Finite Group Databasebeta

← C131×#9938 #45695822

Subgroups — C131×#9938 #45695822

Order 33536.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3006×C131C211yesmaximal, characteristic, complemented
2#2539×C131C211yesmaximal, characteristic, complemented
3#2404×C131C211yesmaximal, characteristic, complemented
4#1789×C131C211yesmaximal, characteristic, complemented
5#1510×C131C211yesmaximal, characteristic, complemented
6#1462×C131C211yesmaximal, characteristic, complemented
7#1284×C131C211yesmaximal, characteristic, complemented
8C22×#41×C131C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C131—21no—
10C2×#123×C131—21no—
11C2×#121×C131C2211yescharacteristic
12C2×#120×C131—21no—
13C2×#120×C131—21no—
14C22×C22⋊C4×C131C2211yescharacteristic
15#449×C131—22no—
16#448×C131—21no—
17#447×C131—21no—
18C2×#104×C131—22no—
19#417×C131—21no—
20#407×C131C2211yescharacteristic
21#407×C131C2211yescharacteristic
22#399×C131—21no—
23#393×C131—21no—
24#392×C131—21no—
25#392×C131—21no—
26#390×C131—22no—
27#386×C131—21no—
28#386×C131—22no—
29#381×C131C2211yescharacteristic
30C4×C22⋊C4×C131C2211yescharacteristic
31#327×C131—22no—
32#323×C131—22no—
33C25×C131D411yescharacteristic
34C2×#41×C131—21no—
35C2×#41×C131—21no—
36C2×#41×C131—21no—
37C2×#41×C131—21no—
38C2×#41×C131—44no—
39C22×Q8×C131D411yescharacteristic, complemented
40C22×D4×C131—21no—
41C22×D4×C131—21no—
42C22×D4×C131—22no—
43C22×D4×C131—22no—
44C22×D4×C131D411yescharacteristic, complemented
45C22×D4×C131D411yescharacteristic, complemented
46C23×C4×C131—21no—
47C23×C4×C131D411yescharacteristic
48C23×C4×C131C2311yescharacteristic
49AGL(1,ℤ/8)×C131—44no—
50C2×SD16×C131—22no—
51C2×D8×C131—22no—
52C2×M16×C131—21no—
53C2×M16×C131—21no—
54#123×C131—44no—
55#121×C131—21no—
56#121×C131—21no—
57#121×C131—21no—
58#121×C131—21no—
59#120×C131—44no—
60#120×C131—44no—
61C2×C4⋊C4×C131—22no—
62C2×C4⋊C4×C131D411yescharacteristic, complemented
63C2×C22⋊C4×C131—21no—
64C2×C22⋊C4×C131—22no—
65C2×C22⋊C4×C131—22no—
66C2×C22⋊C4×C131—22no—
67C2×C22⋊C4×C131—21no—
68C2×C22⋊C4×C131—21no—
69C2×C22⋊C4×C131—21no—
70C2×C22⋊C4×C131—21no—
71C2×C22⋊C4×C131—21no—
72C2×C22⋊C4×C131—21no—
73C2×C22⋊C4×C131—21no—
74C2×C22⋊C4×C131—21no—
75C2×C22⋊C4×C131—22no—
76C2×C42×C131D412yescomplemented
77#104×C131—44no—
78#103×C131—22no—
79#102×C131—22no—
80C22⋊C8×C131—21no—
81C22⋊C8×C131—21no—
82C22⋊C8×C131—21no—
83C22⋊C8×C131D412yescomplemented
84#95×C131—22no—
85#95×C131—21no—
86#95×C131—21no—
87#95×C131D412yescomplemented
88C24×C131—21no—
89C24×C131—21no—
90C24×C131—21no—
91C24×C131—21no—
92C24×C131—21no—
93C24×C131—42no—
94C24×C131—42no—
95C24×C131—42no—
96C24×C131C2×D411yescharacteristic
97#41×C131—24no—
98#41×C131—24no—
99#41×C131—42no—
100#41×C131—42no—
101#41×C131—42no—
102#41×C131—42no—
103#41×C131—42no—
104#41×C131—42no—
105C2×Q8×C131—21no—
106C2×Q8×C131—21no—
107C2×Q8×C131—42no—
108C2×D4×C131—24no—
109C2×D4×C131—21no—
110C2×D4×C131—21no—
111C2×D4×C131—21no—
112C2×D4×C131—21no—
113C2×D4×C131—42no—
114C2×D4×C131—44no—
115C2×D4×C131—42no—
116C2×D4×C131—42no—
117C2×D4×C131—41no—
118C2×D4×C131—41no—
119C2×D4×C131—42no—
120C2×D4×C131—44no—
121C2×D4×C131—42no—
122C2×D4×C131—44no—
123C2×D4×C131—44no—
124C2×D4×C131—41no—
125C2×D4×C131—41no—
126C2×D4×C131—82no—
127C2×D4×C131—82no—
128C22×C4×C131—21no—
129C22×C4×C131—22no—
130C22×C4×C131—22no—
131C22×C4×C131—21no—
132C22×C4×C131—21no—
133C22×C4×C131—21no—
134C22×C4×C131—21no—
135C22×C4×C131—42no—
136C22×C4×C131—42no—
137C22×C4×C131—42no—
138C22×C4×C131—41no—
139C22×C4×C131—41no—
140C22×C4×C131—42no—
141C22×C4×C131C2×D411yescharacteristic
142C22×C4×C131C2×D411yescharacteristic
143C22×C4×C131C2×D411yescharacteristic
144C22×C4×C131C2×D411yescharacteristic
145C22×C4×C131C2×D411yescharacteristic
146C22×C4×C131#4111yescharacteristic
147SD16×C131—44no—
148D8×C131—44no—
149M16×C131—42no—
150M16×C131—42no—
151C2×C8×C131—22no—
152C2×C8×C131—41no—
153C4⋊C4×C131—21no—
154C4⋊C4×C131—21no—
155C4⋊C4×C131—44no—
156C22⋊C4×C131—24no—
157C22⋊C4×C131—44no—
158C22⋊C4×C131—44no—
159C22⋊C4×C131—44no—
160C22⋊C4×C131—42no—
161C22⋊C4×C131—41no—
162C22⋊C4×C131—41no—
163C22⋊C4×C131—41no—
164C22⋊C4×C131—41no—
165C22⋊C4×C131—41no—
166C22⋊C4×C131—41no—
167C22⋊C4×C131—82no—
168C42×C131—42no—
169C23×C131—22no—
170C23×C131—22no—
171C23×C131—22no—
172C23×C131—22no—
173C23×C131—22no—
174C23×C131—22no—
175C23×C131—41no—
176C23×C131—42no—
177C23×C131—42no—
178C23×C131—41no—
179C23×C131—42no—
180C23×C131—41no—
181C23×C131—41no—
182C23×C131—41no—
183C23×C131—41no—
184C23×C131—41no—
185C23×C131—42no—
186C23×C131—41no—
187C23×C131—41no—
188C23×C131—42no—
189C23×C131—42no—
190C23×C131—42no—
191C23×C131—41no—
192C23×C131—42no—
193C23×C131—81no—
194C23×C131—81no—
195C23×C131—88no—
196C23×C131#12011yescharacteristic
197C23×C131#12011yescharacteristic
198C23×C131#12111yescharacteristic
199Q8×C131—22no—
200Q8×C131—22no—
201Q8×C131—41no—
202Q8×C131—41no—
203D4×C131—22no—
204D4×C131—22no—
205D4×C131—41no—
206D4×C131—41no—
207D4×C131—42no—
208D4×C131—44no—
209D4×C131—44no—
210D4×C131—81no—
211D4×C131—88no—
212D4×C131—82no—
213D4×C131—88no—
214D4×C131—82no—
215C2×C4×C131—22no—
216C2×C4×C131—22no—
217C2×C4×C131—24no—
218C2×C4×C131—22no—
219C2×C4×C131—41no—
220C2×C4×C131—41no—
221C2×C4×C131—41no—
222C2×C4×C131—41no—
223C2×C4×C131—44no—
224C2×C4×C131—44no—
225C2×C4×C131—41no—
226C2×C4×C131—42no—
227C2×C4×C131—41no—
228C2×C4×C131—42no—
229C2×C4×C131—42no—
230C2×C4×C131—41no—
231C2×C4×C131—42no—
232C2×C4×C131—41no—
233C2×C4×C131—42no—
234C2×C4×C131—41no—
235C2×C4×C131—41no—
236C2×C4×C131—42no—
237C2×C4×C131—42no—
238C2×C4×C131—81no—
239C2×C4×C131#12011yescharacteristic
240C2×C4×C131#12111yescharacteristic
241C2×C4×C131#12111yescharacteristic
242C2×C4×C131#12711yescharacteristic
243C8×C131—42no—
244C8×C131—81no—
245C22×C131—21no—
246C22×C131—21no—
247C22×C131—21no—
248C22×C131—21no—
249C22×C131—21no—
250C22×C131—21no—
251C22×C131—21no—
252C22×C131—44no—
253C22×C131—44no—
254C22×C131—44no—
255C22×C131—44no—
256C22×C131—42no—
257C22×C131—42no—
258C22×C131—82no—
259C22×C131—82no—
260C22×C131—82no—
261C22×C131—82no—
262C22×C131—82no—
263C22×C131—82no—
264C22×C131—82no—
265C22×C131—81no—
266C22×C131—81no—
267C22×C131—81no—
268C22×C131—81no—
269C22×C131—81no—
270C22×C131—81no—
271C22×C131—81no—
272C22×C131#39211yescharacteristic
273C22×C131#45312yes—
274C22×C131B(4,𝔽2)12yes—
275C4×C131—21no—
276C4×C131—21no—
277C4×C131—21no—
278C4×C131—21no—
279C4×C131—44no—
280C4×C131—42no—
281C4×C131—82no—
282C4×C131—81no—
283C4×C131—81no—
284C2×C131—22no—
285C2×C131—22no—
286C2×C131—41no—
287C2×C131—82no—
288C2×C131—82no—
289C2×C131—161no—
290C2×C131#200211yescharacteristic
291C2×C131#201011yescharacteristic
292C2×C131#202111yescharacteristic
293#9938C13111yesmaximal, characteristic, direct product factor, Sylow
294C131#993811yescharacteristic, direct product factor, Sylow
295#3006C2×C13111yescharacteristic, complemented
296#2539C2×C13111yescharacteristic, complemented
297#2404C2×C13111yescharacteristic, complemented
298#1789C2×C13111yescharacteristic, complemented
299#1510C2×C13111yescharacteristic, complemented
300#1462C2×C13111yescharacteristic, complemented
301#1284C2×C13111yescharacteristic, complemented
302C22×#41C22×C13111yescharacteristic
303C2×AGL(1,ℤ/8)—21no—
304C2×#123—21no—
305C2×#121C22×C13111yescharacteristic
306C2×#120—21no—
307C2×#120—21no—
308C22×C22⋊C4C22×C13111yescharacteristic
309#449—22no—
310#448—21no—
311#447—21no—
312C2×#104—22no—
313#417—21no—
314#407C22×C13111yescharacteristic
315#407C22×C13111yescharacteristic
316#399—21no—
317#393—21no—
318#392—21no—
319#392—21no—
320#390—22no—
321#386—21no—
322#386—22no—
323#381C22×C13111yescharacteristic
324C4×C22⋊C4C22×C13111yescharacteristic
325#327—22no—
326#323—22no—
327C25D4×C13111yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—44no—
333C22×Q8D4×C13111yescharacteristic, complemented
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4D4×C13111yescharacteristic, complemented
339C22×D4D4×C13111yescharacteristic, complemented
340C23×C4—21no—
341C23×C4D4×C13111yescharacteristic
342C23×C4C23×C13111yescharacteristic
343AGL(1,ℤ/8)—44no—
344C2×SD16—22no—
345C2×D8—22no—
346C2×M16—21no—
347C2×M16—21no—
348#123—44no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#120—44no—
354#120—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C13111yescharacteristic, complemented
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C42D4×C13112yescomplemented
371#104—44no—
372#103—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8D4×C13112yescomplemented
378#95—22no—
379#95—21no—
380#95—21no—
381#95D4×C13112yescomplemented
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24C2×D4×C13111yescharacteristic
391#41—24no—
392#41—24no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C2×D4—82no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4C2×D4×C13111yescharacteristic
436C22×C4C2×D4×C13111yescharacteristic
437C22×C4C2×D4×C13111yescharacteristic
438C22×C4C2×D4×C13111yescharacteristic
439C22×C4C2×D4×C13111yescharacteristic
440C22×C4#41×C13111yescharacteristic
441SD16—44no—
442D8—44no—
443M16—42no—
444M16—42no—
445C2×C8—22no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C22⋊C4—24no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—82no—
462C42—42no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23—42no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23#120×C13111yescharacteristic
491C23#120×C13111yescharacteristic
492C23#121×C13111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4#120×C13111yescharacteristic
534C2×C4#121×C13111yescharacteristic
535C2×C4#121×C13111yescharacteristic
536C2×C4#127×C13111yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22#392×C13111yescharacteristic
567C22#453×C13112yes—
568C22B(4,𝔽2)×C13112yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2#2002×C13111yescharacteristic
585C2#2010×C13111yescharacteristic
586C2#2021×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#392
commutator, Frattini, cosocleC23×C4C23×C131
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3006×C131C2semidirect
2. #2539×C131C2semidirect
3. #2404×C131C2semidirect
4. #1789×C131C2semidirect
5. #1510×C131C2semidirect
6. #1462×C131C2semidirect
7. #1284×C131C2semidirect
39. C22×Q8×C131D4semidirect
44. C22×D4×C131D4semidirect
45. C22×D4×C131D4semidirect
62. C2×C4⋊C4×C131D4semidirect
76. C2×C42×C131D4semidirect
83. C22⋊C8×C131D4semidirect
87. #95×C131D4semidirect
293. #9938C131direct (N × H)
294. C131#9938direct (N × H)
295. #3006C2×C131semidirect
296. #2539C2×C131semidirect
297. #2404C2×C131semidirect
298. #1789C2×C131semidirect
299. #1510C2×C131semidirect
300. #1462C2×C131semidirect
301. #1284C2×C131semidirect
333. C22×Q8D4×C131semidirect
338. C22×D4D4×C131semidirect
339. C22×D4D4×C131semidirect
356. C2×C4⋊C4D4×C131semidirect
370. C2×C42D4×C131semidirect
377. C22⋊C8D4×C131semidirect
381. #95D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3006×C1312
#2539×C1312
#2404×C1312
#1789×C1312
#1510×C1312
#1462×C1312
#1284×C1312
#9938131