Finite Group Databasebeta

← C31×#14506 #21471265

Subgroups — C31×#14506 #21471265

Order 7936.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic
2C2×C31×#388C212yesmaximal, complemented
3C31×#1445C212yesmaximal, complemented
4C31×#1439C212yesmaximal, complemented
5C31×#1438C211yesmaximal, characteristic
6C31×#1438C211yesmaximal, characteristic
7C31×#1437C212yesmaximal, complemented
8C31×C4⋊#95C212yesmaximal, complemented
9C31×C22⋊#95C212yesmaximal, complemented
10C23×D4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C2×C31×#123—28no—
13C2×C31×#123C418yescomplemented
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C42×C31C2212yes—
24C31×#388—28no—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C25×C31C2311yescharacteristic
35C25×C31C2311yescharacteristic
36C22×D4×C31—24no—
37C22×D4×C31—42no—
38C22×D4×C31—41no—
39C22×D4×C31—41no—
40C22×D4×C31C2×C414yes—
41C23×C4×C31—24no—
42C23×C4×C31—42no—
43C23×C4×C31—41no—
44C23×C4×C31—41no—
45C23×C4×C31C2×C414yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2312yes—
49C23×C4×C31C2311yescharacteristic
50C23×C4×C31C2312yes—
51C23×C4×C31C2312yes—
52C23×C4×C31C2312yes—
53C31×#123—232no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—42no—
59C2×C4⋊C4×C31C2×C418yes—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—41no—
69C2×C22⋊C4×C31—42no—
70C2×C22⋊C4×C31—42no—
71C2×C22⋊C4×C31—42no—
72C2×C22⋊C4×C31—42no—
73C2×C22⋊C4×C31—41no—
74C2×C22⋊C4×C31—42no—
75C2×C22⋊C4×C31C2×C418yes—
76C2×C22⋊C4×C31C2×C414yes—
77C2×C22⋊C4×C31D418yes—
78C2×C42×C31—24no—
79C2×C42×C31—24no—
80C2×C42×C31—42no—
81C31×#95—24no—
82C31×#95—24no—
83C31×#95—41no—
84C31×#95—42no—
85C31×#95—42no—
86C31×#95—42no—
87C31×#95—42no—
88C31×#95—42no—
89C31×#95—41no—
90C24×C31—22no—
91C24×C31—22no—
92C24×C31—22no—
93C24×C31—22no—
94C24×C31—21no—
95C24×C31—21no—
96C24×C31—22no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—22no—
101C24×C31—22no—
102C24×C31—21no—
103C24×C31—21no—
104C24×C31—22no—
105C24×C31C22×C412yes—
106C24×C31C22×C412yes—
107C24×C31C2×D414yes—
108C24×C31C2411yescharacteristic
109C2×D4×C31—28no—
110C2×D4×C31—44no—
111C2×D4×C31—44no—
112C2×D4×C31—48no—
113C2×D4×C31—48no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—28no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
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—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—44no—
156C22×C4×C31—44no—
157C22×C4×C31—48no—
158C22×C4×C31—48no—
159C22×C4×C31C22×C414yes—
160C22×C4×C31C22×C412yes—
161C22×C4×C31C22×C414yes—
162C22×C4×C31C2×D414yes—
163C22×C4×C31C2×D414yes—
164C22×C4×C31#4114yes—
165C22×C4×C31#4114yes—
166C4⋊C4×C31—216no—
167C4⋊C4×C31—48no—
168C22⋊C4×C31—216no—
169C22⋊C4×C31—44no—
170C22⋊C4×C31—48no—
171C22⋊C4×C31—48no—
172C22⋊C4×C31—48no—
173C22⋊C4×C31—44no—
174C22⋊C4×C31C22⋊C4116yescomplemented
175C42×C31—48no—
176#14506C3111yesmaximal, characteristic, direct product factor, Sylow
177C23×C31—24no—
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—24no—
181C23×C31—24no—
182C23×C31—24no—
183C23×C31—24no—
184C23×C31—24no—
185C23×C31—24no—
186C23×C31—24no—
187C23×C31—22no—
188C23×C31—24no—
189C23×C31—22no—
190C23×C31—22no—
191C23×C31—24no—
192C23×C31—42no—
193C23×C31—42no—
194C23×C31—42no—
195C23×C31—42no—
196C23×C31—41no—
197C23×C31—42no—
198C23×C31—41no—
199C23×C31—41no—
200C23×C31—42no—
201C23×C31—41no—
202C23×C31—42no—
203C23×C31—42no—
204C23×C31—42no—
205C23×C31—42no—
206C23×C31—42no—
207C23×C31—42no—
208C23×C31—42no—
209C23×C31—42no—
210C23×C31—42no—
211C23×C31—42no—
212C23×C31—41no—
213C23×C31—42no—
214C23×C31—41no—
215C23×C31—41no—
216C23×C31—42no—
217C23×C31—41no—
218C23×C31C2×C22⋊C414yes—
219C23×C31C23×C411yescharacteristic
220C23×C31C22×D412yes—
221C23×C31C2×#4112yes—
222C23×C31C2×#4112yes—
223C23×C31H(5,𝔽2)12yes—
224C23×C31H(5,𝔽2)11yescharacteristic
225C23×C31H(5,𝔽2)11yescharacteristic
226C23×C31H(5,𝔽2)12yes—
227C23×C312−1+412yes—
228D4×C31—416no—
229C2×C4×C31—24no—
230C2×C4×C31—24no—
231C2×C4×C31—24no—
232C2×C4×C31—24no—
233C2×C4×C31—24no—
234C2×C4×C31—24no—
235C2×C4×C31—24no—
236C2×C4×C31—22no—
237C2×C4×C31—24no—
238C2×C4×C31—24no—
239C2×C4×C31—22no—
240C2×C4×C31—22no—
241C2×C4×C31—24no—
242C2×C4×C31—24no—
243C2×C4×C31—24no—
244C2×C4×C31—24no—
245C2×C4×C31—24no—
246C2×C4×C31—24no—
247C2×C4×C31—416no—
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×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—42no—
269C2×C4×C31—42no—
270C2×C4×C31—42no—
271C2×C4×C31—42no—
272C2×C4×C31—42no—
273C2×C4×C31—42no—
274C2×C4×C31—42no—
275C2×C4×C31—42no—
276C2×C4×C31C2×C22⋊C418yes—
277C22×#123C2×C3111yescharacteristic
278C2×#388C2×C3112yescomplemented
279#1445C2×C3112yescomplemented
280#1439C2×C3112yescomplemented
281#1438C2×C3111yescharacteristic
282#1438C2×C3111yescharacteristic
283#1437C2×C3112yescomplemented
284C4⋊#95C2×C3112yescomplemented
285C22⋊#95C2×C3112yescomplemented
286C22×C31—24no—
287C22×C31—28no—
288C22×C31—44no—
289C22×C31—42no—
290C22×C31—42no—
291C22×C31—44no—
292C22×C31—44no—
293C22×C31—44no—
294C22×C31—44no—
295C22×C31—42no—
296C22×C31—44no—
297C22×C31—44no—
298C22×C31—42no—
299C22×C31—42no—
300C22×C31—82no—
301C22×C31—82no—
302C22×C31—82no—
303C22×C31—82no—
304C22×C31C22×C22⋊C411yescharacteristic
305C22×C31C4×#4112yes—
306C22×C31#51811yescharacteristic
307C22×C31#51811yescharacteristic
308C22×C31#52012yes—
309C22×C31#53512yes—
310C22×C31#53512yes—
311C22×C31#53812yes—
312C22×C31#53912yes—
313C22×C31#54012yes—
314C22×C31#54212yes—
315C22×C31#54612yes—
316C22×C31#54612yes—
317C22×C31#54712yes—
318C22×C31#54712yes—
319C22×C31#55111yescharacteristic
320C22×C31#55312yes—
321C22×C31#55911yescharacteristic
322C22×C31#56011yescharacteristic
323C22×C31#56212yes—
324C22×C31#56311yescharacteristic
325C4×C31—28no—
326C4×C31—44no—
327C4×C31—42no—
328C4×C31—44no—
329C4×C31—44no—
330C4×C31—82no—
331C4×C31—82no—
332C23×D4C22×C3111yescharacteristic
333C24×C4C22×C3111yescharacteristic
334C2×#123—28no—
335C2×#123C4×C3118yescomplemented
336C22×C4⋊C4C22×C3112yes—
337C22×C4⋊C4C22×C3112yes—
338C22×C22⋊C4C22×C3112yes—
339C22×C22⋊C4C22×C3112yes—
340C22×C22⋊C4C22×C3111yescharacteristic
341C22×C22⋊C4C22×C3112yes—
342C22×C22⋊C4C22×C3112yes—
343C22×C22⋊C4C22×C3111yescharacteristic
344C22×C22⋊C4C22×C3111yescharacteristic
345C22×C42C22×C3112yes—
346#388—28no—
347C2×#95C22×C3112yes—
348C2×#95C22×C3112yes—
349C2×#95C22×C3112yes—
350C2×#95C22×C3112yes—
351C2×#95C22×C3112yes—
352C2×#95C22×C3112yes—
353C2×#95C22×C3111yescharacteristic
354C2×#95C22×C3112yes—
355C2×#95C22×C3111yescharacteristic
356C2×C31—44no—
357C2×C31—82no—
358C2×C31#230911yescharacteristic
359C2×C31#233512yes—
360C2×C31#233912yes—
361C2×C31#237411yescharacteristic
362C2×C31#237611yescharacteristic
363C2×C31#270312yes—
364C2×C31#270612yes—
365C2×C31#271012yes—
366C2×C31#271812yes—
367C25C23×C3111yescharacteristic
368C25C23×C3111yescharacteristic
369C22×D4—24no—
370C22×D4—42no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4C2×C4×C3114yes—
374C23×C4—24no—
375C23×C4—42no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4C2×C4×C3114yes—
379C23×C4C23×C3112yes—
380C23×C4C23×C3112yes—
381C23×C4C23×C3112yes—
382C23×C4C23×C3111yescharacteristic
383C23×C4C23×C3112yes—
384C23×C4C23×C3112yes—
385C23×C4C23×C3112yes—
386#123—232no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4C2×C4×C3118yes—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4C2×C4×C3118yes—
409C2×C22⋊C4C2×C4×C3114yes—
410C2×C22⋊C4D4×C3118yes—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—42no—
414#95—24no—
415#95—24no—
416#95—41no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—41no—
423C31#1450611yescharacteristic, direct product factor, Sylow
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C3112yes—
440C24C22×C4×C3112yes—
441C24C2×D4×C3114yes—
442C24C24×C3111yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
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—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C3114yes—
494C22×C4C22×C4×C3112yes—
495C22×C4C22×C4×C3114yes—
496C22×C4C2×D4×C3114yes—
497C22×C4C2×D4×C3114yes—
498C22×C4#41×C3114yes—
499C22×C4#41×C3114yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C31116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C3114yes—
552C23C23×C4×C3111yescharacteristic
553C23C22×D4×C3112yes—
554C23C2×#41×C3112yes—
555C23C2×#41×C3112yes—
556C23C31×H(5,𝔽2)12yes—
557C23C31×H(5,𝔽2)11yescharacteristic
558C23C31×H(5,𝔽2)11yescharacteristic
559C23C31×H(5,𝔽2)12yes—
560C23C31×2−1+412yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
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×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C3118yes—
610C22—24no—
611C22—28no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—44no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C3111yescharacteristic
629C22C4×#41×C3112yes—
630C22C31×#51811yescharacteristic
631C22C31×#51811yescharacteristic
632C22C31×#52012yes—
633C22C31×#53512yes—
634C22C31×#53512yes—
635C22C31×#53812yes—
636C22C31×#53912yes—
637C22C31×#54012yes—
638C22C31×#54212yes—
639C22C31×#54612yes—
640C22C31×#54612yes—
641C22C31×#54712yes—
642C22C31×#54712yes—
643C22C31×#55111yescharacteristic
644C22C31×#55312yes—
645C22C31×#55911yescharacteristic
646C22C31×#56011yescharacteristic
647C22C31×#56212yes—
648C22C31×#56311yescharacteristic
649C4—28no—
650C4—44no—
651C4—42no—
652C4—44no—
653C4—44no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C31×#230911yescharacteristic
659C2C31×#233512yes—
660C2C31×#233912yes—
661C2C31×#237411yescharacteristic
662C2C31×#237611yescharacteristic
663C2C31×#270312yes—
664C2C31×#270612yes—
665C2C31×#271012yes—
666C2C31×#271812yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#388C2semidirect
3. C31×#1445C2semidirect
4. C31×#1439C2semidirect
7. C31×#1437C2semidirect
8. C31×C4⋊#95C2semidirect
9. C31×C22⋊#95C2semidirect
13. C2×C31×#123C4semidirect
174. C22⋊C4×C31C22⋊C4semidirect
176. #14506C31direct (N × H)
278. C2×#388C2×C31semidirect
279. #1445C2×C31semidirect
280. #1439C2×C31semidirect
283. #1437C2×C31semidirect
284. C4⋊#95C2×C31semidirect
285. C22⋊#95C2×C31semidirect
335. C2×#123C4×C31semidirect
423. C31#14506direct (N × H)
508. C22⋊C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C2×C31×#3882
C31×#14452
C31×#14392
C31×#14382
C31×#14372
C31×C4⋊#952
C31×C22⋊#952
#1450631