Finite Group Databasebeta

← C31×#14135 #21470894

Subgroups — C31×#14135 #21470894

Order 7936.

2634 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic
2C22×C31×#117C211yesmaximal, characteristic, complemented
3C2×C31×#386C212yesmaximal
4C22×C31×#95C211yesmaximal, characteristic, complemented
5C31×#1441C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1437C212yesmaximal, complemented
8C31×#1436C212yesmaximal, complemented
9C31×C22⋊#95C212yesmaximal, complemented
10C23×D4×C31C2211yescharacteristic
11C24×C4×C31C2212yes—
12C24×C4×C31C2211yescharacteristic
13C2×C31×#123—24no—
14C2×C31×#123—24no—
15C2×C31×#123C418yescomplemented
16C2×C31×#117—24no—
17C2×C31×#117—28no—
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2214yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2212yes—
26C22×C42×C31C2212yes—
27C31×#386—28no—
28C2×C31×#95—24no—
29C2×C31×#95C2214yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2214yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2214yes—
34C25×C31C2311yescharacteristic
35C25×C31C2311yescharacteristic
36C22×D4×C31—22no—
37C22×D4×C31—22no—
38C22×D4×C31—24no—
39C22×D4×C31—24no—
40C22×D4×C31C2×C414yes—
41C23×C4×C31—24no—
42C23×C4×C31—24no—
43C23×C4×C31—24no—
44C23×C4×C31—28no—
45C23×C4×C31—24no—
46C23×C4×C31—24no—
47C23×C4×C31—44no—
48C23×C4×C31C2×C414yes—
49C23×C4×C31D414yes—
50C23×C4×C31D414yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2314yes—
55C23×C4×C31C2314yes—
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C31×#123—232no—
59C31×#117—232no—
60C2×C4⋊C4×C31—28no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31C2×C414yescomplemented
67C2×C4⋊C4×C31C2×C414yescomplemented
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31—22no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—22no—
76C2×C22⋊C4×C31—28no—
77C2×C22⋊C4×C31—28no—
78C2×C22⋊C4×C31—44no—
79C2×C22⋊C4×C31C2×C414yes—
80C2×C22⋊C4×C31C2×C414yescomplemented
81C2×C22⋊C4×C31C2×C414yescomplemented
82C2×C22⋊C4×C31D418yes—
83C2×C42×C31—28no—
84C2×C42×C31—24no—
85C31×#95—24no—
86C31×#95—24no—
87C31×#95—28no—
88C31×#95—28no—
89C31×#95—44no—
90C24×C31—24no—
91C24×C31—22no—
92C24×C31—22no—
93C24×C31—21no—
94C24×C31—21no—
95C24×C31—22no—
96C24×C31—24no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31C22×C412yes—
101C24×C31C22×C412yes—
102C24×C31C2×D412yes—
103C24×C31C2×D412yes—
104C24×C31C2×D414yes—
105C24×C31#4114yes—
106C24×C31C2411yescharacteristic
107C2×D4×C31—28no—
108C2×D4×C31—216no—
109C2×D4×C31—44no—
110C2×D4×C31—48no—
111C2×D4×C31—44no—
112C22×C4×C31—216no—
113C22×C4×C31—28no—
114C22×C4×C31—216no—
115C22×C4×C31—28no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—216no—
121C22×C4×C31—24no—
122C22×C4×C31—22no—
123C22×C4×C31—24no—
124C22×C4×C31—24no—
125C22×C4×C31—24no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—21no—
132C22×C4×C31—24no—
133C22×C4×C31—24no—
134C22×C4×C31—24no—
135C22×C4×C31—24no—
136C22×C4×C31—24no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—24no—
140C22×C4×C31—24no—
141C22×C4×C31—24no—
142C22×C4×C31—22no—
143C22×C4×C31—24no—
144C22×C4×C31—416no—
145C22×C4×C31—416no—
146C22×C4×C31—48no—
147C22×C4×C31—48no—
148C22×C4×C31C22⋊C4116yescomplemented
149C22×C4×C31C22×C412yes—
150C22×C4×C31C22×C412yes—
151C22×C4×C31C22×C412yes—
152C22×C4×C31C22×C412yes—
153C22×C4×C31C22×C412yes—
154C22×C4×C31C2×D418yes—
155C22×C4×C31C2×D412yes—
156C22×C4×C31C2×D412yes—
157C22×C4×C31C2×D412yes—
158C22×C4×C31C2×D412yes—
159C22×C4×C31#4118yes—
160C4⋊C4×C31—216no—
161C4⋊C4×C31—28no—
162C4⋊C4×C31—28no—
163C22⋊C4×C31—28no—
164C22⋊C4×C31—216no—
165C22⋊C4×C31—28no—
166C22⋊C4×C31—28no—
167C22⋊C4×C31—416no—
168C42×C31—216no—
169#14135C3111yesmaximal, characteristic, direct product factor, Sylow
170C23×C31—24no—
171C23×C31—24no—
172C23×C31—24no—
173C23×C31—24no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—24no—
177C23×C31—28no—
178C23×C31—28no—
179C23×C31—28no—
180C23×C31—28no—
181C23×C31—22no—
182C23×C31—24no—
183C23×C31—24no—
184C23×C31—24no—
185C23×C31—41no—
186C23×C31—42no—
187C23×C31—41no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—41no—
191C23×C31—41no—
192C23×C31—42no—
193C23×C31—44no—
194C23×C31—44no—
195C23×C31—44no—
196C23×C31—44no—
197C23×C31C2×C22⋊C414yes—
198C23×C31C4×D418yes—
199C23×C31#12014yes—
200C23×C31#12118yes—
201C23×C31#12314yes—
202C23×C31C23×C411yescharacteristic
203C23×C31C22×D411yescharacteristic
204C23×C31C22×D411yescharacteristic
205C23×C31C22×D412yes—
206C23×C31C2×#4112yes—
207C23×C31C2×#4114yes—
208C23×C31H(5,𝔽2)12yes—
209C23×C312−1+412yes—
210D4×C31—416no—
211C2×C4×C31—24no—
212C2×C4×C31—24no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—24no—
216C2×C4×C31—24no—
217C2×C4×C31—22no—
218C2×C4×C31—22no—
219C2×C4×C31—232no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—24no—
224C2×C4×C31—24no—
225C2×C4×C31—24no—
226C2×C4×C31—28no—
227C2×C4×C31—28no—
228C2×C4×C31—28no—
229C2×C4×C31—28no—
230C2×C4×C31—28no—
231C2×C4×C31—28no—
232C2×C4×C31—432no—
233C2×C4×C31—41no—
234C2×C4×C31—44no—
235C2×C4×C31—42no—
236C2×C4×C31—41no—
237C2×C4×C31—42no—
238C2×C4×C31—44no—
239C2×C4×C31—42no—
240C2×C4×C31—41no—
241C2×C4×C31—44no—
242C2×C4×C31—41no—
243C2×C4×C31—42no—
244C2×C4×C31—44no—
245C2×C4×C31—44no—
246C2×C4×C31—44no—
247C2×C4×C31—44no—
248C2×C4×C31—44no—
249C2×C4×C31C2×C22⋊C414yes—
250C2×C4×C31C2×C22⋊C414yes—
251C22×#123C2×C3111yescharacteristic
252C22×#117C2×C3111yescharacteristic, complemented
253C2×#386C2×C3112yes—
254C22×#95C2×C3111yescharacteristic, complemented
255#1441C2×C3112yescomplemented
256#1439C2×C3112yescomplemented
257#1437C2×C3112yescomplemented
258#1436C2×C3112yescomplemented
259C22⋊#95C2×C3112yescomplemented
260C22×C31—24no—
261C22×C31—216no—
262C22×C31—28no—
263C22×C31—28no—
264C22×C31—28no—
265C22×C31—28no—
266C22×C31—24no—
267C22×C31—42no—
268C22×C31—48no—
269C22×C31—42no—
270C22×C31—42no—
271C22×C31—82no—
272C22×C31—82no—
273C22×C31—82no—
274C22×C31—82no—
275C22×C31#38618yes—
276C22×C31C22×C22⋊C411yescharacteristic
277C22×C31C2×C4×D412yes—
278C22×C31C4×#4112yes—
279C22×C31#52012yes—
280C22×C31C2×#12011yescharacteristic
281C22×C31C2×#12112yes—
282C22×C31C2×#12311yescharacteristic
283C22×C31#52512yes—
284C22×C31#53212yes—
285C22×C31#53511yescharacteristic
286C22×C31#53611yescharacteristic
287C22×C31#53712yes—
288C22×C31#54614yes—
289C22×C31#54714yes—
290C22×C31#55114yes—
291C22×C31#55214yes—
292C4×C31—24no—
293C4×C31—24no—
294C4×C31—42no—
295C4×C31—48no—
296C4×C31—48no—
297C4×C31—42no—
298C4×C31—42no—
299C23×D4C22×C3111yescharacteristic
300C24×C4C22×C3112yes—
301C24×C4C22×C3111yescharacteristic
302C2×#123—24no—
303C2×#123—24no—
304C2×#123C4×C3118yescomplemented
305C2×#117—24no—
306C2×#117—28no—
307C22×C4⋊C4C22×C3112yes—
308C22×C4⋊C4C22×C3111yescharacteristic
309C22×C4⋊C4C22×C3111yescharacteristic
310C22×C22⋊C4C22×C3114yes—
311C22×C22⋊C4C22×C3111yescharacteristic
312C22×C22⋊C4C22×C3111yescharacteristic
313C22×C22⋊C4C22×C3111yescharacteristic
314C22×C22⋊C4C22×C3112yes—
315C22×C42C22×C3112yes—
316#386—28no—
317C2×#95—24no—
318C2×#95C22×C3114yes—
319C2×#95C22×C3112yes—
320C2×#95C22×C3114yes—
321C2×#95C22×C3112yes—
322C2×#95C22×C3114yes—
323C2×C31—28no—
324C2×C31—82no—
325C2×C31C2×#38611yescharacteristic
326C2×C31#229711yescharacteristic
327C2×C31#231111yescharacteristic
328C2×C31#235914yes—
329C2×C31#241112yes—
330C2×C31#241312yes—
331C2×C31#243012yes—
332C2×C31#249812yes—
333C25C23×C3111yescharacteristic
334C25C23×C3111yescharacteristic
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4C2×C4×C3114yes—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—28no—
344C23×C4—24no—
345C23×C4—24no—
346C23×C4—44no—
347C23×C4C2×C4×C3114yes—
348C23×C4D4×C3114yes—
349C23×C4D4×C3114yes—
350C23×C4C23×C3111yescharacteristic
351C23×C4C23×C3111yescharacteristic
352C23×C4C23×C3111yescharacteristic
353C23×C4C23×C3114yes—
354C23×C4C23×C3114yes—
355C23×C4C23×C3111yescharacteristic
356C23×C4C23×C3111yescharacteristic
357#123—232no—
358#117—232no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4C2×C4×C3114yescomplemented
366C2×C4⋊C4C2×C4×C3114yescomplemented
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4C2×C4×C3114yes—
379C2×C22⋊C4C2×C4×C3114yescomplemented
380C2×C22⋊C4C2×C4×C3114yescomplemented
381C2×C22⋊C4D4×C3118yes—
382C2×C42—28no—
383C2×C42—24no—
384#95—24no—
385#95—24no—
386#95—28no—
387#95—28no—
388#95—44no—
389C31#1413511yescharacteristic, direct product factor, Sylow
390C24—24no—
391C24—22no—
392C24—22no—
393C24—21no—
394C24—21no—
395C24—22no—
396C24—24no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24C22×C4×C3112yes—
401C24C22×C4×C3112yes—
402C24C2×D4×C3112yes—
403C24C2×D4×C3112yes—
404C24C2×D4×C3114yes—
405C24#41×C3114yes—
406C24C24×C3111yescharacteristic
407C2×D4—28no—
408C2×D4—216no—
409C2×D4—44no—
410C2×D4—48no—
411C2×D4—44no—
412C22×C4—216no—
413C22×C4—28no—
414C22×C4—216no—
415C22×C4—28no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—216no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—416no—
445C22×C4—416no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4C22⋊C4×C31116yescomplemented
449C22×C4C22×C4×C3112yes—
450C22×C4C22×C4×C3112yes—
451C22×C4C22×C4×C3112yes—
452C22×C4C22×C4×C3112yes—
453C22×C4C22×C4×C3112yes—
454C22×C4C2×D4×C3118yes—
455C22×C4C2×D4×C3112yes—
456C22×C4C2×D4×C3112yes—
457C22×C4C2×D4×C3112yes—
458C22×C4C2×D4×C3112yes—
459C22×C4#41×C3118yes—
460C4⋊C4—216no—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C22⋊C4—28no—
464C22⋊C4—216no—
465C22⋊C4—28no—
466C22⋊C4—28no—
467C22⋊C4—416no—
468C42—216no—
469C23—24no—
470C23—24no—
471C23—24no—
472C23—24no—
473C23—22no—
474C23—22no—
475C23—24no—
476C23—28no—
477C23—28no—
478C23—28no—
479C23—28no—
480C23—22no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—42no—
488C23—42no—
489C23—41no—
490C23—41no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23C2×C22⋊C4×C3114yes—
497C23C4×D4×C3118yes—
498C23C31×#12014yes—
499C23C31×#12118yes—
500C23C31×#12314yes—
501C23C23×C4×C3111yescharacteristic
502C23C22×D4×C3111yescharacteristic
503C23C22×D4×C3111yescharacteristic
504C23C22×D4×C3112yes—
505C23C2×#41×C3112yes—
506C23C2×#41×C3114yes—
507C23C31×H(5,𝔽2)12yes—
508C23C31×2−1+412yes—
509D4—416no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—232no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—28no—
526C2×C4—28no—
527C2×C4—28no—
528C2×C4—28no—
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—432no—
532C2×C4—41no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4C2×C22⋊C4×C3114yes—
549C2×C4C2×C22⋊C4×C3114yes—
550C22—24no—
551C22—216no—
552C22—28no—
553C22—28no—
554C22—28no—
555C22—28no—
556C22—24no—
557C22—42no—
558C22—48no—
559C22—42no—
560C22—42no—
561C22—82no—
562C22—82no—
563C22—82no—
564C22—82no—
565C22C31×#38618yes—
566C22C22×C22⋊C4×C3111yescharacteristic
567C22C2×C4×D4×C3112yes—
568C22C4×#41×C3112yes—
569C22C31×#52012yes—
570C22C2×C31×#12011yescharacteristic
571C22C2×C31×#12112yes—
572C22C2×C31×#12311yescharacteristic
573C22C31×#52512yes—
574C22C31×#53212yes—
575C22C31×#53511yescharacteristic
576C22C31×#53611yescharacteristic
577C22C31×#53712yes—
578C22C31×#54614yes—
579C22C31×#54714yes—
580C22C31×#55114yes—
581C22C31×#55214yes—
582C4—24no—
583C4—24no—
584C4—42no—
585C4—48no—
586C4—48no—
587C4—42no—
588C4—42no—
589C2—28no—
590C2—82no—
591C2C2×C31×#38611yescharacteristic
592C2C31×#229711yescharacteristic
593C2C31×#231111yescharacteristic
594C2C31×#235914yes—
595C2C31×#241112yes—
596C2C31×#241312yes—
597C2C31×#243012yes—
598C2C31×#249812yes—
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. C22×C31×#117C2semidirect
4. C22×C31×#95C2semidirect
5. C31×#1441C2semidirect
6. C31×#1439C2semidirect
7. C31×#1437C2semidirect
8. C31×#1436C2semidirect
9. C31×C22⋊#95C2semidirect
15. C2×C31×#123C4semidirect
66. C2×C4⋊C4×C31C2×C4semidirect
67. C2×C4⋊C4×C31C2×C4semidirect
80. C2×C22⋊C4×C31C2×C4semidirect
81. C2×C22⋊C4×C31C2×C4semidirect
148. C22×C4×C31C22⋊C4semidirect
169. #14135C31direct (N × H)
252. C22×#117C2×C31semidirect
254. C22×#95C2×C31semidirect
255. #1441C2×C31semidirect
256. #1439C2×C31semidirect
257. #1437C2×C31semidirect
258. #1436C2×C31semidirect
259. C22⋊#95C2×C31semidirect
304. C2×#123C4×C31semidirect
365. C2×C4⋊C4C2×C4×C31semidirect
366. C2×C4⋊C4C2×C4×C31semidirect
379. C2×C22⋊C4C2×C4×C31semidirect
380. C2×C22⋊C4C2×C4×C31semidirect
389. C31#14135direct (N × H)
448. 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
C22×C31×#1172
C2×C31×#3862
C22×C31×#952
C31×#14412
C31×#14392
C31×#14372
C31×#14362
C31×C22⋊#952
#1413531