Finite Group Databasebeta

← C31×#15313 #21472072

Subgroups — C31×#15313 #21472072

Order 7936.

2830 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#127C211yesmaximal, characteristic
2C2×C31×#394C212yesmaximal, complemented
3C2×C31×#394C212yesmaximal, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#386C212yesmaximal, complemented
6C31×#1438C211yesmaximal, characteristic, complemented
7C31×#1438C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1436C212yesmaximal, complemented
10C23×D4×C31C2212yes—
11C23×D4×C31C2211yescharacteristic
12C23×D4×C31C2212yes—
13C23×D4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C2×C31×#127—24no—
16C2×C31×#127—28no—
17C22×C4⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C42×C31C2211yescharacteristic
28C31×#394—28no—
29C31×#394—28no—
30C31×#386—24no—
31C31×#386—28no—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C25×C31C2311yescharacteristic
38C25×C31C2312yes—
39C25×C31C2311yescharacteristic
40C22×D4×C31—24no—
41C22×D4×C31—24no—
42C22×D4×C31—24no—
43C22×D4×C31—24no—
44C22×D4×C31—24no—
45C22×D4×C31—24no—
46C22×D4×C31—24no—
47C22×D4×C31—22no—
48C22×D4×C31—24no—
49C22×D4×C31—24no—
50C22×D4×C31—24no—
51C22×D4×C31—24no—
52C22×D4×C31—24no—
53C22×D4×C31—24no—
54C22×D4×C31—42no—
55C22×D4×C31—42no—
56C22×D4×C31—41no—
57C22×D4×C31—41no—
58C22×D4×C31—42no—
59C22×D4×C31—42no—
60C22×D4×C31—41no—
61C22×D4×C31—41no—
62C22×D4×C31D414yes—
63C22×D4×C31D418yes—
64C23×C4×C31—22no—
65C23×C4×C31—24no—
66C23×C4×C31—41no—
67C23×C4×C31—42no—
68C23×C4×C31—41no—
69C23×C4×C31C2312yes—
70C23×C4×C31C2312yes—
71C23×C4×C31C2312yes—
72C23×C4×C31C2312yes—
73C23×C4×C31C2312yes—
74C23×C4×C31C2311yescharacteristic
75C31×#127—232no—
76C2×C4⋊C4×C31—24no—
77C2×C4⋊C4×C31—24no—
78C2×C4⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—24no—
92C2×C22⋊C4×C31—41no—
93C2×C22⋊C4×C31—42no—
94C2×C22⋊C4×C31—42no—
95C2×C22⋊C4×C31—42no—
96C2×C22⋊C4×C31—42no—
97C2×C22⋊C4×C31—42no—
98C2×C22⋊C4×C31—42no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31—41no—
103C2×C42×C31—24no—
104C2×C42×C31—22no—
105C31×#95—24no—
106C31×#95—24no—
107C31×#95—24no—
108C31×#95—24no—
109C31×#95D418yescomplemented
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—21no—
115C24×C31—21no—
116C24×C31—22no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—22no—
129C24×C31—22no—
130C24×C31—22no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31C2×D414yes—
140C24×C31C2×D412yes—
141C24×C31C2×D414yes—
142C24×C31C2×D412yes—
143C24×C31C2411yescharacteristic
144C2×D4×C31—28no—
145C2×D4×C31—216no—
146C2×D4×C31—28no—
147C2×D4×C31—216no—
148C2×D4×C31—216no—
149C2×D4×C31—28no—
150C2×D4×C31—44no—
151C2×D4×C31—48no—
152C2×D4×C31—48no—
153C2×D4×C31—48no—
154C2×D4×C31—48no—
155C2×D4×C31—48no—
156C2×D4×C31—48no—
157C2×D4×C31—48no—
158C2×D4×C31—48no—
159C2×D4×C31—48no—
160C2×D4×C31—48no—
161C2×D4×C31—48no—
162C2×D4×C31—48no—
163C2×D4×C31—48no—
164C2×D4×C31—44no—
165C2×D4×C31—48no—
166C2×D4×C31—48no—
167C2×D4×C31—44no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—44no—
202C22×C4×C31—48no—
203C22×C4×C31—48no—
204C22×C4×C31—44no—
205C22×C4×C31—44no—
206C22×C4×C31C2×D414yes—
207C22×C4×C31C2×D414yes—
208C22×C4×C31C2×D414yes—
209C22×C4×C31C2×D414yes—
210C22×C4×C31C2×D412yes—
211C22×C4×C31#4114yes—
212C22×C4×C31#4114yes—
213C4⋊C4×C31—48no—
214C22⋊C4×C31—44no—
215C22⋊C4×C31—48no—
216C22⋊C4×C31—48no—
217C22⋊C4×C31—48no—
218C22⋊C4×C31—48no—
219C22⋊C4×C31—48no—
220C22⋊C4×C31—48no—
221C22⋊C4×C31—44no—
222C22⋊C4×C31—44no—
223C42×C31—28no—
224#15313C3111yesmaximal, characteristic, direct product factor, Sylow
225C23×C31—24no—
226C23×C31—22no—
227C23×C31—22no—
228C23×C31—24no—
229C23×C31—24no—
230C23×C31—24no—
231C23×C31—24no—
232C23×C31—24no—
233C23×C31—24no—
234C23×C31—24no—
235C23×C31—22no—
236C23×C31—24no—
237C23×C31—24no—
238C23×C31—22no—
239C23×C31—24no—
240C23×C31—22no—
241C23×C31—24no—
242C23×C31—24no—
243C23×C31—24no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—24no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—41no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—42no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31—42no—
270C23×C31—42no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—41no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31—42no—
279C23×C31—42no—
280C23×C31—42no—
281C23×C31—42no—
282C23×C31—42no—
283C23×C31—42no—
284C23×C31—42no—
285C23×C31—42no—
286C23×C31—42no—
287C23×C31—42no—
288C23×C31—42no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—41no—
295C23×C31—42no—
296C23×C31—42no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—42no—
300C23×C31—42no—
301C23×C31#12014yes—
302C23×C31C22×D412yes—
303C23×C31C22×D411yescharacteristic
304C23×C31C22×D412yes—
305C23×C31C2×#4112yes—
306C23×C31C2×#4112yes—
307C23×C31H(5,𝔽2)11yescharacteristic
308C23×C31H(5,𝔽2)12yes—
309C23×C31H(5,𝔽2)11yescharacteristic
310C23×C31H(5,𝔽2)12yes—
311D4×C31—416no—
312D4×C31—432no—
313D4×C31—416no—
314D4×C31—432no—
315C2×C4×C31—22no—
316C2×C4×C31—24no—
317C2×C4×C31—22no—
318C2×C4×C31—24no—
319C2×C4×C31—24no—
320C2×C4×C31—24no—
321C2×C4×C31—24no—
322C2×C4×C31—24no—
323C2×C4×C31—24no—
324C2×C4×C31—24no—
325C2×C4×C31—24no—
326C2×C4×C31—24no—
327C2×C4×C31—24no—
328C2×C4×C31—24no—
329C2×C4×C31—24no—
330C2×C4×C31—24no—
331C2×C4×C31—416no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—42no—
345C2×C4×C31—42no—
346C2×C4×C31—42no—
347C2×C4×C31—42no—
348C2×C4×C31—42no—
349C2×C4×C31—42no—
350C2×C4×C31—42no—
351C2×C4×C31—42no—
352C2×C4×C31—42no—
353C2×C4×C31—42no—
354C2×C4×C31#12118yes—
355C2×C4×C31#12314yes—
356C22×#127C2×C3111yescharacteristic
357C2×#394C2×C3112yescomplemented
358C2×#394C2×C3112yescomplemented
359C2×#386C2×C3111yescharacteristic, complemented
360C2×#386C2×C3112yescomplemented
361#1438C2×C3111yescharacteristic, complemented
362#1438C2×C3112yescomplemented
363#1438C2×C3112yescomplemented
364#1436C2×C3112yescomplemented
365C22×C31—24no—
366C22×C31—28no—
367C22×C31—42no—
368C22×C31—44no—
369C22×C31—44no—
370C22×C31—44no—
371C22×C31—42no—
372C22×C31—44no—
373C22×C31—44no—
374C22×C31—42no—
375C22×C31—44no—
376C22×C31—44no—
377C22×C31—44no—
378C22×C31—44no—
379C22×C31—42no—
380C22×C31—44no—
381C22×C31—44no—
382C22×C31—44no—
383C22×C31—44no—
384C22×C31—42no—
385C22×C31—44no—
386C22×C31—82no—
387C22×C31—82no—
388C22×C31—82no—
389C22×C31—82no—
390C22×C31—82no—
391C22×C31—82no—
392C22×C31—82no—
393C22×C31—82no—
394C22×C31—82no—
395C22×C31—82no—
396C22×C31—82no—
397C22×C31—82no—
398C22×C31C2×#12011yescharacteristic
399C22×C31C2×#12112yes—
400C22×C31C2×#12311yescharacteristic
401C22×C31#53212yes—
402C22×C31#53411yescharacteristic
403C22×C31#53412yes—
404C22×C31#53512yes—
405C22×C31#54012yes—
406C22×C31#54012yes—
407C22×C31D4212yes—
408C22×C31D4212yes—
409C22×C31D4211yescharacteristic
410C22×C31#54612yes—
411C22×C31#54612yes—
412C22×C31#54612yes—
413C22×C31#54612yes—
414C22×C31#55012yes—
415C22×C31#55912yes—
416C22×C31#55911yescharacteristic
417C22×C31#56011yescharacteristic
418C22×C31#56011yescharacteristic
419C4×C31—24no—
420C4×C31—28no—
421C4×C31—44no—
422C4×C31—44no—
423C4×C31—82no—
424C4×C31—82no—
425C23×D4C22×C3112yes—
426C23×D4C22×C3111yescharacteristic
427C23×D4C22×C3112yes—
428C23×D4C22×C3111yescharacteristic
429C24×C4C22×C3111yescharacteristic
430C2×#127—24no—
431C2×#127—28no—
432C22×C4⋊C4C22×C3112yes—
433C22×C22⋊C4C22×C3111yescharacteristic
434C22×C22⋊C4C22×C3112yes—
435C22×C22⋊C4C22×C3111yescharacteristic
436C22×C22⋊C4C22×C3112yes—
437C22×C22⋊C4C22×C3112yes—
438C22×C22⋊C4C22×C3112yes—
439C22×C22⋊C4C22×C3112yes—
440C22×C22⋊C4C22×C3112yes—
441C22×C22⋊C4C22×C3111yescharacteristic
442C22×C42C22×C3111yescharacteristic
443#394—28no—
444#394—28no—
445#386—24no—
446#386—28no—
447C2×#95C22×C3112yes—
448C2×#95C22×C3112yes—
449C2×#95C22×C3112yes—
450C2×#95C22×C3112yes—
451C2×#95C22×C3112yes—
452C2×C31—44no—
453C2×C31—82no—
454C2×C31—84no—
455C2×C31#240511yescharacteristic
456C2×C31#241012yes—
457C2×C31#242812yes—
458C2×C31#244512yes—
459C2×C31#254412yes—
460C2×C31#266911yescharacteristic
461C2×C31#267312yes—
462C2×C31#270911yescharacteristic
463C2×C31#270912yes—
464C25C23×C3111yescharacteristic
465C25C23×C3112yes—
466C25C23×C3111yescharacteristic
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—22no—
475C22×D4—24no—
476C22×D4—24no—
477C22×D4—24no—
478C22×D4—24no—
479C22×D4—24no—
480C22×D4—24no—
481C22×D4—42no—
482C22×D4—42no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4—42no—
486C22×D4—42no—
487C22×D4—41no—
488C22×D4—41no—
489C22×D4D4×C3114yes—
490C22×D4D4×C3118yes—
491C23×C4—22no—
492C23×C4—24no—
493C23×C4—41no—
494C23×C4—42no—
495C23×C4—41no—
496C23×C4C23×C3112yes—
497C23×C4C23×C3112yes—
498C23×C4C23×C3112yes—
499C23×C4C23×C3112yes—
500C23×C4C23×C3112yes—
501C23×C4C23×C3111yescharacteristic
502#127—232no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—41no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—41no—
530C2×C42—24no—
531C2×C42—22no—
532#95—24no—
533#95—24no—
534#95—24no—
535#95—24no—
536#95D4×C3118yescomplemented
537C31#1531311yescharacteristic, direct product factor, Sylow
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—21no—
543C24—21no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—21no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24C2×D4×C3114yes—
568C24C2×D4×C3112yes—
569C24C2×D4×C3114yes—
570C24C2×D4×C3112yes—
571C24C24×C3111yescharacteristic
572C2×D4—28no—
573C2×D4—216no—
574C2×D4—28no—
575C2×D4—216no—
576C2×D4—216no—
577C2×D4—28no—
578C2×D4—44no—
579C2×D4—48no—
580C2×D4—48no—
581C2×D4—48no—
582C2×D4—48no—
583C2×D4—48no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—48no—
587C2×D4—48no—
588C2×D4—48no—
589C2×D4—48no—
590C2×D4—48no—
591C2×D4—48no—
592C2×D4—44no—
593C2×D4—48no—
594C2×D4—48no—
595C2×D4—44no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—44no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4C2×D4×C3114yes—
635C22×C4C2×D4×C3114yes—
636C22×C4C2×D4×C3114yes—
637C22×C4C2×D4×C3114yes—
638C22×C4C2×D4×C3112yes—
639C22×C4#41×C3114yes—
640C22×C4#41×C3114yes—
641C4⋊C4—48no—
642C22⋊C4—44no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C42—28no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—22no—
666C23—24no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—42no—
728C23C31×#12014yes—
729C23C22×D4×C3112yes—
730C23C22×D4×C3111yescharacteristic
731C23C22×D4×C3112yes—
732C23C2×#41×C3112yes—
733C23C2×#41×C3112yes—
734C23C31×H(5,𝔽2)11yescharacteristic
735C23C31×H(5,𝔽2)12yes—
736C23C31×H(5,𝔽2)11yescharacteristic
737C23C31×H(5,𝔽2)12yes—
738D4—416no—
739D4—432no—
740D4—416no—
741D4—432no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—416no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4C31×#12118yes—
782C2×C4C31×#12314yes—
783C22—24no—
784C22—28no—
785C22—42no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—42no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—44no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22C2×C31×#12011yescharacteristic
817C22C2×C31×#12112yes—
818C22C2×C31×#12311yescharacteristic
819C22C31×#53212yes—
820C22C31×#53411yescharacteristic
821C22C31×#53412yes—
822C22C31×#53512yes—
823C22C31×#54012yes—
824C22C31×#54012yes—
825C22D42×C3112yes—
826C22D42×C3112yes—
827C22D42×C3111yescharacteristic
828C22C31×#54612yes—
829C22C31×#54612yes—
830C22C31×#54612yes—
831C22C31×#54612yes—
832C22C31×#55012yes—
833C22C31×#55912yes—
834C22C31×#55911yescharacteristic
835C22C31×#56011yescharacteristic
836C22C31×#56011yescharacteristic
837C4—24no—
838C4—28no—
839C4—44no—
840C4—44no—
841C4—82no—
842C4—82no—
843C2—44no—
844C2—82no—
845C2—84no—
846C2C31×#240511yescharacteristic
847C2C31×#241012yes—
848C2C31×#242812yes—
849C2C31×#244512yes—
850C2C31×#254412yes—
851C2C31×#266911yescharacteristic
852C2C31×#267312yes—
853C2C31×#270911yescharacteristic
854C2C31×#270912yes—
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#394C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#386C2semidirect
6. C31×#1438C2semidirect
7. C31×#1438C2semidirect
8. C31×#1438C2semidirect
9. C31×#1436C2semidirect
109. C31×#95D4semidirect
224. #15313C31direct (N × H)
357. C2×#394C2×C31semidirect
358. C2×#394C2×C31semidirect
359. C2×#386C2×C31semidirect
360. C2×#386C2×C31semidirect
361. #1438C2×C31semidirect
362. #1438C2×C31semidirect
363. #1438C2×C31semidirect
364. #1436C2×C31semidirect
536. #95D4×C31semidirect
537. C31#15313direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1272
C2×C31×#3942
C2×C31×#3862
C31×#14382
C31×#14362
#1531331