Finite Group Databasebeta

← #15750405

Subgroups — #15750405

Order 3328.

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

normal subgroups only

This group has 284 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#13112766C211yesmaximal, characteristic, complemented
2#13112744C211yesmaximal, characteristic, complemented
3C13×#2022C211yesmaximal, characteristic
4C13×#534C411yescharacteristic
5C2×C13×#123—21no—
6C2×C13×#99—21no—
7C13×#381C2211yescharacteristic
8#11718868—21no—
9C13×#342C411yescharacteristic
10#11718117—21no—
11C22×D4×C13—21no—
12C23×C4×C13D411yescharacteristic
13C13×#123—42no—
14C13×#123—41no—
15C13×#123—41no—
16C13×#123—41no—
17C13×#121—41no—
18C13×#120—41no—
19C2×C13×C4⋊C4—41no—
20C2×C13×C22⋊C4—21no—
21C2×C13×C22⋊C4—41no—
22C2×C13×C22⋊C4C2×C411yescharacteristic
23C2×C13×C22⋊C4D411yescharacteristic
24C2×#6099—41no—
25C13×#99—42no—
26C13×#95—41no—
27C22⋊#1055—22no—
28C22⋊#1055—41no—
29C22⋊#1055—41no—
30#7395—131nomaximal, Sylow
31C24×C13—21no—
32C24×C13C22⋊C411yescharacteristic
33C2×D4×C13—41no—
34C2×D4×C13—41no—
35C2×D4×C13—41no—
36C2×D4×C13—41no—
37C2×D4×C13—41no—
38C2×D4×C13—41no—
39C2×D4×C13—41no—
40C22×C4×C13—21no—
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13—41no—
46C22×C4×C13—41no—
47C22×C4×C13—41no—
48C22×C4×C13D811yescharacteristic
49C22×C4×C13SD1611yescharacteristic
50C13×C4⋊C4—41no—
51C13×C4⋊C4—42no—
52C13×C4⋊C4—42no—
53C13×C22⋊C4—22no—
54C13×C22⋊C4—42no—
55C13×C22⋊C4—42no—
56C13×C22⋊C4—42no—
57C13×C22⋊C4—41no—
58C13×C22⋊C4—41no—
59C13×C22⋊C4—41no—
60#6099—81no—
61#6099—81no—
62C2×#1055—42no—
63C2×#1055—81no—
64#2022D1311yescharacteristic
65#1317—131no—
66#1306—131no—
67C23×C13—21no—
68C23×C13—21no—
69C23×C13—41no—
70C23×C13—41no—
71C23×C13—41no—
72C23×C13—81no—
73C23×C13—82no—
74C23×C13#9911yescharacteristic
75C23×C13#10211yescharacteristic
76C23×C13#10411yescharacteristic
77D4×C13—81no—
78D4×C13—81no—
79D4×C13—81no—
80D4×C13—81no—
81D4×C13—161no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13—42no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—81no—
95C2×C4×C13—82no—
96C2×C4×C13—81no—
97C2×C4×C13—81no—
98#1055—82no—
99#1055—161no—
100#534Dic1311yescharacteristic
101C2×#123—21no—
102C2×#99—21no—
103#407—261no—
104#381C2×D1311yescharacteristic
105#342Dic1311yescharacteristic
106#323—261no—
107C22×C13—21no—
108C22×C13—21no—
109C22×C13—41no—
110C22×C13—41no—
111C22×C13—41no—
112C22×C13—42no—
113C22×C13—81no—
114C22×C13—82no—
115C22×C13—82no—
116C22×C13—81no—
117C22×C13—161no—
118C22×C13#32711yescharacteristic
119C22×C13AΣL(1,𝔽16)11yescharacteristic
120C22×C13#35311yescharacteristic
121C4×C13—41no—
122C4×C13—41no—
123C4×C13—81no—
124C4×C13—81no—
125C4×C13—82no—
126C4×C13—81no—
127C22×D4—21no—
128C23×C4C22⋊D1311yescharacteristic
129C2×M16—521no—
130#123—42no—
131#123—41no—
132#123—41no—
133#123—41no—
134#121—41no—
135#120—41no—
136C2×C4⋊C4—41no—
137C2×C22⋊C4—21no—
138C2×C22⋊C4—41no—
139C2×C22⋊C4C2×Dic1311yescharacteristic
140C2×C22⋊C4C22⋊D1311yescharacteristic
141#99—42no—
142C22⋊C8—262no—
143C22⋊C8—521no—
144C22⋊C8—521no—
145#95—41no—
146C2×C13—21no—
147C2×C13—21no—
148C2×C13—21no—
149C2×C13—41no—
150C2×C13—41no—
151C2×C13—161no—
152C2×C13#134311yescharacteristic
153C24—21no—
154C24C22⋊Dic1311yescharacteristic
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4#610411yescharacteristic
171C22×C4#610511yescharacteristic
172M16—1041no—
173M16—1041no—
174C2×C8—522no—
175C2×C8—1041no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C22⋊C4—22no—
180C22⋊C4—42no—
181C22⋊C4—42no—
182C22⋊C4—42no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C13#739511yescharacteristic, complemented, Sylow
187C23—21no—
188C23—21no—
189C23—41no—
190C23—41no—
191C23—41no—
192C23—81no—
193C23—82no—
194C23#8807211yescharacteristic
195C23#8807411yescharacteristic
196C23#8807711yescharacteristic
197D4—81no—
198D4—81no—
199D4—81no—
200D4—81no—
201D4—161no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4—81no—
217C2×C4—81no—
218C8—1042no—
219C8—2081no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22—82no—
228C22—82no—
229C22—81no—
230C22—161no—
231C22#1171812811yescharacteristic
232C22#1171812911yescharacteristic
233C22#1171813711yescharacteristic
234C4—41no—
235C4—41no—
236C4—81no—
237C4—81no—
238C4—82no—
239C4—81no—
240C2—21no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2—161no—
246C2#1311283311yescharacteristic
subgroupG/H
centerC2#13112833
commutatorC2×C13×C22⋊C4C2×C4
Frattini#381C2×D13
FittingC13×#2022C2
socleC2×C13#1343
prime radicalC13×#534C4
cosocleC13×#381C22
hypercenter#2022D13
hypocenterC13#7395
LCSG ▷ C2×C13×C22⋊C4 ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #13112766C2semidirect
2. #13112744C2semidirect
186. C13#7395semidirect

Maximal subgroups

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

subgroupindex
#131127662
#131127442
C13×#20222
#739513