Finite Group Databasebeta

← #15765261

Subgroups — #15765261

Order 3328.

712 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#11718669C212yesmaximal, complemented
2#13115637C211yesmaximal, characteristic, complemented
3C2×D4⋊#1055C212yesmaximal, complemented
4#13112719C211yesmaximal, characteristic, complemented
5C13×#2537C211yesmaximal, characteristic
6C2×C13×#121—22no—
7C2×C4×D4×C13C2212yes—
8C2×#88123C2211yescharacteristic
9C13×#394—22no—
10C13×#384C2211yescharacteristic
11C13×#380—22no—
12C2×#88072—22no—
13#11718669—24no—
14#11718669—24no—
15C2×#88050—22no—
16C2×#88048—22no—
17C2×C4⋊#1055C2212yes—
18C2×C4×#1055C2211yescharacteristic
19D4⋊#1055—24no—
20C22×D4×C13—22no—
21C22×D4×C13D412yes—
22C23×C4×C13—22no—
23C22×Dic26—21no—
24C13×#121—44no—
25C13×#121—44no—
26C4×D4×C13—22no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4D412yes—
32C2×C13×C4⋊C4D412yes—
33C2×C13×C22⋊C4—24no—
34C2×C13×C22⋊C4—22no—
35C2×C42×C13C2311yescharacteristic
36C2×C4⋊Dic13—22no—
37C22×#1055—21no—
38C22×#1055—22no—
39#88123—22no—
40#88123—21no—
41#88123D412yescomplemented
42C13×#95—22no—
43#88072—28no—
44#88050—44no—
45#88048—28no—
46C4⋊#1055—22no—
47C4⋊#1055D414yescomplemented
48C4×#1055—22no—
49#10235—131nomaximal, Sylow
50C24×C13—22no—
51C2×D4×C13—22no—
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13—48no—
57C2×D4×C13—82no—
58C2×D4×C13SD1614yes—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D412yes—
69C22×Dic13—41no—
70C2×Dic26—22no—
71C2×Dic26—42no—
72C2×Dic26—42no—
73C2×Dic26—41no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C22⋊C4—48no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—42no—
82C42×C13C2×D411yescharacteristic
83C42×C13C2×D412yes—
84C42×C13#4111yescharacteristic
85C4⋊Dic13—24no—
86C4⋊Dic13—42no—
87C2×#1055—22no—
88C2×#1055—24no—
89C2×#1055—41no—
90C2×#1055—41no—
91C2×#1055—42no—
92C2×#1055—42no—
93C2×#476—132no—
94#2537D1311yescharacteristic
95#1956—131no—
96C2×D4⋊C8—132no—
97#1296—131no—
98C23×C13—24no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13#12011yescharacteristic
106D4×C13—24no—
107D4×C13—24no—
108D4×C13—42no—
109D4×C13—42no—
110D4×C13—88no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—44no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—82no—
119C2×C4×C13—82no—
120C2×C4×C13—82no—
121C2×C4×C13—82no—
122C2×C4×C13#12012yes—
123C2×C4×C13#12111yescharacteristic
124C2×C4×C13#12112yes—
125C2×C4×C13#12711yescharacteristic
126C2×C4×C13C2×SD1612yes—
127C2×C4×C13#13512yes—
128C2×C4×C13AGL(1,ℤ/8)12yes—
129C2×C4×C13#13712yes—
130C2×Dic13—42no—
131C2×Dic13—81no—
132C2×Dic13—81no—
133Dic26—44no—
134Dic26—82no—
135#1055—42no—
136#1055—44no—
137C2×C4⋊Q8—131no—
138C2×#121—22no—
139C2×C4×D4C2×D1312yes—
140#476—264no—
141#476—264no—
142C2×#106—262no—
143C2×C4⋊C8—132no—
144C2×#103—262no—
145C2×#102—262no—
146C2×C4×C8—131no—
147#394—22no—
148#384C2×D1311yescharacteristic
149#380—22no—
150D4⋊C8—264no—
151C22×C13—44no—
152C22×C13—44no—
153C22×C13—44no—
154C22×C13—82no—
155C22×C13—82no—
156C22×C13—82no—
157C22×C13—82no—
158C22×C13#39211yescharacteristic
159C22×C13#45012yes—
160C22×C13#45212yes—
161C22×C13#45311yescharacteristic
162C22×C13#45411yescharacteristic
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—82no—
166C4×C13—82no—
167C4×C13#44812yes—
168C4×C13#44912yes—
169C4×C13#46512yes—
170C4×C13#46812yes—
171Dic13—82no—
172C22×Q8—261no—
173C22×D4—22no—
174C22×D4C22⋊D1312yes—
175C23×C4—22no—
176C22×C8—261no—
177C22×C8—262no—
178C4⋊Q8—132no—
179C4⋊Q8—262no—
180C4⋊Q8—261no—
181#121—44no—
182#121—44no—
183C4×D4—22no—
184C4×D4—22no—
185C4×D4—22no—
186C4×D4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4C22⋊D1312yes—
190C2×C4⋊C4C22⋊D1312yes—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—22no—
193C2×C42C22×D1311yescharacteristic
194#106—268no—
195C4⋊C8—134no—
196C4⋊C8—262no—
197#103—524no—
198#102—268no—
199C4×C8—262no—
200#95—22no—
201C2×C13—84no—
202C2×C13#162911yescharacteristic
203C2×C13#163411yescharacteristic
204C2×C13#163512yes—
205C2×C13#200012yes—
206C2×C13#200611yescharacteristic
207C24—22no—
208C2×Q8—262no—
209C2×Q8—522no—
210C2×Q8—522no—
211C2×Q8—521no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—48no—
218C2×D4—82no—
219C2×D4#610514yes—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—521no—
229C22×C4C2×C22⋊D1311yescharacteristic
230C22×C4C2×C22⋊D1312yes—
231C2×C8—262no—
232C2×C8—264no—
233C2×C8—521no—
234C2×C8—522no—
235C2×C8—521no—
236C2×C8—522no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—264no—
243C4⋊C4—522no—
244C22⋊C4—48no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C42D4×D1311yescharacteristic
248C42D4×D1312yes—
249C42#612911yescharacteristic
250C13#1023511yescharacteristic, complemented, Sylow
251C23—24no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23#8820711yescharacteristic
259Q8—524no—
260Q8—1042no—
261D4—24no—
262D4—24no—
263D4—42no—
264D4—42no—
265D4—88no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—44no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—82no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—522no—
278C2×C4—1041no—
279C2×C4—1041no—
280C2×C4#8818612yes—
281C2×C4C2×#610512yes—
282C2×C4#8819112yes—
283C2×C4#8819211yescharacteristic
284C2×C4#8819312yes—
285C2×C4#8819411yescharacteristic
286C2×C4#8820412yes—
287C2×C4#8820512yes—
288C8—522no—
289C8—524no—
290C22—44no—
291C22—44no—
292C22—44no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22#1171887912yes—
298C22#1171888411yescharacteristic
299C22#1171890012yes—
300C22#1171890211yescharacteristic
301C22#1171890611yescharacteristic
302C4—21no—
303C4—21no—
304C4—82no—
305C4—82no—
306C4—1042no—
307C4#1171869812yes—
308C4#1171870112yes—
309C4#1171870212yes—
310C4#1171870312yes—
311C2—84no—
312C2#1311395211yescharacteristic
313C2#1311398111yescharacteristic
314C2#1311398712yes—
315C2#1311583912yes—
316C2#1311587811yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2537C2
socleC23×C13#120
hypercenter#2537D13
hypocenterC13#10235
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#11718669C2semidirect
2. #13115637C2semidirect
3. C2×D4⋊#1055C2semidirect
4. #13112719C2semidirect
41. #88123D4semidirect
47. C4⋊#1055D4semidirect
250. C13#10235semidirect

Maximal subgroups

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

subgroupindex
C2×#117186692
#131156372
C2×D4⋊#10552
#131127192
C13×#25372
#1023513