Finite Group Databasebeta

← C31×#15257 #21472016

Subgroups — C31×#15257 #21472016

Order 7936.

4462 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic, complemented
2C22×C31×#120C211yesmaximal, characteristic, complemented
3C22×C31×#120C211yesmaximal, characteristic, complemented
4C2×C31×#392C212yesmaximal, complemented
5C2×C31×#386C212yesmaximal, complemented
6C2×C31×#379C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C26×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C23×D4×C31C2212yes—
15C23×D4×C31C2211yescharacteristic
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic, complemented
18C24×C4×C31C2211yescharacteristic, complemented
19C2×C31×#121—24no—
20C2×C31×#121—24no—
21C2×C31×#121—24no—
22C2×C31×#120—24no—
23C2×C31×#120—24no—
24C2×C31×#120—28no—
25C2×C31×#120—28no—
26C22×C4⋊C4×C31C2211yescharacteristic, complemented
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2212yes—
32C22×C22⋊C4×C31C2212yes—
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic, complemented
36C22×C22⋊C4×C31C2212yescomplemented
37C22×C22⋊C4×C31C2212yescomplemented
38C31×#392—28no—
39C31×#386—28no—
40C31×#379—24no—
41C2×C31×#95C2212yescomplemented
42C2×C31×#95C2212yescomplemented
43C2×C31×#95C2212yescomplemented
44C2×C31×#95C2212yescomplemented
45C25×C31—22no—
46C25×C31—22no—
47C25×C31—24no—
48C25×C31—24no—
49C25×C31—22no—
50C25×C31—24no—
51C25×C31—42no—
52C25×C31—42no—
53C25×C31—42no—
54C25×C31C2311yescharacteristic
55C25×C31C2311yescharacteristic
56C25×C31C2311yescharacteristic
57C25×C31C2312yes—
58C22×D4×C31—24no—
59C22×D4×C31—24no—
60C22×D4×C31—24no—
61C22×D4×C31—24no—
62C22×D4×C31—24no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—24no—
70C22×D4×C31—24no—
71C22×D4×C31—24no—
72C22×D4×C31—24no—
73C22×D4×C31—24no—
74C22×D4×C31—24no—
75C22×D4×C31—24no—
76C22×D4×C31—22no—
77C22×D4×C31—42no—
78C22×D4×C31—42no—
79C22×D4×C31—42no—
80C22×D4×C31—42no—
81C22×D4×C31—42no—
82C22×D4×C31—42no—
83C22×D4×C31—42no—
84C22×D4×C31D414yescomplemented
85C22×D4×C31D414yescomplemented
86C22×D4×C31D418yescomplemented
87C23×C4×C31—22no—
88C23×C4×C31—22no—
89C23×C4×C31—22no—
90C23×C4×C31—24no—
91C23×C4×C31—42no—
92C23×C4×C31C2312yes—
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2312yes—
97C23×C4×C31C2312yes—
98C23×C4×C31C2311yescharacteristic
99C31×#121—232no—
100C31×#120—232no—
101C31×#120—232no—
102C2×C4⋊C4×C31—22no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—24no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—24no—
112C2×C22⋊C4×C31—24no—
113C2×C22⋊C4×C31—24no—
114C2×C22⋊C4×C31—24no—
115C2×C22⋊C4×C31—24no—
116C2×C22⋊C4×C31—24no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—24no—
121C2×C22⋊C4×C31—24no—
122C2×C22⋊C4×C31—24no—
123C2×C22⋊C4×C31—24no—
124C2×C22⋊C4×C31—24no—
125C2×C22⋊C4×C31—24no—
126C2×C22⋊C4×C31—24no—
127C2×C22⋊C4×C31—42no—
128C2×C22⋊C4×C31—42no—
129C2×C22⋊C4×C31—42no—
130C2×C22⋊C4×C31—42no—
131C2×C22⋊C4×C31—42no—
132C2×C22⋊C4×C31—42no—
133C2×C22⋊C4×C31D418yescomplemented
134C2×C22⋊C4×C31D414yescomplemented
135C31×#95—24no—
136C31×#95—24no—
137C31×#95—24no—
138C31×#95—42no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—22no—
142C24×C31—22no—
143C24×C31—22no—
144C24×C31—22no—
145C24×C31—22no—
146C24×C31—22no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—22no—
150C24×C31—22no—
151C24×C31—22no—
152C24×C31—22no—
153C24×C31—22no—
154C24×C31—22no—
155C24×C31—22no—
156C24×C31—22no—
157C24×C31—22no—
158C24×C31—22no—
159C24×C31—22no—
160C24×C31—22no—
161C24×C31—22no—
162C24×C31—22no—
163C24×C31—22no—
164C24×C31—28no—
165C24×C31—28no—
166C24×C31—28no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—22no—
170C24×C31—22no—
171C24×C31—22no—
172C24×C31—22no—
173C24×C31—22no—
174C24×C31—22no—
175C24×C31—48no—
176C24×C31—48no—
177C24×C31—48no—
178C24×C31—48no—
179C24×C31—48no—
180C24×C31—48no—
181C24×C31—48no—
182C24×C31—48no—
183C24×C31—48no—
184C24×C31—44no—
185C24×C31—44no—
186C24×C31—48no—
187C24×C31—44no—
188C24×C31—48no—
189C24×C31—48no—
190C24×C31—48no—
191C24×C31—44no—
192C24×C31—48no—
193C24×C31C2×D412yes—
194C24×C31C2×D412yes—
195C24×C31C2×D412yes—
196C24×C31C2×D412yes—
197C24×C31C2×D414yes—
198C24×C31C2×D412yes—
199C24×C31C2×D414yes—
200C24×C31C2×D414yes—
201C24×C31#4114yes—
202C24×C31C2411yescharacteristic
203C2×D4×C31—216no—
204C2×D4×C31—28no—
205C2×D4×C31—28no—
206C2×D4×C31—28no—
207C2×D4×C31—28no—
208C2×D4×C31—216no—
209C2×D4×C31—216no—
210C2×D4×C31—28no—
211C2×D4×C31—44no—
212C2×D4×C31—48no—
213C2×D4×C31—44no—
214C2×D4×C31—48no—
215C2×D4×C31—48no—
216C2×D4×C31—48no—
217C2×D4×C31—48no—
218C2×D4×C31—48no—
219C2×D4×C31—48no—
220C2×D4×C31—48no—
221C2×D4×C31—48no—
222C2×D4×C31—48no—
223C2×D4×C31—48no—
224C2×D4×C31—48no—
225C2×D4×C31—48no—
226C2×D4×C31—48no—
227C2×D4×C31—48no—
228C2×D4×C31—44no—
229C2×D4×C31—48no—
230C2×D4×C31—44no—
231C2×D4×C31—48no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—22no—
235C22×C4×C31—28no—
236C22×C4×C31—22no—
237C22×C4×C31—22no—
238C22×C4×C31—22no—
239C22×C4×C31—22no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—22no—
243C22×C4×C31—22no—
244C22×C4×C31—22no—
245C22×C4×C31—22no—
246C22×C4×C31—22no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—22no—
252C22×C4×C31—22no—
253C22×C4×C31—22no—
254C22×C4×C31—22no—
255C22×C4×C31—22no—
256C22×C4×C31—22no—
257C22×C4×C31—22no—
258C22×C4×C31—22no—
259C22×C4×C31—22no—
260C22×C4×C31—22no—
261C22×C4×C31—22no—
262C22×C4×C31—22no—
263C22×C4×C31—22no—
264C22×C4×C31—22no—
265C22×C4×C31—22no—
266C22×C4×C31—22no—
267C22×C4×C31—48no—
268C22×C4×C31—48no—
269C22×C4×C31—44no—
270C22×C4×C31—44no—
271C22×C4×C31C2×D414yes—
272C22×C4×C31C2×D414yes—
273C22×C4×C31C2×D412yes—
274C22×C4×C31C2×D412yes—
275C22×C4×C31C2×D412yes—
276C22×C4×C31C2×D414yes—
277C22×C4×C31C2×D412yes—
278C4⋊C4×C31—28no—
279C22⋊C4×C31—216no—
280C22⋊C4×C31—28no—
281C22⋊C4×C31—28no—
282C22⋊C4×C31—28no—
283C22⋊C4×C31—28no—
284C22⋊C4×C31—216no—
285C22⋊C4×C31—48no—
286C22⋊C4×C31—48no—
287C22⋊C4×C31—48no—
288C22⋊C4×C31—48no—
289C22⋊C4×C31—44no—
290#15257C3111yesmaximal, characteristic, direct product factor, Sylow
291C23×C31—22no—
292C23×C31—22no—
293C23×C31—24no—
294C23×C31—24no—
295C23×C31—22no—
296C23×C31—24no—
297C23×C31—22no—
298C23×C31—24no—
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—24no—
303C23×C31—24no—
304C23×C31—22no—
305C23×C31—24no—
306C23×C31—24no—
307C23×C31—24no—
308C23×C31—24no—
309C23×C31—24no—
310C23×C31—24no—
311C23×C31—24no—
312C23×C31—24no—
313C23×C31—24no—
314C23×C31—24no—
315C23×C31—24no—
316C23×C31—24no—
317C23×C31—24no—
318C23×C31—24no—
319C23×C31—24no—
320C23×C31—24no—
321C23×C31—24no—
322C23×C31—24no—
323C23×C31—24no—
324C23×C31—24no—
325C23×C31—24no—
326C23×C31—24no—
327C23×C31—24no—
328C23×C31—24no—
329C23×C31—24no—
330C23×C31—24no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—22no—
334C23×C31—24no—
335C23×C31—24no—
336C23×C31—416no—
337C23×C31—416no—
338C23×C31—416no—
339C23×C31—432no—
340C23×C31—432no—
341C23×C31—432no—
342C23×C31—432no—
343C23×C31—432no—
344C23×C31—432no—
345C23×C31—41no—
346C23×C31—42no—
347C23×C31—42no—
348C23×C31—42no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—42no—
352C23×C31—42no—
353C23×C31—42no—
354C23×C31—42no—
355C23×C31—41no—
356C23×C31—42no—
357C23×C31—42no—
358C23×C31—42no—
359C23×C31—42no—
360C23×C31—42no—
361C23×C31—42no—
362C23×C31—42no—
363C23×C31—42no—
364C23×C31—42no—
365C23×C31—42no—
366C23×C31—42no—
367C23×C31—42no—
368C23×C31—42no—
369C23×C31—42no—
370C23×C31—42no—
371C23×C31—42no—
372C23×C31—42no—
373C23×C31—42no—
374C23×C31—42no—
375C23×C31—42no—
376C23×C31—42no—
377C23×C31—42no—
378C23×C31—42no—
379C23×C31—41no—
380C23×C31—42no—
381C23×C31—41no—
382C23×C31—42no—
383C23×C31—41no—
384C23×C31—42no—
385C23×C31—41no—
386C23×C31—42no—
387C23×C31—42no—
388C23×C31—42no—
389C23×C31—42no—
390C23×C31—42no—
391C23×C31—42no—
392C23×C31—42no—
393C23×C31—42no—
394C23×C31—42no—
395C23×C31#12014yes—
396C23×C31#12014yescomplemented
397C23×C31#12118yescomplemented
398C23×C31C22×D411yescharacteristic
399C23×C31C22×D411yescharacteristic
400C23×C31C22×D412yes—
401C23×C31C22×D412yes—
402C23×C31C22×D411yescharacteristic
403C23×C31C2×#4112yes—
404C23×C31H(5,𝔽2)12yes—
405C23×C31H(5,𝔽2)12yes—
406C23×C31H(5,𝔽2)12yes—
407D4×C31—416no—
408D4×C31—416no—
409D4×C31—432no—
410D4×C31—416no—
411D4×C31—432no—
412C2×C4×C31—22no—
413C2×C4×C31—22no—
414C2×C4×C31—24no—
415C2×C4×C31—24no—
416C2×C4×C31—22no—
417C2×C4×C31—22no—
418C2×C4×C31—24no—
419C2×C4×C31—24no—
420C2×C4×C31—22no—
421C2×C4×C31—22no—
422C2×C4×C31—24no—
423C2×C4×C31—24no—
424C2×C4×C31—22no—
425C2×C4×C31—24no—
426C2×C4×C31—24no—
427C2×C4×C31—24no—
428C2×C4×C31—24no—
429C2×C4×C31—416no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—42no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—42no—
436C2×C4×C31—42no—
437C2×C4×C31—42no—
438C2×C4×C31—42no—
439C2×C4×C31—42no—
440C2×C4×C31—42no—
441C2×C4×C31—42no—
442C2×C4×C31—42no—
443C2×C4×C31—42no—
444C2×C4×C31—42no—
445C2×C4×C31—42no—
446C2×C4×C31—42no—
447C2×C4×C31—42no—
448C2×C4×C31—42no—
449C2×C4×C31—42no—
450C2×C4×C31—42no—
451C2×C4×C31—42no—
452C2×C4×C31—42no—
453C2×C4×C31#12014yescomplemented
454C22×#121C2×C3111yescharacteristic, complemented
455C22×#120C2×C3111yescharacteristic, complemented
456C22×#120C2×C3111yescharacteristic, complemented
457C2×#392C2×C3112yescomplemented
458C2×#386C2×C3112yescomplemented
459C2×#379C2×C3111yescharacteristic, complemented
460#1440C2×C3111yescharacteristic, complemented
461#1439C2×C3112yescomplemented
462#1438C2×C3112yescomplemented
463#1438C2×C3111yescharacteristic, complemented
464#1438C2×C3111yescharacteristic, complemented
465C22×C31—24no—
466C22×C31—24no—
467C22×C31—24no—
468C22×C31—24no—
469C22×C31—28no—
470C22×C31—28no—
471C22×C31—28no—
472C22×C31—28no—
473C22×C31—464no—
474C22×C31—42no—
475C22×C31—44no—
476C22×C31—44no—
477C22×C31—42no—
478C22×C31—44no—
479C22×C31—44no—
480C22×C31—44no—
481C22×C31—44no—
482C22×C31—44no—
483C22×C31—44no—
484C22×C31—44no—
485C22×C31—44no—
486C22×C31—44no—
487C22×C31—44no—
488C22×C31—44no—
489C22×C31—44no—
490C22×C31—44no—
491C22×C31—44no—
492C22×C31—44no—
493C22×C31—44no—
494C22×C31—44no—
495C22×C31—44no—
496C22×C31—44no—
497C22×C31—44no—
498C22×C31—44no—
499C22×C31—42no—
500C22×C31—42no—
501C22×C31—42no—
502C22×C31—44no—
503C22×C31—44no—
504C22×C31—82no—
505C22×C31—82no—
506C22×C31—82no—
507C22×C31—82no—
508C22×C31C2×#12011yescharacteristic
509C22×C31C2×#12011yescharacteristic
510C22×C31C2×#12011yescharacteristic
511C22×C31C2×#12112yes—
512C22×C31#52511yescharacteristic
513C22×C31#53411yescharacteristic
514C22×C31#53411yescharacteristic
515C22×C31#53412yes—
516C22×C31#53511yescharacteristic
517C22×C31#53512yes—
518C22×C31#53812yes—
519C22×C31D4212yes—
520C22×C31D4212yes—
521C22×C31D4212yes—
522C22×C31D4212yes—
523C22×C31D4212yes—
524C22×C31#54612yes—
525C22×C31#54612yes—
526C22×C31#54612yes—
527C22×C31#54612yes—
528C22×C31#56012yes—
529C4×C31—24no—
530C4×C31—42no—
531C4×C31—42no—
532C4×C31—42no—
533C4×C31—44no—
534C4×C31—44no—
535C4×C31—82no—
536C26C22×C3111yescharacteristic
537C23×D4C22×C3112yes—
538C23×D4C22×C3112yes—
539C23×D4C22×C3111yescharacteristic
540C23×D4C22×C3111yescharacteristic
541C23×D4C22×C3111yescharacteristic, complemented
542C24×C4C22×C3111yescharacteristic, complemented
543C2×#121—24no—
544C2×#121—24no—
545C2×#121—24no—
546C2×#120—24no—
547C2×#120—24no—
548C2×#120—28no—
549C2×#120—28no—
550C22×C4⋊C4C22×C3111yescharacteristic, complemented
551C22×C22⋊C4C22×C3112yes—
552C22×C22⋊C4C22×C3111yescharacteristic
553C22×C22⋊C4C22×C3111yescharacteristic
554C22×C22⋊C4C22×C3112yes—
555C22×C22⋊C4C22×C3112yes—
556C22×C22⋊C4C22×C3112yes—
557C22×C22⋊C4C22×C3111yescharacteristic
558C22×C22⋊C4C22×C3111yescharacteristic
559C22×C22⋊C4C22×C3111yescharacteristic, complemented
560C22×C22⋊C4C22×C3112yescomplemented
561C22×C22⋊C4C22×C3112yescomplemented
562#392—28no—
563#386—28no—
564#379—24no—
565C2×#95C22×C3112yescomplemented
566C2×#95C22×C3112yescomplemented
567C2×#95C22×C3112yescomplemented
568C2×#95C22×C3112yescomplemented
569C2×C31—44no—
570C2×C31—44no—
571C2×C31—48no—
572C2×C31—82no—
573C2×C31#240311yescharacteristic
574C2×C31#240311yescharacteristic
575C2×C31#240411yescharacteristic
576C2×C31#240812yes—
577C2×C31#241012yes—
578C2×C31#242412yes—
579C2×C31#266812yes—
580C2×C31#266912yes—
581C2×C31#267812yes—
582C25—22no—
583C25—22no—
584C25—24no—
585C25—24no—
586C25—22no—
587C25—24no—
588C25—42no—
589C25—42no—
590C25—42no—
591C25C23×C3111yescharacteristic
592C25C23×C3111yescharacteristic
593C25C23×C3111yescharacteristic
594C25C23×C3112yes—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—24no—
600C22×D4—22no—
601C22×D4—22no—
602C22×D4—22no—
603C22×D4—22no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—24no—
607C22×D4—24no—
608C22×D4—24no—
609C22×D4—24no—
610C22×D4—24no—
611C22×D4—24no—
612C22×D4—24no—
613C22×D4—22no—
614C22×D4—42no—
615C22×D4—42no—
616C22×D4—42no—
617C22×D4—42no—
618C22×D4—42no—
619C22×D4—42no—
620C22×D4—42no—
621C22×D4D4×C3114yescomplemented
622C22×D4D4×C3114yescomplemented
623C22×D4D4×C3118yescomplemented
624C23×C4—22no—
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—24no—
628C23×C4—42no—
629C23×C4C23×C3112yes—
630C23×C4C23×C3111yescharacteristic
631C23×C4C23×C3111yescharacteristic
632C23×C4C23×C3111yescharacteristic
633C23×C4C23×C3112yes—
634C23×C4C23×C3112yes—
635C23×C4C23×C3111yescharacteristic
636#121—232no—
637#120—232no—
638#120—232no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—24no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—24no—
658C2×C22⋊C4—24no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—42no—
665C2×C22⋊C4—42no—
666C2×C22⋊C4—42no—
667C2×C22⋊C4—42no—
668C2×C22⋊C4—42no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4D4×C3118yescomplemented
671C2×C22⋊C4D4×C3114yescomplemented
672#95—24no—
673#95—24no—
674#95—24no—
675#95—42no—
676C31#1525711yescharacteristic, direct product factor, Sylow
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—28no—
703C24—28no—
704C24—28no—
705C24—21no—
706C24—21no—
707C24—22no—
708C24—22no—
709C24—22no—
710C24—22no—
711C24—22no—
712C24—22no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—44no—
723C24—44no—
724C24—48no—
725C24—44no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—44no—
730C24—48no—
731C24C2×D4×C3112yes—
732C24C2×D4×C3112yes—
733C24C2×D4×C3112yes—
734C24C2×D4×C3112yes—
735C24C2×D4×C3114yes—
736C24C2×D4×C3112yes—
737C24C2×D4×C3114yes—
738C24C2×D4×C3114yes—
739C24#41×C3114yes—
740C24C24×C3111yescharacteristic
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—216no—
747C2×D4—216no—
748C2×D4—28no—
749C2×D4—44no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—48no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—28no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4C2×D4×C3114yes—
810C22×C4C2×D4×C3114yes—
811C22×C4C2×D4×C3112yes—
812C22×C4C2×D4×C3112yes—
813C22×C4C2×D4×C3112yes—
814C22×C4C2×D4×C3114yes—
815C22×C4C2×D4×C3112yes—
816C4⋊C4—28no—
817C22⋊C4—216no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—216no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C23—22no—
829C23—22no—
830C23—24no—
831C23—24no—
832C23—22no—
833C23—24no—
834C23—22no—
835C23—24no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—24no—
840C23—24no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—432no—
879C23—432no—
880C23—432no—
881C23—432no—
882C23—41no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—41no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—41no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23—42no—
906C23—42no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—42no—
915C23—42no—
916C23—41no—
917C23—42no—
918C23—41no—
919C23—42no—
920C23—41no—
921C23—42no—
922C23—41no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—42no—
930C23—42no—
931C23—42no—
932C23C31×#12014yes—
933C23C31×#12014yescomplemented
934C23C31×#12118yescomplemented
935C23C22×D4×C3111yescharacteristic
936C23C22×D4×C3111yescharacteristic
937C23C22×D4×C3112yes—
938C23C22×D4×C3112yes—
939C23C22×D4×C3111yescharacteristic
940C23C2×#41×C3112yes—
941C23C31×H(5,𝔽2)12yes—
942C23C31×H(5,𝔽2)12yes—
943C23C31×H(5,𝔽2)12yes—
944D4—416no—
945D4—416no—
946D4—432no—
947D4—416no—
948D4—432no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—416no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4C31×#12014yescomplemented
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—28no—
996C22—28no—
997C22—28no—
998C22—28no—
999C22—464no—
1000C22—42no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—42no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—44no—
1029C22—44no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—82no—
1034C22C2×C31×#12011yescharacteristic
1035C22C2×C31×#12011yescharacteristic
1036C22C2×C31×#12011yescharacteristic
1037C22C2×C31×#12112yes—
1038C22C31×#52511yescharacteristic
1039C22C31×#53411yescharacteristic
1040C22C31×#53411yescharacteristic
1041C22C31×#53412yes—
1042C22C31×#53511yescharacteristic
1043C22C31×#53512yes—
1044C22C31×#53812yes—
1045C22D42×C3112yes—
1046C22D42×C3112yes—
1047C22D42×C3112yes—
1048C22D42×C3112yes—
1049C22D42×C3112yes—
1050C22C31×#54612yes—
1051C22C31×#54612yes—
1052C22C31×#54612yes—
1053C22C31×#54612yes—
1054C22C31×#56012yes—
1055C4—24no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—82no—
1062C2—44no—
1063C2—48no—
1064C2—44no—
1065C2—82no—
1066C2C31×#240311yescharacteristic
1067C2C31×#240311yescharacteristic
1068C2C31×#240411yescharacteristic
1069C2C31×#240812yes—
1070C2C31×#241012yes—
1071C2C31×#242412yes—
1072C2C31×#266812yes—
1073C2C31×#266912yes—
1074C2C31×#267812yes—
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#121C2semidirect
2. C22×C31×#120C2semidirect
3. C22×C31×#120C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#379C2semidirect
7. C31×#1440C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×#1438C2semidirect
17. C23×D4×C31C22semidirect
18. C24×C4×C31C22semidirect
26. C22×C4⋊C4×C31C22semidirect
35. C22×C22⋊C4×C31C22semidirect
36. C22×C22⋊C4×C31C22semidirect
37. C22×C22⋊C4×C31C22semidirect
41. C2×C31×#95C22semidirect
42. C2×C31×#95C22semidirect
43. C2×C31×#95C22semidirect
44. C2×C31×#95C22semidirect
84. C22×D4×C31D4semidirect
85. C22×D4×C31D4semidirect
86. C22×D4×C31D4semidirect
133. C2×C22⋊C4×C31D4semidirect
134. C2×C22⋊C4×C31D4semidirect
290. #15257C31direct (N × H)
396. C23×C31#120semidirect
397. C23×C31#121semidirect
453. C2×C4×C31#120semidirect
454. C22×#121C2×C31semidirect
455. C22×#120C2×C31semidirect
456. C22×#120C2×C31semidirect
457. C2×#392C2×C31semidirect
458. C2×#386C2×C31semidirect
459. C2×#379C2×C31semidirect
460. #1440C2×C31semidirect
461. #1439C2×C31semidirect
462. #1438C2×C31semidirect
463. #1438C2×C31semidirect
464. #1438C2×C31semidirect
541. C23×D4C22×C31semidirect
542. C24×C4C22×C31semidirect
550. C22×C4⋊C4C22×C31semidirect
559. C22×C22⋊C4C22×C31semidirect
560. C22×C22⋊C4C22×C31semidirect
561. C22×C22⋊C4C22×C31semidirect
565. C2×#95C22×C31semidirect
566. C2×#95C22×C31semidirect
567. C2×#95C22×C31semidirect
568. C2×#95C22×C31semidirect
621. C22×D4D4×C31semidirect
622. C22×D4D4×C31semidirect
623. C22×D4D4×C31semidirect
670. C2×C22⋊C4D4×C31semidirect
671. C2×C22⋊C4D4×C31semidirect
676. C31#15257direct (N × H)
933. C23C31×#120semidirect
934. C23C31×#121semidirect
990. C2×C4C31×#120semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C22×C31×#1202
C2×C31×#3922
C2×C31×#3862
C2×C31×#3792
C31×#14402
C31×#14392
C31×#14382
#1525731