Finite Group Databasebeta

← C31×#14735 #21471494

Subgroups — C31×#14735 #21471494

Order 7936.

2110 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#397C211yesmaximal, characteristic, complemented
2C2×C31×#386C211yesmaximal, characteristic
3C2×C31×#386C212yesmaximal
4C2×C31×#380C211yesmaximal, characteristic, complemented
5C22×C31×#95C211yesmaximal, characteristic, complemented
6C31×#1445C211yesmaximal, characteristic, complemented
7C31×#1443C212yesmaximal, complemented
8C31×#1442C211yesmaximal, characteristic, complemented
9C31×#1440C212yesmaximal, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C212yesmaximal, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2212yes—
14C24×C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C31×#397—24no—
24C31×#386—28no—
25C31×#386—24no—
26C31×#380—24no—
27C2×C31×#95—24no—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2211yescharacteristic
40C25×C31C2311yescharacteristic
41C25×C31C2311yescharacteristic
42C22×D4×C31—22no—
43C22×D4×C31—22no—
44C22×D4×C31—24no—
45C22×D4×C31—24no—
46C22×D4×C31D414yes—
47C23×C4×C31—24no—
48C23×C4×C31—24no—
49C23×C4×C31—24no—
50C23×C4×C31—22no—
51C23×C4×C31—24no—
52C23×C4×C31—22no—
53C23×C4×C31—24no—
54C23×C4×C31—24no—
55C23×C4×C31—42no—
56C23×C4×C31—42no—
57C23×C4×C31—42no—
58C23×C4×C31D414yes—
59C23×C4×C31C2312yes—
60C23×C4×C31C2312yes—
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2312yes—
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2312yes—
67C23×C4×C31C2311yescharacteristic
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—42no—
73C2×C22⋊C4×C31—24no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—24no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—42no—
87C2×C22⋊C4×C31—42no—
88C2×C22⋊C4×C31—42no—
89C31×#95—24no—
90C31×#95—24no—
91C31×#95—22no—
92C31×#95—24no—
93C31×#95—22no—
94C31×#95—22no—
95C31×#95—24no—
96C31×#95—24no—
97C31×#95—24no—
98C31×#95—42no—
99C31×#95—42no—
100C31×#95D414yescomplemented
101C24×C31—21no—
102C24×C31—21no—
103C24×C31—22no—
104C24×C31—22no—
105C24×C31—21no—
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—22no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—21no—
115C24×C31—22no—
116C24×C31—21no—
117C24×C31C2×D412yes—
118C24×C31C2×D412yes—
119C24×C31C2×D412yes—
120C24×C31#4112yes—
121C24×C31#4114yes—
122C24×C31#4114yes—
123C24×C31C2411yescharacteristic
124C2×D4×C31—28no—
125C2×D4×C31—216no—
126C2×D4×C31—44no—
127C2×D4×C31—44no—
128C2×D4×C31—48no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—216no—
132C22×C4×C31—28no—
133C22×C4×C31—21no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
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—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—28no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—21no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—21no—
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—21no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—21no—
177C22×C4×C31—22no—
178C22×C4×C31—44no—
179C22×C4×C31—48no—
180C22×C4×C31—48no—
181C22×C4×C31—48no—
182C22×C4×C31—48no—
183C22×C4×C31—48no—
184C22×C4×C31—48no—
185C22×C4×C31—48no—
186C22×C4×C31—48no—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D412yes—
189C22×C4×C31C2×D414yes—
190C22×C4×C31C2×D412yes—
191C22×C4×C31C2×D412yes—
192C22×C4×C31#4114yes—
193C22×C4×C31#4112yes—
194C4⋊C4×C31—44no—
195C4⋊C4×C31—44no—
196C22⋊C4×C31—48no—
197C22⋊C4×C31—48no—
198C22⋊C4×C31—44no—
199C22⋊C4×C31—48no—
200C22⋊C4×C31—44no—
201C22⋊C4×C31—44no—
202#14735C3111yesmaximal, characteristic, direct product factor, Sylow
203C23×C31—22no—
204C23×C31—24no—
205C23×C31—24no—
206C23×C31—22no—
207C23×C31—22no—
208C23×C31—22no—
209C23×C31—24no—
210C23×C31—24no—
211C23×C31—22no—
212C23×C31—24no—
213C23×C31—24no—
214C23×C31—22no—
215C23×C31—22no—
216C23×C31—24no—
217C23×C31—24no—
218C23×C31—24no—
219C23×C31—22no—
220C23×C31—24no—
221C23×C31—22no—
222C23×C31—24no—
223C23×C31—22no—
224C23×C31—24no—
225C23×C31—22no—
226C23×C31—41no—
227C23×C31—41no—
228C23×C31—42no—
229C23×C31—41no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—42no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—41no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—41no—
243C23×C31—42no—
244C23×C31#12114yes—
245C23×C31#12314yes—
246C23×C31#12318yes—
247C23×C31#12414yes—
248C23×C31#12618yes—
249C23×C31C22×D411yescharacteristic
250C23×C31C22×D411yescharacteristic
251C23×C31C22×D411yescharacteristic
252C23×C31C2×#4111yescharacteristic
253C23×C31C2×#4111yescharacteristic
254C23×C31C2×#4112yes—
255C23×C31C2×#4112yes—
256C23×C31C2×#4112yes—
257C23×C31H(5,𝔽2)12yes—
258C23×C31H(5,𝔽2)11yescharacteristic
259C23×C312−1+411yescharacteristic
260D4×C31—416no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—24no—
264C2×C4×C31—24no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—22no—
268C2×C4×C31—24no—
269C2×C4×C31—24no—
270C2×C4×C31—24no—
271C2×C4×C31—22no—
272C2×C4×C31—24no—
273C2×C4×C31—24no—
274C2×C4×C31—24no—
275C2×C4×C31—24no—
276C2×C4×C31—416no—
277C2×C4×C31—432no—
278C2×C4×C31—42no—
279C2×C4×C31—42no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
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—42no—
291C2×C4×C31—41no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—42no—
299C2×C4×C31—41no—
300C2×C4×C31—42no—
301C2×C4×C31—41no—
302C2×C4×C31—42no—
303C2×C4×C31—41no—
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×C4×C31#12114yes—
316C2×#397C2×C3111yescharacteristic, complemented
317C2×#386C2×C3111yescharacteristic
318C2×#386C2×C3112yes—
319C2×#380C2×C3111yescharacteristic, complemented
320C22×#95C2×C3111yescharacteristic, complemented
321#1445C2×C3111yescharacteristic, complemented
322#1443C2×C3112yescomplemented
323#1442C2×C3111yescharacteristic, complemented
324#1440C2×C3112yescomplemented
325#1439C2×C3111yescharacteristic, complemented
326C22⋊#95C2×C3112yescomplemented
327C22×C31—24no—
328C22×C31—24no—
329C22×C31—24no—
330C22×C31—24no—
331C22×C31—28no—
332C22×C31—28no—
333C22×C31—28no—
334C22×C31—24no—
335C22×C31—28no—
336C22×C31—24no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—44no—
340C22×C31—44no—
341C22×C31—42no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31—82no—
346C22×C31—81no—
347C22×C31—82no—
348C22×C31#39718yescomplemented
349C22×C31C2×#12111yescharacteristic
350C22×C31C2×#12111yescharacteristic
351C22×C31C2×#12311yescharacteristic
352C22×C31C2×#12312yes—
353C22×C31#52512yes—
354C22×C31C2×#12411yescharacteristic
355C22×C31C2×#12612yes—
356C22×C31#52912yes—
357C22×C31#53211yescharacteristic
358C22×C31#53411yescharacteristic
359C22×C31#53711yescharacteristic
360C22×C31#53812yes—
361C22×C31#53912yes—
362C22×C31D4211yescharacteristic
363C22×C31#54612yes—
364C22×C31#54612yes—
365C22×C31#54711yescharacteristic
366C22×C31#54811yescharacteristic
367C22×C31#55112yes—
368C22×C31#55112yes—
369C22×C31#55212yes—
370C22×C31#55311yescharacteristic
371C22×C31#55312yes—
372C4×C31—24no—
373C4×C31—42no—
374C4×C31—42no—
375C4×C31—44no—
376C4×C31—44no—
377C4×C31—81no—
378C4×C31—81no—
379C4×C31—82no—
380C4×C31—82no—
381C23×D4C22×C3111yescharacteristic
382C24×C4C22×C3112yes—
383C24×C4C22×C3111yescharacteristic
384C22×C4⋊C4C22×C3111yescharacteristic
385C22×C4⋊C4C22×C3111yescharacteristic
386C22×C22⋊C4C22×C3111yescharacteristic
387C22×C22⋊C4C22×C3111yescharacteristic
388C22×C22⋊C4C22×C3112yes—
389C22×C22⋊C4C22×C3112yes—
390C22×C22⋊C4C22×C3112yes—
391C22×C22⋊C4C22×C3111yescharacteristic
392#397—24no—
393#386—28no—
394#386—24no—
395#380—24no—
396C2×#95—24no—
397C2×#95C22×C3112yes—
398C2×#95C22×C3112yes—
399C2×#95C22×C3111yescharacteristic
400C2×#95C22×C3112yes—
401C2×#95C22×C3112yes—
402C2×#95C22×C3112yes—
403C2×#95C22×C3111yescharacteristic
404C2×#95C22×C3111yescharacteristic
405C2×#95C22×C3112yes—
406C2×#95C22×C3112yes—
407C2×#95C22×C3112yes—
408C2×#95C22×C3111yescharacteristic
409C2×C31—28no—
410C2×C31—82no—
411C2×C31C2×#39711yescharacteristic
412C2×C31#241211yescharacteristic
413C2×C31#241611yescharacteristic
414C2×C31#241812yes—
415C2×C31#241912yes—
416C2×C31#248112yes—
417C2×C31#249811yescharacteristic
418C2×C31#251012yes—
419C2×C31#254311yescharacteristic
420C2×C31#263911yescharacteristic
421C2×C31#285011yescharacteristic
422C25C23×C3111yescharacteristic
423C25C23×C3111yescharacteristic
424C22×D4—22no—
425C22×D4—22no—
426C22×D4—24no—
427C22×D4—24no—
428C22×D4D4×C3114yes—
429C23×C4—24no—
430C23×C4—24no—
431C23×C4—24no—
432C23×C4—22no—
433C23×C4—24no—
434C23×C4—22no—
435C23×C4—24no—
436C23×C4—24no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4D4×C3114yes—
441C23×C4C23×C3112yes—
442C23×C4C23×C3112yes—
443C23×C4C23×C3111yescharacteristic
444C23×C4C23×C3111yescharacteristic
445C23×C4C23×C3111yescharacteristic
446C23×C4C23×C3112yes—
447C23×C4C23×C3111yescharacteristic
448C23×C4C23×C3112yes—
449C23×C4C23×C3111yescharacteristic
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—42no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471#95—24no—
472#95—22no—
473#95—24no—
474#95—22no—
475#95—22no—
476#95—24no—
477#95—24no—
478#95—24no—
479#95—24no—
480#95—42no—
481#95—42no—
482#95D4×C3114yescomplemented
483C31#1473511yescharacteristic, direct product factor, Sylow
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—22no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24C2×D4×C3112yes—
501C24C2×D4×C3112yes—
502C24C2×D4×C3112yes—
503C24#41×C3112yes—
504C24#41×C3114yes—
505C24#41×C3114yes—
506C24C24×C3111yescharacteristic
507C2×D4—28no—
508C2×D4—216no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—48no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—216no—
515C22×C4—28no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—28no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—44no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4C2×D4×C3112yes—
571C22×C4C2×D4×C3112yes—
572C22×C4C2×D4×C3114yes—
573C22×C4C2×D4×C3112yes—
574C22×C4C2×D4×C3112yes—
575C22×C4#41×C3114yes—
576C22×C4#41×C3112yes—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—44no—
582C22⋊C4—48no—
583C22⋊C4—44no—
584C22⋊C4—44no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—22no—
602C23—24no—
603C23—22no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—22no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—41no—
612C23—42no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—41no—
625C23—42no—
626C23C31×#12114yes—
627C23C31×#12314yes—
628C23C31×#12318yes—
629C23C31×#12414yes—
630C23C31×#12618yes—
631C23C22×D4×C3111yescharacteristic
632C23C22×D4×C3111yescharacteristic
633C23C22×D4×C3111yescharacteristic
634C23C2×#41×C3111yescharacteristic
635C23C2×#41×C3111yescharacteristic
636C23C2×#41×C3112yes—
637C23C2×#41×C3112yes—
638C23C2×#41×C3112yes—
639C23C31×H(5,𝔽2)12yes—
640C23C31×H(5,𝔽2)11yescharacteristic
641C23C31×2−1+411yescharacteristic
642D4—416no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—416no—
659C2×C4—432no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
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—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
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×C4C31×#12114yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—24no—
702C22—28no—
703C22—28no—
704C22—28no—
705C22—24no—
706C22—28no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—44no—
711C22—44no—
712C22—42no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—82no—
717C22—81no—
718C22—82no—
719C22C31×#39718yescomplemented
720C22C2×C31×#12111yescharacteristic
721C22C2×C31×#12111yescharacteristic
722C22C2×C31×#12311yescharacteristic
723C22C2×C31×#12312yes—
724C22C31×#52512yes—
725C22C2×C31×#12411yescharacteristic
726C22C2×C31×#12612yes—
727C22C31×#52912yes—
728C22C31×#53211yescharacteristic
729C22C31×#53411yescharacteristic
730C22C31×#53711yescharacteristic
731C22C31×#53812yes—
732C22C31×#53912yes—
733C22D42×C3111yescharacteristic
734C22C31×#54612yes—
735C22C31×#54612yes—
736C22C31×#54711yescharacteristic
737C22C31×#54811yescharacteristic
738C22C31×#55112yes—
739C22C31×#55112yes—
740C22C31×#55212yes—
741C22C31×#55311yescharacteristic
742C22C31×#55312yes—
743C4—24no—
744C4—42no—
745C4—42no—
746C4—44no—
747C4—44no—
748C4—81no—
749C4—81no—
750C4—82no—
751C4—82no—
752C2—28no—
753C2—82no—
754C2C2×C31×#39711yescharacteristic
755C2C31×#241211yescharacteristic
756C2C31×#241611yescharacteristic
757C2C31×#241812yes—
758C2C31×#241912yes—
759C2C31×#248112yes—
760C2C31×#249811yescharacteristic
761C2C31×#251012yes—
762C2C31×#254311yescharacteristic
763C2C31×#263911yescharacteristic
764C2C31×#285011yescharacteristic
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
1. C2×C31×#397C2semidirect
4. C2×C31×#380C2semidirect
5. C22×C31×#95C2semidirect
6. C31×#1445C2semidirect
7. C31×#1443C2semidirect
8. C31×#1442C2semidirect
9. C31×#1440C2semidirect
10. C31×#1439C2semidirect
11. C31×C22⋊#95C2semidirect
100. C31×#95D4semidirect
202. #14735C31direct (N × H)
316. C2×#397C2×C31semidirect
319. C2×#380C2×C31semidirect
320. C22×#95C2×C31semidirect
321. #1445C2×C31semidirect
322. #1443C2×C31semidirect
323. #1442C2×C31semidirect
324. #1440C2×C31semidirect
325. #1439C2×C31semidirect
326. C22⋊#95C2×C31semidirect
348. C22×C31#397semidirect
482. #95D4×C31semidirect
483. C31#14735direct (N × H)
719. C22C31×#397semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3972
C2×C31×#3862
C2×C31×#3802
C22×C31×#952
C31×#14452
C31×#14432
C31×#14422
C31×#14402
C31×#14392
C31×C22⋊#952
#1473531