Finite Group Databasebeta

← #15750414

Subgroups — #15750414

Order 3328.

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

normal subgroups only

This group has 258 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#13112957C211yesmaximal, characteristic, complemented
2#13112774C211yesmaximal, characteristic, complemented
3C13×#2018C211yesmaximal, characteristic
4C2×C13×AGL(1,ℤ/8)—21no—
5C22×C13×D8C411yescharacteristic, complemented
6C2×C13×#100—21no—
7C13×#408C2211yescharacteristic
8#11718901—21no—
9C13×#341C411yescharacteristic, complemented
10#11718145—21no—
11C2×C13×#41D411yescharacteristic
12C22×D4×C13—21no—
13C13×AGL(1,ℤ/8)—42no—
14C13×AGL(1,ℤ/8)—42no—
15C2×C13×SD16—41no—
16C2×C13×D8—41no—
17C2×C13×D8—41no—
18C2×C13×D8—42no—
19C2×C13×M16—21no—
20C2×C13×M16D411yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22#88180—41no—
23C13×#100—42no—
24C13×C22⋊C8—41no—
25#88074—22no—
26#88074—41no—
27#88052—41no—
28#7398—131nomaximal, Sylow
29C24×C13—41no—
30C13×#41—41no—
31C13×#41—41no—
32C2×Q8×C13SD1611yescharacteristic
33C2×D4×C13—22no—
34C2×D4×C13—21no—
35C2×D4×C13—41no—
36C2×D4×C13—41no—
37C2×D4×C13—41no—
38C2×D4×C13—41no—
39C2×D4×C13—41no—
40C2×D4×C13D811yescharacteristic
41C22×C4×C13—21no—
42C22×C4×C13C22⋊C411yescharacteristic
43C13×SD16—44no—
44C13×D8—42no—
45C13×D8—42no—
46C13×D8—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—
54C22⋊Dic13—42no—
55C4⋊Dic13—81no—
56C4×Dic13—81no—
57#6090—81no—
58#2018D1311yescharacteristic
59#1391—131no—
60#1321—131no—
61C23×C13—21no—
62C23×C13—42no—
63C23×C13—81no—
64C23×C13—81no—
65C23×C13—162no—
66C23×C13#10411yescharacteristic
67Q8×C13—41no—
68D4×C13—41no—
69D4×C13—42no—
70D4×C13—42no—
71D4×C13—81no—
72D4×C13—81no—
73D4×C13—81no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13#9911yescharacteristic
80C2×C4×C13#10211yescharacteristic
81C2×Dic13—82no—
82C8×C13—42no—
83C8×C13—41no—
84C8×C13—41no—
85C2×AGL(1,ℤ/8)—21no—
86C22×D8Dic1311yescharacteristic, complemented
87C2×#100—21no—
88#410—261no—
89#408C2×D1311yescharacteristic
90#349—261no—
91#341Dic1311yescharacteristic, complemented
92C22×C13—21no—
93C22×C13—41no—
94C22×C13—41no—
95C22×C13—81no—
96C22×C13—82no—
97C22×C13—162no—
98C22×C13—162no—
99C22×C13—162no—
100C22×C13#32711yescharacteristic
101C4×C13—21no—
102C4×C13—41no—
103C4×C13AΣL(1,𝔽16)11yescharacteristic
104C4×C13#35311yescharacteristic
105Dic13—162no—
106C2×#41C22⋊D1311yescharacteristic
107C22×D4—21no—
108AGL(1,ℤ/8)—42no—
109AGL(1,ℤ/8)—42no—
110C2×SD16—41no—
111C2×D8—41no—
112C2×D8—41no—
113C2×D8—42no—
114C2×M16—21no—
115C2×M16C22⋊D1311yescharacteristic
116C22×C8C2×Dic1311yescharacteristic
117#117—521no—
118M32—521no—
119#100—42no—
120#99—262no—
121#99—521no—
122C22⋊C8—41no—
123C2×C13—21no—
124C2×C13—41no—
125C2×C13—81no—
126C2×C13—162no—
127C2×C13#134311yescharacteristic
128C24—41no—
129#41—41no—
130#41—41no—
131C2×Q8#610511yescharacteristic
132C2×D4—22no—
133C2×D4—21no—
134C2×D4—41no—
135C2×D4—41no—
136C2×D4—41no—
137C2×D4—41no—
138C2×D4—41no—
139C2×D4#610411yescharacteristic
140C22×C4—21no—
141C22×C4C22⋊Dic1311yescharacteristic
142SD16—44no—
143D8—42no—
144D8—42no—
145D8—44no—
146M16—22no—
147M16—41no—
148M16—41no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—41no—
152C2×C8—41no—
153C4⋊C4—1041no—
154C22⋊C4—522no—
155C42—1041no—
156C16—1041no—
157C13#739811yescharacteristic, complemented, Sylow
158C23—21no—
159C23—42no—
160C23—81no—
161C23—81no—
162C23—162no—
163C23#8807711yescharacteristic
164Q8—41no—
165D4—41no—
166D4—42no—
167D4—42no—
168D4—81no—
169D4—81no—
170D4—81no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—1042no—
177C2×C4#8807211yescharacteristic
178C2×C4#8807411yescharacteristic
179C8—42no—
180C8—41no—
181C8—41no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—81no—
186C22—82no—
187C22—162no—
188C22—162no—
189C22—162no—
190C22#1171812911yescharacteristic
191C4—21no—
192C4—41no—
193C4—2082no—
194C4#1171812811yescharacteristic
195C4#1171813711yescharacteristic
196C2—21no—
197C2—41no—
198C2—81no—
199C2—162no—
200C2#1311283311yescharacteristic
subgroupG/H
centerC2#13112833
commutatorC22×C8×C13C2×C4
Frattini#408C2×D13
Fitting, prime radicalC13×#2018C2
socleC2×C13#1343
cosocleC13×#408C22
hypercenter#2018D13
hypocenterC13#7398
LCSG ▷ C22×C8×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #2018

Complements

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

NH ≅ G/Ntype
1. #13112957C2semidirect
2. #13112774C2semidirect
5. C22×C13×D8C4semidirect
9. C13×#341C4semidirect
86. C22×D8Dic13semidirect
91. #341Dic13semidirect
157. C13#7398semidirect

Maximal subgroups

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

subgroupindex
#131129572
#131127742
C13×#20182
#739813