Finite Group Databasebeta

← C31×#24145 #21480904

Subgroups — C31×#24145 #21480904

Order 7936.

1038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3509C211yesmaximal, characteristic, complemented
2C31×#3077C211yesmaximal, characteristic, complemented
3C4×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C31×#2547C211yesmaximal, characteristic, complemented
5C31×#2038C212yesmaximal, complemented
6C31×#2003C212yesmaximal
7C31×#1986C211yesmaximal, characteristic, complemented
8C31×#1966C211yesmaximal, characteristic, complemented
9C31×#1888C212yesmaximal, complemented
10C31×#1857C212yesmaximal, complemented
11C31×#1806C211yesmaximal, characteristic, complemented
12C2×C31×AGL(1,ℤ/8)C2211yescharacteristic
13C31×#557—21no—
14C31×#557—21no—
15C31×#556—21no—
16C31×#556—21no—
17C31×#552—22no—
18C31×#552—22no—
19C31×#541—22no—
20C31×#536C2212yes—
21C31×#533—21no—
22C31×#533—21no—
23C31×#533C2211yescharacteristic
24C2×C31×C4⋊Q8C2211yescharacteristic
25C2×C31×#124C2212yes—
26C31×#519C2212yes—
27C4×#41×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C31×#478—22no—
30C31×#476—21no—
31C31×#474—21no—
32C31×#442—21no—
33C31×#440—21no—
34C4×SD16×C31—21no—
35C4×D8×C31—21no—
36C31×#428C2212yes—
37C31×#428C2211yescharacteristic
38C31×#423C2211yescharacteristic
39C2×C31×#104C2212yes—
40C31×#418C2212yes—
41C31×#418C2211yescharacteristic
42C31×#417C2211yescharacteristic
43C2×C31×#101C2212yes—
44C2×C31×#101C2212yes—
45C4×M16×C31C2211yescharacteristic
46C31×#397—22no—
47C31×#391C2212yes—
48C31×#380—22no—
49C4×C4⋊C4×C31C2211yescharacteristic
50C31×#339C2212yes—
51C31×#339C2212yes—
52C31×#339C2212yes—
53C2×#41×C31C2311yescharacteristic
54C22×Q8×C31C2312yes—
55C22×D4×C31C2311yescharacteristic
56C23×C4×C31—21no—
57C31×AGL(1,ℤ/8)—22no—
58C31×AGL(1,ℤ/8)—22no—
59C2×SD16×C31—21no—
60C2×D8×C31—21no—
61C2×M16×C31C2311yescharacteristic
62C2×M16×C31C2312yes—
63C2×M16×C31C2311yescharacteristic
64C31×C4⋊Q8—22no—
65C31×C4⋊Q8—21no—
66C31×C4⋊Q8—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8—21no—
69C31×C4⋊Q8D411yescharacteristic
70C31×C4⋊Q8D411yescharacteristic
71C31×#126—24no—
72C31×#126—24no—
73C31×#125—22no—
74C31×#125—22no—
75C31×#125—24no—
76C31×#125—24no—
77C31×#125D412yes—
78C31×#124—22no—
79C31×#124—24no—
80C31×#124—42no—
81C31×#123—24no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8—21no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—22no—
88C4×Q8×C31—22no—
89C4×Q8×C31—22no—
90C4×Q8×C31—22no—
91C4×Q8×C31—22no—
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×Q8×C31—21no—
95C4×Q8×C31—21no—
96C4×Q8×C31D411yescharacteristic
97C4×Q8×C31D411yescharacteristic
98C4×D4×C31—21no—
99C4×D4×C31—21no—
100C4×D4×C31—21no—
101C4×D4×C31—21no—
102C4×D4×C31—21no—
103C4×D4×C31—21no—
104C4×D4×C31D411yescharacteristic
105C4×D4×C31D411yescharacteristic
106C31×#117—22no—
107C31×#117—22no—
108C31×#117—24no—
109C31×#117—21no—
110C31×#117C2311yescharacteristic
111C31×#117C2312yes—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31D412yes—
114C2×C4⋊C4×C31D412yes—
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—24no—
118C2×C42×C31—21no—
119C2×C42×C31C2312yes—
120C2×C42×C31C2311yescharacteristic
121C31×#107—21no—
122C31×#107—22no—
123C31×#106—21no—
124C31×#106—22no—
125C31×C4⋊C8—21no—
126C31×C4⋊C8—21no—
127C31×#104—42no—
128C31×#103—21no—
129C31×#102—21no—
130C31×#102—21no—
131C31×#102—21no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#101—24no—
135C31×#101—42no—
136C31×#97—21no—
137C4×C8×C31—21no—
138C31×#95—21no—
139C31×#95—24no—
140C24×C31—21no—
141#41×C31—21no—
142#41×C31—21no—
143#41×C31—21no—
144#41×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—22no—
148C2×Q8×C31—22no—
149C2×Q8×C31—22no—
150C2×Q8×C31—22no—
151C2×Q8×C31—22no—
152C2×Q8×C31—22no—
153C2×Q8×C31C2×D411yescharacteristic
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31C2×D411yescharacteristic
161C2×D4×C31#4112yes—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—22no—
167C22×C4×C31—44no—
168C22×C4×C31—41no—
169C22×C4×C31—41no—
170C22×C4×C31C2×D414yes—
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2411yescharacteristic
174SD16×C31—24no—
175D8×C31—24no—
176M16×C31—21no—
177M16×C31—22no—
178M16×C31—21no—
179M16×C31—22no—
180M16×C31—21no—
181M16×C31#4112yes—
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—22no—
185C4⋊C4×C31—24no—
186C4⋊C4×C31—24no—
187C4⋊C4×C31—24no—
188C4⋊C4×C31—24no—
189C4⋊C4×C31—22no—
190C4⋊C4×C31—22no—
191C4⋊C4×C31—22no—
192C4⋊C4×C31—22no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31C2×D411yescharacteristic
203C4⋊C4×C31C2×D412yes—
204C4⋊C4×C31C2×D411yescharacteristic
205C4⋊C4×C31C2×D412yes—
206C22⋊C4×C31—24no—
207C22⋊C4×C31—24no—
208C22⋊C4×C31—21no—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—21no—
211C22⋊C4×C31—21no—
212C22⋊C4×C31—48no—
213C22⋊C4×C31—41no—
214C22⋊C4×C31—41no—
215C42×C31—24no—
216C42×C31—24no—
217C42×C31—21no—
218C42×C31—21no—
219C42×C31—21no—
220C42×C31—22no—
221C42×C31—22no—
222C42×C31—22no—
223C42×C31C2×D411yescharacteristic
224C42×C31C2×D411yescharacteristic
225C42×C31C2×D411yescharacteristic
226C42×C31C2×D411yescharacteristic
227#24145C3111yesmaximal, characteristic, direct product factor, Sylow
228C23×C31—21no—
229C23×C31—22no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31C22×D411yescharacteristic
235Q8×C31—21no—
236Q8×C31—21no—
237Q8×C31—42no—
238Q8×C31—42no—
239Q8×C31—42no—
240Q8×C31—42no—
241Q8×C31—42no—
242Q8×C31—42no—
243D4×C31—21no—
244D4×C31—22no—
245D4×C31—21no—
246D4×C31—22no—
247D4×C31—41no—
248D4×C31—41no—
249D4×C31—41no—
250D4×C31—41no—
251C2×C4×C31—22no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—22no—
255C2×C4×C31—22no—
256C2×C4×C31—24no—
257C2×C4×C31—21no—
258C2×C4×C31—24no—
259C2×C4×C31—24no—
260C2×C4×C31—41no—
261C2×C4×C31—42no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—42no—
267C2×C4×C31—42no—
268C2×C4×C31—41no—
269C2×C4×C31—42no—
270C2×C4×C31—82no—
271C2×C4×C31—82no—
272C2×C4×C31#12011yescharacteristic
273C2×C4×C31#12011yescharacteristic
274C2×C4×C31#12011yescharacteristic
275C2×C4×C31#12011yescharacteristic
276C2×C4×C31C22×D411yescharacteristic
277C2×C4×C31C22×D411yescharacteristic
278C2×C4×C31C2×#4111yescharacteristic
279C2×C4×C31C2×#4111yescharacteristic
280C2×C4×C31H(5,𝔽2)11yescharacteristic
281C2×C4×C312−1+411yescharacteristic
282C8×C31—22no—
283C8×C31—41no—
284C8×C31—42no—
285#3509C2×C3111yescharacteristic, complemented
286#3077C2×C3111yescharacteristic, complemented
287C4×AGL(1,ℤ/8)C2×C3111yescharacteristic
288#2547C2×C3111yescharacteristic, complemented
289#2038C2×C3112yescomplemented
290#2003C2×C3112yes—
291#1986C2×C3111yescharacteristic, complemented
292#1966C2×C3111yescharacteristic, complemented
293#1888C2×C3112yescomplemented
294#1857C2×C3112yescomplemented
295#1806C2×C3111yescharacteristic, complemented
296C22×C31—21no—
297C22×C31—21no—
298C22×C31—44no—
299C22×C31—41no—
300C22×C31—42no—
301C22×C31—41no—
302C22×C31—41no—
303C22×C31—82no—
304C22×C31—81no—
305C22×C31—81no—
306C22×C31C2×#12011yescharacteristic
307C22×C31#54611yescharacteristic
308C22×C31#54711yescharacteristic
309C4×C31—21no—
310C4×C31—21no—
311C4×C31—21no—
312C4×C31—44no—
313C4×C31—41no—
314C4×C31—41no—
315C4×C31—42no—
316C4×C31—41no—
317C4×C31—42no—
318C4×C31—82no—
319C4×C31—81no—
320C4×C31#45412yes—
321C4×C31#52511yescharacteristic
322C4×C31#53711yescharacteristic
323C4×C31#54811yescharacteristic
324C4×C31#55011yescharacteristic
325C2×AGL(1,ℤ/8)C22×C3111yescharacteristic
326#557—21no—
327#557—21no—
328#556—21no—
329#556—21no—
330#552—22no—
331#552—22no—
332#541—22no—
333#536C22×C3112yes—
334#533—21no—
335#533—21no—
336#533C22×C3111yescharacteristic
337C2×C4⋊Q8C22×C3111yescharacteristic
338C2×#124C22×C3112yes—
339#519C22×C3112yes—
340C4×#41C22×C3111yescharacteristic
341C2×C4×D4C22×C3111yescharacteristic
342#478—22no—
343#476—21no—
344#474—21no—
345#442—21no—
346#440—21no—
347C4×SD16—21no—
348C4×D8—21no—
349#428C22×C3112yes—
350#428C22×C3111yescharacteristic
351#423C22×C3111yescharacteristic
352C2×#104C22×C3112yes—
353#418C22×C3112yes—
354#418C22×C3111yescharacteristic
355#417C22×C3111yescharacteristic
356C2×#101C22×C3112yes—
357C2×#101C22×C3112yes—
358C4×M16C22×C3111yescharacteristic
359#397—22no—
360#391C22×C3112yes—
361#380—22no—
362C4×C4⋊C4C22×C3111yescharacteristic
363#339C22×C3112yes—
364#339C22×C3112yes—
365#339C22×C3112yes—
366C2×C31—21no—
367C2×C31—21no—
368C2×C31—81no—
369C2×C31—82no—
370C2×C31#240711yescharacteristic
371C2×C31C2×#45411yescharacteristic
372C2×C31#302011yescharacteristic
373C2×#41C23×C3111yescharacteristic
374C22×Q8C23×C3112yes—
375C22×D4C23×C3111yescharacteristic
376C23×C4—21no—
377AGL(1,ℤ/8)—22no—
378AGL(1,ℤ/8)—22no—
379C2×SD16—21no—
380C2×D8—21no—
381C2×M16C23×C3111yescharacteristic
382C2×M16C23×C3112yes—
383C2×M16C23×C3111yescharacteristic
384C4⋊Q8—22no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8D4×C3111yescharacteristic
390C4⋊Q8D4×C3111yescharacteristic
391#126—24no—
392#126—24no—
393#125—22no—
394#125—22no—
395#125—24no—
396#125—24no—
397#125D4×C3112yes—
398#124—22no—
399#124—24no—
400#124—42no—
401#123—24no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8D4×C3111yescharacteristic
417C4×Q8D4×C3111yescharacteristic
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4D4×C3111yescharacteristic
425C4×D4D4×C3111yescharacteristic
426#117—22no—
427#117—22no—
428#117—24no—
429#117—21no—
430#117C23×C3111yescharacteristic
431#117C23×C3112yes—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C3112yes—
434C2×C4⋊C4D4×C3112yes—
435C2×C4⋊C4C23×C3111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—24no—
438C2×C42—21no—
439C2×C42C23×C3112yes—
440C2×C42C23×C3111yescharacteristic
441#107—21no—
442#107—22no—
443#106—21no—
444#106—22no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447#104—42no—
448#103—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102—22no—
453#102—22no—
454#101—24no—
455#101—42no—
456#97—21no—
457C4×C8—21no—
458#95—21no—
459#95—24no—
460C31#2414511yescharacteristic, direct product factor, Sylow
461C24—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465#41—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8C2×D4×C3111yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4C2×D4×C3111yescharacteristic
482C2×D4#41×C3112yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—44no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4C2×D4×C3114yes—
492C22×C4C2×D4×C3111yescharacteristic
493C22×C4C2×D4×C3111yescharacteristic
494C22×C4C24×C3111yescharacteristic
495SD16—24no—
496D8—24no—
497M16—21no—
498M16—22no—
499M16—21no—
500M16—22no—
501M16—21no—
502M16#41×C3112yes—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—22no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—24no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4C2×D4×C3111yescharacteristic
524C4⋊C4C2×D4×C3112yes—
525C4⋊C4C2×D4×C3111yescharacteristic
526C4⋊C4C2×D4×C3112yes—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—48no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C42—24no—
537C42—24no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—22no—
542C42—22no—
543C42—22no—
544C42C2×D4×C3111yescharacteristic
545C42C2×D4×C3111yescharacteristic
546C42C2×D4×C3111yescharacteristic
547C42C2×D4×C3111yescharacteristic
548C23—21no—
549C23—22no—
550C23—42no—
551C23—42no—
552C23—41no—
553C23—41no—
554C23C22×D4×C3111yescharacteristic
555Q8—21no—
556Q8—21no—
557Q8—42no—
558Q8—42no—
559Q8—42no—
560Q8—42no—
561Q8—42no—
562Q8—42no—
563D4—21no—
564D4—22no—
565D4—21no—
566D4—22no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4C31×#12011yescharacteristic
593C2×C4C31×#12011yescharacteristic
594C2×C4C31×#12011yescharacteristic
595C2×C4C31×#12011yescharacteristic
596C2×C4C22×D4×C3111yescharacteristic
597C2×C4C22×D4×C3111yescharacteristic
598C2×C4C2×#41×C3111yescharacteristic
599C2×C4C2×#41×C3111yescharacteristic
600C2×C4C31×H(5,𝔽2)11yescharacteristic
601C2×C4C31×2−1+411yescharacteristic
602C8—22no—
603C8—41no—
604C8—42no—
605C22—21no—
606C22—21no—
607C22—44no—
608C22—41no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—82no—
613C22—81no—
614C22—81no—
615C22C2×C31×#12011yescharacteristic
616C22C31×#54611yescharacteristic
617C22C31×#54711yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—44no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—42no—
627C4—82no—
628C4—81no—
629C4C31×#45412yes—
630C4C31×#52511yescharacteristic
631C4C31×#53711yescharacteristic
632C4C31×#54811yescharacteristic
633C4C31×#55011yescharacteristic
634C2—21no—
635C2—21no—
636C2—82no—
637C2—81no—
638C2C31×#240711yescharacteristic
639C2C2×C31×#45411yescharacteristic
640C2C31×#302011yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3509C2semidirect
2. C31×#3077C2semidirect
4. C31×#2547C2semidirect
5. C31×#2038C2semidirect
7. C31×#1986C2semidirect
8. C31×#1966C2semidirect
9. C31×#1888C2semidirect
10. C31×#1857C2semidirect
11. C31×#1806C2semidirect
227. #24145C31direct (N × H)
285. #3509C2×C31semidirect
286. #3077C2×C31semidirect
288. #2547C2×C31semidirect
289. #2038C2×C31semidirect
291. #1986C2×C31semidirect
292. #1966C2×C31semidirect
293. #1888C2×C31semidirect
294. #1857C2×C31semidirect
295. #1806C2×C31semidirect
460. C31#24145direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35092
C31×#30772
C4×C31×AGL(1,ℤ/8)2
C31×#25472
C31×#20382
C31×#20032
C31×#19862
C31×#19662
C31×#18882
C31×#18572
C31×#18062
#2414531