Finite Group Databasebeta

← C31×#9914 #21466673

Subgroups — C31×#9914 #21466673

Order 7936.

1356 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#447C211yesmaximal, characteristic, complemented
2C31×#2617C211yesmaximal, characteristic, complemented
3C2×C31×#392C211yesmaximal, characteristic, complemented
4C31×#1786C211yesmaximal, characteristic, complemented
5C2×C31×#327C211yesmaximal, characteristic, complemented
6C2×C31×#323C211yesmaximal, characteristic, complemented
7C31×#1294C211yesmaximal, characteristic, complemented
8C23×D4×C31—21no—
9C23×D4×C31C2211yescharacteristic
10C22×D8×C31—21no—
11C2×C31×#121C2211yescharacteristic
12C2×C31×#120—21no—
13C22×C22⋊C4×C31—21no—
14C22×C22⋊C4×C31C2211yescharacteristic
15C31×#447—22no—
16C31×#447—22no—
17C2×C31×#102—21no—
18C2×C31×#102—22no—
19C2×C31×C22⋊C8C2211yescharacteristic
20C2×C31×C22⋊C8C2211yescharacteristic
21C31×#397—21no—
22C31×#394—22no—
23C31×#392—21no—
24C31×#392—22no—
25C31×#392—22no—
26C31×#386—21no—
27C31×#380C2211yescharacteristic
28C2×C31×#95C2211yescharacteristic
29C31×#327—22no—
30C31×#323—22no—
31C25×C31—21no—
32C25×C31D411yescharacteristic
33C22×D4×C31—24no—
34C22×D4×C31—21no—
35C22×D4×C31—22no—
36C22×D4×C31—21no—
37C22×D4×C31—21no—
38C22×D4×C31—21no—
39C22×D4×C31—21no—
40C22×D4×C31—21no—
41C22×D4×C31—44no—
42C22×D4×C31—44no—
43C22×D4×C31—44no—
44C22×D4×C31—42no—
45C22×D4×C31—42no—
46C22×D4×C31D412yescomplemented
47C22×D4×C31D411yescharacteristic, complemented
48C23×C4×C31—21no—
49C23×C4×C31D411yescharacteristic
50C23×C4×C31C2311yescharacteristic
51C2×D8×C31—24no—
52C2×D8×C31—44no—
53C22×C8×C31—21no—
54C22×C8×C31—21no—
55C31×#121—21no—
56C31×#121—21no—
57C31×#121—21no—
58C31×#121—21no—
59C31×#120—42no—
60C31×#120—42no—
61C2×C4⋊C4×C31D411yescharacteristic, complemented
62C2×C4⋊C4×C31D412yescomplemented
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—21no—
66C2×C22⋊C4×C31—21no—
67C2×C22⋊C4×C31—21no—
68C2×C22⋊C4×C31—21no—
69C2×C22⋊C4×C31—21no—
70C2×C22⋊C4×C31—21no—
71C2×C22⋊C4×C31—21no—
72C2×C22⋊C4×C31—21no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—44no—
75C31×#102—24no—
76C31×#102—44no—
77C31×C22⋊C8—21no—
78C31×C22⋊C8—21no—
79C31×C22⋊C8—21no—
80C31×C22⋊C8D412yescomplemented
81C31×#95—22no—
82C31×#95—21no—
83C31×#95—21no—
84C31×#95D412yescomplemented
85C24×C31—24no—
86C24×C31—21no—
87C24×C31—22no—
88C24×C31—21no—
89C24×C31—21no—
90C24×C31—21no—
91C24×C31—21no—
92C24×C31—21no—
93C24×C31—21no—
94C24×C31—42no—
95C24×C31—42no—
96C24×C31—42no—
97C24×C31—42no—
98C24×C31—42no—
99C24×C31—41no—
100C24×C31—41no—
101C24×C31—41no—
102C24×C31—41no—
103C24×C31—41no—
104C24×C31—41no—
105C24×C31D812yescomplemented
106C24×C31C2×D411yescharacteristic
107C2×D4×C31—24no—
108C2×D4×C31—24no—
109C2×D4×C31—22no—
110C2×D4×C31—21no—
111C2×D4×C31—22no—
112C2×D4×C31—21no—
113C2×D4×C31—42no—
114C2×D4×C31—42no—
115C2×D4×C31—48no—
116C2×D4×C31—42no—
117C2×D4×C31—44no—
118C2×D4×C31—44no—
119C2×D4×C31—44no—
120C2×D4×C31—44no—
121C2×D4×C31—48no—
122C2×D4×C31—48no—
123C2×D4×C31—416no—
124C2×D4×C31—416no—
125C2×D4×C31—44no—
126C2×D4×C31—41no—
127C2×D4×C31—41no—
128C2×D4×C31—41no—
129C2×D4×C31—41no—
130C2×D4×C31—41no—
131C2×D4×C31—41no—
132C2×D4×C31—41no—
133C2×D4×C31—41no—
134C2×D4×C31—82no—
135C2×D4×C31—82no—
136C22×C4×C31—24no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—42no—
144C22×C4×C31—42no—
145C22×C4×C31—41no—
146C22×C4×C31—41no—
147C22×C4×C31—42no—
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31#4111yescharacteristic
154D8×C31—48no—
155C2×C8×C31—22no—
156C2×C8×C31—42no—
157C2×C8×C31—42no—
158C2×C8×C31—41no—
159C4⋊C4×C31—21no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—42no—
162C22⋊C4×C31—48no—
163C22⋊C4×C31—44no—
164C22⋊C4×C31—41no—
165C22⋊C4×C31—41no—
166C22⋊C4×C31—41no—
167C22⋊C4×C31—41no—
168C22⋊C4×C31—41no—
169C22⋊C4×C31—41no—
170C22⋊C4×C31—41no—
171C22⋊C4×C31—41no—
172C22⋊C4×C31—82no—
173#9914C3111yesmaximal, characteristic, direct product factor, Sylow
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—24no—
177C23×C31—22no—
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—44no—
181C23×C31—42no—
182C23×C31—44no—
183C23×C31—44no—
184C23×C31—44no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—44no—
190C23×C31—44no—
191C23×C31—44no—
192C23×C31—41no—
193C23×C31—42no—
194C23×C31—42no—
195C23×C31—41no—
196C23×C31—41no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31—44no—
200C23×C31—42no—
201C23×C31—41no—
202C23×C31—41no—
203C23×C31—41no—
204C23×C31—41no—
205C23×C31—42no—
206C23×C31—42no—
207C23×C31—82no—
208C23×C31—82no—
209C23×C31—81no—
210C23×C31—81no—
211C23×C31—82no—
212C23×C31—82no—
213C23×C31—82no—
214C23×C31—82no—
215C23×C31—82no—
216C23×C31—81no—
217C23×C31—81no—
218C23×C31—82no—
219C23×C31—81no—
220C23×C31—81no—
221C23×C31#12011yescharacteristic
222C23×C31#12011yescharacteristic
223C23×C31#12111yescharacteristic
224C23×C31C2×D811yescharacteristic
225C23×C31#13511yescharacteristic
226C23×C31AGL(1,ℤ/8)11yescharacteristic
227C23×C31AGL(1,ℤ/8)11yescharacteristic
228D4×C31—24no—
229D4×C31—24no—
230D4×C31—42no—
231D4×C31—44no—
232D4×C31—42no—
233D4×C31—44no—
234D4×C31—42no—
235D4×C31—432no—
236D4×C31—81no—
237D4×C31—88no—
238D4×C31—81no—
239D4×C31—81no—
240D4×C31—81no—
241D4×C31—81no—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—24no—
245C2×C4×C31—41no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—44no—
250C2×C4×C31—44no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—41no—
255C2×C4×C31—41no—
256C2×C4×C31—42no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—42no—
260C2×C4×C31—42no—
261C2×C4×C31—42no—
262C2×C4×C31—81no—
263C2×C4×C31#12011yescharacteristic
264C2×C4×C31#12111yescharacteristic
265C2×C4×C31#12111yescharacteristic
266C2×C4×C31#12711yescharacteristic
267C8×C31—42no—
268C8×C31—81no—
269C2×#447C2×C3111yescharacteristic, complemented
270#2617C2×C3111yescharacteristic, complemented
271C2×#392C2×C3111yescharacteristic, complemented
272#1786C2×C3111yescharacteristic, complemented
273C2×#327C2×C3111yescharacteristic, complemented
274C2×#323C2×C3111yescharacteristic, complemented
275#1294C2×C3111yescharacteristic, complemented
276C22×C31—22no—
277C22×C31—22no—
278C22×C31—22no—
279C22×C31—22no—
280C22×C31—21no—
281C22×C31—21no—
282C22×C31—21no—
283C22×C31—21no—
284C22×C31—44no—
285C22×C31—44no—
286C22×C31—44no—
287C22×C31—44no—
288C22×C31—42no—
289C22×C31—44no—
290C22×C31—82no—
291C22×C31—82no—
292C22×C31—82no—
293C22×C31—82no—
294C22×C31—84no—
295C22×C31—82no—
296C22×C31—84no—
297C22×C31—84no—
298C22×C31—82no—
299C22×C31—84no—
300C22×C31—82no—
301C22×C31—81no—
302C22×C31—82no—
303C22×C31—81no—
304C22×C31—82no—
305C22×C31—82no—
306C22×C31—81no—
307C22×C31—81no—
308C22×C31—81no—
309C22×C31#39211yescharacteristic
310C22×C31#44711yescharacteristic
311C22×C31#44711yescharacteristic
312C22×C31#44911yescharacteristic
313C22×C31#44911yescharacteristic
314C22×C31#45312yes—
315C22×C31B(4,𝔽2)12yes—
316C22×C31#46611yescharacteristic
317C22×C31#46911yescharacteristic
318C4×C31—21no—
319C4×C31—21no—
320C4×C31—21no—
321C4×C31—21no—
322C4×C31—44no—
323C4×C31—82no—
324C4×C31—81no—
325C4×C31—81no—
326C23×D4—21no—
327C23×D4C22×C3111yescharacteristic
328C22×D8—21no—
329C2×#121C22×C3111yescharacteristic
330C2×#120—21no—
331C22×C22⋊C4—21no—
332C22×C22⋊C4C22×C3111yescharacteristic
333#447—22no—
334#447—22no—
335C2×#102—21no—
336C2×#102—22no—
337C2×C22⋊C8C22×C3111yescharacteristic
338C2×C22⋊C8C22×C3111yescharacteristic
339#397—21no—
340#394—22no—
341#392—21no—
342#392—22no—
343#392—22no—
344#386—21no—
345#380C22×C3111yescharacteristic
346C2×#95C22×C3111yescharacteristic
347#327—22no—
348#323—22no—
349C2×C31—21no—
350C2×C31—21no—
351C2×C31—21no—
352C2×C31—21no—
353C2×C31—82no—
354C2×C31—84no—
355C2×C31—161no—
356C2×C31#159512yes—
357C2×C31#160012yes—
358C2×C31#199911yescharacteristic
359C2×C31#200211yescharacteristic
360C2×C31#202111yescharacteristic
361C25—21no—
362C25D4×C3111yescharacteristic
363C22×D4—24no—
364C22×D4—21no—
365C22×D4—22no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—44no—
372C22×D4—44no—
373C22×D4—44no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4D4×C3111yescharacteristic, complemented
377C22×D4D4×C3112yescomplemented
378C23×C4—21no—
379C23×C4D4×C3111yescharacteristic
380C23×C4C23×C3111yescharacteristic
381C2×D8—24no—
382C2×D8—44no—
383C22×C8—21no—
384C22×C8—21no—
385#121—21no—
386#121—21no—
387#121—21no—
388#121—21no—
389#120—42no—
390#120—42no—
391C2×C4⋊C4D4×C3111yescharacteristic, complemented
392C2×C4⋊C4D4×C3112yescomplemented
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—44no—
405#102—24no—
406#102—44no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8D4×C3112yescomplemented
411#95—22no—
412#95—21no—
413#95—21no—
414#95D4×C3112yescomplemented
415C31#991411yescharacteristic, direct product factor, Sylow
416C24—24no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—41no—
431C24—41no—
432C24—41no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24D8×C3112yescomplemented
437C24C2×D4×C3111yescharacteristic
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—48no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—416no—
455C2×D4—416no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—82no—
466C2×D4—82no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4C2×D4×C3111yescharacteristic
480C22×C4C2×D4×C3111yescharacteristic
481C22×C4C2×D4×C3111yescharacteristic
482C22×C4C2×D4×C3111yescharacteristic
483C22×C4C2×D4×C3111yescharacteristic
484C22×C4#41×C3111yescharacteristic
485D8—48no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—41no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C22⋊C4—48no—
494C22⋊C4—44no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—82no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—44no—
511C23—42no—
512C23—44no—
513C23—44no—
514C23—44no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—42no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—44no—
528C23—42no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—41no—
533C23—41no—
534C23—42no—
535C23—42no—
536C23—41no—
537C23—82no—
538C23—82no—
539C23—81no—
540C23—81no—
541C23—82no—
542C23—82no—
543C23—82no—
544C23—82no—
545C23—82no—
546C23—81no—
547C23—81no—
548C23—82no—
549C23—81no—
550C23—81no—
551C23C31×#12011yescharacteristic
552C23C31×#12011yescharacteristic
553C23C31×#12111yescharacteristic
554C23C2×D8×C3111yescharacteristic
555C23C31×#13511yescharacteristic
556C23C31×AGL(1,ℤ/8)11yescharacteristic
557C23C31×AGL(1,ℤ/8)11yescharacteristic
558D4—24no—
559D4—24no—
560D4—42no—
561D4—44no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—432no—
566D4—81no—
567D4—88no—
568D4—81no—
569D4—81no—
570D4—81no—
571D4—81no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—81no—
593C2×C4C31×#12011yescharacteristic
594C2×C4C31×#12111yescharacteristic
595C2×C4C31×#12111yescharacteristic
596C2×C4C31×#12711yescharacteristic
597C8—42no—
598C8—81no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—44no—
611C22—42no—
612C22—44no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—84no—
618C22—82no—
619C22—84no—
620C22—84no—
621C22—82no—
622C22—84no—
623C22—82no—
624C22—81no—
625C22—82no—
626C22—81no—
627C22—82no—
628C22—82no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22C31×#39211yescharacteristic
633C22C31×#44711yescharacteristic
634C22C31×#44711yescharacteristic
635C22C31×#44911yescharacteristic
636C22C31×#44911yescharacteristic
637C22C31×#45312yes—
638C22C31×B(4,𝔽2)12yes—
639C22C31×#46611yescharacteristic
640C22C31×#46911yescharacteristic
641C4—21no—
642C4—21no—
643C4—21no—
644C4—21no—
645C4—44no—
646C4—82no—
647C4—81no—
648C4—81no—
649C2—21no—
650C2—21no—
651C2—21no—
652C2—21no—
653C2—82no—
654C2—84no—
655C2—161no—
656C2C31×#159512yes—
657C2C31×#160012yes—
658C2C31×#199911yescharacteristic
659C2C31×#200211yescharacteristic
660C2C31×#202111yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#447C2semidirect
2. C31×#2617C2semidirect
3. C2×C31×#392C2semidirect
4. C31×#1786C2semidirect
5. C2×C31×#327C2semidirect
6. C2×C31×#323C2semidirect
7. C31×#1294C2semidirect
46. C22×D4×C31D4semidirect
47. C22×D4×C31D4semidirect
61. C2×C4⋊C4×C31D4semidirect
62. C2×C4⋊C4×C31D4semidirect
80. C31×C22⋊C8D4semidirect
84. C31×#95D4semidirect
105. C24×C31D8semidirect
173. #9914C31direct (N × H)
269. C2×#447C2×C31semidirect
270. #2617C2×C31semidirect
271. C2×#392C2×C31semidirect
272. #1786C2×C31semidirect
273. C2×#327C2×C31semidirect
274. C2×#323C2×C31semidirect
275. #1294C2×C31semidirect
376. C22×D4D4×C31semidirect
377. C22×D4D4×C31semidirect
391. C2×C4⋊C4D4×C31semidirect
392. C2×C4⋊C4D4×C31semidirect
410. C22⋊C8D4×C31semidirect
414. #95D4×C31semidirect
415. C31#9914direct (N × H)
436. C24D8×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4472
C31×#26172
C2×C31×#3922
C31×#17862
C2×C31×#3272
C2×C31×#3232
C31×#12942
#991431