Finite Group Databasebeta

← C31×#10970 #21467729

Subgroups — C31×#10970 #21467729

Order 7936.

1578 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
1C22×C31×C22⋊Q8C211yesmaximal, characteristic
2C22×C31×#103C212yesmaximal, complemented
3C22×C31×C22⋊C8C211yesmaximal, characteristic
4C2×C31×#380C211yesmaximal, characteristic
5C2×C31×#340C212yesmaximal, complemented
6C23×Q8×C31C2211yescharacteristic
7C24×C4×C31C2211yescharacteristic
8C23×C8×C31C2212yes—
9C2×C31×C22⋊Q8—24no—
10C2×C31×C22⋊Q8—22no—
11C2×C31×C22⋊Q8—24no—
12C2×C31×C22⋊Q8C414yescomplemented
13C22×C4⋊C4×C31—21no—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31—21no—
17C22×C22⋊C4×C31—21no—
18C2×C31×#103—24no—
19C2×C31×#103—24no—
20C2×C31×#103—24no—
21C2×C31×C22⋊C8—22no—
22C2×C31×C22⋊C8—24no—
23C31×#380—24no—
24C2×C31×#95—21no—
25C31×#340—24no—
26C25×C31D411yescharacteristic
27C22×Q8×C31—21no—
28C22×Q8×C31—22no—
29C22×Q8×C31—22no—
30C22×Q8×C31—22no—
31C22×Q8×C31—22no—
32C22×Q8×C31—22no—
33C22×Q8×C31C2×C412yes—
34C22×Q8×C31D414yes—
35C23×C4×C31—21no—
36C23×C4×C31—21no—
37C23×C4×C31—22no—
38C23×C4×C31—22no—
39C23×C4×C31—22no—
40C23×C4×C31—22no—
41C23×C4×C31—22no—
42C23×C4×C31—22no—
43C23×C4×C31—22no—
44C23×C4×C31C2×C412yes—
45C23×C4×C31D411yescharacteristic
46C23×C4×C31D412yes—
47C23×C4×C31C2311yescharacteristic
48C22×C8×C31—22no—
49C22×C8×C31—22no—
50C22×C8×C31—22no—
51C22×C8×C31—22no—
52C22×C8×C31—22no—
53C22×C8×C31—22no—
54C22×C8×C31D414yes—
55C31×C22⋊Q8—216no—
56C31×C22⋊Q8—28no—
57C31×C22⋊Q8—28no—
58C2×C4⋊C4×C31—28no—
59C2×C4⋊C4×C31—24no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—21no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31C2×C412yes—
68C2×C4⋊C4×C31D414yes—
69C2×C4⋊C4×C31D414yes—
70C2×C22⋊C4×C31—28no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—42no—
74C2×C22⋊C4×C31—42no—
75C31×#103—216no—
76C31×C22⋊C8—28no—
77C31×#95—24no—
78C24×C31—22no—
79C24×C31—21no—
80C24×C31—22no—
81C24×C31—21no—
82C24×C31—22no—
83C24×C31—21no—
84C24×C31—21no—
85C24×C31—22no—
86C24×C31C22⋊C412yes—
87C24×C31SD1612yes—
88C24×C31Q1612yes—
89C24×C31C2×D411yescharacteristic
90C2×Q8×C31—22no—
91C2×Q8×C31—24no—
92C2×Q8×C31—24no—
93C2×Q8×C31—24no—
94C2×Q8×C31—24no—
95C2×Q8×C31—24no—
96C2×Q8×C31—24no—
97C2×Q8×C31—24no—
98C2×Q8×C31—41no—
99C2×Q8×C31—42no—
100C2×Q8×C31—42no—
101C2×Q8×C31—42no—
102C2×Q8×C31—41no—
103C2×Q8×C31—42no—
104C2×Q8×C31—42no—
105C2×Q8×C31C22⋊C414yescomplemented
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—21no—
109C22×C4×C31—24no—
110C22×C4×C31—24no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—21no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—24no—
117C22×C4×C31—24no—
118C22×C4×C31—22no—
119C22×C4×C31—24no—
120C22×C4×C31—24no—
121C22×C4×C31—22no—
122C22×C4×C31—24no—
123C22×C4×C31—41no—
124C22×C4×C31—42no—
125C22×C4×C31—41no—
126C22×C4×C31—42no—
127C22×C4×C31—41no—
128C22×C4×C31—41no—
129C22×C4×C31—42no—
130C22×C4×C31—42no—
131C22×C4×C31—42no—
132C22×C4×C31—42no—
133C22×C4×C31—42no—
134C22×C4×C31—42no—
135C22×C4×C31—42no—
136C22×C4×C31—42no—
137C22×C4×C31—42no—
138C22×C4×C31—42no—
139C22×C4×C31—42no—
140C22×C4×C31—42no—
141C22×C4×C31—42no—
142C22×C4×C31—42no—
143C22×C4×C31C22⋊C412yes—
144C22×C4×C31C22×C411yescharacteristic
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31#4112yes—
151C22×C4×C31#4112yes—
152C2×C8×C31—24no—
153C2×C8×C31—24no—
154C2×C8×C31—24no—
155C2×C8×C31—42no—
156C2×C8×C31—42no—
157C2×C8×C31—42no—
158C2×C8×C31—42no—
159C4⋊C4×C31—216no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—24no—
162C4⋊C4×C31—24no—
163C4⋊C4×C31—24no—
164C4⋊C4×C31—42no—
165C4⋊C4×C31—42no—
166C4⋊C4×C31C22⋊C414yescomplemented
167C22⋊C4×C31—216no—
168C22⋊C4×C31—48no—
169#10970C3111yesmaximal, characteristic, direct product factor, Sylow
170C23×C31—22no—
171C23×C31—22no—
172C23×C31—22no—
173C23×C31—22no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—24no—
177C23×C31—22no—
178C23×C31—22no—
179C23×C31—24no—
180C23×C31—24no—
181C23×C31—24no—
182C23×C31—22no—
183C23×C31—22no—
184C23×C31—42no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31#10314yescomplemented
193C23×C31C2×C22⋊C411yescharacteristic
194C23×C31#12012yes—
195C23×C31#12011yescharacteristic
196C23×C31#12112yes—
197C23×C31#12311yescharacteristic
198C23×C31C2×SD1611yescharacteristic
199C23×C31C2×Q1611yescharacteristic
200C23×C31#13512yes—
201C23×C31AGL(1,ℤ/8)11yescharacteristic
202C23×C31#13711yescharacteristic
203C23×C31#13712yes—
204Q8×C31—28no—
205Q8×C31—44no—
206Q8×C31—44no—
207Q8×C31—44no—
208C2×C4×C31—24no—
209C2×C4×C31—24no—
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—44no—
217C2×C4×C31—42no—
218C2×C4×C31—44no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—44no—
222C2×C4×C31—44no—
223C2×C4×C31—44no—
224C2×C4×C31—44no—
225C2×C4×C31—44no—
226C2×C4×C31—44no—
227C2×C4×C31—44no—
228C2×C4×C31—44no—
229C2×C4×C31—44no—
230C2×C4×C31—82no—
231C2×C4×C31—82no—
232C2×C4×C31—82no—
233C2×C4×C31—82no—
234C2×C4×C31C2×C22⋊C411yescharacteristic
235C2×C4×C31C2×C22⋊C411yescharacteristic
236C2×C4×C31C4×D412yes—
237C2×C4×C31C4×D412yes—
238C2×C4×C31#12012yes—
239C2×C4×C31#12011yescharacteristic
240C2×C4×C31#12012yes—
241C2×C4×C31#12112yes—
242C2×C4×C31#12112yes—
243C2×C4×C31#12112yes—
244C2×C4×C31#12112yes—
245C2×C4×C31#12112yes—
246C2×C4×C31#12312yes—
247C2×C4×C31#12311yescharacteristic
248C2×C4×C31#12412yes—
249C2×C4×C31#12712yes—
250C8×C31—44no—
251C22×C22⋊Q8C2×C3111yescharacteristic
252C22×#103C2×C3112yescomplemented
253C22×C22⋊C8C2×C3111yescharacteristic
254C2×#380C2×C3111yescharacteristic
255C2×#340C2×C3112yescomplemented
256C22×C31—24no—
257C22×C31—24no—
258C22×C31—24no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—42no—
262C22×C31—44no—
263C22×C31—44no—
264C22×C31—44no—
265C22×C31—44no—
266C22×C31—42no—
267C22×C31#37911yescharacteristic
268C22×C31#38611yescharacteristic
269C22×C31#38611yescharacteristic
270C22×C31#39212yes—
271C22×C31#39412yes—
272C22×C31C2×#10311yescharacteristic
273C22×C31#41611yescharacteristic
274C22×C31#41711yescharacteristic
275C22×C31#41911yescharacteristic
276C22×C31#44812yes—
277C22×C31#44912yes—
278C22×C31#45011yescharacteristic
279C22×C31#45111yescharacteristic
280C22×C31#45112yes—
281C22×C31#45212yes—
282C22×C31#45212yes—
283C22×C31#46512yes—
284C22×C31#46712yes—
285C22×C31#46812yes—
286C22×C31#47012yes—
287C22×C31#48311yescharacteristic
288C22×C31#48411yescharacteristic
289C22×C31#48512yes—
290C4×C31—42no—
291C4×C31—44no—
292C4×C31—44no—
293C4×C31—84no—
294C4×C31#38612yes—
295C4×C31#39012yes—
296C4×C31#39212yes—
297C4×C31#39412yes—
298C23×Q8C22×C3111yescharacteristic
299C24×C4C22×C3111yescharacteristic
300C23×C8C22×C3112yes—
301C2×C22⋊Q8—24no—
302C2×C22⋊Q8—22no—
303C2×C22⋊Q8—24no—
304C2×C22⋊Q8C4×C3114yescomplemented
305C22×C4⋊C4—21no—
306C22×C4⋊C4C22×C3112yes—
307C22×C4⋊C4C22×C3111yescharacteristic
308C22×C22⋊C4—21no—
309C22×C22⋊C4—21no—
310C2×#103—24no—
311C2×#103—24no—
312C2×#103—24no—
313C2×C22⋊C8—22no—
314C2×C22⋊C8—24no—
315#380—24no—
316C2×#95—21no—
317#340—24no—
318C2×C31—44no—
319C2×C31#143811yescharacteristic
320C2×C31#178711yescharacteristic
321C2×C31#178811yescharacteristic
322C2×C31#187211yescharacteristic
323C2×C31#187311yescharacteristic
324C2×C31#189211yescharacteristic
325C2×C31#189411yescharacteristic
326C2×C31#200012yes—
327C2×C31#200112yes—
328C2×C31#203512yes—
329C2×C31#203612yes—
330C25D4×C3111yescharacteristic
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8C2×C4×C3112yes—
338C22×Q8D4×C3114yes—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4C2×C4×C3112yes—
349C23×C4D4×C3111yescharacteristic
350C23×C4D4×C3112yes—
351C23×C4C23×C3111yescharacteristic
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8D4×C3114yes—
359C22⋊Q8—216no—
360C22⋊Q8—28no—
361C22⋊Q8—28no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4C2×C4×C3112yes—
372C2×C4⋊C4D4×C3114yes—
373C2×C4⋊C4D4×C3114yes—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379#103—216no—
380C22⋊C8—28no—
381#95—24no—
382C31#1097011yescharacteristic, direct product factor, Sylow
383C24—22no—
384C24—21no—
385C24—22no—
386C24—21no—
387C24—22no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24C22⋊C4×C3112yes—
392C24SD16×C3112yes—
393C24Q16×C3112yes—
394C24C2×D4×C3111yescharacteristic
395C2×Q8—22no—
396C2×Q8—24no—
397C2×Q8—24no—
398C2×Q8—24no—
399C2×Q8—24no—
400C2×Q8—24no—
401C2×Q8—24no—
402C2×Q8—24no—
403C2×Q8—41no—
404C2×Q8—42no—
405C2×Q8—42no—
406C2×Q8—42no—
407C2×Q8—41no—
408C2×Q8—42no—
409C2×Q8—42no—
410C2×Q8C22⋊C4×C3114yescomplemented
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—41no—
429C22×C4—42no—
430C22×C4—41no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4C22⋊C4×C3112yes—
449C22×C4C22×C4×C3111yescharacteristic
450C22×C4C2×D4×C3112yes—
451C22×C4C2×D4×C3112yes—
452C22×C4C2×D4×C3112yes—
453C22×C4C2×D4×C3112yes—
454C22×C4C2×D4×C3111yescharacteristic
455C22×C4#41×C3112yes—
456C22×C4#41×C3112yes—
457C2×C8—24no—
458C2×C8—24no—
459C2×C8—24no—
460C2×C8—42no—
461C2×C8—42no—
462C2×C8—42no—
463C2×C8—42no—
464C4⋊C4—216no—
465C4⋊C4—22no—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4C22⋊C4×C3114yescomplemented
472C22⋊C4—216no—
473C22⋊C4—48no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—24no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—24no—
482C23—24no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23C31×#10314yescomplemented
497C23C2×C22⋊C4×C3111yescharacteristic
498C23C31×#12012yes—
499C23C31×#12011yescharacteristic
500C23C31×#12112yes—
501C23C31×#12311yescharacteristic
502C23C2×SD16×C3111yescharacteristic
503C23C2×Q16×C3111yescharacteristic
504C23C31×#13512yes—
505C23C31×AGL(1,ℤ/8)11yescharacteristic
506C23C31×#13711yescharacteristic
507C23C31×#13712yes—
508Q8—28no—
509Q8—44no—
510Q8—44no—
511Q8—44no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4C2×C22⋊C4×C3111yescharacteristic
539C2×C4C2×C22⋊C4×C3111yescharacteristic
540C2×C4C4×D4×C3112yes—
541C2×C4C4×D4×C3112yes—
542C2×C4C31×#12012yes—
543C2×C4C31×#12011yescharacteristic
544C2×C4C31×#12012yes—
545C2×C4C31×#12112yes—
546C2×C4C31×#12112yes—
547C2×C4C31×#12112yes—
548C2×C4C31×#12112yes—
549C2×C4C31×#12112yes—
550C2×C4C31×#12312yes—
551C2×C4C31×#12311yescharacteristic
552C2×C4C31×#12412yes—
553C2×C4C31×#12712yes—
554C8—44no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—44no—
562C22—44no—
563C22—44no—
564C22—44no—
565C22—42no—
566C22C31×#37911yescharacteristic
567C22C31×#38611yescharacteristic
568C22C31×#38611yescharacteristic
569C22C31×#39212yes—
570C22C31×#39412yes—
571C22C2×C31×#10311yescharacteristic
572C22C31×#41611yescharacteristic
573C22C31×#41711yescharacteristic
574C22C31×#41911yescharacteristic
575C22C31×#44812yes—
576C22C31×#44912yes—
577C22C31×#45011yescharacteristic
578C22C31×#45111yescharacteristic
579C22C31×#45112yes—
580C22C31×#45212yes—
581C22C31×#45212yes—
582C22C31×#46512yes—
583C22C31×#46712yes—
584C22C31×#46812yes—
585C22C31×#47012yes—
586C22C31×#48311yescharacteristic
587C22C31×#48411yescharacteristic
588C22C31×#48512yes—
589C4—42no—
590C4—44no—
591C4—44no—
592C4—84no—
593C4C31×#38612yes—
594C4C31×#39012yes—
595C4C31×#39212yes—
596C4C31×#39412yes—
597C2—44no—
598C2C31×#143811yescharacteristic
599C2C31×#178711yescharacteristic
600C2C31×#178811yescharacteristic
601C2C31×#187211yescharacteristic
602C2C31×#187311yescharacteristic
603C2C31×#189211yescharacteristic
604C2C31×#189411yescharacteristic
605C2C31×#200012yes—
606C2C31×#200112yes—
607C2C31×#203512yes—
608C2C31×#203612yes—
subgroupG/H
center, socleC24×C31C2×D4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×#103C2semidirect
5. C2×C31×#340C2semidirect
12. C2×C31×C22⋊Q8C4semidirect
105. C2×Q8×C31C22⋊C4semidirect
166. C4⋊C4×C31C22⋊C4semidirect
169. #10970C31direct (N × H)
192. C23×C31#103semidirect
252. C22×#103C2×C31semidirect
255. C2×#340C2×C31semidirect
304. C2×C22⋊Q8C4×C31semidirect
382. C31#10970direct (N × H)
410. C2×Q8C22⋊C4×C31semidirect
471. C4⋊C4C22⋊C4×C31semidirect
496. C23C31×#103semidirect

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C22×C31×#1032
C22×C31×C22⋊C82
C2×C31×#3802
C2×C31×#3402
#1097031