Finite Group Databasebeta

← C31×#13913 #21470672

Subgroups — C31×#13913 #21470672

Order 7936.

1586 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×#383C211yesmaximal, characteristic, complemented
2C2×C31×#381C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
4C31×#1442C212yesmaximal, complemented
5C31×#1439C212yesmaximal
6C31×#1437C212yesmaximal
7C31×C4⋊#95C211yesmaximal, characteristic, complemented
8C31×#1434C212yesmaximal, complemented
9C31×#1434C211yesmaximal, characteristic, complemented
10C31×C22⋊#95C211yesmaximal, characteristic
11C4×C31×#95C211yesmaximal, characteristic, complemented
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C22⋊C4×C31C2212yes—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2212yes—
19C22×C42×C31C2211yescharacteristic
20C22×C42×C31C2211yescharacteristic
21C31×#383—24no—
22C31×#381—24no—
23C4×C22⋊C4×C31C418yescomplemented
24C2×C31×#95C2211yescharacteristic
25C2×C31×#95C2212yes—
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C25×C31C2311yescharacteristic
39C23×C4×C31—24no—
40C23×C4×C31—22no—
41C23×C4×C31—22no—
42C23×C4×C31—42no—
43C23×C4×C31C2×C414yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—42no—
56C2×C4⋊C4×C31—42no—
57C2×C22⋊C4×C31—22no—
58C2×C22⋊C4×C31—24no—
59C2×C22⋊C4×C31—22no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—42no—
65C2×C22⋊C4×C31—42no—
66C2×C22⋊C4×C31C2×C414yes—
67C2×C22⋊C4×C31C2×C414yes—
68C2×C42×C31—22no—
69C2×C42×C31—22no—
70C2×C42×C31—24no—
71C2×C42×C31—24no—
72C2×C42×C31—42no—
73C2×C42×C31—42no—
74C2×C42×C31C2×C414yes—
75C2×C42×C31C2×C414yes—
76C31×#95—24no—
77C31×#95—22no—
78C31×#95—24no—
79C31×#95—24no—
80C31×#95—22no—
81C31×#95—24no—
82C31×#95—22no—
83C31×#95—24no—
84C31×#95—24no—
85C31×#95—42no—
86C31×#95—42no—
87C31×#95C2×C414yes—
88C31×#95C2×C414yes—
89C31×#95D414yes—
90C24×C31—21no—
91C24×C31—22no—
92C24×C31—21no—
93C24×C31—21no—
94C24×C31—22no—
95C24×C31—21no—
96C24×C31—21no—
97C24×C31—22no—
98C24×C31—21no—
99C24×C31C22×C412yes—
100C24×C31#4114yes—
101C24×C31C2411yescharacteristic
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—21no—
108C22×C4×C31—21no—
109C22×C4×C31—28no—
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—22no—
117C22×C4×C31—21no—
118C22×C4×C31—21no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
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—21no—
135C22×C4×C31—22no—
136C22×C4×C31—28no—
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×C31—44no—
152C22×C4×C31—48no—
153C22×C4×C31—48no—
154C22×C4×C31C22×C412yes—
155C22×C4×C31C22×C412yes—
156C22×C4×C31C22×C412yes—
157C22×C4×C31C22×C412yes—
158C22×C4×C31C22×C412yes—
159C22×C4×C31C22×C412yes—
160C22×C4×C31C2×D414yes—
161C22×C4×C31C2×D412yes—
162C22×C4×C31#4114yes—
163C22×C4×C31#4112yes—
164C22×C4×C31#4114yes—
165C22×C4×C31#4112yes—
166C22×C4×C31#4112yes—
167C4⋊C4×C31—48no—
168C22⋊C4×C31—28no—
169C22⋊C4×C31—28no—
170C22⋊C4×C31—48no—
171C22⋊C4×C31—48no—
172C42×C31—28no—
173C42×C31—44no—
174C42×C31—48no—
175#13913C3111yesmaximal, characteristic, direct product factor, Sylow
176C23×C31—22no—
177C23×C31—22no—
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—22no—
181C23×C31—22no—
182C23×C31—24no—
183C23×C31—24no—
184C23×C31—24no—
185C23×C31—24no—
186C23×C31—24no—
187C23×C31—24no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31—42no—
195C23×C31—42no—
196C23×C31—41no—
197C23×C31—41no—
198C23×C31#11714yes—
199C23×C31C23×C411yescharacteristic
200C23×C31C22×D411yescharacteristic
201C23×C31C2×#4112yes—
202C23×C31C2×#4112yes—
203C23×C31C2×#4111yescharacteristic
204C23×C31C2×#4111yescharacteristic
205C23×C31C2×#4111yescharacteristic
206C23×C31C2×#4112yes—
207C23×C31H(5,𝔽2)12yes—
208C23×C31H(5,𝔽2)11yescharacteristic
209C23×C312−1+411yescharacteristic
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—24no—
217C2×C4×C31—24no—
218C2×C4×C31—24no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—24no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—22no—
226C2×C4×C31—22no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—22no—
230C2×C4×C31—22no—
231C2×C4×C31—24no—
232C2×C4×C31—24no—
233C2×C4×C31—24no—
234C2×C4×C31—24no—
235C2×C4×C31—24no—
236C2×C4×C31—24no—
237C2×C4×C31—416no—
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—41no—
246C2×C4×C31—41no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—41no—
253C2×C4×C31—41no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—42no—
258C2×C4×C31—42no—
259C2×C4×C31—42no—
260C2×C4×C31—42no—
261C2×C4×C31—42no—
262C2×C4×C31—42no—
263C2×C4×C31—42no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—42no—
267C2×C4×C31—42no—
268C2×C4×C31#11714yes—
269C2×C4×C31#11714yes—
270C2×C4×C31C4×D414yes—
271C2×#383C2×C3111yescharacteristic, complemented
272C2×#381C2×C3111yescharacteristic
273C2×C4×C22⋊C4C2×C3111yescharacteristic
274#1442C2×C3112yescomplemented
275#1439C2×C3112yes—
276#1437C2×C3112yes—
277C4⋊#95C2×C3111yescharacteristic, complemented
278#1434C2×C3111yescharacteristic, complemented
279#1434C2×C3112yescomplemented
280C22⋊#95C2×C3111yescharacteristic
281C4×#95C2×C3111yescharacteristic, complemented
282C22×C31—24no—
283C22×C31—24no—
284C22×C31—24no—
285C22×C31—44no—
286C22×C31—44no—
287C22×C31—42no—
288C22×C31—42no—
289C22×C31—42no—
290C22×C31—42no—
291C22×C31—44no—
292C22×C31—44no—
293C22×C31C2×#11711yescharacteristic
294C22×C31C2×#11711yescharacteristic
295C22×C31C2×#11711yescharacteristic
296C22×C31C2×C4×D411yescharacteristic
297C22×C31C4×#4111yescharacteristic
298C22×C31#51811yescharacteristic
299C22×C31#52011yescharacteristic
300C22×C31#52912yes—
301C22×C31#52912yes—
302C22×C31#52912yes—
303C22×C31#53212yes—
304C22×C31#53812yes—
305C22×C31#53912yes—
306C22×C31#54612yes—
307C22×C31#54711yescharacteristic
308C22×C31#55011yescharacteristic
309C22×C31#55112yes—
310C22×C31#55112yes—
311C22×C31#55112yes—
312C22×C31#55212yes—
313C22×C31#55312yes—
314C22×C31#55511yescharacteristic
315C22×C31#55611yescharacteristic
316C4×C31—24no—
317C4×C31—24no—
318C4×C31—24no—
319C4×C31—44no—
320C4×C31—42no—
321C4×C31—42no—
322C4×C31—42no—
323C4×C31—44no—
324C4×C31—82no—
325C4×C31—82no—
326C24×C4C22×C3111yescharacteristic
327C22×C4⋊C4C22×C3112yes—
328C22×C22⋊C4C22×C3112yes—
329C22×C22⋊C4C22×C3112yes—
330C22×C22⋊C4C22×C3111yescharacteristic
331C22×C22⋊C4C22×C3111yescharacteristic
332C22×C42C22×C3112yes—
333C22×C42C22×C3111yescharacteristic
334C22×C42C22×C3111yescharacteristic
335#383—24no—
336#381—24no—
337C4×C22⋊C4C4×C3118yescomplemented
338C2×#95C22×C3111yescharacteristic
339C2×#95C22×C3112yes—
340C2×#95C22×C3111yescharacteristic
341C2×#95C22×C3112yes—
342C2×#95C22×C3112yes—
343C2×#95C22×C3111yescharacteristic
344C2×#95C22×C3112yes—
345C2×#95C22×C3112yes—
346C2×#95C22×C3112yes—
347C2×#95C22×C3112yes—
348C2×#95C22×C3112yes—
349C2×#95C22×C3111yescharacteristic
350C2×#95C22×C3111yescharacteristic
351C2×#95C22×C3111yescharacteristic
352C2×C31—44no—
353C2×C31#228311yescharacteristic
354C2×C31#229311yescharacteristic
355C2×C31#231811yescharacteristic
356C2×C31#234211yescharacteristic
357C2×C31#234311yescharacteristic
358C2×C31#235311yescharacteristic
359C2×C31#235411yescharacteristic
360C2×C31#255312yes—
361C2×C31#255412yes—
362C2×C31#257212yes—
363C2×C31#257312yes—
364C25C23×C3111yescharacteristic
365C23×C4—24no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—42no—
369C23×C4C2×C4×C3114yes—
370C23×C4C23×C3112yes—
371C23×C4C23×C3112yes—
372C23×C4C23×C3111yescharacteristic
373C23×C4C23×C3111yescharacteristic
374C23×C4C23×C3111yescharacteristic
375C23×C4C23×C3112yes—
376C23×C4C23×C3112yes—
377C23×C4C23×C3111yescharacteristic
378C23×C4C23×C3111yescharacteristic
379C23×C4C23×C3111yescharacteristic
380C2×C4⋊C4—24no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4C2×C4×C3114yes—
393C2×C22⋊C4C2×C4×C3114yes—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42C2×C4×C3114yes—
401C2×C42C2×C4×C3114yes—
402#95—24no—
403#95—22no—
404#95—24no—
405#95—24no—
406#95—22no—
407#95—24no—
408#95—22no—
409#95—24no—
410#95—24no—
411#95—42no—
412#95—42no—
413#95C2×C4×C3114yes—
414#95C2×C4×C3114yes—
415#95D4×C3114yes—
416C31#1391311yescharacteristic, direct product factor, Sylow
417C24—21no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—21no—
426C24C22×C4×C3112yes—
427C24#41×C3114yes—
428C24C24×C3111yescharacteristic
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—28no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—28no—
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×C4—44no—
479C22×C4—48no—
480C22×C4—48no—
481C22×C4C22×C4×C3112yes—
482C22×C4C22×C4×C3112yes—
483C22×C4C22×C4×C3112yes—
484C22×C4C22×C4×C3112yes—
485C22×C4C22×C4×C3112yes—
486C22×C4C22×C4×C3112yes—
487C22×C4C2×D4×C3114yes—
488C22×C4C2×D4×C3112yes—
489C22×C4#41×C3114yes—
490C22×C4#41×C3112yes—
491C22×C4#41×C3114yes—
492C22×C4#41×C3112yes—
493C22×C4#41×C3112yes—
494C4⋊C4—48no—
495C22⋊C4—28no—
496C22⋊C4—28no—
497C22⋊C4—48no—
498C22⋊C4—48no—
499C42—28no—
500C42—44no—
501C42—48no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—41no—
523C23—41no—
524C23C31×#11714yes—
525C23C23×C4×C3111yescharacteristic
526C23C22×D4×C3111yescharacteristic
527C23C2×#41×C3112yes—
528C23C2×#41×C3112yes—
529C23C2×#41×C3111yescharacteristic
530C23C2×#41×C3111yescharacteristic
531C23C2×#41×C3111yescharacteristic
532C23C2×#41×C3112yes—
533C23C31×H(5,𝔽2)12yes—
534C23C31×H(5,𝔽2)11yescharacteristic
535C23C31×2−1+411yescharacteristic
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—416no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4C31×#11714yes—
595C2×C4C31×#11714yes—
596C2×C4C4×D4×C3114yes—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—44no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—44no—
607C22—44no—
608C22C2×C31×#11711yescharacteristic
609C22C2×C31×#11711yescharacteristic
610C22C2×C31×#11711yescharacteristic
611C22C2×C4×D4×C3111yescharacteristic
612C22C4×#41×C3111yescharacteristic
613C22C31×#51811yescharacteristic
614C22C31×#52011yescharacteristic
615C22C31×#52912yes—
616C22C31×#52912yes—
617C22C31×#52912yes—
618C22C31×#53212yes—
619C22C31×#53812yes—
620C22C31×#53912yes—
621C22C31×#54612yes—
622C22C31×#54711yescharacteristic
623C22C31×#55011yescharacteristic
624C22C31×#55112yes—
625C22C31×#55112yes—
626C22C31×#55112yes—
627C22C31×#55212yes—
628C22C31×#55312yes—
629C22C31×#55511yescharacteristic
630C22C31×#55611yescharacteristic
631C4—24no—
632C4—24no—
633C4—24no—
634C4—44no—
635C4—42no—
636C4—42no—
637C4—42no—
638C4—44no—
639C4—82no—
640C4—82no—
641C2—44no—
642C2C31×#228311yescharacteristic
643C2C31×#229311yescharacteristic
644C2C31×#231811yescharacteristic
645C2C31×#234211yescharacteristic
646C2C31×#234311yescharacteristic
647C2C31×#235311yescharacteristic
648C2C31×#235411yescharacteristic
649C2C31×#255312yes—
650C2C31×#255412yes—
651C2C31×#257212yes—
652C2C31×#257312yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#383C2semidirect
4. C31×#1442C2semidirect
7. C31×C4⋊#95C2semidirect
8. C31×#1434C2semidirect
9. C31×#1434C2semidirect
11. C4×C31×#95C2semidirect
23. C4×C22⋊C4×C31C4semidirect
175. #13913C31direct (N × H)
271. C2×#383C2×C31semidirect
274. #1442C2×C31semidirect
277. C4⋊#95C2×C31semidirect
278. #1434C2×C31semidirect
279. #1434C2×C31semidirect
281. C4×#95C2×C31semidirect
337. C4×C22⋊C4C4×C31semidirect
416. C31#13913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3832
C2×C31×#3812
C2×C4×C22⋊C4×C312
C31×#14422
C31×#14392
C31×#14372
C31×C4⋊#952
C31×#14342
C31×C22⋊#952
C4×C31×#952
#1391331