Finite Group Databasebeta

← C131×#29790 #45715674

Subgroups — C131×#29790 #45715674

Order 33536.

726 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3095×C131C211yesmaximal, characteristic, complemented
2#3094×C131C211yesmaximal, characteristic
3C2×#465×C131C211yesmaximal, characteristic
4C2×#424×C131C211yesmaximal, characteristic, complemented
5#2090×C131C212yesmaximal, complemented
6#2064×C131C212yesmaximal, complemented
7#2063×C131C212yesmaximal, complemented
8#2046×C131C212yesmaximal, complemented
9#1901×C131C211yesmaximal, characteristic, complemented
10#1900×C131C211yesmaximal, characteristic
11#1810×C131C211yesmaximal, characteristic, complemented
12C22×SD16×C131C2211yescharacteristic
13C22×M16×C131C2211yescharacteristic
14C23×C8×C131C2211yescharacteristic
15C2×C22⋊Q8×C131C2211yescharacteristic
16C2×#121×C131C2211yescharacteristic
17C2×#117×C131C2211yescharacteristic
18#485×C131—22no—
19#484×C131—21no—
20#483×C131—21no—
21#482×C131—22no—
22#481×C131—21no—
23#480×C131—21no—
24#465×C131—22no—
25#465×C131—22no—
26C2×#108×C131C2212yes—
27#428×C131C2212yes—
28#428×C131C2212yes—
29C2×#106×C131C2211yescharacteristic
30#424×C131—22no—
31#424×C131C2212yes—
32#424×C131C2212yes—
33C2×C4⋊C8×C131—22no—
34#419×C131C2212yes—
35#418×C131C2212yes—
36C2×#103×C131C2211yescharacteristic
37C2×#102×C131C2211yescharacteristic
38C2×#101×C131C2212yes—
39C2×#100×C131C2212yes—
40#407×C131C2211yescharacteristic
41#407×C131C2211yescharacteristic
42#343×C131C2212yes—
43#343×C131C2212yes—
44#341×C131C2212yes—
45C22×Q8×C131C2311yescharacteristic
46C22×D4×C131—21no—
47C22×D4×C131C2311yescharacteristic
48C23×C4×C131C2311yescharacteristic
49C2×SD16×C131—22no—
50C2×SD16×C131—42no—
51C2×M16×C131—21no—
52C2×M16×C131—42no—
53C2×M16×C131C2312yes—
54C2×M16×C131C2312yes—
55C2×M16×C131C2312yes—
56C22×C8×C131—21no—
57C22×C8×C131—42no—
58C22×C8×C131D412yes—
59C22×C8×C131D412yes—
60C22×C8×C131C2311yescharacteristic
61C22×C8×C131C2311yescharacteristic
62C22⋊Q8×C131—21no—
63C22⋊Q8×C131—21no—
64C22⋊Q8×C131—21no—
65C22⋊Q8×C131—21no—
66#121×C131—21no—
67#121×C131—21no—
68#121×C131—21no—
69#121×C131—21no—
70#117×C131—21no—
71#117×C131—21no—
72#117×C131D412yes—
73#117×C131C2312yes—
74C2×C4⋊C4×C131—21no—
75C2×C4⋊C4×C131D411yescharacteristic
76C2×C4⋊C4×C131D411yescharacteristic
77C2×C4⋊C4×C131C2311yescharacteristic
78C2×C4⋊C4×C131C2311yescharacteristic
79C2×C22⋊C4×C131—21no—
80C2×C22⋊C4×C131—21no—
81C2×C22⋊C4×C131—21no—
82C2×C42×C131—21no—
83#108×C131—42no—
84#107×C131—22no—
85#107×C131—22no—
86#106×C131—22no—
87#106×C131—22no—
88#106×C131—22no—
89C4⋊C8×C131—24no—
90C4⋊C8×C131—24no—
91#103×C131—22no—
92#103×C131—22no—
93#103×C131—22no—
94#102×C131—22no—
95#102×C131—22no—
96#102×C131—22no—
97#101×C131—42no—
98#100×C131—42no—
99C22⋊C8×C131—21no—
100C22⋊C8×C131—21no—
101C22⋊C8×C131—21no—
102C22⋊C8×C131—21no—
103C24×C131—21no—
104C24×C131#4111yescharacteristic
105C2×Q8×C131—21no—
106C2×Q8×C131—21no—
107C2×Q8×C131—22no—
108C2×Q8×C131—22no—
109C2×D4×C131—21no—
110C2×D4×C131—21no—
111C2×D4×C131—22no—
112C2×D4×C131—22no—
113C2×D4×C131—41no—
114C2×D4×C131—41no—
115C2×D4×C131—82no—
116C22×C4×C131—22no—
117C22×C4×C131—22no—
118C22×C4×C131—21no—
119C22×C4×C131—21no—
120C22×C4×C131—21no—
121C22×C4×C131—21no—
122C22×C4×C131—21no—
123C22×C4×C131C2×D411yescharacteristic
124C22×C4×C131C2×D411yescharacteristic
125C22×C4×C131C2×D411yescharacteristic
126C22×C4×C131C2×D411yescharacteristic
127C22×C4×C131#4111yescharacteristic
128C22×C4×C131C2411yescharacteristic
129SD16×C131—44no—
130M16×C131—22no—
131M16×C131—22no—
132M16×C131—22no—
133M16×C131—22no—
134M16×C131—22no—
135M16×C131—22no—
136M16×C131—42no—
137C2×C8×C131—22no—
138C2×C8×C131—22no—
139C2×C8×C131—22no—
140C2×C8×C131—22no—
141C2×C8×C131—22no—
142C2×C8×C131—42no—
143C2×C8×C131—42no—
144C2×C8×C131—42no—
145C2×C8×C131C2×D412yes—
146C2×C8×C131C2×D412yes—
147C4⋊C4×C131—21no—
148C4⋊C4×C131—21no—
149C4⋊C4×C131—21no—
150C4⋊C4×C131—21no—
151C4⋊C4×C131—21no—
152C4⋊C4×C131—21no—
153C4⋊C4×C131—41no—
154C4⋊C4×C131—41no—
155C4⋊C4×C131C2×D412yes—
156C4⋊C4×C131C2×D412yes—
157C22⋊C4×C131—22no—
158C22⋊C4×C131—22no—
159C22⋊C4×C131—41no—
160C22⋊C4×C131—41no—
161C22⋊C4×C131—41no—
162C22⋊C4×C131—41no—
163C42×C131—22no—
164C42×C131—22no—
165C23×C131—22no—
166C23×C131—22no—
167C23×C131—41no—
168C23×C131—41no—
169C23×C131—42no—
170C23×C131—81no—
171C23×C131—81no—
172C23×C131#12111yescharacteristic
173C23×C131#12111yescharacteristic
174C23×C131C2×#4111yescharacteristic
175Q8×C131—41no—
176Q8×C131—41no—
177Q8×C131—42no—
178D4×C131—41no—
179D4×C131—41no—
180D4×C131—42no—
181D4×C131—82no—
182D4×C131—82no—
183C2×C4×C131—22no—
184C2×C4×C131—21no—
185C2×C4×C131—21no—
186C2×C4×C131—21no—
187C2×C4×C131—21no—
188C2×C4×C131—22no—
189C2×C4×C131—22no—
190C2×C4×C131—22no—
191C2×C4×C131—22no—
192C2×C4×C131—42no—
193C2×C4×C131—42no—
194C2×C4×C131—41no—
195C2×C4×C131—41no—
196C2×C4×C131—41no—
197C2×C4×C131—42no—
198C2×C4×C131—81no—
199C2×C4×C131—81no—
200C2×C4×C131#12111yescharacteristic
201C2×C4×C131#12111yescharacteristic
202C2×C4×C131C22×D411yescharacteristic
203C2×C4×C131C22×D411yescharacteristic
204C2×C4×C131H(5,𝔽2)12yes—
205C2×C4×C1312−1+412yes—
206C8×C131—22no—
207C8×C131—22no—
208C8×C131—42no—
209C8×C131—42no—
210C8×C131—42no—
211C22×C131—21no—
212C22×C131—21no—
213C22×C131—21no—
214C22×C131—21no—
215C22×C131—21no—
216C22×C131—21no—
217C22×C131—21no—
218C22×C131—44no—
219C22×C131—81no—
220C22×C131—81no—
221C22×C131—81no—
222C22×C131—162no—
223C22×C131#47112yes—
224C22×C131C2×#12111yescharacteristic
225C22×C131#53912yes—
226C4×C131—21no—
227C4×C131—21no—
228C4×C131—42no—
229C4×C131—42no—
230C4×C131—81no—
231C4×C131—81no—
232C4×C131—81no—
233C4×C131#53411yescharacteristic
234C4×C131#53611yescharacteristic
235C4×C131#53712yes—
236C2×C131—22no—
237C2×C131—22no—
238C2×C131—41no—
239C2×C131—161no—
240C2×C131#261811yescharacteristic
241C2×C131C2×#47111yescharacteristic
242C2×C131#306711yescharacteristic
243#29790C13111yesmaximal, characteristic, direct product factor, Sylow
244C131#2979011yescharacteristic, direct product factor, Sylow
245#3095C2×C13111yescharacteristic, complemented
246#3094C2×C13111yescharacteristic
247C2×#465C2×C13111yescharacteristic
248C2×#424C2×C13111yescharacteristic, complemented
249#2090C2×C13112yescomplemented
250#2064C2×C13112yescomplemented
251#2063C2×C13112yescomplemented
252#2046C2×C13112yescomplemented
253#1901C2×C13111yescharacteristic, complemented
254#1900C2×C13111yescharacteristic
255#1810C2×C13111yescharacteristic, complemented
256C22×SD16C22×C13111yescharacteristic
257C22×M16C22×C13111yescharacteristic
258C23×C8C22×C13111yescharacteristic
259C2×C22⋊Q8C22×C13111yescharacteristic
260C2×#121C22×C13111yescharacteristic
261C2×#117C22×C13111yescharacteristic
262#485—22no—
263#484—21no—
264#483—21no—
265#482—22no—
266#481—21no—
267#480—21no—
268#465—22no—
269#465—22no—
270C2×#108C22×C13112yes—
271#428C22×C13112yes—
272#428C22×C13112yes—
273C2×#106C22×C13111yescharacteristic
274#424—22no—
275#424C22×C13112yes—
276#424C22×C13112yes—
277C2×C4⋊C8—22no—
278#419C22×C13112yes—
279#418C22×C13112yes—
280C2×#103C22×C13111yescharacteristic
281C2×#102C22×C13111yescharacteristic
282C2×#101C22×C13112yes—
283C2×#100C22×C13112yes—
284#407C22×C13111yescharacteristic
285#407C22×C13111yescharacteristic
286#343C22×C13112yes—
287#343C22×C13112yes—
288#341C22×C13112yes—
289C22×Q8C23×C13111yescharacteristic
290C22×D4—21no—
291C22×D4C23×C13111yescharacteristic
292C23×C4C23×C13111yescharacteristic
293C2×SD16—22no—
294C2×SD16—42no—
295C2×M16—21no—
296C2×M16—42no—
297C2×M16C23×C13112yes—
298C2×M16C23×C13112yes—
299C2×M16C23×C13112yes—
300C22×C8—21no—
301C22×C8—42no—
302C22×C8D4×C13112yes—
303C22×C8D4×C13112yes—
304C22×C8C23×C13111yescharacteristic
305C22×C8C23×C13111yescharacteristic
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#117—21no—
315#117—21no—
316#117D4×C13112yes—
317#117C23×C13112yes—
318C2×C4⋊C4—21no—
319C2×C4⋊C4D4×C13111yescharacteristic
320C2×C4⋊C4D4×C13111yescharacteristic
321C2×C4⋊C4C23×C13111yescharacteristic
322C2×C4⋊C4C23×C13111yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C42—21no—
327#108—42no—
328#107—22no—
329#107—22no—
330#106—22no—
331#106—22no—
332#106—22no—
333C4⋊C8—24no—
334C4⋊C8—24no—
335#103—22no—
336#103—22no—
337#103—22no—
338#102—22no—
339#102—22no—
340#102—22no—
341#101—42no—
342#100—42no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C24—21no—
348C24#41×C13111yescharacteristic
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—82no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4C2×D4×C13111yescharacteristic
368C22×C4C2×D4×C13111yescharacteristic
369C22×C4C2×D4×C13111yescharacteristic
370C22×C4C2×D4×C13111yescharacteristic
371C22×C4#41×C13111yescharacteristic
372C22×C4C24×C13111yescharacteristic
373SD16—44no—
374M16—22no—
375M16—22no—
376M16—22no—
377M16—22no—
378M16—22no—
379M16—22no—
380M16—42no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—42no—
387C2×C8—42no—
388C2×C8—42no—
389C2×C8C2×D4×C13112yes—
390C2×C8C2×D4×C13112yes—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C13112yes—
400C4⋊C4C2×D4×C13112yes—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C42—22no—
408C42—22no—
409C23—22no—
410C23—22no—
411C23—41no—
412C23—41no—
413C23—42no—
414C23—81no—
415C23—81no—
416C23#121×C13111yescharacteristic
417C23#121×C13111yescharacteristic
418C23C2×#41×C13111yescharacteristic
419Q8—41no—
420Q8—41no—
421Q8—42no—
422D4—41no—
423D4—41no—
424D4—42no—
425D4—82no—
426D4—82no—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4#121×C13111yescharacteristic
445C2×C4#121×C13111yescharacteristic
446C2×C4C22×D4×C13111yescharacteristic
447C2×C4C22×D4×C13111yescharacteristic
448C2×C4H(5,𝔽2)×C13112yes—
449C2×C42−1+4×C13112yes—
450C8—22no—
451C8—22no—
452C8—42no—
453C8—42no—
454C8—42no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—44no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—162no—
467C22#471×C13112yes—
468C22C2×#121×C13111yescharacteristic
469C22#539×C13112yes—
470C4—21no—
471C4—21no—
472C4—42no—
473C4—42no—
474C4—81no—
475C4—81no—
476C4—81no—
477C4#534×C13111yescharacteristic
478C4#536×C13111yescharacteristic
479C4#537×C13112yes—
480C2—22no—
481C2—22no—
482C2—41no—
483C2—161no—
484C2#2618×C13111yescharacteristic
485C2C2×#471×C13111yescharacteristic
486C2#3067×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#121
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3095×C131C2semidirect
4. C2×#424×C131C2semidirect
5. #2090×C131C2semidirect
6. #2064×C131C2semidirect
7. #2063×C131C2semidirect
8. #2046×C131C2semidirect
9. #1901×C131C2semidirect
11. #1810×C131C2semidirect
243. #29790C131direct (N × H)
244. C131#29790direct (N × H)
245. #3095C2×C131semidirect
248. C2×#424C2×C131semidirect
249. #2090C2×C131semidirect
250. #2064C2×C131semidirect
251. #2063C2×C131semidirect
252. #2046C2×C131semidirect
253. #1901C2×C131semidirect
255. #1810C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3095×C1312
#3094×C1312
C2×#465×C1312
C2×#424×C1312
#2090×C1312
#2064×C1312
#2063×C1312
#2046×C1312
#1901×C1312
#1900×C1312
#1810×C1312
#29790131