Finite Group Databasebeta

← #15767698

Subgroups — #15767698

Order 3328.

310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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#13115668C211yesmaximal, characteristic
2#13113486C212yesmaximal
3#13112733C212yesmaximal, complemented
4#13112665C211yesmaximal, characteristic, complemented
5C13×#1832C211yesmaximal, characteristic, complemented
6#11719182C2211yescharacteristic
7C2×C13×C4⋊C8C2212yes—
8C13×#376C2211yescharacteristic
9C2×#88045—22no—
10#11718586C2212yes—
11#11718585C2211yescharacteristic
12C13×#336—22no—
13#11718077—22no—
14#11718074—22no—
15C2×#6127—21no—
16C22×C8×C13—22no—
17C2×C42×C13D412yes—
18C2×C42×C13C2311yescharacteristic
19#88184—22no—
20C2×#6099—21no—
21#88129—21no—
22#88128D411yescharacteristic
23C4×D52—22no—
24#88123D411yescharacteristic
25C13×C4⋊C8—22no—
26C13×C4⋊C8—22no—
27C13×#95—22no—
28C22⋊#1055—22no—
29#88045—44no—
30C4⋊#1055—22no—
31C4⋊#1055—22no—
32C4×#1055—22no—
33#10629—131nomaximal, Sylow
34C22×C4×C13—22no—
35C22×C4×C13C2×D411yescharacteristic
36C22×C4×C13#4112yes—
37C2×C22⋊D13—41no—
38#6127—42no—
39#6127—42no—
40C2×D52—21no—
41C2×D52—22no—
42C2×C4×D13—41no—
43C2×Dic26—21no—
44C2×C8×C13—42no—
45C2×C8×C13—42no—
46C2×C8×C13—42no—
47C42×C13—22no—
48C42×C13—22no—
49C42×C13C2×D411yescharacteristic
50C42×C13#4111yescharacteristic
51C42×C13#4112yes—
52#6103—42no—
53C4⋊Dic13—22no—
54#6099—42no—
55C2×#1055—42no—
56C2×#1055—41no—
57#1963—131no—
58#1832D1311yescharacteristic, complemented
59#1540—132no—
60#1301—132no—
61#1274—131no—
62C23×C13#12311yescharacteristic
63C22×D13—41no—
64C2×C4×C13—42no—
65C2×C4×C13—44no—
66C2×C4×C13—42no—
67C2×C4×C13#12111yescharacteristic
68C2×C4×C13#12312yes—
69C2×C4×C13#12411yescharacteristic
70C2×C4×C13#12612yes—
71C2×C4×C13#13512yes—
72C2×C4×C13AGL(1,ℤ/8)12yes—
73C22⋊D13—82no—
74C2×Dic13—41no—
75D52—42no—
76D52—82no—
77C4×D13—81no—
78C4×D13—81no—
79Dic26—42no—
80C8×C13—82no—
81#1055—82no—
82#1055—81no—
83#532—131no—
84#431—132no—
85#423—131no—
86C2×C4⋊C8C2×D1312yes—
87C2×#104—262no—
88#376C2×D1311yescharacteristic
89#336—22no—
90#332—262no—
91#331—262no—
92C22×C13—22no—
93C22×C13#39711yescharacteristic
94C22×C13#48212yes—
95C2×D13—81no—
96C2×D13—82no—
97C4×C13—22no—
98C4×C13—22no—
99C4×C13—82no—
100C4×C13#46312yes—
101C4×C13#48811yescharacteristic
102C4×C13#49011yescharacteristic
103Dic13—81no—
104C2×#41—261no—
105C2×M16—261no—
106C22×C8—22no—
107C4⋊Q8—131no—
108#127—131no—
109#124—261no—
110#121—262no—
111C4×D4—262no—
112C2×C42C22⋊D1312yes—
113C2×C42C22×D1311yescharacteristic
114C4⋊C8—22no—
115C4⋊C8—22no—
116C4⋊C8—262no—
117C4⋊C8—262no—
118#104—524no—
119C22⋊C8—262no—
120C4×C8—262no—
121#95—22no—
122C2×C13—22no—
123C2×C13#207311yescharacteristic
124C2×C13#208012yes—
125D13—161no—
126#41—522no—
127#41—522no—
128C2×Q8—261no—
129C2×D4—262no—
130C2×D4—261no—
131C2×D4—521no—
132C22×C4—22no—
133C22×C4—521no—
134C22×C4#612712yes—
135C22×C4C2×C22⋊D1311yescharacteristic
136M16—522no—
137C2×C8—42no—
138C2×C8—42no—
139C2×C8—42no—
140C2×C8—522no—
141C2×C8—521no—
142C4⋊C4—262no—
143C22⋊C4—522no—
144C42—22no—
145C42—22no—
146C42D4×D1311yescharacteristic
147C42#612911yescharacteristic
148C42#613112yes—
149C13#1062911yescharacteristic, complemented, Sylow
150C23—521no—
151C23#8818311yescharacteristic
152Q8—522no—
153D4—522no—
154D4—1042no—
155D4—1042no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—42no—
159C2×C4—521no—
160C2×C4—1041no—
161C2×C4—1041no—
162C2×C4#8814812yes—
163C2×C4#8815212yes—
164C2×C4#8819211yescharacteristic
165C2×C4#8820111yescharacteristic
166C2×C4#8820312yes—
167C2×C4#8820412yes—
168C8—82no—
169C8—1042no—
170C8—1041no—
171C22—22no—
172C22—1041no—
173C22—1042no—
174C22#1171865411yescharacteristic
175C22#1171866412yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—1041no—
180C4#1171871812yes—
181C4#1171872811yescharacteristic
182C4#1171872911yescharacteristic
183C2—22no—
184C2—2081no—
185C2#1311625011yescharacteristic
186C2#1311628712yes—
subgroupG/H
centerC2×C4#88201
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1832C2
socleC22×C13#397
prime radical#11719182C22
hypercenter#1832D13
hypocenterC13#10629
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
3. #13112733C2semidirect
4. #13112665C2semidirect
5. C13×#1832C2semidirect
58. #1832D13semidirect
149. C13#10629semidirect

Maximal subgroups

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

subgroupindex
#131156682
#131134862
#131127332
#131126652
C13×#18322
#1062913