Finite Group Databasebeta

← #15777192

Subgroups — #15777192

Order 3328.

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

normal subgroups only

This group has 244 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#13117085C211yesmaximal, characteristic
2#13116741C211yesmaximal, characteristic, complemented
3#13114197C211yesmaximal, characteristic, complemented
4#13114193C211yesmaximal, characteristic, complemented
5#13112909C211yesmaximal, characteristic, complemented
6#13112883C211yesmaximal, characteristic, complemented
7C13×#1361C211yesmaximal, characteristic, complemented
8C13×#493C2211yescharacteristic
9C2×#88066—21no—
10C2×#88066—21no—
11#11718736—21no—
12#11718509—21no—
13#11718356C2211yescharacteristic
14C8×Dic26C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718136—21no—
18#11718094—21no—
19#11718093—21no—
20#11718077—21no—
21C4×#6090C2211yescharacteristic
22#11718050C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C13×#127—21no—
26C2×#6105—41no—
27C2×D104—21no—
28C2×D104—21no—
29C2×#6095—41no—
30#88128—21no—
31C4×Dic26D411yescharacteristic
32C2×C13×C16—21no—
33C13×C4⋊C8—21no—
34C4×C8×C13C2311yescharacteristic
35#88072—41no—
36#88066—42no—
37#88066—42no—
38#88061—41no—
39#88054—21no—
40C8×Dic13—21no—
41C2×#6090D411yescharacteristic
42C2×#6090D411yescharacteristic
43C4⋊#1055—21no—
44C4⋊#1055D411yescharacteristic
45#12442—131nomaximal, Sylow
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D52—41no—
50C2×D52—41no—
51C2×D52—41no—
52C2×Dic26D811yescharacteristic
53C13×D8—41no—
54C13×D8—41no—
55C13×D8—81no—
56C2×C8×C13—41no—
57C2×C8×C13C2×D411yescharacteristic
58C2×C8×C13#4111yescharacteristic
59C42×C13C2×D411yescharacteristic
60#6105—82no—
61C4⋊Dic13D811yescharacteristic
62#6101—21no—
63C4×Dic13—21no—
64C2×#1055—21no—
65C2×#1055—41no—
66D104—41no—
67D104—41no—
68D104—81no—
69#6095—82no—
70C13×C16—41no—
71#6090—21no—
72#6090SD1612yescomplemented
73#2246—131no—
74#2183—131no—
75#1668—131no—
76#1668—131no—
77#1372—131no—
78#1361—131no—
79#1361D1311yescharacteristic, complemented
80C23×C13—81no—
81C22×D13—81no—
82D4×C13—81no—
83D4×C13—81no—
84D4×C13—81no—
85D4×C13—81no—
86D4×C13—161no—
87C2×C4×C13#12111yescharacteristic
88C2×C4×C13C2×D811yescharacteristic
89C2×C4×C13#13511yescharacteristic
90C2×Dic13—21no—
91C2×Dic13—21no—
92D52—81no—
93D52—81no—
94D52—81no—
95D52—81no—
96D52—161no—
97Dic26—21no—
98Dic26—21no—
99C8×C13—21no—
100C8×C13—81no—
101C8×C13C2×SD1611yescharacteristic
102C8×C13AGL(1,ℤ/8)11yescharacteristic
103#1055—41no—
104#1055—81no—
105C2×D16—261no—
106C2×D16—261no—
107#493—131no—
108#493C2×D1311yescharacteristic
109#460—261no—
110#460—261no—
111C8×Q8—131no—
112C4⋊C16—261no—
113C4⋊C16C2×D1311yescharacteristic
114#346—261no—
115C4×C16—131no—
116#335—131no—
117#335C2×D1311yescharacteristic
118#331—261no—
119#331—261no—
120C22×C13—161no—
121C22×C13—161no—
122C22×C13—161no—
123C22×C13#46611yescharacteristic
124C2×D13—161no—
125C2×D13—161no—
126C2×D13—161no—
127C4×C13—21no—
128C4×C13#46011yescharacteristic
129C4×C13#47211yescharacteristic
130C4×C13#50911yescharacteristic
131C4×C13#50911yescharacteristic
132Dic13—41no—
133Dic13—41no—
134C2×SD16—521no—
135C2×SD16—521no—
136C2×D8—21no—
137C2×D8—21no—
138C2×D8—261no—
139C2×D8—261no—
140#127—21no—
141#127—261no—
142C4×Q8—131no—
143D16—522no—
144D16—522no—
145C2×C16—21no—
146C2×C16—131no—
147C2×C16—131no—
148C4⋊C8—21no—
149C4⋊C8—131no—
150C4⋊C8—261no—
151C4⋊C8—261no—
152#102—521no—
153#102—521no—
154C4×C8—261no—
155C4×C8C22×D1311yescharacteristic
156C2×C13—321no—
157C2×C13#166811yescharacteristic
158C2×C13#221811yescharacteristic
159C2×C13#222111yescharacteristic
160D13—321no—
161C2×Q8—131no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—41no—
165C2×D4—521no—
166C2×D4—521no—
167C2×D4—521no—
168SD16—1042no—
169SD16—1042no—
170D8—41no—
171D8—41no—
172D8—81no—
173D8—521no—
174D8—521no—
175D8—1041no—
176C2×C8—41no—
177C2×C8—261no—
178C2×C8—521no—
179C2×C8#612711yescharacteristic
180C2×C8D4×D1311yescharacteristic
181C4⋊C4—131no—
182C4⋊C4—261no—
183C42—261no—
184C42D4×D1311yescharacteristic
185C16—41no—
186C16—132no—
187C16—261no—
188C13#1244211yescharacteristic, complemented, Sylow
189C23—81no—
190C23—1041no—
191Q8—261no—
192Q8—261no—
193D4—81no—
194D4—81no—
195D4—81no—
196D4—81no—
197D4—161no—
198D4—1041no—
199D4—1041no—
200D4—1041no—
201D4—1041no—
202D4—2081no—
203C2×C4—261no—
204C2×C4—261no—
205C2×C4#8813811yescharacteristic
206C2×C4D8×D1311yescharacteristic
207C2×C4#8817011yescharacteristic
208C8—21no—
209C8—81no—
210C8—521no—
211C8—1041no—
212C8#8816511yescharacteristic
213C8SD16×D1311yescharacteristic
214C22—161no—
215C22—161no—
216C22—161no—
217C22—2081no—
218C22—2081no—
219C22—2081no—
220C22#1171843611yescharacteristic
221C4—21no—
222C4—521no—
223C4—521no—
224C4#1171841011yescharacteristic
225C4#1171842311yescharacteristic
226C4#1171857211yescharacteristic
227C4#1171857511yescharacteristic
228C2—321no—
229C2—4161no—
230C2#1311419511yescharacteristic
231C2#1311693811yescharacteristic
232C2#1311695511yescharacteristic
subgroupG/H
centerC22#11718436
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1361C2
socleC22×C13#466
prime radical#13117085C2
hypercenter#1361D13
hypocenterC13#12442
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #13116741C2semidirect
3. #13114197C2semidirect
4. #13114193C2semidirect
5. #13112909C2semidirect
6. #13112883C2semidirect
7. C13×#1361C2semidirect
72. #6090SD16semidirect
79. #1361D13semidirect
188. C13#12442semidirect

Maximal subgroups

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

subgroupindex
#131170852
#131167412
#131141972
#131141932
#131129092
#131128832
C13×#13612
#1244213