Finite Group Databasebeta

← C31×#14628 #21471387

Subgroups — C31×#14628 #21471387

Order 7936.

1326 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#399C211yesmaximal, characteristic
2C2×C31×#389C211yesmaximal, characteristic, complemented
3C2×C31×#388C211yesmaximal, characteristic
4C31×#1445C211yesmaximal, characteristic, complemented
5C31×#1442C211yesmaximal, characteristic, complemented
6C31×#1441C212yesmaximal, complemented
7C31×#1441C212yesmaximal, complemented
8C31×#1440C212yesmaximal
9C31×#1439C211yesmaximal, characteristic
10C31×#1439C212yesmaximal
11C31×#1434C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C42×C31C2211yescharacteristic
23C31×#399C418yescomplemented
24C31×#389—24no—
25C31×#388—24no—
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2212yes—
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C25×C31C2311yescharacteristic
39C23×C4×C31C2312yes—
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2312yes—
43C23×C4×C31C2311yescharacteristic
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—42no—
55C2×C4⋊C4×C31—42no—
56C2×C4⋊C4×C31—42no—
57C2×C4⋊C4×C31—42no—
58C2×C4⋊C4×C31—42no—
59C2×C4⋊C4×C31—42no—
60C2×C4⋊C4×C31C2×C414yes—
61C2×C4⋊C4×C31C2×C418yes—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—42no—
67C2×C22⋊C4×C31—42no—
68C2×C22⋊C4×C31—42no—
69C2×C22⋊C4×C31—42no—
70C2×C22⋊C4×C31—42no—
71C2×C22⋊C4×C31—42no—
72C2×C22⋊C4×C31—42no—
73C2×C22⋊C4×C31C2×C414yes—
74C2×C22⋊C4×C31C2×C418yes—
75C2×C42×C31—42no—
76C2×C42×C31D414yes—
77C31×#95—22no—
78C31×#95—22no—
79C31×#95—24no—
80C31×#95—22no—
81C31×#95—42no—
82C31×#95—42no—
83C31×#95—42no—
84C31×#95—42no—
85C31×#95—42no—
86C31×#95—42no—
87C31×#95—42no—
88C31×#95C2×C414yes—
89C24×C31—21no—
90C24×C31—21no—
91C24×C31—22no—
92C24×C31—22no—
93C24×C31—22no—
94C24×C31—21no—
95C24×C31—21no—
96C24×C31—21no—
97C24×C31—22no—
98C24×C31—21no—
99C24×C31C22×C412yes—
100C24×C31C2411yescharacteristic
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—21no—
104C22×C4×C31—22no—
105C22×C4×C31—21no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—21no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—21no—
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—21no—
145C22×C4×C31—21no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—21no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31C22×C414yes—
152C22×C4×C31C22×C412yes—
153C22×C4×C31C22×C414yes—
154C22×C4×C31C22×C412yes—
155C22×C4×C31C2×D412yes—
156C22×C4×C31C2×D412yes—
157C22×C4×C31C2×D412yes—
158C22×C4×C31#4112yes—
159C4⋊C4×C31—28no—
160C4⋊C4×C31—48no—
161C4⋊C4×C31—44no—
162C4⋊C4×C31—44no—
163C4⋊C4×C31—48no—
164C22⋊C4×C31—28no—
165C22⋊C4×C31—48no—
166C22⋊C4×C31—44no—
167C22⋊C4×C31—44no—
168C22⋊C4×C31—48no—
169C42×C31—44no—
170#14628C3111yesmaximal, characteristic, direct product factor, Sylow
171C23×C31—22no—
172C23×C31—24no—
173C23×C31—22no—
174C23×C31—24no—
175C23×C31—22no—
176C23×C31—41no—
177C23×C31—41no—
178C23×C31—41no—
179C23×C31—41no—
180C23×C31—41no—
181C23×C31—41no—
182C23×C31—42no—
183C23×C31—42no—
184C23×C31—41no—
185C23×C31—41no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31—42no—
194C23×C31C23×C411yescharacteristic
195C23×C31C22×D411yescharacteristic
196C23×C31C2×#4111yescharacteristic
197C23×C31H(5,𝔽2)12yes—
198C23×C31H(5,𝔽2)12yes—
199C23×C31H(5,𝔽2)12yes—
200C23×C31H(5,𝔽2)11yescharacteristic
201C23×C312−1+411yescharacteristic
202C23×C312−1+411yescharacteristic
203C23×C312−1+412yes—
204C23×C312−1+411yescharacteristic
205C2×C4×C31—24no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—24no—
209C2×C4×C31—22no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—24no—
213C2×C4×C31—24no—
214C2×C4×C31—24no—
215C2×C4×C31—24no—
216C2×C4×C31—24no—
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—41no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—41no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—41no—
239C2×C4×C31—42no—
240C2×C4×C31—41no—
241C2×C4×C31—41no—
242C2×C4×C31—42no—
243C2×C4×C31—41no—
244C2×C4×C31—41no—
245C2×C4×C31—41no—
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×C31—42no—
260C2×C4×C31—42no—
261C2×C4×C31—42no—
262C2×C4×C31C4×D414yes—
263C2×#399C2×C3111yescharacteristic
264C2×#389C2×C3111yescharacteristic, complemented
265C2×#388C2×C3111yescharacteristic
266#1445C2×C3111yescharacteristic, complemented
267#1442C2×C3111yescharacteristic, complemented
268#1441C2×C3112yescomplemented
269#1441C2×C3112yescomplemented
270#1440C2×C3112yes—
271#1439C2×C3111yescharacteristic
272#1439C2×C3112yes—
273#1434C2×C3111yescharacteristic, complemented
274C22×C31—42no—
275C22×C31—42no—
276C22×C31—42no—
277C22×C31—44no—
278C22×C31—44no—
279C22×C31—81no—
280C22×C31—81no—
281C22×C31—81no—
282C22×C31—82no—
283C22×C31—82no—
284C22×C31—81no—
285C22×C31C2×C4×D411yescharacteristic
286C22×C31#51812yes—
287C22×C31#51911yescharacteristic
288C22×C31#52012yes—
289C22×C31#52011yescharacteristic
290C22×C31#53411yescharacteristic
291C22×C31#53511yescharacteristic
292C22×C31#53511yescharacteristic
293C22×C31#53611yescharacteristic
294C22×C31#53611yescharacteristic
295C22×C31#53711yescharacteristic
296C22×C31#53912yes—
297C22×C31#54012yes—
298C22×C31#54111yescharacteristic
299C22×C31#54211yescharacteristic
300C22×C31#56012yes—
301C22×C31#56212yes—
302C22×C31#56212yes—
303C22×C31#56212yes—
304C22×C31#56212yes—
305C22×C31#56312yes—
306C22×C31#56312yes—
307C22×C31#56312yes—
308C4×C31—24no—
309C4×C31—42no—
310C4×C31—42no—
311C4×C31—44no—
312C4×C31—44no—
313C4×C31—42no—
314C4×C31—81no—
315C4×C31—81no—
316C4×C31—82no—
317C4×C31—82no—
318C22×C4⋊C4C22×C3111yescharacteristic
319C22×C4⋊C4C22×C3112yes—
320C22×C4⋊C4C22×C3111yescharacteristic
321C22×C4⋊C4C22×C3111yescharacteristic
322C22×C4⋊C4C22×C3112yes—
323C22×C22⋊C4C22×C3111yescharacteristic
324C22×C22⋊C4C22×C3111yescharacteristic
325C22×C22⋊C4C22×C3111yescharacteristic
326C22×C22⋊C4C22×C3112yes—
327C22×C22⋊C4C22×C3112yes—
328C22×C42C22×C3111yescharacteristic
329#399C4×C3118yescomplemented
330#389—24no—
331#388—24no—
332C2×#95C22×C3111yescharacteristic
333C2×#95C22×C3112yes—
334C2×#95C22×C3111yescharacteristic
335C2×#95C22×C3111yescharacteristic
336C2×#95C22×C3112yes—
337C2×#95C22×C3112yes—
338C2×#95C22×C3112yes—
339C2×#95C22×C3112yes—
340C2×#95C22×C3112yes—
341C2×#95C22×C3112yes—
342C2×#95C22×C3112yes—
343C2×#95C22×C3111yescharacteristic
344C2×C31—82no—
345C2×C31#232211yescharacteristic
346C2×C31#232311yescharacteristic
347C2×C31#232811yescharacteristic
348C2×C31#237612yes—
349C2×C31#237812yes—
350C2×C31#281311yescharacteristic
351C2×C31#281611yescharacteristic
352C2×C31#282011yescharacteristic
353C2×C31#282111yescharacteristic
354C2×C31#283612yes—
355C2×C31#283712yes—
356C25C23×C3111yescharacteristic
357C23×C4C23×C3112yes—
358C23×C4C23×C3111yescharacteristic
359C23×C4C23×C3111yescharacteristic
360C23×C4C23×C3112yes—
361C23×C4C23×C3111yescharacteristic
362C23×C4C23×C3112yes—
363C23×C4C23×C3112yes—
364C23×C4C23×C3111yescharacteristic
365C23×C4C23×C3111yescharacteristic
366C23×C4C23×C3111yescharacteristic
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4C2×C4×C3114yes—
379C2×C4⋊C4C2×C4×C3118yes—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4C2×C4×C3114yes—
392C2×C22⋊C4C2×C4×C3118yes—
393C2×C42—42no—
394C2×C42D4×C3114yes—
395#95—22no—
396#95—22no—
397#95—24no—
398#95—22no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95C2×C4×C3114yes—
407C31#1462811yescharacteristic, direct product factor, Sylow
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—21no—
418C24C22×C4×C3112yes—
419C24C24×C3111yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
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—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4C22×C4×C3114yes—
471C22×C4C22×C4×C3112yes—
472C22×C4C22×C4×C3114yes—
473C22×C4C22×C4×C3112yes—
474C22×C4C2×D4×C3112yes—
475C22×C4C2×D4×C3112yes—
476C22×C4C2×D4×C3112yes—
477C22×C4#41×C3112yes—
478C4⋊C4—28no—
479C4⋊C4—48no—
480C4⋊C4—44no—
481C4⋊C4—44no—
482C4⋊C4—48no—
483C22⋊C4—28no—
484C22⋊C4—48no—
485C22⋊C4—44no—
486C22⋊C4—44no—
487C22⋊C4—48no—
488C42—44no—
489C23—22no—
490C23—24no—
491C23—22no—
492C23—24no—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—41no—
503C23—41no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23C23×C4×C3111yescharacteristic
513C23C22×D4×C3111yescharacteristic
514C23C2×#41×C3111yescharacteristic
515C23C31×H(5,𝔽2)12yes—
516C23C31×H(5,𝔽2)12yes—
517C23C31×H(5,𝔽2)12yes—
518C23C31×H(5,𝔽2)11yescharacteristic
519C23C31×2−1+411yescharacteristic
520C23C31×2−1+411yescharacteristic
521C23C31×2−1+412yes—
522C23C31×2−1+411yescharacteristic
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
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×C4C4×D4×C3114yes—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—44no—
585C22—44no—
586C22—81no—
587C22—81no—
588C22—82no—
589C22—82no—
590C22—81no—
591C22—81no—
592C22C2×C4×D4×C3111yescharacteristic
593C22C31×#51812yes—
594C22C31×#51911yescharacteristic
595C22C31×#52012yes—
596C22C31×#52011yescharacteristic
597C22C31×#53411yescharacteristic
598C22C31×#53511yescharacteristic
599C22C31×#53511yescharacteristic
600C22C31×#53611yescharacteristic
601C22C31×#53611yescharacteristic
602C22C31×#53711yescharacteristic
603C22C31×#53912yes—
604C22C31×#54012yes—
605C22C31×#54111yescharacteristic
606C22C31×#54211yescharacteristic
607C22C31×#56012yes—
608C22C31×#56212yes—
609C22C31×#56212yes—
610C22C31×#56212yes—
611C22C31×#56212yes—
612C22C31×#56312yes—
613C22C31×#56312yes—
614C22C31×#56312yes—
615C4—24no—
616C4—42no—
617C4—44no—
618C4—44no—
619C4—42no—
620C4—42no—
621C4—81no—
622C4—82no—
623C4—82no—
624C4—81no—
625C2—82no—
626C2C31×#232211yescharacteristic
627C2C31×#232311yescharacteristic
628C2C31×#232811yescharacteristic
629C2C31×#237612yes—
630C2C31×#237812yes—
631C2C31×#281311yescharacteristic
632C2C31×#281611yescharacteristic
633C2C31×#282011yescharacteristic
634C2C31×#282111yescharacteristic
635C2C31×#283612yes—
636C2C31×#283712yes—
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
2. C2×C31×#389C2semidirect
4. C31×#1445C2semidirect
5. C31×#1442C2semidirect
6. C31×#1441C2semidirect
7. C31×#1441C2semidirect
11. C31×#1434C2semidirect
23. C31×#399C4semidirect
170. #14628C31direct (N × H)
264. C2×#389C2×C31semidirect
266. #1445C2×C31semidirect
267. #1442C2×C31semidirect
268. #1441C2×C31semidirect
269. #1441C2×C31semidirect
273. #1434C2×C31semidirect
329. #399C4×C31semidirect
407. C31#14628direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3992
C2×C31×#3892
C2×C31×#3882
C31×#14452
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×#14342
#1462831