Finite Group Databasebeta

← C31×#10944 #21467703

Subgroups — C31×#10944 #21467703

Order 7936.

930 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#421C211yesmaximal, characteristic
2C2×C31×#416C211yesmaximal, characteristic
3C2×C31×#410C211yesmaximal, characteristic
4C2×C31×#405C211yesmaximal, characteristic, complemented
5C31×#1740C211yesmaximal, characteristic, complemented
6C31×#1735C211yesmaximal, characteristic, complemented
7C31×#1733C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C22×M16×C31C2211yescharacteristic
10C23×C8×C31C2211yescharacteristic
11C2×C31×#117C2211yescharacteristic
12C2×C31×#117C2211yescharacteristic
13C2×C31×#117C2211yescharacteristic
14C2×C31×#117C2211yescharacteristic
15C31×#421—22no—
16C31×#421C414yescomplemented
17C2×C31×#104—22no—
18C31×#416—21no—
19C31×#416—21no—
20C31×#416—22no—
21C2×C31×#103C412yescomplemented
22C2×C31×#102C412yescomplemented
23C31×#410—22no—
24C31×#410C414yescomplemented
25C2×C31×#99—22no—
26C31×#405—22no—
27C31×#405—22no—
28C2×C31×#97—21no—
29C2×C4×C8×C31—21no—
30C31×#342—22no—
31C31×#340—22no—
32C31×#339—22no—
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×C31—21no—
42C2×#41×C31—21no—
43C2×#41×C31C2×C412yes—
44C2×#41×C31C2×C412yes—
45C22×Q8×C31C2×C411yescharacteristic
46C22×D4×C31—21no—
47C22×D4×C31C2×C411yescharacteristic
48C23×C4×C31—21no—
49C23×C4×C31C2311yescharacteristic
50C2×M16×C31—21no—
51C2×M16×C31—21no—
52C2×M16×C31—21no—
53C2×M16×C31C2×C412yes—
54C2×M16×C31D412yes—
55C2×M16×C31D412yes—
56C22×C8×C31—21no—
57C22×C8×C31—21no—
58C22×C8×C31—21no—
59C22×C8×C31—21no—
60C22×C8×C31—21no—
61C22×C8×C31C2×C412yes—
62C22×C8×C31D411yescharacteristic
63C22×C8×C31D411yescharacteristic
64C22×C8×C31D412yes—
65C31×#117—21no—
66C31×#117—21no—
67C31×#117—21no—
68C31×#117—21no—
69C31×#117—21no—
70C31×#117—21no—
71C31×#117—21no—
72C31×#117—21no—
73C31×#117—21no—
74C31×#117—21no—
75C31×#117—21no—
76C31×#117—21no—
77C31×#117C2×C412yes—
78C31×#117C2×C412yes—
79C31×#117C2×C412yes—
80C31×#117D412yes—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31C2×C412yes—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31D412yes—
89C2×C42×C31—21no—
90C2×C42×C31—21no—
91C2×C42×C31—21no—
92C2×C42×C31—21no—
93C31×#104—28no—
94C31×#103—22no—
95C31×#103—22no—
96C31×#102—22no—
97C31×#102—22no—
98C31×#99—28no—
99C31×#97—24no—
100C4×C8×C31—24no—
101C24×C31—21no—
102C24×C31C2×D411yescharacteristic
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—22no—
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—
118#41×C31—41no—
119C2×Q8×C31—21no—
120C2×Q8×C31—21no—
121C2×Q8×C31—21no—
122C2×Q8×C31—21no—
123C2×Q8×C31—21no—
124C2×Q8×C31C4212yes—
125C2×D4×C31—22no—
126C2×D4×C31—22no—
127C2×D4×C31—21no—
128C2×D4×C31—21no—
129C2×D4×C31—21no—
130C2×D4×C31—21no—
131C2×D4×C31—21no—
132C2×D4×C31—41no—
133C2×D4×C31—41no—
134C2×D4×C31—41no—
135C2×D4×C31—41no—
136C2×D4×C31C4212yes—
137C22×C4×C31—21no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—41no—
143C22×C4×C31—41no—
144C22×C4×C31—41no—
145C22×C4×C31—41no—
146C22×C4×C31—41no—
147C22×C4×C31—41no—
148C22×C4×C31C22×C411yescharacteristic
149C22×C4×C31C22×C411yescharacteristic
150C22×C4×C31C22×C411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D411yescharacteristic
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×C31C22⋊C414yes—
166C2×C8×C31—22no—
167C2×C8×C31—22no—
168C2×C8×C31—22no—
169C2×C8×C31—21no—
170C2×C8×C31—22no—
171C2×C8×C31—21no—
172C2×C8×C31—22no—
173C2×C8×C31—22no—
174C2×C8×C31—22no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31C22⋊C412yes—
178C2×C8×C31C22⋊C412yes—
179C4⋊C4×C31—22no—
180C4⋊C4×C31—22no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—22no—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—41no—
186C4⋊C4×C31—41no—
187C22⋊C4×C31—22no—
188C22⋊C4×C31—22no—
189C22⋊C4×C31—22no—
190C22⋊C4×C31—41no—
191C22⋊C4×C31—41no—
192C22⋊C4×C31—41no—
193C22⋊C4×C31—41no—
194C22⋊C4×C31C22⋊C414yes—
195C42×C31—22no—
196C42×C31—22no—
197C42×C31—22no—
198C42×C31—22no—
199C42×C31—41no—
200C42×C31—41no—
201C42×C31—41no—
202C42×C31—41no—
203#10944C3111yesmaximal, characteristic, direct product factor, Sylow
204C23×C31—22no—
205C23×C31—42no—
206C23×C31—41no—
207C23×C31—41no—
208C23×C31—82no—
209C23×C31C2×C22⋊C411yescharacteristic
210C23×C31C4×D411yescharacteristic
211C23×C31C4×D411yescharacteristic
212C23×C31#12111yescharacteristic
213C23×C31#12111yescharacteristic
214C23×C31#12411yescharacteristic
215C23×C31#12711yescharacteristic
216Q8×C31—22no—
217Q8×C31—22no—
218Q8×C31—41no—
219Q8×C31—41no—
220D4×C31—22no—
221D4×C31—22no—
222D4×C31—42no—
223D4×C31—42no—
224D4×C31—42no—
225D4×C31—42no—
226D4×C31—41no—
227D4×C31—41no—
228C2×C4×C31—22no—
229C2×C4×C31—24no—
230C2×C4×C31—44no—
231C2×C4×C31—41no—
232C2×C4×C31—41no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—82no—
241C2×C4×C31—82no—
242C2×C4×C31—82no—
243C2×C4×C31C2×C4211yescharacteristic
244C2×C4×C31C2×C22⋊C411yescharacteristic
245C2×C4×C31C2×C22⋊C411yescharacteristic
246C2×C4×C31#11711yescharacteristic
247C2×C4×C31#11711yescharacteristic
248C2×C4×C31#11711yescharacteristic
249C2×C4×C31C4×D411yescharacteristic
250C2×C4×C31C4×D411yescharacteristic
251C2×C4×C31C4×D411yescharacteristic
252C2×C4×C31C4×D411yescharacteristic
253C2×C4×C31C4×D411yescharacteristic
254C2×C4×C31C4×D411yescharacteristic
255C2×C4×C31C4×D411yescharacteristic
256C2×C4×C31C4×D411yescharacteristic
257C2×C4×C31C4×D411yescharacteristic
258C2×C4×C31C4×D411yescharacteristic
259C2×C4×C31#12011yescharacteristic
260C2×C4×C31#12111yescharacteristic
261C2×C4×C31#12111yescharacteristic
262C2×C4×C31#12111yescharacteristic
263C2×C4×C31#12111yescharacteristic
264C2×C4×C31#12311yescharacteristic
265C2×C4×C31#12311yescharacteristic
266C2×C4×C31#12311yescharacteristic
267C2×C4×C31#12411yescharacteristic
268C2×C4×C31#12411yescharacteristic
269C2×C4×C31#12611yescharacteristic
270C2×C4×C31#12611yescharacteristic
271C8×C31—22no—
272C8×C31—22no—
273C8×C31—24no—
274C2×#421C2×C3111yescharacteristic
275C2×#416C2×C3111yescharacteristic
276C2×#410C2×C3111yescharacteristic
277C2×#405C2×C3111yescharacteristic, complemented
278#1740C2×C3111yescharacteristic, complemented
279#1735C2×C3111yescharacteristic, complemented
280#1733C2×C3111yescharacteristic, complemented
281C22×C31—22no—
282C22×C31—22no—
283C22×C31—22no—
284C22×C31—41no—
285C22×C31—41no—
286C22×C31—41no—
287C22×C31—41no—
288C22×C31—42no—
289C22×C31—82no—
290C22×C31—82no—
291C22×C31—82no—
292C22×C31C4×C22⋊C411yescharacteristic
293C22×C31#38611yescharacteristic
294C22×C31#38811yescharacteristic
295C22×C31#38811yescharacteristic
296C22×C31#39011yescharacteristic
297C22×C31#39011yescharacteristic
298C22×C31#39011yescharacteristic
299C4×C31—44no—
300C4×C31—42no—
301C4×C31—82no—
302C4×C31—82no—
303C4×C31—82no—
304C4×C31C4×C22⋊C411yescharacteristic
305C4×C31C4×C22⋊C411yescharacteristic
306C4×C31#38611yescharacteristic
307C4×C31#38611yescharacteristic
308C4×C31#38811yescharacteristic
309C4×C31#38811yescharacteristic
310C4×C31#38811yescharacteristic
311C4×C31#38811yescharacteristic
312C22×#41C22×C3111yescharacteristic
313C22×M16C22×C3111yescharacteristic
314C23×C8C22×C3111yescharacteristic
315C2×#117C22×C3111yescharacteristic
316C2×#117C22×C3111yescharacteristic
317C2×#117C22×C3111yescharacteristic
318C2×#117C22×C3111yescharacteristic
319#421—22no—
320#421C4×C3114yescomplemented
321C2×#104—22no—
322#416—22no—
323#416—21no—
324#416—21no—
325C2×#103C4×C3112yescomplemented
326C2×#102C4×C3112yescomplemented
327#410—22no—
328#410C4×C3114yescomplemented
329C2×#99—22no—
330#405—22no—
331#405—22no—
332C2×#97—21no—
333C2×C4×C8—21no—
334#342—22no—
335#340—22no—
336#339—22no—
337C2×C31—21no—
338C2×C31—21no—
339C2×C31—21no—
340C2×C31—21no—
341C2×C31—21no—
342C2×C31—21no—
343C2×C31—82no—
344C2×C31#143711yescharacteristic
345C2×C31#197612yes—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41C2×C4×C3112yes—
357C2×#41C2×C4×C3112yes—
358C22×Q8C2×C4×C3111yescharacteristic
359C22×D4—21no—
360C22×D4C2×C4×C3111yescharacteristic
361C23×C4—21no—
362C23×C4C23×C3111yescharacteristic
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16C2×C4×C3112yes—
367C2×M16D4×C3112yes—
368C2×M16D4×C3112yes—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8C2×C4×C3112yes—
375C22×C8D4×C3112yes—
376C22×C8D4×C3111yescharacteristic
377C22×C8D4×C3111yescharacteristic
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117C2×C4×C3112yes—
391#117C2×C4×C3112yes—
392#117C2×C4×C3112yes—
393#117D4×C3112yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4C2×C4×C3112yes—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4D4×C3112yes—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406#104—28no—
407#103—22no—
408#103—22no—
409#102—22no—
410#102—22no—
411#99—28no—
412#97—24no—
413C4×C8—24no—
414C31#1094411yescharacteristic, direct product factor, Sylow
415C24—21no—
416C24C2×D4×C3111yescharacteristic
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—22no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431#41—41no—
432#41—41no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C42×C3112yes—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4C42×C3112yes—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4C22×C4×C3111yescharacteristic
463C22×C4C22×C4×C3111yescharacteristic
464C22×C4C22×C4×C3111yescharacteristic
465C22×C4C2×D4×C3111yescharacteristic
466C22×C4C2×D4×C3111yescharacteristic
467C22×C4C2×D4×C3111yescharacteristic
468C22×C4C2×D4×C3111yescharacteristic
469C22×C4C2×D4×C3111yescharacteristic
470C22×C4#41×C3111yescharacteristic
471C22×C4#41×C3111yescharacteristic
472C22×C4#41×C3111yescharacteristic
473C22×C4#41×C3111yescharacteristic
474C22×C4#41×C3111yescharacteristic
475C22×C4#41×C3111yescharacteristic
476M16—22no—
477M16—22no—
478M16—22no—
479M16C22⋊C4×C3114yes—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8C22⋊C4×C3112yes—
492C2×C8C22⋊C4×C3112yes—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4C22⋊C4×C3114yes—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—41no—
514C42—41no—
515C42—41no—
516C42—41no—
517C23—22no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—82no—
522C23C2×C22⋊C4×C3111yescharacteristic
523C23C4×D4×C3111yescharacteristic
524C23C4×D4×C3111yescharacteristic
525C23C31×#12111yescharacteristic
526C23C31×#12111yescharacteristic
527C23C31×#12411yescharacteristic
528C23C31×#12711yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—41no—
540D4—41no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—44no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4C2×C42×C3111yescharacteristic
557C2×C4C2×C22⋊C4×C3111yescharacteristic
558C2×C4C2×C22⋊C4×C3111yescharacteristic
559C2×C4C31×#11711yescharacteristic
560C2×C4C31×#11711yescharacteristic
561C2×C4C31×#11711yescharacteristic
562C2×C4C4×D4×C3111yescharacteristic
563C2×C4C4×D4×C3111yescharacteristic
564C2×C4C4×D4×C3111yescharacteristic
565C2×C4C4×D4×C3111yescharacteristic
566C2×C4C4×D4×C3111yescharacteristic
567C2×C4C4×D4×C3111yescharacteristic
568C2×C4C4×D4×C3111yescharacteristic
569C2×C4C4×D4×C3111yescharacteristic
570C2×C4C4×D4×C3111yescharacteristic
571C2×C4C4×D4×C3111yescharacteristic
572C2×C4C31×#12011yescharacteristic
573C2×C4C31×#12111yescharacteristic
574C2×C4C31×#12111yescharacteristic
575C2×C4C31×#12111yescharacteristic
576C2×C4C31×#12111yescharacteristic
577C2×C4C31×#12311yescharacteristic
578C2×C4C31×#12311yescharacteristic
579C2×C4C31×#12311yescharacteristic
580C2×C4C31×#12411yescharacteristic
581C2×C4C31×#12411yescharacteristic
582C2×C4C31×#12611yescharacteristic
583C2×C4C31×#12611yescharacteristic
584C8—22no—
585C8—22no—
586C8—24no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—42no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22C4×C22⋊C4×C3111yescharacteristic
599C22C31×#38611yescharacteristic
600C22C31×#38811yescharacteristic
601C22C31×#38811yescharacteristic
602C22C31×#39011yescharacteristic
603C22C31×#39011yescharacteristic
604C22C31×#39011yescharacteristic
605C4—44no—
606C4—42no—
607C4—82no—
608C4—82no—
609C4—82no—
610C4C4×C22⋊C4×C3111yescharacteristic
611C4C4×C22⋊C4×C3111yescharacteristic
612C4C31×#38611yescharacteristic
613C4C31×#38611yescharacteristic
614C4C31×#38811yescharacteristic
615C4C31×#38811yescharacteristic
616C4C31×#38811yescharacteristic
617C4C31×#38811yescharacteristic
618C2—21no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—82no—
625C2C31×#143711yescharacteristic
626C2C31×#197612yes—
subgroupG/H
centerC2×C4×C31#121
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31#390
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#405C2semidirect
5. C31×#1740C2semidirect
6. C31×#1735C2semidirect
7. C31×#1733C2semidirect
16. C31×#421C4semidirect
21. C2×C31×#103C4semidirect
22. C2×C31×#102C4semidirect
24. C31×#410C4semidirect
203. #10944C31direct (N × H)
277. C2×#405C2×C31semidirect
278. #1740C2×C31semidirect
279. #1735C2×C31semidirect
280. #1733C2×C31semidirect
320. #421C4×C31semidirect
325. C2×#103C4×C31semidirect
326. C2×#102C4×C31semidirect
328. #410C4×C31semidirect
414. C31#10944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4212
C2×C31×#4162
C2×C31×#4102
C2×C31×#4052
C31×#17402
C31×#17352
C31×#17332
#1094431