Finite Group Databasebeta

← #16796792

Subgroups — #16796792

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719631C212yesmaximal
2#13130524C216yesmaximal, complemented
3#13130522C213yesmaximal, complemented
4C2×#11718265C213yesmaximal, complemented
5C2×D13×#131C211yesmaximal, characteristic
6C2×#41×D13C2211yescharacteristic
7#11719631—28no—
8#11719631C4116yescomplemented
9C2×Q8×#261—22no—
10C2×D4×#261—26no—
11C2×#88237C2216yes—
12C22×C4⋊#261C2216yes—
13C2×C13×#131C411yescharacteristic, complemented
14C2×#88202C411yescharacteristic, complemented
15D13×#131—28no—
16C2×#88161C413yescomplemented
17C2×M16×D13C2213yes—
18C2×#88155C413yescomplemented
19C22×C8×D13C2213yes—
20#11718265C2213yes—
21#11718265C2216yes—
22#11718265C2211yescharacteristic
23#11718265C2216yes—
24C23×#261—26no—
25C2×C13×#41C2×C411yescharacteristic
26#41×D13C2×C418yes—
27#41×D13D418yes—
28C2×#6131Q811yescharacteristic
29C2×Q8×D13D411yescharacteristic
30C2×#6129Q813yes—
31C2×D4×D13D413yes—
32C2×#6127C2×C413yes—
33C22×C4×D13C2313yes—
34C2×C22⋊#261—26no—
35Q8×#261—216no—
36D4×#261—248no—
37#88237—212no—
38#88237C2×C4124yescomplemented
39C2×C4⋊#261—26no—
40C2×C4⋊#261—212no—
41C2×C4⋊#261C2×C4124yescomplemented
42C2×C4⋊#261C2316yes—
43C2×C4⋊#261C2312yes—
44C2×C4×#261—26no—
45C13×#131—24no—
46C2×C13×M16C2×C413yescomplemented
47C22×C8×C13C2×C413yescomplemented
48#88202—24no—
49C2×#6099C2×C413yescomplemented
50C22×#1055C2×C413yescomplemented
51#88161—212no—
52M16×D13—212no—
53#88155—212no—
54C2×#6094C2×C416yescomplemented
55C2×C8×D13—212no—
56C2×C8×D13C2×C413yescomplemented
57C2×C8×D13C2×C413yescomplemented
58C2×C8×D13C2311yescharacteristic
59C2×C8×D13C2313yes—
60#20348—131nomaximal, Sylow
61C23×D13C2×D413yes—
62C22×#261—22no—
63C22×#261—26no—
64C22×#261—224no—
65C22×#261—86no—
66C22×#261—86no—
67C13×#41C4214yes—
68C13×#41C22⋊C414yes—
69C2×Q8×C13C4⋊C411yescharacteristic
70C2×D4×C13C4⋊C413yes—
71C22×C4×C13C22×C413yes—
72C2×C22⋊D13C4⋊C416yes—
73C22×Dic13C2×Q813yes—
74#6131C4⋊C418yes—
75Q8×D13C22⋊C418yes—
76#6129C4⋊C4124yes—
77D4×D13C22⋊C4124yes—
78#6127C42112yes—
79#6127C22⋊C4112yes—
80C2×D52C4⋊C413yes—
81C2×C4×D13C22×C413yes—
82C2×C4×D13C22×C4112yes—
83C2×C4×D13C2×D413yes—
84C2×C4×D13C2×D4112yes—
85C2×C4×D13C2×Q813yes—
86C2×C4×D13C2411yescharacteristic
87C2×Dic26C4⋊C413yes—
88C22⋊#261—224no—
89C4⋊#261—224no—
90C4⋊#261—26no—
91C4⋊#261—22no—
92C4⋊#261C22×C4112yes—
93C4⋊#261C22×C414yes—
94C4×#261—224no—
95C13×M16—26no—
96C2×C8×C13—26no—
97C2×C8×C13C22×C411yescharacteristic
98C2×C8×C13C22×C413yes—
99#6099—26no—
100C2×#1055—26no—
101C2×#1055C22×C411yescharacteristic
102C2×#1055C22×C413yes—
103#6094—212no—
104C8×D13—26no—
105C8×D13—26no—
106C8×D13—22no—
107C8×D13—26no—
108C22×#131—131no—
109C2×#520—132no—
110#1736—136no—
111#1735—133no—
112C2×#340—133no—
113C23×C13C2×C4⋊C413yes—
114C22×D13—23no—
115C22×D13—26no—
116C22×D13—23no—
117C22×D13C2×C22⋊C4112yes—
118C22×D13C2×C4⋊C413yes—
119C22×D13C22×D411yescharacteristic
120C2×#261—24no—
121C2×#261—212no—
122C2×#261—46no—
123C2×#261—42no—
124C2×#261—46no—
125C2×#261—42no—
126C2×#261—824no—
127Q8×C13#9514yes—
128D4×C13#95112yes—
129C2×C4×C13C2×C4216yes—
130C2×C4×C13C2×C22⋊C416yes—
131C2×C4×C13C2×C4⋊C413yes—
132C2×C4×C13C23×C411yescharacteristic
133C22⋊D13#95124yes—
134C2×Dic13C2×C4⋊C4112yes—
135C2×Dic13C2×C4⋊C413yes—
136C2×Dic13C22×Q811yescharacteristic
137D52#95112yes—
138C4×D13C2×C4216yes—
139C4×D13C2×C22⋊C416yes—
140C4×D13C2×C22⋊C4112yes—
141C4×D13C2×C4⋊C4112yes—
142C4×D13C23×C412yes—
143C4×D13C22×D412yes—
144Dic26#95112yes—
145C8×C13—21no—
146C8×C13—23no—
147#1055—21no—
148#1055—23no—
149C22×#41—131no—
150C2×#131—131no—
151C2×#131—133no—
152C2×#131—133no—
153C2×#131—268no—
154C2×#131#26111yescharacteristic, complemented
155C22×M16—133no—
156C23×C8—133no—
157#520—1316no—
158#520—268no—
159C2×C4×Q8—262no—
160C2×C4×D4—266no—
161C2×#117—136no—
162C22×C4⋊C4—136no—
163#340—133no—
164#340—136no—
165#340—131no—
166#340—136no—
167C22×C13—23no—
168C22×C13—23no—
169C22×C13C2×#9516yes—
170C22×C13C22×C4⋊C411yescharacteristic
171C2×D13—23no—
172C2×D13—23no—
173C2×D13—212no—
174C2×D13—212no—
175C2×D13C2×#9516yes—
176C2×D13C22×C22⋊C412yes—
177C2×D13#57611yescharacteristic
178C2×D13#57712yes—
179C2×D13#57811yescharacteristic
180#261—412no—
181#261—44no—
182C4×C13C2×#9516yes—
183C4×C13C22×C4211yescharacteristic
184C4×C13C22×C22⋊C411yescharacteristic
185Dic13C2×#9516yes—
186Dic13C22×C4⋊C412yes—
187C2×#41—138no—
188C2×#41—138no—
189C2×#41—131no—
190C2×#41—133no—
191C2×#41—133no—
192C2×#41C2×#26111yescharacteristic
193C22×Q8—131no—
194C22×D4—133no—
195C23×C4—133no—
196C23×C4—266no—
197#131—24no—
198#131—2612no—
199#131—2612no—
200#131—264no—
201C2×M16—133no—
202C2×M16—136no—
203C2×M16—2612no—
204C2×M16C2×#26113yescomplemented
205C22×C8—133no—
206C22×C8—131no—
207C22×C8—133no—
208C22×C8—133no—
209C22×C8—133no—
210C22×C8—2612no—
211C22×C8C2×#26113yescomplemented
212C4×Q8—2616no—
213C4×D4—2648no—
214#117—1324no—
215#117—2612no—
216C2×C4⋊C4—136no—
217C2×C4⋊C4—1324no—
218C2×C4⋊C4—132no—
219C2×C4⋊C4—266no—
220C2×C4⋊C4—2612no—
221C2×C22⋊C4—266no—
222C2×C42—266no—
223C2×C13—26no—
224C2×C13C22×#9511yescharacteristic
225C2×C13#291211yescharacteristic
226C2×C13#291311yescharacteristic
227D13—26no—
228D13#289712yes—
229D13#289812yes—
230C24—133no—
231#41—138no—
232#41—1324no—
233#41—1312no—
234#41—1312no—
235#41C4×#26114yes—
236#41C22⋊#26114yes—
237C2×Q8—138no—
238C2×Q8—133no—
239C2×Q8C4⋊#26111yescharacteristic
240C2×D4—136no—
241C2×D4—1324no—
242C2×D4—133no—
243C2×D4C4⋊#26113yes—
244C22×C4—133no—
245C22×C4—1312no—
246C22×C4—133no—
247C22×C4—133no—
248C22×C4—1312no—
249C22×C4—131no—
250C22×C4—133no—
251C22×C4—262no—
252C22×C4—266no—
253C22×C4—2624no—
254C22×C4—1046no—
255C22×C4—1046no—
256C22×C4C22×#26113yes—
257M16—26no—
258M16—2612no—
259M16—266no—
260C2×C8—26no—
261C2×C8—131no—
262C2×C8—133no—
263C2×C8—262no—
264C2×C8—266no—
265C2×C8—266no—
266C2×C8—266no—
267C2×C8—266no—
268C2×C8C22×#26111yescharacteristic
269C2×C8C22×#26113yes—
270C4⋊C4—1312no—
271C4⋊C4—134no—
272C4⋊C4—266no—
273C4⋊C4—2624no—
274C4⋊C4—262no—
275C22⋊C4—2624no—
276C42—2624no—
277C13#2034811yescharacteristic, complemented, Sylow
278C23—131no—
279C23—133no—
280C23—1312no—
281C23—263no—
282C23—266no—
283C23—263no—
284C23C2×C4⋊#26113yes—
285Q8—1312no—
286Q8(C2×#261)⋊C414yes—
287D4—1324no—
288D4—1312no—
289D4(C2×#261)⋊C4112yes—
290C2×C4—133no—
291C2×C4—131no—
292C2×C4—1312no—
293C2×C4—132no—
294C2×C4—136no—
295C2×C4—132no—
296C2×C4—136no—
297C2×C4—1312no—
298C2×C4—1312no—
299C2×C4—264no—
300C2×C4—2612no—
301C2×C4—526no—
302C2×C4—526no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—10424no—
306C2×C4C2×C4×#26116yes—
307C2×C4C2×C4⋊#26113yes—
308C2×C4C2×C22⋊#26116yes—
309C2×C4C23×#26111yescharacteristic
310C8—21no—
311C8—23no—
312C8—261no—
313C8—263no—
314C22—23no—
315C22—23no—
316C22—132no—
317C22—131no—
318C22—131no—
319C22—132no—
320C22—136no—
321C22—2612no—
322C22—2612no—
323C22—263no—
324C22—263no—
325C22C2×(C2×#261)⋊C416yes—
326C22C22×C4⋊#26111yescharacteristic
327C4—132no—
328C4—136no—
329C4—524no—
330C4—5212no—
331C4C2×(C2×#261)⋊C416yes—
332C4C22×C4×#26111yescharacteristic
333C4C22×C22⋊#26111yescharacteristic
334C2—26no—
335C2—132no—
336C2—132no—
337C2—266no—
338C2C22×(C2×#261)⋊C411yescharacteristic
339C2#1313149011yescharacteristic
340C2#1313149111yescharacteristic
subgroupG/H
centerC22C22×C4⋊#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC2×C13×#131C4
socleC22×C13C22×C4⋊C4
prime radicalC2×#41×D13C22
cosocleC2×C4×D13C24
hypercenterC2×#131#261
hypocenterC13#20348
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. #13130524C2semidirect
3. #13130522C2semidirect
4. C2×#11718265C2semidirect
8. #11719631C4semidirect
13. C2×C13×#131C4semidirect
14. C2×#88202C4semidirect
16. C2×#88161C4semidirect
18. C2×#88155C4semidirect
38. #88237C2×C4semidirect
41. C2×C4⋊#261C2×C4semidirect
46. C2×C13×M16C2×C4semidirect
47. C22×C8×C13C2×C4semidirect
49. C2×#6099C2×C4semidirect
50. C22×#1055C2×C4semidirect
54. C2×#6094C2×C4semidirect
56. C2×C8×D13C2×C4semidirect
57. C2×C8×D13C2×C4semidirect
154. C2×#131#261semidirect
204. C2×M16C2×#261semidirect
211. C22×C8C2×#261semidirect
277. C13#20348semidirect

Maximal subgroups

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

subgroupindex
C2×#117196312
#131305242
#131305222
C2×#117182652
C2×D13×#1312
#2034813