Finite Group Databasebeta

← C31×#15814 #21472573

Subgroups — C31×#15814 #21472573

Order 7936.

1722 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#398C211yesmaximal, characteristic, complemented
2C2×C31×#394C212yesmaximal
3C2×C31×#390C211yesmaximal, characteristic
4C2×C31×#387C212yesmaximal, complemented
5C31×#1439C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1437C212yesmaximal, complemented
9C31×#1436C211yesmaximal, characteristic, complemented
10C23×D4×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2212yes—
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
22C22×C42×C31C2211yescharacteristic
23C31×#398—24no—
24C31×#394—28no—
25C31×#390—24no—
26C31×#387—28no—
27C2×C31×#95C2212yes—
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C25×C31C2312yes—
36C22×D4×C31—24no—
37C22×D4×C31—22no—
38C22×D4×C31—24no—
39C22×D4×C31—41no—
40C22×D4×C31—41no—
41C23×C4×C31C2312yes—
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2312yes—
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C2×C4⋊C4×C31—24no—
50C2×C4⋊C4×C31—24no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—41no—
57C2×C4⋊C4×C31—41no—
58C2×C4⋊C4×C31—41no—
59C2×C4⋊C4×C31—41no—
60C2×C4⋊C4×C31D414yes—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—42no—
74C2×C22⋊C4×C31—42no—
75C2×C22⋊C4×C31—42no—
76C2×C22⋊C4×C31—42no—
77C2×C22⋊C4×C31—42no—
78C2×C22⋊C4×C31—42no—
79C2×C42×C31—24no—
80C2×C42×C31—22no—
81C2×C42×C31—42no—
82C2×C42×C31—41no—
83C31×#95—22no—
84C31×#95—24no—
85C31×#95—24no—
86C31×#95—24no—
87C31×#95—24no—
88C31×#95—42no—
89C31×#95—41no—
90C31×#95D418yes—
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×C31—22no—
103C24×C31—22no—
104C24×C31—22no—
105C24×C31#4114yes—
106C24×C31C2411yescharacteristic
107C2×D4×C31—28no—
108C2×D4×C31—48no—
109C2×D4×C31—48no—
110C2×D4×C31—44no—
111C2×D4×C31—44no—
112C22×C4×C31—22no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
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—21no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—21no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
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×C31C2×D414yes—
155C22×C4×C31C2×D412yes—
156C22×C4×C31C2×D414yes—
157C22×C4×C31C2×D412yes—
158C22×C4×C31C2×D414yes—
159C22×C4×C31C2×D412yes—
160C22×C4×C31#4114yes—
161C22×C4×C31#4114yes—
162C4⋊C4×C31—216no—
163C4⋊C4×C31—44no—
164C4⋊C4×C31—44no—
165C4⋊C4×C31—48no—
166C22⋊C4×C31—48no—
167C22⋊C4×C31—48no—
168C22⋊C4×C31—48no—
169C22⋊C4×C31—48no—
170C22⋊C4×C31—48no—
171C22⋊C4×C31—48no—
172C42×C31—44no—
173C42×C31—44no—
174#15814C3111yesmaximal, characteristic, direct product factor, Sylow
175C23×C31—24no—
176C23×C31—24no—
177C23×C31—24no—
178C23×C31—24no—
179C23×C31—24no—
180C23×C31—24no—
181C23×C31—24no—
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×C31—42no—
209C23×C31—42no—
210C23×C31C22×D411yescharacteristic
211C23×C31C22×D412yes—
212C23×C31C2×#4112yes—
213C23×C31C2×#4112yes—
214C23×C31C2×#4112yes—
215C23×C31H(5,𝔽2)11yescharacteristic
216C23×C31H(5,𝔽2)11yescharacteristic
217C23×C31H(5,𝔽2)12yes—
218C23×C312−1+412yes—
219D4×C31—416no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
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—24no—
236C2×C4×C31—24no—
237C2×C4×C31—24no—
238C2×C4×C31—24no—
239C2×C4×C31—24no—
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—41no—
258C2×C4×C31—41no—
259C2×C4×C31—42no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
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#12714yes—
270C2×#398C2×C3111yescharacteristic, complemented
271C2×#394C2×C3112yes—
272C2×#390C2×C3111yescharacteristic
273C2×#387C2×C3112yescomplemented
274#1439C2×C3112yescomplemented
275#1439C2×C3112yescomplemented
276#1439C2×C3112yescomplemented
277#1437C2×C3112yescomplemented
278#1436C2×C3111yescharacteristic, complemented
279C22×C31—44no—
280C22×C31—44no—
281C22×C31—44no—
282C22×C31—44no—
283C22×C31—44no—
284C22×C31—44no—
285C22×C31—44no—
286C22×C31—82no—
287C22×C31—82no—
288C22×C31—82no—
289C22×C31—82no—
290C22×C31—82no—
291C22×C31—82no—
292C22×C31—82no—
293C22×C31—82no—
294C22×C31#52512yes—
295C22×C31#52511yescharacteristic
296C22×C31#52912yes—
297C22×C31C2×#12711yescharacteristic
298C22×C31#53411yescharacteristic
299C22×C31#53712yes—
300C22×C31#53912yes—
301C22×C31#54012yes—
302C22×C31#54212yes—
303C22×C31#54612yes—
304C22×C31#54612yes—
305C22×C31#54612yes—
306C22×C31#54612yes—
307C22×C31#54812yes—
308C22×C31#54812yes—
309C22×C31#55212yes—
310C22×C31#55312yes—
311C22×C31#55511yescharacteristic
312C22×C31#55911yescharacteristic
313C22×C31#56011yescharacteristic
314C22×C31#56311yescharacteristic
315C4×C31—24no—
316C4×C31—44no—
317C4×C31—42no—
318C4×C31—42no—
319C4×C31—44no—
320C4×C31—44no—
321C4×C31—44no—
322C4×C31—82no—
323C23×D4C22×C3111yescharacteristic
324C22×C4⋊C4C22×C3112yes—
325C22×C4⋊C4C22×C3112yes—
326C22×C4⋊C4C22×C3111yescharacteristic
327C22×C4⋊C4C22×C3111yescharacteristic
328C22×C22⋊C4C22×C3112yes—
329C22×C22⋊C4C22×C3112yes—
330C22×C22⋊C4C22×C3112yes—
331C22×C22⋊C4C22×C3112yes—
332C22×C22⋊C4C22×C3112yes—
333C22×C22⋊C4C22×C3112yes—
334C22×C42C22×C3111yescharacteristic
335C22×C42C22×C3111yescharacteristic
336#398—24no—
337#394—28no—
338#390—24no—
339#387—28no—
340C2×#95C22×C3112yes—
341C2×#95C22×C3111yescharacteristic
342C2×#95C22×C3112yes—
343C2×#95C22×C3112yes—
344C2×#95C22×C3112yes—
345C2×#95C22×C3112yes—
346C2×#95C22×C3111yescharacteristic
347C2×#95C22×C3112yes—
348C2×C31—84no—
349C2×C31#245812yes—
350C2×C31#246012yes—
351C2×C31#247612yes—
352C2×C31#253911yescharacteristic
353C2×C31#254012yes—
354C2×C31#269112yes—
355C2×C31#270712yes—
356C2×C31#270911yescharacteristic
357C2×C31#273111yescharacteristic
358C25C23×C3112yes—
359C22×D4—24no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—41no—
363C22×D4—41no—
364C23×C4C23×C3112yes—
365C23×C4C23×C3111yescharacteristic
366C23×C4C23×C3112yes—
367C23×C4C23×C3111yescharacteristic
368C23×C4C23×C3112yes—
369C23×C4C23×C3112yes—
370C23×C4C23×C3112yes—
371C23×C4C23×C3111yescharacteristic
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—41no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4D4×C3114yes—
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—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
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×C42—24no—
403C2×C42—22no—
404C2×C42—42no—
405C2×C42—41no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—22no—
410#95—24no—
411#95—42no—
412#95—41no—
413#95D4×C3118yes—
414C31#1581411yescharacteristic, direct product factor, Sylow
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24#41×C3114yes—
430C24C24×C3111yescharacteristic
431C2×D4—28no—
432C2×D4—48no—
433C2×D4—48no—
434C2×D4—44no—
435C2×D4—44no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
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—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
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×C4C2×D4×C3114yes—
479C22×C4C2×D4×C3112yes—
480C22×C4C2×D4×C3114yes—
481C22×C4C2×D4×C3112yes—
482C22×C4C2×D4×C3114yes—
483C22×C4C2×D4×C3112yes—
484C22×C4#41×C3114yes—
485C22×C4#41×C3114yes—
486C4⋊C4—216no—
487C4⋊C4—44no—
488C4⋊C4—44no—
489C4⋊C4—48no—
490C22⋊C4—48no—
491C22⋊C4—48no—
492C22⋊C4—48no—
493C22⋊C4—48no—
494C22⋊C4—48no—
495C22⋊C4—48no—
496C42—44no—
497C42—44no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
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—
533C23C22×D4×C3111yescharacteristic
534C23C22×D4×C3112yes—
535C23C2×#41×C3112yes—
536C23C2×#41×C3112yes—
537C23C2×#41×C3112yes—
538C23C31×H(5,𝔽2)11yescharacteristic
539C23C31×H(5,𝔽2)11yescharacteristic
540C23C31×H(5,𝔽2)12yes—
541C23C31×2−1+412yes—
542D4—416no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
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—24no—
561C2×C4—24no—
562C2×C4—24no—
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—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4C31×#12714yes—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—82no—
601C22—82no—
602C22—82no—
603C22—82no—
604C22—82no—
605C22—82no—
606C22—82no—
607C22—82no—
608C22C31×#52512yes—
609C22C31×#52511yescharacteristic
610C22C31×#52912yes—
611C22C2×C31×#12711yescharacteristic
612C22C31×#53411yescharacteristic
613C22C31×#53712yes—
614C22C31×#53912yes—
615C22C31×#54012yes—
616C22C31×#54212yes—
617C22C31×#54612yes—
618C22C31×#54612yes—
619C22C31×#54612yes—
620C22C31×#54612yes—
621C22C31×#54812yes—
622C22C31×#54812yes—
623C22C31×#55212yes—
624C22C31×#55312yes—
625C22C31×#55511yescharacteristic
626C22C31×#55911yescharacteristic
627C22C31×#56011yescharacteristic
628C22C31×#56311yescharacteristic
629C4—24no—
630C4—44no—
631C4—42no—
632C4—42no—
633C4—44no—
634C4—44no—
635C4—44no—
636C4—82no—
637C2—84no—
638C2C31×#245812yes—
639C2C31×#246012yes—
640C2C31×#247612yes—
641C2C31×#253911yescharacteristic
642C2C31×#254012yes—
643C2C31×#269112yes—
644C2C31×#270712yes—
645C2C31×#270911yescharacteristic
646C2C31×#273111yescharacteristic
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
1. C2×C31×#398C2semidirect
4. C2×C31×#387C2semidirect
5. C31×#1439C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
8. C31×#1437C2semidirect
9. C31×#1436C2semidirect
174. #15814C31direct (N × H)
270. C2×#398C2×C31semidirect
273. C2×#387C2×C31semidirect
274. #1439C2×C31semidirect
275. #1439C2×C31semidirect
276. #1439C2×C31semidirect
277. #1437C2×C31semidirect
278. #1436C2×C31semidirect
414. C31#15814direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3982
C2×C31×#3942
C2×C31×#3902
C2×C31×#3872
C31×#14392
C31×#14372
C31×#14362
#1581431