Finite Group Databasebeta

← C31×#15232 #21471991

Subgroups — C31×#15232 #21471991

Order 7936.

1166 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C2×C31×#382C211yesmaximal, characteristic
3C31×#1445C212yesmaximal
4C31×#1443C212yesmaximal
5C31×#1443C212yesmaximal
6C31×#1442C212yesmaximal
7C31×C4⋊#95C211yesmaximal, characteristic
8C31×C4⋊#95C211yesmaximal, characteristic
9C31×C4⋊#95C211yesmaximal, characteristic
10C31×C4⋊#95C211yesmaximal, characteristic
11C4×C31×#95C211yesmaximal, characteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C42×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2211yescharacteristic
20C31×#389—24no—
21C31×#382—24no—
22C2×C31×#95C2211yescharacteristic
23C2×C31×#95C2211yescharacteristic
24C2×C31×#95C2211yescharacteristic
25C2×C31×#95C2211yescharacteristic
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C23×C4×C31C2312yes—
38C23×C4×C31C2312yes—
39C23×C4×C31C2312yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2311yescharacteristic
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2311yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C2×C4⋊C4×C31—22no—
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—42no—
62C2×C4⋊C4×C31D414yes—
63C2×C42×C31—22no—
64C2×C42×C31—22no—
65C2×C42×C31—22no—
66C2×C42×C31—22no—
67C2×C42×C31—22no—
68C2×C42×C31—22no—
69C2×C42×C31—22no—
70C2×C42×C31—22no—
71C2×C42×C31Q814yes—
72C31×#95—24no—
73C31×#95—24no—
74C31×#95—24no—
75C31×#95—22no—
76C31×#95—22no—
77C31×#95—22no—
78C31×#95—22no—
79C31×#95—24no—
80C31×#95—24no—
81C31×#95—24no—
82C31×#95—42no—
83C31×#95—42no—
84C31×#95—42no—
85C31×#95—42no—
86C31×#95—42no—
87C24×C31C2411yescharacteristic
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—21no—
96C22×C4×C31—21no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—21no—
100C22×C4×C31—22no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
105C22×C4×C31—21no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—21no—
117C22×C4×C31—21no—
118C22×C4×C31—21no—
119C22×C4×C31—21no—
120C22×C4×C31—21no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—22no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31C2×D414yes—
152C22×C4×C31C2×D412yes—
153C22×C4×C31C2×Q812yes—
154C22×C4×C31C2×Q812yes—
155C22×C4×C31C2×Q812yes—
156C22×C4×C31#4112yes—
157C22×C4×C31#4112yes—
158C22×C4×C31#4112yes—
159C22×C4×C31#4112yes—
160C22×C4×C31#4112yes—
161C22×C4×C31#4112yes—
162C22×C4×C31#4112yes—
163C22×C4×C31#4112yes—
164C22×C4×C31#4112yes—
165C4⋊C4×C31—28no—
166C4⋊C4×C31—48no—
167C4⋊C4×C31—44no—
168C4⋊C4×C31—44no—
169C4⋊C4×C31—44no—
170C42×C31—28no—
171C42×C31—44no—
172C42×C31—44no—
173#15232C3111yesmaximal, characteristic, direct product factor, Sylow
174C23×C31C22×D411yescharacteristic
175C23×C31C22×Q811yescharacteristic
176C23×C31C2×#4111yescharacteristic
177C23×C31C2×#4111yescharacteristic
178C23×C31C2×#4111yescharacteristic
179C23×C31C2×#4111yescharacteristic
180C23×C31C2×#4111yescharacteristic
181C23×C31C2×#4111yescharacteristic
182C23×C31C2×#4111yescharacteristic
183C23×C31C2×#4111yescharacteristic
184C23×C31C2×#4111yescharacteristic
185C23×C31H(5,𝔽2)11yescharacteristic
186C23×C31H(5,𝔽2)11yescharacteristic
187C23×C312−1+411yescharacteristic
188C23×C312−1+411yescharacteristic
189C2×C4×C31—22no—
190C2×C4×C31—22no—
191C2×C4×C31—24no—
192C2×C4×C31—22no—
193C2×C4×C31—22no—
194C2×C4×C31—22no—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—24no—
202C2×C4×C31—24no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—41no—
211C2×C4×C31—41no—
212C2×C4×C31—41no—
213C2×C4×C31—41no—
214C2×C4×C31—42no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—42no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—41no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—41no—
230C2×C4×C31—41no—
231C2×C4×C31—41no—
232C2×C4×C31—41no—
233C2×C4×C31—41no—
234C2×C4×C31—41no—
235C2×C4×C31—42no—
236C2×C4×C31—41no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—42no—
241C2×C4×C31—42no—
242C2×C4×C31—42no—
243C2×C4×C31—42no—
244C2×C4×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—42no—
258C2×C4×C31—42no—
259C2×C4×C31C22⋊Q814yes—
260C2×C4×C31#12314yes—
261C2×C4×C31#12414yes—
262C2×C4×C31#12514yes—
263C2×C4×C31#12514yes—
264C2×C4×C31#12614yes—
265C2×C4×C31#12614yes—
266C2×#389C2×C3111yescharacteristic
267C2×#382C2×C3111yescharacteristic
268#1445C2×C3112yes—
269#1443C2×C3112yes—
270#1443C2×C3112yes—
271#1442C2×C3112yes—
272C4⋊#95C2×C3111yescharacteristic
273C4⋊#95C2×C3111yescharacteristic
274C4⋊#95C2×C3111yescharacteristic
275C4⋊#95C2×C3111yescharacteristic
276C4×#95C2×C3111yescharacteristic
277C22×C31C2×C22⋊Q811yescharacteristic
278C22×C31C2×#12311yescharacteristic
279C22×C31C2×#12411yescharacteristic
280C22×C31C2×#12511yescharacteristic
281C22×C31C2×#12511yescharacteristic
282C22×C31C2×#12611yescharacteristic
283C22×C31C2×#12611yescharacteristic
284C22×C31#52911yescharacteristic
285C22×C31#52911yescharacteristic
286C22×C31#52911yescharacteristic
287C22×C31#52911yescharacteristic
288C22×C31#53311yescharacteristic
289C22×C31#53311yescharacteristic
290C22×C31#54011yescharacteristic
291C22×C31#54111yescharacteristic
292C22×C31#54211yescharacteristic
293C22×C31#54211yescharacteristic
294C22×C31#54411yescharacteristic
295C22×C31#54411yescharacteristic
296C22×C31#54611yescharacteristic
297C22×C31#54711yescharacteristic
298C22×C31#54811yescharacteristic
299C22×C31#55011yescharacteristic
300C22×C31#55211yescharacteristic
301C22×C31#55211yescharacteristic
302C22×C31#55211yescharacteristic
303C22×C31#55311yescharacteristic
304C22×C31#55311yescharacteristic
305C22×C31#55311yescharacteristic
306C22×C31#55511yescharacteristic
307C22×C31#55611yescharacteristic
308C22×C31#55611yescharacteristic
309C22×C31#55611yescharacteristic
310C22×C31#55911yescharacteristic
311C22×C31#55911yescharacteristic
312C4×C31—42no—
313C4×C31—42no—
314C4×C31—44no—
315C4×C31—42no—
316C4×C31—42no—
317C4×C31—42no—
318C4×C31—42no—
319C4×C31—82no—
320C4×C31—82no—
321C4×C31—82no—
322C4×C31#40018yes—
323C22×C4⋊C4C22×C3111yescharacteristic
324C22×C4⋊C4C22×C3111yescharacteristic
325C22×C4⋊C4C22×C3111yescharacteristic
326C22×C4⋊C4C22×C3112yes—
327C22×C4⋊C4C22×C3111yescharacteristic
328C22×C42C22×C3111yescharacteristic
329C22×C42C22×C3111yescharacteristic
330C22×C42C22×C3111yescharacteristic
331#389—24no—
332#382—24no—
333C2×#95C22×C3111yescharacteristic
334C2×#95C22×C3111yescharacteristic
335C2×#95C22×C3111yescharacteristic
336C2×#95C22×C3111yescharacteristic
337C2×#95C22×C3112yes—
338C2×#95C22×C3112yes—
339C2×#95C22×C3112yes—
340C2×#95C22×C3112yes—
341C2×#95C22×C3112yes—
342C2×#95C22×C3112yes—
343C2×#95C22×C3112yes—
344C2×#95C22×C3112yes—
345C2×#95C22×C3112yes—
346C2×#95C22×C3112yes—
347C2×#95C22×C3112yes—
348C2×C31C2×#40011yescharacteristic
349C2×C31#243911yescharacteristic
350C2×C31#244111yescharacteristic
351C2×C31#244711yescharacteristic
352C2×C31#244811yescharacteristic
353C2×C31#248911yescharacteristic
354C2×C31#249011yescharacteristic
355C2×C31#249411yescharacteristic
356C2×C31#249511yescharacteristic
357C2×C31#251311yescharacteristic
358C2×C31#251411yescharacteristic
359C2×C31#257011yescharacteristic
360C2×C31#257011yescharacteristic
361C2×C31#264711yescharacteristic
362C2×C31#286411yescharacteristic
363C23×C4C23×C3112yes—
364C23×C4C23×C3112yes—
365C23×C4C23×C3112yes—
366C23×C4C23×C3112yes—
367C23×C4C23×C3111yescharacteristic
368C23×C4C23×C3111yescharacteristic
369C23×C4C23×C3111yescharacteristic
370C23×C4C23×C3111yescharacteristic
371C23×C4C23×C3111yescharacteristic
372C23×C4C23×C3111yescharacteristic
373C23×C4C23×C3111yescharacteristic
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4D4×C3114yes—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42Q8×C3114yes—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—22no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413C31#1523211yescharacteristic, direct product factor, Sylow
414C24C24×C3111yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4C2×D4×C3114yes—
479C22×C4C2×D4×C3112yes—
480C22×C4C2×Q8×C3112yes—
481C22×C4C2×Q8×C3112yes—
482C22×C4C2×Q8×C3112yes—
483C22×C4#41×C3112yes—
484C22×C4#41×C3112yes—
485C22×C4#41×C3112yes—
486C22×C4#41×C3112yes—
487C22×C4#41×C3112yes—
488C22×C4#41×C3112yes—
489C22×C4#41×C3112yes—
490C22×C4#41×C3112yes—
491C22×C4#41×C3112yes—
492C4⋊C4—28no—
493C4⋊C4—48no—
494C4⋊C4—44no—
495C4⋊C4—44no—
496C4⋊C4—44no—
497C42—28no—
498C42—44no—
499C42—44no—
500C23C22×D4×C3111yescharacteristic
501C23C22×Q8×C3111yescharacteristic
502C23C2×#41×C3111yescharacteristic
503C23C2×#41×C3111yescharacteristic
504C23C2×#41×C3111yescharacteristic
505C23C2×#41×C3111yescharacteristic
506C23C2×#41×C3111yescharacteristic
507C23C2×#41×C3111yescharacteristic
508C23C2×#41×C3111yescharacteristic
509C23C2×#41×C3111yescharacteristic
510C23C2×#41×C3111yescharacteristic
511C23C31×H(5,𝔽2)11yescharacteristic
512C23C31×H(5,𝔽2)11yescharacteristic
513C23C31×2−1+411yescharacteristic
514C23C31×2−1+411yescharacteristic
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4C31×C22⋊Q814yes—
586C2×C4C31×#12314yes—
587C2×C4C31×#12414yes—
588C2×C4C31×#12514yes—
589C2×C4C31×#12514yes—
590C2×C4C31×#12614yes—
591C2×C4C31×#12614yes—
592C22C2×C31×C22⋊Q811yescharacteristic
593C22C2×C31×#12311yescharacteristic
594C22C2×C31×#12411yescharacteristic
595C22C2×C31×#12511yescharacteristic
596C22C2×C31×#12511yescharacteristic
597C22C2×C31×#12611yescharacteristic
598C22C2×C31×#12611yescharacteristic
599C22C31×#52911yescharacteristic
600C22C31×#52911yescharacteristic
601C22C31×#52911yescharacteristic
602C22C31×#52911yescharacteristic
603C22C31×#53311yescharacteristic
604C22C31×#53311yescharacteristic
605C22C31×#54011yescharacteristic
606C22C31×#54111yescharacteristic
607C22C31×#54211yescharacteristic
608C22C31×#54211yescharacteristic
609C22C31×#54411yescharacteristic
610C22C31×#54411yescharacteristic
611C22C31×#54611yescharacteristic
612C22C31×#54711yescharacteristic
613C22C31×#54811yescharacteristic
614C22C31×#55011yescharacteristic
615C22C31×#55211yescharacteristic
616C22C31×#55211yescharacteristic
617C22C31×#55211yescharacteristic
618C22C31×#55311yescharacteristic
619C22C31×#55311yescharacteristic
620C22C31×#55311yescharacteristic
621C22C31×#55511yescharacteristic
622C22C31×#55611yescharacteristic
623C22C31×#55611yescharacteristic
624C22C31×#55611yescharacteristic
625C22C31×#55911yescharacteristic
626C22C31×#55911yescharacteristic
627C4—42no—
628C4—42no—
629C4—44no—
630C4—42no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—82no—
635C4—82no—
636C4—82no—
637C4C31×#40018yes—
638C2C2×C31×#40011yescharacteristic
639C2C31×#243911yescharacteristic
640C2C31×#244111yescharacteristic
641C2C31×#244711yescharacteristic
642C2C31×#244811yescharacteristic
643C2C31×#248911yescharacteristic
644C2C31×#249011yescharacteristic
645C2C31×#249411yescharacteristic
646C2C31×#249511yescharacteristic
647C2C31×#251311yescharacteristic
648C2C31×#251411yescharacteristic
649C2C31×#257011yescharacteristic
650C2C31×#257011yescharacteristic
651C2C31×#264711yescharacteristic
652C2C31×#286411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
173. #15232C31direct (N × H)
413. C31#15232direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C2×C31×#3822
C31×#14452
C31×#14432
C31×#14422
C31×C4⋊#952
C4×C31×#952
#1523231