Finite Group Databasebeta

← #15772205

Subgroups — #15772205

Order 3328.

524 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 119 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#13113154C212yesmaximal, complemented
2#13112780C212yesmaximal, complemented
3#13112768C212yesmaximal, complemented
4C13×#2328C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×C4×D4×C13C411yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#390C411yescharacteristic
9C13×#390C2211yescharacteristic
10C13×#386—22no—
11C13×#386—22no—
12C13×#382C2211yescharacteristic
13C13×#376C411yescharacteristic
14C2×C22⋊#1055—22no—
15#11718120C2214yes—
16#11718117—22no—
17C22×D4×C13—22no—
18C22×D4×C13C2×C411yescharacteristic
19C22×D4×C13C2×C411yescharacteristic
20C23×C4×C13—21no—
21C23×C4×C13D412yes—
22C13×#127—22no—
23C13×#127C814yescomplemented
24C4×D4×C13—42no—
25C4×D4×C13—42no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2311yescharacteristic
28C2×C13×C22⋊C4—21no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4D412yes—
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C22×#1055—42no—
36C13×#95—21no—
37C13×#95—21no—
38C13×#95—22no—
39C22⋊#1055—24no—
40C22⋊#1055—42no—
41#11479—131nomaximal, Sylow
42C24×C13—21no—
43C24×C13C22⋊C412yes—
44C2×D4×C13—28no—
45C2×D4×C13—21no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13—82no—
51C2×D4×C13—82no—
52C2×D4×C13C2×C812yes—
53C2×D4×C13C2×C812yescomplemented
54C2×D4×C13M1612yes—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—42no—
61C22×C4×C13—82no—
62C22×C4×C13—82no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D412yes—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C22⋊C4—42no—
70C13×C22⋊C4—42no—
71C13×C22⋊C4—82no—
72C13×C22⋊C4—82no—
73C42×C13—22no—
74C42×C13—21no—
75C42×C13—41no—
76C42×C13C2×C812yescomplemented
77C2×#1055—44no—
78C2×#1055—84no—
79#2328D1311yescharacteristic
80#1459—132no—
81#1324—132no—
82#1318—132no—
83C23×C13—22no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13—42no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13—42no—
90C23×C13—41no—
91C23×C13—41no—
92C23×C13C22⋊C814yes—
93C23×C13C2×C22⋊C411yescharacteristic
94D4×C13—42no—
95D4×C13—42no—
96D4×C13—42no—
97D4×C13—42no—
98D4×C13—88no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—44no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—82no—
116C2×C4×C13—84no—
117C2×C4×C13#9912yes—
118C2×C4×C13C22×C811yescharacteristic
119C2×C4×C13C2×M1611yescharacteristic
120#1055—84no—
121C2×#127Dic1311yescharacteristic
122C2×C4×D4Dic1311yescharacteristic
123C2×C4×D4C2×D1311yescharacteristic
124C2×C22⋊C8—262no—
125#390Dic1311yescharacteristic
126#390C2×D1311yescharacteristic
127#386—22no—
128#386—22no—
129#382C2×D1311yescharacteristic
130#376Dic1311yescharacteristic
131#324—134no—
132#323—262no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—24no—
136C22×C13—44no—
137C22×C13—44no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13—42no—
141C22×C13—82no—
142C22×C13—82no—
143C22×C13—81no—
144C22×C13—81no—
145C22×C13C2×C22⋊C811yescharacteristic
146C22×C13C2×#9911yescharacteristic
147C22×C13#41311yescharacteristic
148C4×C13—22no—
149C4×C13—21no—
150C4×C13—21no—
151C4×C13—42no—
152C4×C13—42no—
153C4×C13—41no—
154C4×C13—81no—
155C4×C13—81no—
156C22×D4—22no—
157C22×D4C2×Dic1311yescharacteristic
158C22×D4C2×Dic1311yescharacteristic
159C23×C4—21no—
160C23×C4C22⋊D1312yes—
161C22×C8—522no—
162#127—22no—
163#127#105514yescomplemented
164C4×D4—42no—
165C4×D4—42no—
166C2×C4⋊C4C2×Dic1311yescharacteristic
167C2×C4⋊C4C22×D1311yescharacteristic
168C2×C22⋊C4—21no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4C22⋊D1312yes—
172C2×C42C2×Dic1311yescharacteristic
173C2×C42C2×Dic1311yescharacteristic
174C2×C42C2×Dic1311yescharacteristic
175C22⋊C8—264no—
176C22⋊C8—522no—
177#95—21no—
178#95—21no—
179#95—22no—
180C2×C13—21no—
181C2×C13—21no—
182C2×C13—44no—
183C2×C13—82no—
184C2×C13#145911yescharacteristic
185C2×C13#212711yescharacteristic
186C2×C13#213411yescharacteristic
187C24—21no—
188C24C22⋊Dic1312yes—
189C2×D4—28no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—82no—
196C2×D4—82no—
197C2×D4C2×#105512yes—
198C2×D4C2×#105512yescomplemented
199C2×D4#609912yes—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—42no—
206C22×C4—82no—
207C22×C4—82no—
208C22×C4C22⋊Dic1311yescharacteristic
209C22×C4C22⋊Dic1311yescharacteristic
210C22×C4C22×Dic1311yescharacteristic
211C22×C4C2×C22⋊D1312yes—
212C2×C8—524no—
213C2×C8—1044no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—82no—
219C22⋊C4—82no—
220C42—22no—
221C42—21no—
222C42—41no—
223C42C2×#105512yescomplemented
224C13#1147911yescharacteristic, complemented, Sylow
225C23—22no—
226C23—22no—
227C23—22no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—41no—
233C23—41no—
234C23C22⋊#105514yes—
235C23C2×C22⋊Dic1311yescharacteristic
236D4—42no—
237D4—42no—
238D4—42no—
239D4—42no—
240D4—88no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—44no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—84no—
259C2×C4#8807412yes—
260C2×C4C22×#105511yescharacteristic
261C2×C4C2×#609911yescharacteristic
262C8—1044no—
263C22—21no—
264C22—21no—
265C22—24no—
266C22—44no—
267C22—44no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—82no—
272C22—82no—
273C22—81no—
274C22—81no—
275C22C2×C22⋊#105511yescharacteristic
276C22C2×#8807411yescharacteristic
277C22#1171889811yescharacteristic
278C4—21no—
279C4—21no—
280C4—22no—
281C4—42no—
282C4—42no—
283C4—41no—
284C4—81no—
285C4—81no—
286C2—21no—
287C2—21no—
288C2—44no—
289C2—82no—
290C2#1311315411yescharacteristic
291C2#1311650511yescharacteristic
292C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2328C2
socleC22×C13C2×#99
prime radicalC2×C13×#127C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2328D13
hypocenterC13#11479
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2328

Complements

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

NH ≅ G/Ntype
1. #13113154C2semidirect
2. #13112780C2semidirect
3. #13112768C2semidirect
23. C13×#127C8semidirect
53. C2×D4×C13C2×C8semidirect
76. C42×C13C2×C8semidirect
163. #127#1055semidirect
198. C2×D4C2×#1055semidirect
223. C42C2×#1055semidirect
224. C13#11479semidirect

Maximal subgroups

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

subgroupindex
#131131542
#131127802
#131127682
C13×#23282
#1147913