Finite Group Databasebeta

← C31×#14734 #21471493

Subgroups — C31×#14734 #21471493

Order 7936.

3494 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C31C211yesmaximal, characteristic
2C2×C31×#399C212yesmaximal, complemented
3C2×C31×#385C212yesmaximal, complemented
4C2×C31×#380C211yesmaximal, characteristic, complemented
5C2×C31×#379C212yesmaximal
6C31×#1439C214yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×C22⋊#95C211yesmaximal, characteristic, complemented
9C26×C31C2211yescharacteristic
10C24×C4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C22×C4⋊C4×C31C2211yescharacteristic, complemented
13C22×C4⋊C4×C31C2214yescomplemented
14C22×C4⋊C4×C31C2211yescharacteristic, complemented
15C22×C22⋊C4×C31—24no—
16C22×C22⋊C4×C31—28no—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2214yes—
20C22×C22⋊C4×C31C2214yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C31×#399—28no—
24C31×#385—28no—
25C31×#380—24no—
26C31×#379—28no—
27C2×C31×#95C2212yescomplemented
28C2×C31×#95C2212yescomplemented
29C2×C31×#95C2214yescomplemented
30C2×C31×#95C2212yescomplemented
31C25×C31—24no—
32C25×C31—22no—
33C25×C31—24no—
34C25×C31—22no—
35C25×C31—24no—
36C25×C31—24no—
37C25×C31—42no—
38C25×C31—42no—
39C25×C31Q814yes—
40C25×C31C2312yes—
41C25×C31C2311yescharacteristic
42C23×C4×C31—22no—
43C23×C4×C31—24no—
44C23×C4×C31—24no—
45C23×C4×C31—24no—
46C23×C4×C31—24no—
47C23×C4×C31—42no—
48C23×C4×C31—42no—
49C23×C4×C31D414yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2312yes—
52C23×C4×C31C2314yes—
53C23×C4×C31C2312yes—
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C2×C4⋊C4×C31—28no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—28no—
61C2×C4⋊C4×C31—44no—
62C2×C4⋊C4×C31—42no—
63C2×C22⋊C4×C31—232no—
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—28no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—24no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—28no—
76C2×C22⋊C4×C31—28no—
77C2×C22⋊C4×C31—28no—
78C2×C22⋊C4×C31—44no—
79C2×C22⋊C4×C31—44no—
80C2×C22⋊C4×C31D418yes—
81C2×C22⋊C4×C31D418yes—
82C31×#95—24no—
83C31×#95—24no—
84C31×#95—28no—
85C31×#95—42no—
86C24×C31—22no—
87C24×C31—22no—
88C24×C31—22no—
89C24×C31—22no—
90C24×C31—28no—
91C24×C31—28no—
92C24×C31—216no—
93C24×C31—216no—
94C24×C31—28no—
95C24×C31—22no—
96C24×C31—22no—
97C24×C31—24no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—24no—
101C24×C31—24no—
102C24×C31—24no—
103C24×C31—216no—
104C24×C31—48no—
105C24×C31—416no—
106C24×C31—416no—
107C24×C31—416no—
108C24×C31—416no—
109C24×C31—44no—
110C24×C31—44no—
111C24×C31—48no—
112C24×C31—48no—
113C24×C31—44no—
114C24×C31—44no—
115C24×C31C2×D414yes—
116C24×C31C2×D414yes—
117C24×C31C2×D412yes—
118C24×C31C2×Q814yes—
119C24×C31C2×Q812yes—
120C24×C31#4114yes—
121C24×C31#4112yes—
122C24×C31#4114yes—
123C24×C31C2411yescharacteristic
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—28no—
127C22×C4×C31—28no—
128C22×C4×C31—24no—
129C22×C4×C31—24no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—24no—
134C22×C4×C31—24no—
135C22×C4×C31—24no—
136C22×C4×C31—22no—
137C22×C4×C31—24no—
138C22×C4×C31—22no—
139C22×C4×C31—24no—
140C22×C4×C31—24no—
141C22×C4×C31—28no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—24no—
148C22×C4×C31—22no—
149C22×C4×C31—24no—
150C22×C4×C31—24no—
151C22×C4×C31—24no—
152C22×C4×C31—44no—
153C22×C4×C31—416no—
154C22×C4×C31—416no—
155C22×C4×C31—44no—
156C22×C4×C31—44no—
157C22×C4×C31C2×D412yes—
158C22×C4×C31C2×D418yes—
159C22×C4×C31C2×D414yes—
160C22×C4×C31C2×D414yes—
161C22×C4×C31C2×D412yes—
162C4⋊C4×C31—416no—
163C4⋊C4×C31—44no—
164C4⋊C4×C31—44no—
165C22⋊C4×C31—216no—
166C22⋊C4×C31—216no—
167C22⋊C4×C31—216no—
168C22⋊C4×C31—416no—
169C22⋊C4×C31—416no—
170C22⋊C4×C31—48no—
171#14734C3111yesmaximal, characteristic, direct product factor, Sylow
172C23×C31—22no—
173C23×C31—24no—
174C23×C31—22no—
175C23×C31—24no—
176C23×C31—22no—
177C23×C31—22no—
178C23×C31—24no—
179C23×C31—24no—
180C23×C31—28no—
181C23×C31—28no—
182C23×C31—28no—
183C23×C31—28no—
184C23×C31—232no—
185C23×C31—24no—
186C23×C31—24no—
187C23×C31—24no—
188C23×C31—28no—
189C23×C31—24no—
190C23×C31—24no—
191C23×C31—24no—
192C23×C31—28no—
193C23×C31—28no—
194C23×C31—28no—
195C23×C31—28no—
196C23×C31—28no—
197C23×C31—464no—
198C23×C31—416no—
199C23×C31—416no—
200C23×C31—464no—
201C23×C31—416no—
202C23×C31—416no—
203C23×C31—416no—
204C23×C31—42no—
205C23×C31—44no—
206C23×C31—42no—
207C23×C31—42no—
208C23×C31—42no—
209C23×C31—44no—
210C23×C31—44no—
211C23×C31—44no—
212C23×C31—44no—
213C23×C31—44no—
214C23×C31—416no—
215C23×C31C22⋊Q818yes—
216C23×C31C22⋊Q814yes—
217C23×C31C22⋊Q818yes—
218C23×C31#12318yes—
219C23×C31#12314yes—
220C23×C31#12714yes—
221C23×C31C22×D411yescharacteristic
222C23×C31C22×D412yes—
223C23×C31C22×D412yes—
224C23×C31C22×Q811yescharacteristic
225C23×C31C2×#4111yescharacteristic
226C23×C31C2×#4112yes—
227C23×C31C2×#4112yes—
228C23×C31H(5,𝔽2)12yes—
229C23×C31H(5,𝔽2)12yes—
230C2×C4×C31—22no—
231C2×C4×C31—22no—
232C2×C4×C31—28no—
233C2×C4×C31—22no—
234C2×C4×C31—24no—
235C2×C4×C31—28no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—28no—
239C2×C4×C31—28no—
240C2×C4×C31—28no—
241C2×C4×C31—416no—
242C2×C4×C31—416no—
243C2×C4×C31—44no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—44no—
247C2×C4×C31—44no—
248C2×C4×C31—44no—
249C2×C4×C31—44no—
250C2×C4×C31—44no—
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—44no—
258C2×C4×C31—44no—
259C2×C4×C31—44no—
260C2×C4×C31—44no—
261C2×C4×C31#12014yes—
262C23×C22⋊C4C2×C3111yescharacteristic
263C2×#399C2×C3112yescomplemented
264C2×#385C2×C3112yescomplemented
265C2×#380C2×C3111yescharacteristic, complemented
266C2×#379C2×C3112yes—
267#1439C2×C3114yescomplemented
268#1439C2×C3112yescomplemented
269C22⋊#95C2×C3111yescharacteristic, complemented
270C22×C31—24no—
271C22×C31—24no—
272C22×C31—24no—
273C22×C31—216no—
274C22×C31—24no—
275C22×C31—216no—
276C22×C31—24no—
277C22×C31—24no—
278C22×C31—28no—
279C22×C31—216no—
280C22×C31—464no—
281C22×C31—44no—
282C22×C31—44no—
283C22×C31—44no—
284C22×C31—48no—
285C22×C31—48no—
286C22×C31—44no—
287C22×C31—48no—
288C22×C31—44no—
289C22×C31—44no—
290C22×C31#39918yescomplemented
291C22×C31C2×#12011yescharacteristic
292C22×C31C2×C22⋊Q811yescharacteristic
293C22×C31C2×C22⋊Q812yes—
294C22×C31C2×C22⋊Q812yes—
295C22×C31C2×#12311yescharacteristic
296C22×C31C2×#12312yes—
297C22×C31#52512yes—
298C22×C31#52511yescharacteristic
299C22×C31C2×#12711yescharacteristic
300C22×C31#53411yescharacteristic
301C22×C31#53511yescharacteristic
302C22×C31#53812yes—
303C22×C31#54312yes—
304C22×C31D4214yes—
305C22×C31#54614yes—
306C22×C31#54614yes—
307C22×C31#55114yes—
308C4×C31—24no—
309C4×C31—42no—
310C4×C31—48no—
311C4×C31—44no—
312C4×C31—82no—
313C4×C31—82no—
314C26C22×C3111yescharacteristic
315C24×C4C22×C3111yescharacteristic
316C24×C4C22×C3111yescharacteristic
317C22×C4⋊C4C22×C3111yescharacteristic, complemented
318C22×C4⋊C4C22×C3114yescomplemented
319C22×C4⋊C4C22×C3111yescharacteristic, complemented
320C22×C22⋊C4—24no—
321C22×C22⋊C4—28no—
322C22×C22⋊C4C22×C3112yes—
323C22×C22⋊C4C22×C3112yes—
324C22×C22⋊C4C22×C3114yes—
325C22×C22⋊C4C22×C3114yes—
326C22×C22⋊C4C22×C3112yes—
327C22×C22⋊C4C22×C3112yes—
328#399—28no—
329#385—28no—
330#380—24no—
331#379—28no—
332C2×#95C22×C3112yescomplemented
333C2×#95C22×C3112yescomplemented
334C2×#95C22×C3114yescomplemented
335C2×#95C22×C3112yescomplemented
336C2×C31—28no—
337C2×C31—48no—
338C2×C31C2×#39911yescharacteristic
339C2×C31#240511yescharacteristic
340C2×C31#241814yes—
341C2×C31#243311yescharacteristic
342C2×C31#243714yes—
343C2×C31#248211yescharacteristic
344C2×C31#253911yescharacteristic
345C2×C31#262611yescharacteristic
346C2×C31#284811yescharacteristic
347C25—24no—
348C25—22no—
349C25—24no—
350C25—22no—
351C25—24no—
352C25—24no—
353C25—42no—
354C25—42no—
355C25Q8×C3114yes—
356C25C23×C3112yes—
357C25C23×C3111yescharacteristic
358C23×C4—22no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4D4×C3114yes—
366C23×C4C23×C3112yes—
367C23×C4C23×C3112yes—
368C23×C4C23×C3114yes—
369C23×C4C23×C3112yes—
370C23×C4C23×C3111yescharacteristic
371C23×C4C23×C3111yescharacteristic
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—42no—
379C2×C22⋊C4—232no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
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—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4D4×C3118yes—
397C2×C22⋊C4D4×C3118yes—
398#95—24no—
399#95—28no—
400#95—24no—
401#95—42no—
402C31#1473411yescharacteristic, direct product factor, Sylow
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—28no—
408C24—28no—
409C24—216no—
410C24—216no—
411C24—28no—
412C24—22no—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—216no—
421C24—48no—
422C24—416no—
423C24—416no—
424C24—416no—
425C24—416no—
426C24—44no—
427C24—44no—
428C24—48no—
429C24—48no—
430C24—44no—
431C24—44no—
432C24C2×D4×C3114yes—
433C24C2×D4×C3114yes—
434C24C2×D4×C3112yes—
435C24C2×Q8×C3114yes—
436C24C2×Q8×C3112yes—
437C24#41×C3114yes—
438C24#41×C3112yes—
439C24#41×C3114yes—
440C24C24×C3111yescharacteristic
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—28no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—44no—
470C22×C4—416no—
471C22×C4—416no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4C2×D4×C3112yes—
475C22×C4C2×D4×C3118yes—
476C22×C4C2×D4×C3114yes—
477C22×C4C2×D4×C3114yes—
478C22×C4C2×D4×C3112yes—
479C4⋊C4—416no—
480C4⋊C4—44no—
481C4⋊C4—44no—
482C22⋊C4—216no—
483C22⋊C4—216no—
484C22⋊C4—216no—
485C22⋊C4—416no—
486C22⋊C4—416no—
487C22⋊C4—48no—
488C23—22no—
489C23—24no—
490C23—22no—
491C23—24no—
492C23—22no—
493C23—22no—
494C23—24no—
495C23—24no—
496C23—28no—
497C23—28no—
498C23—28no—
499C23—28no—
500C23—232no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—28no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—28no—
509C23—28no—
510C23—28no—
511C23—28no—
512C23—28no—
513C23—464no—
514C23—416no—
515C23—416no—
516C23—464no—
517C23—416no—
518C23—416no—
519C23—416no—
520C23—416no—
521C23—42no—
522C23—44no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23C31×C22⋊Q818yes—
532C23C31×C22⋊Q814yes—
533C23C31×C22⋊Q818yes—
534C23C31×#12318yes—
535C23C31×#12314yes—
536C23C31×#12714yes—
537C23C22×D4×C3111yescharacteristic
538C23C22×D4×C3112yes—
539C23C22×D4×C3112yes—
540C23C22×Q8×C3111yescharacteristic
541C23C2×#41×C3111yescharacteristic
542C23C2×#41×C3112yes—
543C23C2×#41×C3112yes—
544C23C31×H(5,𝔽2)12yes—
545C23C31×H(5,𝔽2)12yes—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—28no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—416no—
558C2×C4—416no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4C31×#12014yes—
578C22—24no—
579C22—24no—
580C22—24no—
581C22—216no—
582C22—24no—
583C22—216no—
584C22—24no—
585C22—24no—
586C22—28no—
587C22—216no—
588C22—464no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—48no—
593C22—48no—
594C22—44no—
595C22—48no—
596C22—44no—
597C22—44no—
598C22C31×#39918yescomplemented
599C22C2×C31×#12011yescharacteristic
600C22C2×C31×C22⋊Q811yescharacteristic
601C22C2×C31×C22⋊Q812yes—
602C22C2×C31×C22⋊Q812yes—
603C22C2×C31×#12311yescharacteristic
604C22C2×C31×#12312yes—
605C22C31×#52512yes—
606C22C31×#52511yescharacteristic
607C22C2×C31×#12711yescharacteristic
608C22C31×#53411yescharacteristic
609C22C31×#53511yescharacteristic
610C22C31×#53812yes—
611C22C31×#54312yes—
612C22D42×C3114yes—
613C22C31×#54614yes—
614C22C31×#54614yes—
615C22C31×#55114yes—
616C4—24no—
617C4—42no—
618C4—48no—
619C4—44no—
620C4—82no—
621C4—82no—
622C2—28no—
623C2—48no—
624C2C2×C31×#39911yescharacteristic
625C2C31×#240511yescharacteristic
626C2C31×#241814yes—
627C2C31×#243311yescharacteristic
628C2C31×#243714yes—
629C2C31×#248211yescharacteristic
630C2C31×#253911yescharacteristic
631C2C31×#262611yescharacteristic
632C2C31×#284811yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#399C2semidirect
3. C2×C31×#385C2semidirect
4. C2×C31×#380C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
8. C31×C22⋊#95C2semidirect
12. C22×C4⋊C4×C31C22semidirect
13. C22×C4⋊C4×C31C22semidirect
14. C22×C4⋊C4×C31C22semidirect
27. C2×C31×#95C22semidirect
28. C2×C31×#95C22semidirect
29. C2×C31×#95C22semidirect
30. C2×C31×#95C22semidirect
171. #14734C31direct (N × H)
263. C2×#399C2×C31semidirect
264. C2×#385C2×C31semidirect
265. C2×#380C2×C31semidirect
267. #1439C2×C31semidirect
268. #1439C2×C31semidirect
269. C22⋊#95C2×C31semidirect
290. C22×C31#399semidirect
317. C22×C4⋊C4C22×C31semidirect
318. C22×C4⋊C4C22×C31semidirect
319. C22×C4⋊C4C22×C31semidirect
332. C2×#95C22×C31semidirect
333. C2×#95C22×C31semidirect
334. C2×#95C22×C31semidirect
335. C2×#95C22×C31semidirect
402. C31#14734direct (N × H)
598. C22C31×#399semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C312
C2×C31×#3992
C2×C31×#3852
C2×C31×#3802
C2×C31×#3792
C31×#14392
C31×C22⋊#952
#1473431