Finite Group Databasebeta

← C2×C31×#1889 #21477716

Subgroups — C2×C31×#1889 #21477716

Order 7936.

3566 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C2×C31×#518C211yesmaximal, characteristic, complemented
3C22×C31×#99C211yesmaximal, characteristic, complemented
4C2×C31×#379C212yesmaximal, complemented
5C31×#1889C218yesmaximal, direct product factor
6C2×C31×#342C212yesmaximal, complemented
7C26×C31C2211yescharacteristic
8C23×D4×C31—21no—
9C23×D4×C31C2211yescharacteristic
10C2×C31×#120—24no—
11C2×C31×#120—22no—
12C2×C31×#120C418yescomplemented
13C2×C31×#120C2214yes—
14C31×#518—22no—
15C31×#518—24no—
16C31×#518C2214yescomplemented
17C2×C4×D4×C31—24no—
18C2×C31×#117—21no—
19C22×C22⋊C4×C31—21no—
20C22×C22⋊C4×C31—21no—
21C22×C22⋊C4×C31—24no—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2211yescharacteristic
25C2×C31×#99—24no—
26C2×C31×#99C2214yescomplemented
27C31×#379—24no—
28C31×#379C2218yescomplemented
29C31×#342C2218yescomplemented
30C25×C31—22no—
31C25×C31—21no—
32C25×C31—22no—
33C25×C31—21no—
34C25×C31—22no—
35C25×C31—24no—
36C25×C31—48no—
37C25×C31C2×C414yescomplemented
38C25×C31D411yescharacteristic
39C25×C31C2312yes—
40C25×C31C2311yescharacteristic
41C22×D4×C31—22no—
42C22×D4×C31—22no—
43C22×D4×C31—24no—
44C22×D4×C31—28no—
45C22×D4×C31—24no—
46C22×D4×C31—48no—
47C22×D4×C31C2×C414yes—
48C22×D4×C31D414yes—
49C22×D4×C31D412yes—
50C22×D4×C31C2312yes—
51C23×C4×C31—21no—
52C23×C4×C31—22no—
53C23×C4×C31—22no—
54C23×C4×C31D411yescharacteristic
55C23×C4×C31D414yescomplemented
56C31×#120—216no—
57C31×#120—28no—
58C31×#120C2×C4116yescomplemented
59C4×D4×C31—216no—
60C4×D4×C31—216no—
61C31×#117—24no—
62C31×#117—24no—
63C2×C4⋊C4×C31—22no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31—22no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—21no—
72C2×C22⋊C4×C31—22no—
73C2×C22⋊C4×C31—28no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—216no—
79C2×C22⋊C4×C31—416no—
80C2×C22⋊C4×C31C2×C414yescomplemented
81C2×C22⋊C4×C31D414yescomplemented
82C2×C22⋊C4×C31C2314yes—
83C2×C22⋊C4×C31C2314yes—
84C2×C22⋊C4×C31C2312yes—
85C2×C42×C31—22no—
86C31×#99—28no—
87C24×C31—216no—
88C24×C31—28no—
89C24×C31—24no—
90C24×C31—28no—
91C24×C31—21no—
92C24×C31—24no—
93C24×C31—22no—
94C24×C31—21no—
95C24×C31—22no—
96C24×C31—24no—
97C24×C31—28no—
98C24×C31—22no—
99C24×C31—24no—
100C24×C31—416no—
101C24×C31—48no—
102C24×C31—44no—
103C24×C31—48no—
104C24×C31—44no—
105C24×C31—416no—
106C24×C31—416no—
107C24×C31—48no—
108C24×C31—432no—
109C24×C31—44no—
110C24×C31—41no—
111C24×C31—42no—
112C24×C31—41no—
113C24×C31—44no—
114C24×C31—44no—
115C24×C31—42no—
116C24×C31—42no—
117C24×C31C22⋊C414yescomplemented
118C24×C31C22×C412yes—
119C24×C31C22×C414yescomplemented
120C24×C31C2×D411yescharacteristic
121C24×C31C2×D412yes—
122C24×C31C2×D412yes—
123C24×C31C2×D411yescharacteristic
124C24×C31C2×D412yes—
125C24×C31C2×D412yes—
126C24×C31#4114yes—
127C24×C31C2411yescharacteristic
128C2×D4×C31—28no—
129C2×D4×C31—28no—
130C2×D4×C31—24no—
131C2×D4×C31—28no—
132C2×D4×C31—28no—
133C2×D4×C31—24no—
134C2×D4×C31—24no—
135C2×D4×C31—24no—
136C2×D4×C31—216no—
137C2×D4×C31—432no—
138C2×D4×C31—416no—
139C2×D4×C31C22⋊C418yescomplemented
140C2×D4×C31C22×C414yes—
141C2×D4×C31C2×D414yes—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—22no—
145C22×C4×C31—24no—
146C22×C4×C31—24no—
147C22×C4×C31—22no—
148C22×C4×C31—28no—
149C22×C4×C31—24no—
150C22×C4×C31—24no—
151C22×C4×C31—44no—
152C22×C4×C31—48no—
153C22×C4×C31—48no—
154C22×C4×C31—44no—
155C22×C4×C31—84no—
156C22×C4×C31C22⋊C414yescomplemented
157C22×C4×C31C2×D412yes—
158C22×C4×C31C2×D418yescomplemented
159C4⋊C4×C31—28no—
160C22⋊C4×C31—28no—
161C22⋊C4×C31—24no—
162C22⋊C4×C31—24no—
163C22⋊C4×C31—24no—
164C22⋊C4×C31—24no—
165C22⋊C4×C31—24no—
166C22⋊C4×C31—22no—
167C22⋊C4×C31—216no—
168C22⋊C4×C31—24no—
169C22⋊C4×C31—24no—
170C22⋊C4×C31—432no—
171C22⋊C4×C31—44no—
172C22⋊C4×C31C22×C414yescomplemented
173C42×C31—28no—
174C2×#1889C3111yesmaximal, characteristic, direct product factor, Sylow
175C23×C31—28no—
176C23×C31—24no—
177C23×C31—216no—
178C23×C31—216no—
179C23×C31—28no—
180C23×C31—232no—
181C23×C31—24no—
182C23×C31—28no—
183C23×C31—22no—
184C23×C31—24no—
185C23×C31—22no—
186C23×C31—24no—
187C23×C31—44no—
188C23×C31—48no—
189C23×C31—44no—
190C23×C31—44no—
191C23×C31—42no—
192C23×C31—48no—
193C23×C31—42no—
194C23×C31—48no—
195C23×C31—432no—
196C23×C31—416no—
197C23×C31—416no—
198C23×C31—48no—
199C23×C31—44no—
200C23×C31—416no—
201C23×C31—48no—
202C23×C31—416no—
203C23×C31—48no—
204C23×C31—432no—
205C23×C31—416no—
206C23×C31—48no—
207C23×C31—44no—
208C23×C31—432no—
209C23×C31—416no—
210C23×C31—42no—
211C23×C31—44no—
212C23×C31—42no—
213C23×C31—44no—
214C23×C31—48no—
215C23×C31—44no—
216C23×C31—44no—
217C23×C31—48no—
218C23×C31—84no—
219C23×C31—82no—
220C23×C31C2×C22⋊C412yes—
221C23×C31C2×C22⋊C412yes—
222C23×C31C2×C22⋊C414yescomplemented
223C23×C31C4×D414yes—
224C23×C31C4×D414yes—
225C23×C31#12011yescharacteristic
226C23×C31#12012yes—
227C23×C31#12011yescharacteristic
228C23×C31#12114yes—
229C23×C31#12114yes—
230C23×C31#12312yes—
231C23×C31#12312yes—
232C23×C31C23×C411yescharacteristic
233C23×C31C22×D411yescharacteristic
234C23×C31C22×D412yes—
235C23×C31C22×D411yescharacteristic
236C23×C31C2×#4112yes—
237D4×C31—28no—
238D4×C31—28no—
239D4×C31—216no—
240D4×C31—432no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—24no—
244C2×C4×C31—24no—
245C2×C4×C31—24no—
246C2×C4×C31—28no—
247C2×C4×C31—48no—
248C2×C4×C31—44no—
249C2×C4×C31—48no—
250C2×C4×C31—48no—
251C2×C4×C31—48no—
252C2×C4×C31—44no—
253C2×C4×C31—84no—
254C2×C4×C31—88no—
255C2×C4×C31—88no—
256C2×C4×C31C2×C22⋊C414yescomplemented
257C22×#120C2×C3111yescharacteristic
258C2×#518C2×C3111yescharacteristic, complemented
259C22×#99C2×C3111yescharacteristic, complemented
260C2×#379C2×C3112yescomplemented
261#1889C2×C3118yesdirect product factor
262C2×#342C2×C3112yescomplemented
263C22×C31—24no—
264C22×C31—28no—
265C22×C31—28no—
266C22×C31—24no—
267C22×C31—24no—
268C22×C31—22no—
269C22×C31—24no—
270C22×C31—22no—
271C22×C31—28no—
272C22×C31—216no—
273C22×C31—24no—
274C22×C31—42no—
275C22×C31—44no—
276C22×C31—44no—
277C22×C31—42no—
278C22×C31—41no—
279C22×C31—41no—
280C22×C31—42no—
281C22×C31—44no—
282C22×C31—44no—
283C22×C31—416no—
284C22×C31—48no—
285C22×C31—48no—
286C22×C31—416no—
287C22×C31—432no—
288C22×C31—416no—
289C22×C31—48no—
290C22×C31—44no—
291C22×C31—48no—
292C22×C31—44no—
293C22×C31—82no—
294C22×C31—84no—
295C22×C31#38612yes—
296C22×C31#38614yes—
297C22×C31#38612yes—
298C22×C31B(4,𝔽2)14yes—
299C22×C31C22×C22⋊C411yescharacteristic
300C22×C31C2×C4×D412yes—
301C22×C31C2×#12011yescharacteristic
302C22×C31C2×#12112yes—
303C22×C31C2×#12311yescharacteristic
304C4×C31—24no—
305C4×C31—44no—
306C4×C31—48no—
307C4×C31—84no—
308C26C22×C3111yescharacteristic
309C23×D4—21no—
310C23×D4C22×C3111yescharacteristic
311C2×#120—24no—
312C2×#120—22no—
313C2×#120C4×C3118yescomplemented
314C2×#120C22×C3114yes—
315#518—22no—
316#518—24no—
317#518C22×C3114yescomplemented
318C2×C4×D4—24no—
319C2×#117—21no—
320C22×C22⋊C4—21no—
321C22×C22⋊C4—21no—
322C22×C22⋊C4—24no—
323C22×C22⋊C4C22×C3112yes—
324C22×C22⋊C4C22×C3112yes—
325C22×C22⋊C4C22×C3111yescharacteristic
326C2×#99—24no—
327C2×#99C22×C3114yescomplemented
328#379—24no—
329#379C22×C3118yescomplemented
330#342C22×C3118yescomplemented
331C2×C31—21no—
332C2×C31—22no—
333C2×C31—22no—
334C2×C31—21no—
335C2×C31—22no—
336C2×C31—24no—
337C2×C31—48no—
338C2×C31—44no—
339C2×C31#188914yesdirect product factor
340C2×C31C2×#38611yescharacteristic
341C2×C31C2×B(4,𝔽2)12yes—
342C25—22no—
343C25—21no—
344C25—22no—
345C25—21no—
346C25—22no—
347C25—24no—
348C25—48no—
349C25C2×C4×C3114yescomplemented
350C25D4×C3111yescharacteristic
351C25C23×C3112yes—
352C25C23×C3111yescharacteristic
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—24no—
356C22×D4—28no—
357C22×D4—24no—
358C22×D4—48no—
359C22×D4C2×C4×C3114yes—
360C22×D4D4×C3114yes—
361C22×D4D4×C3112yes—
362C22×D4C23×C3112yes—
363C23×C4—21no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4D4×C3111yescharacteristic
367C23×C4D4×C3114yescomplemented
368#120—216no—
369#120—28no—
370#120C2×C4×C31116yescomplemented
371C4×D4—216no—
372C4×D4—216no—
373#117—24no—
374#117—24no—
375C2×C4⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—216no—
391C2×C22⋊C4—416no—
392C2×C22⋊C4C2×C4×C3114yescomplemented
393C2×C22⋊C4D4×C3114yescomplemented
394C2×C22⋊C4C23×C3114yes—
395C2×C22⋊C4C23×C3114yes—
396C2×C22⋊C4C23×C3112yes—
397C2×C42—22no—
398#99—28no—
399C31C2×#188911yescharacteristic, direct product factor, Sylow
400C24—216no—
401C24—28no—
402C24—24no—
403C24—28no—
404C24—21no—
405C24—24no—
406C24—22no—
407C24—21no—
408C24—22no—
409C24—24no—
410C24—28no—
411C24—22no—
412C24—24no—
413C24—416no—
414C24—44no—
415C24—48no—
416C24—48no—
417C24—44no—
418C24—416no—
419C24—416no—
420C24—48no—
421C24—432no—
422C24—44no—
423C24—41no—
424C24—42no—
425C24—41no—
426C24—44no—
427C24—44no—
428C24—42no—
429C24—42no—
430C24C22⋊C4×C3114yescomplemented
431C24C22×C4×C3112yes—
432C24C22×C4×C3114yescomplemented
433C24C2×D4×C3111yescharacteristic
434C24C2×D4×C3112yes—
435C24C2×D4×C3112yes—
436C24C2×D4×C3111yescharacteristic
437C24C2×D4×C3112yes—
438C24C2×D4×C3112yes—
439C24#41×C3114yes—
440C24C24×C3111yescharacteristic
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—24no—
444C2×D4—28no—
445C2×D4—28no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—216no—
450C2×D4—432no—
451C2×D4—416no—
452C2×D4C22⋊C4×C3118yescomplemented
453C2×D4C22×C4×C3114yes—
454C2×D4C2×D4×C3114yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—28no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—44no—
465C22×C4—48no—
466C22×C4—48no—
467C22×C4—44no—
468C22×C4—84no—
469C22×C4C22⋊C4×C3114yescomplemented
470C22×C4C2×D4×C3112yes—
471C22×C4C2×D4×C3118yescomplemented
472C4⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—22no—
480C22⋊C4—216no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—432no—
484C22⋊C4—44no—
485C22⋊C4C22×C4×C3114yescomplemented
486C42—28no—
487C23—28no—
488C23—24no—
489C23—216no—
490C23—216no—
491C23—28no—
492C23—232no—
493C23—24no—
494C23—28no—
495C23—22no—
496C23—24no—
497C23—22no—
498C23—24no—
499C23—44no—
500C23—48no—
501C23—44no—
502C23—44no—
503C23—42no—
504C23—48no—
505C23—42no—
506C23—48no—
507C23—432no—
508C23—416no—
509C23—416no—
510C23—48no—
511C23—44no—
512C23—416no—
513C23—48no—
514C23—416no—
515C23—48no—
516C23—432no—
517C23—416no—
518C23—48no—
519C23—44no—
520C23—432no—
521C23—416no—
522C23—44no—
523C23—48no—
524C23—42no—
525C23—44no—
526C23—42no—
527C23—44no—
528C23—48no—
529C23—44no—
530C23—84no—
531C23—82no—
532C23C2×C22⋊C4×C3112yes—
533C23C2×C22⋊C4×C3112yes—
534C23C2×C22⋊C4×C3114yescomplemented
535C23C4×D4×C3114yes—
536C23C4×D4×C3114yes—
537C23C31×#12011yescharacteristic
538C23C31×#12012yes—
539C23C31×#12011yescharacteristic
540C23C31×#12114yes—
541C23C31×#12114yes—
542C23C31×#12312yes—
543C23C31×#12312yes—
544C23C23×C4×C3111yescharacteristic
545C23C22×D4×C3111yescharacteristic
546C23C22×D4×C3112yes—
547C23C22×D4×C3111yescharacteristic
548C23C2×#41×C3112yes—
549D4—28no—
550D4—28no—
551D4—216no—
552D4—432no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—28no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—48no—
562C2×C4—48no—
563C2×C4—48no—
564C2×C4—44no—
565C2×C4—84no—
566C2×C4—88no—
567C2×C4—88no—
568C2×C4C2×C22⋊C4×C3114yescomplemented
569C22—24no—
570C22—28no—
571C22—28no—
572C22—24no—
573C22—24no—
574C22—22no—
575C22—24no—
576C22—22no—
577C22—28no—
578C22—216no—
579C22—24no—
580C22—42no—
581C22—44no—
582C22—44no—
583C22—42no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—44no—
588C22—44no—
589C22—416no—
590C22—48no—
591C22—48no—
592C22—416no—
593C22—432no—
594C22—416no—
595C22—48no—
596C22—44no—
597C22—48no—
598C22—44no—
599C22—82no—
600C22—84no—
601C22C31×#38612yes—
602C22C31×#38614yes—
603C22C31×#38612yes—
604C22C31×B(4,𝔽2)14yes—
605C22C22×C22⋊C4×C3111yescharacteristic
606C22C2×C4×D4×C3112yes—
607C22C2×C31×#12011yescharacteristic
608C22C2×C31×#12112yes—
609C22C2×C31×#12311yescharacteristic
610C4—24no—
611C4—44no—
612C4—48no—
613C4—84no—
614C2—21no—
615C2—22no—
616C2—22no—
617C2—21no—
618C2—22no—
619C2—24no—
620C2—48no—
621C2—44no—
622C2C31×#188914yesdirect product factor
623C2C2×C31×#38611yescharacteristic
624C2C2×C31×B(4,𝔽2)12yes—
subgroupG/H
center, socleC23×C31#120
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC22×C31×#120C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#518C2semidirect
3. C22×C31×#99C2semidirect
4. C2×C31×#379C2semidirect
5. C31×#1889C2direct (N × H)
6. C2×C31×#342C2semidirect
12. C2×C31×#120C4semidirect
16. C31×#518C22semidirect
26. C2×C31×#99C22semidirect
28. C31×#379C22semidirect
29. C31×#342C22semidirect
37. C25×C31C2×C4semidirect
55. C23×C4×C31D4semidirect
58. C31×#120C2×C4semidirect
80. C2×C22⋊C4×C31C2×C4semidirect
81. C2×C22⋊C4×C31D4semidirect
117. C24×C31C22⋊C4semidirect
119. C24×C31C22×C4semidirect
139. C2×D4×C31C22⋊C4semidirect
156. C22×C4×C31C22⋊C4semidirect
158. C22×C4×C31C2×D4semidirect
172. C22⋊C4×C31C22×C4semidirect
174. C2×#1889C31direct (N × H)
222. C23×C31C2×C22⋊C4semidirect
256. C2×C4×C31C2×C22⋊C4semidirect
258. C2×#518C2×C31semidirect
259. C22×#99C2×C31semidirect
260. C2×#379C2×C31semidirect
261. #1889C2×C31direct (N × H)
262. C2×#342C2×C31semidirect
313. C2×#120C4×C31semidirect
317. #518C22×C31semidirect
327. C2×#99C22×C31semidirect
329. #379C22×C31semidirect
330. #342C22×C31semidirect
339. C2×C31#1889direct (N × H)
349. C25C2×C4×C31semidirect
367. C23×C4D4×C31semidirect
370. #120C2×C4×C31semidirect
392. C2×C22⋊C4C2×C4×C31semidirect
393. C2×C22⋊C4D4×C31semidirect
399. C31C2×#1889direct (N × H)
430. C24C22⋊C4×C31semidirect
432. C24C22×C4×C31semidirect
452. C2×D4C22⋊C4×C31semidirect
469. C22×C4C22⋊C4×C31semidirect
471. C22×C4C2×D4×C31semidirect
485. C22⋊C4C22×C4×C31semidirect
534. C23C2×C22⋊C4×C31semidirect
568. C2×C4C2×C22⋊C4×C31semidirect
622. C2C31×#1889direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C2×C31×#5182
C22×C31×#992
C2×C31×#3792
C31×#18892
C2×C31×#3422
C2×#188931