Finite Group Databasebeta

← #15777681

Subgroups — #15777681

Order 3328.

306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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#13117063C211yesmaximal, characteristic, complemented
3#13117060C211yesmaximal, characteristic, complemented
4#13114443C211yesmaximal, characteristic, complemented
5#13114425C211yesmaximal, characteristic, complemented
6#13112755C211yesmaximal, characteristic, complemented
7C13×#2248C211yesmaximal, characteristic, complemented
8C2×C13×SD32—22no—
9C13×#494C2211yescharacteristic
10C13×#493C2211yescharacteristic
11C2×#88066—22no—
12#11718749—21no—
13#11718749—21no—
14#11718737—21no—
15#11718731—21no—
16#11718356C2211yescharacteristic
17#11718343C2211yescharacteristic
18C4×C13×C16C2211yescharacteristic
19#11718156—22no—
20#11718101—22no—
21C4×#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C2×C13×D8—21no—
26C2×C13×D8—21no—
27C13×C4⋊Q8—21no—
28C13×#127—21no—
29C2×#6105—42no—
30C2×D104—21no—
31C2×D104—21no—
32#88128—21no—
33#88123—21no—
34C13×SD32—44no—
35C2×C13×C16D412yes—
36C4×C8×C13C2311yescharacteristic
37#88072—42no—
38#88066—44no—
39#88058—21no—
40#88058—21no—
41C2×#6090D412yes—
42#88049—42no—
43#88049—42no—
44C4×#1055D411yescharacteristic
45C4×#1055D411yescharacteristic
46#12527—131nomaximal, Sylow
47C2×Q8×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C2×D52—41no—
52C2×D52—41no—
53C2×D52—41no—
54C2×Dic26—41no—
55C13×Q16—42no—
56C13×Q16—42no—
57C13×D8—42no—
58C13×D8—42no—
59C2×C8×C13C2×D411yescharacteristic
60C2×C8×C13C2×D411yescharacteristic
61C13×C4⋊C4—41no—
62C13×C4⋊C4—41no—
63C42×C13C2×D411yescharacteristic
64#6105—84no—
65C4⋊Dic13—41no—
66C4⋊Dic13—41no—
67C2×#1055D812yes—
68C2×#1055D812yes—
69D104—42no—
70D104—42no—
71C13×C16—22no—
72#6090—22no—
73#2248D1311yescharacteristic, complemented
74#2246—131no—
75#2241—131no—
76#2240—131no—
77#1709—131no—
78#1706—131no—
79#1312—131no—
80C23×C13—81no—
81C22×D13—81no—
82Q8×C13—81no—
83Q8×C13—81no—
84D4×C13—81no—
85D4×C13—81no—
86D4×C13—82no—
87D4×C13—82no—
88C2×C4×C13—81no—
89C2×C4×C13#12711yescharacteristic
90C2×C4×C13C2×D811yescharacteristic
91C2×C4×C13C2×D811yescharacteristic
92C2×Dic13—81no—
93D52—81no—
94D52—81no—
95D52—82no—
96D52—82no—
97Dic26—82no—
98C8×C13AGL(1,ℤ/8)12yes—
99C8×C13AGL(1,ℤ/8)12yes—
100#1055—22no—
101#1055—22no—
102C2×SD32—22no—
103C2×D16—262no—
104#500—131no—
105#494C2×D1311yescharacteristic
106#493—131no—
107#493C2×D1311yescharacteristic
108#492—261no—
109#486—261no—
110#486—261no—
111#486—261no—
112#358—262no—
113#357—262no—
114C4×C16—131no—
115C4×C16C2×D1311yescharacteristic
116C82—131no—
117C22×C13—161no—
118C22×C13—161no—
119C22×C13—161no—
120C22×C13#49311yescharacteristic
121C2×D13—161no—
122C2×D13—161no—
123C2×D13—161no—
124C4×C13—161no—
125C4×C13#49611yescharacteristic
126C4×C13#49611yescharacteristic
127C4×C13#50812yes—
128C4×C13#50912yes—
129Dic13—161no—
130C2×Q16—21no—
131C2×Q16—21no—
132C2×SD16—522no—
133C2×D8—21no—
134C2×D8—21no—
135C2×D8—261no—
136C2×D8—261no—
137C4⋊Q8—21no—
138C4⋊Q8—261no—
139#127—21no—
140#127—261no—
141SD32—44no—
142D16—524no—
143C2×C16—132no—
144C2×C16C22⋊D1312yes—
145#107—261no—
146#107—261no—
147#102—522no—
148#102—522no—
149#102—522no—
150C4×C8—131no—
151C4×C8—131no—
152C4×C8C22×D1311yescharacteristic
153C2×C13—321no—
154C2×C13#172111yescharacteristic
155C2×C13#224911yescharacteristic
156C2×C13#225011yescharacteristic
157D13—321no—
158C2×Q8—41no—
159C2×Q8—521no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—521no—
164C2×D4—521no—
165C2×D4—521no—
166Q16—42no—
167Q16—42no—
168SD16—1044no—
169D8—42no—
170D8—42no—
171D8—522no—
172D8—522no—
173C2×C8—132no—
174C2×C8—132no—
175C2×C8D4×D1311yescharacteristic
176C2×C8C2×C22⋊D1311yescharacteristic
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—521no—
180C4⋊C4—521no—
181C42D4×D1311yescharacteristic
182C16—22no—
183C16—262no—
184C13#1252711yescharacteristic, complemented, Sylow
185C23—81no—
186C23—1041no—
187Q8—81no—
188Q8—81no—
189Q8—1042no—
190D4—81no—
191D4—81no—
192D4—82no—
193D4—82no—
194D4—1041no—
195D4—1041no—
196D4—1042no—
197D4—1042no—
198C2×C4—81no—
199C2×C4—1041no—
200C2×C4D8×D1311yescharacteristic
201C2×C4D8×D1311yescharacteristic
202C2×C4#8819411yescharacteristic
203C8—262no—
204C8—262no—
205C8#8816512yes—
206C8#8818612yes—
207C22—161no—
208C22—161no—
209C22—161no—
210C22—2081no—
211C22—2081no—
212C22—2081no—
213C22#1171881211yescharacteristic
214C4—161no—
215C4—2081no—
216C4#1171857512yes—
217C4#1171857712yes—
218C4#1171873511yescharacteristic
219C4#1171881511yescharacteristic
220C2—321no—
221C2—4161no—
222C2#1311450111yescharacteristic
223C2#1311709611yescharacteristic
224C2#1311710111yescharacteristic
subgroupG/H
centerC22#11718812
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2248C2
socleC22×C13#493
prime radical#13117085C2
hypercenter#2248D13
hypocenterC13#12527
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
2. #13117063C2semidirect
3. #13117060C2semidirect
4. #13114443C2semidirect
5. #13114425C2semidirect
6. #13112755C2semidirect
7. C13×#2248C2semidirect
73. #2248D13semidirect
184. C13#12527semidirect

Maximal subgroups

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

subgroupindex
#131170852
#131170632
#131170602
#131144432
#131144252
#131127552
C13×#22482
#1252713