Finite Group Databasebeta

← #15749519

Subgroups — #15749519

Order 3328.

284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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#13114979C211yesmaximal, characteristic
2#13114689C211yesmaximal, characteristic
3C13×#1745C211yesmaximal, characteristic
4C2×C13×#97—21no—
5C43×C13C2211yescharacteristic
6C2×C4⋊#1055—21no—
7C2×#88043C412yes—
8C13×#336—21no—
9C13×#336C412yes—
10#11718116—21no—
11#11718116—21no—
12#11718116—21no—
13#11718116C412yes—
14C22×C8×C13—22no—
15C2×C42×C13C2×C411yescharacteristic
16C2×C42×C13C2×C411yescharacteristic
17C2×C42×C13C2×C411yescharacteristic
18C2×C42×C13D411yescharacteristic
19C2×C42×C13D411yescharacteristic
20C2×C42×C13D411yescharacteristic
21C2×C42×C13Q811yescharacteristic
22C22×#1055—22no—
23C22×#1055—22no—
24C13×#97—24no—
25C4⋊#1055—24no—
26#88043—42no—
27#7043—131nomaximal, Sylow
28C22×C4×C13C4211yescharacteristic
29C22×C4×C13C22⋊C411yescharacteristic
30C22×C4×C13C22⋊C411yescharacteristic
31C22×C4×C13C22⋊C411yescharacteristic
32C22×C4×C13C4⋊C411yescharacteristic
33C22×C4×C13C4⋊C411yescharacteristic
34C22×C4×C13C4⋊C411yescharacteristic
35C2×C8×C13—24no—
36C2×C8×C13—42no—
37C2×C8×C13—42no—
38C42×C13—21no—
39C42×C13—21no—
40C42×C13—22no—
41C42×C13—22no—
42C42×C13—22no—
43C42×C13—41no—
44C42×C13—41no—
45C42×C13—41no—
46C2×#1055—24no—
47C2×#1055—42no—
48C2×#1055—42no—
49C2×#1055—42no—
50C2×#1055—42no—
51C2×#1055—42no—
52#1839—131no—
53#1767—131no—
54#1745D1311yescharacteristic
55C23×C13#9511yescharacteristic
56C2×C4×C13—21no—
57C2×C4×C13—21no—
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13#10011yescharacteristic
74C2×C4×C13#10111yescharacteristic
75C2×C4×C13#10412yes—
76C2×C4×C13#10412yes—
77C2×C4×C13#10812yes—
78C8×C13—44no—
79#1055—44no—
80#1055—82no—
81C2×C4⋊C8—261no—
82C2×#97—21no—
83C2×#97—132no—
84C43C2×D1311yescharacteristic
85#336—21no—
86#336—132no—
87#336—261no—
88#336—261no—
89#336—261no—
90#336Dic1312yes—
91C22×C13H(3,ℤ/4)11yescharacteristic
92C22×C13#33911yescharacteristic
93C22×C13#33911yescharacteristic
94C22×C13#34111yescharacteristic
95C22×C13#34311yescharacteristic
96C22×C13#34411yescharacteristic
97C22×C13#34411yescharacteristic
98C4×C13—21no—
99C4×C13—21no—
100C4×C13—22no—
101C4×C13—22no—
102C4×C13—22no—
103C4×C13—41no—
104C4×C13—41no—
105C4×C13—41no—
106C22×C8—22no—
107C22×C8—262no—
108C22×C8—262no—
109C2×C42Dic2611yescharacteristic
110C2×C42C4×D1311yescharacteristic
111C2×C42C4×D1311yescharacteristic
112C2×C42D5211yescharacteristic
113C2×C42C2×Dic1311yescharacteristic
114C2×C42C22⋊D1311yescharacteristic
115C2×C42C22⋊D1311yescharacteristic
116C4⋊C8—264no—
117#97—24no—
118#97—522no—
119C2×C13#128511yescharacteristic
120C2×C13#128711yescharacteristic
121C2×C13#128811yescharacteristic
122C2×C13#129911yescharacteristic
123C2×C13#130011yescharacteristic
124C2×C13#130211yescharacteristic
125C2×C13#130711yescharacteristic
126C22×C4C4×Dic1311yescharacteristic
127C22×C4#610111yescharacteristic
128C22×C4#610111yescharacteristic
129C22×C4C4⋊Dic1311yescharacteristic
130C22×C4#610311yescharacteristic
131C22×C4#610311yescharacteristic
132C22×C4C22⋊Dic1311yescharacteristic
133C2×C8—24no—
134C2×C8—42no—
135C2×C8—42no—
136C2×C8—264no—
137C2×C8—522no—
138C2×C8—522no—
139C2×C8—522no—
140C2×C8—522no—
141C2×C8—522no—
142C42—21no—
143C42—22no—
144C42—22no—
145C42—22no—
146C42—21no—
147C42—41no—
148C42—41no—
149C42—41no—
150C13#704311yescharacteristic, complemented, Sylow
151C23#8807111yescharacteristic
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4#8804512yes—
170C2×C4#8806212yes—
171C2×C4#8806311yescharacteristic
172C2×C4#8806411yescharacteristic
173C2×C4#8807712yes—
174C8—44no—
175C8—524no—
176C8—1042no—
177C22#1171811511yescharacteristic
178C22#1171812411yescharacteristic
179C22#1171812511yescharacteristic
180C22#1171814611yescharacteristic
181C22#1171814811yescharacteristic
182C22#1171814911yescharacteristic
183C22#1171815011yescharacteristic
184C4—21no—
185C4—21no—
186C4—22no—
187C4—22no—
188C4—22no—
189C4—41no—
190C4—41no—
191C4—41no—
192C2#1311269311yescharacteristic
193C2#1311269911yescharacteristic
194C2#1311270111yescharacteristic
195C2#1311272611yescharacteristic
196C2#1311272911yescharacteristic
197C2#1311273411yescharacteristic
198C2#1311274611yescharacteristic
subgroupG/H
centerC23#88071
commutatorC22×C4×C13C42
FrattiniC43C2×D13
FittingC13×#1745C2
socle, prime radicalC23×C13#95
cosocleC43×C13C22
hypercenter#1745D13
hypocenterC13#7043
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
150. C13#7043semidirect

Maximal subgroups

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

subgroupindex
#131149792
#131146892
C13×#17452
#704313