Finite Group Databasebeta

← #15751034

Subgroups — #15751034

Order 3328.

492 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 143 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#13114953C212yesmaximal, complemented
2#13112662C212yesmaximal, complemented
3#13112657C212yesmaximal
4C4×C13×#124C211yesmaximal, characteristic
5C2×C13×#124C411yescharacteristic
6C2×C4×Q8×C13C411yescharacteristic
7C2×C4×D4×C13C411yescharacteristic
8C13×#391C2211yescharacteristic
9C13×#390C2211yescharacteristic
10C13×#388—22no—
11C13×#382C411yescharacteristic
12C4×C13×C22⋊C4—22no—
13C43×C13C2211yescharacteristic
14C2×C4⋊#1055—22no—
15#11718116—22no—
16#11718116C2214yes—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C23×C4×C13—21no—
20C13×#124—22no—
21C13×#124C814yescomplemented
22C4×Q8×C13—42no—
23C4×D4×C13—42no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—21no—
29C2×C13×C22⋊C4—22no—
30C2×C42×C13—21no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D412yes—
34C2×C42×C13D412yes—
35C2×C42×C13C2311yescharacteristic
36C22×#1055—24no—
37C13×#95—22no—
38C13×#95—22no—
39C4⋊#1055—44no—
40#7601—131nomaximal, Sylow
41C24×C13—21no—
42C2×Q8×C13—21no—
43C2×Q8×C13—41no—
44C2×Q8×C13—41no—
45C2×Q8×C13C2×C812yes—
46C2×D4×C13—21no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13C2×C812yes—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—44no—
54C22×C4×C13—42no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D412yes—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—42no—
63C13×C22⋊C4—28no—
64C13×C22⋊C4—42no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—42no—
67C42×C13—22no—
68C42×C13—22no—
69C42×C13—22no—
70C42×C13—42no—
71C42×C13—41no—
72C42×C13—42no—
73C42×C13C2×C812yes—
74C42×C13M1612yes—
75C2×#1055—44no—
76C2×#1055—44no—
77C2×#1055—44no—
78C4×#124D1311yescharacteristic
79#1831—132no—
80#1272—132no—
81#1270—132no—
82C23×C13—22no—
83C23×C13—41no—
84C23×C13—41no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13C2×C22⋊C411yescharacteristic
88Q8×C13—42no—
89Q8×C13—42no—
90D4×C13—42no—
91D4×C13—42no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—84no—
109C2×C4×C13C22⋊C814yes—
110C2×C4×C13#10012yes—
111C2×C4×C13C22×C811yescharacteristic
112C2×C4×C13C2×M1611yescharacteristic
113C2×C4×C13AGL(1,ℤ/8)12yes—
114C2×C4×C13#13712yes—
115#1055—84no—
116C2×#124Dic1311yescharacteristic
117C2×C4×Q8Dic1311yescharacteristic
118C2×C4×D4Dic1311yescharacteristic
119C2×C4⋊C8—262no—
120#391C2×D1311yescharacteristic
121#390C2×D1311yescharacteristic
122#388—22no—
123#382Dic1311yescharacteristic
124C4×C22⋊C4—22no—
125C43C2×D1311yescharacteristic
126#336—134no—
127#336—262no—
128C22×C13—42no—
129C22×C13—44no—
130C22×C13—81no—
131C22×C13—82no—
132C22×C13—81no—
133C22×C13C2×C22⋊C811yescharacteristic
134C22×C13#41011yescharacteristic
135C22×C13C2×#10011yescharacteristic
136C22×C13#41712yes—
137C22×C13#42112yes—
138C4×C13—21no—
139C4×C13—21no—
140C4×C13—24no—
141C4×C13—22no—
142C4×C13—22no—
143C4×C13—22no—
144C4×C13—41no—
145C4×C13—42no—
146C4×C13—81no—
147C4×C13—81no—
148C22×Q8C2×Dic1311yescharacteristic
149C22×D4C2×Dic1311yescharacteristic
150C23×C4—21no—
151C22×C8—264no—
152#124—22no—
153#124#105514yescomplemented
154C4×Q8—42no—
155C4×D4—42no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×Dic1311yescharacteristic
158C2×C4⋊C4C2×Dic1311yescharacteristic
159C2×C22⋊C4—22no—
160C2×C22⋊C4—21no—
161C2×C22⋊C4—22no—
162C2×C42—21no—
163C2×C42C2×Dic1311yescharacteristic
164C2×C42C2×Dic1311yescharacteristic
165C2×C42C22⋊D1312yes—
166C2×C42C22⋊D1312yes—
167C2×C42C22×D1311yescharacteristic
168C4⋊C8—524no—
169#95—22no—
170#95—22no—
171C2×C13—82no—
172C2×C13#146011yescharacteristic
173C2×C13#147712yes—
174C2×C13#151212yes—
175C2×C13#153311yescharacteristic
176C2×C13#156011yescharacteristic
177C24—21no—
178C2×Q8—21no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8C2×#105512yes—
182C2×D4—21no—
183C2×D4—41no—
184C2×D4—41no—
185C2×D4C2×#105512yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—44no—
190C22×C4—42no—
191C22×C4C22⋊Dic1311yescharacteristic
192C22×C4C22⋊Dic1312yes—
193C22×C4C22⋊Dic1311yescharacteristic
194C22×C4C22×Dic1311yescharacteristic
195C22×C4C2×C22⋊D1312yes—
196C2×C8—524no—
197C2×C8—524no—
198C2×C8—524no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C22⋊C4—28no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C42—22no—
207C42—22no—
208C42—22no—
209C42—42no—
210C42—41no—
211C42—42no—
212C42C2×#105512yes—
213C42#609912yes—
214C13#760111yescharacteristic, complemented, Sylow
215C23—22no—
216C23—41no—
217C23—42no—
218C23—42no—
219C23—41no—
220C23C2×C22⋊Dic1311yescharacteristic
221Q8—42no—
222Q8—42no—
223D4—42no—
224D4—42no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—84no—
242C2×C4C22⋊#105514yes—
243C2×C4#8807312yes—
244C2×C4C22×#105511yescharacteristic
245C2×C4C2×#609911yescharacteristic
246C2×C4#8820312yes—
247C2×C4#8820512yes—
248C8—1044no—
249C22—42no—
250C22—44no—
251C22—82no—
252C22—81no—
253C22—81no—
254C22C2×C22⋊#105511yescharacteristic
255C22C2×#8807311yescharacteristic
256C22#1171889312yes—
257C22#1171889712yes—
258C22#1171890111yescharacteristic
259C4—22no—
260C4—22no—
261C4—21no—
262C4—21no—
263C4—22no—
264C4—24no—
265C4—42no—
266C4—41no—
267C4—81no—
268C4—81no—
269C2—82no—
270C2#1311315711yescharacteristic
271C2#1311322312yes—
272C2#1311337412yes—
273C2#1311346011yescharacteristic
274C2#1311357111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC4×C13×#124C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenterC4×#124D13
hypocenterC13#7601
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #13114953C2semidirect
2. #13112662C2semidirect
21. C13×#124C8semidirect
153. #124#1055semidirect
214. C13#7601semidirect

Maximal subgroups

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

subgroupindex
#131149532
#131126622
#131126572
C4×C13×#1242
#760113