Finite Group Databasebeta

← C31×#15266 #21472025

Subgroups — C31×#15266 #21472025

Order 7936.

3618 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C2×C31×#394C212yesmaximal, complemented
3C2×C31×#386C211yesmaximal, characteristic, complemented
4C2×C31×#386C212yesmaximal, complemented
5C2×C31×#379C212yesmaximal, complemented
6C31×#1440C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1438C211yesmaximal, characteristic, complemented
10C26×C31C2211yescharacteristic
11C23×D4×C31C2212yes—
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic, complemented
14C2×C31×#120—24no—
15C2×C31×#120—28no—
16C22×C4⋊C4×C31C2212yescomplemented
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic, complemented
26C22×C22⋊C4×C31C2212yescomplemented
27C31×#394—28no—
28C31×#386—24no—
29C31×#386—28no—
30C31×#379—28no—
31C2×C31×#95C2212yescomplemented
32C2×C31×#95C2212yescomplemented
33C2×C31×#95C2212yescomplemented
34C2×C31×#95C2212yescomplemented
35C2×C31×#95C2211yescharacteristic, complemented
36C2×C31×#95C2211yescharacteristic, complemented
37C25×C31—24no—
38C25×C31—22no—
39C25×C31—24no—
40C25×C31—24no—
41C25×C31—24no—
42C25×C31—41no—
43C25×C31—42no—
44C25×C31—42no—
45C25×C31—41no—
46C25×C31C2311yescharacteristic
47C25×C31C2312yes—
48C25×C31C2311yescharacteristic
49C22×D4×C31—24no—
50C22×D4×C31—24no—
51C22×D4×C31—24no—
52C22×D4×C31—24no—
53C22×D4×C31—24no—
54C22×D4×C31—24no—
55C22×D4×C31—41no—
56C22×D4×C31—41no—
57C22×D4×C31—42no—
58C22×D4×C31—42no—
59C22×D4×C31D414yes—
60C22×D4×C31D418yes—
61C23×C4×C31—22no—
62C23×C4×C31—24no—
63C23×C4×C31—41no—
64C23×C4×C31—42no—
65C23×C4×C31—41no—
66C23×C4×C31C2312yes—
67C23×C4×C31C2312yes—
68C23×C4×C31C2312yes—
69C23×C4×C31C2312yes—
70C23×C4×C31C2312yes—
71C23×C4×C31C2311yescharacteristic
72C31×#120—232no—
73C2×C4⋊C4×C31—24no—
74C2×C4⋊C4×C31—42no—
75C2×C4⋊C4×C31—42no—
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—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—22no—
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—24no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—24no—
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—42no—
103C2×C22⋊C4×C31D418yescomplemented
104C31×#95—24no—
105C31×#95—24no—
106C31×#95—24no—
107C31×#95—24no—
108C31×#95—41no—
109C31×#95—41no—
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×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—21no—
130C24×C31—21no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—28no—
137C24×C31—216no—
138C24×C31—44no—
139C24×C31—48no—
140C24×C31—48no—
141C24×C31—48no—
142C24×C31—48no—
143C24×C31—48no—
144C24×C31—48no—
145C24×C31—48no—
146C24×C31—48no—
147C24×C31—44no—
148C24×C31—48no—
149C24×C31—44no—
150C24×C31—48no—
151C24×C31—48no—
152C24×C31—48no—
153C24×C31—44no—
154C24×C31—44no—
155C24×C31—48no—
156C24×C31—44no—
157C24×C31C2×D414yes—
158C24×C31C2×D412yes—
159C24×C31C2×D414yes—
160C24×C31C2×D414yes—
161C24×C31C2×D412yes—
162C24×C31#4114yes—
163C24×C31#4114yes—
164C24×C31C2411yescharacteristic
165C2×D4×C31—28no—
166C2×D4×C31—216no—
167C2×D4×C31—216no—
168C2×D4×C31—28no—
169C2×D4×C31—48no—
170C2×D4×C31—44no—
171C2×D4×C31—48no—
172C2×D4×C31—48no—
173C2×D4×C31—48no—
174C2×D4×C31—48no—
175C2×D4×C31—48no—
176C2×D4×C31—48no—
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—21no—
189C22×C4×C31—21no—
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—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—44no—
214C22×C4×C31—48no—
215C22×C4×C31—48no—
216C22×C4×C31—44no—
217C22×C4×C31—44no—
218C22×C4×C31C2×D412yes—
219C22×C4×C31C2×D414yes—
220C22×C4×C31C2×D414yes—
221C22×C4×C31C2×D414yes—
222C4⋊C4×C31—48no—
223C22⋊C4×C31—216no—
224C22⋊C4×C31—28no—
225C22⋊C4×C31—48no—
226C22⋊C4×C31—48no—
227C22⋊C4×C31—48no—
228C22⋊C4×C31—48no—
229C22⋊C4×C31—48no—
230C22⋊C4×C31—48no—
231C22⋊C4×C31—44no—
232C22⋊C4×C31—48no—
233#15266C3111yesmaximal, characteristic, direct product factor, Sylow
234C23×C31—22no—
235C23×C31—24no—
236C23×C31—24no—
237C23×C31—22no—
238C23×C31—24no—
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—24no—
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—24no—
247C23×C31—24no—
248C23×C31—24no—
249C23×C31—24no—
250C23×C31—24no—
251C23×C31—24no—
252C23×C31—24no—
253C23×C31—24no—
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—24no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—24no—
260C23×C31—24no—
261C23×C31—24no—
262C23×C31—24no—
263C23×C31—24no—
264C23×C31—24no—
265C23×C31—24no—
266C23×C31—24no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—24no—
270C23×C31—24no—
271C23×C31—24no—
272C23×C31—416no—
273C23×C31—432no—
274C23×C31—432no—
275C23×C31—432no—
276C23×C31—432no—
277C23×C31—432no—
278C23×C31—416no—
279C23×C31—432no—
280C23×C31—416no—
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—42no—
295C23×C31—42no—
296C23×C31—42no—
297C23×C31—41no—
298C23×C31—42no—
299C23×C31—42no—
300C23×C31—41no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—42no—
304C23×C31—42no—
305C23×C31—42no—
306C23×C31—42no—
307C23×C31—42no—
308C23×C31—41no—
309C23×C31—42no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—42no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—42no—
316C23×C31—41no—
317C23×C31#12014yes—
318C23×C31#12118yes—
319C23×C31#12314yes—
320C23×C31C22×D412yes—
321C23×C31C22×D411yescharacteristic
322C23×C31C22×D412yes—
323C23×C31C2×#4112yes—
324C23×C31C2×#4112yes—
325C23×C31H(5,𝔽2)11yescharacteristic
326C23×C31H(5,𝔽2)12yes—
327C23×C31H(5,𝔽2)12yes—
328C23×C31H(5,𝔽2)11yescharacteristic
329D4×C31—416no—
330D4×C31—432no—
331C2×C4×C31—22no—
332C2×C4×C31—24no—
333C2×C4×C31—24no—
334C2×C4×C31—22no—
335C2×C4×C31—24no—
336C2×C4×C31—24no—
337C2×C4×C31—24no—
338C2×C4×C31—22no—
339C2×C4×C31—24no—
340C2×C4×C31—24no—
341C2×C4×C31—24no—
342C2×C4×C31—24no—
343C2×C4×C31—416no—
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—42no—
355C2×C4×C31—42no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—42no—
359C2×C4×C31—42no—
360C2×C4×C31—42no—
361C2×C4×C31—42no—
362C2×C4×C31—42no—
363C2×C4×C31—42no—
364C2×C4×C31—42no—
365C2×C4×C31—42no—
366C2×C4×C31—42no—
367C2×C4×C31—42no—
368C2×C4×C31—42no—
369C2×C4×C31—42no—
370C2×C4×C31—42no—
371C2×C4×C31—42no—
372C22×#120C2×C3111yescharacteristic
373C2×#394C2×C3112yescomplemented
374C2×#386C2×C3111yescharacteristic, complemented
375C2×#386C2×C3112yescomplemented
376C2×#379C2×C3112yescomplemented
377#1440C2×C3112yescomplemented
378#1439C2×C3112yescomplemented
379#1439C2×C3112yescomplemented
380#1438C2×C3111yescharacteristic, complemented
381C22×C31—24no—
382C22×C31—24no—
383C22×C31—28no—
384C22×C31—28no—
385C22×C31—28no—
386C22×C31—28no—
387C22×C31—28no—
388C22×C31—464no—
389C22×C31—44no—
390C22×C31—44no—
391C22×C31—44no—
392C22×C31—44no—
393C22×C31—44no—
394C22×C31—44no—
395C22×C31—44no—
396C22×C31—44no—
397C22×C31—44no—
398C22×C31—44no—
399C22×C31—42no—
400C22×C31—44no—
401C22×C31—42no—
402C22×C31—44no—
403C22×C31—44no—
404C22×C31—44no—
405C22×C31—44no—
406C22×C31—44no—
407C22×C31—44no—
408C22×C31—44no—
409C22×C31—42no—
410C22×C31—42no—
411C22×C31—44no—
412C22×C31—44no—
413C22×C31—44no—
414C22×C31—44no—
415C22×C31C2×#12011yescharacteristic
416C22×C31C2×#12112yes—
417C22×C31C2×#12311yescharacteristic
418C22×C31#52512yes—
419C22×C31#53411yescharacteristic
420C22×C31#53412yes—
421C22×C31#53412yes—
422C22×C31#53812yes—
423C22×C31#53812yes—
424C22×C31D4212yes—
425C22×C31D4212yes—
426C22×C31D4211yescharacteristic
427C22×C31#54612yes—
428C22×C31#54612yes—
429C22×C31#54612yes—
430C22×C31#54612yes—
431C22×C31#54612yes—
432C22×C31#55112yes—
433C22×C31#55111yescharacteristic
434C22×C31#56011yescharacteristic
435C22×C31H(3,𝔽4)11yescharacteristic
436C4×C31—42no—
437C4×C31—44no—
438C4×C31—44no—
439C4×C31—44no—
440C4×C31—82no—
441C4×C31—82no—
442C26C22×C3111yescharacteristic
443C23×D4C22×C3112yes—
444C23×D4C22×C3111yescharacteristic
445C24×C4C22×C3111yescharacteristic, complemented
446C2×#120—24no—
447C2×#120—28no—
448C22×C4⋊C4C22×C3112yescomplemented
449C22×C22⋊C4C22×C3112yes—
450C22×C22⋊C4C22×C3111yescharacteristic
451C22×C22⋊C4C22×C3112yes—
452C22×C22⋊C4C22×C3112yes—
453C22×C22⋊C4C22×C3112yes—
454C22×C22⋊C4C22×C3112yes—
455C22×C22⋊C4C22×C3112yes—
456C22×C22⋊C4C22×C3112yes—
457C22×C22⋊C4C22×C3111yescharacteristic, complemented
458C22×C22⋊C4C22×C3112yescomplemented
459#394—28no—
460#386—24no—
461#386—28no—
462#379—28no—
463C2×#95C22×C3112yescomplemented
464C2×#95C22×C3112yescomplemented
465C2×#95C22×C3112yescomplemented
466C2×#95C22×C3112yescomplemented
467C2×#95C22×C3111yescharacteristic, complemented
468C2×#95C22×C3111yescharacteristic, complemented
469C2×C31—44no—
470C2×C31—44no—
471C2×C31—48no—
472C2×C31#240511yescharacteristic
473C2×C31#241012yes—
474C2×C31#241812yes—
475C2×C31#242412yes—
476C2×C31#253412yes—
477C2×C31#266812yes—
478C2×C31#267911yescharacteristic
479C2×C31#268412yes—
480C2×C31#269711yescharacteristic
481C25—24no—
482C25—22no—
483C25—24no—
484C25—24no—
485C25—24no—
486C25—41no—
487C25—42no—
488C25—42no—
489C25—41no—
490C25C23×C3111yescharacteristic
491C25C23×C3112yes—
492C25C23×C3111yescharacteristic
493C22×D4—24no—
494C22×D4—24no—
495C22×D4—24no—
496C22×D4—24no—
497C22×D4—24no—
498C22×D4—24no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—42no—
502C22×D4—42no—
503C22×D4D4×C3114yes—
504C22×D4D4×C3118yes—
505C23×C4—22no—
506C23×C4—24no—
507C23×C4—41no—
508C23×C4—42no—
509C23×C4—41no—
510C23×C4C23×C3112yes—
511C23×C4C23×C3112yes—
512C23×C4C23×C3112yes—
513C23×C4C23×C3112yes—
514C23×C4C23×C3112yes—
515C23×C4C23×C3111yescharacteristic
516#120—232no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—42no—
519C2×C4⋊C4—42no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4D4×C3118yescomplemented
548#95—24no—
549#95—24no—
550#95—24no—
551#95—24no—
552#95—41no—
553#95—41no—
554C31#1526611yescharacteristic, direct product factor, Sylow
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—21no—
575C24—21no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—21no—
580C24—21no—
581C24—28no—
582C24—216no—
583C24—44no—
584C24—48no—
585C24—48no—
586C24—48no—
587C24—48no—
588C24—48no—
589C24—48no—
590C24—48no—
591C24—48no—
592C24—44no—
593C24—48no—
594C24—44no—
595C24—48no—
596C24—48no—
597C24—48no—
598C24—44no—
599C24—44no—
600C24—48no—
601C24—44no—
602C24C2×D4×C3114yes—
603C24C2×D4×C3112yes—
604C24C2×D4×C3114yes—
605C24C2×D4×C3114yes—
606C24C2×D4×C3112yes—
607C24#41×C3114yes—
608C24#41×C3114yes—
609C24C24×C3111yescharacteristic
610C2×D4—28no—
611C2×D4—216no—
612C2×D4—216no—
613C2×D4—28no—
614C2×D4—48no—
615C2×D4—44no—
616C2×D4—48no—
617C2×D4—48no—
618C2×D4—48no—
619C2×D4—48no—
620C2×D4—48no—
621C2×D4—48no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—44no—
659C22×C4—48no—
660C22×C4—48no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4C2×D4×C3112yes—
664C22×C4C2×D4×C3114yes—
665C22×C4C2×D4×C3114yes—
666C22×C4C2×D4×C3114yes—
667C4⋊C4—48no—
668C22⋊C4—216no—
669C22⋊C4—28no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—44no—
677C22⋊C4—48no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—416no—
717C23—432no—
718C23—432no—
719C23—432no—
720C23—432no—
721C23—432no—
722C23—416no—
723C23—432no—
724C23—416no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—41no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—41no—
753C23—42no—
754C23—41no—
755C23—41no—
756C23—42no—
757C23—41no—
758C23—41no—
759C23—42no—
760C23—41no—
761C23C31×#12014yes—
762C23C31×#12118yes—
763C23C31×#12314yes—
764C23C22×D4×C3112yes—
765C23C22×D4×C3111yescharacteristic
766C23C22×D4×C3112yes—
767C23C2×#41×C3112yes—
768C23C2×#41×C3112yes—
769C23C31×H(5,𝔽2)11yescharacteristic
770C23C31×H(5,𝔽2)12yes—
771C23C31×H(5,𝔽2)12yes—
772C23C31×H(5,𝔽2)11yescharacteristic
773D4—416no—
774D4—432no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—416no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C22—24no—
817C22—24no—
818C22—28no—
819C22—28no—
820C22—28no—
821C22—28no—
822C22—28no—
823C22—464no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—42no—
835C22—44no—
836C22—42no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—42no—
845C22—44no—
846C22—42no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22C2×C31×#12011yescharacteristic
851C22C2×C31×#12112yes—
852C22C2×C31×#12311yescharacteristic
853C22C31×#52512yes—
854C22C31×#53411yescharacteristic
855C22C31×#53412yes—
856C22C31×#53412yes—
857C22C31×#53812yes—
858C22C31×#53812yes—
859C22D42×C3112yes—
860C22D42×C3112yes—
861C22D42×C3111yescharacteristic
862C22C31×#54612yes—
863C22C31×#54612yes—
864C22C31×#54612yes—
865C22C31×#54612yes—
866C22C31×#54612yes—
867C22C31×#55112yes—
868C22C31×#55111yescharacteristic
869C22C31×#56011yescharacteristic
870C22C31×H(3,𝔽4)11yescharacteristic
871C4—42no—
872C4—44no—
873C4—44no—
874C4—44no—
875C4—82no—
876C4—82no—
877C2—44no—
878C2—48no—
879C2—44no—
880C2C31×#240511yescharacteristic
881C2C31×#241012yes—
882C2C31×#241812yes—
883C2C31×#242412yes—
884C2C31×#253412yes—
885C2C31×#266812yes—
886C2C31×#267911yescharacteristic
887C2C31×#268412yes—
888C2C31×#269711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#120C2
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×#386C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#379C2semidirect
6. C31×#1440C2semidirect
7. C31×#1439C2semidirect
8. C31×#1439C2semidirect
9. C31×#1438C2semidirect
13. C24×C4×C31C22semidirect
16. C22×C4⋊C4×C31C22semidirect
25. C22×C22⋊C4×C31C22semidirect
26. C22×C22⋊C4×C31C22semidirect
31. C2×C31×#95C22semidirect
32. C2×C31×#95C22semidirect
33. C2×C31×#95C22semidirect
34. C2×C31×#95C22semidirect
35. C2×C31×#95C22semidirect
36. C2×C31×#95C22semidirect
103. C2×C22⋊C4×C31D4semidirect
233. #15266C31direct (N × H)
373. C2×#394C2×C31semidirect
374. C2×#386C2×C31semidirect
375. C2×#386C2×C31semidirect
376. C2×#379C2×C31semidirect
377. #1440C2×C31semidirect
378. #1439C2×C31semidirect
379. #1439C2×C31semidirect
380. #1438C2×C31semidirect
445. C24×C4C22×C31semidirect
448. C22×C4⋊C4C22×C31semidirect
457. C22×C22⋊C4C22×C31semidirect
458. C22×C22⋊C4C22×C31semidirect
463. C2×#95C22×C31semidirect
464. C2×#95C22×C31semidirect
465. C2×#95C22×C31semidirect
466. C2×#95C22×C31semidirect
467. C2×#95C22×C31semidirect
468. C2×#95C22×C31semidirect
547. C2×C22⋊C4D4×C31semidirect
554. C31#15266direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C2×C31×#3942
C2×C31×#3862
C2×C31×#3792
C31×#14402
C31×#14392
C31×#14382
#1526631