Finite Group Databasebeta

← C31×#16816 #21473575

Subgroups — C31×#16816 #21473575

Order 7936.

1706 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#394C212yesmaximal
2C2×C31×#386C211yesmaximal, characteristic
3C2×C31×#380C211yesmaximal, characteristic, complemented
4C31×#1444C211yesmaximal, characteristic, complemented
5C31×#1442C212yesmaximal, complemented
6C31×#1442C211yesmaximal, characteristic, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1440C212yesmaximal, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C31×#394—28no—
25C31×#386—24no—
26C31×#380—24no—
27C2×C31×#95C2212yes—
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C25×C31C2311yescharacteristic
39C25×C31C2311yescharacteristic
40C22×D4×C31—22no—
41C22×D4×C31—22no—
42C22×D4×C31—42no—
43C22×D4×C31—42no—
44C22×D4×C31D414yes—
45C23×C4×C31—22no—
46C23×C4×C31—22no—
47C23×C4×C31—42no—
48C23×C4×C31—42no—
49C23×C4×C31D414yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2312yes—
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2312yes—
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2312yes—
58C23×C4×C31C2311yescharacteristic
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—22no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—42no—
63C2×C4⋊C4×C31—42no—
64C2×C4⋊C4×C31—42no—
65C2×C4⋊C4×C31—42no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—42no—
80C2×C22⋊C4×C31—42no—
81C2×C22⋊C4×C31—42no—
82C2×C22⋊C4×C31—42no—
83C2×C22⋊C4×C31—42no—
84C2×C22⋊C4×C31—42no—
85C31×#95—24no—
86C31×#95—22no—
87C31×#95—22no—
88C31×#95—24no—
89C31×#95—22no—
90C31×#95—24no—
91C31×#95—22no—
92C31×#95—42no—
93C31×#95—42no—
94C31×#95—42no—
95C31×#95—42no—
96C24×C31—22no—
97C24×C31—21no—
98C24×C31—21no—
99C24×C31—22no—
100C24×C31—22no—
101C24×C31—22no—
102C24×C31—21no—
103C24×C31—21no—
104C24×C31—21no—
105C24×C31—22no—
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31C2×D412yes—
115C24×C31C2×D412yes—
116C24×C31C2×D412yes—
117C24×C31#4112yes—
118C24×C31C2411yescharacteristic
119C2×D4×C31—28no—
120C2×D4×C31—48no—
121C2×D4×C31—44no—
122C2×D4×C31—44no—
123C2×D4×C31—48no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—21no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—21no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—28no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—22no—
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—21no—
170C22×C4×C31—21no—
171C22×C4×C31—22no—
172C22×C4×C31—44no—
173C22×C4×C31—44no—
174C22×C4×C31—48no—
175C22×C4×C31—48no—
176C22×C4×C31C2×D412yes—
177C22×C4×C31C2×D412yes—
178C22×C4×C31C2×D412yes—
179C22×C4×C31#4114yes—
180C22×C4×C31#4112yes—
181C22×C4×C31#4112yes—
182C4⋊C4×C31—44no—
183C4⋊C4×C31—44no—
184C4⋊C4×C31—48no—
185C22⋊C4×C31—48no—
186C22⋊C4×C31—48no—
187C22⋊C4×C31—44no—
188C22⋊C4×C31—48no—
189C22⋊C4×C31—44no—
190C22⋊C4×C31—48no—
191C22⋊C4×C31—44no—
192#16816C3111yesmaximal, characteristic, direct product factor, Sylow
193C23×C31—22no—
194C23×C31—22no—
195C23×C31—22no—
196C23×C31—22no—
197C23×C31—24no—
198C23×C31—22no—
199C23×C31—22no—
200C23×C31—24no—
201C23×C31—24no—
202C23×C31—22no—
203C23×C31—22no—
204C23×C31—22no—
205C23×C31—22no—
206C23×C31—24no—
207C23×C31—22no—
208C23×C31—24no—
209C23×C31—24no—
210C23×C31—22no—
211C23×C31—22no—
212C23×C31—42no—
213C23×C31—42no—
214C23×C31—42no—
215C23×C31—42no—
216C23×C31—42no—
217C23×C31—42no—
218C23×C31—42no—
219C23×C31—42no—
220C23×C31—41no—
221C23×C31—41no—
222C23×C31—41no—
223C23×C31—41no—
224C23×C31—41no—
225C23×C31—41no—
226C23×C31—42no—
227C23×C31—42no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—42no—
234C23×C31—42no—
235C23×C31—42no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31#12114yes—
239C23×C31C22×D411yescharacteristic
240C23×C31C22×D411yescharacteristic
241C23×C31C2×#4111yescharacteristic
242C23×C31C2×#4111yescharacteristic
243C23×C31C2×#4111yescharacteristic
244C23×C31C2×#4112yes—
245C23×C31H(5,𝔽2)12yes—
246C23×C31H(5,𝔽2)12yes—
247C23×C31H(5,𝔽2)12yes—
248C23×C312−1+411yescharacteristic
249C23×C312−1+411yescharacteristic
250D4×C31—416no—
251C2×C4×C31—22no—
252C2×C4×C31—22no—
253C2×C4×C31—24no—
254C2×C4×C31—24no—
255C2×C4×C31—22no—
256C2×C4×C31—22no—
257C2×C4×C31—22no—
258C2×C4×C31—24no—
259C2×C4×C31—22no—
260C2×C4×C31—24no—
261C2×C4×C31—24no—
262C2×C4×C31—24no—
263C2×C4×C31—416no—
264C2×C4×C31—42no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—42no—
270C2×C4×C31—42no—
271C2×C4×C31—42no—
272C2×C4×C31—42no—
273C2×C4×C31—42no—
274C2×C4×C31—42no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—42no—
278C2×C4×C31—41no—
279C2×C4×C31—42no—
280C2×C4×C31—42no—
281C2×C4×C31—42no—
282C2×C4×C31—42no—
283C2×C4×C31—42no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—42no—
287C2×C4×C31—41no—
288C2×C4×C31—42no—
289C2×C4×C31—42no—
290C2×C4×C31—42no—
291C2×C4×C31—42no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
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#12314yes—
305C2×#394C2×C3112yes—
306C2×#386C2×C3111yescharacteristic
307C2×#380C2×C3111yescharacteristic, complemented
308#1444C2×C3111yescharacteristic, complemented
309#1442C2×C3112yescomplemented
310#1442C2×C3111yescharacteristic, complemented
311#1440C2×C3112yescomplemented
312#1440C2×C3112yescomplemented
313#1439C2×C3111yescharacteristic, complemented
314#1439C2×C3111yescharacteristic, complemented
315C22⋊#95C2×C3111yescharacteristic, complemented
316C22×C31—24no—
317C22×C31—24no—
318C22×C31—24no—
319C22×C31—42no—
320C22×C31—42no—
321C22×C31—42no—
322C22×C31—44no—
323C22×C31—44no—
324C22×C31—42no—
325C22×C31—44no—
326C22×C31—44no—
327C22×C31—42no—
328C22×C31—44no—
329C22×C31—44no—
330C22×C31—42no—
331C22×C31—42no—
332C22×C31—81no—
333C22×C31—81no—
334C22×C31—81no—
335C22×C31—81no—
336C22×C31—82no—
337C22×C31—82no—
338C22×C31C2×#12111yescharacteristic
339C22×C31C2×#12311yescharacteristic
340C22×C31#53211yescharacteristic
341C22×C31#53411yescharacteristic
342C22×C31#53411yescharacteristic
343C22×C31#53412yes—
344C22×C31#53511yescharacteristic
345C22×C31#53611yescharacteristic
346C22×C31#53812yes—
347C22×C31#53812yes—
348C22×C31#53812yes—
349C22×C31#53912yes—
350C22×C31#54212yes—
351C22×C31#54612yes—
352C22×C31#54711yescharacteristic
353C22×C31#54711yescharacteristic
354C22×C31#55211yescharacteristic
355C22×C31#55211yescharacteristic
356C22×C31#55312yes—
357C22×C31#55312yes—
358C22×C31#55512yes—
359C22×C31#56212yes—
360C22×C31#56212yes—
361C4×C31—24no—
362C4×C31—42no—
363C4×C31—42no—
364C4×C31—44no—
365C4×C31—81no—
366C4×C31—82no—
367C4×C31—82no—
368C4×C31—81no—
369C4×C31—82no—
370C23×D4C22×C3111yescharacteristic
371C24×C4C22×C3111yescharacteristic
372C22×C4⋊C4C22×C3112yes—
373C22×C4⋊C4C22×C3111yescharacteristic
374C22×C4⋊C4C22×C3111yescharacteristic
375C22×C22⋊C4C22×C3112yes—
376C22×C22⋊C4C22×C3111yescharacteristic
377C22×C22⋊C4C22×C3112yes—
378C22×C22⋊C4C22×C3112yes—
379C22×C22⋊C4C22×C3112yes—
380C22×C22⋊C4C22×C3111yescharacteristic
381C22×C22⋊C4C22×C3111yescharacteristic
382#394—28no—
383#386—24no—
384#380—24no—
385C2×#95C22×C3112yes—
386C2×#95C22×C3111yescharacteristic
387C2×#95C22×C3111yescharacteristic
388C2×#95C22×C3112yes—
389C2×#95C22×C3112yes—
390C2×#95C22×C3111yescharacteristic
391C2×#95C22×C3111yescharacteristic
392C2×#95C22×C3112yes—
393C2×#95C22×C3112yes—
394C2×#95C22×C3112yes—
395C2×#95C22×C3112yes—
396C2×C31—44no—
397C2×C31—82no—
398C2×C31#248611yescharacteristic
399C2×C31#250011yescharacteristic
400C2×C31#254311yescharacteristic
401C2×C31#261711yescharacteristic
402C2×C31#262211yescharacteristic
403C2×C31#266311yescharacteristic
404C2×C31#268612yes—
405C2×C31#270812yes—
406C2×C31#277912yes—
407C2×C31#278112yes—
408C2×C31#281611yescharacteristic
409C25C23×C3111yescharacteristic
410C25C23×C3111yescharacteristic
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—42no—
414C22×D4—42no—
415C22×D4D4×C3114yes—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4D4×C3114yes—
421C23×C4C23×C3112yes—
422C23×C4C23×C3112yes—
423C23×C4C23×C3111yescharacteristic
424C23×C4C23×C3112yes—
425C23×C4C23×C3111yescharacteristic
426C23×C4C23×C3111yescharacteristic
427C23×C4C23×C3111yescharacteristic
428C23×C4C23×C3112yes—
429C23×C4C23×C3111yescharacteristic
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—42no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—42no—
453C2×C22⋊C4—42no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456#95—24no—
457#95—22no—
458#95—22no—
459#95—24no—
460#95—22no—
461#95—24no—
462#95—22no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95—42no—
467C31#1681611yescharacteristic, direct product factor, Sylow
468C24—22no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—22no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24C2×D4×C3112yes—
487C24C2×D4×C3112yes—
488C24C2×D4×C3112yes—
489C24#41×C3112yes—
490C24C24×C3111yescharacteristic
491C2×D4—28no—
492C2×D4—48no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—48no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—28no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4C2×D4×C3112yes—
549C22×C4C2×D4×C3112yes—
550C22×C4C2×D4×C3112yes—
551C22×C4#41×C3114yes—
552C22×C4#41×C3112yes—
553C22×C4#41×C3112yes—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—48no—
557C22⋊C4—48no—
558C22⋊C4—48no—
559C22⋊C4—44no—
560C22⋊C4—48no—
561C22⋊C4—44no—
562C22⋊C4—48no—
563C22⋊C4—44no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—24no—
569C23—22no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23—22no—
579C23—24no—
580C23—24no—
581C23—22no—
582C23—22no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—41no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23C31×#12114yes—
610C23C22×D4×C3111yescharacteristic
611C23C22×D4×C3111yescharacteristic
612C23C2×#41×C3111yescharacteristic
613C23C2×#41×C3111yescharacteristic
614C23C2×#41×C3111yescharacteristic
615C23C2×#41×C3112yes—
616C23C31×H(5,𝔽2)12yes—
617C23C31×H(5,𝔽2)12yes—
618C23C31×H(5,𝔽2)12yes—
619C23C31×2−1+411yescharacteristic
620C23C31×2−1+411yescharacteristic
621D4—416no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—416no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
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—42no—
674C2×C4—42no—
675C2×C4C31×#12314yes—
676C22—24no—
677C22—24no—
678C22—24no—
679C22—42no—
680C22—42no—
681C22—44no—
682C22—44no—
683C22—42no—
684C22—44no—
685C22—44no—
686C22—42no—
687C22—42no—
688C22—44no—
689C22—44no—
690C22—42no—
691C22—42no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—82no—
696C22—82no—
697C22—81no—
698C22C2×C31×#12111yescharacteristic
699C22C2×C31×#12311yescharacteristic
700C22C31×#53211yescharacteristic
701C22C31×#53411yescharacteristic
702C22C31×#53412yes—
703C22C31×#53411yescharacteristic
704C22C31×#53511yescharacteristic
705C22C31×#53611yescharacteristic
706C22C31×#53812yes—
707C22C31×#53812yes—
708C22C31×#53812yes—
709C22C31×#53912yes—
710C22C31×#54212yes—
711C22C31×#54612yes—
712C22C31×#54711yescharacteristic
713C22C31×#54711yescharacteristic
714C22C31×#55211yescharacteristic
715C22C31×#55211yescharacteristic
716C22C31×#55312yes—
717C22C31×#55312yes—
718C22C31×#55512yes—
719C22C31×#56212yes—
720C22C31×#56212yes—
721C4—24no—
722C4—42no—
723C4—42no—
724C4—44no—
725C4—82no—
726C4—82no—
727C4—81no—
728C4—82no—
729C4—81no—
730C2—44no—
731C2—82no—
732C2C31×#248611yescharacteristic
733C2C31×#250011yescharacteristic
734C2C31×#254311yescharacteristic
735C2C31×#261711yescharacteristic
736C2C31×#262211yescharacteristic
737C2C31×#266311yescharacteristic
738C2C31×#268612yes—
739C2C31×#270812yes—
740C2C31×#277912yes—
741C2C31×#278112yes—
742C2C31×#281611yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#380C2semidirect
4. C31×#1444C2semidirect
5. C31×#1442C2semidirect
6. C31×#1442C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×C22⋊#95C2semidirect
192. #16816C31direct (N × H)
307. C2×#380C2×C31semidirect
308. #1444C2×C31semidirect
309. #1442C2×C31semidirect
310. #1442C2×C31semidirect
311. #1440C2×C31semidirect
312. #1440C2×C31semidirect
313. #1439C2×C31semidirect
314. #1439C2×C31semidirect
315. C22⋊#95C2×C31semidirect
467. C31#16816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3942
C2×C31×#3862
C2×C31×#3802
C31×#14442
C31×#14422
C31×#14402
C31×#14392
C31×C22⋊#952
#1681631