Finite Group Databasebeta

← C2×C31×#2021 #21480200

Subgroups — C2×C31×#2021 #21480200

Order 7936.

3986 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#534C211yesmaximal, characteristic, complemented
2C22×C31×#120C212yesmaximal, complemented
3C22×C31×#99C212yesmaximal, complemented
4C2×C31×#379C211yesmaximal, characteristic, complemented
5C31×#2021C218yesmaximal, direct product factor
6C2×C31×#342C211yesmaximal, characteristic, complemented
7C26×C31C2211yescharacteristic
8C23×D4×C31—22no—
9C23×D4×C31C2212yes—
10C31×#534—24no—
11C31×#534—22no—
12C31×#534C2214yescomplemented
13C2×C31×#123—22no—
14C2×C31×#121—22no—
15C2×C31×#120—28no—
16C2×C31×#120—22no—
17C2×C31×#120—24no—
18C2×C31×#120—28no—
19C2×C31×#120C2218yescomplemented
20C22×C22⋊C4×C31—22no—
21C22×C22⋊C4×C31—22no—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C2×C31×#99—28no—
26C2×C31×#99C2218yescomplemented
27C31×#379—22no—
28C31×#379C2214yescomplemented
29C31×#342C2214yescomplemented
30C25×C31—21no—
31C25×C31—22no—
32C25×C31—24no—
33C25×C31—22no—
34C25×C31—21no—
35C25×C31—22no—
36C25×C31—48no—
37C25×C31D414yescomplemented
38C25×C31D412yescomplemented
39C25×C31C2312yes—
40C25×C31C2311yescharacteristic
41C22×D4×C31—216no—
42C22×D4×C31—24no—
43C22×D4×C31—24no—
44C22×D4×C31—24no—
45C22×D4×C31—22no—
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—28no—
50C22×D4×C31—24no—
51C22×D4×C31—22no—
52C22×D4×C31—416no—
53C22×D4×C31D414yescomplemented
54C22×D4×C31C2314yes—
55C23×C4×C31—22no—
56C23×C4×C31—21no—
57C23×C4×C31D412yescomplemented
58C23×C4×C31D412yescomplemented
59C31×#123—28no—
60C31×#123—28no—
61C31×#121—28no—
62C31×#121—28no—
63C31×#120—232no—
64C31×#120—28no—
65C31×#120—216no—
66C31×#120—28no—
67C31×#120—216no—
68C2×C4⋊C4×C31—22no—
69C2×C22⋊C4×C31—216no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—28no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—21no—
78C2×C22⋊C4×C31—28no—
79C2×C22⋊C4×C31—48no—
80C2×C22⋊C4×C31D412yescomplemented
81C2×C22⋊C4×C31D418yescomplemented
82C2×C22⋊C4×C31C2312yes—
83C2×C22⋊C4×C31C2312yes—
84C2×C22⋊C4×C31C2314yes—
85C31×#99—216no—
86C24×C31—28no—
87C24×C31—216no—
88C24×C31—28no—
89C24×C31—24no—
90C24×C31—22no—
91C24×C31—24no—
92C24×C31—28no—
93C24×C31—24no—
94C24×C31—22no—
95C24×C31—24no—
96C24×C31—24no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—24no—
100C24×C31—416no—
101C24×C31—48no—
102C24×C31—44no—
103C24×C31—44no—
104C24×C31—48no—
105C24×C31—48no—
106C24×C31—416no—
107C24×C31—432no—
108C24×C31—416no—
109C24×C31—48no—
110C24×C31—42no—
111C24×C31—41no—
112C24×C31—41no—
113C24×C31—44no—
114C24×C31—44no—
115C24×C31—42no—
116C24×C31—42no—
117C24×C31C2×D412yes—
118C24×C31C2×D411yescharacteristic
119C24×C31C2×D412yes—
120C24×C31C2×D412yes—
121C24×C31C2×D411yescharacteristic
122C24×C31C2×D414yes—
123C24×C31C2×D414yescomplemented
124C24×C31C2×D414yescomplemented
125C24×C31#4112yes—
126C24×C31C2411yescharacteristic
127C2×D4×C31—232no—
128C2×D4×C31—28no—
129C2×D4×C31—24no—
130C2×D4×C31—24no—
131C2×D4×C31—28no—
132C2×D4×C31—24no—
133C2×D4×C31—24no—
134C2×D4×C31—24no—
135C2×D4×C31—24no—
136C2×D4×C31—24no—
137C2×D4×C31—24no—
138C2×D4×C31—28no—
139C2×D4×C31—432no—
140C2×D4×C31—464no—
141C2×D4×C31—44no—
142C2×D4×C31—44no—
143C2×D4×C31—44no—
144C2×D4×C31—44no—
145C2×D4×C31—44no—
146C2×D4×C31—44no—
147C2×D4×C31—44no—
148C2×D4×C31—44no—
149C2×D4×C31—84no—
150C22×C4×C31—24no—
151C22×C4×C31—28no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—24no—
156C22×C4×C31—24no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—48no—
160C22×C4×C31—44no—
161C22×C4×C31—44no—
162C22×C4×C31—42no—
163C22×C4×C31C2×D414yescomplemented
164C22×C4×C31C2×D414yescomplemented
165C4⋊C4×C31—28no—
166C22⋊C4×C31—232no—
167C22⋊C4×C31—216no—
168C22⋊C4×C31—28no—
169C22⋊C4×C31—24no—
170C22⋊C4×C31—24no—
171C22⋊C4×C31—24no—
172C22⋊C4×C31—24no—
173C22⋊C4×C31—416no—
174C22⋊C4×C31—42no—
175C22⋊C4×C31C2×D418yescomplemented
176C2×#2021C3111yesmaximal, characteristic, direct product factor, Sylow
177C23×C31—24no—
178C23×C31—28no—
179C23×C31—28no—
180C23×C31—216no—
181C23×C31—232no—
182C23×C31—216no—
183C23×C31—28no—
184C23×C31—24no—
185C23×C31—24no—
186C23×C31—24no—
187C23×C31—24no—
188C23×C31—42no—
189C23×C31—44no—
190C23×C31—44no—
191C23×C31—48no—
192C23×C31—48no—
193C23×C31—44no—
194C23×C31—42no—
195C23×C31—44no—
196C23×C31—48no—
197C23×C31—48no—
198C23×C31—416no—
199C23×C31—416no—
200C23×C31—416no—
201C23×C31—48no—
202C23×C31—432no—
203C23×C31—432no—
204C23×C31—416no—
205C23×C31—416no—
206C23×C31—48no—
207C23×C31—48no—
208C23×C31—416no—
209C23×C31—432no—
210C23×C31—416no—
211C23×C31—42no—
212C23×C31—44no—
213C23×C31—42no—
214C23×C31—48no—
215C23×C31—44no—
216C23×C31—44no—
217C23×C31—48no—
218C23×C31—44no—
219C23×C31—44no—
220C23×C31—48no—
221C23×C31—84no—
222C23×C31—88no—
223C23×C31#12012yes—
224C23×C31#12014yes—
225C23×C31#12011yescharacteristic
226C23×C31#12014yes—
227C23×C31#12011yescharacteristic
228C23×C31#12114yes—
229C23×C31#12112yes—
230C23×C31#12114yes—
231C23×C31#12112yes—
232C23×C31#12712yes—
233C23×C31#12712yes—
234C23×C31C22×D412yes—
235C23×C31C22×D411yescharacteristic
236C23×C31C22×D411yescharacteristic
237C23×C31C22×D412yes—
238C23×C31C2×#4111yescharacteristic
239D4×C31—464no—
240D4×C31—44no—
241D4×C31—44no—
242D4×C31—44no—
243D4×C31—44no—
244D4×C31—48no—
245D4×C31—48no—
246D4×C31—88no—
247C2×C4×C31—24no—
248C2×C4×C31—24no—
249C2×C4×C31—28no—
250C2×C4×C31—24no—
251C2×C4×C31—24no—
252C2×C4×C31—48no—
253C2×C4×C31—416no—
254C2×C4×C31—44no—
255C2×C4×C31—44no—
256C2×C4×C31—44no—
257C2×C4×C31—44no—
258C2×C4×C31—44no—
259C2×C4×C31—42no—
260C2×C4×C31—82no—
261C2×C4×C31—84no—
262C2×#534C2×C3111yescharacteristic, complemented
263C22×#120C2×C3112yescomplemented
264C22×#99C2×C3112yescomplemented
265C2×#379C2×C3111yescharacteristic, complemented
266#2021C2×C3118yesdirect product factor
267C2×#342C2×C3111yescharacteristic, complemented
268C22×C31—22no—
269C22×C31—24no—
270C22×C31—22no—
271C22×C31—24no—
272C22×C31—28no—
273C22×C31—24no—
274C22×C31—24no—
275C22×C31—28no—
276C22×C31—216no—
277C22×C31—28no—
278C22×C31—44no—
279C22×C31—42no—
280C22×C31—44no—
281C22×C31—42no—
282C22×C31—41no—
283C22×C31—42no—
284C22×C31—41no—
285C22×C31—48no—
286C22×C31—48no—
287C22×C31—44no—
288C22×C31—416no—
289C22×C31—432no—
290C22×C31—416no—
291C22×C31—48no—
292C22×C31—44no—
293C22×C31—48no—
294C22×C31—416no—
295C22×C31—44no—
296C22×C31—48no—
297C22×C31—84no—
298C22×C31—88no—
299C22×C31—88no—
300C22×C31#39214yes—
301C22×C31#39212yes—
302C22×C31#39212yes—
303C22×C31B(4,𝔽2)14yes—
304C22×C31C2×#12012yes—
305C22×C31C2×#12011yescharacteristic
306C22×C31C2×#12112yes—
307C22×C31C2×#12111yescharacteristic
308C22×C31C2×#12711yescharacteristic
309C4×C31—48no—
310C4×C31—44no—
311C4×C31—44no—
312C4×C31—82no—
313C26C22×C3111yescharacteristic
314C23×D4—22no—
315C23×D4C22×C3112yes—
316#534—24no—
317#534—22no—
318#534C22×C3114yescomplemented
319C2×#123—22no—
320C2×#121—22no—
321C2×#120—28no—
322C2×#120—22no—
323C2×#120—24no—
324C2×#120—28no—
325C2×#120C22×C3118yescomplemented
326C22×C22⋊C4—22no—
327C22×C22⋊C4—22no—
328C22×C22⋊C4C22×C3111yescharacteristic
329C22×C22⋊C4C22×C3111yescharacteristic
330C22×C22⋊C4C22×C3112yes—
331C2×#99—28no—
332C2×#99C22×C3118yescomplemented
333#379—22no—
334#379C22×C3114yescomplemented
335#342C22×C3114yescomplemented
336C2×C31—22no—
337C2×C31—21no—
338C2×C31—21no—
339C2×C31—22no—
340C2×C31—24no—
341C2×C31—22no—
342C2×C31—48no—
343C2×C31—84no—
344C2×C31#202114yesdirect product factor
345C2×C31C2×#39211yescharacteristic
346C2×C31C2×B(4,𝔽2)12yes—
347C25—21no—
348C25—22no—
349C25—24no—
350C25—22no—
351C25—21no—
352C25—22no—
353C25—48no—
354C25D4×C3114yescomplemented
355C25D4×C3112yescomplemented
356C25C23×C3112yes—
357C25C23×C3111yescharacteristic
358C22×D4—216no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—24no—
366C22×D4—28no—
367C22×D4—24no—
368C22×D4—22no—
369C22×D4—416no—
370C22×D4D4×C3114yescomplemented
371C22×D4C23×C3114yes—
372C23×C4—22no—
373C23×C4—21no—
374C23×C4D4×C3112yescomplemented
375C23×C4D4×C3112yescomplemented
376#123—28no—
377#123—28no—
378#121—28no—
379#121—28no—
380#120—232no—
381#120—28no—
382#120—216no—
383#120—28no—
384#120—216no—
385C2×C4⋊C4—22no—
386C2×C22⋊C4—216no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—48no—
397C2×C22⋊C4D4×C3112yescomplemented
398C2×C22⋊C4D4×C3118yescomplemented
399C2×C22⋊C4C23×C3112yes—
400C2×C22⋊C4C23×C3112yes—
401C2×C22⋊C4C23×C3114yes—
402#99—216no—
403C31C2×#202111yescharacteristic, direct product factor, Sylow
404C24—28no—
405C24—216no—
406C24—28no—
407C24—24no—
408C24—22no—
409C24—24no—
410C24—22no—
411C24—28no—
412C24—24no—
413C24—24no—
414C24—24no—
415C24—22no—
416C24—22no—
417C24—24no—
418C24—416no—
419C24—44no—
420C24—48no—
421C24—44no—
422C24—48no—
423C24—48no—
424C24—416no—
425C24—432no—
426C24—416no—
427C24—48no—
428C24—42no—
429C24—41no—
430C24—41no—
431C24—44no—
432C24—44no—
433C24—42no—
434C24—42no—
435C24C2×D4×C3112yes—
436C24C2×D4×C3111yescharacteristic
437C24C2×D4×C3112yes—
438C24C2×D4×C3112yes—
439C24C2×D4×C3111yescharacteristic
440C24C2×D4×C3114yes—
441C24C2×D4×C3114yescomplemented
442C24C2×D4×C3114yescomplemented
443C24#41×C3112yes—
444C24C24×C3111yescharacteristic
445C2×D4—232no—
446C2×D4—28no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—28no—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—28no—
457C2×D4—432no—
458C2×D4—464no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—84no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—48no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—42no—
481C22×C4C2×D4×C3114yescomplemented
482C22×C4C2×D4×C3114yescomplemented
483C4⋊C4—28no—
484C22⋊C4—232no—
485C22⋊C4—216no—
486C22⋊C4—28no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—416no—
492C22⋊C4—42no—
493C22⋊C4C2×D4×C3118yescomplemented
494C23—24no—
495C23—28no—
496C23—28no—
497C23—216no—
498C23—232no—
499C23—216no—
500C23—28no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—42no—
506C23—44no—
507C23—44no—
508C23—48no—
509C23—48no—
510C23—44no—
511C23—42no—
512C23—44no—
513C23—48no—
514C23—48no—
515C23—416no—
516C23—416no—
517C23—416no—
518C23—48no—
519C23—432no—
520C23—432no—
521C23—416no—
522C23—416no—
523C23—48no—
524C23—48no—
525C23—416no—
526C23—432no—
527C23—416no—
528C23—48no—
529C23—42no—
530C23—44no—
531C23—42no—
532C23—48no—
533C23—44no—
534C23—44no—
535C23—48no—
536C23—44no—
537C23—44no—
538C23—84no—
539C23—88no—
540C23C31×#12012yes—
541C23C31×#12014yes—
542C23C31×#12011yescharacteristic
543C23C31×#12014yes—
544C23C31×#12011yescharacteristic
545C23C31×#12114yes—
546C23C31×#12112yes—
547C23C31×#12114yes—
548C23C31×#12112yes—
549C23C31×#12712yes—
550C23C31×#12712yes—
551C23C22×D4×C3112yes—
552C23C22×D4×C3111yescharacteristic
553C23C22×D4×C3111yescharacteristic
554C23C22×D4×C3112yes—
555C23C2×#41×C3111yescharacteristic
556D4—464no—
557D4—44no—
558D4—44no—
559D4—44no—
560D4—44no—
561D4—48no—
562D4—48no—
563D4—88no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—28no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—48no—
570C2×C4—416no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4—42no—
577C2×C4—82no—
578C2×C4—84no—
579C22—22no—
580C22—24no—
581C22—22no—
582C22—24no—
583C22—28no—
584C22—24no—
585C22—24no—
586C22—28no—
587C22—216no—
588C22—28no—
589C22—44no—
590C22—42no—
591C22—44no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—41no—
596C22—48no—
597C22—48no—
598C22—44no—
599C22—416no—
600C22—432no—
601C22—416no—
602C22—48no—
603C22—44no—
604C22—48no—
605C22—416no—
606C22—44no—
607C22—48no—
608C22—84no—
609C22—88no—
610C22—88no—
611C22C31×#39214yes—
612C22C31×#39212yes—
613C22C31×#39212yes—
614C22C31×B(4,𝔽2)14yes—
615C22C2×C31×#12012yes—
616C22C2×C31×#12011yescharacteristic
617C22C2×C31×#12112yes—
618C22C2×C31×#12111yescharacteristic
619C22C2×C31×#12711yescharacteristic
620C4—48no—
621C4—44no—
622C4—44no—
623C4—82no—
624C2—22no—
625C2—21no—
626C2—21no—
627C2—22no—
628C2—24no—
629C2—22no—
630C2—48no—
631C2—84no—
632C2C31×#202114yesdirect product factor
633C2C2×C31×#39211yescharacteristic
634C2C2×C31×B(4,𝔽2)12yes—
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#534C2semidirect
2. C22×C31×#120C2semidirect
3. C22×C31×#99C2semidirect
4. C2×C31×#379C2semidirect
5. C31×#2021C2direct (N × H)
6. C2×C31×#342C2semidirect
12. C31×#534C22semidirect
19. C2×C31×#120C22semidirect
26. C2×C31×#99C22semidirect
28. C31×#379C22semidirect
29. C31×#342C22semidirect
37. C25×C31D4semidirect
38. C25×C31D4semidirect
53. C22×D4×C31D4semidirect
57. C23×C4×C31D4semidirect
58. C23×C4×C31D4semidirect
80. C2×C22⋊C4×C31D4semidirect
81. C2×C22⋊C4×C31D4semidirect
123. C24×C31C2×D4semidirect
124. C24×C31C2×D4semidirect
163. C22×C4×C31C2×D4semidirect
164. C22×C4×C31C2×D4semidirect
175. C22⋊C4×C31C2×D4semidirect
176. C2×#2021C31direct (N × H)
262. C2×#534C2×C31semidirect
263. C22×#120C2×C31semidirect
264. C22×#99C2×C31semidirect
265. C2×#379C2×C31semidirect
266. #2021C2×C31direct (N × H)
267. C2×#342C2×C31semidirect
318. #534C22×C31semidirect
325. C2×#120C22×C31semidirect
332. C2×#99C22×C31semidirect
334. #379C22×C31semidirect
335. #342C22×C31semidirect
344. C2×C31#2021direct (N × H)
354. C25D4×C31semidirect
355. C25D4×C31semidirect
370. C22×D4D4×C31semidirect
374. C23×C4D4×C31semidirect
375. C23×C4D4×C31semidirect
397. C2×C22⋊C4D4×C31semidirect
398. C2×C22⋊C4D4×C31semidirect
403. C31C2×#2021direct (N × H)
441. C24C2×D4×C31semidirect
442. C24C2×D4×C31semidirect
481. C22×C4C2×D4×C31semidirect
482. C22×C4C2×D4×C31semidirect
493. C22⋊C4C2×D4×C31semidirect
632. C2C31×#2021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5342
C22×C31×#1202
C22×C31×#992
C2×C31×#3792
C31×#20212
C2×C31×#3422
C2×#202131