Finite Group Databasebeta

← C131×#12690 #45698574

Subgroups — C131×#12690 #45698574

Order 33536.

1228 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C131C211yesmaximal, characteristic
2C2×#352×C131C212yesmaximal, complemented
3C2×AΣL(1,𝔽16)×C131C212yesmaximal, complemented
4#1783×C131C211yesmaximal, characteristic, complemented
5#1781×C131C211yesmaximal, characteristic, complemented
6C23×D4×C131C411yescharacteristic, complemented
7C23×D4×C131C2211yescharacteristic
8#534×C131—24no—
9#534×C131—24no—
10C2×#123×C131—21no—
11C2×#123×C131C411yescharacteristic, complemented
12C2×#123×C131C2211yescharacteristic
13C2×#121×C131—21no—
14C2×#121×C131—21no—
15C2×#120×C131—21no—
16C2×#120×C131C411yescharacteristic, complemented
17C2×#120×C131C2211yescharacteristic
18C22×C22⋊C4×C131C411yescharacteristic, complemented
19C2×#100×C131—21no—
20C2×#100×C131C2212yes—
21C2×#99×C131—21no—
22C2×#99×C131C2212yes—
23#407×C131—21no—
24#379×C131—21no—
25#352×C131—24no—
26AΣL(1,𝔽16)×C131—24no—
27C25×C131C2×C411yescharacteristic
28C25×C131C2×C411yescharacteristic
29C25×C131D411yescharacteristic
30C22×D4×C131—21no—
31C22×D4×C131—21no—
32C22×D4×C131—22no—
33C22×D4×C131—21no—
34C22×D4×C131—21no—
35C22×D4×C131—22no—
36C22×D4×C131—22no—
37C22×D4×C131—22no—
38C22×D4×C131—42no—
39C22×D4×C131—42no—
40C22×D4×C131—42no—
41C22×D4×C131—42no—
42C22×D4×C131C2×C411yescharacteristic
43C22×D4×C131D411yescharacteristic
44C22×D4×C131D411yescharacteristic
45C22×D4×C131C2311yescharacteristic
46C23×C4×C131—21no—
47C23×C4×C131C2×C411yescharacteristic
48C23×C4×C131D411yescharacteristic
49C2×M16×C131—22no—
50#123×C131—28no—
51#123×C131—22no—
52#123×C131—22no—
53#123×C131—22no—
54#123×C131D414yes—
55#121×C131—28no—
56#121×C131—28no—
57#120×C131—28no—
58#120×C131—22no—
59#120×C131—22no—
60#120×C131—22no—
61#120×C131D414yes—
62C2×C4⋊C4×C131—21no—
63C2×C4⋊C4×C131—21no—
64C2×C22⋊C4×C131—21no—
65C2×C22⋊C4×C131—21no—
66C2×C22⋊C4×C131—21no—
67C2×C22⋊C4×C131—21no—
68C2×C22⋊C4×C131—21no—
69C2×C22⋊C4×C131—22no—
70C2×C22⋊C4×C131—22no—
71C2×C22⋊C4×C131—22no—
72C2×C22⋊C4×C131—42no—
73C2×C22⋊C4×C131C2×C411yescharacteristic
74C2×C22⋊C4×C131C2×C411yescharacteristic
75#100×C131—22no—
76#100×C131—22no—
77#100×C131—42no—
78#99×C131—22no—
79#99×C131—22no—
80#99×C131—42no—
81C22⋊C8×C131—42no—
82C24×C131—22no—
83C24×C131—22no—
84C24×C131—21no—
85C24×C131—21no—
86C24×C131—21no—
87C24×C131—22no—
88C24×C131—21no—
89C24×C131—22no—
90C24×C131—41no—
91C24×C131—41no—
92C24×C131—41no—
93C24×C131—82no—
94C24×C131—82no—
95C24×C131—82no—
96C24×C131C22⋊C411yescharacteristic
97C24×C131C22⋊C411yescharacteristic
98C24×C131C22⋊C411yescharacteristic
99C24×C131C22⋊C412yescomplemented
100C24×C131C22×C411yescharacteristic
101C24×C131C2×D411yescharacteristic
102C2×D4×C131—24no—
103C2×D4×C131—24no—
104C2×D4×C131—22no—
105C2×D4×C131—22no—
106C2×D4×C131—21no—
107C2×D4×C131—21no—
108C2×D4×C131—22no—
109C2×D4×C131—24no—
110C2×D4×C131—24no—
111C2×D4×C131—22no—
112C2×D4×C131—41no—
113C2×D4×C131—41no—
114C2×D4×C131—41no—
115C2×D4×C131—41no—
116C2×D4×C131—41no—
117C2×D4×C131—41no—
118C2×D4×C131—48no—
119C2×D4×C131—48no—
120C2×D4×C131—48no—
121C2×D4×C131—42no—
122C2×D4×C131—42no—
123C2×D4×C131—48no—
124C2×D4×C131—42no—
125C2×D4×C131—42no—
126C2×D4×C131—82no—
127C2×D4×C131—82no—
128C2×D4×C131C2×D412yes—
129C2×D4×C131C2×D412yes—
130C22×C4×C131—22no—
131C22×C4×C131—21no—
132C22×C4×C131—21no—
133C22×C4×C131—21no—
134C22×C4×C131—21no—
135C22×C4×C131—24no—
136C22×C4×C131—22no—
137C22×C4×C131—41no—
138C22×C4×C131—41no—
139C22×C4×C131—41no—
140C22×C4×C131—42no—
141C22×C4×C131—82no—
142C22×C4×C131C22⋊C411yescharacteristic
143C22×C4×C131C22⋊C412yescomplemented
144C22×C4×C131C2×D411yescharacteristic
145M16×C131—42no—
146M16×C131—42no—
147C2×C8×C131—42no—
148C4⋊C4×C131—24no—
149C4⋊C4×C131—24no—
150C22⋊C4×C131—24no—
151C22⋊C4×C131—24no—
152C22⋊C4×C131—24no—
153C22⋊C4×C131—21no—
154C22⋊C4×C131—21no—
155C22⋊C4×C131—24no—
156C22⋊C4×C131—24no—
157C22⋊C4×C131—42no—
158C22⋊C4×C131—42no—
159C22⋊C4×C131—84no—
160C22⋊C4×C131C22⋊C412yescomplemented
161C22⋊C4×C131C22⋊C412yescomplemented
162C23×C131—24no—
163C23×C131—24no—
164C23×C131—21no—
165C23×C131—21no—
166C23×C131—21no—
167C23×C131—21no—
168C23×C131—21no—
169C23×C131—21no—
170C23×C131—21no—
171C23×C131—21no—
172C23×C131—21no—
173C23×C131—22no—
174C23×C131—21no—
175C23×C131—21no—
176C23×C131—42no—
177C23×C131—44no—
178C23×C131—42no—
179C23×C131—42no—
180C23×C131—42no—
181C23×C131—42no—
182C23×C131—44no—
183C23×C131—42no—
184C23×C131—42no—
185C23×C131—42no—
186C23×C131—42no—
187C23×C131—41no—
188C23×C131—41no—
189C23×C131—82no—
190C23×C131—82no—
191C23×C131—82no—
192C23×C131—82no—
193C23×C131—84no—
194C23×C131—82no—
195C23×C131—82no—
196C23×C131—82no—
197C23×C131—84no—
198C23×C131—84no—
199C23×C131—84no—
200C23×C131—84no—
201C23×C131#9912yes—
202C23×C131#9912yes—
203C23×C131C2×C22⋊C411yescharacteristic
204C23×C131C2×C22⋊C411yescharacteristic
205C23×C131C2×C22⋊C411yescharacteristic
206C23×C131#12012yes—
207D4×C131—42no—
208D4×C131—42no—
209D4×C131—44no—
210D4×C131—44no—
211D4×C131—42no—
212D4×C131—42no—
213D4×C131—48no—
214D4×C131—48no—
215D4×C131—84no—
216D4×C131—84no—
217C2×C4×C131—21no—
218C2×C4×C131—21no—
219C2×C4×C131—22no—
220C2×C4×C131—22no—
221C2×C4×C131—21no—
222C2×C4×C131—22no—
223C2×C4×C131—21no—
224C2×C4×C131—21no—
225C2×C4×C131—44no—
226C2×C4×C131—42no—
227C2×C4×C131—42no—
228C2×C4×C131—42no—
229C2×C4×C131—41no—
230C2×C4×C131—41no—
231C2×C4×C131—42no—
232C2×C4×C131—84no—
233C2×C4×C131—82no—
234C2×C4×C131—84no—
235C2×C4×C131#12012yes—
236C8×C131—82no—
237C22×C131—22no—
238C22×C131—22no—
239C22×C131—22no—
240C22×C131—22no—
241C22×C131—21no—
242C22×C131—21no—
243C22×C131—22no—
244C22×C131—22no—
245C22×C131—42no—
246C22×C131—41no—
247C22×C131—41no—
248C22×C131—42no—
249C22×C131—42no—
250C22×C131—42no—
251C22×C131—42no—
252C22×C131—42no—
253C22×C131—42no—
254C22×C131—42no—
255C22×C131—42no—
256C22×C131—42no—
257C22×C131—42no—
258C22×C131—42no—
259C22×C131—42no—
260C22×C131—41no—
261C22×C131—42no—
262C22×C131—81no—
263C22×C131—81no—
264C22×C131—82no—
265C22×C131—84no—
266C22×C131—84no—
267C22×C131—88no—
268C22×C131—84no—
269C22×C131—84no—
270C22×C131—82no—
271C22×C131#37911yescharacteristic
272C22×C131C2×#9911yescharacteristic
273C22×C131C2×#9911yescharacteristic
274C4×C131—22no—
275C4×C131—42no—
276C4×C131—42no—
277C4×C131—41no—
278C4×C131—42no—
279C4×C131—162no—
280C2×C131—21no—
281C2×C131—21no—
282C2×C131—42no—
283C2×C131—42no—
284C2×C131—42no—
285C2×C131—41no—
286C2×C131—41no—
287C2×C131—81no—
288C2×C131—82no—
289C2×C131#178111yescharacteristic
290C2×C131#212112yes—
291#12690C13111yesmaximal, characteristic, direct product factor, Sylow
292C131#1269011yescharacteristic, direct product factor, Sylow
293C2×#534C2×C13111yescharacteristic
294C2×#352C2×C13112yescomplemented
295C2×AΣL(1,𝔽16)C2×C13112yescomplemented
296#1783C2×C13111yescharacteristic, complemented
297#1781C2×C13111yescharacteristic, complemented
298C23×D4C4×C13111yescharacteristic, complemented
299C23×D4C22×C13111yescharacteristic
300#534—24no—
301#534—24no—
302C2×#123—21no—
303C2×#123C4×C13111yescharacteristic, complemented
304C2×#123C22×C13111yescharacteristic
305C2×#121—21no—
306C2×#121—21no—
307C2×#120—21no—
308C2×#120C4×C13111yescharacteristic, complemented
309C2×#120C22×C13111yescharacteristic
310C22×C22⋊C4C4×C13111yescharacteristic, complemented
311C2×#100—21no—
312C2×#100C22×C13112yes—
313C2×#99—21no—
314C2×#99C22×C13112yes—
315#407—21no—
316#379—21no—
317#352—24no—
318AΣL(1,𝔽16)—24no—
319C25C2×C4×C13111yescharacteristic
320C25C2×C4×C13111yescharacteristic
321C25D4×C13111yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—22no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4C2×C4×C13111yescharacteristic
335C22×D4D4×C13111yescharacteristic
336C22×D4D4×C13111yescharacteristic
337C22×D4C23×C13111yescharacteristic
338C23×C4—21no—
339C23×C4C2×C4×C13111yescharacteristic
340C23×C4D4×C13111yescharacteristic
341C2×M16—22no—
342#123—28no—
343#123—22no—
344#123—22no—
345#123—22no—
346#123D4×C13114yes—
347#121—28no—
348#121—28no—
349#120—28no—
350#120—22no—
351#120—22no—
352#120—22no—
353#120D4×C13114yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4C2×C4×C13111yescharacteristic
366C2×C22⋊C4C2×C4×C13111yescharacteristic
367#100—22no—
368#100—22no—
369#100—42no—
370#99—22no—
371#99—22no—
372#99—42no—
373C22⋊C8—42no—
374C24—22no—
375C24—22no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—82no—
386C24—82no—
387C24—82no—
388C24C22⋊C4×C13111yescharacteristic
389C24C22⋊C4×C13111yescharacteristic
390C24C22⋊C4×C13111yescharacteristic
391C24C22⋊C4×C13112yescomplemented
392C24C22×C4×C13111yescharacteristic
393C24C2×D4×C13111yescharacteristic
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—48no—
411C2×D4—48no—
412C2×D4—48no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—48no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—82no—
419C2×D4—82no—
420C2×D4C2×D4×C13112yes—
421C2×D4C2×D4×C13112yes—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—42no—
433C22×C4—82no—
434C22×C4C22⋊C4×C13111yescharacteristic
435C22×C4C22⋊C4×C13112yescomplemented
436C22×C4C2×D4×C13111yescharacteristic
437M16—42no—
438M16—42no—
439C2×C8—42no—
440C4⋊C4—24no—
441C4⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—42no—
450C22⋊C4—42no—
451C22⋊C4—84no—
452C22⋊C4C22⋊C4×C13112yescomplemented
453C22⋊C4C22⋊C4×C13112yescomplemented
454C23—24no—
455C23—24no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—22no—
467C23—21no—
468C23—42no—
469C23—44no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—44no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—82no—
482C23—82no—
483C23—82no—
484C23—82no—
485C23—84no—
486C23—82no—
487C23—82no—
488C23—82no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23#99×C13112yes—
494C23#99×C13112yes—
495C23C2×C22⋊C4×C13111yescharacteristic
496C23C2×C22⋊C4×C13111yescharacteristic
497C23C2×C22⋊C4×C13111yescharacteristic
498C23#120×C13112yes—
499D4—42no—
500D4—42no—
501D4—44no—
502D4—44no—
503D4—42no—
504D4—42no—
505D4—48no—
506D4—48no—
507D4—84no—
508D4—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—84no—
525C2×C4—82no—
526C2×C4—84no—
527C2×C4#120×C13112yes—
528C8—82no—
529C22—22no—
530C22—22no—
531C22—21no—
532C22—21no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—42no—
538C22—41no—
539C22—41no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—41no—
552C22—42no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—82no—
557C22—84no—
558C22—84no—
559C22—88no—
560C22—84no—
561C22—84no—
562C22—82no—
563C22#379×C13111yescharacteristic
564C22C2×#99×C13111yescharacteristic
565C22C2×#99×C13111yescharacteristic
566C4—22no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—162no—
572C2—21no—
573C2—21no—
574C2—42no—
575C2—42no—
576C2—41no—
577C2—41no—
578C2—42no—
579C2—81no—
580C2—82no—
581C2#1781×C13111yescharacteristic
582C2#2121×C13112yes—
subgroupG/H
center, socleC22×C131C2×#99
commutatorC24C22×C4×C131
Frattini, cosocleC22×D4C23×C131
prime radicalC2×#534×C131C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C24×C131 ◁ C23×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#352×C131C2semidirect
3. C2×AΣL(1,𝔽16)×C131C2semidirect
4. #1783×C131C2semidirect
5. #1781×C131C2semidirect
6. C23×D4×C131C4semidirect
11. C2×#123×C131C4semidirect
16. C2×#120×C131C4semidirect
18. C22×C22⋊C4×C131C4semidirect
99. C24×C131C22⋊C4semidirect
143. C22×C4×C131C22⋊C4semidirect
160. C22⋊C4×C131C22⋊C4semidirect
161. C22⋊C4×C131C22⋊C4semidirect
291. #12690C131direct (N × H)
292. C131#12690direct (N × H)
294. C2×#352C2×C131semidirect
295. C2×AΣL(1,𝔽16)C2×C131semidirect
296. #1783C2×C131semidirect
297. #1781C2×C131semidirect
298. C23×D4C4×C131semidirect
303. C2×#123C4×C131semidirect
308. C2×#120C4×C131semidirect
310. C22×C22⋊C4C4×C131semidirect
391. C24C22⋊C4×C131semidirect
435. C22×C4C22⋊C4×C131semidirect
452. C22⋊C4C22⋊C4×C131semidirect
453. C22⋊C4C22⋊C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1312
C2×#352×C1312
C2×AΣL(1,𝔽16)×C1312
#1783×C1312
#1781×C1312
#12690131