Finite Group Databasebeta

← C31×#10956 #21467715

Subgroups — C31×#10956 #21467715

Order 7936.

918 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#421C211yesmaximal, characteristic
2C31×#2896C211yesmaximal, characteristic
3C2×C31×#408C211yesmaximal, characteristic
4C31×#2873C211yesmaximal, characteristic, complemented
5C2×C31×#344C211yesmaximal, characteristic, complemented
6C2×C31×#341C211yesmaximal, characteristic, complemented
7C31×#1735C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C22×M16×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C23×C8×C31C2211yescharacteristic
13C2×C31×#117C2211yescharacteristic
14C2×C31×#117C2211yescharacteristic
15C31×#421—22no—
16C31×#421C414yescomplemented
17C2×C31×#104—22no—
18C31×#419C412yescomplemented
19C31×#418C412yescomplemented
20C31×#417—22no—
21C31×#416—22no—
22C31×#408—22no—
23C31×#408C414yescomplemented
24C2×C31×C22⋊C8—22no—
25C31×#405—22no—
26C31×#405—22no—
27C4×M16×C31—22no—
28C31×#344—22no—
29C31×#341—22no—
30C31×#340—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×C31C2311yescharacteristic
48C2×M16×C31—21no—
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×C31—21no—
60C2×M16×C31C2×C412yes—
61C2×M16×C31C2×C412yes—
62C2×M16×C31C2×C412yes—
63C2×M16×C31D412yes—
64C2×M16×C31D412yes—
65C2×M16×C31D412yes—
66C22×C8×C31—21no—
67C22×C8×C31—21no—
68C22×C8×C31—21no—
69C22×C8×C31—21no—
70C22×C8×C31—21no—
71C22×C8×C31—21no—
72C22×C8×C31—21no—
73C22×C8×C31—21no—
74C22×C8×C31C2×C412yes—
75C22×C8×C31D412yes—
76C31×#117—21no—
77C31×#117—21no—
78C31×#117—21no—
79C31×#117—21no—
80C31×#117—21no—
81C31×#117C2×C412yes—
82C31×#117C2×C412yes—
83C31×#117D412yes—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31D412yes—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C42×C31—21no—
89C2×C42×C31—21no—
90C31×#104—28no—
91C31×#103—24no—
92C31×#102—24no—
93C31×C22⋊C8—28no—
94C31×#97—24no—
95C4×C8×C31—24no—
96C24×C31—21no—
97C24×C31#4111yescharacteristic
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—22no—
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—
113#41×C31—41no—
114C2×Q8×C31—21no—
115C2×Q8×C31—21no—
116C2×Q8×C31—21no—
117C2×Q8×C31—21no—
118C2×Q8×C31—21no—
119C2×Q8×C31C4212yes—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—21no—
123C2×D4×C31—21no—
124C2×D4×C31—21no—
125C2×D4×C31—21no—
126C2×D4×C31—21no—
127C2×D4×C31—41no—
128C2×D4×C31—41no—
129C2×D4×C31—41no—
130C2×D4×C31—41no—
131C2×D4×C31C4212yes—
132C22×C4×C31—21no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—41no—
137C22×C4×C31—41no—
138C22×C4×C31—41no—
139C22×C4×C31—41no—
140C22×C4×C31—41no—
141C22×C4×C31C22×C411yescharacteristic
142C22×C4×C31C22×C411yescharacteristic
143C22×C4×C31C22×C411yescharacteristic
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31#4111yescharacteristic
151C22×C4×C31#4111yescharacteristic
152C22×C4×C31#4111yescharacteristic
153C22×C4×C31#4111yescharacteristic
154C22×C4×C31#4111yescharacteristic
155M16×C31—22no—
156M16×C31—22no—
157M16×C31—22no—
158M16×C31—22no—
159M16×C31—22no—
160M16×C31—22no—
161M16×C31—22no—
162M16×C31—22no—
163M16×C31—22no—
164M16×C31—41no—
165M16×C31—41no—
166M16×C31C22⋊C414yes—
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—41no—
177C2×C8×C31—41no—
178C2×C8×C31—41no—
179C2×C8×C31—41no—
180C2×C8×C31—41no—
181C2×C8×C31—41no—
182C2×C8×C31C22⋊C414yes—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—41no—
186C4⋊C4×C31C22⋊C414yes—
187C22⋊C4×C31—22no—
188C22⋊C4×C31—22no—
189C22⋊C4×C31—22no—
190C22⋊C4×C31—41no—
191C42×C31—22no—
192C42×C31—22no—
193C42×C31—22no—
194C42×C31—41no—
195#10956C3111yesmaximal, characteristic, direct product factor, Sylow
196C23×C31—22no—
197C23×C31—42no—
198C23×C31—44no—
199C23×C31—41no—
200C23×C31—41no—
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—22no—
221C2×C4×C31—24no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—82no—
230C2×C4×C31—82no—
231C2×C4×C31C2×C4211yescharacteristic
232C2×C4×C31C2×C22⋊C411yescharacteristic
233C2×C4×C31C2×C22⋊C411yescharacteristic
234C2×C4×C31C2×C22⋊C411yescharacteristic
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×C31C4×D411yescharacteristic
246C2×C4×C31C4×D411yescharacteristic
247C2×C4×C31#12011yescharacteristic
248C2×C4×C31#12111yescharacteristic
249C2×C4×C31#12111yescharacteristic
250C2×C4×C31#12111yescharacteristic
251C2×C4×C31#12111yescharacteristic
252C2×C4×C31#12111yescharacteristic
253C2×C4×C31#12311yescharacteristic
254C2×C4×C31#12311yescharacteristic
255C2×C4×C31#12411yescharacteristic
256C2×C4×C31#12411yescharacteristic
257C2×C4×C31#12611yescharacteristic
258C2×C4×C31#12711yescharacteristic
259C8×C31—24no—
260C8×C31—24no—
261C8×C31—42no—
262C8×C31—42no—
263C2×#421C2×C3111yescharacteristic
264#2896C2×C3111yescharacteristic
265C2×#408C2×C3111yescharacteristic
266#2873C2×C3111yescharacteristic, complemented
267C2×#344C2×C3111yescharacteristic, complemented
268C2×#341C2×C3111yescharacteristic, complemented
269#1735C2×C3111yescharacteristic, complemented
270C22×C31—22no—
271C22×C31—22no—
272C22×C31—22no—
273C22×C31—41no—
274C22×C31—41no—
275C22×C31—41no—
276C22×C31—41no—
277C22×C31—44no—
278C22×C31—42no—
279C22×C31—82no—
280C22×C31—82no—
281C22×C31C4×C22⋊C411yescharacteristic
282C22×C31#38611yescharacteristic
283C22×C31#38811yescharacteristic
284C22×C31#38811yescharacteristic
285C22×C31#38811yescharacteristic
286C22×C31#38811yescharacteristic
287C22×C31#39011yescharacteristic
288C4×C31—44no—
289C4×C31—42no—
290C4×C31—82no—
291C4×C31C4×C22⋊C411yescharacteristic
292C4×C31C4×C22⋊C411yescharacteristic
293C4×C31#38611yescharacteristic
294C4×C31#38611yescharacteristic
295C4×C31#38811yescharacteristic
296C4×C31#38811yescharacteristic
297C4×C31#39011yescharacteristic
298C4×C31#39011yescharacteristic
299C22×#41C22×C3111yescharacteristic
300C22×M16C22×C3111yescharacteristic
301C22×M16C22×C3111yescharacteristic
302C22×M16C22×C3111yescharacteristic
303C23×C8C22×C3111yescharacteristic
304C2×#117C22×C3111yescharacteristic
305C2×#117C22×C3111yescharacteristic
306#421—22no—
307#421C4×C3114yescomplemented
308C2×#104—22no—
309#419C4×C3112yescomplemented
310#418C4×C3112yescomplemented
311#417—22no—
312#416—22no—
313#408—22no—
314#408C4×C3114yescomplemented
315C2×C22⋊C8—22no—
316#405—22no—
317#405—22no—
318C4×M16—22no—
319#344—22no—
320#341—22no—
321#340—22no—
322C2×C31—21no—
323C2×C31—21no—
324C2×C31—21no—
325C2×C31—21no—
326C2×C31—21no—
327C2×C31—21no—
328C2×C31—82no—
329C2×C31#143711yescharacteristic
330C2×C31#188112yes—
331C2×#41—21no—
332C2×#41—21no—
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×#41C2×C4×C3112yes—
342C2×#41C2×C4×C3112yes—
343C22×Q8C2×C4×C3111yescharacteristic
344C22×D4—21no—
345C22×D4C2×C4×C3111yescharacteristic
346C23×C4—21no—
347C23×C4C23×C3111yescharacteristic
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
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×M16C2×C4×C3112yes—
361C2×M16C2×C4×C3112yes—
362C2×M16C2×C4×C3112yes—
363C2×M16D4×C3112yes—
364C2×M16D4×C3112yes—
365C2×M16D4×C3112yes—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8C2×C4×C3112yes—
375C22×C8D4×C3112yes—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117C2×C4×C3112yes—
382#117C2×C4×C3112yes—
383#117D4×C3112yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D4×C3112yes—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389C2×C42—21no—
390#104—28no—
391#103—24no—
392#102—24no—
393C22⋊C8—28no—
394#97—24no—
395C4×C8—24no—
396C31#1095611yescharacteristic, direct product factor, Sylow
397C24—21no—
398C24#41×C3111yescharacteristic
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8C42×C3112yes—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4C42×C3112yes—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4C22×C4×C3111yescharacteristic
443C22×C4C22×C4×C3111yescharacteristic
444C22×C4C22×C4×C3111yescharacteristic
445C22×C4C2×D4×C3111yescharacteristic
446C22×C4C2×D4×C3111yescharacteristic
447C22×C4C2×D4×C3111yescharacteristic
448C22×C4C2×D4×C3111yescharacteristic
449C22×C4C2×D4×C3111yescharacteristic
450C22×C4C2×D4×C3111yescharacteristic
451C22×C4#41×C3111yescharacteristic
452C22×C4#41×C3111yescharacteristic
453C22×C4#41×C3111yescharacteristic
454C22×C4#41×C3111yescharacteristic
455C22×C4#41×C3111yescharacteristic
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—41no—
466M16—41no—
467M16C22⋊C4×C3114yes—
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—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8C22⋊C4×C3114yes—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4C22⋊C4×C3114yes—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—41no—
492C42—22no—
493C42—22no—
494C42—22no—
495C42—41no—
496C23—22no—
497C23—42no—
498C23—44no—
499C23—41no—
500C23—41no—
501C23C31×#11711yescharacteristic
502C23C4×D4×C3111yescharacteristic
503C23C4×D4×C3111yescharacteristic
504C23C31×#12111yescharacteristic
505C23C31×#12311yescharacteristic
506C23C31×#12411yescharacteristic
507C23C31×#12611yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—41no—
519D4—41no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4C2×C42×C3111yescharacteristic
532C2×C4C2×C22⋊C4×C3111yescharacteristic
533C2×C4C2×C22⋊C4×C3111yescharacteristic
534C2×C4C2×C22⋊C4×C3111yescharacteristic
535C2×C4C31×#11711yescharacteristic
536C2×C4C31×#11711yescharacteristic
537C2×C4C4×D4×C3111yescharacteristic
538C2×C4C4×D4×C3111yescharacteristic
539C2×C4C4×D4×C3111yescharacteristic
540C2×C4C4×D4×C3111yescharacteristic
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×C4C31×#12011yescharacteristic
548C2×C4C31×#12111yescharacteristic
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×#12711yescharacteristic
559C8—24no—
560C8—24no—
561C8—42no—
562C8—42no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—44no—
571C22—42no—
572C22—82no—
573C22—82no—
574C22C4×C22⋊C4×C3111yescharacteristic
575C22C31×#38611yescharacteristic
576C22C31×#38811yescharacteristic
577C22C31×#38811yescharacteristic
578C22C31×#38811yescharacteristic
579C22C31×#38811yescharacteristic
580C22C31×#39011yescharacteristic
581C4—44no—
582C4—42no—
583C4—82no—
584C4C4×C22⋊C4×C3111yescharacteristic
585C4C4×C22⋊C4×C3111yescharacteristic
586C4C31×#38611yescharacteristic
587C4C31×#38611yescharacteristic
588C4C31×#38811yescharacteristic
589C4C31×#38811yescharacteristic
590C4C31×#39011yescharacteristic
591C4C31×#39011yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—82no—
599C2C31×#143711yescharacteristic
600C2C31×#188112yes—
subgroupG/H
centerC2×C4×C31#120
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31#386
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. C31×#2873C2semidirect
5. C2×C31×#344C2semidirect
6. C2×C31×#341C2semidirect
7. C31×#1735C2semidirect
16. C31×#421C4semidirect
18. C31×#419C4semidirect
19. C31×#418C4semidirect
23. C31×#408C4semidirect
195. #10956C31direct (N × H)
266. #2873C2×C31semidirect
267. C2×#344C2×C31semidirect
268. C2×#341C2×C31semidirect
269. #1735C2×C31semidirect
307. #421C4×C31semidirect
309. #419C4×C31semidirect
310. #418C4×C31semidirect
314. #408C4×C31semidirect
396. C31#10956direct (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
C31×#28962
C2×C31×#4082
C31×#28732
C2×C31×#3442
C2×C31×#3412
C31×#17352
#1095631