Finite Group Databasebeta

← C31×#10943 #21467702

Subgroups — C31×#10943 #21467702

Order 7936.

1054 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#418C211yesmaximal, characteristic
2C22×C31×#102C211yesmaximal, characteristic
3C22×C31×#100C211yesmaximal, characteristic
4C2×C31×#405C211yesmaximal, characteristic, complemented
5C2×C31×#343C211yesmaximal, characteristic, complemented
6C2×C31×#341C211yesmaximal, characteristic, complemented
7C31×#1736C211yesmaximal, characteristic, complemented
8C23×D4×C31C2211yescharacteristic
9C22×M16×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C23×C8×C31C2211yescharacteristic
13C2×C31×#117C2211yescharacteristic
14C22×C4⋊C4×C31C2211yescharacteristic
15C31×#418—22no—
16C31×#418C414yescomplemented
17C2×C31×#102—21no—
18C2×C31×#102—21no—
19C2×C31×#102—22no—
20C2×C31×#102—22no—
21C2×C31×#102C414yescomplemented
22C2×C31×#100—22no—
23C2×C31×#100—22no—
24C2×C31×#100C414yescomplemented
25C31×#405—22no—
26C31×#405—22no—
27C2×C31×#97—21no—
28C2×C4×C8×C31—21no—
29C31×#343—22no—
30C31×#341—22no—
31C31×#340—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×C31C2×C412yes—
46C22×D4×C31C2×C412yes—
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×C31—21no—
60C2×M16×C31—21no—
61C2×M16×C31—21no—
62C2×M16×C31C2×C412yes—
63C2×M16×C31C2×C412yes—
64C2×M16×C31C2×C412yes—
65C2×M16×C31D412yes—
66C2×M16×C31D412yes—
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×C31D411yescharacteristic
76C22×C8×C31D411yescharacteristic
77C22×C8×C31D412yes—
78C31×#117—21no—
79C31×#117—21no—
80C31×#117C2×C412yes—
81C31×#117D412yes—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31C2×C412yes—
88C2×C4⋊C4×C31D412yes—
89C2×C22⋊C4×C31—21no—
90C2×C42×C31—21no—
91C31×#102—24no—
92C31×#102—24no—
93C31×#102—28no—
94C31×#100—28no—
95C31×#97—24no—
96C4×C8×C31—24no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—41no—
101C24×C31—41no—
102C24×C31—41no—
103C24×C31—41no—
104C24×C31—82no—
105C24×C31—82no—
106C24×C31#4111yescharacteristic
107C2×D4×C31—22no—
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—41no—
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×C31C4214yes—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—41no—
138C22×C4×C31—41no—
139C22×C4×C31—82no—
140C22×C4×C31C22×C411yescharacteristic
141C22×C4×C31C22×C411yescharacteristic
142C22×C4×C31C22×C411yescharacteristic
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D411yescharacteristic
148C22×C4×C31C2×D411yescharacteristic
149C22×C4×C31#4111yescharacteristic
150C22×C4×C31#4111yescharacteristic
151C22×C4×C31#4111yescharacteristic
152C22×C4×C31#4111yescharacteristic
153C22×C4×C31#4111yescharacteristic
154M16×C31—22no—
155M16×C31—22no—
156M16×C31—22no—
157M16×C31—22no—
158M16×C31—22no—
159M16×C31—22no—
160M16×C31—22no—
161M16×C31—41no—
162M16×C31—41no—
163M16×C31—41no—
164M16×C31—41no—
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×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⋊C412yes—
184C2×C8×C31C22⋊C412yes—
185C4⋊C4×C31—22no—
186C4⋊C4×C31—22no—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—41no—
189C4⋊C4×C31—41no—
190C4⋊C4×C31C22⋊C414yes—
191C22⋊C4×C31—22no—
192C22⋊C4×C31—22no—
193C42×C31—22no—
194C42×C31—22no—
195#10943C3111yesmaximal, characteristic, direct product factor, Sylow
196C23×C31—22no—
197C23×C31—22no—
198C23×C31—24no—
199C23×C31—42no—
200C23×C31—42no—
201C23×C31—42no—
202C23×C31—42no—
203C23×C31—42no—
204C23×C31—42no—
205C23×C31—84no—
206C23×C31—84no—
207C23×C31—82no—
208C23×C31—82no—
209C23×C31—84no—
210C23×C31—84no—
211C23×C31—82no—
212C23×C31—82no—
213C23×C31—82no—
214C23×C31—82no—
215C23×C31#11711yescharacteristic
216C23×C31C4×D411yescharacteristic
217C23×C31C4×D411yescharacteristic
218C23×C31#12111yescharacteristic
219C23×C31#12311yescharacteristic
220C23×C31#12411yescharacteristic
221C23×C31#12611yescharacteristic
222D4×C31—24no—
223D4×C31—24no—
224D4×C31—42no—
225D4×C31—42no—
226D4×C31—42no—
227D4×C31—42no—
228D4×C31—42no—
229D4×C31—42no—
230C2×C4×C31—24no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—82no—
235C2×C4×C31—82no—
236C2×C4×C31—82no—
237C2×C4×C31C2×C4211yescharacteristic
238C2×C4×C31C2×C22⋊C411yescharacteristic
239C2×C4×C31C2×C22⋊C411yescharacteristic
240C2×C4×C31C2×C22⋊C411yescharacteristic
241C2×C4×C31#11711yescharacteristic
242C2×C4×C31#11711yescharacteristic
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×C31C4×D411yescharacteristic
250C2×C4×C31C4×D411yescharacteristic
251C2×C4×C31C4×D411yescharacteristic
252C2×C4×C31C4×D411yescharacteristic
253C2×C4×C31#12011yescharacteristic
254C2×C4×C31#12111yescharacteristic
255C2×C4×C31#12111yescharacteristic
256C2×C4×C31#12111yescharacteristic
257C2×C4×C31#12111yescharacteristic
258C2×C4×C31#12111yescharacteristic
259C2×C4×C31#12311yescharacteristic
260C2×C4×C31#12311yescharacteristic
261C2×C4×C31#12411yescharacteristic
262C2×C4×C31#12411yescharacteristic
263C2×C4×C31#12611yescharacteristic
264C2×C4×C31#12711yescharacteristic
265C8×C31—22no—
266C8×C31—22no—
267C8×C31—24no—
268C8×C31—42no—
269C8×C31—42no—
270C2×#418C2×C3111yescharacteristic
271C22×#102C2×C3111yescharacteristic
272C22×#100C2×C3111yescharacteristic
273C2×#405C2×C3111yescharacteristic, complemented
274C2×#343C2×C3111yescharacteristic, complemented
275C2×#341C2×C3111yescharacteristic, complemented
276#1736C2×C3111yescharacteristic, complemented
277C22×C31—22no—
278C22×C31—22no—
279C22×C31—22no—
280C22×C31—22no—
281C22×C31—21no—
282C22×C31—21no—
283C22×C31—21no—
284C22×C31—21no—
285C22×C31—44no—
286C22×C31—84no—
287C22×C31—84no—
288C22×C31—84no—
289C22×C31—84no—
290C22×C31—84no—
291C22×C31—84no—
292C22×C31—82no—
293C22×C31—82no—
294C22×C31C4×C22⋊C411yescharacteristic
295C22×C31#38611yescharacteristic
296C22×C31#38811yescharacteristic
297C22×C31#38811yescharacteristic
298C22×C31#38811yescharacteristic
299C22×C31#38811yescharacteristic
300C22×C31#39011yescharacteristic
301C22×C31#47112yes—
302C22×C31#47212yes—
303C4×C31—44no—
304C4×C31—82no—
305C4×C31C4×C22⋊C411yescharacteristic
306C4×C31C4×C22⋊C411yescharacteristic
307C4×C31#38611yescharacteristic
308C4×C31#38611yescharacteristic
309C4×C31#38811yescharacteristic
310C4×C31#38811yescharacteristic
311C4×C31#39011yescharacteristic
312C4×C31#39011yescharacteristic
313C23×D4C22×C3111yescharacteristic
314C22×M16C22×C3111yescharacteristic
315C22×M16C22×C3111yescharacteristic
316C22×M16C22×C3111yescharacteristic
317C23×C8C22×C3111yescharacteristic
318C2×#117C22×C3111yescharacteristic
319C22×C4⋊C4C22×C3111yescharacteristic
320#418—22no—
321#418C4×C3114yescomplemented
322C2×#102—22no—
323C2×#102—21no—
324C2×#102—21no—
325C2×#102—22no—
326C2×#102C4×C3114yescomplemented
327C2×#100—22no—
328C2×#100—22no—
329C2×#100C4×C3114yescomplemented
330#405—22no—
331#405—22no—
332C2×#97—21no—
333C2×C4×C8—21no—
334#343—22no—
335#341—22no—
336#340—22no—
337C2×C31—21no—
338C2×C31—21no—
339C2×C31—21no—
340C2×C31—21no—
341C2×C31—84no—
342C2×C31#143711yescharacteristic
343C2×C31#190712yes—
344C2×C31#193112yes—
345C2×C31#197711yescharacteristic
346C2×C31#197811yescharacteristic
347C25—21no—
348C22×D4—21no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4C2×C4×C3112yes—
360C22×D4C2×C4×C3112yes—
361C22×D4C2×C4×C3112yes—
362C23×C4—21no—
363C23×C4C23×C3111yescharacteristic
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16C2×C4×C3112yes—
378C2×M16C2×C4×C3112yes—
379C2×M16C2×C4×C3112yes—
380C2×M16D4×C3112yes—
381C2×M16D4×C3112yes—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8C2×C4×C3112yes—
390C22×C8D4×C3112yes—
391C22×C8D4×C3111yescharacteristic
392C22×C8D4×C3111yescharacteristic
393#117—21no—
394#117—21no—
395#117C2×C4×C3112yes—
396#117D4×C3112yes—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4C2×C4×C3112yes—
403C2×C4⋊C4D4×C3112yes—
404C2×C22⋊C4—21no—
405C2×C42—21no—
406#102—24no—
407#102—24no—
408#102—28no—
409#100—28no—
410#97—24no—
411C4×C8—24no—
412C31#1094311yescharacteristic, direct product factor, Sylow
413C24—22no—
414C24—22no—
415C24—22no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—41no—
420C24—82no—
421C24—82no—
422C24#41×C3111yescharacteristic
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4C42×C3114yes—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—82no—
456C22×C4C22×C4×C3111yescharacteristic
457C22×C4C22×C4×C3111yescharacteristic
458C22×C4C22×C4×C3111yescharacteristic
459C22×C4C2×D4×C3111yescharacteristic
460C22×C4C2×D4×C3111yescharacteristic
461C22×C4C2×D4×C3111yescharacteristic
462C22×C4C2×D4×C3111yescharacteristic
463C22×C4C2×D4×C3111yescharacteristic
464C22×C4C2×D4×C3111yescharacteristic
465C22×C4#41×C3111yescharacteristic
466C22×C4#41×C3111yescharacteristic
467C22×C4#41×C3111yescharacteristic
468C22×C4#41×C3111yescharacteristic
469C22×C4#41×C3111yescharacteristic
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16—41no—
481M16C22⋊C4×C3114yes—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8—21no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8C22⋊C4×C3112yes—
500C2×C8C22⋊C4×C3112yes—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C22⋊C4×C3114yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C42—22no—
510C42—22no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—84no—
521C23—84no—
522C23—82no—
523C23—82no—
524C23—84no—
525C23—84no—
526C23—82no—
527C23—82no—
528C23—82no—
529C23—82no—
530C23C31×#11711yescharacteristic
531C23C4×D4×C3111yescharacteristic
532C23C4×D4×C3111yescharacteristic
533C23C31×#12111yescharacteristic
534C23C31×#12311yescharacteristic
535C23C31×#12411yescharacteristic
536C23C31×#12611yescharacteristic
537D4—24no—
538D4—24no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4C2×C42×C3111yescharacteristic
553C2×C4C2×C22⋊C4×C3111yescharacteristic
554C2×C4C2×C22⋊C4×C3111yescharacteristic
555C2×C4C2×C22⋊C4×C3111yescharacteristic
556C2×C4C31×#11711yescharacteristic
557C2×C4C31×#11711yescharacteristic
558C2×C4C4×D4×C3111yescharacteristic
559C2×C4C4×D4×C3111yescharacteristic
560C2×C4C4×D4×C3111yescharacteristic
561C2×C4C4×D4×C3111yescharacteristic
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×C4C31×#12011yescharacteristic
569C2×C4C31×#12111yescharacteristic
570C2×C4C31×#12111yescharacteristic
571C2×C4C31×#12111yescharacteristic
572C2×C4C31×#12111yescharacteristic
573C2×C4C31×#12111yescharacteristic
574C2×C4C31×#12311yescharacteristic
575C2×C4C31×#12311yescharacteristic
576C2×C4C31×#12411yescharacteristic
577C2×C4C31×#12411yescharacteristic
578C2×C4C31×#12611yescharacteristic
579C2×C4C31×#12711yescharacteristic
580C8—22no—
581C8—22no—
582C8—24no—
583C8—42no—
584C8—42no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—44no—
594C22—84no—
595C22—84no—
596C22—84no—
597C22—84no—
598C22—84no—
599C22—84no—
600C22—82no—
601C22—82no—
602C22C4×C22⋊C4×C3111yescharacteristic
603C22C31×#38611yescharacteristic
604C22C31×#38811yescharacteristic
605C22C31×#38811yescharacteristic
606C22C31×#38811yescharacteristic
607C22C31×#38811yescharacteristic
608C22C31×#39011yescharacteristic
609C22C31×#47112yes—
610C22C31×#47212yes—
611C4—44no—
612C4—82no—
613C4C4×C22⋊C4×C3111yescharacteristic
614C4C4×C22⋊C4×C3111yescharacteristic
615C4C31×#38611yescharacteristic
616C4C31×#38611yescharacteristic
617C4C31×#38811yescharacteristic
618C4C31×#38811yescharacteristic
619C4C31×#39011yescharacteristic
620C4C31×#39011yescharacteristic
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—84no—
626C2C31×#143711yescharacteristic
627C2C31×#190712yes—
628C2C31×#193112yes—
629C2C31×#197711yescharacteristic
630C2C31×#197811yescharacteristic
subgroupG/H
center, socleC23×C31#121
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#405C2semidirect
5. C2×C31×#343C2semidirect
6. C2×C31×#341C2semidirect
7. C31×#1736C2semidirect
16. C31×#418C4semidirect
21. C2×C31×#102C4semidirect
24. C2×C31×#100C4semidirect
195. #10943C31direct (N × H)
273. C2×#405C2×C31semidirect
274. C2×#343C2×C31semidirect
275. C2×#341C2×C31semidirect
276. #1736C2×C31semidirect
321. #418C4×C31semidirect
326. C2×#102C4×C31semidirect
329. C2×#100C4×C31semidirect
412. C31#10943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4182
C22×C31×#1022
C22×C31×#1002
C2×C31×#4052
C2×C31×#3432
C2×C31×#3412
C31×#17362
#1094331