Finite Group Databasebeta

← C31×#32925 #21489684

Subgroups — C31×#32925 #21489684

Order 7936.

1352 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C31×2−1+4C211yesmaximal, characteristic, complemented
2C31×#3040C212yesmaximal, complemented
3C2×C31×#456C211yesmaximal, characteristic, complemented
4C2×C31×#454C211yesmaximal, characteristic
5C31×#2545C211yesmaximal, characteristic, complemented
6C31×#1888C211yesmaximal, characteristic, complemented
7C31×#1886C211yesmaximal, characteristic, complemented
8C31×#1883C212yesmaximal, complemented
9C31×#1882C212yesmaximal, complemented
10C31×#1806C212yesmaximal, complemented
11C31×#1801C211yesmaximal, characteristic, complemented
12C2×C31×2−1+4C2211yescharacteristic
13C2×C31×#137C2212yes—
14C2×C31×AGL(1,ℤ/8)C2212yes—
15C2×C31×C4⋊Q8C2211yescharacteristic
16C2×C31×#124C2211yescharacteristic
17C2×C31×#124C2211yescharacteristic
18C31×#520—22no—
19C31×#520—22no—
20C31×#520C2212yes—
21C31×#519—22no—
22C31×#519C2211yescharacteristic
23C4×#41×C31—22no—
24C4×#41×C31—22no—
25C4×#41×C31C2212yes—
26C2×C4×Q8×C31—22no—
27C2×C4×Q8×C31C2211yescharacteristic
28C31×#464—22no—
29C31×#464—22no—
30C31×#463—22no—
31C31×#463—22no—
32C31×#456—24no—
33C31×#454—24no—
34C31×#423C2212yes—
35C2×C31×#104C2212yes—
36C2×C31×#104C2212yes—
37C31×#419C2212yes—
38C31×#418C2212yes—
39C2×C31×#101C2211yescharacteristic
40C2×C31×#101C2211yescharacteristic
41C31×#396—22no—
42C31×#391C2211yescharacteristic
43C31×#390C2211yescharacteristic
44C31×#388—22no—
45C4×C4⋊C4×C31C2211yescharacteristic
46C31×#343C2212yes—
47C31×#339C2212yes—
48C31×#339C2212yes—
49C31×2−1+4—24no—
50C31×2−1+4—22no—
51C31×2−1+4D414yes—
52C2×#41×C31—22no—
53C2×#41×C31—22no—
54C2×#41×C31C2312yes—
55C22×Q8×C31—22no—
56C22×Q8×C31C2311yescharacteristic
57C22×Q8×C31C2311yescharacteristic
58C22×D4×C31C2311yescharacteristic
59C31×#137—24no—
60C31×#137—24no—
61C31×AGL(1,ℤ/8)—24no—
62C31×AGL(1,ℤ/8)—24no—
63C2×Q16×C31—22no—
64C2×SD16×C31—22no—
65C2×SD16×C31—22no—
66C2×D8×C31—22no—
67C2×M16×C31C2312yes—
68C2×M16×C31C2312yes—
69C31×C4⋊Q8—22no—
70C31×C4⋊Q8—22no—
71C31×#124—22no—
72C31×#124—22no—
73C31×#124—22no—
74C31×#124—22no—
75C4×Q8×C31—22no—
76C4×Q8×C31—24no—
77C4×Q8×C31—22no—
78C4×Q8×C31—22no—
79C4×Q8×C31—22no—
80C4×Q8×C31—22no—
81C4×Q8×C31—22no—
82C4×Q8×C31—22no—
83C4×Q8×C31D412yes—
84C4×Q8×C31D412yes—
85C4×D4×C31—22no—
86C4×D4×C31—24no—
87C4×D4×C31—22no—
88C4×D4×C31—22no—
89C4×D4×C31—22no—
90C4×D4×C31—24no—
91C4×D4×C31—22no—
92C4×D4×C31D412yes—
93C4×D4×C31D412yes—
94C31×#117—24no—
95C31×#117—24no—
96C31×#117—22no—
97C31×#117—22no—
98C31×#117—22no—
99C31×#117C2312yes—
100C2×C4⋊C4×C31—24no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31D412yes—
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—21no—
110C2×C42×C31—24no—
111C2×C42×C31—22no—
112C2×C42×C31D412yes—
113C2×C42×C31C2311yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C31×C4⋊C8—22no—
117C31×C4⋊C8—22no—
118C31×#104—24no—
119C31×#104—24no—
120C31×#103—22no—
121C31×#103—22no—
122C31×#102—22no—
123C31×#102—22no—
124C31×#101—22no—
125C31×#101—22no—
126C31×#95—22no—
127C31×#95—21no—
128C24×C31—21no—
129#41×C31—28no—
130#41×C31—28no—
131#41×C31—28no—
132#41×C31—28no—
133#41×C31—22no—
134#41×C31—22no—
135#41×C31C2×D414yes—
136#41×C31#4114yes—
137C2×Q8×C31—22no—
138C2×Q8×C31—28no—
139C2×Q8×C31—28no—
140C2×Q8×C31—22no—
141C2×Q8×C31—22no—
142C2×Q8×C31—22no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—22no—
146C2×Q8×C31C2×D412yes—
147C2×Q8×C31C2×D412yes—
148C2×Q8×C31#4112yes—
149C2×D4×C31—22no—
150C2×D4×C31—22no—
151C2×D4×C31—22no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—22no—
155C2×D4×C31C2×D412yes—
156C22×C4×C31—24no—
157C22×C4×C31—22no—
158C22×C4×C31—21no—
159C22×C4×C31—24no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31C2×D412yes—
165C22×C4×C31C2×D412yes—
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2411yescharacteristic
169Q16×C31—44no—
170SD16×C31—44no—
171SD16×C31—44no—
172D8×C31—44no—
173M16×C31—22no—
174M16×C31—22no—
175M16×C31—22no—
176M16×C31—22no—
177C2×C8×C31—22no—
178C2×C8×C31—22no—
179C4⋊C4×C31—24no—
180C4⋊C4×C31—22no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—22no—
183C4⋊C4×C31—24no—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—22no—
186C4⋊C4×C31—42no—
187C4⋊C4×C31—44no—
188C4⋊C4×C31C2×D412yes—
189C4⋊C4×C31C2×D412yes—
190C22⋊C4×C31—24no—
191C22⋊C4×C31—22no—
192C22⋊C4×C31—22no—
193C22⋊C4×C31—22no—
194C22⋊C4×C31—44no—
195C22⋊C4×C31—41no—
196C22⋊C4×C31—41no—
197C22⋊C4×C31—42no—
198C22⋊C4×C31—44no—
199C42×C31—24no—
200C42×C31—24no—
201C42×C31—22no—
202C42×C31—22no—
203C42×C31—22no—
204C42×C31—22no—
205C42×C31—22no—
206C42×C31—21no—
207C42×C31—21no—
208C42×C31—21no—
209C42×C31—21no—
210C42×C31C2×D412yes—
211C42×C31C2×D412yes—
212#32925C3111yesmaximal, characteristic, direct product factor, Sylow
213C23×C31—22no—
214C23×C31—42no—
215C23×C31—42no—
216C23×C31—41no—
217C23×C31—41no—
218C23×C31—41no—
219C23×C31C22×D411yescharacteristic
220Q8×C31—28no—
221Q8×C31—24no—
222Q8×C31—22no—
223Q8×C31—24no—
224Q8×C31—42no—
225Q8×C31—42no—
226Q8×C31#12114yes—
227D4×C31—28no—
228D4×C31—24no—
229D4×C31—24no—
230D4×C31—22no—
231D4×C31—42no—
232D4×C31—42no—
233D4×C31#12114yes—
234C2×C4×C31—216no—
235C2×C4×C31—22no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—24no—
239C2×C4×C31—24no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—41no—
245C2×C4×C31—41no—
246C2×C4×C31—44no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—42no—
250C2×C4×C31—41no—
251C2×C4×C31—41no—
252C2×C4×C31—41no—
253C2×C4×C31—41no—
254C2×C4×C31—41no—
255C2×C4×C31—41no—
256C2×C4×C31—82no—
257C2×C4×C31—84no—
258C2×C4×C31#12011yescharacteristic
259C2×C4×C31#12011yescharacteristic
260C2×C4×C31#12012yes—
261C2×C4×C31#12114yes—
262C2×C4×C31C22×D411yescharacteristic
263C2×C4×C31C22×D412yes—
264C2×C4×C31C2×#4112yes—
265C2×C4×C31C2×#4111yescharacteristic
266C8×C31—42no—
267C8×C31—42no—
268C4×2−1+4C2×C3111yescharacteristic, complemented
269#3040C2×C3112yescomplemented
270C2×#456C2×C3111yescharacteristic, complemented
271C2×#454C2×C3111yescharacteristic
272#2545C2×C3111yescharacteristic, complemented
273#1888C2×C3111yescharacteristic, complemented
274#1886C2×C3111yescharacteristic, complemented
275#1883C2×C3112yescomplemented
276#1882C2×C3112yescomplemented
277#1806C2×C3112yescomplemented
278#1801C2×C3111yescharacteristic, complemented
279C22×C31—21no—
280C22×C31—21no—
281C22×C31—24no—
282C22×C31—42no—
283C22×C31—42no—
284C22×C31—82no—
285C22×C31—82no—
286C22×C31—81no—
287C22×C31—81no—
288C22×C31—81no—
289C22×C31C2×#12011yescharacteristic
290C22×C31C2×#12111yescharacteristic
291C22×C31#52511yescharacteristic
292C4×C31—24no—
293C4×C31—24no—
294C4×C31—22no—
295C4×C31—21no—
296C4×C31—21no—
297C4×C31—42no—
298C4×C31—42no—
299C4×C31—42no—
300C4×C31—42no—
301C4×C31—81no—
302C4×C31—81no—
303C4×C31C2×#12112yes—
304C4×C31#52512yes—
305C2×2−1+4C22×C3111yescharacteristic
306C2×#137C22×C3112yes—
307C2×AGL(1,ℤ/8)C22×C3112yes—
308C2×C4⋊Q8C22×C3111yescharacteristic
309C2×#124C22×C3111yescharacteristic
310C2×#124C22×C3111yescharacteristic
311#520—22no—
312#520—22no—
313#520C22×C3112yes—
314#519—22no—
315#519C22×C3111yescharacteristic
316C4×#41—22no—
317C4×#41—22no—
318C4×#41C22×C3112yes—
319C2×C4×Q8—22no—
320C2×C4×Q8C22×C3111yescharacteristic
321#464—22no—
322#464—22no—
323#463—22no—
324#463—22no—
325#456—24no—
326#454—24no—
327#423C22×C3112yes—
328C2×#104C22×C3112yes—
329C2×#104C22×C3112yes—
330#419C22×C3112yes—
331#418C22×C3112yes—
332C2×#101C22×C3111yescharacteristic
333C2×#101C22×C3111yescharacteristic
334#396—22no—
335#391C22×C3111yescharacteristic
336#390C22×C3111yescharacteristic
337#388—22no—
338C4×C4⋊C4C22×C3111yescharacteristic
339#343C22×C3112yes—
340#339C22×C3112yes—
341#339C22×C3112yes—
342C2×C31—21no—
343C2×C31—21no—
344C2×C31—44no—
345C2×C31—161no—
346C2×C31#284711yescharacteristic
347C2×C31#301811yescharacteristic
348C2×C31#302011yescharacteristic
3492−1+4—24no—
3502−1+4—22no—
3512−1+4D4×C3114yes—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41C23×C3112yes—
355C22×Q8—22no—
356C22×Q8C23×C3111yescharacteristic
357C22×Q8C23×C3111yescharacteristic
358C22×D4C23×C3111yescharacteristic
359#137—24no—
360#137—24no—
361AGL(1,ℤ/8)—24no—
362AGL(1,ℤ/8)—24no—
363C2×Q16—22no—
364C2×SD16—22no—
365C2×SD16—22no—
366C2×D8—22no—
367C2×M16C23×C3112yes—
368C2×M16C23×C3112yes—
369C4⋊Q8—22no—
370C4⋊Q8—22no—
371#124—22no—
372#124—22no—
373#124—22no—
374#124—22no—
375C4×Q8—22no—
376C4×Q8—24no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8D4×C3112yes—
384C4×Q8D4×C3112yes—
385C4×D4—22no—
386C4×D4—24no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—24no—
391C4×D4—22no—
392C4×D4D4×C3112yes—
393C4×D4D4×C3112yes—
394#117—24no—
395#117—24no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117C23×C3112yes—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4D4×C3112yes—
405C2×C4⋊C4C23×C3111yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—22no—
410C2×C42—24no—
411C2×C42—22no—
412C2×C42D4×C3112yes—
413C2×C42C23×C3111yescharacteristic
414C2×C42C23×C3111yescharacteristic
415C2×C42C23×C3111yescharacteristic
416C4⋊C8—22no—
417C4⋊C8—22no—
418#104—24no—
419#104—24no—
420#103—22no—
421#103—22no—
422#102—22no—
423#102—22no—
424#101—22no—
425#101—22no—
426#95—21no—
427#95—22no—
428C31#3292511yescharacteristic, direct product factor, Sylow
429C24—21no—
430#41—28no—
431#41—28no—
432#41—28no—
433#41—28no—
434#41—22no—
435#41—22no—
436#41C2×D4×C3114yes—
437#41#41×C3114yes—
438C2×Q8—22no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—22no—
447C2×Q8C2×D4×C3112yes—
448C2×Q8C2×D4×C3112yes—
449C2×Q8#41×C3112yes—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4C2×D4×C3112yes—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4C2×D4×C3112yes—
466C22×C4C2×D4×C3112yes—
467C22×C4C2×D4×C3111yescharacteristic
468C22×C4C2×D4×C3111yescharacteristic
469C22×C4C24×C3111yescharacteristic
470Q16—44no—
471SD16—44no—
472SD16—44no—
473D8—44no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478C2×C8—22no—
479C2×C8—22no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—42no—
488C4⋊C4—44no—
489C4⋊C4C2×D4×C3112yes—
490C4⋊C4C2×D4×C3112yes—
491C22⋊C4—24no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—44no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—42no—
499C22⋊C4—44no—
500C42—24no—
501C42—24no—
502C42—22no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42C2×D4×C3112yes—
512C42C2×D4×C3112yes—
513C23—22no—
514C23—42no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23C22×D4×C3111yescharacteristic
520Q8—28no—
521Q8—24no—
522Q8—22no—
523Q8—24no—
524Q8—42no—
525Q8—42no—
526Q8C31×#12114yes—
527D4—28no—
528D4—24no—
529D4—24no—
530D4—22no—
531D4—42no—
532D4—42no—
533D4C31×#12114yes—
534C2×C4—216no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—44no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—84no—
558C2×C4C31×#12011yescharacteristic
559C2×C4C31×#12011yescharacteristic
560C2×C4C31×#12012yes—
561C2×C4C31×#12114yes—
562C2×C4C22×D4×C3111yescharacteristic
563C2×C4C22×D4×C3112yes—
564C2×C4C2×#41×C3112yes—
565C2×C4C2×#41×C3111yescharacteristic
566C8—42no—
567C8—42no—
568C22—21no—
569C22—21no—
570C22—24no—
571C22—42no—
572C22—42no—
573C22—82no—
574C22—82no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22C2×C31×#12011yescharacteristic
579C22C2×C31×#12111yescharacteristic
580C22C31×#52511yescharacteristic
581C4—24no—
582C4—24no—
583C4—22no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4C2×C31×#12112yes—
593C4C31×#52512yes—
594C2—21no—
595C2—21no—
596C2—44no—
597C2—161no—
598C2C31×#284711yescharacteristic
599C2C31×#301811yescharacteristic
600C2C31×#302011yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#454C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×C31×2−1+4C2semidirect
2. C31×#3040C2semidirect
3. C2×C31×#456C2semidirect
5. C31×#2545C2semidirect
6. C31×#1888C2semidirect
7. C31×#1886C2semidirect
8. C31×#1883C2semidirect
9. C31×#1882C2semidirect
10. C31×#1806C2semidirect
11. C31×#1801C2semidirect
212. #32925C31direct (N × H)
268. C4×2−1+4C2×C31semidirect
269. #3040C2×C31semidirect
270. C2×#456C2×C31semidirect
272. #2545C2×C31semidirect
273. #1888C2×C31semidirect
274. #1886C2×C31semidirect
275. #1883C2×C31semidirect
276. #1882C2×C31semidirect
277. #1806C2×C31semidirect
278. #1801C2×C31semidirect
428. C31#32925direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C31×2−1+42
C31×#30402
C2×C31×#4562
C2×C31×#4542
C31×#25452
C31×#18882
C31×#18862
C31×#18832
C31×#18822
C31×#18062
C31×#18012
#3292531