Finite Group Databasebeta

← #15780361

Subgroups — #15780361

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718803C211yesmaximal, characteristic
2C2×#11718108C211yesmaximal, characteristic, complemented
3C2×#11718101C211yesmaximal, characteristic, complemented
4#13114900C211yesmaximal, characteristic, complemented
5#13112945C211yesmaximal, characteristic, complemented
6#13112930C211yesmaximal, characteristic, complemented
7C2×C13×#504C211yesmaximal, characteristic, complemented
8C2×C13×#131C2211yescharacteristic
9C2×#88203—21no—
10C22×D104C2211yescharacteristic
11C13×#504—22no—
12C13×#504—22no—
13C2×C13×M32—21no—
14C2×C13×M32C2211yescharacteristic
15C22×C13×C16—21no—
16C22×C13×C16C2211yescharacteristic
17#11718893—21no—
18#11718803—22no—
19#11718803C414yescomplemented
20C2×#88063—21no—
21C2×#88059C2211yescharacteristic
22C2×#88059C2211yescharacteristic
23C2×#88058C2211yescharacteristic
24#11718146—21no—
25#11718108—22no—
26#11718101—21no—
27#11718101—21no—
28C2×C13×#41D411yescharacteristic
29C22×D52—21no—
30C13×#131—21no—
31C13×#131—21no—
32C13×#131C2×C412yes—
33C13×#131D412yes—
34C2×C13×M16—21no—
35C2×C13×M16D411yescharacteristic
36C22×C8×C13—21no—
37C22×C8×C13C2311yescharacteristic
38#88203—24no—
39#88203—42no—
40C2×#6106—41no—
41C2×#6104—41no—
42C2×C4⋊Dic13—21no—
43C2×#6099—21no—
44C2×#6099—21no—
45C2×D104—21no—
46C2×D104—21no—
47C2×D104—21no—
48C2×D104—21no—
49C2×D104—21no—
50C2×D104C2×C412yes—
51C13×M32—24no—
52C13×M32—21no—
53C13×M32D412yes—
54C2×C13×C16—24no—
55C2×C13×C16—21no—
56C2×C13×C16—21no—
57C2×C13×C16—21no—
58C2×C13×C16D411yescharacteristic
59C2×C13×C16D411yescharacteristic
60#88075—41no—
61#88072—41no—
62#88063—24no—
63#88059—21no—
64#88059—21no—
65#88059—21no—
66#88059C2×C412yes—
67#88058—21no—
68#88058—21no—
69#13073—131nomaximal, Sylow
70C23×D13—41no—
71C13×#41—21no—
72C13×#41—21no—
73C13×#41C22⋊C412yes—
74C13×#41SD1612yes—
75C2×Q8×C13D811yescharacteristic
76C2×D4×C13—21no—
77C2×D4×C13D811yescharacteristic
78C22×C4×C13—21no—
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—41no—
81C2×D52—22no—
82C2×D52—41no—
83C2×D52—41no—
84C2×D52—41no—
85C2×D52—41no—
86C2×D52—41no—
87C13×M16—21no—
88C13×M16—22no—
89C13×M16—22no—
90C13×M16C22⋊C412yes—
91C2×C8×C13—21no—
92C2×C8×C13—22no—
93C2×C8×C13—22no—
94C2×C8×C13C22×C411yescharacteristic
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13C2×D411yescharacteristic
97C2×C8×C13C2×D411yescharacteristic
98C2×C8×C13#4111yescharacteristic
99C2×C8×C13#4111yescharacteristic
100#6106—44no—
101#6104—44no—
102C4⋊Dic13—41no—
103C4⋊Dic13—41no—
104#6099—22no—
105#6099—41no—
106#6099—41no—
107#6099—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110D104—22no—
111D104—22no—
112D104—41no—
113D104—41no—
114C13×C16—21no—
115C13×C16—22no—
116C13×C16—21no—
117C2×#504D1311yescharacteristic, complemented
118C2×#472—131no—
119C2×#361—131no—
120C2×#357—131no—
121#1816—131no—
122#1387—131no—
123#1381—131no—
124C23×C13—21no—
125C23×C13#13511yescharacteristic
126C22×D13—42no—
127C22×D13—81no—
128C22×D13—81no—
129C22×D13—161no—
130C22×D13—161no—
131Q8×C13—21no—
132Q8×C13#10212yes—
133D4×C13—22no—
134D4×C13—22no—
135D4×C13—21no—
136D4×C13#10212yes—
137C2×C4×C13—21no—
138C2×C4×C13—22no—
139C2×C4×C13—22no—
140C2×C4×C13C2×C22⋊C411yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13C2×D811yescharacteristic
144C2×C4×C13C2×SD1611yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×Dic13—81no—
147C2×Dic13—161no—
148D52—42no—
149D52—42no—
150D52—81no—
151D52—81no—
152C8×C13—22no—
153C8×C13C4×D411yescharacteristic
154C8×C13C4×D411yescharacteristic
155C8×C13#12011yescharacteristic
156C8×C13#12311yescharacteristic
157#1055—42no—
158#1055—81no—
159C2×AGL(1,ℤ/8)—261no—
160C22×D8—131no—
161C2×#131C2×D1311yescharacteristic
162#504—22no—
163#504—22no—
164C2×M32—21no—
165C2×M32C2×D1311yescharacteristic
166C22×C16—21no—
167C22×C16C2×D1311yescharacteristic
168#472—134no—
169#472—262no—
170C2×#108—131no—
171C2×#108—131no—
172C2×#107—131no—
173#417—261no—
174C2×#100—261no—
175#361—262no—
176#357—261no—
177#357—261no—
178#343—261no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—22no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13#41611yescharacteristic
185C22×C13#46511yescharacteristic
186C22×C13#46611yescharacteristic
187C2×D13—82no—
188C2×D13—162no—
189C2×D13—161no—
190C2×D13—161no—
191C2×D13—162no—
192C4×C13—22no—
193C4×C13#38611yescharacteristic
194C4×C13C2×#10211yescharacteristic
195C4×C13#46511yescharacteristic
196C4×C13#46611yescharacteristic
197Dic13—161no—
198C2×#41D5211yescharacteristic
199C22×D4—261no—
200AGL(1,ℤ/8)—264no—
201AGL(1,ℤ/8)—522no—
202C2×SD16—521no—
203C2×D8—132no—
204C2×D8—261no—
205C2×D8—261no—
206C2×D8—261no—
207C2×D8—261no—
208C2×D8—261no—
209C2×D8—521no—
210#131—21no—
211#131—21no—
212#131C4×D1312yes—
213#131C22⋊D1312yes—
214C2×M16—21no—
215C2×M16—261no—
216C2×M16—261no—
217C2×M16D5211yescharacteristic
218C22×C8—21no—
219C22×C8C22×D1311yescharacteristic
220C2×C4⋊C4—261no—
221M32—24no—
222M32—21no—
223M32C22⋊D1312yes—
224C2×C16—24no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—21no—
228C2×C16C22⋊D1311yescharacteristic
229C2×C16C22⋊D1311yescharacteristic
230#108—132no—
231#108—261no—
232#108—261no—
233#108—261no—
234#107—261no—
235#107—261no—
236#103—521no—
237#102—521no—
238#100—264no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—42no—
242C2×C13#189311yescharacteristic
243C2×C13#222111yescharacteristic
244C2×C13#222311yescharacteristic
245D13—162no—
246C24—521no—
247#41—21no—
248#41—21no—
249#41#609512yes—
250#41#610312yes—
251C2×Q8D10411yescharacteristic
252C2×D4—21no—
253C2×D4—262no—
254C2×D4—521no—
255C2×D4—521no—
256C2×D4—521no—
257C2×D4—521no—
258C2×D4—521no—
259C2×D4D10411yescharacteristic
260C22×C4—21no—
261C22×C4—521no—
262C22×C4C2×D5211yescharacteristic
263SD16—524no—
264D8—262no—
265D8—262no—
266D8—524no—
267D8—521no—
268D8—521no—
269M16—21no—
270M16—22no—
271M16—22no—
272M16—262no—
273M16—521no—
274M16—521no—
275M16—521no—
276M16#610312yes—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—521no—
281C2×C8—521no—
282C2×C8C2×C4×D1311yescharacteristic
283C2×C8#612711yescharacteristic
284C2×C8#612711yescharacteristic
285C2×C8C2×C22⋊D1311yescharacteristic
286C2×C8C2×C22⋊D1311yescharacteristic
287C2×C8C2×C22⋊D1311yescharacteristic
288C4⋊C4—521no—
289C4⋊C4—521no—
290C16—21no—
291C16—22no—
292C16—21no—
293C13#1307311yescharacteristic, complemented, Sylow
294C23—21no—
295C23—522no—
296C23—1041no—
297C23—1041no—
298C23—2081no—
299C23—2081no—
300C23#8815811yescharacteristic
301Q8—21no—
302Q8#8806112yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—522no—
307D4—522no—
308D4—1041no—
309D4—1041no—
310D4#8806112yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—1041no—
315C2×C4—2081no—
316C2×C4C2×#609511yescharacteristic
317C2×C4C2×D10411yescharacteristic
318C2×C4#8815811yescharacteristic
319C2×C4C2×#610311yescharacteristic
320C2×C4#8818411yescharacteristic
321C2×C4#8818411yescharacteristic
322C8—22no—
323C8—522no—
324C8—1041no—
325C8C4×C22⋊D1311yescharacteristic
326C8C4×C22⋊D1311yescharacteristic
327C8#8818311yescharacteristic
328C8#8820711yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—1042no—
335C22—2082no—
336C22—2082no—
337C22—2081no—
338C22—2081no—
339C22#1171877411yescharacteristic
340C22#1171877511yescharacteristic
341C22#1171877611yescharacteristic
342C4—22no—
343C4—2081no—
344C4C2×#8806111yescharacteristic
345C4#1171877511yescharacteristic
346C4#1171877611yescharacteristic
347C4#1171887411yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—2082no—
352C2#1311526411yescharacteristic
353C2#1311695611yescharacteristic
354C2#1311696611yescharacteristic
subgroupG/H
centerC22#11718776
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#504C2
socleC22×C13#466
prime radicalC2×#11718803C2
cosocleC22×C8×C13C23
hypercenterC2×#504D13
hypocenterC13#13073
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
2. C2×#11718108C2semidirect
3. C2×#11718101C2semidirect
4. #13114900C2semidirect
5. #13112945C2semidirect
6. #13112930C2semidirect
7. C2×C13×#504C2semidirect
19. #11718803C4semidirect
117. C2×#504D13semidirect
293. C13#13073semidirect

Maximal subgroups

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

subgroupindex
C2×#117188032
C2×#117181082
C2×#117181012
#131149002
#131129452
#131129302
C2×C13×#5042
#1307313