Finite Group Databasebeta

← #15758685

Subgroups — #15758685

Order 3328.

586 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 135 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×#11718598C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic
3C2×#11718130C212yesmaximal
4#13112714C212yesmaximal
5C13×#2855C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2211yescharacteristic
7C22×C42×C13C2211yescharacteristic
8C13×#391C412yescomplemented
9C13×#389C412yescomplemented
10C13×#387—22no—
11C13×#385—21no—
12C13×#381—21no—
13C13×#380C2211yescharacteristic
14C2×#88071—21no—
15C2×#88071—21no—
16C2×#88071C2212yes—
17C2×C22⋊#1055C2212yes—
18#11718598—24no—
19#11718130—24no—
20#11718116—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C23×Dic13—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C42×C13—22no—
35C2×C42×C13—22no—
36C2×C42×C13C2×C412yes—
37C2×C42×C13D412yes—
38C22×#1055—22no—
39C13×#95—22no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95—21no—
43#88071—24no—
44#88071—24no—
45#88071—22no—
46#88071D414yes—
47C22⋊#1055—22no—
48C22⋊#1055—22no—
49#9153—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C2×Q8×C13—22no—
52C2×Q8×C13—42no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22⋊C412yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13#4112yes—
70C22×Dic13—24no—
71C22×Dic13—44no—
72C22×Dic13—44no—
73C22×Dic13—42no—
74C22×Dic13—42no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—44no—
78C13×C4⋊C4—42no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—42no—
82C42×C13—24no—
83C42×C13—24no—
84C2×#1055—44no—
85C2×#1055—42no—
86#2855D1311yescharacteristic
87C2×#383—131no—
88#1817—131no—
89C2×#328—132no—
90#1294—132no—
91C23×C13—22no—
92C23×C13—22no—
93C23×C13C2×C22⋊C411yescharacteristic
94C23×C13#12011yescharacteristic
95C23×C13#12311yescharacteristic
96C23×C13#13512yes—
97C23×C13#13712yes—
98Q8×C13—82no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13C4×D412yes—
121C2×C4×C13#12112yes—
122C2×Dic13—44no—
123C2×Dic13—44no—
124C2×Dic13—44no—
125C2×Dic13—84no—
126C2×Dic13—84no—
127#1055—82no—
128C2×C22⋊Q8C2×D1311yescharacteristic
129C22×C42C2×D1311yescharacteristic
130C2×C22⋊C8—132no—
131#391Dic1312yescomplemented
132#389Dic1312yescomplemented
133#387—22no—
134#385—21no—
135#383—264no—
136#381—21no—
137#380C2×D1311yescharacteristic
138C2×#95—132no—
139C2×#95—261no—
140C2×#95—261no—
141#336—262no—
142#328—264no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—24no—
148C22×C13—24no—
149C22×C13#38611yescharacteristic
150C22×C13#41012yes—
151C22×C13#41611yescharacteristic
152C22×C13#41911yescharacteristic
153C22×C13#42112yes—
154C22×C13#45212yes—
155C22×C13#48512yes—
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—42no—
159C4×C13—42no—
160C4×C13—81no—
161C4×C13—81no—
162C4×C13—82no—
163Dic13—84no—
164C22×Q8C2×Dic1311yescharacteristic
165C23×C4—262no—
166C23×C4C22⋊D1311yescharacteristic
167C23×C4C22⋊D1311yescharacteristic
168C23×C4C22×D1311yescharacteristic
169C22×C8—262no—
170C22⋊Q8—22no—
171C22⋊Q8—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×Dic1311yescharacteristic
175C2×C4⋊C4C2×Dic1312yes—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C42—22no—
179C2×C42—22no—
180C2×C42C2×Dic1312yes—
181C2×C42C22⋊D1312yes—
182C22⋊C8—262no—
183C22⋊C8—262no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—21no—
188#95—134no—
189#95—264no—
190#95—264no—
191#95—262no—
192C2×C13—22no—
193C2×C13—22no—
194C2×C13#151512yes—
195C2×C13#152112yes—
196C2×C13#187311yescharacteristic
197C2×C13#189711yescharacteristic
198C2×C13#189911yescharacteristic
199C24C2×C22⋊D1311yescharacteristic
200C2×Q8—22no—
201C2×Q8—42no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—264no—
214C22×C4—524no—
215C22×C4—524no—
216C22×C4—522no—
217C22×C4—522no—
218C22×C4C22⋊Dic1312yes—
219C22×C4C22⋊Dic1312yes—
220C22×C4D4×D1312yes—
221C22×C4#612912yes—
222C22×C4C22×Dic1311yescharacteristic
223C22×C4C2×C22⋊D1311yescharacteristic
224C2×C8—524no—
225C2×C8—522no—
226C4⋊C4—22no—
227C4⋊C4—42no—
228C4⋊C4—44no—
229C4⋊C4—42no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—42no—
233C42—24no—
234C42—24no—
235C13#915311yescharacteristic, complemented, Sylow
236C23—22no—
237C23—22no—
238C23#8818911yescharacteristic
239C23#8819111yescharacteristic
240C23#8819612yes—
241C23#8820412yes—
242C23C2×C22⋊Dic1311yescharacteristic
243Q8—82no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—524no—
266C2×C4—524no—
267C2×C4—524no—
268C2×C4—1044no—
269C2×C4—1044no—
270C2×C4D4×Dic1312yes—
271C2×C4#8819312yes—
272C8—1042no—
273C22—24no—
274C22—24no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22#1171870612yes—
280C22#1171870812yes—
281C22#1171888111yescharacteristic
282C22#1171888611yescharacteristic
283C22#1171889411yescharacteristic
284C22#1171889712yes—
285C22#1171890112yes—
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—82no—
291C4—81no—
292C4—81no—
293C4—1044no—
294C2—22no—
295C2—22no—
296C2#1311338712yes—
297C2#1311341312yes—
298C2#1311514911yescharacteristic
299C2#1311528511yescharacteristic
300C2#1311529511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2855C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2855D13
hypocenterC13#9153
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
8. C13×#391C4semidirect
9. C13×#389C4semidirect
131. #391Dic13semidirect
132. #389Dic13semidirect
235. C13#9153semidirect

Maximal subgroups

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

subgroupindex
C2×#117185982
#131149042
C2×#117181302
#131127142
C13×#28552
#915313