Finite Group Databasebeta

← #15776283

Subgroups — #15776283

Order 3328.

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

normal subgroups only

This group has 262 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
2#13116416C211yesmaximal, characteristic
3#13112830C212yesmaximal
4#13112789C211yesmaximal, characteristic
5C13×#3261C211yesmaximal, characteristic
6C13×#541—21no—
7C13×#479—22no—
8C13×#470C2212yes—
9C13×#467—21no—
10C13×#462—22no—
11C13×#424C2211yescharacteristic
12#11718786C2211yescharacteristic
13#11718157—22no—
14#11718152C2211yescharacteristic
15#11718145C2212yes—
16#11718144—21no—
17#11718125—21no—
18#11718079—22no—
19C2×C13×Q16—21no—
20C2×C13×Q16D412yes—
21C2×C13×M16C2311yescharacteristic
22C22×C8×C13D411yescharacteristic
23C13×C4⋊Q8—21no—
24C13×#126—42no—
25C13×#125—21no—
26C13×#125—42no—
27C13×C22⋊Q8—22no—
28C4×Q8×C13—22no—
29C13×#117D411yescharacteristic
30C2×#6099—21no—
31C2×#6099—21no—
32C13×#107—21no—
33C13×#106D412yes—
34C13×C4⋊C8—22no—
35C13×#103—22no—
36C13×#103—22no—
37#88059—22no—
38#88052—22no—
39#12305—131nomaximal, Sylow
40C2×Q8×C13—22no—
41C22×C4×C13C2×D411yescharacteristic
42C13×Q16—42no—
43C13×Q16—81no—
44C13×M16—41no—
45C2×C8×C13—21no—
46C2×C8×C13—41no—
47C2×C8×C13C2×D412yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4—22no—
50C13×C4⋊C4—42no—
51C13×C4⋊C4—42no—
52C13×C4⋊C4—42no—
53C13×C4⋊C4—42no—
54C13×C22⋊C4—42no—
55C13×C22⋊C4SD1612yes—
56C42×C13—21no—
57C42×C13—42no—
58#6099—41no—
59#6099—41no—
60#6099—41no—
61#6099—41no—
62C2×#1055—41no—
63C2×#1055—41no—
64#6090—42no—
65#3261D1311yescharacteristic
66#2239—132no—
67#2103—131no—
68#1342—132no—
69#1328—131no—
70C23×C13C2×SD1611yescharacteristic
71Q8×C13—42no—
72Q8×C13—42no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13#12011yescharacteristic
79C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
80C8×C13—22no—
81C8×C13—41no—
82#1055—81no—
83#1055—81no—
84#541—21no—
85#479—22no—
86#470C2×D1312yes—
87#467—21no—
88#462—22no—
89#430—131no—
90#424C2×D1311yescharacteristic
91#365—262no—
92#362—262no—
93#349—132no—
94#344—261no—
95#341—261no—
96#338—131no—
97C22×C13—21no—
98C22×C13—41no—
99C22×C13#45011yescharacteristic
100C4×C13—21no—
101C4×C13—42no—
102C4×C13—82no—
103C4×C13—82no—
104C4×C13#45411yescharacteristic
105C4×C13#45811yescharacteristic
106C2×Q16—21no—
107C2×Q16C22⋊D1312yes—
108C2×M16—261no—
109C2×M16—261no—
110C2×M16C22×D1311yescharacteristic
111C22×C8C22⋊D1311yescharacteristic
112C4⋊Q8—21no—
113#126—42no—
114#125—21no—
115#125—42no—
116C22⋊Q8—22no—
117C4×Q8—22no—
118#117C22⋊D1311yescharacteristic
119M32—262no—
120#108—262no—
121#107—21no—
122#106C22⋊D1312yes—
123C4⋊C8—22no—
124#103—22no—
125#103—22no—
126C2×C13—21no—
127C2×C13—41no—
128C2×C13#161611yescharacteristic
129C2×Q8—22no—
130C22×C4C2×C22⋊D1311yescharacteristic
131Q16—42no—
132Q16—81no—
133M16—41no—
134M16—521no—
135M16—521no—
136M16—521no—
137M16—521no—
138C2×C8—21no—
139C2×C8—41no—
140C2×C8—521no—
141C2×C8—521no—
142C2×C8C2×C22⋊D1312yes—
143C4⋊C4—21no—
144C4⋊C4—22no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C22⋊C4—42no—
150C22⋊C4#610512yes—
151C42—21no—
152C42—42no—
153C16—522no—
154C13#1230511yescharacteristic, complemented, Sylow
155C23C2×#610511yescharacteristic
156Q8—42no—
157Q8—42no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4#8818611yescharacteristic
164C2×C4#8820711yescharacteristic
165C8—22no—
166C8—41no—
167C8—1041no—
168C8—1041no—
169C22—21no—
170C22—41no—
171C22#1171887911yescharacteristic
172C4—21no—
173C4—42no—
174C4—82no—
175C4—82no—
176C4#1171890411yescharacteristic
177C4#1171890611yescharacteristic
178C2—21no—
179C2—41no—
180C2#1311387311yescharacteristic
subgroupG/H
centerC2#13113873
commutator, cosocleC2×C13×M16C23
FrattiniC2×M16C22×D13
FittingC13×#3261C2
socleC2×C13#1616
prime radicalC23×C13C2×SD16
hypercenter#3261D13
hypocenterC13#12305
LCSG ▷ C2×C13×M16 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3261

Complements

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

NH ≅ G/Ntype
154. C13#12305semidirect

Maximal subgroups

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

subgroupindex
#131170532
#131164162
#131128302
#131127892
C13×#32612
#1230513