Finite Group Databasebeta

← C31×#19026 #21475785

Subgroups — C31×#19026 #21475785

Order 7936.

1012 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3561C211yesmaximal, characteristic, complemented
2C31×#3217C211yesmaximal, characteristic, complemented
3C2×C31×#496C211yesmaximal, characteristic, complemented
4C31×#3138C211yesmaximal, characteristic, complemented
5C31×#1657C214yesmaximal, complemented
6C31×#1656C214yesmaximal, complemented
7C31×#1531C211yesmaximal, characteristic, complemented
8C31×#1527C211yesmaximal, characteristic, complemented
9C31×#1524C211yesmaximal, characteristic, complemented
10C22×SD16×C31—21no—
11C22×D8×C31—21no—
12C31×#563C2212yescomplemented
13C31×#562C2212yescomplemented
14C31×#556—21no—
15C31×#551—22no—
16D4×Q8×C31—21no—
17C31×#548—21no—
18C31×#546—21no—
19C31×#543—21no—
20C31×#542—21no—
21C31×#542—22no—
22C31×#538—21no—
23C31×#536—21no—
24C31×#533C2211yescharacteristic
25C2×C31×#127C2211yescharacteristic
26C31×#529C2211yescharacteristic
27C2×C31×#124C2211yescharacteristic
28C31×#496—22no—
29C31×#496C2214yes—
30C31×#496C2212yescomplemented
31C31×#490C2214yescomplemented
32C31×#490C2212yescomplemented
33C31×#486—21no—
34C31×#486—21no—
35C31×#460—21no—
36C31×#459—21no—
37C31×#450—21no—
38C31×#447—21no—
39C31×#432C2211yescharacteristic
40C31×#418—22no—
41C4×M16×C31C2211yescharacteristic
42C2×C31×#97C2211yescharacteristic
43C31×#330C2214yescomplemented
44C31×#330C2212yescomplemented
45C31×#329C2212yescomplemented
46C31×#329C2214yescomplemented
47C2×#41×C31—21no—
48C22×Q8×C31—21no—
49C22×Q8×C31D411yescharacteristic
50C22×D4×C31—21no—
51C22×D4×C31—21no—
52C22×D4×C31—21no—
53C22×D4×C31D411yescharacteristic
54C2×SD16×C31—24no—
55C2×SD16×C31—22no—
56C2×SD16×C31—44no—
57C2×D8×C31—24no—
58C2×D8×C31—22no—
59C2×D8×C31—44no—
60C2×M16×C31—21no—
61C22×C8×C31—21no—
62C31×C4⋊Q8—21no—
63C31×C4⋊Q8—22no—
64C31×C4⋊Q8D411yescharacteristic
65C31×C4⋊Q8D411yescharacteristic
66C31×#127—21no—
67C31×#127—21no—
68C31×#127—21no—
69C31×#127C2312yes—
70C31×#126—22no—
71C31×#126—22no—
72C31×#126—22no—
73C31×#126—21no—
74C31×#125C2311yescharacteristic
75C31×#125C2312yes—
76C31×#124—21no—
77C31×#124—22no—
78C31×#124—22no—
79C31×#124—21no—
80C31×#124—21no—
81C31×#124D412yes—
82C31×#124C2312yes—
83C31×#124C2311yescharacteristic
84C31×#123—22no—
85C31×#123—22no—
86C31×#123—21no—
87C31×#123—22no—
88C31×#123—22no—
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8—21no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8—21no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8D411yescharacteristic
100C31×#121—21no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121D411yescharacteristic
104C31×#120—22no—
105C4×Q8×C31—21no—
106C4×Q8×C31—21no—
107C4×Q8×C31—21no—
108C4×Q8×C31D411yescharacteristic
109C4×D4×C31—22no—
110C4×D4×C31—21no—
111C4×D4×C31—22no—
112C4×D4×C31—21no—
113C4×D4×C31D411yescharacteristic
114C31×#117—22no—
115C31×#117—21no—
116C31×#117D412yes—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C42×C31C2311yescharacteristic
121C31×C4⋊C8—21no—
122C31×#102—24no—
123C31×#102—24no—
124C31×#102—22no—
125C31×#102—22no—
126C31×C22⋊C8—21no—
127C31×#97—21no—
128C31×#97C2312yes—
129C31×#97C2312yes—
130C31×#97C2312yes—
131C4×C8×C31—21no—
132C24×C31—21no—
133C24×C31—41no—
134#41×C31—82no—
135C2×Q8×C31—22no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—42no—
140C2×Q8×C31—82no—
141C2×Q8×C31C2×D411yescharacteristic
142C2×Q8×C31C2×D412yes—
143C2×D4×C31—21no—
144C2×D4×C31—22no—
145C2×D4×C31—22no—
146C2×D4×C31—21no—
147C2×D4×C31—22no—
148C2×D4×C31—22no—
149C2×D4×C31—22no—
150C2×D4×C31—42no—
151C2×D4×C31—42no—
152C2×D4×C31—42no—
153C2×D4×C31—44no—
154C2×D4×C31—41no—
155C2×D4×C31—41no—
156C2×D4×C31—41no—
157C2×D4×C31—82no—
158C2×D4×C31C2×D411yescharacteristic
159C2×D4×C31C2×D412yes—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168SD16×C31—48no—
169SD16×C31—82no—
170D8×C31—48no—
171D8×C31—82no—
172M16×C31—42no—
173C2×C8×C31—24no—
174C2×C8×C31—22no—
175C2×C8×C31—22no—
176C2×C8×C31—22no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—22no—
180C4⋊C4×C31—22no—
181C4⋊C4×C31—21no—
182C4⋊C4×C31—21no—
183C4⋊C4×C31—21no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—22no—
189C4⋊C4×C31C2×D412yes—
190C4⋊C4×C31C2×D412yes—
191C4⋊C4×C31C2×D411yescharacteristic
192C4⋊C4×C31C2×D411yescharacteristic
193C22⋊C4×C31—22no—
194C22⋊C4×C31—22no—
195C22⋊C4×C31—22no—
196C22⋊C4×C31—22no—
197C22⋊C4×C31—22no—
198C22⋊C4×C31—21no—
199C22⋊C4×C31—22no—
200C22⋊C4×C31—22no—
201C22⋊C4×C31—22no—
202C22⋊C4×C31—21no—
203C22⋊C4×C31—21no—
204C22⋊C4×C31—22no—
205C22⋊C4×C31—22no—
206C22⋊C4×C31—21no—
207C22⋊C4×C31—21no—
208C42×C31—22no—
209C42×C31—22no—
210C42×C31—21no—
211C42×C31C2×D411yescharacteristic
212C42×C31C2×D411yescharacteristic
213C42×C31C2×D411yescharacteristic
214C42×C31C2411yescharacteristic
215#19026C3111yesmaximal, characteristic, direct product factor, Sylow
216C23×C31—22no—
217C23×C31—21no—
218C23×C31—42no—
219C23×C31—42no—
220C23×C31—81no—
221C23×C31—81no—
222C23×C31—82no—
223C23×C31—82no—
224C23×C31—82no—
225C23×C31#12011yescharacteristic
226Q8×C31—42no—
227Q8×C31—41no—
228Q8×C31—42no—
229Q8×C31—42no—
230Q8×C31—81no—
231Q8×C31—82no—
232D4×C31—42no—
233D4×C31—41no—
234D4×C31—42no—
235D4×C31—42no—
236D4×C31—42no—
237D4×C31—42no—
238D4×C31—44no—
239D4×C31—42no—
240D4×C31—42no—
241D4×C31—82no—
242D4×C31—82no—
243D4×C31—82no—
244D4×C31—82no—
245D4×C31—82no—
246C2×C4×C31—22no—
247C2×C4×C31—22no—
248C2×C4×C31—21no—
249C2×C4×C31—22no—
250C2×C4×C31—21no—
251C2×C4×C31—22no—
252C2×C4×C31—22no—
253C2×C4×C31—21no—
254C2×C4×C31—41no—
255C2×C4×C31—42no—
256C2×C4×C31—81no—
257C2×C4×C31—82no—
258C2×C4×C31—82no—
259C2×C4×C31—82no—
260C2×C4×C31#12011yescharacteristic
261C2×C4×C31#12011yescharacteristic
262C2×C4×C31#12011yescharacteristic
263C2×C4×C31C22×D411yescharacteristic
264C2×C4×C31C22×D411yescharacteristic
265C2×C4×C31C22×D411yescharacteristic
266C8×C31—24no—
267C8×C31—42no—
268C8×C31—42no—
269#3561C2×C3111yescharacteristic, complemented
270#3217C2×C3111yescharacteristic, complemented
271C2×#496C2×C3111yescharacteristic, complemented
272#3138C2×C3111yescharacteristic, complemented
273#1657C2×C3114yescomplemented
274#1656C2×C3114yescomplemented
275#1531C2×C3111yescharacteristic, complemented
276#1527C2×C3111yescharacteristic, complemented
277#1524C2×C3111yescharacteristic, complemented
278C22×C31—21no—
279C22×C31—21no—
280C22×C31—41no—
281C22×C31—42no—
282C22×C31—41no—
283C22×C31—42no—
284C22×C31—42no—
285C22×C31—41no—
286C22×C31—82no—
287C22×C31—82no—
288C22×C31—82no—
289C22×C31—162no—
290C22×C31—164no—
291C22×C31#45412yes—
292C22×C31C2×#12011yescharacteristic
293C4×C31—21no—
294C4×C31—21no—
295C4×C31—21no—
296C4×C31—21no—
297C4×C31—21no—
298C4×C31—41no—
299C4×C31—42no—
300C4×C31—42no—
301C4×C31—41no—
302C4×C31—41no—
303C4×C31—42no—
304C4×C31#45312yes—
305C22×SD16—21no—
306C22×D8—21no—
307#563C22×C3112yescomplemented
308#562C22×C3112yescomplemented
309#556—21no—
310#551—22no—
311D4×Q8—21no—
312#548—21no—
313#546—21no—
314#543—21no—
315#542—21no—
316#542—22no—
317#538—21no—
318#536—21no—
319#533C22×C3111yescharacteristic
320C2×#127C22×C3111yescharacteristic
321#529C22×C3111yescharacteristic
322C2×#124C22×C3111yescharacteristic
323#496—22no—
324#496C22×C3114yes—
325#496C22×C3112yescomplemented
326#490C22×C3114yescomplemented
327#490C22×C3112yescomplemented
328#486—21no—
329#486—21no—
330#460—21no—
331#459—21no—
332#450—21no—
333#447—21no—
334#432C22×C3111yescharacteristic
335#418—22no—
336C4×M16C22×C3111yescharacteristic
337C2×#97C22×C3111yescharacteristic
338#330C22×C3114yescomplemented
339#330C22×C3112yescomplemented
340#329C22×C3112yescomplemented
341#329C22×C3114yescomplemented
342C2×C31—22no—
343C2×C31—81no—
344C2×C31—82no—
345C2×C31—162no—
346C2×C31C2×#45311yescharacteristic
347C2×C31C2×#45411yescharacteristic
348C2×C31#302111yescharacteristic
349C2×#41—21no—
350C22×Q8—21no—
351C22×Q8D4×C3111yescharacteristic
352C22×D4—21no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4D4×C3111yescharacteristic
356C2×SD16—24no—
357C2×SD16—22no—
358C2×SD16—44no—
359C2×D8—24no—
360C2×D8—22no—
361C2×D8—44no—
362C2×M16—21no—
363C22×C8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—22no—
366C4⋊Q8D4×C3111yescharacteristic
367C4⋊Q8D4×C3111yescharacteristic
368#127—21no—
369#127—21no—
370#127—21no—
371#127C23×C3112yes—
372#126—22no—
373#126—22no—
374#126—22no—
375#126—21no—
376#125C23×C3111yescharacteristic
377#125C23×C3112yes—
378#124—21no—
379#124—22no—
380#124—22no—
381#124—21no—
382#124—21no—
383#124D4×C3112yes—
384#124C23×C3112yes—
385#124C23×C3111yescharacteristic
386#123—22no—
387#123—22no—
388#123—21no—
389#123—22no—
390#123—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8D4×C3111yescharacteristic
402#121—21no—
403#121—22no—
404#121—22no—
405#121D4×C3111yescharacteristic
406#120—22no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8D4×C3111yescharacteristic
411C4×D4—22no—
412C4×D4—21no—
413C4×D4—22no—
414C4×D4—21no—
415C4×D4D4×C3111yescharacteristic
416#117—22no—
417#117—21no—
418#117D4×C3112yes—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C42C23×C3111yescharacteristic
423C4⋊C8—21no—
424#102—24no—
425#102—24no—
426#102—22no—
427#102—22no—
428C22⋊C8—21no—
429#97—21no—
430#97C23×C3112yes—
431#97C23×C3112yes—
432#97C23×C3112yes—
433C4×C8—21no—
434C31#1902611yescharacteristic, direct product factor, Sylow
435C24—21no—
436C24—41no—
437#41—82no—
438C2×Q8—22no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—42no—
443C2×Q8—82no—
444C2×Q8C2×D4×C3111yescharacteristic
445C2×Q8C2×D4×C3112yes—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—82no—
461C2×D4C2×D4×C3111yescharacteristic
462C2×D4C2×D4×C3112yes—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4C2×D4×C3111yescharacteristic
469C22×C4C2×D4×C3111yescharacteristic
470C22×C4C2×D4×C3111yescharacteristic
471SD16—48no—
472SD16—82no—
473D8—48no—
474D8—82no—
475M16—42no—
476C2×C8—24no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4C2×D4×C3112yes—
493C4⋊C4C2×D4×C3112yes—
494C4⋊C4C2×D4×C3111yescharacteristic
495C4⋊C4C2×D4×C3111yescharacteristic
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—21no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C42—22no—
512C42—22no—
513C42—21no—
514C42C2×D4×C3111yescharacteristic
515C42C2×D4×C3111yescharacteristic
516C42C2×D4×C3111yescharacteristic
517C42C24×C3111yescharacteristic
518C23—22no—
519C23—21no—
520C23—42no—
521C23—42no—
522C23—81no—
523C23—81no—
524C23—82no—
525C23—82no—
526C23—82no—
527C23C31×#12011yescharacteristic
528Q8—42no—
529Q8—41no—
530Q8—42no—
531Q8—42no—
532Q8—81no—
533Q8—82no—
534D4—42no—
535D4—41no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—44no—
541D4—42no—
542D4—42no—
543D4—82no—
544D4—82no—
545D4—82no—
546D4—82no—
547D4—82no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—81no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4C31×#12011yescharacteristic
563C2×C4C31×#12011yescharacteristic
564C2×C4C31×#12011yescharacteristic
565C2×C4C22×D4×C3111yescharacteristic
566C2×C4C22×D4×C3111yescharacteristic
567C2×C4C22×D4×C3111yescharacteristic
568C8—24no—
569C8—42no—
570C8—42no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—42no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—162no—
583C22—164no—
584C22C31×#45412yes—
585C22C2×C31×#12011yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4C31×#45312yes—
598C2—22no—
599C2—82no—
600C2—81no—
601C2—162no—
602C2C2×C31×#45311yescharacteristic
603C2C2×C31×#45411yescharacteristic
604C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3561C2semidirect
2. C31×#3217C2semidirect
3. C2×C31×#496C2semidirect
4. C31×#3138C2semidirect
5. C31×#1657C2semidirect
6. C31×#1656C2semidirect
7. C31×#1531C2semidirect
8. C31×#1527C2semidirect
9. C31×#1524C2semidirect
12. C31×#563C22semidirect
13. C31×#562C22semidirect
30. C31×#496C22semidirect
31. C31×#490C22semidirect
32. C31×#490C22semidirect
43. C31×#330C22semidirect
44. C31×#330C22semidirect
45. C31×#329C22semidirect
46. C31×#329C22semidirect
215. #19026C31direct (N × H)
269. #3561C2×C31semidirect
270. #3217C2×C31semidirect
271. C2×#496C2×C31semidirect
272. #3138C2×C31semidirect
273. #1657C2×C31semidirect
274. #1656C2×C31semidirect
275. #1531C2×C31semidirect
276. #1527C2×C31semidirect
277. #1524C2×C31semidirect
307. #563C22×C31semidirect
308. #562C22×C31semidirect
325. #496C22×C31semidirect
326. #490C22×C31semidirect
327. #490C22×C31semidirect
338. #330C22×C31semidirect
339. #330C22×C31semidirect
340. #329C22×C31semidirect
341. #329C22×C31semidirect
434. C31#19026direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35612
C31×#32172
C2×C31×#4962
C31×#31382
C31×#16572
C31×#16562
C31×#15312
C31×#15272
C31×#15242
#1902631