Finite Group Databasebeta

← #15860368

Subgroups — #15860368

Order 3328.

2046 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719524C211yesmaximal, characteristic
2C2×#11719532C211yesmaximal, characteristic
3#13114574C216yesmaximal, complemented
4C2×#11718146C216yesmaximal, complemented
5C2×C13×#568C211yesmaximal, characteristic
6C22×C13×#41C2211yescharacteristic
7C13×#568—24no—
8C13×#568C418yescomplemented
9C2×C13×#131—24no—
10C22×C13×M16C2216yes—
11#11719532—24no—
12#11719532—24no—
13#11719524—24no—
14#11719524C418yescomplemented
15C2×#88202—24no—
16C2×Q8×Dic13C412yes—
17C2×D4×Dic13C416yes—
18C2×#88180C2213yes—
19C22×C4⋊Dic13C2213yes—
20C22×#6099C2216yes—
21#11718146C22112yes—
22#11718146C2214yes—
23C2×C13×#41C2×C414yes—
24C2×C13×#41C2×C414yes—
25C2×C13×#41D414yes—
26C2×C13×#41D414yes—
27C2×C13×#41D414yes—
28C2×C13×#41Q814yes—
29C22×Q8×C13C2×C411yescharacteristic
30C22×D4×C13C2×C413yes—
31C23×C4×C13C2313yes—
32C23×Dic13C2×C416yes—
33C13×#131—232no—
34C2×C13×M16—26no—
35C2×C13×M16—212no—
36C2×C13×M16C2×C4124yescomplemented
37C2×C13×M16C2314yes—
38C22×C8×C13—26no—
39C2×C22⋊Dic13C2×C416yes—
40#88202—232no—
41Q8×Dic13—28no—
42D4×Dic13—224no—
43#88180—26no—
44#88180—26no—
45C2×C4⋊Dic13—26no—
46C2×C4⋊Dic13—26no—
47C2×C4⋊Dic13C2×C416yes—
48C2×C4⋊Dic13C2313yes—
49C2×C4⋊Dic13C2311yescharacteristic
50C2×C4×Dic13C2×C416yes—
51C2×#6099—26no—
52C2×#6099—212no—
53C2×#6099C2×C4124yescomplemented
54C2×#6099C2314yes—
55C22×#1055—26no—
56#20358—131nomaximal, Sylow
57C24×C13C22×C413yes—
58C13×#41C22⋊C4116yes—
59C13×#41C22⋊C4116yes—
60C13×#41C4⋊C4116yes—
61C13×#41C4⋊C4116yes—
62C2×Q8×C13C4214yes—
63C2×Q8×C13C22⋊C414yes—
64C2×Q8×C13C4⋊C414yes—
65C2×D4×C13C42112yes—
66C2×D4×C13C22⋊C4112yes—
67C2×D4×C13C4⋊C4112yes—
68C22×C4×C13C22×C413yes—
69C22×C4×C13C22×C416yes—
70C22×C4×C13C22×C416yes—
71C22×C4×C13C2×D416yes—
72C22×C4×C13C2×D416yes—
73C22×C4×C13C2×D416yes—
74C22×C4×C13C2×Q816yes—
75C22×C4×C13C2411yescharacteristic
76C22×Dic13—212no—
77C22×Dic13—86no—
78C22×Dic13C22×C412yes—
79C22×Dic13C22×C416yes—
80C13×M16—224no—
81C13×M16—24no—
82C13×M16C22×C418yes—
83C2×C8×C13—224no—
84C2×C8×C13—24no—
85C22⋊Dic13—212no—
86C4⋊Dic13—212no—
87C4⋊Dic13—23no—
88C4⋊Dic13—23no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4×Dic13—212no—
92#6099—224no—
93#6099—24no—
94#6099C22×C418yes—
95C2×#1055—224no—
96C2×#1055—24no—
97C2×#568—131no—
98C2×#568D1311yescharacteristic
99C2×#520—131no—
100#1742—136no—
101C2×#343—136no—
102C23×C13—43no—
103C23×C13—43no—
104C23×C13C2×C4216yes—
105C23×C13C2×C22⋊C416yes—
106C23×C13C2×C4⋊C416yes—
107C23×C13C23×C411yescharacteristic
108Q8×C13#95116yes—
109D4×C13#95148yes—
110C2×C4×C13C2×C4216yes—
111C2×C4×C13C2×C22⋊C4112yes—
112C2×C4×C13C2×C22⋊C4112yes—
113C2×C4×C13C2×C22⋊C416yes—
114C2×C4×C13C2×C4⋊C4112yes—
115C2×C4×C13C2×C4⋊C4112yes—
116C2×C4×C13C2×C4⋊C416yes—
117C2×C4×C13C23×C411yescharacteristic
118C2×C4×C13C23×C411yescharacteristic
119C2×C4×C13C22×D411yescharacteristic
120C2×C4×C13C22×D411yescharacteristic
121C2×C4×C13C22×D411yescharacteristic
122C2×C4×C13C22×Q811yescharacteristic
123C2×Dic13—22no—
124C2×Dic13—26no—
125C2×Dic13—46no—
126C2×Dic13—42no—
127C2×Dic13—812no—
128C8×C13—28no—
129#1055—28no—
130C22×#41C2×D1311yescharacteristic
131#568—24no—
132#568—138no—
133#568—264no—
134#568Dic1318yescomplemented
135C2×#131—24no—
136C2×#131—264no—
137C22×M16—136no—
138C22×M16C2×D1316yes—
139#520—264no—
140#520—264no—
141C2×C4×Q8—132no—
142C2×C4×D4—136no—
143C2×#117—133no—
144C22×C4⋊C4—133no—
145#343—1312no—
146#343—134no—
147C22×C13—21no—
148C22×C13—26no—
149C22×C13—21no—
150C22×C13—26no—
151C22×C13—46no—
152C22×C13—46no—
153C22×C13C2×#95112yes—
154C22×C13C22×C4211yescharacteristic
155C22×C13C22×C22⋊C411yescharacteristic
156C22×C13C22×C4⋊C411yescharacteristic
157C4×C13C2×#95112yes—
158C4×C13C22×C22⋊C411yescharacteristic
159C4×C13C22×C22⋊C411yescharacteristic
160C4×C13C22×C4⋊C411yescharacteristic
161C4×C13C22×C4⋊C411yescharacteristic
162Dic13—46no—
163Dic13—42no—
164C2×#41Dic2614yes—
165C2×#41C4×D1314yes—
166C2×#41D5214yes—
167C2×#41C2×Dic1314yes—
168C2×#41C22⋊D1314yes—
169C2×#41C22⋊D1314yes—
170C22×Q8C4×D1311yescharacteristic
171C22×D4C4×D1313yes—
172C23×C4—136no—
173C23×C4C22×D1313yes—
174#131—232no—
175#131—2632no—
176C2×M16—26no—
177C2×M16—212no—
178C2×M16—1324no—
179C2×M16—134no—
180C2×M16—266no—
181C2×M16—2612no—
182C2×M16C2×Dic13124yescomplemented
183C2×M16C22×D1314yes—
184C22×C8—26no—
185C22×C8—266no—
186C4×Q8—268no—
187C4×D4—2624no—
188#117—266no—
189#117—266no—
190C2×C4⋊C4—136no—
191C2×C4⋊C4—133no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—266no—
194C2×C4⋊C4—266no—
195C2×C22⋊C4—136no—
196C2×C42—136no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13—212no—
200C2×C13C22×#9511yescharacteristic
201C2×C13#288811yescharacteristic
202C2×C13#288911yescharacteristic
203C24C2×C4×D1313yes—
204#41#6101116yes—
205#41C4⋊Dic13116yes—
206#41#6103116yes—
207#41C22⋊Dic13116yes—
208C2×Q8C4×Dic1314yes—
209C2×Q8#610114yes—
210C2×Q8#610314yes—
211C2×D4C4×Dic13112yes—
212C2×D4#6101112yes—
213C2×D4#6103112yes—
214C22×C4—132no—
215C22×C4—136no—
216C22×C4—2612no—
217C22×C4—1046no—
218C22×C4C2×Dic2616yes—
219C22×C4C2×C4×D1313yes—
220C22×C4C2×C4×D1316yes—
221C22×C4C2×D5216yes—
222C22×C4C22×Dic1316yes—
223C22×C4C2×C22⋊D1316yes—
224C22×C4C2×C22⋊D1316yes—
225C22×C4C23×D1311yescharacteristic
226M16—224no—
227M16—24no—
228M16—138no—
229M16—2624no—
230M16—264no—
231M16C22×Dic1318yes—
232C2×C8—224no—
233C2×C8—24no—
234C2×C8—2624no—
235C2×C8—264no—
236C4⋊C4—2612no—
237C4⋊C4—263no—
238C4⋊C4—261no—
239C4⋊C4—263no—
240C4⋊C4—261no—
241C22⋊C4—2612no—
242C42—2612no—
243C13#2035811yescharacteristic, complemented, Sylow
244C23—43no—
245C23—43no—
246C23C2×C4×Dic1316yes—
247C23C2×#610116yes—
248C23C2×#610316yes—
249C23C22×C4×D1311yescharacteristic
250Q8#88071116yes—
251D4#88071148yes—
252C2×C4—262no—
253C2×C4—266no—
254C2×C4—522no—
255C2×C4—526no—
256C2×C4—10412no—
257C2×C4C2×C4×Dic1316yes—
258C2×C4C2×#6101112yes—
259C2×C4C2×#610116yes—
260C2×C4C2×C4⋊Dic13112yes—
261C2×C4C2×#6103112yes—
262C2×C4C2×#610316yes—
263C2×C4C2×C22⋊Dic13112yes—
264C2×C4C22×Dic2611yescharacteristic
265C2×C4C22×C4×D1311yescharacteristic
266C2×C4C22×D5211yescharacteristic
267C2×C4C23×Dic1311yescharacteristic
268C2×C4C22×C22⋊D1311yescharacteristic
269C2×C4C22×C22⋊D1311yescharacteristic
270C8—28no—
271C8—268no—
272C22—21no—
273C22—26no—
274C22—21no—
275C22—26no—
276C22—46no—
277C22—46no—
278C22C2×#88071112yes—
279C22C22×C4×Dic1311yescharacteristic
280C22C22×#610111yescharacteristic
281C22C22×#610311yescharacteristic
282C4—526no—
283C4—522no—
284C4C2×#88071112yes—
285C4C22×#610111yescharacteristic
286C4C22×C4⋊Dic1311yescharacteristic
287C4C22×#610311yescharacteristic
288C4C22×C22⋊Dic1311yescharacteristic
289C2—21no—
290C2—21no—
291C2—212no—
292C2C22×#8807111yescharacteristic
293C2#1312331411yescharacteristic
294C2#1312331811yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC22×C13C22×C42
FrattiniC22×C4C23×D13
FittingC2×C13×#568C2
socleC22×C13C22×C22⋊C4
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC2×#568D13
hypocenterC13#20358
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
3. #13114574C2semidirect
4. C2×#11718146C2semidirect
8. C13×#568C4semidirect
14. #11719524C4semidirect
36. C2×C13×M16C2×C4semidirect
53. C2×#6099C2×C4semidirect
134. #568Dic13semidirect
182. C2×M16C2×Dic13semidirect
243. C13#20358semidirect

Maximal subgroups

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

subgroupindex
C2×#117195242
C2×#117195322
#131145742
C2×#117181462
C2×C13×#5682
#2035813