Finite Group Databasebeta

← #15776249

Subgroups — #15776249

Order 3328.

324 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 59 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#13117053C212yesmaximal, complemented
2#13116352C211yesmaximal, characteristic
3#13112830C212yesmaximal, complemented
4#13112772C211yesmaximal, characteristic
5C13×#3195C211yesmaximal, characteristic
6C2×C13×C22⋊Q8—21no—
7C13×#483—22no—
8C13×#470—21no—
9C13×#470C2212yes—
10C13×#451—22no—
11C13×#407C2211yescharacteristic
12#11718868—21no—
13#11718786C2211yescharacteristic
14#11718785—21no—
15#11718157—22no—
16#11718152C2211yescharacteristic
17#11718145C2212yes—
18#11718079—22no—
19C22×Q8×C13—21no—
20C23×C4×C13D411yescharacteristic
21C2×C13×Q16—21no—
22C2×C13×Q16D412yes—
23C2×C13×M16D411yescharacteristic
24C2×C13×M16C2311yescharacteristic
25C13×C22⋊Q8—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—41no—
28C13×C22⋊Q8—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C22⋊C4—41no—
32C2×#6099—21no—
33C2×#6099—21no—
34C13×#106—21no—
35C13×#106D412yes—
36C13×#103—22no—
37C13×#103—22no—
38C13×C22⋊C8—22no—
39C22⋊#1055—42no—
40#88062—42no—
41#88059—22no—
42#88052—22no—
43#12299—131nomaximal, Sylow
44C24×C13SD1611yescharacteristic
45C2×Q8×C13—22no—
46C2×Q8×C13—41no—
47C2×Q8×C13—81no—
48C2×Q8×C13—81no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—41no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13—41no—
55C22×C4×C13SD1611yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C13×Q16—42no—
58C13×Q16—81no—
59C13×M16—41no—
60C13×M16—41no—
61C2×C8×C13—21no—
62C2×C8×C13C2×D412yes—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—42no—
67C13×C22⋊C4—42no—
68C13×C22⋊C4—42no—
69#6099—41no—
70#6099—41no—
71#6099—41no—
72#6099—41no—
73C2×#1055—22no—
74C2×#1055—41no—
75#6090—42no—
76#3195D1311yescharacteristic
77#2239—132no—
78#2091—131no—
79#1342—132no—
80#1320—131no—
81C23×C13—21no—
82C23×C13—41no—
83C23×C13—42no—
84C23×C13C2×SD1611yescharacteristic
85Q8×C13—42no—
86Q8×C13—42no—
87Q8×C13—82no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—81no—
97C2×C4×C13—82no—
98C2×C4×C13—82no—
99C2×C4×C13#12011yescharacteristic
100C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
101C8×C13—22no—
102C8×C13—41no—
103#1055—42no—
104#1055—81no—
105C2×C22⋊Q8—21no—
106#483—22no—
107#470—21no—
108#470C2×D1312yes—
109#451—22no—
110#430—131no—
111#430—261no—
112#407—261no—
113#407C2×D1311yescharacteristic
114#365—262no—
115#362—262no—
116#349—132no—
117#338—131no—
118C22×C13—22no—
119C22×C13—21no—
120C22×C13—41no—
121C22×C13—41no—
122C22×C13—42no—
123C22×C13—41no—
124C22×C13—81no—
125C22×C13#45011yescharacteristic
126C4×C13—21no—
127C4×C13—41no—
128C4×C13—82no—
129C4×C13—82no—
130C4×C13#45311yescharacteristic
131C4×C13#45811yescharacteristic
132C22×Q8—21no—
133C23×C4C22⋊D1311yescharacteristic
134C2×Q16—21no—
135C2×Q16C22⋊D1312yes—
136C2×M16—261no—
137C2×M16—261no—
138C2×M16C22⋊D1311yescharacteristic
139C2×M16C22×D1311yescharacteristic
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—41no—
143C22⋊Q8—41no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—41no—
146C2×C22⋊C4—41no—
147M32—262no—
148#108—262no—
149#108—522no—
150#106—21no—
151#106C22⋊D1312yes—
152#103—22no—
153#103—22no—
154C22⋊C8—22no—
155C22⋊C8—522no—
156C2×C13—21no—
157C2×C13—42no—
158C2×C13—41no—
159C2×C13#161311yescharacteristic
160C24#610511yescharacteristic
161C2×Q8—22no—
162C2×Q8—41no—
163C2×Q8—81no—
164C2×Q8—81no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4#610511yescharacteristic
172C22×C4C2×C22⋊D1311yescharacteristic
173Q16—42no—
174Q16—81no—
175M16—41no—
176M16—41no—
177M16—521no—
178M16—521no—
179M16—521no—
180M16—521no—
181C2×C8—21no—
182C2×C8—262no—
183C2×C8—521no—
184C2×C8C2×C22⋊D1312yes—
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C22⋊C4—42no—
190C22⋊C4—42no—
191C16—522no—
192C13#1229911yescharacteristic, complemented, Sylow
193C23—21no—
194C23—41no—
195C23—42no—
196C23C2×#610511yescharacteristic
197Q8—42no—
198Q8—42no—
199Q8—82no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—81no—
209C2×C4—82no—
210C2×C4—82no—
211C2×C4#8818611yescharacteristic
212C2×C4#8820711yescharacteristic
213C8—22no—
214C8—41no—
215C8—522no—
216C8—1041no—
217C22—22no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22#1171887911yescharacteristic
225C4—21no—
226C4—41no—
227C4—82no—
228C4—82no—
229C4#1171890211yescharacteristic
230C4#1171890411yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1311385611yescharacteristic
subgroupG/H
centerC2#13113856
commutator, cosocleC2×C13×M16C23
FrattiniC2×M16C22×D13
FittingC13×#3195C2
socleC2×C13#1613
prime radicalC24×C13SD16
hypercenter#3195D13
hypocenterC13#12299
LCSG ▷ C2×C13×M16 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3195

Complements

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

NH ≅ G/Ntype
1. #13117053C2semidirect
3. #13112830C2semidirect
192. C13#12299semidirect

Maximal subgroups

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

subgroupindex
#131170532
#131163522
#131128302
#131127722
C13×#31952
#1229913