Finite Group Databasebeta

← #15750498

Subgroups — #15750498

Order 3328.

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

normal subgroups only

This group has 332 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#13112764C211yesmaximal, characteristic
2#13112740C211yesmaximal, characteristic
3C13×#2029C211yesmaximal, characteristic
4C13×#543C411yescharacteristic, complemented
5C13×#379—21no—
6C13×#379C2211yescharacteristic
7#11718908—21no—
8C13×#342—21no—
9C13×#342C411yescharacteristic, complemented
10#11718117—21no—
11C25×C13D411yescharacteristic
12C13×C22⋊Q8—42no—
13C13×C22⋊Q8—41no—
14C2×C13×C22⋊C4—21no—
15C2×C13×C22⋊C4—21no—
16C2×C13×C22⋊C4—41no—
17C2×C13×C22⋊C4—42no—
18C2×C13×C22⋊C4C2×C411yescharacteristic
19C2×C13×C22⋊C4D411yescharacteristic
20C2×C22⋊Dic13—22no—
21C2×C22⋊Dic13—41no—
22C2×C22⋊Dic13—41no—
23C22⋊#1055—41no—
24#7426—131nomaximal, Sylow
25C24×C13—21no—
26C24×C13—21no—
27C24×C13—41no—
28C24×C13—41no—
29C24×C13—82no—
30C24×C13C22⋊C411yescharacteristic
31C24×C13SD1611yescharacteristic
32C24×C13Q1611yescharacteristic
33C2×Q8×C13—41no—
34C22×C4×C13—22no—
35C22×C4×C13—21no—
36C22×C4×C13—21no—
37C22×C4×C13—41no—
38C22×Dic13—42no—
39C13×C4⋊C4—42no—
40C13×C4⋊C4—41no—
41C13×C22⋊C4—41no—
42C13×C22⋊C4—41no—
43C13×C22⋊C4—41no—
44C13×C22⋊C4—41no—
45C13×C22⋊C4—41no—
46C13×C22⋊C4—41no—
47C13×C22⋊C4—82no—
48C13×C22⋊C4—84no—
49C22⋊Dic13—82no—
50C22⋊Dic13—81no—
51C22⋊Dic13—81no—
52C22⋊Dic13—82no—
53C2×#1055—81no—
54#2029D1311yescharacteristic
55#1316—131no—
56#1304—131no—
57C23×C13—21no—
58C23×C13—21no—
59C23×C13—21no—
60C23×C13—21no—
61C23×C13—42no—
62C23×C13—41no—
63C23×C13—41no—
64C23×C13—42no—
65C23×C13—42no—
66C23×C13—44no—
67C23×C13—41no—
68C23×C13—41no—
69C23×C13—81no—
70C23×C13—81no—
71C23×C13—81no—
72C23×C13—81no—
73C23×C13—81no—
74C23×C13—82no—
75C23×C13—82no—
76C23×C13—82no—
77C23×C13#9911yescharacteristic
78C23×C13#10311yescharacteristic
79C23×C13#10411yescharacteristic
80Q8×C13—161no—
81C2×C4×C13—42no—
82C2×C4×C13—41no—
83C2×C4×C13—41no—
84C2×C4×C13—81no—
85C2×C4×C13—81no—
86C2×C4×C13—82no—
87C2×C4×C13—81no—
88C2×C4×C13—82no—
89C2×Dic13—82no—
90C2×Dic13—82no—
91C2×Dic13—82no—
92#1055—161no—
93#543Dic1311yescharacteristic, complemented
94#379—21no—
95#379—261no—
96#379C2×D1311yescharacteristic
97#342—21no—
98#342Dic1311yescharacteristic, complemented
99#323—261no—
100C22×C13—22no—
101C22×C13—21no—
102C22×C13—21no—
103C22×C13—41no—
104C22×C13—41no—
105C22×C13—41no—
106C22×C13—41no—
107C22×C13—42no—
108C22×C13—41no—
109C22×C13—41no—
110C22×C13—42no—
111C22×C13—41no—
112C22×C13—42no—
113C22×C13—41no—
114C22×C13—81no—
115C22×C13—82no—
116C22×C13—82no—
117C22×C13—81no—
118C22×C13—84no—
119C22×C13—81no—
120C22×C13#32811yescharacteristic
121C22×C13AΣL(1,𝔽16)11yescharacteristic
122C22×C13#35411yescharacteristic
123C4×C13—81no—
124C4×C13—82no—
125C4×C13—81no—
126C4×C13—161no—
127Dic13—162no—
128C25C22⋊D1311yescharacteristic
129C22⋊Q8—42no—
130C22⋊Q8—41no—
131C2×C22⋊C4—21no—
132C2×C22⋊C4—21no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—42no—
135C2×C22⋊C4—262no—
136C2×C22⋊C4—521no—
137C2×C22⋊C4—521no—
138C2×C22⋊C4C2×Dic1311yescharacteristic
139C2×C22⋊C4C22⋊D1311yescharacteristic
140C22⋊C8—521no—
141C2×C13—21no—
142C2×C13—21no—
143C2×C13—21no—
144C2×C13—42no—
145C2×C13—41no—
146C2×C13—41no—
147C2×C13—81no—
148C2×C13#135111yescharacteristic
149C24—21no—
150C24—21no—
151C24—41no—
152C24—41no—
153C24—82no—
154C24#610611yescharacteristic
155C24#610711yescharacteristic
156C24C22⋊Dic1311yescharacteristic
157C2×Q8—41no—
158C22×C4—22no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—41no—
162C22×C4—522no—
163C2×C8—1041no—
164C4⋊C4—42no—
165C4⋊C4—41no—
166C22⋊C4—41no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—41no—
170C22⋊C4—41no—
171C22⋊C4—41no—
172C22⋊C4—82no—
173C22⋊C4—84no—
174C22⋊C4—1042no—
175C22⋊C4—1041no—
176C22⋊C4—1041no—
177C22⋊C4—1042no—
178C13#742611yescharacteristic, complemented, Sylow
179C23—21no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23—42no—
184C23—41no—
185C23—41no—
186C23—42no—
187C23—42no—
188C23—44no—
189C23—41no—
190C23—41no—
191C23—81no—
192C23—81no—
193C23—81no—
194C23—81no—
195C23—81no—
196C23—82no—
197C23—82no—
198C23—82no—
199C23#8807411yescharacteristic
200C23#8807511yescharacteristic
201C23#8807711yescharacteristic
202Q8—161no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—81no—
207C2×C4—81no—
208C2×C4—82no—
209C2×C4—81no—
210C2×C4—82no—
211C2×C4—1042no—
212C2×C4—1042no—
213C2×C4—1042no—
214C8—2081no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—41no—
227C22—42no—
228C22—41no—
229C22—81no—
230C22—82no—
231C22—82no—
232C22—81no—
233C22—84no—
234C22—81no—
235C22#1171812811yescharacteristic
236C22#1171813011yescharacteristic
237C22#1171813311yescharacteristic
238C4—81no—
239C4—82no—
240C4—81no—
241C4—161no—
242C4—2082no—
243C2—21no—
244C2—21no—
245C2—21no—
246C2—41no—
247C2—42no—
248C2—41no—
249C2—81no—
250C2#1311285711yescharacteristic
subgroupG/H
centerC2#13112857
commutatorC2×C13×C22⋊C4C2×C4
Frattini#379C2×D13
FittingC13×#2029C2
socleC2×C13#1351
prime radicalC25×C13D4
cosocleC13×#379C22
hypercenter#2029D13
hypocenterC13#7426
LCSG ▷ C2×C13×C22⋊C4 ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #379 ◁ #2029

Complements

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

NH ≅ G/Ntype
4. C13×#543C4semidirect
9. C13×#342C4semidirect
93. #543Dic13semidirect
98. #342Dic13semidirect
178. C13#7426semidirect

Maximal subgroups

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

subgroupindex
#131127642
#131127402
C13×#20292
#742613