Finite Group Databasebeta

← C31×#24658 #21481417

Subgroups — C31×#24658 #21481417

Order 7936.

1100 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#459C211yesmaximal, characteristic, complemented
2C2×C31×#432C211yesmaximal, characteristic, complemented
3C31×#2856C211yesmaximal, characteristic, complemented
4C4×C31×#121C211yesmaximal, characteristic, complemented
5C31×#2034C212yesmaximal, complemented
6C31×#1999C212yesmaximal, complemented
7C31×#1982C211yesmaximal, characteristic, complemented
8C31×#1972C212yesmaximal, complemented
9C31×#1948C211yesmaximal, characteristic, complemented
10C31×#1936C212yesmaximal, complemented
11C31×#1802C211yesmaximal, characteristic, complemented
12C22×D8×C31C2212yes—
13C2×C31×#127C2211yescharacteristic
14C2×C31×#121—21no—
15C2×C31×#121—21no—
16C2×C31×#121C2211yescharacteristic
17C2×C31×#121C2212yes—
18C2×C4×D4×C31—21no—
19C2×C4×D4×C31C2211yescharacteristic
20C22×C42×C31C2211yescharacteristic
21C31×#459—24no—
22C31×#432—24no—
23C2×C31×#106C2212yes—
24C2×C31×C4⋊C8C2211yescharacteristic
25C2×C31×C4⋊C8C2211yescharacteristic
26C2×C31×#102C2212yes—
27C2×C31×#102C2212yes—
28C2×C31×#102C2212yes—
29C2×C31×#102C2212yes—
30C2×C31×C22⋊C8C2212yes—
31C2×C31×#97C2212yes—
32C31×#390—21no—
33C31×#390—21no—
34C31×#390C2212yes—
35C31×#390C2211yescharacteristic
36C31×#389C2211yescharacteristic
37C31×#388—21no—
38C31×#386—21no—
39C31×#384C2211yescharacteristic
40C31×#380C2211yescharacteristic
41C4×C4⋊C4×C31C2211yescharacteristic
42C4×C22⋊C4×C31—21no—
43C31×#340C2212yes—
44C31×#340C2212yes—
45C22×D4×C31—21no—
46C22×D4×C31—22no—
47C22×D4×C31—21no—
48C22×D4×C31—21no—
49C22×D4×C31C2312yes—
50C22×D4×C31C2311yescharacteristic
51C23×C4×C31—21no—
52C23×C4×C31D411yescharacteristic
53C23×C4×C31D411yescharacteristic
54C23×C4×C31C2311yescharacteristic
55C2×D8×C31—24no—
56C2×D8×C31—24no—
57C2×D8×C31—42no—
58C22×C8×C31C2312yes—
59C22×C8×C31C2312yes—
60C31×#127—22no—
61C31×#127—22no—
62C31×#121—22no—
63C31×#121—22no—
64C31×#121—42no—
65C31×#121—42no—
66C31×#121—44no—
67C31×#121—44no—
68C4×D4×C31—22no—
69C4×D4×C31—22no—
70C4×D4×C31—44no—
71C2×C4⋊C4×C31—21no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31C2311yescharacteristic
75C2×C4⋊C4×C31C2311yescharacteristic
76C2×C4⋊C4×C31C2312yes—
77C2×C4⋊C4×C31C2311yescharacteristic
78C2×C22⋊C4×C31—21no—
79C2×C22⋊C4×C31—21no—
80C2×C22⋊C4×C31—21no—
81C2×C22⋊C4×C31—21no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—21no—
86C2×C42×C31—22no—
87C2×C42×C31—22no—
88C2×C42×C31—21no—
89C2×C42×C31D411yescharacteristic
90C2×C42×C31D411yescharacteristic
91C2×C42×C31C2311yescharacteristic
92C2×C42×C31C2311yescharacteristic
93C31×#106—42no—
94C31×C4⋊C8—22no—
95C31×C4⋊C8D414yescomplemented
96C31×#102—24no—
97C31×#102—24no—
98C31×#102—42no—
99C31×#102—42no—
100C31×C22⋊C8—24no—
101C31×#97—24no—
102C31×#95—21no—
103C31×#95—21no—
104C31×#95—21no—
105C24×C31—21no—
106C24×C31—22no—
107C24×C31C2×D411yescharacteristic
108C2×D4×C31—24no—
109C2×D4×C31—21no—
110C2×D4×C31—22no—
111C2×D4×C31—21no—
112C2×D4×C31—21no—
113C2×D4×C31—22no—
114C2×D4×C31—22no—
115C2×D4×C31—22no—
116C2×D4×C31—21no—
117C2×D4×C31—21no—
118C2×D4×C31—22no—
119C2×D4×C31—22no—
120C2×D4×C31—42no—
121C2×D4×C31—42no—
122C2×D4×C31—42no—
123C2×D4×C31—42no—
124C2×D4×C31—44no—
125C2×D4×C31—44no—
126C2×D4×C31—44no—
127C2×D4×C31—42no—
128C2×D4×C31—42no—
129C2×D4×C31—42no—
130C2×D4×C31—42no—
131C2×D4×C31#4112yes—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—22no—
147C22×C4×C31—41no—
148C22×C4×C31—42no—
149C22×C4×C31—42no—
150C22×C4×C31—42no—
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D411yescharacteristic
156C22×C4×C31C2411yescharacteristic
157D8×C31—48no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C2×C8×C31C2×D414yes—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—21no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—42no—
172C4⋊C4×C31—42no—
173C4⋊C4×C31—42no—
174C4⋊C4×C31#4112yes—
175C22⋊C4×C31—24no—
176C22⋊C4×C31—42no—
177C22⋊C4×C31—42no—
178C22⋊C4×C31—44no—
179C22⋊C4×C31—44no—
180C22⋊C4×C31—44no—
181C22⋊C4×C31—42no—
182C22⋊C4×C31—42no—
183C42×C31—22no—
184C42×C31—22no—
185C42×C31—21no—
186C42×C31—21no—
187C42×C31—42no—
188C42×C31C2×D412yes—
189C42×C31#4112yes—
190#24658C3111yesmaximal, characteristic, direct product factor, Sylow
191C23×C31—21no—
192C23×C31—21no—
193C23×C31—21no—
194C23×C31—21no—
195C23×C31—21no—
196C23×C31—21no—
197C23×C31—22no—
198C23×C31—41no—
199C23×C31—41no—
200C23×C31—41no—
201C23×C31—41no—
202C23×C31—41no—
203C23×C31—41no—
204C23×C31—42no—
205C23×C31—42no—
206C23×C31—42no—
207C23×C31—42no—
208C23×C31—42no—
209C23×C31—42no—
210C23×C31—42no—
211C23×C31AGL(1,ℤ/8)12yes—
212C23×C31C22×D411yescharacteristic
213D4×C31—22no—
214D4×C31—22no—
215D4×C31—48no—
216D4×C31—42no—
217D4×C31—41no—
218D4×C31—42no—
219D4×C31—42no—
220D4×C31—41no—
221D4×C31—42no—
222D4×C31—84no—
223D4×C31—88no—
224D4×C31—84no—
225C2×C4×C31—21no—
226C2×C4×C31—21no—
227C2×C4×C31—21no—
228C2×C4×C31—21no—
229C2×C4×C31—21no—
230C2×C4×C31—21no—
231C2×C4×C31—22no—
232C2×C4×C31—21no—
233C2×C4×C31—21no—
234C2×C4×C31—21no—
235C2×C4×C31—21no—
236C2×C4×C31—21no—
237C2×C4×C31—44no—
238C2×C4×C31—41no—
239C2×C4×C31—41no—
240C2×C4×C31—41no—
241C2×C4×C31—41no—
242C2×C4×C31—41no—
243C2×C4×C31—41no—
244C2×C4×C31—44no—
245C2×C4×C31—41no—
246C2×C4×C31—42no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—41no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—41no—
253C2×C4×C31—41no—
254C2×C4×C31—84no—
255C2×C4×C31#12112yes—
256C2×C4×C31#12112yes—
257C2×C4×C31AGL(1,ℤ/8)12yes—
258C2×C4×C31AGL(1,ℤ/8)12yes—
259C2×C4×C31C22×D411yescharacteristic
260C2×C4×C31C2×#4111yescharacteristic
261C2×C4×C31C2×#4111yescharacteristic
262C2×C4×C31C2×#4111yescharacteristic
263C2×C4×C31H(5,𝔽2)11yescharacteristic
264C2×C4×C31H(5,𝔽2)11yescharacteristic
265C8×C31—24no—
266C8×C31—42no—
267C2×#459C2×C3111yescharacteristic, complemented
268C2×#432C2×C3111yescharacteristic, complemented
269#2856C2×C3111yescharacteristic, complemented
270C4×#121C2×C3111yescharacteristic, complemented
271#2034C2×C3112yescomplemented
272#1999C2×C3112yescomplemented
273#1982C2×C3111yescharacteristic, complemented
274#1972C2×C3112yescomplemented
275#1948C2×C3111yescharacteristic, complemented
276#1936C2×C3112yescomplemented
277#1802C2×C3111yescharacteristic, complemented
278C22×C31—22no—
279C22×C31—22no—
280C22×C31—22no—
281C22×C31—41no—
282C22×C31—41no—
283C22×C31—41no—
284C22×C31—41no—
285C22×C31—42no—
286C22×C31—42no—
287C22×C31—42no—
288C22×C31—81no—
289C22×C31—81no—
290C22×C31—81no—
291C22×C31—81no—
292C22×C31—82no—
293C22×C31—82no—
294C22×C31—82no—
295C22×C31—82no—
296C22×C31—82no—
297C22×C31—82no—
298C22×C31—82no—
299C22×C31C2×#12111yescharacteristic
300C22×C31#52511yescharacteristic
301C22×C31#53511yescharacteristic
302C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
304C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C31#57511yescharacteristic
306C4×C31—22no—
307C4×C31—42no—
308C4×C31—41no—
309C4×C31—41no—
310C4×C31—41no—
311C4×C31—81no—
312C4×C31—82no—
313C4×C31—81no—
314C4×C31#46914yes—
315C4×C31#54611yescharacteristic
316C4×C31#55011yescharacteristic
317C4×C31#55311yescharacteristic
318C4×C31#55511yescharacteristic
319C22×D8C22×C3112yes—
320C2×#127C22×C3111yescharacteristic
321C2×#121—21no—
322C2×#121—21no—
323C2×#121C22×C3111yescharacteristic
324C2×#121C22×C3112yes—
325C2×C4×D4—21no—
326C2×C4×D4C22×C3111yescharacteristic
327C22×C42C22×C3111yescharacteristic
328#459—24no—
329#432—24no—
330C2×#106C22×C3112yes—
331C2×C4⋊C8C22×C3111yescharacteristic
332C2×C4⋊C8C22×C3111yescharacteristic
333C2×#102C22×C3112yes—
334C2×#102C22×C3112yes—
335C2×#102C22×C3112yes—
336C2×#102C22×C3112yes—
337C2×C22⋊C8C22×C3112yes—
338C2×#97C22×C3112yes—
339#390—21no—
340#390—21no—
341#390C22×C3112yes—
342#390C22×C3111yescharacteristic
343#389C22×C3111yescharacteristic
344#388—21no—
345#386—21no—
346#384C22×C3111yescharacteristic
347#380C22×C3111yescharacteristic
348C4×C4⋊C4C22×C3111yescharacteristic
349C4×C22⋊C4—21no—
350#340C22×C3112yes—
351#340C22×C3112yes—
352C2×C31—42no—
353C2×C31—82no—
354C2×C31—162no—
355C2×C31#241411yescharacteristic
356C2×C31C2×#46911yescharacteristic
357C2×C31#305511yescharacteristic
358C2×C31#310911yescharacteristic
359C2×C31#311511yescharacteristic
360C2×C31#321411yescharacteristic
361C2×C31#321711yescharacteristic
362C22×D4—21no—
363C22×D4—22no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4C23×C3112yes—
367C22×D4C23×C3111yescharacteristic
368C23×C4—21no—
369C23×C4D4×C3111yescharacteristic
370C23×C4D4×C3111yescharacteristic
371C23×C4C23×C3111yescharacteristic
372C2×D8—24no—
373C2×D8—24no—
374C2×D8—42no—
375C22×C8C23×C3112yes—
376C22×C8C23×C3112yes—
377#127—22no—
378#127—22no—
379#121—22no—
380#121—22no—
381#121—42no—
382#121—42no—
383#121—44no—
384#121—44no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—44no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4C23×C3111yescharacteristic
392C2×C4⋊C4C23×C3112yes—
393C2×C4⋊C4C23×C3111yescharacteristic
394C2×C4⋊C4C23×C3111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—21no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—21no—
406C2×C42D4×C3111yescharacteristic
407C2×C42D4×C3111yescharacteristic
408C2×C42C23×C3111yescharacteristic
409C2×C42C23×C3111yescharacteristic
410#106—42no—
411C4⋊C8—22no—
412C4⋊C8D4×C3114yescomplemented
413#102—24no—
414#102—24no—
415#102—42no—
416#102—42no—
417C22⋊C8—24no—
418#97—24no—
419#95—21no—
420#95—21no—
421#95—21no—
422C31#2465811yescharacteristic, direct product factor, Sylow
423C24—21no—
424C24—22no—
425C24C2×D4×C3111yescharacteristic
426C2×D4—24no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4#41×C3112yes—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—41no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4C2×D4×C3111yescharacteristic
470C22×C4C2×D4×C3111yescharacteristic
471C22×C4C2×D4×C3111yescharacteristic
472C22×C4C2×D4×C3111yescharacteristic
473C22×C4C2×D4×C3111yescharacteristic
474C22×C4C24×C3111yescharacteristic
475D8—48no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8C2×D4×C3114yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4#41×C3112yes—
493C22⋊C4—24no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—44no—
497C22⋊C4—44no—
498C22⋊C4—44no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42C2×D4×C3112yes—
507C42#41×C3112yes—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C31×AGL(1,ℤ/8)12yes—
529C23C22×D4×C3111yescharacteristic
530D4—22no—
531D4—22no—
532D4—48no—
533D4—42no—
534D4—41no—
535D4—42no—
536D4—42no—
537D4—41no—
538D4—42no—
539D4—84no—
540D4—88no—
541D4—84no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—44no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—84no—
572C2×C4C31×#12112yes—
573C2×C4C31×#12112yes—
574C2×C4C31×AGL(1,ℤ/8)12yes—
575C2×C4C31×AGL(1,ℤ/8)12yes—
576C2×C4C22×D4×C3111yescharacteristic
577C2×C4C2×#41×C3111yescharacteristic
578C2×C4C2×#41×C3111yescharacteristic
579C2×C4C2×#41×C3111yescharacteristic
580C2×C4C31×H(5,𝔽2)11yescharacteristic
581C2×C4C31×H(5,𝔽2)11yescharacteristic
582C8—24no—
583C8—42no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22—82no—
605C22C2×C31×#12111yescharacteristic
606C22C31×#52511yescharacteristic
607C22C31×#53511yescharacteristic
608C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
609C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
610C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
611C22C31×#57511yescharacteristic
612C4—22no—
613C4—42no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—82no—
619C4—81no—
620C4C31×#46914yes—
621C4C31×#54611yescharacteristic
622C4C31×#55011yescharacteristic
623C4C31×#55311yescharacteristic
624C4C31×#55511yescharacteristic
625C2—42no—
626C2—82no—
627C2—162no—
628C2C31×#241411yescharacteristic
629C2C2×C31×#46911yescharacteristic
630C2C31×#305511yescharacteristic
631C2C31×#310911yescharacteristic
632C2C31×#311511yescharacteristic
633C2C31×#321411yescharacteristic
634C2C31×#321711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#459C2semidirect
2. C2×C31×#432C2semidirect
3. C31×#2856C2semidirect
4. C4×C31×#121C2semidirect
5. C31×#2034C2semidirect
6. C31×#1999C2semidirect
7. C31×#1982C2semidirect
8. C31×#1972C2semidirect
9. C31×#1948C2semidirect
10. C31×#1936C2semidirect
11. C31×#1802C2semidirect
95. C31×C4⋊C8D4semidirect
190. #24658C31direct (N × H)
267. C2×#459C2×C31semidirect
268. C2×#432C2×C31semidirect
269. #2856C2×C31semidirect
270. C4×#121C2×C31semidirect
271. #2034C2×C31semidirect
272. #1999C2×C31semidirect
273. #1982C2×C31semidirect
274. #1972C2×C31semidirect
275. #1948C2×C31semidirect
276. #1936C2×C31semidirect
277. #1802C2×C31semidirect
412. C4⋊C8D4×C31semidirect
422. C31#24658direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4592
C2×C31×#4322
C31×#28562
C4×C31×#1212
C31×#20342
C31×#19992
C31×#19822
C31×#19722
C31×#19482
C31×#19362
C31×#18022
#2465831