Finite Group Databasebeta

← #15763777

Subgroups — #15763777

Order 3328.

696 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 105 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#13124844C212yesmaximal, complemented
2#13115817C211yesmaximal, characteristic, complemented
3#13113261C212yesmaximal, complemented
4#13112665C211yesmaximal, characteristic, complemented
5C13×#2397C211yesmaximal, characteristic
6C2×C4×D4×C13—22no—
7C2×C4×D4×C13C2212yes—
8#11719175C2211yescharacteristic
9C13×#399—22no—
10C13×#392—22no—
11C13×#376C2211yescharacteristic
12#11718879—22no—
13#11718680—22no—
14C4×#6105—24no—
15#11718669—22no—
16#11718632—22no—
17#11718586C2212yes—
18#11718585C2211yescharacteristic
19D4⋊#1055—24no—
20#11718115—22no—
21C22×D4×C13—22no—
22C22×D4×C13D412yes—
23C23×C4×C13—22no—
24C4×D4×C13—22no—
25C4×D4×C13—22no—
26C4×D4×C13—22no—
27C4×D4×C13—22no—
28C4×D4×C13—44no—
29C4×D4×C13—44no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4D412yes—
32C2×C13×C22⋊C4—24no—
33C2×C13×C22⋊C4—22no—
34C2×C42×C13D412yes—
35C2×C42×C13C2311yescharacteristic
36C2×#6105—24no—
37#88180—21no—
38#88178—22no—
39C2×#6099—21no—
40#88124—21no—
41#88123D412yescomplemented
42C4×Dic26—22no—
43C13×#95—22no—
44#88072—24no—
45C22⋊#1055—22no—
46#88050—24no—
47#88048—24no—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50C4×#1055D414yescomplemented
51#10015—131nomaximal, Sylow
52C24×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—22no—
55C2×D4×C13—44no—
56C2×D4×C13—44no—
57C2×D4×C13—48no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—42no—
61C22×C4×C13—42no—
62C22×C4×C13—44no—
63C22×C4×C13—44no—
64C22×C4×C13C2×D412yes—
65C22×C4×C13C2×D411yescharacteristic
66C2×Dic26—22no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—44no—
70C13×C22⋊C4—48no—
71C13×C22⋊C4—42no—
72C13×C22⋊C4—42no—
73C42×C13—22no—
74C42×C13SD1614yescomplemented
75C42×C13C2×D411yescharacteristic
76C42×C13C2×D412yes—
77C42×C13#4111yescharacteristic
78C22⋊Dic13—41no—
79#6105—48no—
80C4⋊Dic13—22no—
81C4⋊Dic13—22no—
82#6101—42no—
83C4×Dic13—41no—
84#6099—42no—
85C2×#1055—24no—
86C2×#1055—41no—
87#3101—132no—
88#2397D1311yescharacteristic
89#1995—131no—
90#1486—132no—
91#1274—131no—
92C23×C13—24no—
93C23×C13—44no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—44no—
97C23×C13#12011yescharacteristic
98D4×C13—24no—
99D4×C13—24no—
100D4×C13—42no—
101D4×C13—42no—
102D4×C13—416no—
103C2×C4×C13—24no—
104C2×C4×C13—42no—
105C2×C4×C13—44no—
106C2×C4×C13—42no—
107C2×C4×C13—44no—
108C2×C4×C13—84no—
109C2×C4×C13—82no—
110C2×C4×C13—82no—
111C2×C4×C13#12012yes—
112C2×C4×C13#12112yes—
113C2×C4×C13#12111yescharacteristic
114C2×C4×C13#12711yescharacteristic
115C2×C4×C13C2×SD1612yes—
116C2×C4×C13AGL(1,ℤ/8)12yes—
117C2×Dic13—42no—
118Dic26—44no—
119#1055—44no—
120#1055—81no—
121#533—131no—
122C2×C4×D4—22no—
123C2×C4×D4C2×D1312yes—
124#483—262no—
125#476—262no—
126#461—262no—
127#450—262no—
128C4×SD16—264no—
129#431—132no—
130#423—131no—
131#399—22no—
132#392—22no—
133#376C2×D1311yescharacteristic
134#339—262no—
135D4⋊C8—264no—
136C22×C13—22no—
137C22×C13—48no—
138C22×C13—44no—
139C22×C13—84no—
140C22×C13—82no—
141C22×C13—82no—
142C22×C13#39211yescharacteristic
143C22×C13#45012yes—
144C4×C13—22no—
145C4×C13—22no—
146C4×C13—44no—
147C4×C13—82no—
148C4×C13#46012yes—
149C4×C13#49211yescharacteristic
150C4×C13#49611yescharacteristic
151Dic13—82no—
152C22×D4—22no—
153C22×D4C22⋊D1312yes—
154C23×C4—22no—
155C2×SD16—264no—
156C2×M16—261no—
157C4⋊Q8—132no—
158#125—261no—
159C22⋊Q8—262no—
160C4×Q8—262no—
161C4×D4—22no—
162C4×D4—22no—
163C4×D4—22no—
164C4×D4—22no—
165C4×D4—44no—
166C4×D4—44no—
167#117—261no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4C22⋊D1312yes—
170C2×C22⋊C4—24no—
171C2×C22⋊C4—22no—
172C2×C42C22⋊D1312yes—
173C2×C42C22×D1311yescharacteristic
174#106—264no—
175C4⋊C8—262no—
176C4⋊C8—262no—
177#103—264no—
178#102—264no—
179C22⋊C8—262no—
180C4×C8—134no—
181#95—22no—
182C2×C13—22no—
183C2×C13—84no—
184C2×C13#201012yes—
185C2×C13#201411yescharacteristic
186C24—22no—
187C2×Q8—262no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—44no—
191C2×D4—44no—
192C2×D4—48no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—44no—
196C22×C4—44no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4C2×C22⋊D1312yes—
200C22×C4C2×C22⋊D1311yescharacteristic
201SD16—528no—
202M16—522no—
203C2×C8—264no—
204C2×C8—521no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—44no—
208C4⋊C4—262no—
209C4⋊C4—262no—
210C4⋊C4—522no—
211C22⋊C4—48no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C22⋊C4—521no—
215C42—22no—
216C42—521no—
217C42#610514yescomplemented
218C42D4×D1311yescharacteristic
219C42D4×D1312yes—
220C42#612911yescharacteristic
221C13#1001511yescharacteristic, complemented, Sylow
222C23—24no—
223C23—44no—
224C23—42no—
225C23—44no—
226C23—42no—
227C23#8820711yescharacteristic
228Q8—524no—
229D4—24no—
230D4—24no—
231D4—42no—
232D4—42no—
233D4—416no—
234C2×C4—24no—
235C2×C4—42no—
236C2×C4—44no—
237C2×C4—44no—
238C2×C4—42no—
239C2×C4—82no—
240C2×C4—84no—
241C2×C4—82no—
242C2×C4—522no—
243C2×C4#8818612yes—
244C2×C4C2×#610512yes—
245C2×C4#8819112yes—
246C2×C4#8819211yescharacteristic
247C2×C4#8819312yes—
248C2×C4#8819411yescharacteristic
249C8—524no—
250C8—1041no—
251C22—22no—
252C22—48no—
253C22—44no—
254C22—84no—
255C22—82no—
256C22—82no—
257C22#1171887912yes—
258C22#1171888411yescharacteristic
259C4—22no—
260C4—22no—
261C4—44no—
262C4—82no—
263C4—1042no—
264C4#1171873511yescharacteristic
265C4#1171873612yes—
266C4#1171873711yescharacteristic
267C2—22no—
268C2—84no—
269C2#1311590112yes—
270C2#1311592411yescharacteristic
subgroupG/H
centerC2×C4#88194
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2397C2
socleC22×C13#392
hypercenter#2397D13
hypocenterC13#10015
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #13124844C2semidirect
2. #13115817C2semidirect
3. #13113261C2semidirect
4. #13112665C2semidirect
41. #88123D4semidirect
50. C4×#1055D4semidirect
74. C42×C13SD16semidirect
217. C42#6105semidirect
221. C13#10015semidirect

Maximal subgroups

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

subgroupindex
#131248442
#131158172
#131132612
#131126652
C13×#23972
#1001513