Finite Group Databasebeta

← #15749565

Subgroups — #15749565

Order 3328.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#13112760C211yesmaximal, characteristic
2#13112760C211yesmaximal, characteristic
3C13×#1851C211yesmaximal, characteristic
4C22×C13×M16C411yescharacteristic
5C2×C13×C4⋊C8—21no—
6C2×C13×C22⋊C8C2211yescharacteristic
7C4×C13×C22⋊C4C411yescharacteristic
8C13×#336—21no—
9C22⋊#6090—21no—
10C22⋊#6090—21no—
11C23×C4×C13C2×C411yescharacteristic
12C2×C13×M16—42no—
13C2×C13×M16—41no—
14C22×C8×C13—21no—
15C22×C8×C13D411yescharacteristic
16C22×C8×C13D411yescharacteristic
17C2×C13×C22⋊C4—21no—
18C2×C42×C13—21no—
19C13×C4⋊C8—42no—
20C13×C22⋊C8—41no—
21C13×#95C811yescharacteristic
22C13×#95C811yescharacteristic
23C2×#6090—41no—
24C2×#6090—41no—
25#7067—131nomaximal, Sylow
26C24×C13M1611yescharacteristic
27C22×C4×C13—21no—
28C22×C4×C13—21no—
29C22×C4×C13—21no—
30C22×C4×C13—21no—
31C22×C4×C13—41no—
32C22×C4×C13—41no—
33C22×C4×C13C22⋊C411yescharacteristic
34C22×C4×C13C2×C811yescharacteristic
35C13×M16—42no—
36C13×M16—42no—
37C2×C8×C13—22no—
38C2×C8×C13—21no—
39C2×C8×C13—21no—
40C2×C8×C13—41no—
41C2×C8×C13—41no—
42C2×C8×C13—41no—
43C2×C8×C13—41no—
44C13×C22⋊C4—42no—
45C42×C13—41no—
46C42×C13—41no—
47#6090—81no—
48#6090—81no—
49#1851D1311yescharacteristic
50#1314—131no—
51#1314—131no—
52C23×C13—21no—
53C23×C13—21no—
54C23×C13—21no—
55C23×C13—41no—
56C23×C13—41no—
57C23×C13C22⋊C811yescharacteristic
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—22no—
61C2×C4×C13—21no—
62C2×C4×C13—42no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13—41no—
69C2×C4×C13—41no—
70C2×C4×C13—41no—
71C2×C4×C13#9911yescharacteristic
72C2×C4×C13#10111yescharacteristic
73C8×C13—41no—
74C8×C13—42no—
75C8×C13—41no—
76C22×M16Dic1311yescharacteristic
77C2×C4⋊C8—21no—
78C2×C22⋊C8C2×D1311yescharacteristic
79C4×C22⋊C4Dic1311yescharacteristic
80C22⋊C16—261no—
81C22⋊C16—261no—
82#336—21no—
83C22×C13—21no—
84C22×C13—21no—
85C22×C13—41no—
86C22×C13—41no—
87C22×C13—41no—
88C22×C13—81no—
89C22×C13—81no—
90C22×C13#32411yescharacteristic
91C22×C13#35011yescharacteristic
92C22×C13#35011yescharacteristic
93C4×C13—21no—
94C4×C13—42no—
95C4×C13—41no—
96C4×C13—81no—
97C4×C13AΣL(1,𝔽16)11yescharacteristic
98C4×C13#35211yescharacteristic
99C23×C4C2×Dic1311yescharacteristic
100C2×M16—42no—
101C2×M16—41no—
102C22×C8—21no—
103C22×C8C22⋊D1311yescharacteristic
104C22×C8C22⋊D1311yescharacteristic
105C2×C22⋊C4—21no—
106C2×C42—21no—
107C2×C16—521no—
108C2×C16—521no—
109C4⋊C8—42no—
110C22⋊C8—41no—
111#95#105511yescharacteristic
112#95#105511yescharacteristic
113C2×C13—21no—
114C2×C13—21no—
115C2×C13—81no—
116C2×C13#132311yescharacteristic
117C2×C13#132611yescharacteristic
118C2×C13#132711yescharacteristic
119C24#609911yescharacteristic
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—41no—
125C22×C4—41no—
126C22×C4C2×#105511yescharacteristic
127C22×C4C22⋊Dic1311yescharacteristic
128M16—42no—
129M16—42no—
130C2×C8—22no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—41no—
134C2×C8—41no—
135C2×C8—41no—
136C2×C8—41no—
137C22⋊C4—42no—
138C42—41no—
139C42—41no—
140C16—1041no—
141C16—1041no—
142C13#706711yescharacteristic, complemented, Sylow
143C23—21no—
144C23—21no—
145C23—21no—
146C23—41no—
147C23—41no—
148C23C22⋊#105511yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4#8807411yescharacteristic
163C2×C4#8807611yescharacteristic
164C8—41no—
165C8—42no—
166C8—41no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—81no—
173C22—81no—
174C22#1171812011yescharacteristic
175C22#1171815311yescharacteristic
176C22#1171815311yescharacteristic
177C4—21no—
178C4—42no—
179C4—41no—
180C4—81no—
181C4#1171812811yescharacteristic
182C4#1171813111yescharacteristic
183C2—21no—
184C2—21no—
185C2—81no—
186C2#1311277811yescharacteristic
187C2#1311278411yescharacteristic
188C2#1311278711yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC22×C4×C13C2×C8
FrattiniC2×C22⋊C8C2×D13
FittingC13×#1851C2
socleC22×C13#324
prime radicalC24×C13M16
cosocleC2×C13×C22⋊C8C22
hypercenter#1851D13
hypocenterC13#7067
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #1851

Complements

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

NH ≅ G/Ntype
142. C13#7067semidirect

Maximal subgroups

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

subgroupindex
#131127602
C13×#18512
#706713