Finite Group Databasebeta

← C131×#26019 #45711903

Subgroups — C131×#26019 #45711903

Order 33536.

696 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
1#2442×C131C211yesmaximal, characteristic
2#2346×C131C211yesmaximal, characteristic
3#2101×C131C211yesmaximal, characteristic, complemented
4#2088×C131C211yesmaximal, characteristic, complemented
5#2088×C131C211yesmaximal, characteristic, complemented
6#2059×C131C211yesmaximal, characteristic, complemented
7#1989×C131C211yesmaximal, characteristic, complemented
8#1949×C131C211yesmaximal, characteristic, complemented
9#1919×C131C211yesmaximal, characteristic, complemented
10#1919×C131C211yesmaximal, characteristic, complemented
11#1853×C131C211yesmaximal, characteristic
12#1851×C131C211yesmaximal, characteristic
13#1825×C131C211yesmaximal, characteristic
14#1809×C131C211yesmaximal, characteristic
15#1736×C131C211yesmaximal, characteristic
16C22×M16×C131C2211yescharacteristic
17C2×#125×C131C2211yescharacteristic
18C2×#117×C131C2211yescharacteristic
19C22×C4⋊C4×C131C2211yescharacteristic
20C2×#107×C131C2211yescharacteristic
21C2×#106×C131C2211yescharacteristic
22C2×#106×C131C2211yescharacteristic
23C2×#106×C131C2211yescharacteristic
24C2×C4⋊C8×C131C2211yescharacteristic
25C2×C4⋊C8×C131C2211yescharacteristic
26C2×C22⋊C8×C131C2211yescharacteristic
27#400×C131—21no—
28#398×C131—21no—
29#389×C131C2211yescharacteristic
30#389×C131C2211yescharacteristic
31#389×C131C2211yescharacteristic
32#389×C131C2211yescharacteristic
33#388×C131—21no—
34#388×C131—21no—
35#385×C131—21no—
36#382×C131—21no—
37#382×C131C2211yescharacteristic
38#380×C131—21no—
39#380×C131C2211yescharacteristic
40#380×C131C2211yescharacteristic
41C4×C4⋊C4×C131C2211yescharacteristic
42C4×C4⋊C4×C131C2211yescharacteristic
43C4×C22⋊C4×C131C2211yescharacteristic
44#376×C131—21no—
45#340×C131C2211yescharacteristic
46#340×C131C2211yescharacteristic
47#340×C131C2211yescharacteristic
48#340×C131C2211yescharacteristic
49#340×C131C2211yescharacteristic
50#340×C131C2211yescharacteristic
51#340×C131C2211yescharacteristic
52#340×C131C2211yescharacteristic
53#340×C131C2211yescharacteristic
54#340×C131C2211yescharacteristic
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#336×C131C2211yescharacteristic
58#336×C131C2211yescharacteristic
59C23×C4×C131—21no—
60C23×C4×C131C2311yescharacteristic
61C2×M16×C131—22no—
62C2×M16×C131—22no—
63C2×M16×C131—41no—
64C22×C8×C131C2311yescharacteristic
65C22×C8×C131C2311yescharacteristic
66C22×C8×C131C2311yescharacteristic
67C22×C8×C131C2311yescharacteristic
68#125×C131—22no—
69#125×C131—41no—
70#117×C131—22no—
71#117×C131Q814yes—
72C2×C4⋊C4×C131—22no—
73C2×C4⋊C4×C131—21no—
74C2×C4⋊C4×C131—21no—
75C2×C4⋊C4×C131—21no—
76C2×C4⋊C4×C131—21no—
77C2×C4⋊C4×C131—21no—
78C2×C4⋊C4×C131—21no—
79C2×C4⋊C4×C131—21no—
80C2×C4⋊C4×C131—41no—
81C2×C4⋊C4×C131C2311yescharacteristic
82C2×C4⋊C4×C131C2311yescharacteristic
83C2×C4⋊C4×C131C2311yescharacteristic
84C2×C4⋊C4×C131C2311yescharacteristic
85C2×C4⋊C4×C131C2311yescharacteristic
86C2×C4⋊C4×C131C2311yescharacteristic
87C2×C4⋊C4×C131C2311yescharacteristic
88C2×C4⋊C4×C131C2311yescharacteristic
89C2×C22⋊C4×C131—21no—
90C2×C22⋊C4×C131—21no—
91C2×C22⋊C4×C131—21no—
92C2×C22⋊C4×C131D411yescharacteristic
93C2×C22⋊C4×C131D411yescharacteristic
94C2×C42×C131—21no—
95C2×C42×C131—21no—
96C2×C42×C131—21no—
97C2×C42×C131C2311yescharacteristic
98C2×C42×C131C2311yescharacteristic
99#107×C131—41no—
100#106×C131—22no—
101#106×C131—22no—
102#106×C131—41no—
103C4⋊C8×C131—22no—
104C4⋊C8×C131—41no—
105C22⋊C8×C131—22no—
106#95×C131—21no—
107#95×C131—21no—
108#95×C131—21no—
109#95×C131—21no—
110#95×C131—21no—
111#95×C131—21no—
112#95×C131—21no—
113#95×C131—21no—
114#95×C131—21no—
115#95×C131—21no—
116#95×C131D411yescharacteristic
117#95×C131D411yescharacteristic
118C24×C131C2×D411yescharacteristic
119C22×C4×C131—21no—
120C22×C4×C131—21no—
121C22×C4×C131—21no—
122C22×C4×C131—21no—
123C22×C4×C131—21no—
124C22×C4×C131—21no—
125C22×C4×C131—21no—
126C22×C4×C131—21no—
127C22×C4×C131—21no—
128C22×C4×C131—21no—
129C22×C4×C131—21no—
130C22×C4×C131—21no—
131C22×C4×C131—42no—
132C22×C4×C131—42no—
133C22×C4×C131—81no—
134C22×C4×C131C2×D411yescharacteristic
135C22×C4×C131C2×D411yescharacteristic
136C22×C4×C131C2×D411yescharacteristic
137C22×C4×C131C2×D411yescharacteristic
138C22×C4×C131C2×D411yescharacteristic
139C22×C4×C131C2×Q812yes—
140C22×C4×C131#4112yes—
141C22×C4×C131C2411yescharacteristic
142M16×C131—44no—
143C2×C8×C131—21no—
144C2×C8×C131—21no—
145C2×C8×C131—21no—
146C2×C8×C131—21no—
147C2×C8×C131—21no—
148C2×C8×C131—21no—
149C2×C8×C131—21no—
150C2×C8×C131—21no—
151C2×C8×C131—21no—
152C2×C8×C131—21no—
153C2×C8×C131—21no—
154C2×C8×C131#4112yes—
155C4⋊C4×C131—21no—
156C4⋊C4×C131—21no—
157C4⋊C4×C131—21no—
158C4⋊C4×C131—21no—
159C4⋊C4×C131—21no—
160C4⋊C4×C131—21no—
161C4⋊C4×C131—21no—
162C4⋊C4×C131—21no—
163C4⋊C4×C131—21no—
164C4⋊C4×C131—21no—
165C4⋊C4×C131—21no—
166C4⋊C4×C131—21no—
167C4⋊C4×C131—21no—
168C4⋊C4×C131—42no—
169C4⋊C4×C131—42no—
170C4⋊C4×C131—42no—
171C4⋊C4×C131—81no—
172C4⋊C4×C131—81no—
173C4⋊C4×C131—81no—
174C4⋊C4×C131—81no—
175C4⋊C4×C131C2×Q812yes—
176C4⋊C4×C131C2×Q812yes—
177C4⋊C4×C131#4112yes—
178C22⋊C4×C131—24no—
179C22⋊C4×C131—41no—
180C22⋊C4×C131—41no—
181C22⋊C4×C131—42no—
182C22⋊C4×C131—81no—
183C42×C131—24no—
184C42×C131—21no—
185C42×C131—21no—
186C42×C131—21no—
187C42×C131—21no—
188C42×C131—42no—
189C42×C131—42no—
190C23×C131—21no—
191C23×C131—21no—
192C23×C131—21no—
193C23×C131—21no—
194C23×C131—21no—
195C23×C131—21no—
196C23×C131C22⋊Q812yes—
197C23×C131C22×D411yescharacteristic
198C2×C4×C131—21no—
199C2×C4×C131—21no—
200C2×C4×C131—22no—
201C2×C4×C131—22no—
202C2×C4×C131—22no—
203C2×C4×C131—22no—
204C2×C4×C131—22no—
205C2×C4×C131—22no—
206C2×C4×C131—21no—
207C2×C4×C131—21no—
208C2×C4×C131—22no—
209C2×C4×C131—21no—
210C2×C4×C131—21no—
211C2×C4×C131—21no—
212C2×C4×C131—21no—
213C2×C4×C131—21no—
214C2×C4×C131—21no—
215C2×C4×C131—21no—
216C2×C4×C131—21no—
217C2×C4×C131—21no—
218C2×C4×C131—21no—
219C2×C4×C131—41no—
220C2×C4×C131—41no—
221C2×C4×C131—41no—
222C2×C4×C131—41no—
223C2×C4×C131—41no—
224C2×C4×C131—41no—
225C2×C4×C131—41no—
226C2×C4×C131—41no—
227C2×C4×C131—41no—
228C2×C4×C131—41no—
229C2×C4×C131—41no—
230C2×C4×C131—41no—
231C2×C4×C131—41no—
232C2×C4×C131—41no—
233C2×C4×C131—41no—
234C2×C4×C131—41no—
235C2×C4×C131—41no—
236C2×C4×C131—41no—
237C2×C4×C131—41no—
238C2×C4×C131—41no—
239C2×C4×C131—41no—
240C2×C4×C131—84no—
241C2×C4×C131C22⋊Q812yes—
242C2×C4×C131C22×Q811yescharacteristic
243C2×C4×C131C2×#4111yescharacteristic
244C2×C4×C131C2×#4111yescharacteristic
245C2×C4×C131C2×#4111yescharacteristic
246C2×C4×C131H(5,𝔽2)11yescharacteristic
247C2×C4×C1312−1+411yescharacteristic
248C8×C131—22no—
249C8×C131—41no—
250C8×C131—41no—
251C8×C131—41no—
252C22×C131—22no—
253C22×C131—22no—
254C22×C131—22no—
255C22×C131—41no—
256C22×C131—41no—
257C22×C131—41no—
258C22×C131—41no—
259C22×C131C2×C22⋊Q811yescharacteristic
260C22×C131#54611yescharacteristic
261C22×C131#54711yescharacteristic
262C22×C131#57511yescharacteristic
263C22×C131#57511yescharacteristic
264C22×C131#57711yescharacteristic
265C22×C131#57711yescharacteristic
266C4×C131—22no—
267C4×C131—42no—
268C4×C131—42no—
269C4×C131—41no—
270C4×C131—41no—
271C4×C131—41no—
272C4×C131—41no—
273C4×C131—42no—
274C4×C131—81no—
275C4×C131—81no—
276C4×C131—81no—
277C4×C131—81no—
278C4×C131—81no—
279C4×C131#53311yescharacteristic
280C4×C131#54411yescharacteristic
281C4×C131#55111yescharacteristic
282C4×C131#55211yescharacteristic
283C2×C131—42no—
284C2×C131#243811yescharacteristic
285C2×C131#308011yescharacteristic
286C2×C131#308411yescharacteristic
287C2×C131#332111yescharacteristic
288C2×C131#332311yescharacteristic
289C2×C131#334811yescharacteristic
290C2×C131#335111yescharacteristic
291#26019C13111yesmaximal, characteristic, direct product factor, Sylow
292C131#2601911yescharacteristic, direct product factor, Sylow
293#2442C2×C13111yescharacteristic
294#2346C2×C13111yescharacteristic
295#2101C2×C13111yescharacteristic, complemented
296#2088C2×C13111yescharacteristic, complemented
297#2088C2×C13111yescharacteristic, complemented
298#2059C2×C13111yescharacteristic, complemented
299#1989C2×C13111yescharacteristic, complemented
300#1949C2×C13111yescharacteristic, complemented
301#1919C2×C13111yescharacteristic, complemented
302#1919C2×C13111yescharacteristic, complemented
303#1853C2×C13111yescharacteristic
304#1851C2×C13111yescharacteristic
305#1825C2×C13111yescharacteristic
306#1809C2×C13111yescharacteristic
307#1736C2×C13111yescharacteristic
308C22×M16C22×C13111yescharacteristic
309C2×#125C22×C13111yescharacteristic
310C2×#117C22×C13111yescharacteristic
311C22×C4⋊C4C22×C13111yescharacteristic
312C2×#107C22×C13111yescharacteristic
313C2×#106C22×C13111yescharacteristic
314C2×#106C22×C13111yescharacteristic
315C2×#106C22×C13111yescharacteristic
316C2×C4⋊C8C22×C13111yescharacteristic
317C2×C4⋊C8C22×C13111yescharacteristic
318C2×C22⋊C8C22×C13111yescharacteristic
319#400—21no—
320#398—21no—
321#389C22×C13111yescharacteristic
322#389C22×C13111yescharacteristic
323#389C22×C13111yescharacteristic
324#389C22×C13111yescharacteristic
325#388—21no—
326#388—21no—
327#385—21no—
328#382—21no—
329#382C22×C13111yescharacteristic
330#380—21no—
331#380C22×C13111yescharacteristic
332#380C22×C13111yescharacteristic
333C4×C4⋊C4C22×C13111yescharacteristic
334C4×C4⋊C4C22×C13111yescharacteristic
335C4×C22⋊C4C22×C13111yescharacteristic
336#376—21no—
337#340C22×C13111yescharacteristic
338#340C22×C13111yescharacteristic
339#340C22×C13111yescharacteristic
340#340C22×C13111yescharacteristic
341#340C22×C13111yescharacteristic
342#340C22×C13111yescharacteristic
343#340C22×C13111yescharacteristic
344#340C22×C13111yescharacteristic
345#340C22×C13111yescharacteristic
346#340C22×C13111yescharacteristic
347#340C22×C13111yescharacteristic
348#340C22×C13111yescharacteristic
349#336C22×C13111yescharacteristic
350#336C22×C13111yescharacteristic
351C23×C4—21no—
352C23×C4C23×C13111yescharacteristic
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—41no—
356C22×C8C23×C13111yescharacteristic
357C22×C8C23×C13111yescharacteristic
358C22×C8C23×C13111yescharacteristic
359C22×C8C23×C13111yescharacteristic
360#125—22no—
361#125—41no—
362#117—22no—
363#117Q8×C13114yes—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—41no—
373C2×C4⋊C4C23×C13111yescharacteristic
374C2×C4⋊C4C23×C13111yescharacteristic
375C2×C4⋊C4C23×C13111yescharacteristic
376C2×C4⋊C4C23×C13111yescharacteristic
377C2×C4⋊C4C23×C13111yescharacteristic
378C2×C4⋊C4C23×C13111yescharacteristic
379C2×C4⋊C4C23×C13111yescharacteristic
380C2×C4⋊C4C23×C13111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4D4×C13111yescharacteristic
385C2×C22⋊C4D4×C13111yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C13111yescharacteristic
390C2×C42C23×C13111yescharacteristic
391#107—41no—
392#106—22no—
393#106—22no—
394#106—41no—
395C4⋊C8—22no—
396C4⋊C8—41no—
397C22⋊C8—22no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95D4×C13111yescharacteristic
409#95D4×C13111yescharacteristic
410C24C2×D4×C13111yescharacteristic
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—81no—
426C22×C4C2×D4×C13111yescharacteristic
427C22×C4C2×D4×C13111yescharacteristic
428C22×C4C2×D4×C13111yescharacteristic
429C22×C4C2×D4×C13111yescharacteristic
430C22×C4C2×D4×C13111yescharacteristic
431C22×C4C2×Q8×C13112yes—
432C22×C4#41×C13112yes—
433C22×C4C24×C13111yescharacteristic
434M16—44no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8#41×C13112yes—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—81no—
467C4⋊C4C2×Q8×C13112yes—
468C4⋊C4C2×Q8×C13112yes—
469C4⋊C4#41×C13112yes—
470C22⋊C4—24no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—42no—
474C22⋊C4—81no—
475C42—24no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—42no—
481C42—42no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23C22⋊Q8×C13112yes—
489C23C22×D4×C13111yescharacteristic
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—84no—
533C2×C4C22⋊Q8×C13112yes—
534C2×C4C22×Q8×C13111yescharacteristic
535C2×C4C2×#41×C13111yescharacteristic
536C2×C4C2×#41×C13111yescharacteristic
537C2×C4C2×#41×C13111yescharacteristic
538C2×C4H(5,𝔽2)×C13111yescharacteristic
539C2×C42−1+4×C13111yescharacteristic
540C8—22no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×C22⋊Q8×C13111yescharacteristic
552C22#546×C13111yescharacteristic
553C22#547×C13111yescharacteristic
554C22#575×C13111yescharacteristic
555C22#575×C13111yescharacteristic
556C22#577×C13111yescharacteristic
557C22#577×C13111yescharacteristic
558C4—22no—
559C4—41no—
560C4—41no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4#533×C13111yescharacteristic
572C4#544×C13111yescharacteristic
573C4#551×C13111yescharacteristic
574C4#552×C13111yescharacteristic
575C2—42no—
576C2#2438×C13111yescharacteristic
577C2#3080×C13111yescharacteristic
578C2#3084×C13111yescharacteristic
579C2#3321×C13111yescharacteristic
580C2#3323×C13111yescharacteristic
581C2#3348×C13111yescharacteristic
582C2#3351×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC24×C131C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2101×C131C2semidirect
4. #2088×C131C2semidirect
5. #2088×C131C2semidirect
6. #2059×C131C2semidirect
7. #1989×C131C2semidirect
8. #1949×C131C2semidirect
9. #1919×C131C2semidirect
10. #1919×C131C2semidirect
291. #26019C131direct (N × H)
292. C131#26019direct (N × H)
295. #2101C2×C131semidirect
296. #2088C2×C131semidirect
297. #2088C2×C131semidirect
298. #2059C2×C131semidirect
299. #1989C2×C131semidirect
300. #1949C2×C131semidirect
301. #1919C2×C131semidirect
302. #1919C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2442×C1312
#2346×C1312
#2101×C1312
#2088×C1312
#2059×C1312
#1989×C1312
#1949×C1312
#1919×C1312
#1853×C1312
#1851×C1312
#1825×C1312
#1809×C1312
#1736×C1312
#26019131