Finite Group Databasebeta

← C31×#14516 #21471275

Subgroups — C31×#14516 #21471275

Order 7936.

1666 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#386C211yesmaximal, characteristic
2C31×#1443C212yesmaximal, complemented
3C31×#1440C212yesmaximal, complemented
4C31×#1438C211yesmaximal, characteristic
5C31×#1438C211yesmaximal, characteristic
6C31×#1437C212yesmaximal, complemented
7C31×#1437C212yesmaximal, complemented
8C31×#1434C212yesmaximal, complemented
9C31×C22⋊#95C212yesmaximal, complemented
10C23×D4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C22×C22⋊C4×C31C2212yes—
13C22×C22⋊C4×C31C2212yes—
14C22×C22⋊C4×C31C2211yescharacteristic
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2212yes—
19C22×C42×C31C2212yes—
20C31×#386C418yescomplemented
21C2×C31×#95C2212yes—
22C2×C31×#95C2212yes—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C25×C31C2311yescharacteristic
33C25×C31C2311yescharacteristic
34C22×D4×C31—24no—
35C22×D4×C31—42no—
36C22×D4×C31—41no—
37C22×D4×C31—41no—
38C22×D4×C31C2×C414yes—
39C23×C4×C31—41no—
40C23×C4×C31—41no—
41C23×C4×C31—42no—
42C23×C4×C31—42no—
43C23×C4×C31C2×C414yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C2×C22⋊C4×C31—24no—
52C2×C22⋊C4×C31—24no—
53C2×C22⋊C4×C31—24no—
54C2×C22⋊C4×C31—24no—
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31—24no—
57C2×C22⋊C4×C31—42no—
58C2×C22⋊C4×C31—42no—
59C2×C22⋊C4×C31—42no—
60C2×C22⋊C4×C31—41no—
61C2×C22⋊C4×C31—42no—
62C2×C22⋊C4×C31—42no—
63C2×C22⋊C4×C31—42no—
64C2×C22⋊C4×C31—42no—
65C2×C22⋊C4×C31—41no—
66C2×C22⋊C4×C31—42no—
67C2×C22⋊C4×C31C2×C414yes—
68C2×C22⋊C4×C31C2×C418yes—
69C2×C42×C31—24no—
70C2×C42×C31—42no—
71C2×C42×C31—42no—
72C31×#95—24no—
73C31×#95—41no—
74C31×#95—42no—
75C31×#95—42no—
76C31×#95—42no—
77C31×#95—42no—
78C31×#95—42no—
79C31×#95—42no—
80C31×#95—42no—
81C31×#95—41no—
82C31×#95C2×C418yes—
83C24×C31—22no—
84C24×C31—22no—
85C24×C31—22no—
86C24×C31—22no—
87C24×C31—22no—
88C24×C31—21no—
89C24×C31—21no—
90C24×C31—22no—
91C24×C31—22no—
92C24×C31—22no—
93C24×C31—22no—
94C24×C31—22no—
95C24×C31—22no—
96C24×C31—21no—
97C24×C31—21no—
98C24×C31C22×C412yes—
99C24×C31C22×C412yes—
100C24×C31#4114yes—
101C24×C31C2411yescharacteristic
102C2×D4×C31—28no—
103C2×D4×C31—44no—
104C2×D4×C31—44no—
105C2×D4×C31—48no—
106C2×D4×C31—48no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
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—21no—
128C22×C4×C31—21no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
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—48no—
150C22×C4×C31—44no—
151C22×C4×C31—48no—
152C22×C4×C31—44no—
153C22×C4×C31—44no—
154C22×C4×C31C22×C412yes—
155C22×C4×C31C22×C414yes—
156C22×C4×C31C22×C414yes—
157C22×C4×C31#4114yes—
158C22×C4×C31#4114yes—
159C22⋊C4×C31—48no—
160C22⋊C4×C31—44no—
161C22⋊C4×C31—44no—
162C22⋊C4×C31—48no—
163C22⋊C4×C31—48no—
164C22⋊C4×C31—48no—
165C22⋊C4×C31—44no—
166C42×C31—48no—
167#14516C3111yesmaximal, characteristic, direct product factor, Sylow
168C23×C31—24no—
169C23×C31—22no—
170C23×C31—22no—
171C23×C31—24no—
172C23×C31—24no—
173C23×C31—24no—
174C23×C31—24no—
175C23×C31—24no—
176C23×C31—24no—
177C23×C31—24no—
178C23×C31—22no—
179C23×C31—24no—
180C23×C31—24no—
181C23×C31—22no—
182C23×C31—22no—
183C23×C31—42no—
184C23×C31—42no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—41no—
188C23×C31—42no—
189C23×C31—41no—
190C23×C31—42no—
191C23×C31—41no—
192C23×C31—41no—
193C23×C31—42no—
194C23×C31—42no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31—41no—
200C23×C31—42no—
201C23×C31—42no—
202C23×C31—42no—
203C23×C31—42no—
204C23×C31—42no—
205C23×C31—41no—
206C23×C31—42no—
207C23×C31—41no—
208C23×C31—41no—
209C23×C31#11714yes—
210C23×C31C23×C411yescharacteristic
211C23×C31C2×#4112yes—
212C23×C31C2×#4112yes—
213C23×C31C2×#4112yes—
214C23×C31H(5,𝔽2)12yes—
215C23×C31H(5,𝔽2)12yes—
216C23×C31H(5,𝔽2)11yescharacteristic
217C23×C31H(5,𝔽2)11yescharacteristic
218C23×C31H(5,𝔽2)12yes—
219D4×C31—416no—
220C2×C4×C31—22no—
221C2×C4×C31—24no—
222C2×C4×C31—24no—
223C2×C4×C31—24no—
224C2×C4×C31—24no—
225C2×C4×C31—24no—
226C2×C4×C31—24no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—24no—
230C2×C4×C31—24no—
231C2×C4×C31—24no—
232C2×C4×C31—24no—
233C2×C4×C31—24no—
234C2×C4×C31—24no—
235C2×C4×C31—416no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—42no—
241C2×C4×C31—42no—
242C2×C4×C31—42no—
243C2×C4×C31—42no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
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×#386C2×C3111yescharacteristic
269#1443C2×C3112yescomplemented
270#1440C2×C3112yescomplemented
271#1438C2×C3111yescharacteristic
272#1438C2×C3111yescharacteristic
273#1437C2×C3112yescomplemented
274#1437C2×C3112yescomplemented
275#1434C2×C3112yescomplemented
276C22⋊#95C2×C3112yescomplemented
277C22×C31—24no—
278C22×C31—28no—
279C22×C31—44no—
280C22×C31—42no—
281C22×C31—42no—
282C22×C31—44no—
283C22×C31—44no—
284C22×C31—44no—
285C22×C31—44no—
286C22×C31—42no—
287C22×C31—44no—
288C22×C31—44no—
289C22×C31—42no—
290C22×C31—42no—
291C22×C31—82no—
292C22×C31—82no—
293C22×C31—82no—
294C22×C31—82no—
295C22×C31C2×#11711yescharacteristic
296C22×C31C4×#4112yes—
297C22×C31#51811yescharacteristic
298C22×C31#51811yescharacteristic
299C22×C31#51812yes—
300C22×C31#53812yes—
301C22×C31#53812yes—
302C22×C31#53812yes—
303C22×C31#53812yes—
304C22×C31#54012yes—
305C22×C31#54012yes—
306C22×C31#55112yes—
307C22×C31#55112yes—
308C22×C31#55111yescharacteristic
309C22×C31#55312yes—
310C22×C31#55312yes—
311C22×C31#55312yes—
312C22×C31#55911yescharacteristic
313C22×C31#56012yes—
314C22×C31#56011yescharacteristic
315C22×C31H(3,𝔽4)11yescharacteristic
316C4×C31—42no—
317C4×C31—44no—
318C4×C31—44no—
319C4×C31—44no—
320C4×C31—44no—
321C4×C31—82no—
322C4×C31—82no—
323C23×D4C22×C3111yescharacteristic
324C24×C4C22×C3111yescharacteristic
325C22×C22⋊C4C22×C3112yes—
326C22×C22⋊C4C22×C3112yes—
327C22×C22⋊C4C22×C3111yescharacteristic
328C22×C22⋊C4C22×C3112yes—
329C22×C22⋊C4C22×C3111yescharacteristic
330C22×C22⋊C4C22×C3111yescharacteristic
331C22×C22⋊C4C22×C3112yes—
332C22×C42C22×C3112yes—
333#386C4×C3118yescomplemented
334C2×#95C22×C3112yes—
335C2×#95C22×C3112yes—
336C2×#95C22×C3112yes—
337C2×#95C22×C3112yes—
338C2×#95C22×C3112yes—
339C2×#95C22×C3111yescharacteristic
340C2×#95C22×C3112yes—
341C2×#95C22×C3112yes—
342C2×#95C22×C3112yes—
343C2×#95C22×C3111yescharacteristic
344C2×#95C22×C3112yes—
345C2×C31—44no—
346C2×C31—82no—
347C2×C31#231211yescharacteristic
348C2×C31#233312yes—
349C2×C31#235312yes—
350C2×C31#237411yescharacteristic
351C2×C31#237511yescharacteristic
352C2×C31#274912yes—
353C2×C31#275312yes—
354C2×C31#277812yes—
355C2×C31#279712yes—
356C25C23×C3111yescharacteristic
357C25C23×C3111yescharacteristic
358C22×D4—24no—
359C22×D4—42no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C2×C4×C3114yes—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4C2×C4×C3114yes—
368C23×C4C23×C3112yes—
369C23×C4C23×C3112yes—
370C23×C4C23×C3112yes—
371C23×C4C23×C3112yes—
372C23×C4C23×C3111yescharacteristic
373C23×C4C23×C3112yes—
374C23×C4C23×C3112yes—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4C2×C4×C3114yes—
392C2×C22⋊C4C2×C4×C3118yes—
393C2×C42—24no—
394C2×C42—42no—
395C2×C42—42no—
396#95—24no—
397#95—41no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—41no—
406#95C2×C4×C3118yes—
407C31#1451611yescharacteristic, direct product factor, Sylow
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—21no—
422C24—21no—
423C24C22×C4×C3112yes—
424C24C22×C4×C3112yes—
425C24#41×C3114yes—
426C24C24×C3111yescharacteristic
427C2×D4—28no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—48no—
431C2×D4—48no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
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—48no—
475C22×C4—44no—
476C22×C4—48no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4C22×C4×C3112yes—
480C22×C4C22×C4×C3114yes—
481C22×C4C22×C4×C3114yes—
482C22×C4#41×C3114yes—
483C22×C4#41×C3114yes—
484C22⋊C4—48no—
485C22⋊C4—44no—
486C22⋊C4—44no—
487C22⋊C4—48no—
488C22⋊C4—48no—
489C22⋊C4—48no—
490C22⋊C4—44no—
491C42—48no—
492C23—24no—
493C23—22no—
494C23—22no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—24no—
504C23—24no—
505C23—22no—
506C23—22no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—41no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23C31×#11714yes—
534C23C23×C4×C3111yescharacteristic
535C23C2×#41×C3112yes—
536C23C2×#41×C3112yes—
537C23C2×#41×C3112yes—
538C23C31×H(5,𝔽2)12yes—
539C23C31×H(5,𝔽2)12yes—
540C23C31×H(5,𝔽2)11yescharacteristic
541C23C31×H(5,𝔽2)11yescharacteristic
542C23C31×H(5,𝔽2)12yes—
543D4—416no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—416no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
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—
592C22—24no—
593C22—28no—
594C22—44no—
595C22—42no—
596C22—42no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—42no—
602C22—44no—
603C22—44no—
604C22—42no—
605C22—42no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22C2×C31×#11711yescharacteristic
611C22C4×#41×C3112yes—
612C22C31×#51811yescharacteristic
613C22C31×#51811yescharacteristic
614C22C31×#51812yes—
615C22C31×#53812yes—
616C22C31×#53812yes—
617C22C31×#53812yes—
618C22C31×#53812yes—
619C22C31×#54012yes—
620C22C31×#54012yes—
621C22C31×#55112yes—
622C22C31×#55112yes—
623C22C31×#55111yescharacteristic
624C22C31×#55312yes—
625C22C31×#55312yes—
626C22C31×#55312yes—
627C22C31×#55911yescharacteristic
628C22C31×#56012yes—
629C22C31×#56011yescharacteristic
630C22C31×H(3,𝔽4)11yescharacteristic
631C4—42no—
632C4—44no—
633C4—44no—
634C4—44no—
635C4—44no—
636C4—82no—
637C4—82no—
638C2—44no—
639C2—82no—
640C2C31×#231211yescharacteristic
641C2C31×#233312yes—
642C2C31×#235312yes—
643C2C31×#237411yescharacteristic
644C2C31×#237511yescharacteristic
645C2C31×#274912yes—
646C2C31×#275312yes—
647C2C31×#277812yes—
648C2C31×#279712yes—
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. C31×#1443C2semidirect
3. C31×#1440C2semidirect
6. C31×#1437C2semidirect
7. C31×#1437C2semidirect
8. C31×#1434C2semidirect
9. C31×C22⋊#95C2semidirect
20. C31×#386C4semidirect
167. #14516C31direct (N × H)
269. #1443C2×C31semidirect
270. #1440C2×C31semidirect
273. #1437C2×C31semidirect
274. #1437C2×C31semidirect
275. #1434C2×C31semidirect
276. C22⋊#95C2×C31semidirect
333. #386C4×C31semidirect
407. C31#14516direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3862
C31×#14432
C31×#14402
C31×#14382
C31×#14372
C31×#14342
C31×C22⋊#952
#1451631