Finite Group Databasebeta

← #15777048

Subgroups — #15777048

Order 3328.

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

normal subgroups only

This group has 256 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#13116984C211yesmaximal, characteristic, complemented
2#13116868C211yesmaximal, characteristic
3#13114425C211yesmaximal, characteristic, complemented
4#13113630C211yesmaximal, characteristic, complemented
5#13112899C211yesmaximal, characteristic, complemented
6#13112895C211yesmaximal, characteristic, complemented
7C13×#1361C211yesmaximal, characteristic, complemented
8C13×#493C2211yescharacteristic
9C2×#88066—21no—
10#11718737—21no—
11#11718731—21no—
12#11718495—21no—
13C4×D104C2211yescharacteristic
14#11718343C2211yescharacteristic
15C13×C4⋊C16C2211yescharacteristic
16C13×#335C2211yescharacteristic
17#11718154—21no—
18#11718101—21no—
19#11718097—21no—
20#11718075—21no—
21C4⋊#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×D8—21no—
24C2×C13×D8—21no—
25C13×#127—21no—
26C2×#6105—42no—
27C2×D104D411yescharacteristic
28C2×C8×D13—41no—
29C4×D52—21no—
30#88123—21no—
31C2×C13×C16—21no—
32C13×C4⋊C8—21no—
33C4×C8×C13C2311yescharacteristic
34#88072—41no—
35#88072—41no—
36#88066—42no—
37#88061—21no—
38#88060—41no—
39#88058—21no—
40#88058—21no—
41#88058D411yescharacteristic
42C2×#6090—21no—
43C4×#1055D411yescharacteristic
44C4×#1055D411yescharacteristic
45#12418—131nomaximal, Sylow
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D52—21no—
50C2×C4×D13—41no—
51C2×Dic26—41no—
52C13×D8—41no—
53C13×D8—41no—
54C13×D8—81no—
55C2×C8×C13—41no—
56C2×C8×C13C2×D411yescharacteristic
57C2×C8×C13#4111yescharacteristic
58C42×C13C2×D411yescharacteristic
59#6105—84no—
60#6103—41no—
61C4⋊Dic13—21no—
62C4⋊Dic13—41no—
63C4⋊Dic13—41no—
64C2×#1055—21no—
65C2×#1055D811yescharacteristic
66C2×#1055D811yescharacteristic
67D104—21no—
68D104SD1612yescomplemented
69C8×D13—82no—
70C13×C16—41no—
71#6090—41no—
72#2226—131no—
73#2206—131no—
74#1706—131no—
75C8×D8—131no—
76#1367—131no—
77#1365—131no—
78#1361D1311yescharacteristic, complemented
79C23×C13—81no—
80C22×D13—41no—
81D4×C13—82no—
82D4×C13—81no—
83D4×C13—81no—
84D4×C13—81no—
85D4×C13—81no—
86C2×C4×C13#12111yescharacteristic
87C2×C4×C13C2×D811yescharacteristic
88C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
89C2×Dic13—41no—
90C2×Dic13—81no—
91D52—22no—
92D52—41no—
93C4×D13—81no—
94C4×D13—81no—
95Dic26—82no—
96C8×C13—21no—
97C8×C13—81no—
98C8×C13C2×SD1611yescharacteristic
99C8×C13#13511yescharacteristic
100#1055—22no—
101#1055—21no—
102#1055—21no—
103C2×D16—261no—
104#500—131no—
105#493C2×D1311yescharacteristic
106#492—261no—
107#486—261no—
108C4×D8—131no—
109C8×D4—261no—
110#367—261no—
111C4⋊C16—131no—
112C4⋊C16C2×D1311yescharacteristic
113#357—261no—
114#357—261no—
115#335C2×D1311yescharacteristic
116D4⋊C8—261no—
117C82—131no—
118C22×C13—161no—
119C22×C13—161no—
120C22×C13—161no—
121C22×C13#45911yescharacteristic
122C2×D13—42no—
123C2×D13—81no—
124C2×D13—81no—
125C4×C13—21no—
126C4×C13#46511yescharacteristic
127C4×C13#47111yescharacteristic
128C4×C13#50811yescharacteristic
129C4×C13#50911yescharacteristic
130Dic13—81no—
131Dic13—161no—
132C2×SD16—522no—
133C2×D8—21no—
134C2×D8—21no—
135C2×D8—131no—
136C22×C8—521no—
137C4⋊Q8—261no—
138#127—21no—
139C4×D4—261no—
140D16—522no—
141C2×C16—21no—
142C2×C16—261no—
143#107—131no—
144#107—261no—
145#107—261no—
146C4⋊C8—21no—
147#102—261no—
148#102—521no—
149#102—521no—
150C22⋊C8—521no—
151C4×C8—131no—
152C4×C8—131no—
153C4×C8C22×D1311yescharacteristic
154C2×C13—321no—
155C2×C13#166511yescharacteristic
156C2×C13#221011yescharacteristic
157C2×C13#221311yescharacteristic
158D13—82no—
159C2×Q8—521no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—261no—
164C22×C4—521no—
165SD16—1044no—
166D8—41no—
167D8—41no—
168D8—81no—
169D8—132no—
170D8—261no—
171C2×C8—41no—
172C2×C8—131no—
173C2×C8—131no—
174C2×C8—261no—
175C2×C8—1042no—
176C2×C8#612711yescharacteristic
177C2×C8D4×D1311yescharacteristic
178C4⋊C4—261no—
179C4⋊C4—521no—
180C4⋊C4—521no—
181C22⋊C4—521no—
182C42D4×D1311yescharacteristic
183C16—41no—
184C16—521no—
185C13#1241811yescharacteristic, complemented, Sylow
186C23—81no—
187C23—521no—
188Q8—1042no—
189D4—82no—
190D4—81no—
191D4—81no—
192D4—81no—
193D4—81no—
194D4—262no—
195D4—521no—
196C2×C4—521no—
197C2×C4—1041no—
198C2×C4—1041no—
199C2×C4—1041no—
200C2×C4#8813811yescharacteristic
201C2×C4D8×D1311yescharacteristic
202C2×C4#8816811yescharacteristic
203C8—21no—
204C8—81no—
205C8—262no—
206C8—261no—
207C8—261no—
208C8#8816611yescharacteristic
209C8SD16×D1311yescharacteristic
210C22—161no—
211C22—161no—
212C22—161no—
213C22—522no—
214C22—1041no—
215C22—1041no—
216C22#1171844711yescharacteristic
217C4—21no—
218C4—1041no—
219C4—2081no—
220C4#1171840911yescharacteristic
221C4#1171843911yescharacteristic
222C4#1171857211yescharacteristic
223C4#1171857711yescharacteristic
224C2—321no—
225C2—1042no—
226C2#1311417611yescharacteristic
227C2#1311689011yescharacteristic
228C2#1311691111yescharacteristic
subgroupG/H
centerC22#11718447
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1361C2
socleC22×C13#459
prime radical#13116868C2
hypercenter#1361D13
hypocenterC13#12418
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
1. #13116984C2semidirect
3. #13114425C2semidirect
4. #13113630C2semidirect
5. #13112899C2semidirect
6. #13112895C2semidirect
7. C13×#1361C2semidirect
68. D104SD16semidirect
78. #1361D13semidirect
185. C13#12418semidirect

Maximal subgroups

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

subgroupindex
#131169842
#131168682
#131144252
#131136302
#131128992
#131128952
C13×#13612
#1241813