Finite Group Databasebeta

← C131×#29679 #45715563

Subgroups — C131×#29679 #45715563

Order 33536.

1106 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3461×C131C211yesmaximal, characteristic, complemented
2#3038×C131C212yesmaximal, complemented
3#2548×C131C211yesmaximal, characteristic, complemented
4#2027×C131C212yesmaximal, complemented
5#2006×C131C212yesmaximal, complemented
6#2003×C131C214yesmaximal, complemented
7#1806×C131C212yesmaximal, complemented
8#1801×C131C211yesmaximal, characteristic, complemented
9C2×AGL(1,ℤ/8)×C131C2214yes—
10#544×C131C2211yescharacteristic
11#542×C131—22no—
12#541×C131—22no—
13#539×C131—22no—
14#537×C131C2211yescharacteristic
15#536×C131C2212yes—
16#533×C131—22no—
17C2×#127×C131C2211yescharacteristic
18#529×C131—22no—
19#529×C131—22no—
20C2×#124×C131C2212yes—
21C4×#41×C131C2212yes—
22C2×C4×Q8×C131C2211yescharacteristic
23#460×C131—22no—
24#460×C131—22no—
25#459×C131—22no—
26#459×C131—22no—
27#423×C131C2212yes—
28C2×#104×C131C2214yes—
29#418×C131C2214yes—
30C2×#101×C131C2212yes—
31#394×C131—22no—
32#390×C131—22no—
33#390×C131C2212yes—
34C4×C4⋊C4×C131C2211yescharacteristic
35#343×C131C2212yes—
36#339×C131C2214yes—
37C2×#41×C131C2312yes—
38C22×Q8×C131C2311yescharacteristic
39C22×D4×C131—21no—
40C22×D4×C131—21no—
41C22×D4×C131C2312yes—
42AGL(1,ℤ/8)×C131—44no—
43AGL(1,ℤ/8)×C131—44no—
44C2×SD16×C131—24no—
45C2×D8×C131—24no—
46C2×M16×C131C2314yes—
47C4⋊Q8×C131—22no—
48C4⋊Q8×C131—22no—
49#127×C131—22no—
50#127×C131—22no—
51#126×C131—24no—
52#126×C131—24no—
53#125×C131—22no—
54#125×C131—24no—
55#125×C131—22no—
56#124×C131—22no—
57#124×C131—22no—
58#124×C131—44no—
59#123×C131—24no—
60#123×C131—24no—
61C22⋊Q8×C131—24no—
62C22⋊Q8×C131—22no—
63C22⋊Q8×C131—22no—
64C22⋊Q8×C131—22no—
65C22⋊Q8×C131—22no—
66#121×C131—22no—
67#121×C131—22no—
68C4×Q8×C131—22no—
69C4×Q8×C131—22no—
70C4×Q8×C131—22no—
71C4×Q8×C131D412yes—
72C4×Q8×C131D412yes—
73C4×D4×C131—22no—
74C4×D4×C131—22no—
75C4×D4×C131—22no—
76C4×D4×C131D412yes—
77C4×D4×C131D412yes—
78#117×C131—24no—
79#117×C131—22no—
80#117×C131C2312yes—
81C2×C4⋊C4×C131—21no—
82C2×C4⋊C4×C131D412yes—
83C2×C4⋊C4×C131C2311yescharacteristic
84C2×C22⋊C4×C131—24no—
85C2×C22⋊C4×C131—24no—
86C2×C42×C131—22no—
87C2×C42×C131D412yes—
88C2×C42×C131C2312yes—
89C2×C42×C131C2311yescharacteristic
90C4⋊C8×C131—22no—
91C4⋊C8×C131—22no—
92#104×C131—44no—
93#102×C131—24no—
94#102×C131—24no—
95#101×C131—42no—
96#95×C131—21no—
97C24×C131—22no—
98#41×C131—22no—
99#41×C131—22no—
100#41×C131—22no—
101#41×C131—22no—
102C2×Q8×C131—22no—
103C2×Q8×C131—22no—
104C2×Q8×C131—21no—
105C2×Q8×C131—22no—
106C2×Q8×C131—21no—
107C2×Q8×C131C2×D412yes—
108C2×D4×C131—22no—
109C2×D4×C131—22no—
110C2×D4×C131—24no—
111C2×D4×C131—24no—
112C2×D4×C131—22no—
113C2×D4×C131—22no—
114C2×D4×C131—44no—
115C2×D4×C131—41no—
116C2×D4×C131—42no—
117C2×D4×C131—41no—
118C2×D4×C131—82no—
119C2×D4×C131C2×D412yes—
120C22×C4×C131—22no—
121C22×C4×C131—22no—
122C22×C4×C131—22no—
123C22×C4×C131—22no—
124C22×C4×C131C2×D412yes—
125C22×C4×C131C2×D411yescharacteristic
126C22×C4×C131C2×D412yes—
127C22×C4×C131C2×D411yescharacteristic
128C22×C4×C131C2411yescharacteristic
129SD16×C131—48no—
130D8×C131—48no—
131M16×C131—24no—
132M16×C131—24no—
133C2×C8×C131—24no—
134C4⋊C4×C131—24no—
135C4⋊C4×C131—24no—
136C4⋊C4×C131—22no—
137C4⋊C4×C131—22no—
138C4⋊C4×C131—24no—
139C4⋊C4×C131—24no—
140C4⋊C4×C131—22no—
141C4⋊C4×C131—22no—
142C4⋊C4×C131—22no—
143C4⋊C4×C131—42no—
144C4⋊C4×C131C2×D412yes—
145C4⋊C4×C131C2×D412yes—
146C22⋊C4×C131—24no—
147C22⋊C4×C131—24no—
148C22⋊C4×C131—24no—
149C22⋊C4×C131—22no—
150C22⋊C4×C131—22no—
151C22⋊C4×C131—22no—
152C22⋊C4×C131—48no—
153C22⋊C4×C131—84no—
154C42×C131—22no—
155C42×C131—22no—
156C42×C131—22no—
157C42×C131—22no—
158C42×C131—22no—
159C42×C131—24no—
160C42×C131C2×D412yes—
161C42×C131C2×D412yes—
162C23×C131—22no—
163C23×C131—44no—
164C23×C131—44no—
165C23×C131—42no—
166C23×C131—42no—
167C23×C131—42no—
168C23×C131C22×D411yescharacteristic
169Q8×C131—22no—
170Q8×C131—22no—
171Q8×C131—42no—
172Q8×C131—42no—
173Q8×C131—82no—
174D4×C131—22no—
175D4×C131—22no—
176D4×C131—42no—
177D4×C131—42no—
178D4×C131—44no—
179D4×C131—44no—
180D4×C131—82no—
181D4×C131—84no—
182D4×C131—82no—
183D4×C131—82no—
184C2×C4×C131—22no—
185C2×C4×C131—22no—
186C2×C4×C131—22no—
187C2×C4×C131—22no—
188C2×C4×C131—22no—
189C2×C4×C131—22no—
190C2×C4×C131—22no—
191C2×C4×C131—22no—
192C2×C4×C131—41no—
193C2×C4×C131—42no—
194C2×C4×C131—42no—
195C2×C4×C131—44no—
196C2×C4×C131—42no—
197C2×C4×C131—42no—
198C2×C4×C131—42no—
199C2×C4×C131—42no—
200C2×C4×C131—82no—
201C2×C4×C131#12011yescharacteristic
202C2×C4×C131#12012yes—
203C2×C4×C131#12011yescharacteristic
204C2×C4×C131C22×D412yes—
205C2×C4×C131H(5,𝔽2)11yescharacteristic
206C2×C4×C131H(5,𝔽2)12yes—
207C2×C4×C1312−1+411yescharacteristic
208C8×C131—44no—
209C22×C131—21no—
210C22×C131—21no—
211C22×C131—42no—
212C22×C131—42no—
213C22×C131—42no—
214C22×C131—84no—
215C22×C131—84no—
216C22×C131—82no—
217C22×C131—82no—
218C22×C131—82no—
219C22×C131C2×#12011yescharacteristic
220C22×C131#53511yescharacteristic
221C22×C131#53711yescharacteristic
222C4×C131—21no—
223C4×C131—22no—
224C4×C131—42no—
225C4×C131—42no—
226C4×C131—42no—
227C4×C131—42no—
228C4×C131—42no—
229C4×C131—82no—
230C4×C131#45412yes—
231C4×C131#53512yes—
232C4×C131#53712yes—
233C2×C131—21no—
234C2×C131—21no—
235C2×C131—82no—
236C2×C131—162no—
237C2×C131#261511yescharacteristic
238C2×C131C2×#45411yescharacteristic
239C2×C131#302111yescharacteristic
240#29679C13111yesmaximal, characteristic, direct product factor, Sylow
241C131#2967911yescharacteristic, direct product factor, Sylow
242#3461C2×C13111yescharacteristic, complemented
243#3038C2×C13112yescomplemented
244#2548C2×C13111yescharacteristic, complemented
245#2027C2×C13112yescomplemented
246#2006C2×C13112yescomplemented
247#2003C2×C13114yescomplemented
248#1806C2×C13112yescomplemented
249#1801C2×C13111yescharacteristic, complemented
250C2×AGL(1,ℤ/8)C22×C13114yes—
251#544C22×C13111yescharacteristic
252#542—22no—
253#541—22no—
254#539—22no—
255#537C22×C13111yescharacteristic
256#536C22×C13112yes—
257#533—22no—
258C2×#127C22×C13111yescharacteristic
259#529—22no—
260#529—22no—
261C2×#124C22×C13112yes—
262C4×#41C22×C13112yes—
263C2×C4×Q8C22×C13111yescharacteristic
264#460—22no—
265#460—22no—
266#459—22no—
267#459—22no—
268#423C22×C13112yes—
269C2×#104C22×C13114yes—
270#418C22×C13114yes—
271C2×#101C22×C13112yes—
272#394—22no—
273#390—22no—
274#390C22×C13112yes—
275C4×C4⋊C4C22×C13111yescharacteristic
276#343C22×C13112yes—
277#339C22×C13114yes—
278C2×#41C23×C13112yes—
279C22×Q8C23×C13111yescharacteristic
280C22×D4—21no—
281C22×D4—21no—
282C22×D4C23×C13112yes—
283AGL(1,ℤ/8)—44no—
284AGL(1,ℤ/8)—44no—
285C2×SD16—24no—
286C2×D8—24no—
287C2×M16C23×C13114yes—
288C4⋊Q8—22no—
289C4⋊Q8—22no—
290#127—22no—
291#127—22no—
292#126—24no—
293#126—24no—
294#125—22no—
295#125—24no—
296#125—22no—
297#124—22no—
298#124—22no—
299#124—44no—
300#123—24no—
301#123—24no—
302C22⋊Q8—24no—
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C22⋊Q8—22no—
306C22⋊Q8—22no—
307#121—22no—
308#121—22no—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×Q8—22no—
312C4×Q8D4×C13112yes—
313C4×Q8D4×C13112yes—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4D4×C13112yes—
318C4×D4D4×C13112yes—
319#117—24no—
320#117—22no—
321#117C23×C13112yes—
322C2×C4⋊C4—21no—
323C2×C4⋊C4D4×C13112yes—
324C2×C4⋊C4C23×C13111yescharacteristic
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C42—22no—
328C2×C42D4×C13112yes—
329C2×C42C23×C13112yes—
330C2×C42C23×C13111yescharacteristic
331C4⋊C8—22no—
332C4⋊C8—22no—
333#104—44no—
334#102—24no—
335#102—24no—
336#101—42no—
337#95—21no—
338C24—22no—
339#41—22no—
340#41—22no—
341#41—22no—
342#41—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—22no—
347C2×Q8—21no—
348C2×Q8C2×D4×C13112yes—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—44no—
356C2×D4—41no—
357C2×D4—42no—
358C2×D4—41no—
359C2×D4—82no—
360C2×D4C2×D4×C13112yes—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4C2×D4×C13112yes—
366C22×C4C2×D4×C13111yescharacteristic
367C22×C4C2×D4×C13112yes—
368C22×C4C2×D4×C13111yescharacteristic
369C22×C4C24×C13111yescharacteristic
370SD16—48no—
371D8—48no—
372M16—24no—
373M16—24no—
374C2×C8—24no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—24no—
380C4⋊C4—24no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4C2×D4×C13112yes—
386C4⋊C4C2×D4×C13112yes—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C22⋊C4—24no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—48no—
394C22⋊C4—84no—
395C42—22no—
396C42—22no—
397C42—22no—
398C42—22no—
399C42—22no—
400C42—24no—
401C42C2×D4×C13112yes—
402C42C2×D4×C13112yes—
403C23—22no—
404C23—44no—
405C23—44no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23C22×D4×C13111yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—42no—
413Q8—42no—
414Q8—82no—
415D4—22no—
416D4—22no—
417D4—42no—
418D4—42no—
419D4—44no—
420D4—44no—
421D4—82no—
422D4—84no—
423D4—82no—
424D4—82no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—82no—
442C2×C4#120×C13111yescharacteristic
443C2×C4#120×C13112yes—
444C2×C4#120×C13111yescharacteristic
445C2×C4C22×D4×C13112yes—
446C2×C4H(5,𝔽2)×C13111yescharacteristic
447C2×C4H(5,𝔽2)×C13112yes—
448C2×C42−1+4×C13111yescharacteristic
449C8—44no—
450C22—21no—
451C22—21no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—84no—
456C22—84no—
457C22—82no—
458C22—82no—
459C22—82no—
460C22C2×#120×C13111yescharacteristic
461C22#535×C13111yescharacteristic
462C22#537×C13111yescharacteristic
463C4—21no—
464C4—22no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—42no—
470C4—82no—
471C4#454×C13112yes—
472C4#535×C13112yes—
473C4#537×C13112yes—
474C2—21no—
475C2—21no—
476C2—82no—
477C2—162no—
478C2#2615×C13111yescharacteristic
479C2C2×#454×C13111yescharacteristic
480C2#3021×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3461×C131C2semidirect
2. #3038×C131C2semidirect
3. #2548×C131C2semidirect
4. #2027×C131C2semidirect
5. #2006×C131C2semidirect
6. #2003×C131C2semidirect
7. #1806×C131C2semidirect
8. #1801×C131C2semidirect
240. #29679C131direct (N × H)
241. C131#29679direct (N × H)
242. #3461C2×C131semidirect
243. #3038C2×C131semidirect
244. #2548C2×C131semidirect
245. #2027C2×C131semidirect
246. #2006C2×C131semidirect
247. #2003C2×C131semidirect
248. #1806C2×C131semidirect
249. #1801C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3461×C1312
#3038×C1312
#2548×C1312
#2027×C1312
#2006×C1312
#2003×C1312
#1806×C1312
#1801×C1312
#29679131