Finite Group Databasebeta

← C131×#29707 #45715591

Subgroups — C131×#29707 #45715591

Order 33536.

1010 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3460×C131C211yesmaximal, characteristic
2#3080×C131C212yesmaximal, complemented
3#2566×C131C211yesmaximal, characteristic, complemented
4#2061×C131C211yesmaximal, characteristic, complemented
5#2060×C131C211yesmaximal, characteristic, complemented
6#2040×C131C211yesmaximal, characteristic, complemented
7#2039×C131C211yesmaximal, characteristic, complemented
8#2037×C131C212yesmaximal, complemented
9#2037×C131C212yesmaximal, complemented
10#1806×C131C212yesmaximal, complemented
11#1800×C131C211yesmaximal, characteristic, complemented
12#544×C131C2211yescharacteristic
13#542×C131—22no—
14#540×C131—22no—
15#538×C131—22no—
16#537×C131C2211yescharacteristic
17#535×C131C2212yes—
18#532×C131—22no—
19#529×C131—22no—
20C2×#125×C131C2211yescharacteristic
21#525×C131—22no—
22C4×#41×C131C2212yes—
23C2×C4×D4×C131C2211yescharacteristic
24#479×C131—22no—
25#479×C131—22no—
26#478×C131—22no—
27#478×C131—22no—
28#428×C131C2212yes—
29#428×C131C2212yes—
30#423×C131C2212yes—
31C2×#104×C131C2212yes—
32C2×#104×C131C2212yes—
33#417×C131C2212yes—
34#417×C131C2212yes—
35C2×#100×C131C2212yes—
36#396×C131—22no—
37#390×C131C2211yescharacteristic
38#390×C131C2211yescharacteristic
39#385×C131—22no—
40#384×C131C2211yescharacteristic
41#382×C131C2211yescharacteristic
42C4×C4⋊C4×C131C2211yescharacteristic
43#343×C131C2211yescharacteristic
44#343×C131C2211yescharacteristic
45#339×C131C2212yes—
46#339×C131C2212yes—
47C2×#41×C131—22no—
48C2×#41×C131C2312yes—
49C22×D4×C131C2311yescharacteristic
50C23×C4×C131D412yes—
51C2×M16×C131C2312yes—
52C2×M16×C131C2312yes—
53C4⋊Q8×C131—22no—
54#127×C131—22no—
55#126×C131—24no—
56#125×C131—22no—
57#125×C131—22no—
58#125×C131—22no—
59#124×C131—24no—
60#124×C131—22no—
61#123×C131—24no—
62#123×C131—24no—
63C22⋊Q8×C131—22no—
64C22⋊Q8×C131—22no—
65C22⋊Q8×C131—22no—
66#121×C131—22no—
67#121×C131—24no—
68#121×C131—22no—
69#121×C131—22no—
70#121×C131—22no—
71#121×C131—22no—
72#120×C131—24no—
73C4×Q8×C131D412yes—
74C4×Q8×C131D412yes—
75C4×D4×C131—24no—
76C4×D4×C131—22no—
77C4×D4×C131—22no—
78C4×D4×C131—22no—
79C4×D4×C131—22no—
80C4×D4×C131D412yes—
81C4×D4×C131D412yes—
82#117×C131—22no—
83#117×C131—22no—
84#117×C131C2312yes—
85C2×C4⋊C4×C131—21no—
86C2×C4⋊C4×C131—21no—
87C2×C4⋊C4×C131—21no—
88C2×C4⋊C4×C131—22no—
89C2×C4⋊C4×C131C2311yescharacteristic
90C2×C4⋊C4×C131C2311yescharacteristic
91C2×C4⋊C4×C131C2311yescharacteristic
92C2×C22⋊C4×C131—22no—
93C2×C22⋊C4×C131—22no—
94C2×C22⋊C4×C131D412yes—
95C2×C42×C131—22no—
96C2×C42×C131C2311yescharacteristic
97C2×C42×C131C2311yescharacteristic
98C2×C42×C131C2311yescharacteristic
99#107×C131—22no—
100#107×C131—22no—
101#106×C131—22no—
102#106×C131—22no—
103C4⋊C8×C131—22no—
104C4⋊C8×C131—22no—
105#104×C131—42no—
106#104×C131—42no—
107#103×C131—22no—
108#103×C131—22no—
109#102×C131—22no—
110#102×C131—22no—
111#100×C131—42no—
112#95×C131—22no—
113#95×C131—21no—
114C24×C131C2×D412yes—
115#41×C131—22no—
116#41×C131—22no—
117#41×C131—22no—
118#41×C131—22no—
119#41×C131—84no—
120C2×Q8×C131—22no—
121C2×Q8×C131C2×D412yes—
122C2×D4×C131—22no—
123C2×D4×C131—24no—
124C2×D4×C131—24no—
125C2×D4×C131—22no—
126C2×D4×C131—22no—
127C2×D4×C131—21no—
128C2×D4×C131—21no—
129C2×D4×C131—22no—
130C2×D4×C131C2×D412yes—
131C22×C4×C131—21no—
132C22×C4×C131—22no—
133C22×C4×C131—22no—
134C22×C4×C131—22no—
135C22×C4×C131—22no—
136C22×C4×C131—22no—
137C22×C4×C131—21no—
138C22×C4×C131—21no—
139C22×C4×C131—21no—
140C22×C4×C131—82no—
141C22×C4×C131C2×D412yes—
142C22×C4×C131C2×D411yescharacteristic
143C22×C4×C131C2×D411yescharacteristic
144C22×C4×C131C2411yescharacteristic
145M16×C131—22no—
146M16×C131—22no—
147M16×C131—22no—
148M16×C131—22no—
149C2×C8×C131—22no—
150C2×C8×C131—22no—
151C4⋊C4×C131—22no—
152C4⋊C4×C131—22no—
153C4⋊C4×C131—24no—
154C4⋊C4×C131—22no—
155C4⋊C4×C131—22no—
156C4⋊C4×C131—22no—
157C4⋊C4×C131—22no—
158C4⋊C4×C131—22no—
159C4⋊C4×C131—42no—
160C4⋊C4×C131—41no—
161C4⋊C4×C131—42no—
162C4⋊C4×C131—41no—
163C4⋊C4×C131—82no—
164C4⋊C4×C131C2×D412yes—
165C4⋊C4×C131C2×D412yes—
166C22⋊C4×C131—24no—
167C22⋊C4×C131—24no—
168C22⋊C4×C131—24no—
169C22⋊C4×C131—22no—
170C22⋊C4×C131—24no—
171C22⋊C4×C131—22no—
172C22⋊C4×C131—22no—
173C22⋊C4×C131—44no—
174C22⋊C4×C131—82no—
175C42×C131—22no—
176C42×C131—22no—
177C42×C131—22no—
178C42×C131—21no—
179C42×C131—21no—
180C42×C131—21no—
181C42×C131—21no—
182C42×C131C2×D412yes—
183C42×C131C2×D412yes—
184C23×C131—22no—
185C23×C131—22no—
186C23×C131—22no—
187C23×C131—22no—
188C23×C131—42no—
189C23×C131—42no—
190C23×C131C22×D411yescharacteristic
191Q8×C131—22no—
192Q8×C131—22no—
193Q8×C131—82no—
194D4×C131—22no—
195D4×C131—22no—
196D4×C131—42no—
197D4×C131—42no—
198D4×C131—42no—
199D4×C131—42no—
200D4×C131—84no—
201D4×C131—82no—
202D4×C131—84no—
203C2×C4×C131—22no—
204C2×C4×C131—22no—
205C2×C4×C131—22no—
206C2×C4×C131—22no—
207C2×C4×C131—22no—
208C2×C4×C131—41no—
209C2×C4×C131—41no—
210C2×C4×C131—44no—
211C2×C4×C131—44no—
212C2×C4×C131—41no—
213C2×C4×C131—41no—
214C2×C4×C131—42no—
215C2×C4×C131—42no—
216C2×C4×C131—42no—
217C2×C4×C131—42no—
218C2×C4×C131—41no—
219C2×C4×C131—42no—
220C2×C4×C131—41no—
221C2×C4×C131—41no—
222C2×C4×C131—41no—
223C2×C4×C131—41no—
224C2×C4×C131—82no—
225C2×C4×C131—82no—
226C2×C4×C131#12011yescharacteristic
227C2×C4×C131#12012yes—
228C2×C4×C131#12011yescharacteristic
229C2×C4×C131C22×D412yes—
230C2×C4×C131H(5,𝔽2)11yescharacteristic
231C2×C4×C1312−1+411yescharacteristic
232C2×C4×C1312−1+412yes—
233C8×C131—42no—
234C8×C131—42no—
235C22×C131—21no—
236C22×C131—21no—
237C22×C131—44no—
238C22×C131—42no—
239C22×C131—42no—
240C22×C131—42no—
241C22×C131—42no—
242C22×C131—42no—
243C22×C131—42no—
244C22×C131—82no—
245C22×C131C2×#12011yescharacteristic
246C22×C131#53611yescharacteristic
247C22×C131#53711yescharacteristic
248C4×C131—22no—
249C4×C131—21no—
250C4×C131—21no—
251C4×C131—42no—
252C4×C131—42no—
253C4×C131—42no—
254C4×C131—42no—
255C4×C131—42no—
256C4×C131—81no—
257C4×C131—81no—
258C4×C131—81no—
259C4×C131#53612yes—
260C4×C131#53712yes—
261C2×C131—21no—
262C2×C131—21no—
263C2×C131—82no—
264C2×C131—82no—
265C2×C131#261611yescharacteristic
266C2×C131#301811yescharacteristic
267C2×C131#301911yescharacteristic
268#29707C13111yesmaximal, characteristic, direct product factor, Sylow
269C131#2970711yescharacteristic, direct product factor, Sylow
270#3460C2×C13111yescharacteristic
271#3080C2×C13112yescomplemented
272#2566C2×C13111yescharacteristic, complemented
273#2061C2×C13111yescharacteristic, complemented
274#2060C2×C13111yescharacteristic, complemented
275#2040C2×C13111yescharacteristic, complemented
276#2039C2×C13111yescharacteristic, complemented
277#2037C2×C13112yescomplemented
278#2037C2×C13112yescomplemented
279#1806C2×C13112yescomplemented
280#1800C2×C13111yescharacteristic, complemented
281#544C22×C13111yescharacteristic
282#542—22no—
283#540—22no—
284#538—22no—
285#537C22×C13111yescharacteristic
286#535C22×C13112yes—
287#532—22no—
288#529—22no—
289C2×#125C22×C13111yescharacteristic
290#525—22no—
291C4×#41C22×C13112yes—
292C2×C4×D4C22×C13111yescharacteristic
293#479—22no—
294#479—22no—
295#478—22no—
296#478—22no—
297#428C22×C13112yes—
298#428C22×C13112yes—
299#423C22×C13112yes—
300C2×#104C22×C13112yes—
301C2×#104C22×C13112yes—
302#417C22×C13112yes—
303#417C22×C13112yes—
304C2×#100C22×C13112yes—
305#396—22no—
306#390C22×C13111yescharacteristic
307#390C22×C13111yescharacteristic
308#385—22no—
309#384C22×C13111yescharacteristic
310#382C22×C13111yescharacteristic
311C4×C4⋊C4C22×C13111yescharacteristic
312#343C22×C13111yescharacteristic
313#343C22×C13111yescharacteristic
314#339C22×C13112yes—
315#339C22×C13112yes—
316C2×#41—22no—
317C2×#41C23×C13112yes—
318C22×D4C23×C13111yescharacteristic
319C23×C4D4×C13112yes—
320C2×M16C23×C13112yes—
321C2×M16C23×C13112yes—
322C4⋊Q8—22no—
323#127—22no—
324#126—24no—
325#125—22no—
326#125—22no—
327#125—22no—
328#124—24no—
329#124—22no—
330#123—24no—
331#123—24no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335#121—22no—
336#121—24no—
337#121—22no—
338#121—22no—
339#121—22no—
340#121—22no—
341#120—24no—
342C4×Q8D4×C13112yes—
343C4×Q8D4×C13112yes—
344C4×D4—24no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4D4×C13112yes—
350C4×D4D4×C13112yes—
351#117—22no—
352#117—22no—
353#117C23×C13112yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4C23×C13111yescharacteristic
359C2×C4⋊C4C23×C13111yescharacteristic
360C2×C4⋊C4C23×C13111yescharacteristic
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4D4×C13112yes—
364C2×C42—22no—
365C2×C42C23×C13111yescharacteristic
366C2×C42C23×C13111yescharacteristic
367C2×C42C23×C13111yescharacteristic
368#107—22no—
369#107—22no—
370#106—22no—
371#106—22no—
372C4⋊C8—22no—
373C4⋊C8—22no—
374#104—42no—
375#104—42no—
376#103—22no—
377#103—22no—
378#102—22no—
379#102—22no—
380#100—42no—
381#95—21no—
382#95—22no—
383C24C2×D4×C13112yes—
384#41—22no—
385#41—22no—
386#41—22no—
387#41—22no—
388#41—84no—
389C2×Q8—22no—
390C2×Q8C2×D4×C13112yes—
391C2×D4—22no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4C2×D4×C13112yes—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—82no—
410C22×C4C2×D4×C13112yes—
411C22×C4C2×D4×C13111yescharacteristic
412C22×C4C2×D4×C13111yescharacteristic
413C22×C4C24×C13111yescharacteristic
414M16—22no—
415M16—22no—
416M16—22no—
417M16—22no—
418C2×C8—22no—
419C2×C8—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—42no—
429C4⋊C4—41no—
430C4⋊C4—42no—
431C4⋊C4—41no—
432C4⋊C4—82no—
433C4⋊C4C2×D4×C13112yes—
434C4⋊C4C2×D4×C13112yes—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—22no—
439C22⋊C4—24no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—44no—
443C22⋊C4—82no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—21no—
448C42—21no—
449C42—21no—
450C42—21no—
451C42C2×D4×C13112yes—
452C42C2×D4×C13112yes—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—42no—
458C23—42no—
459C23C22×D4×C13111yescharacteristic
460Q8—22no—
461Q8—22no—
462Q8—82no—
463D4—22no—
464D4—22no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4—42no—
469D4—82no—
470D4—84no—
471D4—84no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—44no—
480C2×C4—44no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4#120×C13111yescharacteristic
496C2×C4#120×C13112yes—
497C2×C4#120×C13111yescharacteristic
498C2×C4C22×D4×C13112yes—
499C2×C4H(5,𝔽2)×C13111yescharacteristic
500C2×C42−1+4×C13111yescharacteristic
501C2×C42−1+4×C13112yes—
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—44no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—82no—
514C22C2×#120×C13111yescharacteristic
515C22#536×C13111yescharacteristic
516C22#537×C13111yescharacteristic
517C4—22no—
518C4—21no—
519C4—21no—
520C4—42no—
521C4—42no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—81no—
526C4—81no—
527C4—81no—
528C4#536×C13112yes—
529C4#537×C13112yes—
530C2—21no—
531C2—21no—
532C2—82no—
533C2—82no—
534C2#2616×C13111yescharacteristic
535C2#3018×C13111yescharacteristic
536C2#3019×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3460×C131C2
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
2. #3080×C131C2semidirect
3. #2566×C131C2semidirect
4. #2061×C131C2semidirect
5. #2060×C131C2semidirect
6. #2040×C131C2semidirect
7. #2039×C131C2semidirect
8. #2037×C131C2semidirect
9. #2037×C131C2semidirect
10. #1806×C131C2semidirect
11. #1800×C131C2semidirect
268. #29707C131direct (N × H)
269. C131#29707direct (N × H)
271. #3080C2×C131semidirect
272. #2566C2×C131semidirect
273. #2061C2×C131semidirect
274. #2060C2×C131semidirect
275. #2040C2×C131semidirect
276. #2039C2×C131semidirect
277. #2037C2×C131semidirect
278. #2037C2×C131semidirect
279. #1806C2×C131semidirect
280. #1800C2×C131semidirect

Maximal subgroups

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

subgroupindex
#3460×C1312
#3080×C1312
#2566×C1312
#2061×C1312
#2060×C1312
#2040×C1312
#2039×C1312
#2037×C1312
#1806×C1312
#1800×C1312
#29707131