×#1055—41no—
82#2582D1311yescharacteristic, complemented
83#2039—131no—
84#1610—132no—
85#1346—132no—
86#1325—131no—
87C23×C13#12011yescharacteristic
88C22×D13—41no—
89Q8×C13—48no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—24no—
96C2×C4×C13—22no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13C2×D811yescharacteristic
106C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
107C22⋊D13—81no—
108C22⋊D13—81no—
109C2×Dic13—41no—
110D52—41no—
111D52—41no—
112D52—82no—
113C4×D13—81no—
114C4×D13—81no—
115Dic26—41no—
116Dic26—41no—
117#1055—81no—
118#1055—82no—
119#537—131no—
120C2×C4×Q8—21no—
121#480—262no—
122C2×#104—261no—
123#417—261no—
124#398—21no—
125#398C2×D1312yes—
126#391—22no—
127#389—22no—
128#384C2×D1311yescharacteristic
129#343—131no—
130#327—262no—
131#324—132no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13#44711yescharacteristic
135C22×C13#45411yescharacteristic
136C22×C13B(4,𝔽2)11yescharacteristic
137C2×D13—81no—
138C2×D13—81no—
139C2×D13—81no—
140C4×C13—24no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—44no—
144C4×C13—42no—
145C4×C13—82no—
146C4×C13—81no—
147Dic13—81no—
148C2×#41—261no—
149C22×Q8—21no—
150C2×M16—261no—
151C22⋊Q8—521no—
152#121—262no—
153#121—521no—
154C4×Q8—42no—
155C4×Q8—42no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4C22⋊D1311yescharacteristic
161C2×C4⋊C4C22⋊D1312yes—
162C2×C4⋊C4C22×D1311yescharacteristic
163C2×C42—22no—
164C2×C42C22⋊D1311yescharacteristic
165#107—522no—
166#104—522no—
167#103—521no—
168#102—521no—
169#102—522no—
170C22⋊C8—262no—
171#95—22no—
172#95—21no—
173#95—22no—
174#95C22⋊D1312yes—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13#159811yescharacteristic
178C2×C13#219811yescharacteristic
179C2×C13#220511yescharacteristic
180D13—161no—
181#41—521no—
182#41—521no—
183#41—521no—
184#41—521no—
185C2×Q8—24no—
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—261no—
189C2×D4—261no—
190C2×D4—262no—
191C2×D4—521no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—521no—
197C22×C4C2×C22⋊D1311yescharacteristic
198C22×C4C2×C22⋊D1312yes—
199M16—521no—
200M16—521no—
201C2×C8—522no—
202C2×C8—521no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—44no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—81no—
211C4⋊C4—262no—
212C22⋊C4—522no—
213C42—21no—
214C42—44no—
215C42#610412yes—
216C13#1215311yescharacteristic, complemented, Sylow
217C23—521no—
218C23#8820711yescharacteristic
219Q8—48no—
220Q8—521no—
221Q8—521no—
222D4—521no—
223D4—521no—
224D4—1042no—
225D4—1041no—
226D4—1041no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—521no—
243C2×C4—1041no—
244C2×C4—1041no—
245C2×C4C2×#610411yescharacteristic
246C2×C4#8818611yescharacteristic
247C8—1041no—
248C8—1042no—
249C22—21no—
250C22—21no—
251C22—1041no—
252C22—1041no—
253C22—1041no—
254C22#1171887811yescharacteristic
255C22#1171890511yescharacteristic
256C22#1171890611yescharacteristic
257C4—24no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—42no—
262C4—81no—
263C4—82no—
264C4—1041no—
265C2—21no—
266C2—21no—
267C2—2081no—
268C2#1311377111yescharacteristic
269C2#1311683211yescharacteristic
270C2#1311686611yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2582C2
socleC22×C13B(4,𝔽2)
prime radical#11719215C22
hypercenter#2582D13
hypocenterC13#12153
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2582

Complements

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

NH ≅ G/Ntype
3. #13112842C2semidirect
4. #13112782C2semidirect
5. C13×#2582C2semidirect
82. #2582D13semidirect
216. C13#12153semidirect

Maximal subgroups

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

subgroupindex
#131160602
#131138382
#131128422
#131127822
C13×#25822
#1215313