Finite Group Databasebeta

← C31×#16074 #21472833

Subgroups — C31×#16074 #21472833

Order 7936.

1654 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#390C211yesmaximal, characteristic
2C2×C31×#386C211yesmaximal, characteristic
3C31×#1442C212yesmaximal, complemented
4C31×#1440C212yesmaximal, complemented
5C31×#1440C212yesmaximal, complemented
6C31×#1440C212yesmaximal, complemented
7C31×#1438C211yesmaximal, characteristic
8C31×#1434C212yesmaximal, complemented
9C31×C22⋊#95C212yesmaximal, complemented
10C23×D4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C22⋊C4×C31C2211yescharacteristic
14C22×C22⋊C4×C31C2212yes—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C42×C31C2211yescharacteristic
21C31×#390—24no—
22C31×#386—24no—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C25×C31C2311yescharacteristic
34C25×C31C2311yescharacteristic
35C22×D4×C31—24no—
36C22×D4×C31—24no—
37C22×D4×C31—41no—
38C22×D4×C31—41no—
39C22×D4×C31D414yes—
40C23×C4×C31—22no—
41C23×C4×C31—24no—
42C23×C4×C31—41no—
43C23×C4×C31—41no—
44C23×C4×C31—42no—
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2312yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2311yescharacteristic
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—41no—
54C2×C4⋊C4×C31—41no—
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31—22no—
57C2×C22⋊C4×C31—24no—
58C2×C22⋊C4×C31—24no—
59C2×C22⋊C4×C31—24no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—24no—
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—41no—
70C2×C22⋊C4×C31—41no—
71C2×C22⋊C4×C31—42no—
72C2×C22⋊C4×C31—42no—
73C2×C42×C31—22no—
74C2×C42×C31—24no—
75C31×#95—24no—
76C31×#95—24no—
77C31×#95—24no—
78C31×#95—24no—
79C31×#95—42no—
80C31×#95—42no—
81C31×#95—42no—
82C31×#95—42no—
83C31×#95—42no—
84C31×#95—42no—
85C24×C31—22no—
86C24×C31—22no—
87C24×C31—22no—
88C24×C31—22no—
89C24×C31—22no—
90C24×C31—21no—
91C24×C31—21no—
92C24×C31—22no—
93C24×C31—22no—
94C24×C31—22no—
95C24×C31—22no—
96C24×C31—22no—
97C24×C31—22no—
98C24×C31—21no—
99C24×C31—21no—
100C24×C31C2×D412yes—
101C24×C31C2×D412yes—
102C24×C31#4114yes—
103C24×C31C2411yescharacteristic
104C2×D4×C31—28no—
105C2×D4×C31—28no—
106C2×D4×C31—44no—
107C2×D4×C31—48no—
108C2×D4×C31—48no—
109C22×C4×C31—22no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
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—22no—
128C22×C4×C31—22no—
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—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—44no—
153C22×C4×C31—48no—
154C22×C4×C31—48no—
155C22×C4×C31—44no—
156C22×C4×C31—44no—
157C22×C4×C31C2×D412yes—
158C22×C4×C31#4114yes—
159C22×C4×C31#4114yes—
160C22×C4×C31#4114yes—
161C4⋊C4×C31—44no—
162C22⋊C4×C31—48no—
163C22⋊C4×C31—48no—
164C22⋊C4×C31—48no—
165C22⋊C4×C31—48no—
166C22⋊C4×C31—44no—
167C22⋊C4×C31—44no—
168C22⋊C4×C31—44no—
169C42×C31—44no—
170#16074C3111yesmaximal, characteristic, direct product factor, Sylow
171C23×C31—22no—
172C23×C31—24no—
173C23×C31—22no—
174C23×C31—24no—
175C23×C31—24no—
176C23×C31—24no—
177C23×C31—24no—
178C23×C31—24no—
179C23×C31—24no—
180C23×C31—24no—
181C23×C31—22no—
182C23×C31—22no—
183C23×C31—22no—
184C23×C31—24no—
185C23×C31—24no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—41no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31—41no—
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—41no—
205C23×C31—42no—
206C23×C31—42no—
207C23×C31—42no—
208C23×C31—42no—
209C23×C31—41no—
210C23×C31—41no—
211C23×C31—41no—
212C23×C31#12314yes—
213C23×C31C22×D411yescharacteristic
214C23×C31C2×#4112yes—
215C23×C31C2×#4112yes—
216C23×C31C2×#4112yes—
217C23×C31C2×#4112yes—
218C23×C31H(5,𝔽2)11yescharacteristic
219C23×C31H(5,𝔽2)11yescharacteristic
220C23×C31H(5,𝔽2)12yes—
221C23×C31H(5,𝔽2)12yes—
222D4×C31—416no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—24no—
226C2×C4×C31—24no—
227C2×C4×C31—24no—
228C2×C4×C31—24no—
229C2×C4×C31—24no—
230C2×C4×C31—24no—
231C2×C4×C31—24no—
232C2×C4×C31—24no—
233C2×C4×C31—416no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
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×C4×C31—42no—
269C2×C4×C31—42no—
270C2×C4×C31#12314yes—
271C2×#390C2×C3111yescharacteristic
272C2×#386C2×C3111yescharacteristic
273#1442C2×C3112yescomplemented
274#1440C2×C3112yescomplemented
275#1440C2×C3112yescomplemented
276#1440C2×C3112yescomplemented
277#1438C2×C3111yescharacteristic
278#1434C2×C3112yescomplemented
279C22⋊#95C2×C3112yescomplemented
280C22×C31—28no—
281C22×C31—24no—
282C22×C31—44no—
283C22×C31—44no—
284C22×C31—42no—
285C22×C31—42no—
286C22×C31—44no—
287C22×C31—44no—
288C22×C31—44no—
289C22×C31—44no—
290C22×C31—42no—
291C22×C31—44no—
292C22×C31—42no—
293C22×C31—42no—
294C22×C31—82no—
295C22×C31—82no—
296C22×C31—82no—
297C22×C31—82no—
298C22×C31C2×#12311yescharacteristic
299C22×C31C2×#12311yescharacteristic
300C22×C31#52912yes—
301C22×C31#52912yes—
302C22×C31#53411yescharacteristic
303C22×C31#53812yes—
304C22×C31#53812yes—
305C22×C31#54012yes—
306C22×C31#54012yes—
307C22×C31#54612yes—
308C22×C31#54612yes—
309C22×C31#55112yes—
310C22×C31#55111yescharacteristic
311C22×C31#55112yes—
312C22×C31#55312yes—
313C22×C31#55312yes—
314C22×C31#55312yes—
315C22×C31#55512yes—
316C22×C31#55911yescharacteristic
317C22×C31#56011yescharacteristic
318C22×C31H(3,𝔽4)11yescharacteristic
319C4×C31—24no—
320C4×C31—44no—
321C4×C31—44no—
322C4×C31—82no—
323C4×C31—82no—
324C4×C31—82no—
325C4×C31—82no—
326C23×D4C22×C3111yescharacteristic
327C24×C4C22×C3111yescharacteristic
328C22×C4⋊C4C22×C3111yescharacteristic
329C22×C22⋊C4C22×C3111yescharacteristic
330C22×C22⋊C4C22×C3112yes—
331C22×C22⋊C4C22×C3112yes—
332C22×C22⋊C4C22×C3112yes—
333C22×C22⋊C4C22×C3112yes—
334C22×C22⋊C4C22×C3111yescharacteristic
335C22×C22⋊C4C22×C3111yescharacteristic
336C22×C42C22×C3111yescharacteristic
337#390—24no—
338#386—24no—
339C2×#95C22×C3112yes—
340C2×#95C22×C3112yes—
341C2×#95C22×C3112yes—
342C2×#95C22×C3112yes—
343C2×#95C22×C3112yes—
344C2×#95C22×C3112yes—
345C2×#95C22×C3112yes—
346C2×#95C22×C3112yes—
347C2×#95C22×C3112yes—
348C2×#95C22×C3112yes—
349C2×C31—44no—
350C2×C31—82no—
351C2×C31#242012yes—
352C2×C31#244412yes—
353C2×C31#248311yescharacteristic
354C2×C31#253112yes—
355C2×C31#259712yes—
356C2×C31#268411yescharacteristic
357C2×C31#270911yescharacteristic
358C2×C31#275312yes—
359C2×C31#275612yes—
360C25C23×C3111yescharacteristic
361C25C23×C3111yescharacteristic
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4D4×C3114yes—
367C23×C4—22no—
368C23×C4—24no—
369C23×C4—41no—
370C23×C4—41no—
371C23×C4—42no—
372C23×C4C23×C3112yes—
373C23×C4C23×C3112yes—
374C23×C4C23×C3112yes—
375C23×C4C23×C3112yes—
376C23×C4C23×C3112yes—
377C23×C4C23×C3112yes—
378C23×C4C23×C3111yescharacteristic
379C2×C4⋊C4—22no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
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—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C42—22no—
401C2×C42—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412C31#1607411yescharacteristic, direct product factor, Sylow
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24C2×D4×C3112yes—
429C24C2×D4×C3112yes—
430C24#41×C3114yes—
431C24C24×C3111yescharacteristic
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—44no—
435C2×D4—48no—
436C2×D4—48no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
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—22no—
453C22×C4—22no—
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—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—44no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4C2×D4×C3112yes—
486C22×C4#41×C3114yes—
487C22×C4#41×C3114yes—
488C22×C4#41×C3114yes—
489C4⋊C4—44no—
490C22⋊C4—48no—
491C22⋊C4—48no—
492C22⋊C4—48no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C22⋊C4—44no—
496C22⋊C4—44no—
497C42—44no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—24no—
512C23—24no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23—42no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—41no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23C31×#12314yes—
540C23C22×D4×C3111yescharacteristic
541C23C2×#41×C3112yes—
542C23C2×#41×C3112yes—
543C23C2×#41×C3112yes—
544C23C2×#41×C3112yes—
545C23C31×H(5,𝔽2)11yescharacteristic
546C23C31×H(5,𝔽2)11yescharacteristic
547C23C31×H(5,𝔽2)12yes—
548C23C31×H(5,𝔽2)12yes—
549D4—416no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—416no—
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—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4C31×#12314yes—
598C22—28no—
599C22—24no—
600C22—44no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—42no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22C2×C31×#12311yescharacteristic
617C22C2×C31×#12311yescharacteristic
618C22C31×#52912yes—
619C22C31×#52912yes—
620C22C31×#53411yescharacteristic
621C22C31×#53812yes—
622C22C31×#53812yes—
623C22C31×#54012yes—
624C22C31×#54012yes—
625C22C31×#54612yes—
626C22C31×#54612yes—
627C22C31×#55112yes—
628C22C31×#55111yescharacteristic
629C22C31×#55112yes—
630C22C31×#55312yes—
631C22C31×#55312yes—
632C22C31×#55312yes—
633C22C31×#55512yes—
634C22C31×#55911yescharacteristic
635C22C31×#56011yescharacteristic
636C22C31×H(3,𝔽4)11yescharacteristic
637C4—24no—
638C4—44no—
639C4—44no—
640C4—82no—
641C4—82no—
642C4—82no—
643C4—82no—
644C2—44no—
645C2—82no—
646C2C31×#242012yes—
647C2C31×#244412yes—
648C2C31×#248311yescharacteristic
649C2C31×#253112yes—
650C2C31×#259712yes—
651C2C31×#268411yescharacteristic
652C2C31×#270911yescharacteristic
653C2C31×#275312yes—
654C2C31×#275612yes—
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1442C2semidirect
4. C31×#1440C2semidirect
5. C31×#1440C2semidirect
6. C31×#1440C2semidirect
8. C31×#1434C2semidirect
9. C31×C22⋊#95C2semidirect
170. #16074C31direct (N × H)
273. #1442C2×C31semidirect
274. #1440C2×C31semidirect
275. #1440C2×C31semidirect
276. #1440C2×C31semidirect
278. #1434C2×C31semidirect
279. C22⋊#95C2×C31semidirect
412. C31#16074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3902
C2×C31×#3862
C31×#14422
C31×#14402
C31×#14382
C31×#14342
C31×C22⋊#952
#1607431