Finite Group Databasebeta

← #15760648

Subgroups — #15760648

Order 3328.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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#13119310C211yesmaximal, characteristic
2#13114916C211yesmaximal, characteristic
3#13113368C212yesmaximal
4#13112688C212yesmaximal
5C13×#2313C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88178C2211yescharacteristic
8C13×#387—24no—
9C13×#381C2212yes—
10C13×#380—21no—
11C4×C13×C22⋊C4—21no—
12#11718871—21no—
13#11718871—21no—
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2212yes—
16#11718641—22no—
17#11718637C412yescomplemented
18#11718635C412yescomplemented
19#11718122—22no—
20#11718044—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13—22no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35#88178—22no—
36#88178—22no—
37C2×#6101—21no—
38C2×#6101—22no—
39C2×#6101—22no—
40C2×C4×Dic13C2×C412yes—
41C2×#6099—22no—
42C13×#95—22no—
43C13×#95—22no—
44C13×#95—22no—
45C13×#95D414yes—
46#88071—22no—
47#88071—22no—
48#88071—21no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9461—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—24no—
58C22×C4×C13—42no—
59C22×C4×C13—81no—
60C22×C4×C13—81no—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D412yes—
66C22×C4×C13#4112yes—
67C22×Dic13—22no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C2×Dic26—22no—
71C2×Dic26—42no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—82no—
75C13×C22⋊C4—44no—
76C42×C13—82no—
77C22⋊Dic13—24no—
78C22⋊Dic13—41no—
79C22⋊Dic13—41no—
80C4⋊Dic13—22no—
81#6101—42no—
82#6101—82no—
83#6101—82no—
84C4×Dic13—42no—
85#6099—44no—
86C2×#1055—42no—
87#2502—131no—
88#2313D1311yescharacteristic
89#1821—131no—
90#1511—132no—
91#1284—132no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—41no—
95C23×C13C2×C22⋊C411yescharacteristic
96C23×C13#12011yescharacteristic
97C23×C13#12311yescharacteristic
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—44no—
109C2×C4×C13—44no—
110C2×C4×C13—44no—
111C2×C4×C13—81no—
112C2×C4×C13—81no—
113C2×C4×C13C4×D412yes—
114C2×C4×C13#12112yes—
115C2×Dic13—24no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—42no—
122Dic26—82no—
123#1055—82no—
124C2×C22⋊Q8—131no—
125C22×C4⋊C4C2×D1311yescharacteristic
126#407—132no—
127#398—262no—
128#391—132no—
129#387—24no—
130#385—261no—
131#385—261no—
132#384—132no—
133#381C2×D1312yes—
134#380—21no—
135C4×C22⋊C4—21no—
136C4×C22⋊C4—131no—
137#343—262no—
138#328—264no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—44no—
147C22×C13#38611yescharacteristic
148C22×C13#41012yes—
149C22×C13#45612yes—
150C4×C13—22no—
151C4×C13—22no—
152C4×C13—42no—
153C4×C13—42no—
154C4×C13—84no—
155Dic13—44no—
156Dic13—81no—
157Dic13—81no—
158C22×Q8—131no—
159C23×C4C22⋊D1311yescharacteristic
160C23×C4C22⋊D1311yescharacteristic
161C23×C4C22×D1311yescharacteristic
162C2×M16—262no—
163C22⋊Q8—262no—
164C22⋊Q8—262no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—262no—
171C2×C4⋊C4—262no—
172C2×C4⋊C4C4×D1312yes—
173C2×C4⋊C4D5212yes—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—261no—
176C2×C22⋊C4—261no—
177C2×C42—22no—
178C2×C42—132no—
179C22⋊C8—262no—
180C22⋊C8—262no—
181#95—22no—
182#95—22no—
183#95—22no—
184#95—262no—
185#95—262no—
186#95—261no—
187#95C22⋊D1314yes—
188C2×C13—22no—
189C2×C13—22no—
190C2×C13—41no—
191C2×C13#188611yescharacteristic
192C2×C13#189911yescharacteristic
193C2×C13#191111yescharacteristic
194C24C2×C22⋊D1311yescharacteristic
195C2×Q8—262no—
196C2×Q8—522no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—24no—
202C22×C4—42no—
203C22×C4—81no—
204C22×C4—81no—
205C22×C4—262no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4#610312yes—
209C22×C4#610312yes—
210C22×C4C2×C4×D1311yescharacteristic
211C22×C4C2×D5211yescharacteristic
212C22×C4#612712yes—
213C22×C4C2×C22⋊D1312yes—
214M16—524no—
215C2×C8—522no—
216C4⋊C4—24no—
217C4⋊C4—24no—
218C4⋊C4—82no—
219C4⋊C4—262no—
220C4⋊C4—522no—
221C4⋊C4—1042no—
222C4⋊C4—1042no—
223C22⋊C4—44no—
224C22⋊C4—264no—
225C22⋊C4—521no—
226C22⋊C4—521no—
227C42—82no—
228C42—522no—
229C13#946111yescharacteristic, complemented, Sylow
230C23—22no—
231C23—22no—
232C23—41no—
233C23C2×#610311yescharacteristic
234C23#8818311yescharacteristic
235C23#8820711yescharacteristic
236Q8—1042no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4—44no—
249C2×C4—44no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—264no—
253C2×C4—522no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4C4×C22⋊D1312yes—
260C2×C4#8818412yes—
261C8—1042no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22#1171866712yes—
271C22#1171887411yescharacteristic
272C22#1171890712yes—
273C4—22no—
274C4—22no—
275C4—42no—
276C4—42no—
277C4—84no—
278C4—524no—
279C4—1041no—
280C4—1041no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2#1311522911yescharacteristic
285C2#1311529411yescharacteristic
286C2#1311536811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2313C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2313D13
hypocenterC13#9461
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
17. #11718637C4semidirect
18. #11718635C4semidirect
229. C13#9461semidirect

Maximal subgroups

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

subgroupindex
#131193102
#131149162
#131133682
#131126882
C13×#23132
#946113