Finite Group Databasebeta

← C31×#24186 #21480945

Subgroups — C31×#24186 #21480945

Order 7936.

1214 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#559C211yesmaximal, characteristic, complemented
2C2×C31×#459C211yesmaximal, characteristic
3C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
4C31×#2538C211yesmaximal, characteristic, complemented
5C31×#2042C212yesmaximal, complemented
6C31×#2012C212yesmaximal, complemented
7C31×#1984C211yesmaximal, characteristic, complemented
8C31×#1957C211yesmaximal, characteristic, complemented
9C31×#1879C212yesmaximal, complemented
10C31×#1864C212yesmaximal, complemented
11C31×#1803C211yesmaximal, characteristic, complemented
12C22×SD16×C31C2211yescharacteristic
13C22×D8×C31C2212yes—
14C31×#559—24no—
15C31×#559—24no—
16C2×C31×#127C2211yescharacteristic
17C2×C31×#124—21no—
18C2×C31×#124C2212yes—
19C2×C31×#123—22no—
20C2×C31×C22⋊Q8—21no—
21C2×C4×Q8×C31C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×D4×C31—21no—
24C2×C4×D4×C31C2212yes—
25C2×C4×D4×C31C2211yescharacteristic
26C31×#459—24no—
27C4×SD16×C31—24no—
28C2×C31×#106C2211yescharacteristic
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2212yes—
32C2×C31×#102C2212yes—
33C2×C31×#102C2212yes—
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2212yes—
36C2×C4×C8×C31C2211yescharacteristic
37C31×#396—22no—
38C31×#390C2212yes—
39C31×#389C2212yes—
40C31×#384C2211yescharacteristic
41C31×#380—21no—
42C31×#340C2212yes—
43C31×#336C2212yes—
44C31×#336C2212yes—
45C22×Q8×C31D411yescharacteristic
46C22×Q8×C31C2311yescharacteristic
47C22×D4×C31—21no—
48C22×D4×C31—21no—
49C22×D4×C31C2312yes—
50C22×D4×C31C2311yescharacteristic
51C23×C4×C31—22no—
52C23×C4×C31—21no—
53C2×SD16×C31—22no—
54C2×SD16×C31—22no—
55C2×SD16×C31—22no—
56C2×D8×C31—24no—
57C2×D8×C31—24no—
58C2×D8×C31—42no—
59C22×C8×C31C2311yescharacteristic
60C22×C8×C31C2312yes—
61C22×C8×C31C2311yescharacteristic
62C31×#127—22no—
63C31×#127D414yes—
64C31×#124—28no—
65C31×#124—24no—
66C31×#124—24no—
67C31×#123—216no—
68C31×C22⋊Q8—44no—
69C4×Q8×C31—22no—
70C4×Q8×C31—22no—
71C4×Q8×C31—22no—
72C4×Q8×C31D414yes—
73C4×D4×C31—28no—
74C4×D4×C31—24no—
75C4×D4×C31—24no—
76C4×D4×C31—22no—
77C4×D4×C31—22no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—21no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31D412yes—
83C2×C4⋊C4×C31D411yescharacteristic
84C2×C4⋊C4×C31C2311yescharacteristic
85C2×C4⋊C4×C31C2312yes—
86C2×C4⋊C4×C31C2311yescharacteristic
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C42×C31—21no—
94C2×C42×C31C2312yes—
95C2×C42×C31C2311yescharacteristic
96C31×#106—22no—
97C31×C4⋊C8—22no—
98C31×#103—22no—
99C31×#103—42no—
100C31×#102—24no—
101C31×#102—24no—
102C31×#102—22no—
103C31×#102—42no—
104C4×C8×C31—22no—
105C31×#95—22no—
106C24×C31—21no—
107C24×C31—22no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—22no—
111C2×Q8×C31—21no—
112C2×Q8×C31—21no—
113C2×Q8×C31—21no—
114C2×Q8×C31—21no—
115C2×Q8×C31—21no—
116C2×Q8×C31C2×D412yes—
117C2×D4×C31—24no—
118C2×D4×C31—24no—
119C2×D4×C31—21no—
120C2×D4×C31—21no—
121C2×D4×C31—22no—
122C2×D4×C31—22no—
123C2×D4×C31—22no—
124C2×D4×C31—21no—
125C2×D4×C31—22no—
126C2×D4×C31—21no—
127C2×D4×C31—22no—
128C2×D4×C31—21no—
129C2×D4×C31—42no—
130C2×D4×C31—42no—
131C2×D4×C31—81no—
132C2×D4×C31—81no—
133C2×D4×C31C2×D414yes—
134C2×D4×C31#4112yes—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—28no—
138C22×C4×C31—21no—
139C22×C4×C31—22no—
140C22×C4×C31—42no—
141C22×C4×C31—42no—
142C22×C4×C31—42no—
143C22×C4×C31—82no—
144C22×C4×C31—82no—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2411yescharacteristic
150SD16×C31—28no—
151D8×C31—48no—
152C2×C8×C31—21no—
153C2×C8×C31—21no—
154C2×C8×C31—21no—
155C2×C8×C31—22no—
156C2×C8×C31—22no—
157C2×C8×C31—21no—
158C2×C8×C31—22no—
159C2×C8×C31—21no—
160C2×C8×C31#4112yes—
161C4⋊C4×C31—24no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—24no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—44no—
170C4⋊C4×C31—42no—
171C4⋊C4×C31—81no—
172C4⋊C4×C31C2×D412yes—
173C22⋊C4×C31—28no—
174C22⋊C4×C31—28no—
175C22⋊C4×C31—28no—
176C22⋊C4×C31—44no—
177C22⋊C4×C31—42no—
178C22⋊C4×C31—82no—
179C42×C31—24no—
180C42×C31—22no—
181C42×C31—22no—
182C42×C31C2×D412yes—
183C42×C31C2×D412yes—
184#24186C3111yesmaximal, characteristic, direct product factor, Sylow
185C23×C31—24no—
186C23×C31—22no—
187C23×C31—41no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—41no—
191C23×C31—41no—
192C23×C31—42no—
193C23×C31—41no—
194C23×C31—42no—
195C23×C31—41no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—41no—
199C23×C31C22×D411yescharacteristic
200Q8×C31—22no—
201Q8×C31—22no—
202Q8×C31—41no—
203Q8×C31—41no—
204Q8×C31—44no—
205D4×C31—22no—
206D4×C31—22no—
207D4×C31—24no—
208D4×C31—24no—
209D4×C31—42no—
210D4×C31—41no—
211D4×C31—42no—
212D4×C31—41no—
213D4×C31—48no—
214D4×C31—84no—
215C2×C4×C31—21no—
216C2×C4×C31—21no—
217C2×C4×C31—22no—
218C2×C4×C31—22no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—41no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—41no—
230C2×C4×C31—42no—
231C2×C4×C31—41no—
232C2×C4×C31—42no—
233C2×C4×C31—41no—
234C2×C4×C31—42no—
235C2×C4×C31—88no—
236C2×C4×C31—84no—
237C2×C4×C31#12012yes—
238C2×C4×C31#12012yes—
239C2×C4×C31#13512yes—
240C2×C4×C31AGL(1,ℤ/8)12yes—
241C2×C4×C31C22×D411yescharacteristic
242C2×C4×C31C22×D411yescharacteristic
243C2×C4×C31C2×#4111yescharacteristic
244C2×C4×C31C2×#4111yescharacteristic
245C2×C4×C31H(5,𝔽2)11yescharacteristic
246C2×C4×C312−1+411yescharacteristic
247C8×C31—22no—
248C8×C31—41no—
249C8×C31—42no—
250C2×#559C2×C3111yescharacteristic, complemented
251C2×#459C2×C3111yescharacteristic
252C2×C4×SD16C2×C3111yescharacteristic, complemented
253#2538C2×C3111yescharacteristic, complemented
254#2042C2×C3112yescomplemented
255#2012C2×C3112yescomplemented
256#1984C2×C3111yescharacteristic, complemented
257#1957C2×C3111yescharacteristic, complemented
258#1879C2×C3112yescomplemented
259#1864C2×C3112yescomplemented
260#1803C2×C3111yescharacteristic, complemented
261C22×C31—42no—
262C22×C31—42no—
263C22×C31—42no—
264C22×C31—44no—
265C22×C31—44no—
266C22×C31—44no—
267C22×C31—82no—
268C22×C31—82no—
269C22×C31—81no—
270C22×C31—82no—
271C22×C31—81no—
272C22×C31—82no—
273C22×C31—81no—
274C22×C31—81no—
275C22×C31C2×#12011yescharacteristic
276C22×C31#54811yescharacteristic
277C22×C31#55011yescharacteristic
278C22×C31C2×#13511yescharacteristic
279C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
280C22×C31#57611yescharacteristic
281C22×C31#57711yescharacteristic
282C4×C31—22no—
283C4×C31—42no—
284C4×C31—42no—
285C4×C31—42no—
286C4×C31—42no—
287C4×C31—82no—
288C4×C31—81no—
289C4×C31#44914yes—
290C4×C31#52511yescharacteristic
291C4×C31#53711yescharacteristic
292C4×C31#54611yescharacteristic
293C4×C31#54711yescharacteristic
294C22×SD16C22×C3111yescharacteristic
295C22×D8C22×C3112yes—
296#559—24no—
297#559—24no—
298C2×#127C22×C3111yescharacteristic
299C2×#124—21no—
300C2×#124C22×C3112yes—
301C2×#123—22no—
302C2×C22⋊Q8—21no—
303C2×C4×Q8C22×C3111yescharacteristic
304C2×C4×Q8C22×C3111yescharacteristic
305C2×C4×D4—21no—
306C2×C4×D4C22×C3112yes—
307C2×C4×D4C22×C3111yescharacteristic
308#459—24no—
309C4×SD16—24no—
310C2×#106C22×C3111yescharacteristic
311C2×C4⋊C8C22×C3111yescharacteristic
312C2×#103C22×C3111yescharacteristic
313C2×#103C22×C3112yes—
314C2×#102C22×C3112yes—
315C2×#102C22×C3112yes—
316C2×#102C22×C3111yescharacteristic
317C2×#102C22×C3112yes—
318C2×C4×C8C22×C3111yescharacteristic
319#396—22no—
320#390C22×C3112yes—
321#389C22×C3112yes—
322#384C22×C3111yescharacteristic
323#380—21no—
324#340C22×C3112yes—
325#336C22×C3112yes—
326#336C22×C3112yes—
327C2×C31—82no—
328C2×C31—84no—
329C2×C31#240711yescharacteristic
330C2×C31C2×#44911yescharacteristic
331C2×C31#301211yescharacteristic
332C2×C31#336111yescharacteristic
333C2×C31#337311yescharacteristic
334C2×C31#339411yescharacteristic
335C2×C31#339911yescharacteristic
336C22×Q8D4×C3111yescharacteristic
337C22×Q8C23×C3111yescharacteristic
338C22×D4—21no—
339C22×D4—21no—
340C22×D4C23×C3112yes—
341C22×D4C23×C3111yescharacteristic
342C23×C4—22no—
343C23×C4—21no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—22no—
347C2×D8—24no—
348C2×D8—24no—
349C2×D8—42no—
350C22×C8C23×C3112yes—
351C22×C8C23×C3111yescharacteristic
352C22×C8C23×C3111yescharacteristic
353#127—22no—
354#127D4×C3114yes—
355#124—28no—
356#124—24no—
357#124—24no—
358#123—216no—
359C22⋊Q8—44no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8D4×C3114yes—
364C4×D4—28no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—22no—
368C4×D4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C3111yescharacteristic
374C2×C4⋊C4D4×C3112yes—
375C2×C4⋊C4C23×C3111yescharacteristic
376C2×C4⋊C4C23×C3112yes—
377C2×C4⋊C4C23×C3111yescharacteristic
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C42—21no—
385C2×C42C23×C3112yes—
386C2×C42C23×C3111yescharacteristic
387#106—22no—
388C4⋊C8—22no—
389#103—22no—
390#103—42no—
391#102—24no—
392#102—24no—
393#102—22no—
394#102—42no—
395C4×C8—22no—
396#95—22no—
397C31#2418611yescharacteristic, direct product factor, Sylow
398C24—21no—
399C24—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C2×D4×C3112yes—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—81no—
424C2×D4—81no—
425C2×D4C2×D4×C3114yes—
426C2×D4#41×C3112yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—28no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—82no—
436C22×C4—82no—
437C22×C4C2×D4×C3112yes—
438C22×C4C2×D4×C3112yes—
439C22×C4C2×D4×C3111yescharacteristic
440C22×C4C2×D4×C3111yescharacteristic
441C22×C4C24×C3111yescharacteristic
442SD16—28no—
443D8—48no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—21no—
452C2×C8#41×C3112yes—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—44no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4C2×D4×C3112yes—
465C22⋊C4—28no—
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—44no—
469C22⋊C4—42no—
470C22⋊C4—82no—
471C42—24no—
472C42—22no—
473C42—22no—
474C42C2×D4×C3112yes—
475C42C2×D4×C3112yes—
476C23—24no—
477C23—22no—
478C23—41no—
479C23—42no—
480C23—42no—
481C23—41no—
482C23—41no—
483C23—42no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—42no—
488C23—42no—
489C23—41no—
490C23C22×D4×C3111yescharacteristic
491Q8—22no—
492Q8—22no—
493Q8—44no—
494Q8—41no—
495Q8—41no—
496D4—22no—
497D4—22no—
498D4—24no—
499D4—24no—
500D4—48no—
501D4—42no—
502D4—41no—
503D4—42no—
504D4—41no—
505D4—84no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—88no—
527C2×C4—84no—
528C2×C4C31×#12012yes—
529C2×C4C31×#12012yes—
530C2×C4C31×#13512yes—
531C2×C4C31×AGL(1,ℤ/8)12yes—
532C2×C4C22×D4×C3111yescharacteristic
533C2×C4C22×D4×C3111yescharacteristic
534C2×C4C2×#41×C3111yescharacteristic
535C2×C4C2×#41×C3111yescharacteristic
536C2×C4C31×H(5,𝔽2)11yescharacteristic
537C2×C4C31×2−1+411yescharacteristic
538C8—22no—
539C8—41no—
540C8—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—44no—
545C22—44no—
546C22—44no—
547C22—82no—
548C22—82no—
549C22—81no—
550C22—82no—
551C22—81no—
552C22—82no—
553C22—81no—
554C22—81no—
555C22C2×C31×#12011yescharacteristic
556C22C31×#54811yescharacteristic
557C22C31×#55011yescharacteristic
558C22C2×C31×#13511yescharacteristic
559C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
560C22C31×#57611yescharacteristic
561C22C31×#57711yescharacteristic
562C4—22no—
563C4—42no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—82no—
568C4—81no—
569C4C31×#44914yes—
570C4C31×#52511yescharacteristic
571C4C31×#53711yescharacteristic
572C4C31×#54611yescharacteristic
573C4C31×#54711yescharacteristic
574C2—82no—
575C2—84no—
576C2C31×#240711yescharacteristic
577C2C2×C31×#44911yescharacteristic
578C2C31×#301211yescharacteristic
579C2C31×#336111yescharacteristic
580C2C31×#337311yescharacteristic
581C2C31×#339411yescharacteristic
582C2C31×#339911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#459C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#559C2semidirect
3. C2×C4×SD16×C31C2semidirect
4. C31×#2538C2semidirect
5. C31×#2042C2semidirect
6. C31×#2012C2semidirect
7. C31×#1984C2semidirect
8. C31×#1957C2semidirect
9. C31×#1879C2semidirect
10. C31×#1864C2semidirect
11. C31×#1803C2semidirect
184. #24186C31direct (N × H)
250. C2×#559C2×C31semidirect
252. C2×C4×SD16C2×C31semidirect
253. #2538C2×C31semidirect
254. #2042C2×C31semidirect
255. #2012C2×C31semidirect
256. #1984C2×C31semidirect
257. #1957C2×C31semidirect
258. #1879C2×C31semidirect
259. #1864C2×C31semidirect
260. #1803C2×C31semidirect
397. C31#24186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5592
C2×C31×#4592
C2×C4×SD16×C312
C31×#25382
C31×#20422
C31×#20122
C31×#19842
C31×#19572
C31×#18792
C31×#18642
C31×#18032
#2418631