Finite Group Databasebeta

← C31×#11063 #21467822

Subgroups — C31×#11063 #21467822

Order 7936.

1174 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#418C211yesmaximal, characteristic
2C2×C31×#418C211yesmaximal, characteristic
3C31×#2317C211yesmaximal, characteristic, complemented
4C2×C31×#390C211yesmaximal, characteristic
5C2×C31×#343C211yesmaximal, characteristic, complemented
6C2×C31×#339C211yesmaximal, characteristic, complemented
7C2×C31×#339C211yesmaximal, characteristic, complemented
8C23×D4×C31C2211yescharacteristic
9C22×M16×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C2×C31×#117C2211yescharacteristic
12C2×C31×#117C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C22⋊C4×C31—22no—
15C22×C42×C31C2211yescharacteristic
16C31×#418—22no—
17C31×#418—22no—
18C31×#418—22no—
19C31×#418C414yescomplemented
20C2×C31×#102—21no—
21C2×C31×#102—21no—
22C2×C31×#102—22no—
23C31×#390—22no—
24C31×#390—22no—
25C31×#389—22no—
26C31×#385—22no—
27C31×#384—21no—
28C31×#382—21no—
29C31×#343—22no—
30C31×#339—22no—
31C31×#339—22no—
32C25×C31—21no—
33C22×D4×C31—21no—
34C22×D4×C31—21no—
35C22×D4×C31—21no—
36C22×D4×C31—21no—
37C22×D4×C31—21no—
38C22×D4×C31—21no—
39C22×D4×C31—21no—
40C22×D4×C31—21no—
41C22×D4×C31—21no—
42C22×D4×C31—21no—
43C22×D4×C31—21no—
44C22×D4×C31C2×C412yes—
45C22×D4×C31D412yes—
46C22×D4×C31Q812yes—
47C23×C4×C31—21no—
48C23×C4×C31D412yes—
49C23×C4×C31C2311yescharacteristic
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×C31—21no—
60C2×M16×C31C2×C412yes—
61C2×M16×C31D412yes—
62C22×C8×C31—21no—
63C22×C8×C31—21no—
64C31×#117—21no—
65C31×#117—21no—
66C31×#117—21no—
67C31×#117—21no—
68C31×#117—21no—
69C31×#117—21no—
70C31×#117C2×C412yes—
71C31×#117D412yes—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31D411yescharacteristic
80C2×C4⋊C4×C31D411yescharacteristic
81C2×C4⋊C4×C31D412yes—
82C2×C22⋊C4×C31—21no—
83C2×C22⋊C4×C31—28no—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—48no—
86C2×C42×C31—21no—
87C2×C42×C31—21no—
88C2×C42×C31—21no—
89C2×C42×C31—21no—
90C2×C42×C31—21no—
91C2×C42×C31—21no—
92C2×C42×C31—21no—
93C2×C42×C31D412yes—
94C31×#102—24no—
95C31×#102—24no—
96C31×#102—28no—
97C31×#95—24no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—22no—
101C24×C31—44no—
102C24×C31—44no—
103C24×C31—41no—
104C24×C31—41no—
105C24×C31—41no—
106C24×C31—41no—
107C24×C31C2×D411yescharacteristic
108C2×D4×C31—22no—
109C2×D4×C31—22no—
110C2×D4×C31—22no—
111C2×D4×C31—22no—
112C2×D4×C31—22no—
113C2×D4×C31—22no—
114C2×D4×C31—22no—
115C2×D4×C31—22no—
116C2×D4×C31—22no—
117C2×D4×C31—22no—
118C2×D4×C31—22no—
119C2×D4×C31—22no—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—22no—
123C2×D4×C31—41no—
124C2×D4×C31—41no—
125C2×D4×C31—41no—
126C2×D4×C31—41no—
127C2×D4×C31—41no—
128C2×D4×C31—41no—
129C2×D4×C31—41no—
130C2×D4×C31—41no—
131C2×D4×C31—41no—
132C2×D4×C31—41no—
133C2×D4×C31—41no—
134C2×D4×C31—41no—
135C2×D4×C31C4⋊C414yescomplemented
136C22×C4×C31—24no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—21no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—22no—
144C22×C4×C31—42no—
145C22×C4×C31—41no—
146C22×C4×C31—41no—
147C22×C4×C31—44no—
148C22×C4×C31C22×C411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×Q811yescharacteristic
156C22×C4×C31#4111yescharacteristic
157C22×C4×C31#4111yescharacteristic
158C22×C4×C31#4111yescharacteristic
159C22×C4×C31#4111yescharacteristic
160C22×C4×C31#4111yescharacteristic
161C22×C4×C31#4111yescharacteristic
162M16×C31—22no—
163M16×C31—22no—
164M16×C31—22no—
165M16×C31—22no—
166M16×C31—41no—
167M16×C31—41no—
168M16×C31—41no—
169M16×C31—41no—
170C2×C8×C31—22no—
171C2×C8×C31—22no—
172C2×C8×C31—41no—
173C2×C8×C31—41no—
174C2×C8×C31—41no—
175C2×C8×C31—41no—
176C4⋊C4×C31—22no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—21no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—21no—
181C4⋊C4×C31—41no—
182C4⋊C4×C31—41no—
183C4⋊C4×C31—41no—
184C4⋊C4×C31—41no—
185C4⋊C4×C31—84no—
186C4⋊C4×C31C22⋊C414yescomplemented
187C22⋊C4×C31—22no—
188C22⋊C4×C31—22no—
189C22⋊C4×C31—416no—
190C22⋊C4×C31—41no—
191C22⋊C4×C31—41no—
192C42×C31—22no—
193C42×C31—22no—
194C42×C31—22no—
195C42×C31—22no—
196C42×C31—41no—
197C42×C31—41no—
198C42×C31—41no—
199C42×C31—41no—
200#11063C3111yesmaximal, characteristic, direct product factor, Sylow
201C23×C31—22no—
202C23×C31—22no—
203C23×C31—24no—
204C23×C31—44no—
205C23×C31—48no—
206C23×C31—44no—
207C23×C31—48no—
208C23×C31—42no—
209C23×C31—42no—
210C23×C31—42no—
211C23×C31—42no—
212C23×C31—42no—
213C23×C31—42no—
214C23×C31—84no—
215C23×C31—82no—
216C23×C31—82no—
217C23×C31—84no—
218C23×C31—82no—
219C23×C31—82no—
220C23×C31C4×D411yescharacteristic
221C23×C31#12011yescharacteristic
222C23×C31#12011yescharacteristic
223C23×C31#12111yescharacteristic
224C23×C31#12111yescharacteristic
225C23×C31C22⋊Q811yescharacteristic
226C23×C31#12411yescharacteristic
227D4×C31—24no—
228D4×C31—24no—
229D4×C31—42no—
230D4×C31—42no—
231D4×C31—42no—
232D4×C31—42no—
233D4×C31—42no—
234D4×C31—42no—
235C2×C4×C31—24no—
236C2×C4×C31—24no—
237C2×C4×C31—44no—
238C2×C4×C31—42no—
239C2×C4×C31—44no—
240C2×C4×C31—42no—
241C2×C4×C31—42no—
242C2×C4×C31—42no—
243C2×C4×C31—44no—
244C2×C4×C31—41no—
245C2×C4×C31—41no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
248C2×C4×C31—44no—
249C2×C4×C31—42no—
250C2×C4×C31—82no—
251C2×C4×C31C2×C22⋊C411yescharacteristic
252C2×C4×C31C2×C4⋊C411yescharacteristic
253C2×C4×C31#11711yescharacteristic
254C2×C4×C31C4×D411yescharacteristic
255C2×C4×C31C4×D411yescharacteristic
256C2×C4×C31C4×D411yescharacteristic
257C2×C4×C31#12011yescharacteristic
258C2×C4×C31#12111yescharacteristic
259C2×C4×C31#12111yescharacteristic
260C2×C4×C31#12111yescharacteristic
261C2×C4×C31#12111yescharacteristic
262C2×C4×C31#12111yescharacteristic
263C2×C4×C31#12111yescharacteristic
264C2×C4×C31C22⋊Q811yescharacteristic
265C2×C4×C31C22⋊Q811yescharacteristic
266C2×C4×C31C22⋊Q811yescharacteristic
267C2×C4×C31C22⋊Q811yescharacteristic
268C2×C4×C31C22⋊Q811yescharacteristic
269C2×C4×C31#12311yescharacteristic
270C2×C4×C31#12311yescharacteristic
271C2×C4×C31#12311yescharacteristic
272C2×C4×C31#12311yescharacteristic
273C2×C4×C31#12311yescharacteristic
274C2×C4×C31#12411yescharacteristic
275C2×C4×C31#12411yescharacteristic
276C2×C4×C31#12611yescharacteristic
277C2×C4×C31#12611yescharacteristic
278C2×C4×C31#12711yescharacteristic
279C8×C31—42no—
280C8×C31—42no—
281C2×#418C2×C3111yescharacteristic
282C2×#418C2×C3111yescharacteristic
283#2317C2×C3111yescharacteristic, complemented
284C2×#390C2×C3111yescharacteristic
285C2×#343C2×C3111yescharacteristic, complemented
286C2×#339C2×C3111yescharacteristic, complemented
287C2×#339C2×C3111yescharacteristic, complemented
288C22×C31—22no—
289C22×C31—22no—
290C22×C31—21no—
291C22×C31—21no—
292C22×C31—21no—
293C22×C31—21no—
294C22×C31—22no—
295C22×C31—22no—
296C22×C31—48no—
297C22×C31—44no—
298C22×C31—84no—
299C22×C31—84no—
300C22×C31—84no—
301C22×C31—84no—
302C22×C31—82no—
303C22×C31—82no—
304C22×C31—84no—
305C22×C31#38511yescharacteristic
306C22×C31#38611yescharacteristic
307C22×C31#38811yescharacteristic
308C22×C31#39211yescharacteristic
309C22×C31#39311yescharacteristic
310C22×C31#39411yescharacteristic
311C22×C31#39611yescharacteristic
312C22×C31#45312yes—
313C22×C31#45412yes—
314C4×C31—44no—
315C4×C31—44no—
316C4×C31—81no—
317C4×C31—82no—
318C4×C31—81no—
319C4×C31#38011yescharacteristic
320C4×C31#38511yescharacteristic
321C4×C31#38811yescharacteristic
322C4×C31#39011yescharacteristic
323C4×C31#39411yescharacteristic
324C4×C31#39611yescharacteristic
325C4×C31#39711yescharacteristic
326C4×C31#39911yescharacteristic
327C23×D4C22×C3111yescharacteristic
328C22×M16C22×C3111yescharacteristic
329C22×M16C22×C3111yescharacteristic
330C2×#117C22×C3111yescharacteristic
331C2×#117C22×C3111yescharacteristic
332C22×C4⋊C4C22×C3111yescharacteristic
333C22×C22⋊C4—22no—
334C22×C42C22×C3111yescharacteristic
335#418—22no—
336#418—22no—
337#418—22no—
338#418C4×C3114yescomplemented
339C2×#102—21no—
340C2×#102—21no—
341C2×#102—22no—
342#390—22no—
343#390—22no—
344#389—22no—
345#385—22no—
346#384—21no—
347#382—21no—
348#343—22no—
349#339—22no—
350#339—22no—
351C2×C31—21no—
352C2×C31—21no—
353C2×C31—21no—
354C2×C31—21no—
355C2×C31—84no—
356C2×C31#143911yescharacteristic
357C2×C31#188312yes—
358C2×C31#200211yescharacteristic
359C2×C31#200311yescharacteristic
360C2×C31#202712yes—
361C25—21no—
362C22×D4—21no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—21no—
373C22×D4C2×C4×C3112yes—
374C22×D4D4×C3112yes—
375C22×D4Q8×C3112yes—
376C23×C4—21no—
377C23×C4D4×C3112yes—
378C23×C4C23×C3111yescharacteristic
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16C2×C4×C3112yes—
390C2×M16D4×C3112yes—
391C22×C8—21no—
392C22×C8—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117C2×C4×C3112yes—
400#117D4×C3112yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4D4×C3111yescharacteristic
409C2×C4⋊C4D4×C3111yescharacteristic
410C2×C4⋊C4D4×C3112yes—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—48no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42D4×C3112yes—
423#102—24no—
424#102—24no—
425#102—28no—
426#95—24no—
427C31#1106311yescharacteristic, direct product factor, Sylow
428C24—22no—
429C24—22no—
430C24—22no—
431C24—44no—
432C24—44no—
433C24—41no—
434C24—41no—
435C24—41no—
436C24—41no—
437C24C2×D4×C3111yescharacteristic
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4C4⋊C4×C3114yescomplemented
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—42no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—44no—
478C22×C4C22×C4×C3111yescharacteristic
479C22×C4C2×D4×C3111yescharacteristic
480C22×C4C2×D4×C3111yescharacteristic
481C22×C4C2×D4×C3111yescharacteristic
482C22×C4C2×D4×C3111yescharacteristic
483C22×C4C2×D4×C3111yescharacteristic
484C22×C4C2×D4×C3111yescharacteristic
485C22×C4C2×Q8×C3111yescharacteristic
486C22×C4#41×C3111yescharacteristic
487C22×C4#41×C3111yescharacteristic
488C22×C4#41×C3111yescharacteristic
489C22×C4#41×C3111yescharacteristic
490C22×C4#41×C3111yescharacteristic
491C22×C4#41×C3111yescharacteristic
492M16—22no—
493M16—22no—
494M16—22no—
495M16—22no—
496M16—41no—
497M16—41no—
498M16—41no—
499M16—41no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—84no—
516C4⋊C4C22⋊C4×C3114yescomplemented
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—416no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—41no—
527C42—41no—
528C42—41no—
529C42—41no—
530C23—22no—
531C23—22no—
532C23—24no—
533C23—44no—
534C23—48no—
535C23—44no—
536C23—48no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—84no—
544C23—82no—
545C23—82no—
546C23—84no—
547C23—82no—
548C23—82no—
549C23C4×D4×C3111yescharacteristic
550C23C31×#12011yescharacteristic
551C23C31×#12011yescharacteristic
552C23C31×#12111yescharacteristic
553C23C31×#12111yescharacteristic
554C23C31×C22⋊Q811yescharacteristic
555C23C31×#12411yescharacteristic
556D4—24no—
557D4—24no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563D4—42no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—44no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—82no—
580C2×C4C2×C22⋊C4×C3111yescharacteristic
581C2×C4C2×C4⋊C4×C3111yescharacteristic
582C2×C4C31×#11711yescharacteristic
583C2×C4C4×D4×C3111yescharacteristic
584C2×C4C4×D4×C3111yescharacteristic
585C2×C4C4×D4×C3111yescharacteristic
586C2×C4C31×#12011yescharacteristic
587C2×C4C31×#12111yescharacteristic
588C2×C4C31×#12111yescharacteristic
589C2×C4C31×#12111yescharacteristic
590C2×C4C31×#12111yescharacteristic
591C2×C4C31×#12111yescharacteristic
592C2×C4C31×#12111yescharacteristic
593C2×C4C31×C22⋊Q811yescharacteristic
594C2×C4C31×C22⋊Q811yescharacteristic
595C2×C4C31×C22⋊Q811yescharacteristic
596C2×C4C31×C22⋊Q811yescharacteristic
597C2×C4C31×C22⋊Q811yescharacteristic
598C2×C4C31×#12311yescharacteristic
599C2×C4C31×#12311yescharacteristic
600C2×C4C31×#12311yescharacteristic
601C2×C4C31×#12311yescharacteristic
602C2×C4C31×#12311yescharacteristic
603C2×C4C31×#12411yescharacteristic
604C2×C4C31×#12411yescharacteristic
605C2×C4C31×#12611yescharacteristic
606C2×C4C31×#12611yescharacteristic
607C2×C4C31×#12711yescharacteristic
608C8—42no—
609C8—42no—
610C22—22no—
611C22—22no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—22no—
617C22—22no—
618C22—48no—
619C22—44no—
620C22—84no—
621C22—84no—
622C22—84no—
623C22—84no—
624C22—82no—
625C22—82no—
626C22—84no—
627C22C31×#38511yescharacteristic
628C22C31×#38611yescharacteristic
629C22C31×#38811yescharacteristic
630C22C31×#39211yescharacteristic
631C22C31×#39311yescharacteristic
632C22C31×#39411yescharacteristic
633C22C31×#39611yescharacteristic
634C22C31×#45312yes—
635C22C31×#45412yes—
636C4—44no—
637C4—44no—
638C4—82no—
639C4—81no—
640C4—81no—
641C4C31×#38011yescharacteristic
642C4C31×#38511yescharacteristic
643C4C31×#38811yescharacteristic
644C4C31×#39011yescharacteristic
645C4C31×#39411yescharacteristic
646C4C31×#39611yescharacteristic
647C4C31×#39711yescharacteristic
648C4C31×#39911yescharacteristic
649C2—21no—
650C2—21no—
651C2—21no—
652C2—21no—
653C2—84no—
654C2C31×#143911yescharacteristic
655C2C31×#188312yes—
656C2C31×#200211yescharacteristic
657C2C31×#200311yescharacteristic
658C2C31×#202712yes—
subgroupG/H
center, socleC23×C31#120
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#2317C2semidirect
5. C2×C31×#343C2semidirect
6. C2×C31×#339C2semidirect
7. C2×C31×#339C2semidirect
19. C31×#418C4semidirect
135. C2×D4×C31C4⋊C4semidirect
186. C4⋊C4×C31C22⋊C4semidirect
200. #11063C31direct (N × H)
283. #2317C2×C31semidirect
285. C2×#343C2×C31semidirect
286. C2×#339C2×C31semidirect
287. C2×#339C2×C31semidirect
338. #418C4×C31semidirect
427. C31#11063direct (N × H)
465. C2×D4C4⋊C4×C31semidirect
516. C4⋊C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4182
C31×#23172
C2×C31×#3902
C2×C31×#3432
C2×C31×#3392
#1106331