Finite Group Databasebeta

← C31×#21080 #21477839

Subgroups — C31×#21080 #21477839

Order 7936.

1000 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#430C211yesmaximal, characteristic, complemented
2C2×C31×#421C211yesmaximal, characteristic
3C2×C31×#421C211yesmaximal, characteristic
4C2×C31×#413C211yesmaximal, characteristic
5C31×#2873C211yesmaximal, characteristic, complemented
6C31×#1932C218yesmaximal, complemented
7C2×C31×#344C211yesmaximal, characteristic, complemented
8C31×#1733C211yesmaximal, characteristic, complemented
9C22×#41×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C22×M16×C31C2211yescharacteristic
13C22×M16×C31C2211yescharacteristic
14C2×C31×#117C2211yescharacteristic
15C2×C31×#117C2211yescharacteristic
16C31×#430—22no—
17C31×#430C2214yescomplemented
18C2×C31×#108—22no—
19C31×#421—22no—
20C31×#421—22no—
21C31×#421—22no—
22C31×#421C2214yes—
23C2×C31×#104—22no—
24C2×C31×#104C2214yes—
25C31×#413C414yescomplemented
26C31×#413C2214yes—
27C2×C31×#101C412yescomplemented
28C2×C31×#100C412yescomplemented
29C31×#405—22no—
30C31×#405—22no—
31C4×M16×C31C2214yescomplemented
32C31×#344C2214yescomplemented
33C31×#339C2214yescomplemented
34C2×#41×C31—21no—
35C2×#41×C31—21no—
36C2×#41×C31—21no—
37C2×#41×C31—21no—
38C2×#41×C31—21no—
39C2×#41×C31—21no—
40C2×#41×C31—21no—
41C2×#41×C31—21no—
42C2×#41×C31—21no—
43C2×#41×C31—21no—
44C2×#41×C31C2×C412yes—
45C2×#41×C31C2312yes—
46C22×Q8×C31C2×C411yescharacteristic
47C22×D4×C31—21no—
48C22×D4×C31C2×C411yescharacteristic
49C23×C4×C31—21no—
50C23×C4×C31C2311yescharacteristic
51C2×M16×C31—21no—
52C2×M16×C31—21no—
53C2×M16×C31—21no—
54C2×M16×C31—21no—
55C2×M16×C31—21no—
56C2×M16×C31—21no—
57C2×M16×C31—21no—
58C2×M16×C31—21no—
59C2×M16×C31—21no—
60C2×M16×C31—21no—
61C2×M16×C31—21no—
62C2×M16×C31—21no—
63C2×M16×C31—21no—
64C2×M16×C31—21no—
65C2×M16×C31C2×C412yes—
66C2×M16×C31C2×C412yes—
67C2×M16×C31C2×C412yes—
68C2×M16×C31C2×C412yes—
69C2×M16×C31D412yes—
70C2×M16×C31D412yes—
71C2×M16×C31C2312yes—
72C2×M16×C31C2312yes—
73C2×M16×C31C2312yes—
74C2×M16×C31C2312yes—
75C22×C8×C31—21no—
76C22×C8×C31—21no—
77C22×C8×C31—21no—
78C22×C8×C31—21no—
79C31×#117—21no—
80C31×#117—21no—
81C31×#117—21no—
82C31×#117—21no—
83C31×#117—21no—
84C31×#117D412yes—
85C31×#117D412yes—
86C31×#117C2312yes—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—21no—
91C2×C42×C31—21no—
92C2×C42×C31C2312yes—
93C31×#108—28no—
94C31×#104—28no—
95C31×#104—28no—
96C31×#101C2×C418yescomplemented
97C31×#100C2×C418yescomplemented
98C31×#97—24no—
99C4×C8×C31—24no—
100C24×C31—21no—
101C24×C31#4111yescharacteristic
102#41×C31—22no—
103#41×C31—22no—
104#41×C31—22no—
105#41×C31—22no—
106#41×C31—22no—
107#41×C31—22no—
108#41×C31—22no—
109#41×C31—22no—
110#41×C31—41no—
111#41×C31—41no—
112#41×C31—41no—
113#41×C31—41no—
114#41×C31—41no—
115#41×C31—41no—
116#41×C31—41no—
117#41×C31—41no—
118C2×Q8×C31—21no—
119C2×Q8×C31—21no—
120C2×Q8×C31—21no—
121C2×Q8×C31—21no—
122C2×Q8×C31—21no—
123C2×Q8×C31C22×C412yes—
124C2×D4×C31—22no—
125C2×D4×C31—22no—
126C2×D4×C31—21no—
127C2×D4×C31—21no—
128C2×D4×C31—21no—
129C2×D4×C31—21no—
130C2×D4×C31—21no—
131C2×D4×C31—41no—
132C2×D4×C31—41no—
133C2×D4×C31—41no—
134C2×D4×C31—41no—
135C2×D4×C31C22×C412yes—
136C22×C4×C31—21no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—41no—
141C22×C4×C31—41no—
142C22×C4×C31—41no—
143C22×C4×C31—41no—
144C22×C4×C31—41no—
145C22×C4×C31C22×C411yescharacteristic
146C22×C4×C31C22×C411yescharacteristic
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31#4111yescharacteristic
152C22×C4×C31#4111yescharacteristic
153C22×C4×C31#4111yescharacteristic
154C22×C4×C31#4111yescharacteristic
155C22×C4×C31#4111yescharacteristic
156C22×C4×C31#4111yescharacteristic
157C22×C4×C31#4111yescharacteristic
158C22×C4×C31C2411yescharacteristic
159M16×C31—22no—
160M16×C31—22no—
161M16×C31—22no—
162M16×C31—22no—
163M16×C31—22no—
164M16×C31—22no—
165M16×C31—22no—
166M16×C31—22no—
167M16×C31—22no—
168M16×C31—22no—
169M16×C31—22no—
170M16×C31—41no—
171M16×C31—41no—
172M16×C31C22×C414yes—
173M16×C31C22×C414yes—
174M16×C31C2×D414yes—
175C2×C8×C31—22no—
176C2×C8×C31—22no—
177C2×C8×C31—22no—
178C2×C8×C31—22no—
179C2×C8×C31—22no—
180C2×C8×C31—22no—
181C2×C8×C31—22no—
182C2×C8×C31—22no—
183C2×C8×C31—22no—
184C2×C8×C31—22no—
185C2×C8×C31—41no—
186C2×C8×C31—41no—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—22no—
189C4⋊C4×C31—22no—
190C4⋊C4×C31—41no—
191C22⋊C4×C31—22no—
192C22⋊C4×C31—22no—
193C22⋊C4×C31—22no—
194C22⋊C4×C31—41no—
195C42×C31—22no—
196C42×C31—22no—
197C42×C31—41no—
198C42×C31C2×D414yes—
199#21080C3111yesmaximal, characteristic, direct product factor, Sylow
200C23×C31—22no—
201C23×C31—41no—
202C23×C31—41no—
203C23×C31—81no—
204C23×C31—82no—
205C23×C31#11711yescharacteristic
206C23×C31#11711yescharacteristic
207C23×C31#12311yescharacteristic
208C23×C31#12311yescharacteristic
209C23×C31#12411yescharacteristic
210C23×C31#12411yescharacteristic
211C23×C31C2×#4111yescharacteristic
212Q8×C31—22no—
213Q8×C31—22no—
214Q8×C31—41no—
215Q8×C31—41no—
216D4×C31—22no—
217D4×C31—22no—
218D4×C31—42no—
219D4×C31—42no—
220D4×C31—42no—
221D4×C31—42no—
222D4×C31—41no—
223D4×C31—41no—
224C2×C4×C31—22no—
225C2×C4×C31—24no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—82no—
234C2×C4×C31—82no—
235C2×C4×C31#11711yescharacteristic
236C2×C4×C31#11711yescharacteristic
237C2×C4×C31C4×D411yescharacteristic
238C2×C4×C31C4×D411yescharacteristic
239C2×C4×C31C4×D411yescharacteristic
240C2×C4×C31C4×D411yescharacteristic
241C2×C4×C31C4×D411yescharacteristic
242C2×C4×C31C4×D411yescharacteristic
243C2×C4×C31C4×D411yescharacteristic
244C2×C4×C31C4×D411yescharacteristic
245C2×C4×C31#12111yescharacteristic
246C2×C4×C31#12111yescharacteristic
247C2×C4×C31#12111yescharacteristic
248C2×C4×C31#12111yescharacteristic
249C2×C4×C31#12311yescharacteristic
250C2×C4×C31#12311yescharacteristic
251C2×C4×C31#12411yescharacteristic
252C2×C4×C31#12411yescharacteristic
253C2×C4×C31#12611yescharacteristic
254C2×C4×C31#12611yescharacteristic
255C2×C4×C31#12611yescharacteristic
256C2×C4×C31#12611yescharacteristic
257C2×C4×C31C23×C411yescharacteristic
258C2×C4×C31C22×D411yescharacteristic
259C2×C4×C31C22×D411yescharacteristic
260C2×C4×C31C2×#4111yescharacteristic
261C2×C4×C31C2×#4111yescharacteristic
262C2×C4×C31C2×#4111yescharacteristic
263C8×C31—24no—
264C8×C31—24no—
265C8×C31—24no—
266C8×C31—42no—
267C2×#430C2×C3111yescharacteristic, complemented
268C2×#421C2×C3111yescharacteristic
269C2×#421C2×C3111yescharacteristic
270C2×#413C2×C3111yescharacteristic
271#2873C2×C3111yescharacteristic, complemented
272#1932C2×C3118yescomplemented
273C2×#344C2×C3111yescharacteristic, complemented
274#1733C2×C3111yescharacteristic, complemented
275C22×C31—41no—
276C22×C31—41no—
277C22×C31—41no—
278C22×C31—41no—
279C22×C31—41no—
280C22×C31—41no—
281C22×C31—41no—
282C22×C31—42no—
283C22×C31—82no—
284C22×C31—82no—
285C22×C31—82no—
286C22×C31#38811yescharacteristic
287C22×C31#38811yescharacteristic
288C22×C31#38811yescharacteristic
289C22×C31#38811yescharacteristic
290C22×C31C2×#11711yescharacteristic
291C22×C31C2×#12311yescharacteristic
292C22×C31C2×#12411yescharacteristic
293C4×C31—44no—
294C4×C31—42no—
295C4×C31—82no—
296C4×C31#38811yescharacteristic
297C4×C31#38811yescharacteristic
298C4×C31#38811yescharacteristic
299C4×C31#38811yescharacteristic
300C4×C31C2×C4×D411yescharacteristic
301C4×C31C2×C4×D411yescharacteristic
302C4×C31C2×#12111yescharacteristic
303C4×C31C2×#12611yescharacteristic
304C22×#41C22×C3111yescharacteristic
305C22×M16C22×C3111yescharacteristic
306C22×M16C22×C3111yescharacteristic
307C22×M16C22×C3111yescharacteristic
308C22×M16C22×C3111yescharacteristic
309C2×#117C22×C3111yescharacteristic
310C2×#117C22×C3111yescharacteristic
311#430—22no—
312#430C22×C3114yescomplemented
313C2×#108—22no—
314#421—22no—
315#421—22no—
316#421—22no—
317#421C22×C3114yes—
318C2×#104—22no—
319C2×#104C22×C3114yes—
320#413C4×C3114yescomplemented
321#413C22×C3114yes—
322C2×#101C4×C3112yescomplemented
323C2×#100C4×C3112yescomplemented
324#405—22no—
325#405—22no—
326C4×M16C22×C3114yescomplemented
327#344C22×C3114yescomplemented
328#339C22×C3114yescomplemented
329C2×C31—21no—
330C2×C31—21no—
331C2×C31—21no—
332C2×C31—21no—
333C2×C31—21no—
334C2×C31—21no—
335C2×C31—21no—
336C2×C31—82no—
337C2×C31C2×#38811yescharacteristic
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41C2×C4×C3112yes—
349C2×#41C23×C3112yes—
350C22×Q8C2×C4×C3111yescharacteristic
351C22×D4—21no—
352C22×D4C2×C4×C3111yescharacteristic
353C23×C4—21no—
354C23×C4C23×C3111yescharacteristic
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16C2×C4×C3112yes—
370C2×M16C2×C4×C3112yes—
371C2×M16C2×C4×C3112yes—
372C2×M16C2×C4×C3112yes—
373C2×M16D4×C3112yes—
374C2×M16D4×C3112yes—
375C2×M16C23×C3112yes—
376C2×M16C23×C3112yes—
377C2×M16C23×C3112yes—
378C2×M16C23×C3112yes—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117D4×C3112yes—
389#117D4×C3112yes—
390#117C23×C3112yes—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42C23×C3112yes—
397#108—28no—
398#104—28no—
399#104—28no—
400#101C2×C4×C3118yescomplemented
401#100C2×C4×C3118yescomplemented
402#97—24no—
403C4×C8—24no—
404C31#2108011yescharacteristic, direct product factor, Sylow
405C24—21no—
406C24#41×C3111yescharacteristic
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C22×C4×C3112yes—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C22×C4×C3112yes—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4C22×C4×C3111yescharacteristic
451C22×C4C22×C4×C3111yescharacteristic
452C22×C4C2×D4×C3111yescharacteristic
453C22×C4C2×D4×C3111yescharacteristic
454C22×C4C2×D4×C3111yescharacteristic
455C22×C4C2×D4×C3111yescharacteristic
456C22×C4#41×C3111yescharacteristic
457C22×C4#41×C3111yescharacteristic
458C22×C4#41×C3111yescharacteristic
459C22×C4#41×C3111yescharacteristic
460C22×C4#41×C3111yescharacteristic
461C22×C4#41×C3111yescharacteristic
462C22×C4#41×C3111yescharacteristic
463C22×C4C24×C3111yescharacteristic
464M16—22no—
465M16—22no—
466M16—22no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—41no—
476M16—41no—
477M16C22×C4×C3114yes—
478M16C22×C4×C3114yes—
479M16C2×D4×C3114yes—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—41no—
491C2×C8—41no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C42—22no—
501C42—22no—
502C42—41no—
503C42C2×D4×C3114yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—81no—
508C23—82no—
509C23C31×#11711yescharacteristic
510C23C31×#11711yescharacteristic
511C23C31×#12311yescharacteristic
512C23C31×#12311yescharacteristic
513C23C31×#12411yescharacteristic
514C23C31×#12411yescharacteristic
515C23C2×#41×C3111yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—41no—
519Q8—41no—
520D4—22no—
521D4—22no—
522D4—42no—
523D4—42no—
524D4—42no—
525D4—42no—
526D4—41no—
527D4—41no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4C31×#11711yescharacteristic
540C2×C4C31×#11711yescharacteristic
541C2×C4C4×D4×C3111yescharacteristic
542C2×C4C4×D4×C3111yescharacteristic
543C2×C4C4×D4×C3111yescharacteristic
544C2×C4C4×D4×C3111yescharacteristic
545C2×C4C4×D4×C3111yescharacteristic
546C2×C4C4×D4×C3111yescharacteristic
547C2×C4C4×D4×C3111yescharacteristic
548C2×C4C4×D4×C3111yescharacteristic
549C2×C4C31×#12111yescharacteristic
550C2×C4C31×#12111yescharacteristic
551C2×C4C31×#12111yescharacteristic
552C2×C4C31×#12111yescharacteristic
553C2×C4C31×#12311yescharacteristic
554C2×C4C31×#12311yescharacteristic
555C2×C4C31×#12411yescharacteristic
556C2×C4C31×#12411yescharacteristic
557C2×C4C31×#12611yescharacteristic
558C2×C4C31×#12611yescharacteristic
559C2×C4C31×#12611yescharacteristic
560C2×C4C31×#12611yescharacteristic
561C2×C4C23×C4×C3111yescharacteristic
562C2×C4C22×D4×C3111yescharacteristic
563C2×C4C22×D4×C3111yescharacteristic
564C2×C4C2×#41×C3111yescharacteristic
565C2×C4C2×#41×C3111yescharacteristic
566C2×C4C2×#41×C3111yescharacteristic
567C8—24no—
568C8—24no—
569C8—24no—
570C8—42no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22C31×#38811yescharacteristic
583C22C31×#38811yescharacteristic
584C22C31×#38811yescharacteristic
585C22C31×#38811yescharacteristic
586C22C2×C31×#11711yescharacteristic
587C22C2×C31×#12311yescharacteristic
588C22C2×C31×#12411yescharacteristic
589C4—44no—
590C4—42no—
591C4—82no—
592C4C31×#38811yescharacteristic
593C4C31×#38811yescharacteristic
594C4C31×#38811yescharacteristic
595C4C31×#38811yescharacteristic
596C4C2×C4×D4×C3111yescharacteristic
597C4C2×C4×D4×C3111yescharacteristic
598C4C2×C31×#12111yescharacteristic
599C4C2×C31×#12611yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—82no—
608C2C2×C31×#38811yescharacteristic
subgroupG/H
centerC4×C31C2×#121
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC2×C31C2×#388
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#430C2semidirect
5. C31×#2873C2semidirect
6. C31×#1932C2semidirect
7. C2×C31×#344C2semidirect
8. C31×#1733C2semidirect
17. C31×#430C22semidirect
25. C31×#413C4semidirect
27. C2×C31×#101C4semidirect
28. C2×C31×#100C4semidirect
31. C4×M16×C31C22semidirect
32. C31×#344C22semidirect
33. C31×#339C22semidirect
96. C31×#101C2×C4semidirect
97. C31×#100C2×C4semidirect
199. #21080C31direct (N × H)
267. C2×#430C2×C31semidirect
271. #2873C2×C31semidirect
272. #1932C2×C31semidirect
273. C2×#344C2×C31semidirect
274. #1733C2×C31semidirect
312. #430C22×C31semidirect
320. #413C4×C31semidirect
322. C2×#101C4×C31semidirect
323. C2×#100C4×C31semidirect
326. C4×M16C22×C31semidirect
327. #344C22×C31semidirect
328. #339C22×C31semidirect
400. #101C2×C4×C31semidirect
401. #100C2×C4×C31semidirect
404. C31#21080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4302
C2×C31×#4212
C2×C31×#4132
C31×#28732
C31×#19322
C2×C31×#3442
C31×#17332
#2108031