Finite Group Databasebeta

← C31×#14027 #21470786

Subgroups — C31×#14027 #21470786

Order 7936.

2574 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic
2C22×C4×D4×C31C211yesmaximal, characteristic
3C2×C31×#391C211yesmaximal, characteristic, complemented
4C2×C31×#391C211yesmaximal, characteristic, complemented
5C2×C31×#390C211yesmaximal, characteristic
6C31×#1440C214yesmaximal, complemented
7C31×C4⋊#95C211yesmaximal, characteristic, complemented
8C31×C22⋊#95C214yesmaximal, complemented
9C4×C31×#95C211yesmaximal, characteristic, complemented
10C23×Q8×C31C2211yescharacteristic
11C23×D4×C31C2211yescharacteristic
12C24×C4×C31C2212yes—
13C2×C31×#124—24no—
14C2×C31×#124—24no—
15C2×C31×#124C418yescomplemented
16C2×C4×D4×C31—24no—
17C2×C4×D4×C31—24no—
18C2×C4×D4×C31—24no—
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2214yes—
23C22×C22⋊C4×C31C2214yes—
24C22×C42×C31C2211yescharacteristic
25C22×C42×C31C2211yescharacteristic
26C22×C42×C31C2211yescharacteristic
27C31×#391—24no—
28C31×#391—24no—
29C31×#390—24no—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2214yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2214yes—
36C25×C31C2312yes—
37C22×Q8×C31—22no—
38C22×Q8×C31—22no—
39C22×Q8×C31—22no—
40C22×Q8×C31—22no—
41C22×Q8×C31—22no—
42C22×Q8×C31—22no—
43C22×Q8×C31C2×C414yescomplemented
44C22×D4×C31—22no—
45C22×D4×C31—22no—
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31C2×C414yes—
49C22×D4×C31D414yes—
50C22×D4×C31D414yes—
51C23×C4×C31—24no—
52C23×C4×C31—24no—
53C23×C4×C31—24no—
54C23×C4×C31—28no—
55C23×C4×C31—44no—
56C23×C4×C31C2312yes—
57C23×C4×C31C2312yes—
58C23×C4×C31C2312yes—
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2312yes—
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C31×#124—232no—
65C4×D4×C31—232no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31D414yes—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—28no—
74C2×C22⋊C4×C31—28no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—28no—
78C2×C22⋊C4×C31—28no—
79C2×C22⋊C4×C31—44no—
80C2×C22⋊C4×C31C2×C4116yescomplemented
81C2×C42×C31—22no—
82C2×C42×C31—22no—
83C2×C42×C31—22no—
84C2×C42×C31—22no—
85C2×C42×C31—22no—
86C2×C42×C31—22no—
87C2×C42×C31—22no—
88C2×C42×C31C2×C414yescomplemented
89C2×C42×C31D414yes—
90C31×#95—28no—
91C31×#95—24no—
92C31×#95—24no—
93C31×#95—24no—
94C31×#95—24no—
95C31×#95—44no—
96C24×C31—22no—
97C24×C31—22no—
98C24×C31—24no—
99C24×C31—24no—
100C24×C31—22no—
101C24×C31—22no—
102C24×C31—24no—
103C24×C31—24no—
104C24×C31C22×C414yes—
105C24×C31C2×D414yes—
106C24×C31C2×D414yes—
107C24×C31C2411yescharacteristic
108C2×Q8×C31—28no—
109C2×Q8×C31—28no—
110C2×Q8×C31—28no—
111C2×Q8×C31—44no—
112C2×Q8×C31—44no—
113C2×Q8×C31—44no—
114C2×Q8×C31—44no—
115C2×D4×C31—28no—
116C2×D4×C31—28no—
117C2×D4×C31—28no—
118C2×D4×C31—28no—
119C2×D4×C31—28no—
120C2×D4×C31—28no—
121C2×D4×C31C22⋊C4116yes—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—22no—
125C22×C4×C31—216no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
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—24no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—24no—
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—24no—
155C22×C4×C31—22no—
156C22×C4×C31—24no—
157C22×C4×C31—416no—
158C22×C4×C31—416no—
159C22×C4×C31—48no—
160C22×C4×C31—48no—
161C22×C4×C31C22×C414yes—
162C22×C4×C31C22×C414yes—
163C22×C4×C31C22×C412yes—
164C22×C4×C31C2×D412yes—
165C22×C4×C31C2×D414yes—
166C22×C4×C31C2×D412yes—
167C22×C4×C31C2×D412yes—
168C22×C4×C31C2×D412yes—
169C22×C4×C31C2×D412yes—
170C22×C4×C31C2×D412yes—
171C22×C4×C31#4114yes—
172C22×C4×C31#4114yes—
173C22×C4×C31#4112yes—
174C22×C4×C31#4112yes—
175C4⋊C4×C31—28no—
176C4⋊C4×C31—44no—
177C22⋊C4×C31—216no—
178C22⋊C4×C31—232no—
179C22⋊C4×C31—416no—
180C42×C31—28no—
181C42×C31—28no—
182C42×C31—44no—
183#14027C3111yesmaximal, characteristic, direct product factor, Sylow
184C23×C31—24no—
185C23×C31—24no—
186C23×C31—28no—
187C23×C31—28no—
188C23×C31—24no—
189C23×C31—24no—
190C23×C31—24no—
191C23×C31—24no—
192C23×C31—28no—
193C23×C31—28no—
194C23×C31—28no—
195C23×C31—28no—
196C23×C31—42no—
197C23×C31—44no—
198C23×C31—42no—
199C23×C31—42no—
200C23×C31—42no—
201C23×C31—44no—
202C23×C31—44no—
203C23×C31—44no—
204C23×C31—44no—
205C23×C31—44no—
206C23×C31C2×C22⋊C418yes—
207C23×C31C23×C411yescharacteristic
208C23×C31C22×D411yescharacteristic
209C23×C31C22×D411yescharacteristic
210C23×C31C22×D411yescharacteristic
211C23×C31C22×D411yescharacteristic
212C23×C31C2×#4111yescharacteristic
213C23×C31C2×#4111yescharacteristic
214C23×C31C2×#4112yes—
215C23×C31C2×#4112yes—
216C23×C31H(5,𝔽2)12yes—
217C23×C312−1+412yes—
218Q8×C31—416no—
219D4×C31—232no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—24no—
223C2×C4×C31—24no—
224C2×C4×C31—24no—
225C2×C4×C31—24no—
226C2×C4×C31—24no—
227C2×C4×C31—24no—
228C2×C4×C31—24no—
229C2×C4×C31—24no—
230C2×C4×C31—22no—
231C2×C4×C31—24no—
232C2×C4×C31—24no—
233C2×C4×C31—22no—
234C2×C4×C31—22no—
235C2×C4×C31—24no—
236C2×C4×C31—28no—
237C2×C4×C31—24no—
238C2×C4×C31—432no—
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—44no—
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—44no—
260C2×C4×C31—44no—
261C2×C4×C31C2×C22⋊C414yes—
262C2×C4×C31C4×D414yes—
263C2×C4×C31C4×D414yes—
264C2×C4×C31#12014yes—
265C2×C4×C31#12114yes—
266C2×C4×C31#12114yes—
267C2×C4×C31#12314yes—
268C2×C4×C31#12414yescomplemented
269C22×#124C2×C3111yescharacteristic
270C22×C4×D4C2×C3111yescharacteristic
271C2×#391C2×C3111yescharacteristic, complemented
272C2×#391C2×C3111yescharacteristic, complemented
273C2×#390C2×C3111yescharacteristic
274#1440C2×C3114yescomplemented
275C4⋊#95C2×C3111yescharacteristic, complemented
276C22⋊#95C2×C3114yescomplemented
277C4×#95C2×C3111yescharacteristic, complemented
278C22×C31—216no—
279C22×C31—28no—
280C22×C31—44no—
281C22×C31—48no—
282C22×C31—48no—
283C22×C31—44no—
284C22×C31—44no—
285C22×C31—48no—
286C22×C31—44no—
287C22×C31—44no—
288C22×C31—44no—
289C22×C31C22×C22⋊C411yescharacteristic
290C22×C31C2×C4×D411yescharacteristic
291C22×C31C2×C4×D411yescharacteristic
292C22×C31C4×#4112yes—
293C22×C31#52012yes—
294C22×C31C2×#12011yescharacteristic
295C22×C31C2×#12111yescharacteristic
296C22×C31C2×#12111yescharacteristic
297C22×C31C2×#12311yescharacteristic
298C22×C31C2×#12411yescharacteristic
299C22×C31#52912yes—
300C22×C31#53211yescharacteristic
301C22×C31#53511yescharacteristic
302C22×C31#53611yescharacteristic
303C22×C31#54212yes—
304C22×C31#54612yes—
305C22×C31#54612yes—
306C22×C31#54612yes—
307C22×C31#54712yes—
308C22×C31#54712yes—
309C22×C31#54812yes—
310C22×C31#55612yes—
311C22×C31#55912yes—
312C4×C31—24no—
313C4×C31—44no—
314C4×C31—44no—
315C4×C31—42no—
316C4×C31—44no—
317C4×C31—44no—
318C4×C31—82no—
319C4×C31#38618yes—
320C23×Q8C22×C3111yescharacteristic
321C23×D4C22×C3111yescharacteristic
322C24×C4C22×C3112yes—
323C2×#124—24no—
324C2×#124—24no—
325C2×#124C4×C3118yescomplemented
326C2×C4×D4—24no—
327C2×C4×D4—24no—
328C2×C4×D4—24no—
329C22×C4⋊C4C22×C3111yescharacteristic
330C22×C4⋊C4C22×C3111yescharacteristic
331C22×C22⋊C4C22×C3112yes—
332C22×C22⋊C4C22×C3114yes—
333C22×C22⋊C4C22×C3114yes—
334C22×C42C22×C3111yescharacteristic
335C22×C42C22×C3111yescharacteristic
336C22×C42C22×C3111yescharacteristic
337#391—24no—
338#391—24no—
339#390—24no—
340C2×#95C22×C3112yes—
341C2×#95C22×C3112yes—
342C2×#95C22×C3112yes—
343C2×#95C22×C3114yes—
344C2×#95C22×C3112yes—
345C2×#95C22×C3114yes—
346C2×C31—48no—
347C2×C31C2×#38611yescharacteristic
348C2×C31C4×#12411yescharacteristic
349C2×C31#232611yescharacteristic
350C2×C31#233912yes—
351C2×C31#236712yes—
352C2×C31#242712yes—
353C2×C31#243211yescharacteristic
354C2×C31#243511yescharacteristic
355C2×C31#244712yes—
356C2×C31#254411yescharacteristic
357C2×C31#254711yescharacteristic
358C25C23×C3112yes—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—22no—
363C22×Q8—22no—
364C22×Q8—22no—
365C22×Q8C2×C4×C3114yescomplemented
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4C2×C4×C3114yes—
371C22×D4D4×C3114yes—
372C22×D4D4×C3114yes—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—28no—
377C23×C4—44no—
378C23×C4C23×C3112yes—
379C23×C4C23×C3112yes—
380C23×C4C23×C3112yes—
381C23×C4C23×C3111yescharacteristic
382C23×C4C23×C3112yes—
383C23×C4C23×C3112yes—
384C23×C4C23×C3111yescharacteristic
385C23×C4C23×C3111yescharacteristic
386#124—232no—
387C4×D4—232no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4D4×C3114yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4C2×C4×C31116yescomplemented
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42C2×C4×C3114yescomplemented
411C2×C42D4×C3114yes—
412#95—28no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—44no—
418C31#1402711yescharacteristic, direct product factor, Sylow
419C24—22no—
420C24—22no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—22no—
425C24—24no—
426C24—24no—
427C24C22×C4×C3114yes—
428C24C2×D4×C3114yes—
429C24C2×D4×C3114yes—
430C24C24×C3111yescharacteristic
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—28no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—28no—
444C2×D4C22⋊C4×C31116yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—216no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
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—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—416no—
481C22×C4—416no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4C22×C4×C3114yes—
485C22×C4C22×C4×C3114yes—
486C22×C4C22×C4×C3112yes—
487C22×C4C2×D4×C3112yes—
488C22×C4C2×D4×C3114yes—
489C22×C4C2×D4×C3112yes—
490C22×C4C2×D4×C3112yes—
491C22×C4C2×D4×C3112yes—
492C22×C4C2×D4×C3112yes—
493C22×C4C2×D4×C3112yes—
494C22×C4#41×C3114yes—
495C22×C4#41×C3114yes—
496C22×C4#41×C3112yes—
497C22×C4#41×C3112yes—
498C4⋊C4—28no—
499C4⋊C4—44no—
500C22⋊C4—216no—
501C22⋊C4—232no—
502C22⋊C4—416no—
503C42—28no—
504C42—28no—
505C42—44no—
506C23—24no—
507C23—24no—
508C23—28no—
509C23—28no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—28no—
515C23—28no—
516C23—28no—
517C23—28no—
518C23—42no—
519C23—44no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23C2×C22⋊C4×C3118yes—
529C23C23×C4×C3111yescharacteristic
530C23C22×D4×C3111yescharacteristic
531C23C22×D4×C3111yescharacteristic
532C23C22×D4×C3111yescharacteristic
533C23C22×D4×C3111yescharacteristic
534C23C2×#41×C3111yescharacteristic
535C23C2×#41×C3111yescharacteristic
536C23C2×#41×C3112yes—
537C23C2×#41×C3112yes—
538C23C31×H(5,𝔽2)12yes—
539C23C31×2−1+412yes—
540Q8—416no—
541D4—232no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—28no—
559C2×C4—24no—
560C2×C4—432no—
561C2×C4—42no—
562C2×C4—42no—
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—44no—
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—44no—
582C2×C4—44no—
583C2×C4C2×C22⋊C4×C3114yes—
584C2×C4C4×D4×C3114yes—
585C2×C4C4×D4×C3114yes—
586C2×C4C31×#12014yes—
587C2×C4C31×#12114yes—
588C2×C4C31×#12114yes—
589C2×C4C31×#12314yes—
590C2×C4C31×#12414yescomplemented
591C22—216no—
592C22—28no—
593C22—44no—
594C22—48no—
595C22—48no—
596C22—44no—
597C22—44no—
598C22—48no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22C22×C22⋊C4×C3111yescharacteristic
603C22C2×C4×D4×C3111yescharacteristic
604C22C2×C4×D4×C3111yescharacteristic
605C22C4×#41×C3112yes—
606C22C31×#52012yes—
607C22C2×C31×#12011yescharacteristic
608C22C2×C31×#12111yescharacteristic
609C22C2×C31×#12111yescharacteristic
610C22C2×C31×#12311yescharacteristic
611C22C2×C31×#12411yescharacteristic
612C22C31×#52912yes—
613C22C31×#53211yescharacteristic
614C22C31×#53511yescharacteristic
615C22C31×#53611yescharacteristic
616C22C31×#54212yes—
617C22C31×#54612yes—
618C22C31×#54612yes—
619C22C31×#54612yes—
620C22C31×#54712yes—
621C22C31×#54712yes—
622C22C31×#54812yes—
623C22C31×#55612yes—
624C22C31×#55912yes—
625C4—24no—
626C4—44no—
627C4—44no—
628C4—42no—
629C4—44no—
630C4—44no—
631C4—82no—
632C4C31×#38618yes—
633C2—48no—
634C2C2×C31×#38611yescharacteristic
635C2C4×C31×#12411yescharacteristic
636C2C31×#232611yescharacteristic
637C2C31×#233912yes—
638C2C31×#236712yes—
639C2C31×#242712yes—
640C2C31×#243211yescharacteristic
641C2C31×#243511yescharacteristic
642C2C31×#244712yes—
643C2C31×#254411yescharacteristic
644C2C31×#254711yescharacteristic
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
3. C2×C31×#391C2semidirect
4. C2×C31×#391C2semidirect
6. C31×#1440C2semidirect
7. C31×C4⋊#95C2semidirect
8. C31×C22⋊#95C2semidirect
9. C4×C31×#95C2semidirect
15. C2×C31×#124C4semidirect
43. C22×Q8×C31C2×C4semidirect
80. C2×C22⋊C4×C31C2×C4semidirect
88. C2×C42×C31C2×C4semidirect
183. #14027C31direct (N × H)
268. C2×C4×C31#124semidirect
271. C2×#391C2×C31semidirect
272. C2×#391C2×C31semidirect
274. #1440C2×C31semidirect
275. C4⋊#95C2×C31semidirect
276. C22⋊#95C2×C31semidirect
277. C4×#95C2×C31semidirect
325. C2×#124C4×C31semidirect
365. C22×Q8C2×C4×C31semidirect
402. C2×C22⋊C4C2×C4×C31semidirect
410. C2×C42C2×C4×C31semidirect
418. C31#14027direct (N × H)
590. C2×C4C31×#124semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C22×C4×D4×C312
C2×C31×#3912
C2×C31×#3902
C31×#14402
C31×C4⋊#952
C31×C22⋊#952
C4×C31×#952
#1402731