Finite Group Databasebeta

← C31×#10929 #21467688

Subgroups — C31×#10929 #21467688

Order 7936.

1010 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#104C211yesmaximal, characteristic
2C2×C31×#416C211yesmaximal, characteristic
3C2×C31×#408C211yesmaximal, characteristic
4C22×C4×C8×C31C211yesmaximal, characteristic, complemented
5C2×C31×#341C211yesmaximal, characteristic, complemented
6C2×C31×#339C211yesmaximal, characteristic, complemented
7C31×#1729C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C22×M16×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C23×C8×C31C2211yescharacteristic
12C23×C8×C31C2211yescharacteristic
13C2×C31×#117C2211yescharacteristic
14C22×C42×C31C2211yescharacteristic
15C2×C31×#104—22no—
16C2×C31×#104—22no—
17C2×C31×#104C414yescomplemented
18C31×#416—22no—
19C31×#416—22no—
20C2×C31×#103C412yescomplemented
21C2×C31×#102C412yescomplemented
22C31×#408—22no—
23C31×#408C414yescomplemented
24C2×C31×C22⋊C8—22no—
25C2×C4×C8×C31—22no—
26C2×C4×C8×C31—22no—
27C2×C4×C8×C31—22no—
28C31×#341—22no—
29C31×#339—22no—
30C31×#336—22no—
31C2×#41×C31—21no—
32C2×#41×C31—21no—
33C2×#41×C31—21no—
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×C31C2×C412yes—
42C2×#41×C31C2×C412yes—
43C22×Q8×C31C2×C411yescharacteristic
44C22×D4×C31—21no—
45C22×D4×C31C2×C411yescharacteristic
46C23×C4×C31—21no—
47C23×C4×C31—21no—
48C23×C4×C31C2311yescharacteristic
49C2×M16×C31—21no—
50C2×M16×C31—21no—
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×C31C2×C412yes—
60C2×M16×C31C2×C412yes—
61C22×C8×C31—21no—
62C22×C8×C31—21no—
63C22×C8×C31—21no—
64C22×C8×C31—21no—
65C22×C8×C31—21no—
66C22×C8×C31—21no—
67C22×C8×C31—21no—
68C22×C8×C31—21no—
69C22×C8×C31—21no—
70C22×C8×C31—21no—
71C22×C8×C31C2×C412yes—
72C22×C8×C31C2×C412yes—
73C22×C8×C31D412yes—
74C22×C8×C31D412yes—
75C22×C8×C31D412yes—
76C22×C8×C31D412yes—
77C31×#117—21no—
78C31×#117—21no—
79C31×#117—21no—
80C31×#117—21no—
81C2×C4⋊C4×C31C2×C412yes—
82C2×C22⋊C4×C31—21no—
83C2×C42×C31—21no—
84C2×C42×C31—21no—
85C2×C42×C31—21no—
86C2×C42×C31—21no—
87C2×C42×C31C2×C412yes—
88C2×C42×C31D412yes—
89C2×C42×C31D412yes—
90C31×#104—28no—
91C31×#103—24no—
92C31×#102—24no—
93C31×C22⋊C8—28no—
94C4×C8×C31—28no—
95C24×C31—21no—
96C24×C31#4111yescharacteristic
97#41×C31—22no—
98#41×C31—22no—
99#41×C31—22no—
100#41×C31—22no—
101#41×C31—22no—
102#41×C31—22no—
103#41×C31—22no—
104#41×C31—22no—
105#41×C31—41no—
106#41×C31—41no—
107#41×C31—41no—
108#41×C31—41no—
109#41×C31—41no—
110#41×C31—41no—
111#41×C31—41no—
112#41×C31—41no—
113C2×Q8×C31—21no—
114C2×Q8×C31—21no—
115C2×Q8×C31—21no—
116C2×Q8×C31—21no—
117C2×Q8×C31—21no—
118C2×Q8×C31C4212yes—
119C2×D4×C31—22no—
120C2×D4×C31—22no—
121C2×D4×C31—21no—
122C2×D4×C31—21no—
123C2×D4×C31—21no—
124C2×D4×C31—21no—
125C2×D4×C31—21no—
126C2×D4×C31—41no—
127C2×D4×C31—41no—
128C2×D4×C31—41no—
129C2×D4×C31—41no—
130C2×D4×C31C4212yes—
131C22×C4×C31—28no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—41no—
140C22×C4×C31—41no—
141C22×C4×C31—41no—
142C22×C4×C31—41no—
143C22×C4×C31C22×C411yescharacteristic
144C22×C4×C31C22×C411yescharacteristic
145C22×C4×C31C22×C411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31#4111yescharacteristic
153C22×C4×C31#4111yescharacteristic
154C22×C4×C31#4111yescharacteristic
155C22×C4×C31#4111yescharacteristic
156C22×C4×C31#4111yescharacteristic
157M16×C31—22no—
158M16×C31—22no—
159M16×C31—22no—
160M16×C31—22no—
161M16×C31—41no—
162M16×C31—41no—
163M16×C31—41no—
164M16×C31—41no—
165C2×C8×C31—22no—
166C2×C8×C31—22no—
167C2×C8×C31—22no—
168C2×C8×C31—22no—
169C2×C8×C31—22no—
170C2×C8×C31—22no—
171C2×C8×C31—22no—
172C2×C8×C31—22no—
173C2×C8×C31—22no—
174C2×C8×C31—22no—
175C2×C8×C31—22no—
176C2×C8×C31—22no—
177C2×C8×C31—22no—
178C2×C8×C31—22no—
179C2×C8×C31—41no—
180C2×C8×C31—41no—
181C2×C8×C31—41no—
182C2×C8×C31—41no—
183C2×C8×C31C22⋊C414yes—
184C2×C8×C31C22⋊C414yes—
185C4⋊C4×C31—22no—
186C4⋊C4×C31—22no—
187C22⋊C4×C31—41no—
188C22⋊C4×C31—41no—
189C42×C31—22no—
190C42×C31—22no—
191C42×C31—22no—
192C42×C31—41no—
193C42×C31—41no—
194C42×C31C22⋊C414yes—
195#10929C3111yesmaximal, characteristic, direct product factor, Sylow
196C23×C31—24no—
197C23×C31—22no—
198C23×C31—41no—
199C23×C31—41no—
200C23×C31—44no—
201C23×C31#11711yescharacteristic
202C23×C31C4×D411yescharacteristic
203C23×C31C4×D411yescharacteristic
204C23×C31#12111yescharacteristic
205C23×C31#12311yescharacteristic
206C23×C31#12411yescharacteristic
207C23×C31#12611yescharacteristic
208Q8×C31—22no—
209Q8×C31—22no—
210Q8×C31—41no—
211Q8×C31—41no—
212D4×C31—22no—
213D4×C31—22no—
214D4×C31—42no—
215D4×C31—42no—
216D4×C31—42no—
217D4×C31—42no—
218D4×C31—41no—
219D4×C31—41no—
220C2×C4×C31—28no—
221C2×C4×C31—28no—
222C2×C4×C31—28no—
223C2×C4×C31—24no—
224C2×C4×C31—22no—
225C2×C4×C31—41no—
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—44no—
233C2×C4×C31C2×C4211yescharacteristic
234C2×C4×C31C2×C22⋊C411yescharacteristic
235C2×C4×C31C2×C22⋊C411yescharacteristic
236C2×C4×C31C2×C22⋊C411yescharacteristic
237C2×C4×C31#11711yescharacteristic
238C2×C4×C31#11711yescharacteristic
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×C31C4×D411yescharacteristic
246C2×C4×C31C4×D411yescharacteristic
247C2×C4×C31C4×D411yescharacteristic
248C2×C4×C31C4×D411yescharacteristic
249C2×C4×C31#12011yescharacteristic
250C2×C4×C31#12111yescharacteristic
251C2×C4×C31#12111yescharacteristic
252C2×C4×C31#12111yescharacteristic
253C2×C4×C31#12111yescharacteristic
254C2×C4×C31#12111yescharacteristic
255C2×C4×C31#12311yescharacteristic
256C2×C4×C31#12311yescharacteristic
257C2×C4×C31#12411yescharacteristic
258C2×C4×C31#12411yescharacteristic
259C2×C4×C31#12611yescharacteristic
260C2×C4×C31#12711yescharacteristic
261C8×C31—24no—
262C8×C31—24no—
263C8×C31—42no—
264C8×C31—42no—
265C22×#104C2×C3111yescharacteristic
266C2×#416C2×C3111yescharacteristic
267C2×#408C2×C3111yescharacteristic
268C22×C4×C8C2×C3111yescharacteristic, complemented
269C2×#341C2×C3111yescharacteristic, complemented
270C2×#339C2×C3111yescharacteristic, complemented
271#1729C2×C3111yescharacteristic, complemented
272C22×C31—22no—
273C22×C31—22no—
274C22×C31—22no—
275C22×C31—22no—
276C22×C31—22no—
277C22×C31—22no—
278C22×C31—42no—
279C22×C31—44no—
280C22×C31—82no—
281C22×C31—82no—
282C22×C31C4×C22⋊C411yescharacteristic
283C22×C31#38611yescharacteristic
284C22×C31#38811yescharacteristic
285C22×C31#38811yescharacteristic
286C22×C31#38811yescharacteristic
287C22×C31#38811yescharacteristic
288C22×C31#39011yescharacteristic
289C22×C31#44314yes—
290C4×C31—28no—
291C4×C31—42no—
292C4×C31—82no—
293C4×C31C4×C22⋊C411yescharacteristic
294C4×C31C4×C22⋊C411yescharacteristic
295C4×C31#38611yescharacteristic
296C4×C31#38611yescharacteristic
297C4×C31#38811yescharacteristic
298C4×C31#38811yescharacteristic
299C4×C31#39011yescharacteristic
300C4×C31#39011yescharacteristic
301C22×#41C22×C3111yescharacteristic
302C22×M16C22×C3111yescharacteristic
303C22×M16C22×C3111yescharacteristic
304C23×C8C22×C3111yescharacteristic
305C23×C8C22×C3111yescharacteristic
306C2×#117C22×C3111yescharacteristic
307C22×C42C22×C3111yescharacteristic
308C2×#104—22no—
309C2×#104—22no—
310C2×#104C4×C3114yescomplemented
311#416—22no—
312#416—22no—
313C2×#103C4×C3112yescomplemented
314C2×#102C4×C3112yescomplemented
315#408—22no—
316#408C4×C3114yescomplemented
317C2×C22⋊C8—22no—
318C2×C4×C8—22no—
319C2×C4×C8—22no—
320C2×C4×C8—22no—
321#341—22no—
322#339—22no—
323#336—22no—
324C2×C31—21no—
325C2×C31—21no—
326C2×C31—21no—
327C2×C31—21no—
328C2×C31—82no—
329C2×C31#143711yescharacteristic
330C2×C31#176412yes—
331C2×C31#193712yes—
332C2×C31#197412yes—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41C2×C4×C3112yes—
344C2×#41C2×C4×C3112yes—
345C22×Q8C2×C4×C3111yescharacteristic
346C22×D4—21no—
347C22×D4C2×C4×C3111yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4C23×C3111yescharacteristic
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16C2×C4×C3112yes—
362C2×M16C2×C4×C3112yes—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8C2×C4×C3112yes—
374C22×C8C2×C4×C3112yes—
375C22×C8D4×C3112yes—
376C22×C8D4×C3112yes—
377C22×C8D4×C3112yes—
378C22×C8D4×C3112yes—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383C2×C4⋊C4C2×C4×C3112yes—
384C2×C22⋊C4—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C2×C4×C3112yes—
390C2×C42D4×C3112yes—
391C2×C42D4×C3112yes—
392#104—28no—
393#103—24no—
394#102—24no—
395C22⋊C8—28no—
396C4×C8—28no—
397C31#1092911yescharacteristic, direct product factor, Sylow
398C24—21no—
399C24#41×C3111yescharacteristic
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8C42×C3112yes—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4C42×C3112yes—
434C22×C4—28no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4C22×C4×C3111yescharacteristic
447C22×C4C22×C4×C3111yescharacteristic
448C22×C4C22×C4×C3111yescharacteristic
449C22×C4C2×D4×C3111yescharacteristic
450C22×C4C2×D4×C3111yescharacteristic
451C22×C4C2×D4×C3111yescharacteristic
452C22×C4C2×D4×C3111yescharacteristic
453C22×C4C2×D4×C3111yescharacteristic
454C22×C4C2×D4×C3111yescharacteristic
455C22×C4#41×C3111yescharacteristic
456C22×C4#41×C3111yescharacteristic
457C22×C4#41×C3111yescharacteristic
458C22×C4#41×C3111yescharacteristic
459C22×C4#41×C3111yescharacteristic
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8C22⋊C4×C3114yes—
487C2×C8C22⋊C4×C3114yes—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—22no—
493C42—22no—
494C42—22no—
495C42—41no—
496C42—41no—
497C42C22⋊C4×C3114yes—
498C23—24no—
499C23—22no—
500C23—44no—
501C23—41no—
502C23—41no—
503C23C31×#11711yescharacteristic
504C23C4×D4×C3111yescharacteristic
505C23C4×D4×C3111yescharacteristic
506C23C31×#12111yescharacteristic
507C23C31×#12311yescharacteristic
508C23C31×#12411yescharacteristic
509C23C31×#12611yescharacteristic
510Q8—22no—
511Q8—22no—
512Q8—41no—
513Q8—41no—
514D4—22no—
515D4—22no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—41no—
521D4—41no—
522C2×C4—28no—
523C2×C4—28no—
524C2×C4—28no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4C2×C42×C3111yescharacteristic
536C2×C4C2×C22⋊C4×C3111yescharacteristic
537C2×C4C2×C22⋊C4×C3111yescharacteristic
538C2×C4C2×C22⋊C4×C3111yescharacteristic
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×C4C4×D4×C3111yescharacteristic
550C2×C4C4×D4×C3111yescharacteristic
551C2×C4C31×#12011yescharacteristic
552C2×C4C31×#12111yescharacteristic
553C2×C4C31×#12111yescharacteristic
554C2×C4C31×#12111yescharacteristic
555C2×C4C31×#12111yescharacteristic
556C2×C4C31×#12111yescharacteristic
557C2×C4C31×#12311yescharacteristic
558C2×C4C31×#12311yescharacteristic
559C2×C4C31×#12411yescharacteristic
560C2×C4C31×#12411yescharacteristic
561C2×C4C31×#12611yescharacteristic
562C2×C4C31×#12711yescharacteristic
563C8—24no—
564C8—24no—
565C8—42no—
566C8—42no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—42no—
574C22—44no—
575C22—82no—
576C22—82no—
577C22C4×C22⋊C4×C3111yescharacteristic
578C22C31×#38611yescharacteristic
579C22C31×#38811yescharacteristic
580C22C31×#38811yescharacteristic
581C22C31×#38811yescharacteristic
582C22C31×#38811yescharacteristic
583C22C31×#39011yescharacteristic
584C22C31×#44314yes—
585C4—28no—
586C4—42no—
587C4—82no—
588C4C4×C22⋊C4×C3111yescharacteristic
589C4C4×C22⋊C4×C3111yescharacteristic
590C4C31×#38611yescharacteristic
591C4C31×#38611yescharacteristic
592C4C31×#38811yescharacteristic
593C4C31×#38811yescharacteristic
594C4C31×#39011yescharacteristic
595C4C31×#39011yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—82no—
601C2C31×#143711yescharacteristic
602C2C31×#176412yes—
603C2C31×#193712yes—
604C2C31×#197412yes—
subgroupG/H
centerC22×C4×C31C2×D4
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
socleC23×C31C4×D4
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C23×C8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C22×C4×C8×C31C2semidirect
5. C2×C31×#341C2semidirect
6. C2×C31×#339C2semidirect
7. C31×#1729C2semidirect
17. C2×C31×#104C4semidirect
20. C2×C31×#103C4semidirect
21. C2×C31×#102C4semidirect
23. C31×#408C4semidirect
195. #10929C31direct (N × H)
268. C22×C4×C8C2×C31semidirect
269. C2×#341C2×C31semidirect
270. C2×#339C2×C31semidirect
271. #1729C2×C31semidirect
310. C2×#104C4×C31semidirect
313. C2×#103C4×C31semidirect
314. C2×#102C4×C31semidirect
316. #408C4×C31semidirect
397. C31#10929direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1042
C2×C31×#4162
C2×C31×#4082
C22×C4×C8×C312
C2×C31×#3412
C2×C31×#3392
C31×#17292
#1092931