Finite Group Databasebeta

← #15750232

Subgroups — #15750232

Order 3328.

338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 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#13115635C211yesmaximal, characteristic
2#13114824C211yesmaximal, characteristic
3C13×#1465C211yesmaximal, characteristic
4C2×C4×D4×C13C2211yescharacteristic
5C13×#407—21no—
6C2×#88074C412yes—
7#11718873—21no—
8C2×C22⋊#1055—21no—
9C2×C22⋊#1055—21no—
10C2×C4⋊#1055C411yescharacteristic, complemented
11C2×#88043C411yescharacteristic, complemented
12C13×#324C412yescomplemented
13C13×#323—21no—
14#11718118—21no—
15C22×D4×C13C2×C411yescharacteristic
16C23×C4×C13D411yescharacteristic
17C23×C4×C13D411yescharacteristic
18C2×C13×M16—41no—
19C4×D4×C13—41no—
20C4×D4×C13—41no—
21C2×C13×C4⋊C4C2×C411yescharacteristic
22C2×C13×C22⋊C4D411yescharacteristic
23C2×C13×C22⋊C4Q811yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×C22⋊Dic13—22no—
26C2×C4⋊Dic13—41no—
27C22×#1055—21no—
28C22×#1055—21no—
29C13×C22⋊C8—22no—
30C13×C22⋊C8—41no—
31#88074—42no—
32#88071—41no—
33C22⋊#1055—42no—
34C22⋊#1055—42no—
35C4⋊#1055—41no—
36#88043—41no—
37#7322—131nomaximal, Sylow
38C24×C13C22⋊C411yescharacteristic
39C24×C13C4⋊C411yescharacteristic
40C2×D4×C13—21no—
41C2×D4×C13—21no—
42C2×D4×C13—41no—
43C2×D4×C13—41no—
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13—41no—
51C22×C4×C13—41no—
52C22×C4×C13C4211yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C4⋊C411yescharacteristic
56C22×C4×C13C4⋊C411yescharacteristic
57C22×Dic13—42no—
58C13×M16—81no—
59C13×M16—81no—
60C2×C8×C13—42no—
61C13×C4⋊C4—41no—
62C13×C22⋊C4—41no—
63C13×C22⋊C4—41no—
64C42×C13—21no—
65C42×C13—21no—
66C22⋊Dic13—42no—
67C22⋊Dic13—42no—
68C4⋊Dic13—81no—
69C4⋊Dic13—81no—
70C2×#1055—22no—
71C2×#1055—41no—
72C2×#1055—41no—
73C2×#1055—41no—
74C2×#1055—41no—
75C2×#1055—41no—
76#1955—131no—
77#1799—131no—
78#1465D1311yescharacteristic
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—21no—
83C23×C13—21no—
84C23×C13—41no—
85C23×C13—41no—
86C23×C13—41no—
87C23×C13—41no—
88C23×C13#9511yescharacteristic
89C23×C13#10011yescharacteristic
90C23×C13#10111yescharacteristic
91D4×C13—42no—
92D4×C13—42no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—81no—
109C2×C4×C13—81no—
110C2×C4×C13#9911yescharacteristic
111C2×C4×C13#9911yescharacteristic
112C2×Dic13—82no—
113C2×Dic13—82no—
114C2×Dic13—82no—
115C8×C13—82no—
116#1055—42no—
117#1055—81no—
118C2×C4×D4C2×D1311yescharacteristic
119C2×C4⋊C8—131no—
120C2×#99—132no—
121#407—21no—
122C2×C22⋊C8—261no—
123C2×C22⋊C8—261no—
124C2×#97—131no—
125#380—261no—
126#342—261no—
127#324Dic1312yescomplemented
128#323—21no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—41no—
134C22×C13—41no—
135C22×C13—42no—
136C22×C13—41no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—81no—
142C22×C13—81no—
143C22×C13#34211yescharacteristic
144C22×C13#34311yescharacteristic
145C22×C13#34411yescharacteristic
146C4×C13—21no—
147C4×C13—41no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13#35311yescharacteristic
152C4×C13#35411yescharacteristic
153Dic13—162no—
154C22×D4C4×D1311yescharacteristic
155C23×C4D5211yescharacteristic
156C23×C4C22⋊D1311yescharacteristic
157C2×M16—41no—
158C22×C8—261no—
159C22×C8—261no—
160C4×D4—41no—
161C4×D4—41no—
162C2×C4⋊C4—521no—
163C2×C4⋊C4C2×Dic1311yescharacteristic
164C2×C22⋊C4—262no—
165C2×C22⋊C4Dic2611yescharacteristic
166C2×C22⋊C4C22⋊D1311yescharacteristic
167C2×C42C4×D1311yescharacteristic
168C4⋊C8—521no—
169#99—522no—
170C22⋊C8—22no—
171C22⋊C8—41no—
172C22⋊C8—522no—
173C22⋊C8—522no—
174#97—521no—
175#95—521no—
176C2×C13—21no—
177C2×C13—21no—
178C2×C13—41no—
179C2×C13—41no—
180C2×C13—81no—
181C2×C13#130511yescharacteristic
182C2×C13#139311yescharacteristic
183C2×C13#139511yescharacteristic
184C24#610111yescharacteristic
185C24#610311yescharacteristic
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4—41no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—522no—
199C22×C4C4×Dic1311yescharacteristic
200C22×C4#610111yescharacteristic
201C22×C4C4⋊Dic1311yescharacteristic
202C22×C4#610311yescharacteristic
203C22×C4C22⋊Dic1311yescharacteristic
204M16—81no—
205M16—81no—
206C2×C8—42no—
207C2×C8—262no—
208C2×C8—521no—
209C2×C8—521no—
210C2×C8—521no—
211C2×C8—521no—
212C2×C8—521no—
213C4⋊C4—41no—
214C4⋊C4—1041no—
215C4⋊C4—1041no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—522no—
219C22⋊C4—522no—
220C42—21no—
221C42—21no—
222C13#732211yescharacteristic, complemented, Sylow
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23—41no—
231C23—41no—
232C23#8806311yescharacteristic
233C23#8806411yescharacteristic
234C23#8807111yescharacteristic
235D4—42no—
236D4—42no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—1042no—
255C2×C4—1042no—
256C2×C4—1042no—
257C2×C4#8804611yescharacteristic
258C2×C4#8804611yescharacteristic
259C8—82no—
260C8—522no—
261C8—1041no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—42no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22—81no—
276C22#1171811911yescharacteristic
277C22#1171814611yescharacteristic
278C22#1171814811yescharacteristic
279C4—21no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—2082no—
285C4#1171806511yescharacteristic
286C4#1171806611yescharacteristic
287C2—21no—
288C2—21no—
289C2—41no—
290C2—41no—
291C2—81no—
292C2#1311274311yescharacteristic
293C2#1311296011yescharacteristic
294C2#1311296611yescharacteristic
subgroupG/H
centerC22#11718119
commutatorC22×C4×C13C42
FrattiniC2×C4×D4C2×D13
FittingC13×#1465C2
socleC22×C13#342
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×D4×C13C22
hypercenter#1465D13
hypocenterC13#7322
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
10. C2×C4⋊#1055C4semidirect
11. C2×#88043C4semidirect
12. C13×#324C4semidirect
127. #324Dic13semidirect
222. C13#7322semidirect

Maximal subgroups

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

subgroupindex
#131156352
#131148242
C13×#14652
#732213