Finite Group Databasebeta

← C31×#32959 #21489718

Subgroups — C31×#32959 #21489718

Order 7936.

1720 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic
2C2×C31×#478C212yesmaximal, complemented
3C31×#2851C211yesmaximal, characteristic, complemented
4C31×#1864C212yesmaximal, complemented
5C31×#1862C212yesmaximal, complemented
6C31×#1853C211yesmaximal, characteristic, complemented
7C31×#1852C211yesmaximal, characteristic, complemented
8C31×#1804C212yesmaximal, complemented
9C31×#1797C211yesmaximal, characteristic, complemented
10C31×#1786C211yesmaximal, characteristic
11C31×#1786C211yesmaximal, characteristic
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31—21no—
14C2×C31×#125C2211yescharacteristic, complemented
15C2×C4×D4×C31—28no—
16C2×C4×D4×C31—21no—
17C2×C4×D4×C31—21no—
18C2×C4×D4×C31C2212yes—
19C2×C4×D4×C31C2212yes—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31—21no—
22C22×C42×C31C2211yescharacteristic
23C31×#478—28no—
24C2×C31×#107C2212yescomplemented
25C2×C31×#106C2212yescomplemented
26C2×C31×C4⋊C8C2212yescomplemented
27C2×C31×#102C2212yes—
28C2×C31×#102C2212yes—
29C2×C31×#102C2212yes—
30C2×C31×#102C2212yes—
31C2×C31×C22⋊C8C2211yescharacteristic
32C2×C31×C22⋊C8C2211yescharacteristic
33C31×#389C2211yescharacteristic, complemented
34C31×#389C2211yescharacteristic, complemented
35C31×#387—21no—
36C31×#387—21no—
37C31×#385—21no—
38C31×#385—21no—
39C31×#382C2211yescharacteristic, complemented
40C31×#380C2211yescharacteristic
41C31×#380C2211yescharacteristic
42C31×#340C2212yescomplemented
43C31×#340C2212yescomplemented
44C31×#336C2212yescomplemented
45C25×C31—21no—
46C22×D4×C31—24no—
47C22×D4×C31—24no—
48C22×D4×C31—21no—
49C22×D4×C31—22no—
50C22×D4×C31Q814yes—
51C22×D4×C31C2312yes—
52C23×C4×C31—28no—
53C23×C4×C31—21no—
54C23×C4×C31—22no—
55C23×C4×C31—22no—
56C23×C4×C31—44no—
57C23×C4×C31—44no—
58C23×C4×C31D411yescharacteristic
59C23×C4×C31D411yescharacteristic
60C23×C4×C31C2311yescharacteristic
61C22×C8×C31C2312yes—
62C22×C8×C31C2312yes—
63C31×#125—24no—
64C4×D4×C31—28no—
65C4×D4×C31—28no—
66C4×D4×C31—24no—
67C4×D4×C31—24no—
68C4×D4×C31—24no—
69C4×D4×C31D418yes—
70C2×C4⋊C4×C31—21no—
71C2×C4⋊C4×C31—24no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31C2311yescharacteristic
77C2×C4⋊C4×C31C2311yescharacteristic
78C2×C4⋊C4×C31C2311yescharacteristic
79C2×C4⋊C4×C31C2311yescharacteristic
80C2×C4⋊C4×C31C2312yes—
81C2×C22⋊C4×C31—28no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—21no—
86C2×C42×C31—24no—
87C2×C42×C31D411yescharacteristic
88C2×C42×C31D411yescharacteristic
89C2×C42×C31C2311yescharacteristic
90C2×C42×C31C2311yescharacteristic
91C31×#107—24no—
92C31×#106—24no—
93C31×C4⋊C8—24no—
94C31×#102—24no—
95C31×#102—24no—
96C31×#102—24no—
97C31×#102—24no—
98C31×C22⋊C8—22no—
99C31×C22⋊C8—22no—
100C31×#95—21no—
101C31×#95—21no—
102C31×#95—21no—
103C31×#95—21no—
104C31×#95—21no—
105C31×#95—21no—
106C24×C31—24no—
107C24×C31—24no—
108C24×C31—24no—
109C24×C31—22no—
110C24×C31—42no—
111C24×C31—42no—
112C24×C31—42no—
113C24×C31—42no—
114C24×C31C2×D411yescharacteristic
115C2×D4×C31—24no—
116C2×D4×C31—24no—
117C2×D4×C31—216no—
118C2×D4×C31—216no—
119C2×D4×C31—24no—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—22no—
123C2×D4×C31C2×D414yes—
124C2×D4×C31C2×Q814yes—
125C2×D4×C31#4114yes—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—24no—
132C22×C4×C31—28no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—28no—
137C22×C4×C31—21no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—41no—
142C22×C4×C31—432no—
143C22×C4×C31—44no—
144C22×C4×C31—44no—
145C22×C4×C31—44no—
146C22×C4×C31—42no—
147C22×C4×C31—42no—
148C22×C4×C31—44no—
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×Q812yes—
155C22×C4×C31#4112yes—
156C22×C4×C31C2411yescharacteristic
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C4⋊C4×C31—24no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—42no—
170C4⋊C4×C31—42no—
171C4⋊C4×C31—42no—
172C4⋊C4×C31—42no—
173C4⋊C4×C31C2×D414yes—
174C22⋊C4×C31—28no—
175C22⋊C4×C31—28no—
176C22⋊C4×C31—42no—
177C22⋊C4×C31—42no—
178C42×C31—22no—
179C42×C31—22no—
180C42×C31—22no—
181C42×C31C2×D414yes—
182#32959C3111yesmaximal, characteristic, direct product factor, Sylow
183C23×C31—21no—
184C23×C31—21no—
185C23×C31—21no—
186C23×C31—21no—
187C23×C31—216no—
188C23×C31—24no—
189C23×C31—24no—
190C23×C31—24no—
191C23×C31—48no—
192C23×C31—48no—
193C23×C31—48no—
194C23×C31—48no—
195C23×C31—48no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31—42no—
200C23×C31—48no—
201C23×C31C22⋊Q812yes—
202C23×C31#13512yes—
203C23×C31AGL(1,ℤ/8)12yes—
204C23×C31C22×D411yescharacteristic
205D4×C31—216no—
206D4×C31—24no—
207D4×C31—24no—
208D4×C31—24no—
209D4×C31C22⋊Q818yes—
210C2×C4×C31—28no—
211C2×C4×C31—21no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—21no—
215C2×C4×C31—21no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—21no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—21no—
222C2×C4×C31—24no—
223C2×C4×C31—21no—
224C2×C4×C31—21no—
225C2×C4×C31—44no—
226C2×C4×C31—416no—
227C2×C4×C31—416no—
228C2×C4×C31—48no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—41no—
232C2×C4×C31—41no—
233C2×C4×C31—41no—
234C2×C4×C31—41no—
235C2×C4×C31—41no—
236C2×C4×C31—41no—
237C2×C4×C31—41no—
238C2×C4×C31—41no—
239C2×C4×C31—41no—
240C2×C4×C31—41no—
241C2×C4×C31—41no—
242C2×C4×C31—41no—
243C2×C4×C31#12012yes—
244C2×C4×C31#12012yes—
245C2×C4×C31C22⋊Q812yes—
246C2×C4×C31AGL(1,ℤ/8)12yes—
247C2×C4×C31C22×D412yes—
248C2×C4×C31C22×Q811yescharacteristic
249C2×C4×C31C2×#4112yes—
250C2×C4×C31C2×#4111yescharacteristic
251C8×C31—42no—
252C8×C31—42no—
253C22×C4×D4C2×C3111yescharacteristic
254C2×#478C2×C3112yescomplemented
255#2851C2×C3111yescharacteristic, complemented
256#1864C2×C3112yescomplemented
257#1862C2×C3112yescomplemented
258#1853C2×C3111yescharacteristic, complemented
259#1852C2×C3111yescharacteristic, complemented
260#1804C2×C3112yescomplemented
261#1797C2×C3111yescharacteristic, complemented
262#1786C2×C3111yescharacteristic
263#1786C2×C3111yescharacteristic
264C22×C31—22no—
265C22×C31—22no—
266C22×C31—22no—
267C22×C31—22no—
268C22×C31—22no—
269C22×C31—22no—
270C22×C31—28no—
271C22×C31—432no—
272C22×C31—44no—
273C22×C31—44no—
274C22×C31—44no—
275C22×C31—44no—
276C22×C31—44no—
277C22×C31—44no—
278C22×C31#47814yescomplemented
279C22×C31C2×#12011yescharacteristic
280C22×C31C2×C22⋊Q811yescharacteristic
281C22×C31#52511yescharacteristic
282C22×C31C2×#13511yescharacteristic
283C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C31#57511yescharacteristic
286C4×C31—22no—
287C4×C31—22no—
288C4×C31—22no—
289C4×C31—22no—
290C4×C31—41no—
291C4×C31—44no—
292C4×C31—81no—
293C4×C31—81no—
294C4×C31—81no—
295C4×C31—81no—
296C4×C31C2×C22⋊Q812yes—
297C4×C31#52512yes—
298C23×D4C22×C3111yescharacteristic
299C24×C4—21no—
300C2×#125C22×C3111yescharacteristic, complemented
301C2×C4×D4—28no—
302C2×C4×D4—21no—
303C2×C4×D4—21no—
304C2×C4×D4C22×C3112yes—
305C2×C4×D4C22×C3112yes—
306C22×C4⋊C4C22×C3111yescharacteristic
307C22×C22⋊C4—21no—
308C22×C42C22×C3111yescharacteristic
309#478—28no—
310C2×#107C22×C3112yescomplemented
311C2×#106C22×C3112yescomplemented
312C2×C4⋊C8C22×C3112yescomplemented
313C2×#102C22×C3112yes—
314C2×#102C22×C3112yes—
315C2×#102C22×C3112yes—
316C2×#102C22×C3112yes—
317C2×C22⋊C8C22×C3111yescharacteristic
318C2×C22⋊C8C22×C3111yescharacteristic
319#389C22×C3111yescharacteristic, complemented
320#389C22×C3111yescharacteristic, complemented
321#387—21no—
322#387—21no—
323#385—21no—
324#385—21no—
325#382C22×C3111yescharacteristic, complemented
326#380C22×C3111yescharacteristic
327#380C22×C3111yescharacteristic
328#340C22×C3112yescomplemented
329#340C22×C3112yescomplemented
330#336C22×C3112yescomplemented
331C2×C31—24no—
332C2×C31—48no—
333C2×C31#284811yescharacteristic
334C2×C31#300211yescharacteristic
335C2×C31#300311yescharacteristic
336C2×C31C2×#47811yescharacteristic
337C2×C31#307711yescharacteristic
338C2×C31#310511yescharacteristic
339C2×C31#311411yescharacteristic
340C25—21no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—21no—
344C22×D4—22no—
345C22×D4Q8×C3114yes—
346C22×D4C23×C3112yes—
347C23×C4—28no—
348C23×C4—21no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—44no—
352C23×C4—44no—
353C23×C4D4×C3111yescharacteristic
354C23×C4D4×C3111yescharacteristic
355C23×C4C23×C3111yescharacteristic
356C22×C8C23×C3112yes—
357C22×C8C23×C3112yes—
358#125—24no—
359C4×D4—28no—
360C4×D4—28no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4D4×C3118yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4C23×C3111yescharacteristic
372C2×C4⋊C4C23×C3111yescharacteristic
373C2×C4⋊C4C23×C3111yescharacteristic
374C2×C4⋊C4C23×C3111yescharacteristic
375C2×C4⋊C4C23×C3112yes—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—24no—
382C2×C42D4×C3111yescharacteristic
383C2×C42D4×C3111yescharacteristic
384C2×C42C23×C3111yescharacteristic
385C2×C42C23×C3111yescharacteristic
386#107—24no—
387#106—24no—
388C4⋊C8—24no—
389#102—24no—
390#102—24no—
391#102—24no—
392#102—24no—
393C22⋊C8—22no—
394C22⋊C8—22no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401C31#3295911yescharacteristic, direct product factor, Sylow
402C24—24no—
403C24—24no—
404C24—24no—
405C24—22no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24C2×D4×C3111yescharacteristic
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—216no—
414C2×D4—216no—
415C2×D4—24no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4C2×D4×C3114yes—
420C2×D4C2×Q8×C3114yes—
421C2×D4#41×C3114yes—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—28no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—28no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—432no—
439C22×C4—44no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—44no—
445C22×C4C2×D4×C3111yescharacteristic
446C22×C4C2×D4×C3111yescharacteristic
447C22×C4C2×D4×C3111yescharacteristic
448C22×C4C2×D4×C3111yescharacteristic
449C22×C4C2×D4×C3111yescharacteristic
450C22×C4C2×Q8×C3112yes—
451C22×C4#41×C3112yes—
452C22×C4C24×C3111yescharacteristic
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4C2×D4×C3114yes—
470C22⋊C4—28no—
471C22⋊C4—28no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C42—22no—
475C42—22no—
476C42—22no—
477C42C2×D4×C3114yes—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—216no—
483C23—24no—
484C23—24no—
485C23—24no—
486C23—48no—
487C23—48no—
488C23—48no—
489C23—48no—
490C23—48no—
491C23—48no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23C31×C22⋊Q812yes—
497C23C31×#13512yes—
498C23C31×AGL(1,ℤ/8)12yes—
499C23C22×D4×C3111yescharacteristic
500D4—216no—
501D4—24no—
502D4—24no—
503D4—24no—
504D4C31×C22⋊Q818yes—
505C2×C4—28no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—21no—
517C2×C4—24no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—44no—
521C2×C4—416no—
522C2×C4—416no—
523C2×C4—48no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4C31×#12012yes—
539C2×C4C31×#12012yes—
540C2×C4C31×C22⋊Q812yes—
541C2×C4C31×AGL(1,ℤ/8)12yes—
542C2×C4C22×D4×C3112yes—
543C2×C4C22×Q8×C3111yescharacteristic
544C2×C4C2×#41×C3112yes—
545C2×C4C2×#41×C3111yescharacteristic
546C8—42no—
547C8—42no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—28no—
555C22—432no—
556C22—44no—
557C22—44no—
558C22—44no—
559C22—44no—
560C22—44no—
561C22—44no—
562C22C31×#47814yescomplemented
563C22C2×C31×#12011yescharacteristic
564C22C2×C31×C22⋊Q811yescharacteristic
565C22C31×#52511yescharacteristic
566C22C2×C31×#13511yescharacteristic
567C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
568C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
569C22C31×#57511yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—41no—
575C4—44no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4C2×C31×C22⋊Q812yes—
581C4C31×#52512yes—
582C2—24no—
583C2—48no—
584C2C31×#284811yescharacteristic
585C2C31×#300211yescharacteristic
586C2C31×#300311yescharacteristic
587C2C2×C31×#47811yescharacteristic
588C2C31×#307711yescharacteristic
589C2C31×#310511yescharacteristic
590C2C31×#311411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
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×#478C2semidirect
3. C31×#2851C2semidirect
4. C31×#1864C2semidirect
5. C31×#1862C2semidirect
6. C31×#1853C2semidirect
7. C31×#1852C2semidirect
8. C31×#1804C2semidirect
9. C31×#1797C2semidirect
14. C2×C31×#125C22semidirect
24. C2×C31×#107C22semidirect
25. C2×C31×#106C22semidirect
26. C2×C31×C4⋊C8C22semidirect
33. C31×#389C22semidirect
34. C31×#389C22semidirect
39. C31×#382C22semidirect
42. C31×#340C22semidirect
43. C31×#340C22semidirect
44. C31×#336C22semidirect
182. #32959C31direct (N × H)
254. C2×#478C2×C31semidirect
255. #2851C2×C31semidirect
256. #1864C2×C31semidirect
257. #1862C2×C31semidirect
258. #1853C2×C31semidirect
259. #1852C2×C31semidirect
260. #1804C2×C31semidirect
261. #1797C2×C31semidirect
278. C22×C31#478semidirect
300. C2×#125C22×C31semidirect
310. C2×#107C22×C31semidirect
311. C2×#106C22×C31semidirect
312. C2×C4⋊C8C22×C31semidirect
319. #389C22×C31semidirect
320. #389C22×C31semidirect
325. #382C22×C31semidirect
328. #340C22×C31semidirect
329. #340C22×C31semidirect
330. #336C22×C31semidirect
401. C31#32959direct (N × H)
562. C22C31×#478semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C312
C2×C31×#4782
C31×#28512
C31×#18642
C31×#18622
C31×#18532
C31×#18522
C31×#18042
C31×#17972
C31×#17862
#3295931