Finite Group Databasebeta

← #15780306

Subgroups — #15780306

Order 3328.

488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 131 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#13124417C211yesmaximal, characteristic
2C2×#11718102C212yesmaximal, complemented
3#13114874C211yesmaximal, characteristic, complemented
4#13112932C212yesmaximal, complemented
5C22×C13×M32C211yesmaximal, characteristic, complemented
6C23×C8×C13C2211yescharacteristic
7#11719496—21no—
8C2×#88158C2211yescharacteristic
9C2×C13×M32—22no—
10C2×C13×M32—24no—
11C22×C13×C16C2212yes—
12#11718868—21no—
13#11718777C412yes—
14#11718776C412yes—
15#11718775—22no—
16#11718774—21no—
17C2×#88059C2212yes—
18#11718767C2211yescharacteristic
19#11718144—21no—
20#11718102—24no—
21C23×C4×C13D411yescharacteristic
22C2×#6127—21no—
23C22×C8×C13—22no—
24C22×C8×C13—22no—
25C22×C8×C13C2×C412yes—
26C22×C8×C13D411yescharacteristic
27C22×C8×C13D412yes—
28C22×C8×C13C2311yescharacteristic
29#88207—41no—
30#88184—22no—
31#88183—41no—
32C4×C22⋊D13—42no—
33#88180—21no—
34#88178—22no—
35C2×#6099—22no—
36C2×Dic52C2×C411yescharacteristic
37#88158—22no—
38#88158—22no—
39C2×D104C2×C411yescharacteristic
40C2×#6095—21no—
41C13×M32—28no—
42C2×C13×C16—22no—
43C2×C13×C16—22no—
44C2×C13×C16D414yescomplemented
45C22⋊#1055—42no—
46#88061—22no—
47#88059—22no—
48#88059—22no—
49#88058C2×C412yes—
50#88057—21no—
51#88056—22no—
52#13064—131nomaximal, Sylow
53C24×C13SD1611yescharacteristic
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13D812yes—
58C22×C4×C13SD1611yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C2×C22⋊D13—42no—
61C2×C22⋊D13—41no—
62#6127—42no—
63#6127—42no—
64C2×D52—21no—
65C2×C4×D13—41no—
66C2×Dic26—21no—
67C2×C8×C13—22no—
68C2×C8×C13—24no—
69C2×C8×C13—22no—
70C2×C8×C13—22no—
71C2×C8×C13C22⋊C412yes—
72C2×C8×C13C22×C411yescharacteristic
73C2×C8×C13C2×D412yes—
74C2×C8×C13C2×D411yescharacteristic
75C2×C8×C13#4112yes—
76C22⋊Dic13—42no—
77C22⋊Dic13—41no—
78#6103—42no—
79C4⋊Dic13—22no—
80#6101—42no—
81C4×Dic13—41no—
82#6099—42no—
83#6099—42no—
84C2×#1055—42no—
85Dic52—22no—
86D104—22no—
87#6095—41no—
88#6095—41no—
89C13×C16—24no—
90C22×M32D1311yescharacteristic, complemented
91#3050—131no—
92C2×#359—132no—
93#1810—131no—
94#1382—132no—
95C23×C13—22no—
96C23×C13—42no—
97C23×C13#10212yes—
98C23×C13C2×SD1611yescharacteristic
99C22×D13—41no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—24no—
104C2×C4×C13#10212yes—
105C2×C4×C13C2×C22⋊C411yescharacteristic
106C2×C4×C13#12112yes—
107C2×C4×C13C2×D811yescharacteristic
108C2×C4×C13#13512yes—
109C22⋊D13—84no—
110C22⋊D13—82no—
111C2×Dic13—42no—
112C2×Dic13—41no—
113D52—41no—
114D52—41no—
115C4×D13—82no—
116Dic26—41no—
117Dic26—41no—
118C8×C13—22no—
119C8×C13C4×D412yes—
120C8×C13#12011yescharacteristic
121C8×C13#12311yescharacteristic
122#1055—82no—
123C2×#135—131no—
124C23×C8C2×D1311yescharacteristic
125#525—261no—
126C2×M32—22no—
127C2×M32—24no—
128C22×C16C2×D1312yes—
129#467—132no—
130#466—132no—
131#465—262no—
132C2×#108—132no—
133#427—131no—
134#416—261no—
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×C13C2×#10211yescharacteristic
144C22×C13#46512yes—
145C2×D13—82no—
146C2×D13—81no—
147C4×C13—22no—
148C4×C13#38611yescharacteristic
149C4×C13#41611yescharacteristic
150C4×C13#46612yes—
151Dic13—82no—
152Dic13—81no—
153C2×#41—261no—
154C23×C4D5211yescharacteristic
155#135—262no—
156#135—262no—
157C2×Q16—131no—
158C2×SD16—261no—
159C2×D8—131no—
160C2×M16—262no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8C4×D1312yes—
164C22×C8D5211yescharacteristic
165C22×C8C22⋊D1312yes—
166C22×C8C22×D1311yescharacteristic
167#123—521no—
168C22⋊Q8—262no—
169#121—262no—
170#120—521no—
171C4×D4—522no—
172#117—261no—
173M32—28no—
174C2×C16—22no—
175C2×C16—22no—
176C2×C16C22⋊D1314yescomplemented
177#108—262no—
178#108—262no—
179#107—132no—
180#106—261no—
181#103—262no—
182#102—262no—
183C22⋊C8—522no—
184C2×C13—22no—
185C2×C13—42no—
186C2×C13#189311yescharacteristic
187C2×C13#214312yes—
188D13—161no—
189C24#609511yescharacteristic
190#41—522no—
191#41—522no—
192C2×Q8—261no—
193C2×D4—261no—
194C2×D4—521no—
195C2×D4—522no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—521no—
199C22×C4#609511yescharacteristic
200C22×C4D10412yes—
201C22×C4#610312yes—
202C22×C4C2×D5211yescharacteristic
203Q16—262no—
204SD16—521no—
205SD16—521no—
206D8—262no—
207M16—522no—
208M16—522no—
209C2×C8—22no—
210C2×C8—24no—
211C2×C8—22no—
212C2×C8—22no—
213C2×C8—522no—
214C2×C8#610312yes—
215C2×C8C2×C4×D1311yescharacteristic
216C2×C8#612712yes—
217C2×C8C2×C22⋊D1312yes—
218C2×C8C2×C22⋊D1311yescharacteristic
219C4⋊C4—262no—
220C4⋊C4—522no—
221C22⋊C4—521no—
222C22⋊C4—522no—
223C22⋊C4—522no—
224C42—521no—
225C16—24no—
226C13#1306411yescharacteristic, complemented, Sylow
227C23—22no—
228C23—42no—
229C23—521no—
230C23#8806112yes—
231C23C2×#609511yescharacteristic
232Q8—521no—
233Q8—521no—
234D4—521no—
235D4—521no—
236D4—1044no—
237D4—1042no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—24no—
241C2×C4—22no—
242C2×C4—522no—
243C2×C4—521no—
244C2×C4—1042no—
245C2×C4#8806112yes—
246C2×C4C2×D10411yescharacteristic
247C2×C4#8815812yes—
248C2×C4C2×#610311yescharacteristic
249C2×C4#8818412yes—
250C8—22no—
251C8—1042no—
252C8C4×C22⋊D1312yes—
253C8#8818311yescharacteristic
254C8#8820711yescharacteristic
255C22—22no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—44no—
260C22—1041no—
261C22—1042no—
262C22C2×#8806111yescharacteristic
263C22#1171877512yes—
264C4—22no—
265C4—1041no—
266C4—1042no—
267C4#1171877411yescharacteristic
268C4#1171877612yes—
269C4#1171887411yescharacteristic
270C2—22no—
271C2—42no—
272C2—2081no—
273C2#1311526411yescharacteristic
274C2#1311656512yes—
subgroupG/H
centerC2×C4C2×D104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC22×C13×M32C2
socleC22×C13C2×#102
prime radical#13124417C2
cosocleC22×C8×C13C23
hypercenterC22×M32D13
hypocenterC13#13064
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

Complements

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

NH ≅ G/Ntype
2. C2×#11718102C2semidirect
3. #13114874C2semidirect
4. #13112932C2semidirect
5. C22×C13×M32C2semidirect
44. C2×C13×C16D4semidirect
90. C22×M32D13semidirect
176. C2×C16C22⋊D13semidirect
226. C13#13064semidirect

Maximal subgroups

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

subgroupindex
#131244172
C2×#117181022
#131148742
#131129322
C22×C13×M322
#1306413