Finite Group Databasebeta

← C31×#23977 #21480736

Subgroups — C31×#23977 #21480736

Order 7936.

1286 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#555C211yesmaximal, characteristic
2C2×C31×#448C211yesmaximal, characteristic, complemented
3C2×C31×#419C211yesmaximal, characteristic, complemented
4C31×#2409C211yesmaximal, characteristic, complemented
5C31×#2024C212yesmaximal, complemented
6C31×#2000C212yesmaximal, complemented
7C31×#1895C211yesmaximal, characteristic, complemented
8C31×#1877C212yesmaximal, complemented
9C31×#1873C212yesmaximal, complemented
10C31×#1870C211yesmaximal, characteristic, complemented
11C31×#1825C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic
13C22×SD16×C31C2212yes—
14C22×M16×C31C2211yescharacteristic
15C31×#555—24no—
16C31×#555—24no—
17C2×C31×C4⋊Q8C2211yescharacteristic
18C2×C31×#124—21no—
19C2×C31×#124—21no—
20C2×C31×C22⋊Q8C2212yes—
21C2×C31×#121—21no—
22C2×C31×#121C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C31×#117—21no—
27C2×C31×#117C2211yescharacteristic
28C2×C31×#117C2211yescharacteristic
29C31×#448—24no—
30C31×#419—24no—
31C2×C31×#103C2212yes—
32C2×C31×#103C2212yes—
33C2×C31×#103C2212yes—
34C2×C31×#102C2212yes—
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2212yes—
37C31×#395—21no—
38C31×#393—21no—
39C31×#391C2212yes—
40C31×#386—21no—
41C31×#385—21no—
42C31×#380C2211yescharacteristic
43C31×#340C2212yes—
44C31×#340C2212yes—
45C31×#340C2212yes—
46C31×#336C2212yes—
47C22×Q8×C31—21no—
48C22×Q8×C31—21no—
49C22×Q8×C31—24no—
50C22×Q8×C31—22no—
51C22×Q8×C31—22no—
52C22×Q8×C31—42no—
53C22×Q8×C31C2312yes—
54C22×D4×C31—21no—
55C22×D4×C31—21no—
56C22×D4×C31D411yescharacteristic
57C22×D4×C31C2311yescharacteristic
58C23×C4×C31—21no—
59C23×C4×C31—21no—
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C2×SD16×C31—24no—
63C2×SD16×C31—24no—
64C2×SD16×C31—42no—
65C2×M16×C31—22no—
66C2×M16×C31—42no—
67C22×C8×C31C2312yes—
68C22×C8×C31C2312yes—
69C31×C4⋊Q8—22no—
70C31×C4⋊Q8—22no—
71C31×#124—28no—
72C31×#124—28no—
73C31×C22⋊Q8—24no—
74C31×C22⋊Q8—42no—
75C31×#121—28no—
76C31×#121—22no—
77C31×#121—22no—
78C31×#121—22no—
79C31×#121D414yes—
80C4×D4×C31—22no—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C4×D4×C31—22no—
84C31×#117—28no—
85C31×#117—22no—
86C31×#117—22no—
87C31×#117—22no—
88C31×#117D414yes—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31D411yescharacteristic
92C2×C4⋊C4×C31C2312yes—
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C22⋊C4×C31—21no—
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31D411yescharacteristic
104C2×C22⋊C4×C31D411yescharacteristic
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31C2311yescharacteristic
108C31×#103—24no—
109C31×#103—24no—
110C31×#103—24no—
111C31×#102—42no—
112C31×C22⋊C8—22no—
113C31×C22⋊C8—42no—
114C31×#95—21no—
115C31×#95—22no—
116C31×#95—22no—
117C24×C31—21no—
118C24×C31C2×D411yescharacteristic
119C24×C31C2×D411yescharacteristic
120C2×Q8×C31—24no—
121C2×Q8×C31—22no—
122C2×Q8×C31—28no—
123C2×Q8×C31—22no—
124C2×Q8×C31—22no—
125C2×Q8×C31—22no—
126C2×Q8×C31—22no—
127C2×Q8×C31—44no—
128C2×Q8×C31—48no—
129C2×Q8×C31—44no—
130C2×Q8×C31—42no—
131C2×Q8×C31—82no—
132C2×Q8×C31#4114yes—
133C2×D4×C31—22no—
134C2×D4×C31—24no—
135C2×D4×C31—24no—
136C2×D4×C31—22no—
137C2×D4×C31—21no—
138C2×D4×C31—22no—
139C2×D4×C31—22no—
140C2×D4×C31—41no—
141C2×D4×C31—82no—
142C2×D4×C31—82no—
143C2×D4×C31C2×D412yes—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—24no—
147C22×C4×C31—22no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—44no—
157C22×C4×C31—42no—
158C22×C4×C31—42no—
159C22×C4×C31—42no—
160C22×C4×C31C2×D411yescharacteristic
161C22×C4×C31C2×D411yescharacteristic
162C22×C4×C31C2×D411yescharacteristic
163C22×C4×C31C2×D412yes—
164C22×C4×C31C2×D412yes—
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2411yescharacteristic
167SD16×C31—48no—
168M16×C31—44no—
169C2×C8×C31—22no—
170C2×C8×C31—22no—
171C2×C8×C31—22no—
172C2×C8×C31—22no—
173C2×C8×C31—22no—
174C2×C8×C31—22no—
175C4⋊C4×C31—24no—
176C4⋊C4×C31—22no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—21no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—22no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—44no—
183C4⋊C4×C31C2×D412yes—
184C4⋊C4×C31C2×D412yes—
185C4⋊C4×C31C2×D412yes—
186C22⋊C4×C31—24no—
187C22⋊C4×C31—24no—
188C22⋊C4×C31—24no—
189C22⋊C4×C31—24no—
190C22⋊C4×C31—22no—
191C22⋊C4×C31—24no—
192C22⋊C4×C31—22no—
193C22⋊C4×C31—44no—
194C22⋊C4×C31—42no—
195C42×C31—24no—
196C42×C31—24no—
197C42×C31—21no—
198C42×C31—21no—
199#23977C3111yesmaximal, characteristic, direct product factor, Sylow
200C23×C31—22no—
201C23×C31—21no—
202C23×C31—21no—
203C23×C31—22no—
204C23×C31—21no—
205C23×C31—22no—
206C23×C31—22no—
207C23×C31—21no—
208C23×C31—21no—
209C23×C31—22no—
210C23×C31—42no—
211C23×C31—41no—
212C23×C31—41no—
213C23×C31—42no—
214C23×C31#12012yes—
215C23×C31C22×D411yescharacteristic
216Q8×C31—24no—
217Q8×C31—24no—
218Q8×C31—48no—
219Q8×C31—42no—
220Q8×C31—42no—
221Q8×C31—84no—
222D4×C31—24no—
223D4×C31—44no—
224D4×C31—41no—
225D4×C31—41no—
226D4×C31—84no—
227D4×C31—84no—
228C2×C4×C31—21no—
229C2×C4×C31—22no—
230C2×C4×C31—21no—
231C2×C4×C31—22no—
232C2×C4×C31—22no—
233C2×C4×C31—24no—
234C2×C4×C31—21no—
235C2×C4×C31—22no—
236C2×C4×C31—21no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—24no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—48no—
243C2×C4×C31—48no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—41no—
251C2×C4×C31—41no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31#12012yes—
257C2×C4×C31#13712yes—
258C2×C4×C31C22×D411yescharacteristic
259C2×C4×C31C22×D411yescharacteristic
260C2×C4×C31C2×#4112yes—
261C2×C4×C31H(5,𝔽2)12yes—
262C8×C31—42no—
263C8×C31—42no—
264C2×#555C2×C3111yescharacteristic
265C2×#448C2×C3111yescharacteristic, complemented
266C2×#419C2×C3111yescharacteristic, complemented
267#2409C2×C3111yescharacteristic, complemented
268#2024C2×C3112yescomplemented
269#2000C2×C3112yescomplemented
270#1895C2×C3111yescharacteristic, complemented
271#1877C2×C3112yescomplemented
272#1873C2×C3112yescomplemented
273#1870C2×C3111yescharacteristic, complemented
274#1825C2×C3111yescharacteristic, complemented
275C22×C31—22no—
276C22×C31—22no—
277C22×C31—22no—
278C22×C31—42no—
279C22×C31—42no—
280C22×C31—42no—
281C22×C31—41no—
282C22×C31—42no—
283C22×C31—42no—
284C22×C31—41no—
285C22×C31—41no—
286C22×C31—42no—
287C22×C31—42no—
288C22×C31—82no—
289C22×C31—82no—
290C22×C31C2×#12011yescharacteristic
291C22×C31#54612yes—
292C22×C31C2×#13711yescharacteristic
293C22×C31#57511yescharacteristic
294C22×C31#57712yes—
295C4×C31—22no—
296C4×C31—22no—
297C4×C31—41no—
298C4×C31—44no—
299C4×C31—42no—
300C4×C31—41no—
301C4×C31—42no—
302C4×C31—42no—
303C4×C31—82no—
304C4×C31#52511yescharacteristic
305C4×C31#53511yescharacteristic
306C4×C31#54612yes—
307C23×Q8C22×C3111yescharacteristic
308C22×SD16C22×C3112yes—
309C22×M16C22×C3111yescharacteristic
310#555—24no—
311#555—24no—
312C2×C4⋊Q8C22×C3111yescharacteristic
313C2×#124—21no—
314C2×#124—21no—
315C2×C22⋊Q8C22×C3112yes—
316C2×#121—21no—
317C2×#121C22×C3111yescharacteristic
318C2×#121C22×C3111yescharacteristic
319C2×C4×D4C22×C3111yescharacteristic
320C2×C4×D4C22×C3111yescharacteristic
321C2×#117—21no—
322C2×#117C22×C3111yescharacteristic
323C2×#117C22×C3111yescharacteristic
324#448—24no—
325#419—24no—
326C2×#103C22×C3112yes—
327C2×#103C22×C3112yes—
328C2×#103C22×C3112yes—
329C2×#102C22×C3112yes—
330C2×C22⋊C8C22×C3111yescharacteristic
331C2×C22⋊C8C22×C3112yes—
332#395—21no—
333#393—21no—
334#391C22×C3112yes—
335#386—21no—
336#385—21no—
337#380C22×C3111yescharacteristic
338#340C22×C3112yes—
339#340C22×C3112yes—
340#340C22×C3112yes—
341#336C22×C3112yes—
342C2×C31—42no—
343C2×C31—81no—
344C2×C31—82no—
345C2×C31#240411yescharacteristic
346C2×C31#300711yescharacteristic
347C2×C31#300911yescharacteristic
348C2×C31#332112yes—
349C2×C31#332912yes—
350C22×Q8—21no—
351C22×Q8—21no—
352C22×Q8—24no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—42no—
356C22×Q8C23×C3112yes—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4D4×C3111yescharacteristic
360C22×D4C23×C3111yescharacteristic
361C23×C4—21no—
362C23×C4—21no—
363C23×C4C23×C3111yescharacteristic
364C23×C4C23×C3111yescharacteristic
365C2×SD16—24no—
366C2×SD16—24no—
367C2×SD16—42no—
368C2×M16—22no—
369C2×M16—42no—
370C22×C8C23×C3112yes—
371C22×C8C23×C3112yes—
372C4⋊Q8—22no—
373C4⋊Q8—22no—
374#124—28no—
375#124—28no—
376C22⋊Q8—24no—
377C22⋊Q8—42no—
378#121—28no—
379#121—22no—
380#121—22no—
381#121—22no—
382#121D4×C3114yes—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387#117—28no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117D4×C3114yes—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4D4×C3111yescharacteristic
395C2×C4⋊C4C23×C3112yes—
396C2×C4⋊C4C23×C3111yescharacteristic
397C2×C4⋊C4C23×C3111yescharacteristic
398C2×C4⋊C4C23×C3111yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4D4×C3111yescharacteristic
407C2×C22⋊C4D4×C3111yescharacteristic
408C2×C42—21no—
409C2×C42—21no—
410C2×C42C23×C3111yescharacteristic
411#103—24no—
412#103—24no—
413#103—24no—
414#102—42no—
415C22⋊C8—22no—
416C22⋊C8—42no—
417#95—21no—
418#95—22no—
419#95—22no—
420C31#2397711yescharacteristic, direct product factor, Sylow
421C24—21no—
422C24C2×D4×C3111yescharacteristic
423C24C2×D4×C3111yescharacteristic
424C2×Q8—24no—
425C2×Q8—22no—
426C2×Q8—28no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—44no—
432C2×Q8—48no—
433C2×Q8—44no—
434C2×Q8—42no—
435C2×Q8—82no—
436C2×Q8#41×C3114yes—
437C2×D4—22no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—41no—
445C2×D4—82no—
446C2×D4—82no—
447C2×D4C2×D4×C3112yes—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4C2×D4×C3111yescharacteristic
465C22×C4C2×D4×C3111yescharacteristic
466C22×C4C2×D4×C3111yescharacteristic
467C22×C4C2×D4×C3112yes—
468C22×C4C2×D4×C3112yes—
469C22×C4C2×D4×C3111yescharacteristic
470C22×C4C24×C3111yescharacteristic
471SD16—48no—
472M16—44no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—44no—
487C4⋊C4C2×D4×C3112yes—
488C4⋊C4C2×D4×C3112yes—
489C4⋊C4C2×D4×C3112yes—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—22no—
495C22⋊C4—24no—
496C22⋊C4—22no—
497C22⋊C4—44no—
498C22⋊C4—42no—
499C42—24no—
500C42—24no—
501C42—21no—
502C42—21no—
503C23—22no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—21no—
508C23—22no—
509C23—22no—
510C23—21no—
511C23—21no—
512C23—22no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23C31×#12012yes—
518C23C22×D4×C3111yescharacteristic
519Q8—24no—
520Q8—24no—
521Q8—48no—
522Q8—42no—
523Q8—42no—
524Q8—84no—
525D4—24no—
526D4—44no—
527D4—41no—
528D4—41no—
529D4—84no—
530D4—84no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—48no—
546C2×C4—48no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4C31×#12012yes—
560C2×C4C31×#13712yes—
561C2×C4C22×D4×C3111yescharacteristic
562C2×C4C22×D4×C3111yescharacteristic
563C2×C4C2×#41×C3112yes—
564C2×C4C31×H(5,𝔽2)12yes—
565C8—42no—
566C8—42no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—42no—
571C22—42no—
572C22—41no—
573C22—42no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—82no—
581C22—82no—
582C22C2×C31×#12011yescharacteristic
583C22C31×#54612yes—
584C22C2×C31×#13711yescharacteristic
585C22C31×#57511yescharacteristic
586C22C31×#57712yes—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—44no—
591C4—42no—
592C4—41no—
593C4—42no—
594C4—42no—
595C4—82no—
596C4C31×#52511yescharacteristic
597C4C31×#53511yescharacteristic
598C4C31×#54612yes—
599C2—42no—
600C2—81no—
601C2—82no—
602C2C31×#240411yescharacteristic
603C2C31×#300711yescharacteristic
604C2C31×#300911yescharacteristic
605C2C31×#332112yes—
606C2C31×#332912yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#555C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#448C2semidirect
3. C2×C31×#419C2semidirect
4. C31×#2409C2semidirect
5. C31×#2024C2semidirect
6. C31×#2000C2semidirect
7. C31×#1895C2semidirect
8. C31×#1877C2semidirect
9. C31×#1873C2semidirect
10. C31×#1870C2semidirect
11. C31×#1825C2semidirect
199. #23977C31direct (N × H)
265. C2×#448C2×C31semidirect
266. C2×#419C2×C31semidirect
267. #2409C2×C31semidirect
268. #2024C2×C31semidirect
269. #2000C2×C31semidirect
270. #1895C2×C31semidirect
271. #1877C2×C31semidirect
272. #1873C2×C31semidirect
273. #1870C2×C31semidirect
274. #1825C2×C31semidirect
420. C31#23977direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5552
C2×C31×#4482
C2×C31×#4192
C31×#24092
C31×#20242
C31×#20002
C31×#18952
C31×#18772
C31×#18732
C31×#18702
C31×#18252
#2397731