Finite Group Databasebeta

← #15775936

Subgroups — #15775936

Order 3328.

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

normal subgroups only

This group has 454 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#13116186C211yesmaximal, characteristic, complemented
2#13113775C212yesmaximal, complemented
3#13112839C212yesmaximal, complemented
4#13112780C211yesmaximal, characteristic, complemented
5C13×#2819C211yesmaximal, characteristic
6C2×C13×#124—21no—
7#11719205C2211yescharacteristic
8C13×#394—21no—
9C13×#394C2212yes—
10C13×#393—22no—
11C13×#392—22no—
12C13×#382C2211yescharacteristic
13#11718879—22no—
14#11718625—21no—
15#11718122C2211yescharacteristic
16#11718120C2212yes—
17#11718115—21no—
18#11718044—22no—
19C22×Q8×C13—21no—
20C22×D4×C13—21no—
21C22×D4×C13—21no—
22C22×D4×C13D412yes—
23C13×#124—42no—
24C13×#124—42no—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13D411yescharacteristic
32C2×#6105—42no—
33#88180—21no—
34#88178—22no—
35C2×#6099—21no—
36#88144—41no—
37#88142—41no—
38C13×#95—21no—
39C13×#95—22no—
40C13×#95D412yes—
41#88072—42no—
42C22⋊#1055—22no—
43#88048—41no—
44#88047—41no—
45#12250—131nomaximal, Sylow
46C24×C13—22no—
47C2×Q8×C13—42no—
48C2×Q8×C13—81no—
49C2×Q8×C13—81no—
50C2×D4×C13—42no—
51C2×D4×C13—42no—
52C2×D4×C13—82no—
53C2×D4×C13—81no—
54C2×D4×C13—81no—
55C2×D4×C13—82no—
56C2×D4×C13—81no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D412yes—
62C2×Dic26—22no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C22⋊C4—44no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—42no—
68C13×C22⋊C4—82no—
69C13×C22⋊C4—82no—
70C42×C13—21no—
71C42×C13SD1612yescomplemented
72C22⋊Dic13—41no—
73#6105—84no—
74C4⋊Dic13—22no—
75C4⋊Dic13—21no—
76C4⋊Dic13—21no—
77#6101—42no—
78C4×Dic13—41no—
79#6099—22no—
80#6099—41no—
81C2×#1055—41no—
82C2×#1055—42no—
83#2819D1311yescharacteristic
84#2061—131no—
85#1599—132no—
86#1345—132no—
87#1324—131no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13#12011yescharacteristic
96Q8×C13—84no—
97D4×C13—44no—
98D4×C13—84no—
99D4×C13—82no—
100D4×C13—84no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13C2×SD1611yescharacteristic
114C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
115C2×Dic13—41no—
116C2×Dic13—41no—
117Dic26—82no—
118#1055—42no—
119#1055—82no—
120#544—131no—
121C2×#124—21no—
122#450—262no—
123#428—261no—
124#394—21no—
125#394C2×D1312yes—
126#393—22no—
127#392—22no—
128#382C2×D1311yescharacteristic
129#343—131no—
130#339—261no—
131#328—262no—
132#324—132no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—82no—
136C22×C13—82no—
137C22×C13—82no—
138C22×C13—82no—
139C22×C13—82no—
140C22×C13—82no—
141C22×C13—82no—
142C22×C13#45011yescharacteristic
143C22×C13#45611yescharacteristic
144C22×C13B(4,𝔽2)11yescharacteristic
145C4×C13—21no—
146C4×C13—21no—
147C4×C13—42no—
148C4×C13—42no—
149C4×C13—82no—
150C4×C13—81no—
151Dic13—81no—
152Dic13—81no—
153C22×Q8—21no—
154C22×D4—21no—
155C22×D4—21no—
156C22×D4C22⋊D1312yes—
157C2×SD16—522no—
158C2×M16—261no—
159C4⋊Q8—521no—
160#125—521no—
161#124—42no—
162#124—42no—
163C22⋊Q8—262no—
164#117—261no—
165C2×C4⋊C4C22⋊D1311yescharacteristic
166C2×C4⋊C4C22×D1311yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C42C22⋊D1311yescharacteristic
172#107—521no—
173#106—521no—
174#102—522no—
175C22⋊C8—262no—
176#95—21no—
177#95—22no—
178#95C22⋊D1312yes—
179C2×C13—21no—
180C2×C13—21no—
181C2×C13—162no—
182C2×C13#160411yescharacteristic
183C2×C13#219911yescharacteristic
184C2×C13#220211yescharacteristic
185C24—22no—
186C2×Q8—42no—
187C2×Q8—81no—
188C2×Q8—81no—
189C2×Q8—262no—
190C2×D4—42no—
191C2×D4—42no—
192C2×D4—82no—
193C2×D4—81no—
194C2×D4—81no—
195C2×D4—82no—
196C2×D4—81no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4C2×C22⋊D1311yescharacteristic
201C22×C4C2×C22⋊D1312yes—
202SD16—1044no—
203M16—262no—
204M16—521no—
205C2×C8—521no—
206C2×C8—522no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—262no—
210C4⋊C4—261no—
211C4⋊C4—261no—
212C4⋊C4—522no—
213C22⋊C4—44no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C22⋊C4—82no—
218C22⋊C4—521no—
219C42—21no—
220C42—521no—
221C42#610512yescomplemented
222C13#1225011yescharacteristic, complemented, Sylow
223C23—42no—
224C23—42no—
225C23—42no—
226C23—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23#8820711yescharacteristic
231Q8—84no—
232Q8—1042no—
233D4—44no—
234D4—82no—
235D4—84no—
236D4—84no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—521no—
250C2×C4—521no—
251C2×C4#8818611yescharacteristic
252C2×C4C2×#610511yescharacteristic
253C8—522no—
254C8—1042no—
255C22—21no—
256C22—21no—
257C22—82no—
258C22—82no—
259C22—82no—
260C22—82no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22#1171887911yescharacteristic
265C22#1171890511yescharacteristic
266C22#1171890711yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—82no—
272C4—81no—
273C4—1041no—
274C4—1041no—
275C2—21no—
276C2—21no—
277C2—162no—
278C2#1311380511yescharacteristic
279C2#1311683711yescharacteristic
280C2#1311685311yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
Fitting, prime radicalC13×#2819C2
socleC22×C13B(4,𝔽2)
hypercenter#2819D13
hypocenterC13#12250
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2819

Complements

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

NH ≅ G/Ntype
1. #13116186C2semidirect
2. #13113775C2semidirect
3. #13112839C2semidirect
4. #13112780C2semidirect
71. C42×C13SD16semidirect
221. C42#6105semidirect
222. C13#12250semidirect

Maximal subgroups

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

subgroupindex
#131161862
#131137752
#131128392
#131127802
C13×#28192
#1225013