Finite Group Databasebeta

← #15772189

Subgroups — #15772189

Order 3328.

616 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 123 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#13112782C212yesmaximal, complemented
3#13112768C212yesmaximal, complemented
4C4×C13×#127C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×C4×D4×C13—22no—
7C2×C4×D4×C13C411yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C13×#390—22no—
10C13×#390C411yescharacteristic
11C13×#390C2211yescharacteristic
12C13×#384C2211yescharacteristic
13C43×C13C411yescharacteristic
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—41no—
25C4×D4×C13—41no—
26C4×D4×C13—48no—
27C4×D4×C13—41no—
28C4×D4×C13—41no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4D412yes—
36C2×C42×C13—21no—
37C2×C42×C13—21no—
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C22×#1055—42no—
42C22⋊#1055—24no—
43C22⋊#1055—42no—
44#11475—131nomaximal, Sylow
45C24×C13—21no—
46C24×C13C22⋊C412yes—
47C2×D4×C13—28no—
48C2×D4×C13—21no—
49C2×D4×C13—41no—
50C2×D4×C13—41no—
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13—44no—
54C2×D4×C13—44no—
55C2×D4×C13C2×C812yes—
56C2×D4×C13C2×C812yescomplemented
57C2×D4×C13M1612yes—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—44no—
64C22×C4×C13—44no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D412yes—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—44no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—44no—
76C13×C22⋊C4—44no—
77C13×C22⋊C4—42no—
78C42×C13—24no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—41no—
83C42×C13—42no—
84C42×C13C2×C812yescomplemented
85C2×#1055—44no—
86C2×#1055—84no—
87C4×#127D1311yescharacteristic
88#1459—132no—
89#1325—132no—
90#1318—132no—
91C23×C13—22no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13C22⋊C814yes—
101C23×C13C2×C22⋊C411yescharacteristic
102D4×C13—42no—
103D4×C13—42no—
104D4×C13—416no—
105D4×C13—42no—
106D4×C13—42no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—44no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—82no—
124C2×C4×C13—82no—
125C2×C4×C13—82no—
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13#9911yescharacteristic
128C2×C4×C13C22×C811yescharacteristic
129C2×C4×C13C2×M1611yescharacteristic
130#1055—84no—
131C2×#127Dic1311yescharacteristic
132C2×C4×D4—22no—
133C2×C4×D4Dic1311yescharacteristic
134C2×C4×D4C2×D1311yescharacteristic
135C2×C22⋊C8—262no—
136#390—22no—
137#390Dic1311yescharacteristic
138#390C2×D1311yescharacteristic
139#384C2×D1311yescharacteristic
140C43Dic1311yescharacteristic
141#324—134no—
142#323—262no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—24no—
146C22×C13—44no—
147C22×C13—44no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—42no—
151C22×C13—82no—
152C22×C13—82no—
153C22×C13—81no—
154C22×C13—81no—
155C22×C13C2×C22⋊C811yescharacteristic
156C22×C13C2×#9911yescharacteristic
157C22×C13#41311yescharacteristic
158C4×C13—24no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—42no—
163C4×C13—42no—
164C4×C13—41no—
165C4×C13—81no—
166C4×C13#35312yes—
167C22×D4—22no—
168C22×D4C2×Dic1311yescharacteristic
169C22×D4C2×Dic1311yescharacteristic
170C23×C4—21no—
171C23×C4C22⋊D1312yes—
172C22×C8—522no—
173#127—22no—
174#127#105514yescomplemented
175C4×D4—41no—
176C4×D4—41no—
177C4×D4—48no—
178C4×D4—41no—
179C4×D4—41no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4C2×Dic1311yescharacteristic
182C2×C4⋊C4C22×D1311yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4C22⋊D1312yes—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42C2×Dic1311yescharacteristic
190C2×C42C2×Dic1311yescharacteristic
191C2×C42C2×Dic1311yescharacteristic
192C22⋊C8—264no—
193C22⋊C8—522no—
194C2×C13—21no—
195C2×C13—21no—
196C2×C13—44no—
197C2×C13—82no—
198C2×C13#145911yescharacteristic
199C2×C13C2×#35311yescharacteristic
200C2×C13#213211yescharacteristic
201C24—21no—
202C24C22⋊Dic1312yes—
203C2×D4—28no—
204C2×D4—21no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—44no—
210C2×D4—44no—
211C2×D4C2×#105512yes—
212C2×D4C2×#105512yescomplemented
213C2×D4#609912yes—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—44no—
220C22×C4—44no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4C22⋊Dic1311yescharacteristic
224C22×C4C22⋊Dic1311yescharacteristic
225C22×C4C22×Dic1311yescharacteristic
226C22×C4C2×C22⋊D1312yes—
227C2×C8—524no—
228C2×C8—1044no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—44no—
232C22⋊C4—42no—
233C22⋊C4—44no—
234C22⋊C4—44no—
235C22⋊C4—42no—
236C42—24no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—41no—
241C42—42no—
242C42C2×#105512yescomplemented
243C13#1147511yescharacteristic, complemented, Sylow
244C23—22no—
245C23—22no—
246C23—22no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—41no—
252C23—41no—
253C23C22⋊#105514yes—
254C23C2×C22⋊Dic1311yescharacteristic
255D4—42no—
256D4—42no—
257D4—42no—
258D4—416no—
259D4—42no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—44no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4#8807411yescharacteristic
280C2×C4#8807411yescharacteristic
281C2×C4C22×#105511yescharacteristic
282C2×C4C2×#609911yescharacteristic
283C8—1044no—
284C22—21no—
285C22—21no—
286C22—24no—
287C22—44no—
288C22—44no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—82no—
293C22—82no—
294C22—81no—
295C22—81no—
296C22C2×C22⋊#105511yescharacteristic
297C22C2×#8807411yescharacteristic
298C22#1171889811yescharacteristic
299C4—24no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—42no—
305C4—41no—
306C4—81no—
307C4#1171813712yes—
308C2—21no—
309C2—21no—
310C2—44no—
311C2—82no—
312C2#1311315411yescharacteristic
313C2C2×#1171813711yescharacteristic
314C2#1311652111yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC4×C13×#127C2
socleC22×C13C2×#99
prime radicalC2×C13×#127C4
cosocleC2×C13×C4⋊C4C23
hypercenterC4×#127D13
hypocenterC13#11475
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#127

Complements

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

NH ≅ G/Ntype
1. #13113154C2semidirect
2. #13112782C2semidirect
3. #13112768C2semidirect
23. C13×#127C8semidirect
56. C2×D4×C13C2×C8semidirect
84. C42×C13C2×C8semidirect
174. #127#1055semidirect
212. C2×D4C2×#1055semidirect
242. C42C2×#1055semidirect
243. C13#11475semidirect

Maximal subgroups

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

subgroupindex
#131131542
#131127822
#131127682
C4×C13×#1272
#1147513