Finite Group Databasebeta

← #15750423

Subgroups — #15750423

Order 3328.

234 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 39 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#13112959C211yesmaximal, characteristic
2#13112774C211yesmaximal, characteristic
3C13×#2020C211yesmaximal, characteristic
4C2×C13×#137—21no—
5C22×C13×Q16C411yescharacteristic
6C2×C13×#101—21no—
7C13×#408C2211yescharacteristic
8#11718898—21no—
9C13×#341C411yescharacteristic
10#11718145—21no—
11C2×C13×#41D411yescharacteristic
12C22×Q8×C13—21no—
13C13×#137—42no—
14C13×#137—42no—
15C2×C13×Q16—41no—
16C2×C13×Q16—41no—
17C2×C13×Q16—42no—
18C2×C13×SD16—41no—
19C2×C13×M16—21no—
20C2×C13×M16D411yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22C2×#6099—41no—
23C13×#101—42no—
24C13×C22⋊C8—41no—
25#88076—41no—
26#88073—22no—
27#88052—41no—
28#7401—131nomaximal, Sylow
29C13×#41—41no—
30C13×#41—41no—
31C2×Q8×C13—22no—
32C2×Q8×C13—41no—
33C2×Q8×C13—41no—
34C2×Q8×C13—41no—
35C2×Q8×C13—41no—
36C2×Q8×C13—41no—
37C2×Q8×C13D811yescharacteristic
38C2×D4×C13—21no—
39C2×D4×C13SD1611yescharacteristic
40C22×C4×C13—21no—
41C22×C4×C13—41no—
42C22×C4×C13C22⋊C411yescharacteristic
43C13×Q16—42no—
44C13×Q16—42no—
45C13×Q16—44no—
46C13×SD16—44no—
47C13×M16—22no—
48C13×M16—41no—
49C13×M16—41no—
50C2×C8×C13—21no—
51C2×C8×C13—21no—
52C2×C8×C13—41no—
53C2×C8×C13—41no—
54#6099—42no—
55#6099—81no—
56C2×#1055—81no—
57#6090—81no—
58#2020D1311yescharacteristic
59#1392—131no—
60#1321—131no—
61C23×C13—21no—
62C23×C13#10411yescharacteristic
63Q8×C13—41no—
64Q8×C13—42no—
65Q8×C13—42no—
66Q8×C13—81no—
67Q8×C13—81no—
68D4×C13—41no—
69D4×C13—81no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—41no—
74C2×C4×C13—41no—
75C2×C4×C13—42no—
76C2×C4×C13—81no—
77C2×C4×C13—81no—
78C2×C4×C13#9911yescharacteristic
79C2×C4×C13#10211yescharacteristic
80C8×C13—42no—
81C8×C13—41no—
82C8×C13—41no—
83#1055—82no—
84C2×#137—21no—
85C22×Q16Dic1311yescharacteristic
86#413—261no—
87C2×#101—21no—
88#408C2×D1311yescharacteristic
89#349—261no—
90#341Dic1311yescharacteristic
91C22×C13—21no—
92C22×C13—41no—
93C22×C13—41no—
94C22×C13—81no—
95C22×C13#32711yescharacteristic
96C4×C13—21no—
97C4×C13—41no—
98C4×C13—82no—
99C4×C13AΣL(1,𝔽16)11yescharacteristic
100C4×C13#35311yescharacteristic
101C2×#41C22⋊D1311yescharacteristic
102C22×Q8—21no—
103#137—42no—
104#137—42no—
105C2×Q16—41no—
106C2×Q16—41no—
107C2×Q16—42no—
108C2×SD16—41no—
109C2×M16—21no—
110C2×M16—521no—
111C2×M16C22⋊D1311yescharacteristic
112C22×C8C2×Dic1311yescharacteristic
113M32—521no—
114#101—42no—
115#101—521no—
116#100—262no—
117C22⋊C8—41no—
118C2×C13—21no—
119C2×C13—41no—
120C2×C13—81no—
121C2×C13#134311yescharacteristic
122#41—41no—
123#41—41no—
124C2×Q8—22no—
125C2×Q8—41no—
126C2×Q8—41no—
127C2×Q8—41no—
128C2×Q8—41no—
129C2×Q8—41no—
130C2×Q8#610411yescharacteristic
131C2×D4—21no—
132C2×D4#610511yescharacteristic
133C22×C4—21no—
134C22×C4—41no—
135C22×C4C22⋊Dic1311yescharacteristic
136Q16—42no—
137Q16—42no—
138Q16—44no—
139SD16—44no—
140M16—22no—
141M16—41no—
142M16—41no—
143M16—522no—
144M16—1041no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—41no—
148C2×C8—41no—
149C2×C8—1041no—
150C16—1041no—
151C13#740111yescharacteristic, complemented, Sylow
152C23—21no—
153C23#8807711yescharacteristic
154Q8—41no—
155Q8—42no—
156Q8—42no—
157Q8—81no—
158Q8—81no—
159D4—41no—
160D4—81no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4#8807211yescharacteristic
170C2×C4#8807411yescharacteristic
171C8—42no—
172C8—41no—
173C8—41no—
174C8—1042no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—81no—
179C22#1171812911yescharacteristic
180C4—21no—
181C4—41no—
182C4—82no—
183C4#1171812811yescharacteristic
184C4#1171813711yescharacteristic
185C2—21no—
186C2—41no—
187C2—81no—
188C2#1311283311yescharacteristic
subgroupG/H
centerC2#13112833
commutatorC22×C8×C13C2×C4
Frattini#408C2×D13
FittingC13×#2020C2
socleC2×C13#1343
prime radicalC2×C13×#41D4
cosocleC13×#408C22
hypercenter#2020D13
hypocenterC13#7401
LCSG ▷ C22×C8×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #2020

Complements

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

NH ≅ G/Ntype
151. C13#7401semidirect

Maximal subgroups

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

subgroupindex
#131129592
#131127742
C13×#20202
#740113