Finite Group Databasebeta

← C31×#24066 #21480825

Subgroups — C31×#24066 #21480825

Order 7936.

1176 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C211yesmaximal, characteristic
2C2×C31×#483C211yesmaximal, characteristic, complemented
3C2×C31×#480C211yesmaximal, characteristic
4C2×C31×#389C211yesmaximal, characteristic, complemented
5C31×#2059C212yesmaximal, complemented
6C31×#2042C212yesmaximal, complemented
7C31×#1874C211yesmaximal, characteristic
8C31×#1872C211yesmaximal, characteristic, complemented
9C31×#1864C212yesmaximal, complemented
10C31×#1863C212yesmaximal, complemented
11C31×#1817C211yesmaximal, characteristic, complemented
12C31×#529—24no—
13C31×#529—24no—
14C2×C31×#126—21no—
15C2×C31×#125C2211yescharacteristic
16C2×C31×#124C2211yescharacteristic
17C2×C31×#123—21no—
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×D4×C31—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C2×C31×#117—21no—
24C22×C4⋊C4×C31—21no—
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C42×C31C2211yescharacteristic
28C31×#483—24no—
29C31×#480—24no—
30C2×C31×#107C2212yes—
31C2×C31×#106C2212yes—
32C2×C31×#103C2212yes—
33C2×C31×#103C2212yes—
34C2×C31×#102C2212yes—
35C2×C31×#102C2212yes—
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C31×#389—21no—
39C31×#389—21no—
40C31×#389C2212yes—
41C31×#389C2212yes—
42C2×C31×#95—21no—
43C31×#340C2212yes—
44C31×#340C2212yes—
45C31×#336C2212yes—
46C31×#336C2212yes—
47C22×Q8×C31C2311yescharacteristic
48C22×D4×C31—21no—
49C22×D4×C31C2311yescharacteristic
50C23×C4×C31—21no—
51C23×C4×C31—21no—
52C23×C4×C31—21no—
53C23×C4×C31D411yescharacteristic
54C23×C4×C31D411yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C22×C8×C31C2312yes—
57C22×C8×C31C2312yes—
58C31×#126—28no—
59C31×#125—22no—
60C31×#125—22no—
61C31×#124—22no—
62C31×#124—22no—
63C31×#123—28no—
64C31×C22⋊Q8—22no—
65C31×C22⋊Q8D414yes—
66C31×#121—22no—
67C31×#121D414yes—
68C4×Q8×C31—22no—
69C4×Q8×C31—22no—
70C4×D4×C31—28no—
71C4×D4×C31—22no—
72C4×D4×C31—22no—
73C31×#117—28no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—44no—
86C2×C4⋊C4×C31C2312yes—
87C2×C4⋊C4×C31C2311yescharacteristic
88C2×C4⋊C4×C31C2311yescharacteristic
89C2×C4⋊C4×C31C2312yes—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—21no—
92C2×C22⋊C4×C31—21no—
93C2×C22⋊C4×C31—21no—
94C2×C22⋊C4×C31—21no—
95C2×C42×C31—22no—
96C2×C42×C31—22no—
97C2×C42×C31—21no—
98C2×C42×C31D411yescharacteristic
99C2×C42×C31D411yescharacteristic
100C2×C42×C31C2311yescharacteristic
101C2×C42×C31C2311yescharacteristic
102C31×#107—24no—
103C31×#106—24no—
104C31×#103—24no—
105C31×#103—24no—
106C31×#102—24no—
107C31×#102—24no—
108C31×C22⋊C8—22no—
109C31×C22⋊C8—22no—
110C31×#95—22no—
111C31×#95—22no—
112C24×C31—21no—
113C24×C31C2×D411yescharacteristic
114C2×Q8×C31—21no—
115C2×Q8×C31—22no—
116C2×Q8×C31—22no—
117C2×Q8×C31C2×D412yes—
118C2×D4×C31—24no—
119C2×D4×C31—21no—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—42no—
123C2×D4×C31—42no—
124C2×D4×C31C2×D412yes—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—24no—
128C22×C4×C31—24no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—41no—
140C22×C4×C31—42no—
141C22×C4×C31—42no—
142C22×C4×C31—42no—
143C22×C4×C31—42no—
144C22×C4×C31—42no—
145C22×C4×C31—42no—
146C22×C4×C31—42no—
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D412yes—
152C22×C4×C31C2×D412yes—
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2411yescharacteristic
155C2×C8×C31—22no—
156C2×C8×C31—22no—
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C4⋊C4×C31—24no—
162C4⋊C4×C31—24no—
163C4⋊C4×C31—24no—
164C4⋊C4×C31—24no—
165C4⋊C4×C31—24no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—44no—
172C4⋊C4×C31—44no—
173C4⋊C4×C31—42no—
174C4⋊C4×C31C2×D412yes—
175C4⋊C4×C31C2×D412yes—
176C4⋊C4×C31#4114yes—
177C22⋊C4×C31—24no—
178C22⋊C4×C31—24no—
179C22⋊C4×C31—24no—
180C22⋊C4×C31—24no—
181C22⋊C4×C31—24no—
182C42×C31—24no—
183C42×C31—22no—
184C42×C31—22no—
185C42×C31—21no—
186C42×C31—21no—
187C42×C31—21no—
188C42×C31—21no—
189#24066C3111yesmaximal, characteristic, direct product factor, Sylow
190C23×C31—21no—
191C23×C31—21no—
192C23×C31—21no—
193C23×C31—21no—
194C23×C31—22no—
195C23×C31—41no—
196C23×C31—41no—
197C23×C31—41no—
198C23×C31—41no—
199C23×C31—41no—
200C23×C31—41no—
201C23×C31#12012yes—
202C23×C31#13512yes—
203C23×C31AGL(1,ℤ/8)12yes—
204C23×C31C22×D411yescharacteristic
205Q8×C31—24no—
206Q8×C31—42no—
207D4×C31—24no—
208D4×C31—48no—
209D4×C31—42no—
210C2×C4×C31—21no—
211C2×C4×C31—21no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—24no—
215C2×C4×C31—24no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—21no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—24no—
223C2×C4×C31—21no—
224C2×C4×C31—21no—
225C2×C4×C31—21no—
226C2×C4×C31—21no—
227C2×C4×C31—21no—
228C2×C4×C31—21no—
229C2×C4×C31—44no—
230C2×C4×C31—48no—
231C2×C4×C31—48no—
232C2×C4×C31—41no—
233C2×C4×C31—41no—
234C2×C4×C31—41no—
235C2×C4×C31—42no—
236C2×C4×C31—41no—
237C2×C4×C31—41no—
238C2×C4×C31—42no—
239C2×C4×C31—41no—
240C2×C4×C31—44no—
241C2×C4×C31—42no—
242C2×C4×C31—42no—
243C2×C4×C31—42no—
244C2×C4×C31—84no—
245C2×C4×C31#12012yes—
246C2×C4×C31#13712yes—
247C2×C4×C31C22×D411yescharacteristic
248C2×C4×C31C22×D411yescharacteristic
249C2×C4×C31C2×#4112yes—
250C2×C4×C312−1+412yes—
251C8×C31—42no—
252C8×C31—42no—
253C2×#529C2×C3111yescharacteristic
254C2×#483C2×C3111yescharacteristic, complemented
255C2×#480C2×C3111yescharacteristic
256C2×#389C2×C3111yescharacteristic, complemented
257#2059C2×C3112yescomplemented
258#2042C2×C3112yescomplemented
259#1874C2×C3111yescharacteristic
260#1872C2×C3111yescharacteristic, complemented
261#1864C2×C3112yescomplemented
262#1863C2×C3112yescomplemented
263#1817C2×C3111yescharacteristic, complemented
264C22×C31—22no—
265C22×C31—22no—
266C22×C31—22no—
267C22×C31—22no—
268C22×C31—22no—
269C22×C31—22no—
270C22×C31—42no—
271C22×C31—42no—
272C22×C31—42no—
273C22×C31—81no—
274C22×C31—81no—
275C22×C31—81no—
276C22×C31—81no—
277C22×C31#44914yes—
278C22×C31C2×#12011yescharacteristic
279C22×C31#52511yescharacteristic
280C22×C31#53611yescharacteristic
281C22×C31C2×#13511yescharacteristic
282C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C31C2×#13711yescharacteristic
284C22×C31#57511yescharacteristic
285C4×C31—22no—
286C4×C31—22no—
287C4×C31—44no—
288C4×C31—42no—
289C4×C31—41no—
290C4×C31—41no—
291C4×C31—42no—
292C4×C31—41no—
293C4×C31—42no—
294C4×C31—82no—
295C4×C31#54712yes—
296C4×C31#54712yes—
297#529—24no—
298#529—24no—
299C2×#126—21no—
300C2×#125C22×C3111yescharacteristic
301C2×#124C22×C3111yescharacteristic
302C2×#123—21no—
303C2×C22⋊Q8C22×C3111yescharacteristic
304C2×#121C22×C3111yescharacteristic
305C2×C4×Q8C22×C3111yescharacteristic
306C2×C4×D4—21no—
307C2×C4×D4C22×C3111yescharacteristic
308C2×#117—21no—
309C22×C4⋊C4—21no—
310C22×C4⋊C4C22×C3111yescharacteristic
311C22×C4⋊C4C22×C3111yescharacteristic
312C22×C42C22×C3111yescharacteristic
313#483—24no—
314#480—24no—
315C2×#107C22×C3112yes—
316C2×#106C22×C3112yes—
317C2×#103C22×C3112yes—
318C2×#103C22×C3112yes—
319C2×#102C22×C3112yes—
320C2×#102C22×C3112yes—
321C2×C22⋊C8C22×C3111yescharacteristic
322C2×C22⋊C8C22×C3111yescharacteristic
323#389—21no—
324#389—21no—
325#389C22×C3112yes—
326#389C22×C3112yes—
327C2×#95—21no—
328#340C22×C3112yes—
329#340C22×C3112yes—
330#336C22×C3112yes—
331#336C22×C3112yes—
332C2×C31—24no—
333C2×C31—82no—
334C2×C31#240611yescharacteristic
335C2×C31C2×#44911yescharacteristic
336C2×C31#300711yescharacteristic
337C2×C31#310811yescharacteristic
338C2×C31#311411yescharacteristic
339C2×C31#323211yescharacteristic
340C2×C31#323811yescharacteristic
341C22×Q8C23×C3111yescharacteristic
342C22×D4—21no—
343C22×D4C23×C3111yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4D4×C3111yescharacteristic
348C23×C4D4×C3111yescharacteristic
349C23×C4C23×C3111yescharacteristic
350C22×C8C23×C3112yes—
351C22×C8C23×C3112yes—
352#126—28no—
353#125—22no—
354#125—22no—
355#124—22no—
356#124—22no—
357#123—28no—
358C22⋊Q8—22no—
359C22⋊Q8D4×C3114yes—
360#121—22no—
361#121D4×C3114yes—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×D4—28no—
365C4×D4—22no—
366C4×D4—22no—
367#117—28no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4C23×C3112yes—
381C2×C4⋊C4C23×C3111yescharacteristic
382C2×C4⋊C4C23×C3111yescharacteristic
383C2×C4⋊C4C23×C3112yes—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C42—21no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42D4×C3111yescharacteristic
393C2×C42D4×C3111yescharacteristic
394C2×C42C23×C3111yescharacteristic
395C2×C42C23×C3111yescharacteristic
396#107—24no—
397#106—24no—
398#103—24no—
399#103—24no—
400#102—24no—
401#102—24no—
402C22⋊C8—22no—
403C22⋊C8—22no—
404#95—22no—
405#95—22no—
406C31#2406611yescharacteristic, direct product factor, Sylow
407C24—21no—
408C24C2×D4×C3111yescharacteristic
409C2×Q8—21no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8C2×D4×C3112yes—
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4C2×D4×C3112yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—41no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4C2×D4×C3111yescharacteristic
443C22×C4C2×D4×C3111yescharacteristic
444C22×C4C2×D4×C3111yescharacteristic
445C22×C4C2×D4×C3111yescharacteristic
446C22×C4C2×D4×C3112yes—
447C22×C4C2×D4×C3112yes—
448C22×C4C2×D4×C3111yescharacteristic
449C22×C4C24×C3111yescharacteristic
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—44no—
467C4⋊C4—44no—
468C4⋊C4—42no—
469C4⋊C4C2×D4×C3112yes—
470C4⋊C4C2×D4×C3112yes—
471C4⋊C4#41×C3114yes—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C42—24no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23C31×#12012yes—
496C23C31×#13512yes—
497C23C31×AGL(1,ℤ/8)12yes—
498C23C22×D4×C3111yescharacteristic
499Q8—24no—
500Q8—42no—
501D4—24no—
502D4—48no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—48no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—84no—
539C2×C4C31×#12012yes—
540C2×C4C31×#13712yes—
541C2×C4C22×D4×C3111yescharacteristic
542C2×C4C22×D4×C3111yescharacteristic
543C2×C4C2×#41×C3112yes—
544C2×C4C31×2−1+412yes—
545C8—42no—
546C8—42no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22C31×#44914yes—
561C22C2×C31×#12011yescharacteristic
562C22C31×#52511yescharacteristic
563C22C31×#53611yescharacteristic
564C22C2×C31×#13511yescharacteristic
565C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
566C22C2×C31×#13711yescharacteristic
567C22C31×#57511yescharacteristic
568C4—22no—
569C4—22no—
570C4—44no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—42no—
575C4—41no—
576C4—42no—
577C4—82no—
578C4C31×#54712yes—
579C4C31×#54712yes—
580C2—24no—
581C2—82no—
582C2C31×#240611yescharacteristic
583C2C2×C31×#44911yescharacteristic
584C2C31×#300711yescharacteristic
585C2C31×#310811yescharacteristic
586C2C31×#311411yescharacteristic
587C2C31×#323211yescharacteristic
588C2C31×#323811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#483C2semidirect
4. C2×C31×#389C2semidirect
5. C31×#2059C2semidirect
6. C31×#2042C2semidirect
8. C31×#1872C2semidirect
9. C31×#1864C2semidirect
10. C31×#1863C2semidirect
11. C31×#1817C2semidirect
189. #24066C31direct (N × H)
254. C2×#483C2×C31semidirect
256. C2×#389C2×C31semidirect
257. #2059C2×C31semidirect
258. #2042C2×C31semidirect
260. #1872C2×C31semidirect
261. #1864C2×C31semidirect
262. #1863C2×C31semidirect
263. #1817C2×C31semidirect
406. C31#24066direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5292
C2×C31×#4832
C2×C31×#4802
C2×C31×#3892
C31×#20592
C31×#20422
C31×#18742
C31×#18722
C31×#18642
C31×#18632
C31×#18172
#2406631