Finite Group Databasebeta

← #15780307

Subgroups — #15780307

Order 3328.

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

normal subgroups only

This group has 488 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
1C22×#88052C211yesmaximal, characteristic, complemented
2C2×#11718159C212yesmaximal, complemented
3#13114874C211yesmaximal, characteristic, complemented
4#13112931C212yesmaximal, complemented
5C13×#3050C211yesmaximal, characteristic
6C2×C13×#135C2211yescharacteristic
7C23×C8×C13C2211yescharacteristic
8C13×#525—21no—
9C13×#467C412yes—
10C13×#466C412yes—
11C13×#465—22no—
12C13×#427C2211yescharacteristic
13C13×#416—21no—
14#11718868—21no—
15C2×#88059C2212yes—
16C2×#88052—24no—
17C2×#88052—22no—
18C22×#6090C2212yes—
19#11718159—24no—
20#11718144—21no—
21C2×C13×#41—21no—
22C23×C4×C13D411yescharacteristic
23C13×#135—22no—
24C13×#135—22no—
25C2×C13×Q16C2×C411yescharacteristic
26C2×C13×SD16—21no—
27C2×C13×D8C2×C411yescharacteristic
28C22×C8×C13—22no—
29C22×C8×C13—22no—
30C22×C8×C13C2×C412yes—
31C22×C8×C13D411yescharacteristic
32C22×C8×C13D412yes—
33C22×C8×C13C2311yescharacteristic
34C13×#123—41no—
35C13×C22⋊Q8—22no—
36C13×#121—22no—
37C13×#120—41no—
38C4×D4×C13—42no—
39C13×#117—21no—
40C2×#6099—22no—
41C13×#107C2×C412yes—
42C13×#106—21no—
43C13×#103—22no—
44C13×#102—22no—
45C22⋊#1055—42no—
46#88059—22no—
47#88059—22no—
48#88052—28no—
49C2×#6090—22no—
50C2×#6090—22no—
51C2×#6090D414yescomplemented
52#13064—131nomaximal, Sylow
53C24×C13SD1611yescharacteristic
54C13×#41—42no—
55C13×#41—42no—
56C2×Q8×C13—21no—
57C2×D4×C13—21no—
58C2×D4×C13—42no—
59C2×D4×C13—41no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—41no—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13D812yes—
65C22×C4×C13SD1611yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C13×Q16—22no—
68C13×SD16—41no—
69C13×SD16—41no—
70C13×D8—22no—
71C2×C8×C13—22no—
72C2×C8×C13—24no—
73C2×C8×C13—22no—
74C2×C8×C13—22no—
75C2×C8×C13C22⋊C412yes—
76C2×C8×C13C22×C411yescharacteristic
77C2×C8×C13C2×D412yes—
78C2×C8×C13C2×D411yescharacteristic
79C2×C8×C13#4112yes—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—42no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C42×C13—41no—
86#6099—42no—
87#6099—42no—
88C2×#1055—42no—
89#6090—24no—
90C22×M32—131no—
91#3050D1311yescharacteristic
92C2×#359—132no—
93#1810—131no—
94#1382—132no—
95C23×C13—22no—
96C23×C13—42no—
97C23×C13—41no—
98C23×C13#10212yes—
99C23×C13C2×SD1611yescharacteristic
100Q8×C13—41no—
101Q8×C13—41no—
102D4×C13—41no—
103D4×C13—41no—
104D4×C13—84no—
105D4×C13—82no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—24no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—82no—
113C2×C4×C13#10212yes—
114C2×C4×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13#12112yes—
116C2×C4×C13C2×D811yescharacteristic
117C2×C4×C13#13512yes—
118C8×C13—22no—
119C8×C13C4×D412yes—
120C8×C13#12011yescharacteristic
121C8×C13#12311yescharacteristic
122#1055—82no—
123C2×#135C2×D1311yescharacteristic
124C23×C8C2×D1311yescharacteristic
125#525—21no—
126C2×M32—264no—
127C2×M32—262no—
128C22×C16—132no—
129#467Dic1312yes—
130#466Dic1312yes—
131#465—22no—
132C2×#108—132no—
133#427C2×D1311yescharacteristic
134#416—21no—
135#407—261no—
136#359—264no—
137#341—261no—
138C22×C13—22no—
139C22×C13—22no—
140C22×C13—22no—
141C22×C13—22no—
142C22×C13—44no—
143C22×C13—82no—
144C22×C13—81no—
145C22×C13C2×#10211yescharacteristic
146C22×C13#46512yes—
147C4×C13—22no—
148C4×C13—82no—
149C4×C13—81no—
150C4×C13#38611yescharacteristic
151C4×C13#41611yescharacteristic
152C4×C13#46612yes—
153C2×#41—21no—
154C23×C4C22⋊D1311yescharacteristic
155#135—22no—
156#135—22no—
157C2×Q16C2×Dic1311yescharacteristic
158C2×SD16—21no—
159C2×D8C2×Dic1311yescharacteristic
160C2×M16—262no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8C2×Dic1312yes—
164C22×C8C22⋊D1311yescharacteristic
165C22×C8C22⋊D1312yes—
166C22×C8C22×D1311yescharacteristic
167#123—41no—
168C22⋊Q8—22no—
169#121—22no—
170#120—41no—
171C4×D4—42no—
172#117—21no—
173M32—268no—
174C2×C16—134no—
175C2×C16—262no—
176C2×C16—262no—
177#108—262no—
178#108—262no—
179#107C2×Dic1312yes—
180#106—21no—
181#103—22no—
182#102—22no—
183C22⋊C8—522no—
184C2×C13—22no—
185C2×C13—42no—
186C2×C13—161no—
187C2×C13#189311yescharacteristic
188C2×C13#214312yes—
189C24#610511yescharacteristic
190#41—42no—
191#41—42no—
192C2×Q8—21no—
193C2×D4—21no—
194C2×D4—42no—
195C2×D4—41no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—41no—
199C22×C4#610412yes—
200C22×C4#610511yescharacteristic
201C22×C4C22⋊Dic1312yes—
202C22×C4C2×C22⋊D1311yescharacteristic
203Q16—22no—
204SD16—41no—
205SD16—41no—
206D8—22no—
207M16—522no—
208M16—522no—
209C2×C8—22no—
210C2×C8—24no—
211C2×C8—22no—
212C2×C8—22no—
213C2×C8—522no—
214C2×C8C22⋊Dic1312yes—
215C2×C8D4×D1312yes—
216C2×C8#612912yes—
217C2×C8C22×Dic1311yescharacteristic
218C2×C8C2×C22⋊D1311yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—41no—
223C22⋊C4—42no—
224C42—41no—
225C16—264no—
226C13#1306411yescharacteristic, complemented, Sylow
227C23—22no—
228C23—42no—
229C23—41no—
230C23#8807212yes—
231C23C2×#610511yescharacteristic
232Q8—41no—
233Q8—41no—
234D4—41no—
235D4—41no—
236D4—84no—
237D4—82no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—82no—
245C2×C4#8807212yes—
246C2×C4C2×#610411yescharacteristic
247C2×C4#8819312yes—
248C2×C4#8820412yes—
249C2×C4C2×C22⋊Dic1311yescharacteristic
250C8—22no—
251C8—1042no—
252C8D4×Dic1312yes—
253C8#8818911yescharacteristic
254C8#8819111yescharacteristic
255C22—22no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—44no—
260C22—81no—
261C22—82no—
262C22#1171870212yes—
263C22C2×#8807211yescharacteristic
264C4—22no—
265C4—81no—
266C4—82no—
267C4#1171869912yes—
268C4#1171888111yescharacteristic
269C4#1171889411yescharacteristic
270C2—22no—
271C2—42no—
272C2—161no—
273C2#1311526511yescharacteristic
274C2#1311656412yes—
subgroupG/H
centerC2×C4C2×#6104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC13×#3050C2
socleC22×C13C2×#102
cosocleC22×C8×C13C23
hypercenter#3050D13
hypocenterC13#13064
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C22×#88052C2semidirect
2. C2×#11718159C2semidirect
3. #13114874C2semidirect
4. #13112931C2semidirect
51. C2×#6090D4semidirect
226. C13#13064semidirect

Maximal subgroups

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

subgroupindex
C22×#880522
C2×#117181592
#131148742
#131129312
C13×#30502
#1306413