Finite Group Databasebeta

← #15780363

Subgroups — #15780363

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×#11718801C211yesmaximal, characteristic, complemented
2C2×#11718155C211yesmaximal, characteristic, complemented
3C2×#11718154C211yesmaximal, characteristic, complemented
4#13114900C211yesmaximal, characteristic, complemented
5#13112946C211yesmaximal, characteristic, complemented
6#13112929C211yesmaximal, characteristic, complemented
7C2×C13×#472C211yesmaximal, characteristic
8C2×C13×AGL(1,ℤ/8)—21no—
9C22×C13×D8C2211yescharacteristic
10C2×C13×#131C2211yescharacteristic
11C13×#472—22no—
12C13×#472C414yescomplemented
13C2×C13×#108C2211yescharacteristic
14C2×C13×#100—21no—
15#11718893—21no—
16#11718801—22no—
17#11718801—22no—
18C2×#88059C2211yescharacteristic
19C2×#88058C2211yescharacteristic
20C2×#88052—21no—
21C2×#88052C2211yescharacteristic
22C22×#6090—21no—
23C22×#6090C2211yescharacteristic
24#11718155—22no—
25#11718154—21no—
26#11718154—21no—
27#11718146—21no—
28C2×C13×#41D411yescharacteristic
29C22×D4×C13—21no—
30C13×AGL(1,ℤ/8)—24no—
31C13×AGL(1,ℤ/8)—42no—
32C2×C13×SD16—41no—
33C2×C13×D8—21no—
34C2×C13×D8—21no—
35C2×C13×D8—21no—
36C2×C13×D8—21no—
37C2×C13×D8—21no—
38C2×C13×D8—41no—
39C2×C13×D8C2×C412yes—
40C13×#131—21no—
41C13×#131—21no—
42C13×#131C2×C412yes—
43C13×#131D412yes—
44C2×C13×M16—21no—
45C2×C13×M16—21no—
46C2×C13×M16D411yescharacteristic
47C22×C8×C13—21no—
48C22×C8×C13C2311yescharacteristic
49C2×C4⋊Dic13—21no—
50C2×#6099—21no—
51C13×#108—21no—
52C13×#108C2×C412yes—
53C13×#100—24no—
54#88075—41no—
55#88072—41no—
56#88059—21no—
57#88059—21no—
58#88058—21no—
59#88058—21no—
60#88052—24no—
61#88052—21no—
62#88052D412yes—
63C2×#6090—24no—
64C2×#6090—21no—
65C2×#6090—21no—
66C2×#6090—21no—
67C2×#6090D411yescharacteristic
68C2×#6090D411yescharacteristic
69#13073—131nomaximal, Sylow
70C24×C13—41no—
71C13×#41—21no—
72C13×#41—21no—
73C13×#41C22⋊C412yes—
74C13×#41SD1612yes—
75C2×Q8×C13D811yescharacteristic
76C2×D4×C13—21no—
77C2×D4×C13—22no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13D811yescharacteristic
84C22×C4×C13—21no—
85C22×C4×C13C2×D411yescharacteristic
86C22×Dic13—41no—
87C13×SD16—44no—
88C13×D8—22no—
89C13×D8—22no—
90C13×D8—44no—
91C13×D8—41no—
92C13×D8—41no—
93C13×M16—21no—
94C13×M16—22no—
95C13×M16—22no—
96C13×M16—22no—
97C13×M16—41no—
98C13×M16C22⋊C412yes—
99C2×C8×C13—21no—
100C2×C8×C13—22no—
101C2×C8×C13—22no—
102C2×C8×C13—41no—
103C2×C8×C13C22×C411yescharacteristic
104C2×C8×C13C2×D411yescharacteristic
105C2×C8×C13C2×D411yescharacteristic
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13#4111yescharacteristic
108C2×C8×C13#4111yescharacteristic
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111#6099—41no—
112#6099—41no—
113C2×#1055—41no—
114#6090—21no—
115#6090—22no—
116#6090—21no—
117C2×#504—131no—
118C2×#472D1311yescharacteristic
119C2×#361—131no—
120C2×#357—131no—
121#1816—131no—
122#1387—131no—
123#1381—131no—
124C23×C13—21no—
125C23×C13—42no—
126C23×C13—81no—
127C23×C13—81no—
128C23×C13—161no—
129C23×C13—161no—
130C23×C13#13511yescharacteristic
131Q8×C13—21no—
132Q8×C13#10212yes—
133D4×C13—22no—
134D4×C13—22no—
135D4×C13—21no—
136D4×C13—42no—
137D4×C13—42no—
138D4×C13—81no—
139D4×C13—81no—
140D4×C13#10212yes—
141C2×C4×C13—21no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13C2×D811yescharacteristic
148C2×C4×C13C2×SD1611yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C2×Dic13—81no—
151C2×Dic13—161no—
152C8×C13—22no—
153C8×C13—42no—
154C8×C13C4×D411yescharacteristic
155C8×C13C4×D411yescharacteristic
156C8×C13#12011yescharacteristic
157C8×C13#12311yescharacteristic
158#1055—81no—
159C2×AGL(1,ℤ/8)—21no—
160C22×D8C2×D1311yescharacteristic
161C2×#131C2×D1311yescharacteristic
162#504—262no—
163#504—262no—
164C2×M32—131no—
165C2×M32—261no—
166C22×C16—131no—
167C22×C16—261no—
168#472—22no—
169#472Dic1314yescomplemented
170C2×#108—131no—
171C2×#108C2×D1311yescharacteristic
172C2×#107—131no—
173#417—261no—
174C2×#100—21no—
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—82no—
185C22×C13—162no—
186C22×C13—162no—
187C22×C13—161no—
188C22×C13—161no—
189C22×C13#41611yescharacteristic
190C22×C13#46511yescharacteristic
191C22×C13#46611yescharacteristic
192C4×C13—22no—
193C4×C13#38611yescharacteristic
194C4×C13C2×#10211yescharacteristic
195C4×C13#46511yescharacteristic
196C4×C13#46611yescharacteristic
197Dic13—161no—
198C2×#41C22⋊D1311yescharacteristic
199C22×D4—21no—
200AGL(1,ℤ/8)—24no—
201AGL(1,ℤ/8)—42no—
202C2×SD16—41no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—21no—
208C2×D8—41no—
209C2×D8C2×Dic1312yes—
210#131—21no—
211#131—21no—
212#131C2×Dic1312yes—
213#131C22⋊D1312yes—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—261no—
217C2×M16C22⋊D1311yescharacteristic
218C22×C8—21no—
219C22×C8C22×D1311yescharacteristic
220C2×C4⋊C4—261no—
221M32—132no—
222M32—264no—
223M32—261no—
224C2×C16—131no—
225C2×C16—131no—
226C2×C16—264no—
227C2×C16—261no—
228C2×C16—261no—
229C2×C16—261no—
230#108—21no—
231#108—261no—
232#108—261no—
233#108C2×Dic1312yes—
234#107—261no—
235#107—261no—
236#103—521no—
237#102—521no—
238#100—24no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—42no—
242C2×C13—162no—
243C2×C13#189311yescharacteristic
244C2×C13#222111yescharacteristic
245C2×C13#222311yescharacteristic
246C24—41no—
247#41—21no—
248#41—21no—
249#41#610512yes—
250#41C22⋊Dic1312yes—
251C2×Q8#610411yescharacteristic
252C2×D4—21no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4#610411yescharacteristic
260C22×C4—21no—
261C22×C4—521no—
262C22×C4C2×C22⋊D1311yescharacteristic
263SD16—44no—
264D8—22no—
265D8—22no—
266D8—44no—
267D8—41no—
268D8—41no—
269M16—21no—
270M16—22no—
271M16—22no—
272M16—22no—
273M16—41no—
274M16—521no—
275M16—521no—
276M16C22⋊Dic1312yes—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—521no—
282C2×C8D4×D1311yescharacteristic
283C2×C8D4×D1311yescharacteristic
284C2×C8#612911yescharacteristic
285C2×C8#612911yescharacteristic
286C2×C8C22×Dic1311yescharacteristic
287C2×C8C2×C22⋊D1311yescharacteristic
288C4⋊C4—521no—
289C4⋊C4—521no—
290C16—261no—
291C16—261no—
292C16—262no—
293C13#1307311yescharacteristic, complemented, Sylow
294C23—21no—
295C23—42no—
296C23—81no—
297C23—81no—
298C23—161no—
299C23—161no—
300C23#8820411yescharacteristic
301Q8—21no—
302Q8#8807212yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—42no—
307D4—42no—
308D4—81no—
309D4—81no—
310D4#8807212yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—1041no—
315C2×C4—2081no—
316C2×C4C2×#610411yescharacteristic
317C2×C4C2×#610511yescharacteristic
318C2×C4#8819311yescharacteristic
319C2×C4#8819311yescharacteristic
320C2×C4#8820411yescharacteristic
321C2×C4C2×C22⋊Dic1311yescharacteristic
322C8—22no—
323C8—42no—
324C8—1041no—
325C8D4×Dic1311yescharacteristic
326C8D4×Dic1311yescharacteristic
327C8#8818911yescharacteristic
328C8#8819111yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—82no—
335C22—162no—
336C22—162no—
337C22—161no—
338C22—161no—
339C22#1171869911yescharacteristic
340C22#1171870211yescharacteristic
341C22#1171889411yescharacteristic
342C4—22no—
343C4—2081no—
344C4#1171869911yescharacteristic
345C4#1171870211yescharacteristic
346C4C2×#8807211yescharacteristic
347C4#1171888111yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—162no—
352C2#1311526511yescharacteristic
353C2#1311695411yescharacteristic
354C2#1311696411yescharacteristic
subgroupG/H
centerC22#11718699
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC2×C13×#472C2
socleC22×C13#466
cosocleC22×C8×C13C23
hypercenterC2×#472D13
hypocenterC13#13073
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C2×#11718801C2semidirect
2. C2×#11718155C2semidirect
3. C2×#11718154C2semidirect
4. #13114900C2semidirect
5. #13112946C2semidirect
6. #13112929C2semidirect
12. C13×#472C4semidirect
169. #472Dic13semidirect
293. C13#13073semidirect

Maximal subgroups

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

subgroupindex
C2×#117188012
C2×#117181552
C2×#117181542
#131149002
#131129462
#131129292
C2×C13×#4722
#1307313