Finite Group Databasebeta

← C31×#14632 #21471391

Subgroups — C31×#14632 #21471391

Order 7936.

1586 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#394C211yesmaximal, characteristic
2C2×C31×#388C212yesmaximal, complemented
3C31×#1442C212yesmaximal, complemented
4C31×#1441C211yesmaximal, characteristic, complemented
5C31×#1439C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C212yesmaximal
9C31×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D4×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2211yescharacteristic
12C22×C4⋊C4×C31C2212yes—
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C42×C31C2211yescharacteristic
22C31×#394C418yescomplemented
23C31×#388—28no—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2211yescharacteristic
33C25×C31C2312yes—
34C22×D4×C31—42no—
35C22×D4×C31—42no—
36C22×D4×C31—41no—
37C22×D4×C31—41no—
38C22×D4×C31C2×C414yes—
39C23×C4×C31C2312yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2312yes—
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2312yes—
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C2×C4⋊C4×C31—24no—
48C2×C4⋊C4×C31—22no—
49C2×C4⋊C4×C31—41no—
50C2×C4⋊C4×C31—41no—
51C2×C4⋊C4×C31—41no—
52C2×C4⋊C4×C31—41no—
53C2×C4⋊C4×C31—42no—
54C2×C4⋊C4×C31—42no—
55C2×C4⋊C4×C31—42no—
56C2×C4⋊C4×C31—41no—
57C2×C4⋊C4×C31C2×C414yes—
58C2×C22⋊C4×C31—24no—
59C2×C22⋊C4×C31—24no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—42no—
63C2×C22⋊C4×C31—42no—
64C2×C22⋊C4×C31—42no—
65C2×C22⋊C4×C31—42no—
66C2×C22⋊C4×C31—42no—
67C2×C22⋊C4×C31—42no—
68C2×C22⋊C4×C31—42no—
69C2×C22⋊C4×C31—42no—
70C2×C22⋊C4×C31—42no—
71C2×C22⋊C4×C31—42no—
72C2×C22⋊C4×C31—42no—
73C2×C22⋊C4×C31—42no—
74C2×C22⋊C4×C31C2×C418yes—
75C2×C22⋊C4×C31C2×C418yes—
76C2×C42×C31—41no—
77C2×C42×C31—41no—
78C2×C42×C31D414yescomplemented
79C31×#95—24no—
80C31×#95—24no—
81C31×#95—42no—
82C31×#95—42no—
83C31×#95—42no—
84C31×#95—41no—
85C31×#95—42no—
86C31×#95—42no—
87C31×#95C2×C414yes—
88C24×C31—22no—
89C24×C31—22no—
90C24×C31—22no—
91C24×C31—22no—
92C24×C31—22no—
93C24×C31—22no—
94C24×C31—22no—
95C24×C31—22no—
96C24×C31—22no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—22no—
101C24×C31—22no—
102C24×C31C22×C414yes—
103C24×C31C2411yescharacteristic
104C2×D4×C31—44no—
105C2×D4×C31—48no—
106C2×D4×C31—44no—
107C2×D4×C31—48no—
108C2×D4×C31—44no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—21no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31C22×C414yes—
155C22×C4×C31C22×C412yes—
156C22×C4×C31C22×C412yes—
157C22×C4×C31C22×C412yes—
158C22×C4×C31C2×D414yes—
159C22×C4×C31C2×D412yes—
160C22×C4×C31#4112yes—
161C4⋊C4×C31—44no—
162C4⋊C4×C31—44no—
163C4⋊C4×C31—48no—
164C4⋊C4×C31—44no—
165C22⋊C4×C31—216no—
166C22⋊C4×C31—48no—
167C22⋊C4×C31—48no—
168C22⋊C4×C31—48no—
169C22⋊C4×C31—48no—
170C22⋊C4×C31—48no—
171C42×C31—44no—
172#14632C3111yesmaximal, characteristic, direct product factor, Sylow
173C23×C31—24no—
174C23×C31—24no—
175C23×C31—24no—
176C23×C31—24no—
177C23×C31—24no—
178C23×C31—24no—
179C23×C31—24no—
180C23×C31—42no—
181C23×C31—42no—
182C23×C31—42no—
183C23×C31—42no—
184C23×C31—42no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31—42no—
194C23×C31—42no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31—42no—
200C23×C31—42no—
201C23×C31—42no—
202C23×C31—42no—
203C23×C31—42no—
204C23×C31—42no—
205C23×C31—42no—
206C23×C31—42no—
207C23×C31—42no—
208C23×C31C23×C411yescharacteristic
209C23×C31C22×D411yescharacteristic
210C23×C31C2×#4111yescharacteristic
211C23×C31H(5,𝔽2)11yescharacteristic
212C23×C31H(5,𝔽2)12yes—
213C23×C31H(5,𝔽2)11yescharacteristic
214C23×C31H(5,𝔽2)12yes—
215C23×C31H(5,𝔽2)11yescharacteristic
216C23×C31H(5,𝔽2)12yes—
217C23×C312−1+411yescharacteristic
218C23×C312−1+412yes—
219D4×C31—416no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—22no—
226C2×C4×C31—24no—
227C2×C4×C31—24no—
228C2×C4×C31—24no—
229C2×C4×C31—22no—
230C2×C4×C31—22no—
231C2×C4×C31—24no—
232C2×C4×C31—24no—
233C2×C4×C31—24no—
234C2×C4×C31—24no—
235C2×C4×C31—24no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—41no—
241C2×C4×C31—42no—
242C2×C4×C31—42no—
243C2×C4×C31—42no—
244C2×C4×C31—41no—
245C2×C4×C31—42no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—42no—
258C2×C4×C31—42no—
259C2×C4×C31—42no—
260C2×C4×C31—42no—
261C2×C4×C31—42no—
262C2×C4×C31—42no—
263C2×C4×C31—42no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—42no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—42no—
270C2×C4×C31—42no—
271C2×C4×C31C4×D414yes—
272C2×#394C2×C3111yescharacteristic
273C2×#388C2×C3112yescomplemented
274#1442C2×C3112yescomplemented
275#1441C2×C3111yescharacteristic, complemented
276#1439C2×C3112yescomplemented
277#1439C2×C3112yescomplemented
278#1439C2×C3112yescomplemented
279#1438C2×C3112yes—
280C4⋊#95C2×C3111yescharacteristic, complemented
281C22×C31—44no—
282C22×C31—44no—
283C22×C31—44no—
284C22×C31—44no—
285C22×C31—44no—
286C22×C31—44no—
287C22×C31—44no—
288C22×C31—82no—
289C22×C31—82no—
290C22×C31—82no—
291C22×C31—82no—
292C22×C31—82no—
293C22×C31—82no—
294C22×C31—82no—
295C22×C31—82no—
296C22×C31C2×C4×D411yescharacteristic
297C22×C31#51812yes—
298C22×C31#51811yescharacteristic
299C22×C31#52012yes—
300C22×C31#52011yescharacteristic
301C22×C31#53411yescharacteristic
302C22×C31#53512yes—
303C22×C31#53711yescharacteristic
304C22×C31#53712yes—
305C22×C31#53811yescharacteristic
306C22×C31#53911yescharacteristic
307C22×C31#54012yes—
308C22×C31#54212yes—
309C22×C31#56011yescharacteristic
310C22×C31#56012yes—
311C22×C31#56012yes—
312C22×C31H(3,𝔽4)11yescharacteristic
313C22×C31H(3,𝔽4)11yescharacteristic
314C22×C31#56212yes—
315C22×C31#56212yes—
316C22×C31#56212yes—
317C22×C31#56311yescharacteristic
318C22×C31#56312yes—
319C4×C31—24no—
320C4×C31—44no—
321C4×C31—42no—
322C4×C31—42no—
323C4×C31—44no—
324C4×C31—82no—
325C4×C31—82no—
326C4×C31—82no—
327C23×D4C22×C3111yescharacteristic
328C22×C4⋊C4C22×C3111yescharacteristic
329C22×C4⋊C4C22×C3112yes—
330C22×C4⋊C4C22×C3111yescharacteristic
331C22×C4⋊C4C22×C3111yescharacteristic
332C22×C22⋊C4C22×C3112yes—
333C22×C22⋊C4C22×C3112yes—
334C22×C22⋊C4C22×C3112yes—
335C22×C22⋊C4C22×C3112yes—
336C22×C22⋊C4C22×C3112yes—
337C22×C22⋊C4C22×C3112yes—
338C22×C42C22×C3111yescharacteristic
339#394C4×C3118yescomplemented
340#388—28no—
341C2×#95C22×C3112yes—
342C2×#95C22×C3112yes—
343C2×#95C22×C3112yes—
344C2×#95C22×C3112yes—
345C2×#95C22×C3112yes—
346C2×#95C22×C3111yescharacteristic
347C2×#95C22×C3112yes—
348C2×#95C22×C3112yes—
349C2×#95C22×C3111yescharacteristic
350C2×C31—84no—
351C2×C31#232412yes—
352C2×C31#232511yescharacteristic
353C2×C31#237511yescharacteristic
354C2×C31#237612yes—
355C2×C31#237911yescharacteristic
356C2×C31#281312yes—
357C2×C31#281911yescharacteristic
358C2×C31#282311yescharacteristic
359C2×C31#282811yescharacteristic
360C2×C31#283211yescharacteristic
361C2×C31#283712yes—
362C25C23×C3112yes—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—41no—
366C22×D4—41no—
367C22×D4C2×C4×C3114yes—
368C23×C4C23×C3112yes—
369C23×C4C23×C3112yes—
370C23×C4C23×C3112yes—
371C23×C4C23×C3111yescharacteristic
372C23×C4C23×C3112yes—
373C23×C4C23×C3111yescharacteristic
374C23×C4C23×C3112yes—
375C23×C4C23×C3111yescharacteristic
376C2×C4⋊C4—24no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—41no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4C2×C4×C3114yes—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4C2×C4×C3118yes—
404C2×C22⋊C4C2×C4×C3118yes—
405C2×C42—41no—
406C2×C42—41no—
407C2×C42D4×C3114yescomplemented
408#95—24no—
409#95—24no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—41no—
414#95—42no—
415#95—42no—
416#95C2×C4×C3114yes—
417C31#1463211yescharacteristic, direct product factor, Sylow
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24C22×C4×C3114yes—
433C24C24×C3111yescharacteristic
434C2×D4—44no—
435C2×D4—48no—
436C2×D4—44no—
437C2×D4—48no—
438C2×D4—44no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4C22×C4×C3114yes—
485C22×C4C22×C4×C3112yes—
486C22×C4C22×C4×C3112yes—
487C22×C4C22×C4×C3112yes—
488C22×C4C2×D4×C3114yes—
489C22×C4C2×D4×C3112yes—
490C22×C4#41×C3112yes—
491C4⋊C4—44no—
492C4⋊C4—44no—
493C4⋊C4—48no—
494C4⋊C4—44no—
495C22⋊C4—216no—
496C22⋊C4—48no—
497C22⋊C4—48no—
498C22⋊C4—48no—
499C22⋊C4—48no—
500C22⋊C4—48no—
501C42—44no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23C23×C4×C3111yescharacteristic
538C23C22×D4×C3111yescharacteristic
539C23C2×#41×C3111yescharacteristic
540C23C31×H(5,𝔽2)11yescharacteristic
541C23C31×H(5,𝔽2)12yes—
542C23C31×H(5,𝔽2)11yescharacteristic
543C23C31×H(5,𝔽2)12yes—
544C23C31×H(5,𝔽2)11yescharacteristic
545C23C31×H(5,𝔽2)12yes—
546C23C31×2−1+411yescharacteristic
547C23C31×2−1+412yes—
548D4—416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4C4×D4×C3114yes—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22C2×C4×D4×C3111yescharacteristic
617C22C31×#51812yes—
618C22C31×#51811yescharacteristic
619C22C31×#52012yes—
620C22C31×#52011yescharacteristic
621C22C31×#53411yescharacteristic
622C22C31×#53512yes—
623C22C31×#53711yescharacteristic
624C22C31×#53712yes—
625C22C31×#53811yescharacteristic
626C22C31×#53911yescharacteristic
627C22C31×#54012yes—
628C22C31×#54212yes—
629C22C31×#56011yescharacteristic
630C22C31×#56012yes—
631C22C31×#56012yes—
632C22C31×H(3,𝔽4)11yescharacteristic
633C22C31×H(3,𝔽4)11yescharacteristic
634C22C31×#56212yes—
635C22C31×#56212yes—
636C22C31×#56212yes—
637C22C31×#56311yescharacteristic
638C22C31×#56312yes—
639C4—24no—
640C4—44no—
641C4—42no—
642C4—42no—
643C4—44no—
644C4—82no—
645C4—82no—
646C4—82no—
647C2—84no—
648C2C31×#232412yes—
649C2C31×#232511yescharacteristic
650C2C31×#237511yescharacteristic
651C2C31×#237612yes—
652C2C31×#237911yescharacteristic
653C2C31×#281312yes—
654C2C31×#281911yescharacteristic
655C2C31×#282311yescharacteristic
656C2C31×#282811yescharacteristic
657C2C31×#283211yescharacteristic
658C2C31×#283712yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#388C2semidirect
3. C31×#1442C2semidirect
4. C31×#1441C2semidirect
5. C31×#1439C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
9. C31×C4⋊#95C2semidirect
22. C31×#394C4semidirect
78. C2×C42×C31D4semidirect
172. #14632C31direct (N × H)
273. C2×#388C2×C31semidirect
274. #1442C2×C31semidirect
275. #1441C2×C31semidirect
276. #1439C2×C31semidirect
277. #1439C2×C31semidirect
278. #1439C2×C31semidirect
280. C4⋊#95C2×C31semidirect
339. #394C4×C31semidirect
407. C2×C42D4×C31semidirect
417. C31#14632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3942
C2×C31×#3882
C31×#14422
C31×#14412
C31×#14392
C31×#14382
C31×C4⋊#952
#1463231