Finite Group Databasebeta

← C31×#15281 #21472040

Subgroups — C31×#15281 #21472040

Order 7936.

3510 conjugacy classes of subgroups.

The subgroup lattice has 884 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×#390C211yesmaximal, characteristic, complemented
4C2×C31×#388C212yesmaximal, complemented
5C2×C31×#379C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C211yesmaximal, characteristic, complemented
9C31×#1438C212yesmaximal, complemented
10C26×C31C2211yescharacteristic
11C23×D4×C31C2212yes—
12C23×D4×C31C2211yescharacteristic
13C2×C31×#120—24no—
14C2×C31×#120—28no—
15C22×C4⋊C4×C31C2212yescomplemented
16C22×C4⋊C4×C31C2211yescharacteristic, complemented
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C22⋊C4×C31C2212yes—
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
27C22×C22⋊C4×C31C2211yescharacteristic, complemented
28C22×C42×C31C2211yescharacteristic, complemented
29C31×#394—28no—
30C31×#390—24no—
31C31×#388—28no—
32C31×#379—28no—
33C2×C31×#95C2212yescomplemented
34C2×C31×#95C2212yescomplemented
35C2×C31×#95C2212yescomplemented
36C2×C31×#95C2212yescomplemented
37C25×C31—24no—
38C25×C31—22no—
39C25×C31—24no—
40C25×C31—24no—
41C25×C31—24no—
42C25×C31—41no—
43C25×C31—42no—
44C25×C31—41no—
45C25×C31—42no—
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—24no—
56C22×D4×C31—41no—
57C22×D4×C31—41no—
58C22×D4×C31—42no—
59C22×D4×C31—42no—
60C22×D4×C31D414yes—
61C23×C4×C31C2312yes—
62C23×C4×C31C2312yes—
63C23×C4×C31C2312yes—
64C23×C4×C31C2312yes—
65C23×C4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C31×#120—232no—
68C2×C4⋊C4×C31—24no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—24no—
71C2×C4⋊C4×C31—42no—
72C2×C4⋊C4×C31—41no—
73C2×C4⋊C4×C31—41no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—24no—
77C2×C22⋊C4×C31—24no—
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—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—42no—
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—41no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—41no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31D418yes—
103C2×C22⋊C4×C31D418yescomplemented
104C2×C42×C31—24no—
105C2×C42×C31—22no—
106C31×#95—24no—
107C31×#95—24no—
108C31×#95—24no—
109C31×#95—42no—
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—21no—
126C24×C31—21no—
127C24×C31—22no—
128C24×C31—22no—
129C24×C31—28no—
130C24×C31—216no—
131C24×C31—22no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31—22no—
135C24×C31—21no—
136C24×C31—21no—
137C24×C31—22no—
138C24×C31—22no—
139C24×C31—44no—
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—48no—
154C24×C31—44no—
155C24×C31—44no—
156C24×C31—48no—
157C24×C31—44no—
158C24×C31C2×D412yes—
159C24×C31C2×D414yes—
160C24×C31C2×D414yes—
161C24×C31C2×D412yes—
162C24×C31#4114yes—
163C24×C31#4114yes—
164C24×C31C2411yescharacteristic
165C2×D4×C31—216no—
166C2×D4×C31—28no—
167C2×D4×C31—28no—
168C2×D4×C31—44no—
169C2×D4×C31—48no—
170C2×D4×C31—48no—
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—21no—
179C22×C4×C31—21no—
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—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×C31C2×D414yes—
213C22×C4×C31C2×D414yes—
214C22×C4×C31C2×D414yes—
215C22×C4×C31C2×D414yes—
216C22×C4×C31C2×D412yes—
217C4⋊C4×C31—48no—
218C4⋊C4×C31—44no—
219C22⋊C4×C31—28no—
220C22⋊C4×C31—216no—
221C22⋊C4×C31—216no—
222C22⋊C4×C31—44no—
223C22⋊C4×C31—48no—
224C22⋊C4×C31—48no—
225C22⋊C4×C31—48no—
226C22⋊C4×C31—48no—
227C22⋊C4×C31—48no—
228C22⋊C4×C31—48no—
229C22⋊C4×C31—44no—
230C42×C31—44no—
231#15281C3111yesmaximal, characteristic, direct product factor, Sylow
232C23×C31—22no—
233C23×C31—24no—
234C23×C31—24no—
235C23×C31—24no—
236C23×C31—24no—
237C23×C31—22no—
238C23×C31—24no—
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—24no—
242C23×C31—24no—
243C23×C31—24no—
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—22no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—24no—
264C23×C31—24no—
265C23×C31—416no—
266C23×C31—432no—
267C23×C31—432no—
268C23×C31—432no—
269C23×C31—432no—
270C23×C31—416no—
271C23×C31—432no—
272C23×C31—416no—
273C23×C31—432no—
274C23×C31—42no—
275C23×C31—42no—
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—41no—
289C23×C31—42no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—41no—
295C23×C31—42no—
296C23×C31—41no—
297C23×C31—42no—
298C23×C31—42no—
299C23×C31—41no—
300C23×C31—42no—
301C23×C31—42no—
302C23×C31—42no—
303C23×C31—42no—
304C23×C31—42no—
305C23×C31—42no—
306C23×C31—41no—
307C23×C31—42no—
308C23×C31—42no—
309C23×C31—42no—
310C23×C31—42no—
311C23×C31—42no—
312C23×C31—42no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31#12118yes—
317C23×C31#12314yes—
318C23×C31C22×D412yes—
319C23×C31C22×D411yescharacteristic
320C23×C31C22×D412yes—
321C23×C31C2×#4112yes—
322C23×C31C2×#4112yes—
323C23×C31H(5,𝔽2)11yescharacteristic
324C23×C31H(5,𝔽2)11yescharacteristic
325C23×C31H(5,𝔽2)12yes—
326C23×C31H(5,𝔽2)12yes—
327D4×C31—416no—
328D4×C31—432no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—24no—
332C2×C4×C31—24no—
333C2×C4×C31—24no—
334C2×C4×C31—24no—
335C2×C4×C31—24no—
336C2×C4×C31—24no—
337C2×C4×C31—24no—
338C2×C4×C31—24no—
339C2×C4×C31—24no—
340C2×C4×C31—24no—
341C2×C4×C31—24no—
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—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#12014yes—
369C22×#120C2×C3111yescharacteristic
370C2×#394C2×C3112yescomplemented
371C2×#390C2×C3111yescharacteristic, complemented
372C2×#388C2×C3112yescomplemented
373C2×#379C2×C3112yescomplemented
374#1439C2×C3112yescomplemented
375#1439C2×C3112yescomplemented
376#1438C2×C3111yescharacteristic, complemented
377#1438C2×C3112yescomplemented
378C22×C31—24no—
379C22×C31—28no—
380C22×C31—28no—
381C22×C31—28no—
382C22×C31—28no—
383C22×C31—464no—
384C22×C31—44no—
385C22×C31—44no—
386C22×C31—44no—
387C22×C31—44no—
388C22×C31—44no—
389C22×C31—42no—
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—42no—
399C22×C31—44no—
400C22×C31—44no—
401C22×C31—44no—
402C22×C31—44no—
403C22×C31—42no—
404C22×C31—44no—
405C22×C31—42no—
406C22×C31—44no—
407C22×C31—42no—
408C22×C31—82no—
409C22×C31—82no—
410C22×C31—82no—
411C22×C31—82no—
412C22×C31C2×#12011yescharacteristic
413C22×C31C2×#12112yes—
414C22×C31C2×#12311yescharacteristic
415C22×C31#52512yes—
416C22×C31#53411yescharacteristic
417C22×C31#53512yes—
418C22×C31#53512yes—
419C22×C31#53812yes—
420C22×C31#53812yes—
421C22×C31D4212yes—
422C22×C31D4212yes—
423C22×C31D4211yescharacteristic
424C22×C31#54612yes—
425C22×C31#54612yes—
426C22×C31#54612yes—
427C22×C31#54612yes—
428C22×C31#54612yes—
429C22×C31#55111yescharacteristic
430C22×C31#55112yes—
431C22×C31#56011yescharacteristic
432C22×C31H(3,𝔽4)11yescharacteristic
433C4×C31—24no—
434C4×C31—44no—
435C4×C31—44no—
436C4×C31—44no—
437C4×C31—82no—
438C4×C31—82no—
439C26C22×C3111yescharacteristic
440C23×D4C22×C3112yes—
441C23×D4C22×C3111yescharacteristic
442C2×#120—24no—
443C2×#120—28no—
444C22×C4⋊C4C22×C3112yescomplemented
445C22×C4⋊C4C22×C3111yescharacteristic, complemented
446C22×C22⋊C4C22×C3111yescharacteristic
447C22×C22⋊C4C22×C3112yes—
448C22×C22⋊C4C22×C3112yes—
449C22×C22⋊C4C22×C3112yes—
450C22×C22⋊C4C22×C3112yes—
451C22×C22⋊C4C22×C3112yes—
452C22×C22⋊C4C22×C3112yes—
453C22×C22⋊C4C22×C3112yes—
454C22×C22⋊C4C22×C3111yescharacteristic, complemented
455C22×C22⋊C4C22×C3112yescomplemented
456C22×C22⋊C4C22×C3111yescharacteristic, complemented
457C22×C42C22×C3111yescharacteristic, complemented
458#394—28no—
459#390—24no—
460#388—28no—
461#379—28no—
462C2×#95C22×C3112yescomplemented
463C2×#95C22×C3112yescomplemented
464C2×#95C22×C3112yescomplemented
465C2×#95C22×C3112yescomplemented
466C2×C31—44no—
467C2×C31—48no—
468C2×C31—82no—
469C2×C31#240511yescharacteristic
470C2×C31#240812yes—
471C2×C31#241112yes—
472C2×C31#241812yes—
473C2×C31#242412yes—
474C2×C31#266911yescharacteristic
475C2×C31#267012yes—
476C2×C31#268411yescharacteristic
477C2×C31#268512yes—
478C25—24no—
479C25—22no—
480C25—24no—
481C25—24no—
482C25—24no—
483C25—41no—
484C25—42no—
485C25—41no—
486C25—42no—
487C25C23×C3111yescharacteristic
488C25C23×C3112yes—
489C25C23×C3111yescharacteristic
490C22×D4—24no—
491C22×D4—24no—
492C22×D4—24no—
493C22×D4—24no—
494C22×D4—24no—
495C22×D4—24no—
496C22×D4—24no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—42no—
500C22×D4—42no—
501C22×D4D4×C3114yes—
502C23×C4C23×C3112yes—
503C23×C4C23×C3112yes—
504C23×C4C23×C3112yes—
505C23×C4C23×C3112yes—
506C23×C4C23×C3112yes—
507C23×C4C23×C3111yescharacteristic
508#120—232no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—42no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
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—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4D4×C3118yes—
544C2×C22⋊C4D4×C3118yescomplemented
545C2×C42—24no—
546C2×C42—22no—
547#95—24no—
548#95—24no—
549#95—24no—
550#95—42no—
551C31#1528111yescharacteristic, direct product factor, Sylow
552C24—22no—
553C24—22no—
554C24—22no—
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—21no—
568C24—21no—
569C24—22no—
570C24—22no—
571C24—28no—
572C24—216no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—21no—
578C24—21no—
579C24—22no—
580C24—22no—
581C24—44no—
582C24—48no—
583C24—48no—
584C24—48no—
585C24—48no—
586C24—48no—
587C24—48no—
588C24—48no—
589C24—44no—
590C24—48no—
591C24—44no—
592C24—48no—
593C24—48no—
594C24—48no—
595C24—48no—
596C24—44no—
597C24—44no—
598C24—48no—
599C24—44no—
600C24C2×D4×C3112yes—
601C24C2×D4×C3114yes—
602C24C2×D4×C3114yes—
603C24C2×D4×C3112yes—
604C24#41×C3114yes—
605C24#41×C3114yes—
606C24C24×C3111yescharacteristic
607C2×D4—216no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—44no—
611C2×D4—48no—
612C2×D4—48no—
613C2×D4—48no—
614C2×D4—48no—
615C2×D4—48no—
616C2×D4—48no—
617C2×D4—48no—
618C2×D4—48no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
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—22no—
634C22×C4—22no—
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×C4C2×D4×C3114yes—
655C22×C4C2×D4×C3114yes—
656C22×C4C2×D4×C3114yes—
657C22×C4C2×D4×C3114yes—
658C22×C4C2×D4×C3112yes—
659C4⋊C4—48no—
660C4⋊C4—44no—
661C22⋊C4—28no—
662C22⋊C4—216no—
663C22⋊C4—216no—
664C22⋊C4—44no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—44no—
672C42—44no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
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—22no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—24no—
706C23—416no—
707C23—432no—
708C23—432no—
709C23—432no—
710C23—432no—
711C23—416no—
712C23—432no—
713C23—416no—
714C23—432no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—41no—
736C23—42no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—41no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—41no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23C31×#12118yes—
758C23C31×#12314yes—
759C23C22×D4×C3112yes—
760C23C22×D4×C3111yescharacteristic
761C23C22×D4×C3112yes—
762C23C2×#41×C3112yes—
763C23C2×#41×C3112yes—
764C23C31×H(5,𝔽2)11yescharacteristic
765C23C31×H(5,𝔽2)11yescharacteristic
766C23C31×H(5,𝔽2)12yes—
767C23C31×H(5,𝔽2)12yes—
768D4—416no—
769D4—432no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
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×C4C31×#12014yes—
810C22—24no—
811C22—28no—
812C22—28no—
813C22—28no—
814C22—28no—
815C22—464no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—42no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—42no—
836C22—44no—
837C22—42no—
838C22—44no—
839C22—42no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22C2×C31×#12011yescharacteristic
845C22C2×C31×#12112yes—
846C22C2×C31×#12311yescharacteristic
847C22C31×#52512yes—
848C22C31×#53411yescharacteristic
849C22C31×#53512yes—
850C22C31×#53512yes—
851C22C31×#53812yes—
852C22C31×#53812yes—
853C22D42×C3112yes—
854C22D42×C3112yes—
855C22D42×C3111yescharacteristic
856C22C31×#54612yes—
857C22C31×#54612yes—
858C22C31×#54612yes—
859C22C31×#54612yes—
860C22C31×#54612yes—
861C22C31×#55111yescharacteristic
862C22C31×#55112yes—
863C22C31×#56011yescharacteristic
864C22C31×H(3,𝔽4)11yescharacteristic
865C4—24no—
866C4—44no—
867C4—44no—
868C4—44no—
869C4—82no—
870C4—82no—
871C2—44no—
872C2—48no—
873C2—82no—
874C2C31×#240511yescharacteristic
875C2C31×#240812yes—
876C2C31×#241112yes—
877C2C31×#241812yes—
878C2C31×#242412yes—
879C2C31×#266911yescharacteristic
880C2C31×#267012yes—
881C2C31×#268411yescharacteristic
882C2C31×#268512yes—
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×#390C2semidirect
4. C2×C31×#388C2semidirect
5. C2×C31×#379C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
15. C22×C4⋊C4×C31C22semidirect
16. C22×C4⋊C4×C31C22semidirect
25. C22×C22⋊C4×C31C22semidirect
26. C22×C22⋊C4×C31C22semidirect
27. C22×C22⋊C4×C31C22semidirect
28. C22×C42×C31C22semidirect
33. C2×C31×#95C22semidirect
34. C2×C31×#95C22semidirect
35. C2×C31×#95C22semidirect
36. C2×C31×#95C22semidirect
103. C2×C22⋊C4×C31D4semidirect
231. #15281C31direct (N × H)
370. C2×#394C2×C31semidirect
371. C2×#390C2×C31semidirect
372. C2×#388C2×C31semidirect
373. C2×#379C2×C31semidirect
374. #1439C2×C31semidirect
375. #1439C2×C31semidirect
376. #1438C2×C31semidirect
377. #1438C2×C31semidirect
444. C22×C4⋊C4C22×C31semidirect
445. C22×C4⋊C4C22×C31semidirect
454. C22×C22⋊C4C22×C31semidirect
455. C22×C22⋊C4C22×C31semidirect
456. C22×C22⋊C4C22×C31semidirect
457. C22×C42C22×C31semidirect
462. C2×#95C22×C31semidirect
463. C2×#95C22×C31semidirect
464. C2×#95C22×C31semidirect
465. C2×#95C22×C31semidirect
544. C2×C22⋊C4D4×C31semidirect
551. C31#15281direct (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×#3902
C2×C31×#3882
C2×C31×#3792
C31×#14392
C31×#14382
#1528131