Finite Group Databasebeta

← C31×#16660 #21473419

Subgroups — C31×#16660 #21473419

Order 7936.

2038 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#392C211yesmaximal, characteristic
2C2×C31×#386C212yesmaximal, complemented
3C2×C31×#381C211yesmaximal, characteristic, complemented
4C31×#1443C212yesmaximal, complemented
5C31×#1440C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1439C211yesmaximal, characteristic, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1438C212yesmaximal, complemented
10C23×D4×C31C2212yes—
11C23×D4×C31C2211yescharacteristic
12C24×C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C22⋊C4×C31C2212yes—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2211yescharacteristic
22C31×#392—24no—
23C31×#386—28no—
24C31×#381—24no—
25C2×C31×#95C2211yescharacteristic
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C25×C31C2312yes—
35C25×C31C2311yescharacteristic
36C22×D4×C31—24no—
37C22×D4×C31—24no—
38C22×D4×C31—24no—
39C22×D4×C31—24no—
40C22×D4×C31—24no—
41C22×D4×C31—22no—
42C22×D4×C31—24no—
43C22×D4×C31—42no—
44C22×D4×C31—42no—
45C22×D4×C31—42no—
46C22×D4×C31—41no—
47C22×D4×C31—41no—
48C23×C4×C31—22no—
49C23×C4×C31—22no—
50C23×C4×C31—41no—
51C23×C4×C31—41no—
52C23×C4×C31—41no—
53C23×C4×C31—41no—
54C23×C4×C31D414yescomplemented
55C23×C4×C31C2312yes—
56C23×C4×C31C2312yes—
57C23×C4×C31C2312yes—
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2312yes—
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2312yes—
62C2×C4⋊C4×C31—41no—
63C2×C4⋊C4×C31—42no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—41no—
72C2×C22⋊C4×C31—41no—
73C2×C22⋊C4×C31—42no—
74C2×C22⋊C4×C31—42no—
75C2×C22⋊C4×C31—42no—
76C2×C22⋊C4×C31—42no—
77C2×C22⋊C4×C31—42no—
78C2×C22⋊C4×C31—42no—
79C2×C22⋊C4×C31—41no—
80C2×C22⋊C4×C31—41no—
81C2×C22⋊C4×C31—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31—42no—
84C2×C22⋊C4×C31—42no—
85C2×C22⋊C4×C31—42no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31D414yes—
88C31×#95—24no—
89C31×#95—24no—
90C31×#95—24no—
91C31×#95—24no—
92C31×#95—22no—
93C31×#95—24no—
94C31×#95—41no—
95C31×#95—42no—
96C31×#95—42no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—21no—
100C24×C31—21no—
101C24×C31—21no—
102C24×C31—21no—
103C24×C31—22no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—22no—
108C24×C31—22no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31C2×D412yes—
120C24×C31C2×D412yes—
121C24×C31#4114yes—
122C24×C31#4112yes—
123C24×C31C2411yescharacteristic
124C2×D4×C31—216no—
125C2×D4×C31—48no—
126C2×D4×C31—48no—
127C2×D4×C31—48no—
128C2×D4×C31—44no—
129C2×D4×C31—48no—
130C2×D4×C31—48no—
131C2×D4×C31—44no—
132C2×D4×C31—48no—
133C2×D4×C31—48no—
134C2×D4×C31—44no—
135C2×D4×C31—48no—
136C22×C4×C31—28no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—21no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—21no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—44no—
179C22×C4×C31—44no—
180C22×C4×C31—44no—
181C22×C4×C31—44no—
182C22×C4×C31—44no—
183C22×C4×C31—44no—
184C22×C4×C31C2×D412yes—
185C22×C4×C31C2×D412yes—
186C22×C4×C31C2×D414yes—
187C22×C4×C31#4114yes—
188C4⋊C4×C31—44no—
189C22⋊C4×C31—44no—
190C22⋊C4×C31—48no—
191C22⋊C4×C31—48no—
192C22⋊C4×C31—48no—
193C22⋊C4×C31—44no—
194C22⋊C4×C31—48no—
195C22⋊C4×C31—48no—
196C22⋊C4×C31—48no—
197#16660C3111yesmaximal, characteristic, direct product factor, Sylow
198C23×C31—24no—
199C23×C31—22no—
200C23×C31—22no—
201C23×C31—22no—
202C23×C31—22no—
203C23×C31—24no—
204C23×C31—22no—
205C23×C31—22no—
206C23×C31—24no—
207C23×C31—24no—
208C23×C31—24no—
209C23×C31—24no—
210C23×C31—24no—
211C23×C31—24no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—24no—
215C23×C31—24no—
216C23×C31—24no—
217C23×C31—42no—
218C23×C31—42no—
219C23×C31—42no—
220C23×C31—42no—
221C23×C31—41no—
222C23×C31—42no—
223C23×C31—41no—
224C23×C31—41no—
225C23×C31—42no—
226C23×C31—41no—
227C23×C31—42no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—42no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—42no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—42no—
244C23×C31—42no—
245C23×C31—42no—
246C23×C31—42no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31#12114yes—
256C23×C31C22×D411yescharacteristic
257C23×C31C22×D411yescharacteristic
258C23×C31C2×#4111yescharacteristic
259C23×C31C2×#4112yes—
260C23×C31C2×#4112yes—
261C23×C31H(5,𝔽2)11yescharacteristic
262C23×C31H(5,𝔽2)11yescharacteristic
263C23×C31H(5,𝔽2)11yescharacteristic
264C23×C31H(5,𝔽2)11yescharacteristic
265C23×C31H(5,𝔽2)12yes—
266C23×C31H(5,𝔽2)12yes—
267D4×C31—432no—
268D4×C31—416no—
269C2×C4×C31—24no—
270C2×C4×C31—24no—
271C2×C4×C31—24no—
272C2×C4×C31—24no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—24no—
276C2×C4×C31—24no—
277C2×C4×C31—24no—
278C2×C4×C31—24no—
279C2×C4×C31—416no—
280C2×C4×C31—42no—
281C2×C4×C31—42no—
282C2×C4×C31—42no—
283C2×C4×C31—42no—
284C2×C4×C31—42no—
285C2×C4×C31—42no—
286C2×C4×C31—42no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
289C2×C4×C31—42no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×#392C2×C3111yescharacteristic
316C2×#386C2×C3112yescomplemented
317C2×#381C2×C3111yescharacteristic, complemented
318#1443C2×C3112yescomplemented
319#1440C2×C3112yescomplemented
320#1439C2×C3112yescomplemented
321#1439C2×C3111yescharacteristic, complemented
322#1438C2×C3112yescomplemented
323#1438C2×C3112yescomplemented
324C22×C31—24no—
325C22×C31—28no—
326C22×C31—42no—
327C22×C31—44no—
328C22×C31—42no—
329C22×C31—44no—
330C22×C31—42no—
331C22×C31—44no—
332C22×C31—42no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31—44no—
336C22×C31—44no—
337C22×C31—44no—
338C22×C31—44no—
339C22×C31—44no—
340C22×C31—44no—
341C22×C31—44no—
342C22×C31—82no—
343C22×C31—82no—
344C22×C31—82no—
345C22×C31—82no—
346C22×C31—82no—
347C22×C31—82no—
348C22×C31—82no—
349C22×C31—82no—
350C22×C31C2×#12111yescharacteristic
351C22×C31#52512yes—
352C22×C31#53411yescharacteristic
353C22×C31#53411yescharacteristic
354C22×C31#53411yescharacteristic
355C22×C31#53511yescharacteristic
356C22×C31#53512yes—
357C22×C31#53811yescharacteristic
358C22×C31#53811yescharacteristic
359C22×C31#53812yes—
360C22×C31#53812yes—
361C22×C31#54012yes—
362C22×C31#54012yes—
363C22×C31#54612yes—
364C22×C31#54612yes—
365C22×C31#55111yescharacteristic
366C22×C31#55112yes—
367C22×C31#55112yes—
368C22×C31#55312yes—
369C22×C31#55911yescharacteristic
370C22×C31#56011yescharacteristic
371C22×C31#56012yes—
372C22×C31#56011yescharacteristic
373C4×C31—44no—
374C4×C31—44no—
375C4×C31—42no—
376C4×C31—42no—
377C4×C31—82no—
378C4×C31—82no—
379C4×C31—82no—
380C23×D4C22×C3112yes—
381C23×D4C22×C3111yescharacteristic
382C24×C4C22×C3111yescharacteristic
383C22×C4⋊C4C22×C3111yescharacteristic
384C22×C22⋊C4C22×C3112yes—
385C22×C22⋊C4C22×C3112yes—
386C22×C22⋊C4C22×C3111yescharacteristic
387C22×C22⋊C4C22×C3112yes—
388C22×C22⋊C4C22×C3112yes—
389C22×C22⋊C4C22×C3112yes—
390C22×C22⋊C4C22×C3112yes—
391C22×C22⋊C4C22×C3111yescharacteristic
392#392—24no—
393#386—28no—
394#381—24no—
395C2×#95C22×C3111yescharacteristic
396C2×#95C22×C3112yes—
397C2×#95C22×C3112yes—
398C2×#95C22×C3112yes—
399C2×#95C22×C3112yes—
400C2×#95C22×C3112yes—
401C2×#95C22×C3112yes—
402C2×#95C22×C3112yes—
403C2×#95C22×C3111yescharacteristic
404C2×C31—44no—
405C2×C31—84no—
406C2×C31#241112yes—
407C2×C31#260011yescharacteristic
408C2×C31#261711yescharacteristic
409C2×C31#263512yes—
410C2×C31#269711yescharacteristic
411C2×C31#270312yes—
412C2×C31#270911yescharacteristic
413C2×C31#274912yes—
414C2×C31#275211yescharacteristic
415C2×C31#276011yescharacteristic
416C2×C31#281511yescharacteristic
417C25C23×C3112yes—
418C25C23×C3111yescharacteristic
419C22×D4—24no—
420C22×D4—24no—
421C22×D4—24no—
422C22×D4—24no—
423C22×D4—24no—
424C22×D4—22no—
425C22×D4—24no—
426C22×D4—42no—
427C22×D4—42no—
428C22×D4—42no—
429C22×D4—41no—
430C22×D4—41no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—41no—
434C23×C4—41no—
435C23×C4—41no—
436C23×C4—41no—
437C23×C4D4×C3114yescomplemented
438C23×C4C23×C3112yes—
439C23×C4C23×C3112yes—
440C23×C4C23×C3112yes—
441C23×C4C23×C3111yescharacteristic
442C23×C4C23×C3112yes—
443C23×C4C23×C3111yescharacteristic
444C23×C4C23×C3112yes—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—42no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—41no—
455C2×C22⋊C4—41no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—41no—
463C2×C22⋊C4—41no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4D4×C3114yes—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—22no—
476#95—24no—
477#95—41no—
478#95—42no—
479#95—42no—
480C31#1666011yescharacteristic, direct product factor, Sylow
481C24—22no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24C2×D4×C3112yes—
504C24C2×D4×C3112yes—
505C24#41×C3114yes—
506C24#41×C3112yes—
507C24C24×C3111yescharacteristic
508C2×D4—216no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—44no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—44no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—44no—
519C2×D4—48no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4C2×D4×C3112yes—
569C22×C4C2×D4×C3112yes—
570C22×C4C2×D4×C3114yes—
571C22×C4#41×C3114yes—
572C4⋊C4—44no—
573C22⋊C4—44no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—44no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C23—24no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—41no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C31×#12114yes—
639C23C22×D4×C3111yescharacteristic
640C23C22×D4×C3111yescharacteristic
641C23C2×#41×C3111yescharacteristic
642C23C2×#41×C3112yes—
643C23C2×#41×C3112yes—
644C23C31×H(5,𝔽2)11yescharacteristic
645C23C31×H(5,𝔽2)11yescharacteristic
646C23C31×H(5,𝔽2)11yescharacteristic
647C23C31×H(5,𝔽2)11yescharacteristic
648C23C31×H(5,𝔽2)12yes—
649C23C31×H(5,𝔽2)12yes—
650D4—432no—
651D4—416no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—416no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C22—24no—
699C22—28no—
700C22—42no—
701C22—44no—
702C22—42no—
703C22—44no—
704C22—42no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—44no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—82no—
717C22—82no—
718C22—82no—
719C22—82no—
720C22—82no—
721C22—82no—
722C22—82no—
723C22—82no—
724C22C2×C31×#12111yescharacteristic
725C22C31×#52512yes—
726C22C31×#53411yescharacteristic
727C22C31×#53411yescharacteristic
728C22C31×#53411yescharacteristic
729C22C31×#53511yescharacteristic
730C22C31×#53512yes—
731C22C31×#53811yescharacteristic
732C22C31×#53811yescharacteristic
733C22C31×#53812yes—
734C22C31×#53812yes—
735C22C31×#54012yes—
736C22C31×#54012yes—
737C22C31×#54612yes—
738C22C31×#54612yes—
739C22C31×#55111yescharacteristic
740C22C31×#55112yes—
741C22C31×#55112yes—
742C22C31×#55312yes—
743C22C31×#55911yescharacteristic
744C22C31×#56011yescharacteristic
745C22C31×#56012yes—
746C22C31×#56011yescharacteristic
747C4—44no—
748C4—44no—
749C4—42no—
750C4—42no—
751C4—82no—
752C4—82no—
753C4—82no—
754C2—44no—
755C2—84no—
756C2C31×#241112yes—
757C2C31×#260011yescharacteristic
758C2C31×#261711yescharacteristic
759C2C31×#263512yes—
760C2C31×#269711yescharacteristic
761C2C31×#270312yes—
762C2C31×#270911yescharacteristic
763C2C31×#274912yes—
764C2C31×#275211yescharacteristic
765C2C31×#276011yescharacteristic
766C2C31×#281511yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#386C2semidirect
3. C2×C31×#381C2semidirect
4. C31×#1443C2semidirect
5. C31×#1440C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
54. C23×C4×C31D4semidirect
197. #16660C31direct (N × H)
316. C2×#386C2×C31semidirect
317. C2×#381C2×C31semidirect
318. #1443C2×C31semidirect
319. #1440C2×C31semidirect
320. #1439C2×C31semidirect
321. #1439C2×C31semidirect
322. #1438C2×C31semidirect
323. #1438C2×C31semidirect
437. C23×C4D4×C31semidirect
480. C31#16660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3922
C2×C31×#3862
C2×C31×#3812
C31×#14432
C31×#14402
C31×#14392
C31×#14382
#1666031