Finite Group Databasebeta

← C131×#10281 #45696165

Subgroups — C131×#10281 #45696165

Order 33536.

690 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3206×C131C211yesmaximal, characteristic, complemented
2#3205×C131C211yesmaximal, characteristic
3#2858×C131C211yesmaximal, characteristic, complemented
4#1962×C131C211yesmaximal, characteristic, complemented
5#1548×C131C211yesmaximal, characteristic, complemented
6#1545×C131C211yesmaximal, characteristic, complemented
7#1276×C131C211yesmaximal, characteristic, complemented
8#532×C131C2211yescharacteristic
9C2×C4⋊Q8×C131C2211yescharacteristic
10C2×#127×C131C2211yescharacteristic
11C2×#124×C131—22no—
12#493×C131—21no—
13#492×C131—21no—
14#487×C131—21no—
15#486×C131—21no—
16#461×C131—22no—
17#459×C131—22no—
18#448×C131—22no—
19#447×C131—22no—
20#431×C131C2211yescharacteristic
21#431×C131C2211yescharacteristic
22#423×C131C2211yescharacteristic
23C2×#104×C131—22no—
24#390×C131—22no—
25#390×C131—22no—
26C43×C131C2211yescharacteristic
27#333×C131—22no—
28#331×C131—22no—
29C2×#41×C131—21no—
30C22×Q8×C131D412yes—
31C22×D4×C131—21no—
32C22×D4×C131—21no—
33C22×D4×C131D412yes—
34C2×SD16×C131—24no—
35C2×D8×C131—24no—
36C2×M16×C131—21no—
37C4⋊Q8×C131—21no—
38C4⋊Q8×C131—21no—
39C4⋊Q8×C131—21no—
40C4⋊Q8×C131—21no—
41C4⋊Q8×C131D411yescharacteristic
42#127×C131—21no—
43#127×C131—21no—
44#127×C131—21no—
45#127×C131—21no—
46#127×C131D411yescharacteristic
47#124×C131—21no—
48#124×C131—48no—
49#121×C131—21no—
50#121×C131—21no—
51C4×D4×C131—21no—
52C4×D4×C131—21no—
53C2×C4⋊C4×C131—21no—
54C2×C4⋊C4×C131—21no—
55C2×C22⋊C4×C131—28no—
56C2×C42×C131—21no—
57C2×C42×C131—21no—
58C2×C42×C131D412yes—
59C2×C42×C131C2311yescharacteristic
60C4⋊C8×C131—21no—
61C4⋊C8×C131—21no—
62C4⋊C8×C131D412yes—
63C4⋊C8×C131D412yes—
64#104×C131—44no—
65#103×C131—24no—
66#102×C131—24no—
67C22⋊C8×C131—21no—
68C22⋊C8×C131—21no—
69C4×C8×C131—21no—
70C4×C8×C131—21no—
71C24×C131—22no—
72#41×C131—42no—
73#41×C131—42no—
74C2×Q8×C131—22no—
75C2×Q8×C131—21no—
76C2×Q8×C131—22no—
77C2×Q8×C131—44no—
78C2×D4×C131—22no—
79C2×D4×C131—21no—
80C2×D4×C131—21no—
81C2×D4×C131—21no—
82C2×D4×C131—22no—
83C2×D4×C131—44no—
84C2×D4×C131—44no—
85C2×D4×C131—41no—
86C2×D4×C131—41no—
87C2×D4×C131—41no—
88C2×D4×C131—41no—
89C2×D4×C131—41no—
90C2×D4×C131—42no—
91C2×D4×C131—42no—
92C22×C4×C131—22no—
93C22×C4×C131—22no—
94C22×C4×C131—41no—
95C22×C4×C131C2×D411yescharacteristic
96C22×C4×C131C2×D411yescharacteristic
97C22×C4×C131C2×D411yescharacteristic
98SD16×C131—84no—
99D8×C131—84no—
100M16×C131—42no—
101C2×C8×C131—22no—
102C2×C8×C131—22no—
103C2×C8×C131—41no—
104C4⋊C4×C131—21no—
105C4⋊C4×C131—21no—
106C4⋊C4×C131—41no—
107C4⋊C4×C131—41no—
108C4⋊C4×C131—41no—
109C4⋊C4×C131—41no—
110C22⋊C4×C131—416no—
111C22⋊C4×C131—41no—
112C22⋊C4×C131—41no—
113C42×C131—24no—
114C42×C131—22no—
115C42×C131—22no—
116C42×C131—42no—
117C42×C131C2×D411yescharacteristic
118C42×C131C2×D411yescharacteristic
119C42×C131C2×D411yescharacteristic
120C42×C131#4111yescharacteristic
121C23×C131—44no—
122C23×C131—44no—
123C23×C131—41no—
124C23×C131—42no—
125C23×C131—44no—
126C23×C131#12011yescharacteristic
127Q8×C131—44no—
128Q8×C131—42no—
129Q8×C131—82no—
130D4×C131—42no—
131D4×C131—42no—
132D4×C131—44no—
133D4×C131—42no—
134D4×C131—82no—
135D4×C131—82no—
136D4×C131—82no—
137D4×C131—82no—
138D4×C131—82no—
139D4×C131—81no—
140D4×C131—81no—
141C2×C4×C131—22no—
142C2×C4×C131—22no—
143C2×C4×C131—24no—
144C2×C4×C131—42no—
145C2×C4×C131—42no—
146C2×C4×C131—44no—
147C2×C4×C131—41no—
148C2×C4×C131—42no—
149C2×C4×C131—81no—
150C2×C4×C131—81no—
151C2×C4×C131#12011yescharacteristic
152C2×C4×C131#12011yescharacteristic
153C2×C4×C131#12111yescharacteristic
154C2×C4×C131#12111yescharacteristic
155C2×C4×C131#12111yescharacteristic
156C2×C4×C131#12711yescharacteristic
157C2×C4×C131#13512yes—
158C2×C4×C131AGL(1,ℤ/8)12yes—
159C8×C131—42no—
160C8×C131—42no—
161C8×C131—81no—
162C22×C131—21no—
163C22×C131—21no—
164C22×C131—88no—
165C22×C131—81no—
166C22×C131—82no—
167C22×C131—82no—
168C22×C131—81no—
169C22×C131—81no—
170C22×C131—82no—
171C22×C131#39211yescharacteristic
172C22×C131#44912yes—
173C4×C131—21no—
174C4×C131—21no—
175C4×C131—44no—
176C4×C131—82no—
177C4×C131—81no—
178C4×C131#45312yes—
179C4×C131#45512yes—
180C4×C131#46312yes—
181C4×C131#49511yescharacteristic
182C4×C131#49611yescharacteristic
183C2×C131—22no—
184C2×C131—161no—
185C2×C131—162no—
186C2×C131#200211yescharacteristic
187C2×C131#200411yescharacteristic
188C2×C131#201211yescharacteristic
189#10281C13111yesmaximal, characteristic, direct product factor, Sylow
190C131#1028111yescharacteristic, direct product factor, Sylow
191#3206C2×C13111yescharacteristic, complemented
192#3205C2×C13111yescharacteristic
193#2858C2×C13111yescharacteristic, complemented
194#1962C2×C13111yescharacteristic, complemented
195#1548C2×C13111yescharacteristic, complemented
196#1545C2×C13111yescharacteristic, complemented
197#1276C2×C13111yescharacteristic, complemented
198#532C22×C13111yescharacteristic
199C2×C4⋊Q8C22×C13111yescharacteristic
200C2×#127C22×C13111yescharacteristic
201C2×#124—22no—
202#493—21no—
203#492—21no—
204#487—21no—
205#486—21no—
206#461—22no—
207#459—22no—
208#448—22no—
209#447—22no—
210#431C22×C13111yescharacteristic
211#431C22×C13111yescharacteristic
212#423C22×C13111yescharacteristic
213C2×#104—22no—
214#390—22no—
215#390—22no—
216C43C22×C13111yescharacteristic
217#333—22no—
218#331—22no—
219C2×#41—21no—
220C22×Q8D4×C13112yes—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4D4×C13112yes—
224C2×SD16—24no—
225C2×D8—24no—
226C2×M16—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8D4×C13111yescharacteristic
232#127—21no—
233#127—21no—
234#127—21no—
235#127—21no—
236#127D4×C13111yescharacteristic
237#124—21no—
238#124—48no—
239#121—21no—
240#121—21no—
241C4×D4—21no—
242C4×D4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C22⋊C4—28no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42D4×C13112yes—
249C2×C42C23×C13111yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8D4×C13112yes—
253C4⋊C8D4×C13112yes—
254#104—44no—
255#103—24no—
256#102—24no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C4×C8—21no—
260C4×C8—21no—
261C24—22no—
262#41—42no—
263#41—42no—
264C2×Q8—22no—
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—44no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—22no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—42no—
281C2×D4—42no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4C2×D4×C13111yescharacteristic
286C22×C4C2×D4×C13111yescharacteristic
287C22×C4C2×D4×C13111yescharacteristic
288SD16—84no—
289D8—84no—
290M16—42no—
291C2×C8—22no—
292C2×C8—22no—
293C2×C8—41no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—416no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42—24no—
304C42—22no—
305C42—22no—
306C42—42no—
307C42C2×D4×C13111yescharacteristic
308C42C2×D4×C13111yescharacteristic
309C42C2×D4×C13111yescharacteristic
310C42#41×C13111yescharacteristic
311C23—44no—
312C23—44no—
313C23—41no—
314C23—42no—
315C23—44no—
316C23#120×C13111yescharacteristic
317Q8—44no—
318Q8—42no—
319Q8—82no—
320D4—42no—
321D4—42no—
322D4—44no—
323D4—42no—
324D4—82no—
325D4—82no—
326D4—82no—
327D4—82no—
328D4—82no—
329D4—81no—
330D4—81no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4#120×C13111yescharacteristic
342C2×C4#120×C13111yescharacteristic
343C2×C4#121×C13111yescharacteristic
344C2×C4#121×C13111yescharacteristic
345C2×C4#121×C13111yescharacteristic
346C2×C4#127×C13111yescharacteristic
347C2×C4#135×C13112yes—
348C2×C4AGL(1,ℤ/8)×C13112yes—
349C8—42no—
350C8—42no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—88no—
355C22—81no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22—82no—
361C22#392×C13111yescharacteristic
362C22#449×C13112yes—
363C4—21no—
364C4—21no—
365C4—44no—
366C4—82no—
367C4—81no—
368C4#453×C13112yes—
369C4#455×C13112yes—
370C4#463×C13112yes—
371C4#495×C13111yescharacteristic
372C4#496×C13111yescharacteristic
373C2—22no—
374C2—162no—
375C2—161no—
376C2#2002×C13111yescharacteristic
377C2#2004×C13111yescharacteristic
378C2#2012×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC2×C42C23×C131
prime radical#3205×C131C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3206×C131C2semidirect
3. #2858×C131C2semidirect
4. #1962×C131C2semidirect
5. #1548×C131C2semidirect
6. #1545×C131C2semidirect
7. #1276×C131C2semidirect
189. #10281C131direct (N × H)
190. C131#10281direct (N × H)
191. #3206C2×C131semidirect
193. #2858C2×C131semidirect
194. #1962C2×C131semidirect
195. #1548C2×C131semidirect
196. #1545C2×C131semidirect
197. #1276C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3206×C1312
#3205×C1312
#2858×C1312
#1962×C1312
#1548×C1312
#1545×C1312
#1276×C1312
#10281131