Finite Group Databasebeta

← C31×#16680 #21473439

Subgroups — C31×#16680 #21473439

Order 7936.

2182 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic, complemented
2C2×C31×#393C211yesmaximal, characteristic, complemented
3C2×C31×#392C211yesmaximal, characteristic
4C2×C31×#388C211yesmaximal, characteristic, complemented
5C31×#1446C211yesmaximal, characteristic, complemented
6C31×#1440C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C212yesmaximal, complemented
9C31×#1438C212yesmaximal, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×#1434C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic
13C23×D4×C31C2212yes—
14C23×D4×C31C2211yescharacteristic
15C2×C31×#124—24no—
16C2×C31×#124—24no—
17C2×C31×#124—24no—
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2212yes—
28C22×C42×C31C2211yescharacteristic
29C31×#393—24no—
30C31×#392—24no—
31C31×#388—24no—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C25×C31C2312yes—
42C25×C31C2311yescharacteristic
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—42no—
46C22×Q8×C31—42no—
47C22×Q8×C31D414yescomplemented
48C22×D4×C31—24no—
49C22×D4×C31—24no—
50C22×D4×C31—22no—
51C22×D4×C31—22no—
52C22×D4×C31—24no—
53C22×D4×C31—42no—
54C22×D4×C31—42no—
55C22×D4×C31—42no—
56C22×D4×C31—42no—
57C22×D4×C31—42no—
58C22×D4×C31—42no—
59C22×D4×C31D414yes—
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2312yes—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2312yes—
68C23×C4×C31C2311yescharacteristic
69C31×#124—232no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—42no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—24no—
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—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—42no—
90C2×C22⋊C4×C31—42no—
91C2×C22⋊C4×C31—42no—
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×C42×C31—22no—
99C2×C42×C31—22no—
100C2×C42×C31D414yescomplemented
101C31×#95—22no—
102C31×#95—22no—
103C31×#95—22no—
104C31×#95—24no—
105C31×#95—22no—
106C31×#95—24no—
107C31×#95—42no—
108C31×#95—42no—
109C31×#95—42no—
110C24×C31—21no—
111C24×C31—21no—
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—22no—
133C24×C31—21no—
134C24×C31C2×D414yes—
135C24×C31#4112yes—
136C24×C31C2411yescharacteristic
137C2×Q8×C31—28no—
138C2×Q8×C31—48no—
139C2×Q8×C31—48no—
140C2×Q8×C31—44no—
141C2×Q8×C31—44no—
142C2×D4×C31—28no—
143C2×D4×C31—48no—
144C2×D4×C31—48no—
145C2×D4×C31—48no—
146C2×D4×C31—48no—
147C2×D4×C31—44no—
148C2×D4×C31—44no—
149C2×D4×C31—48no—
150C2×D4×C31—48no—
151C2×D4×C31—48no—
152C2×D4×C31—48no—
153C2×D4×C31—48no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—21no—
157C22×C4×C31—22no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—22no—
169C22×C4×C31—21no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
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—21no—
182C22×C4×C31—21no—
183C22×C4×C31—22no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
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—21no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—21no—
199C22×C4×C31C2×D412yes—
200C22×C4×C31C2×D414yes—
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×D412yes—
203C22×C4×C31C2×D412yes—
204C22×C4×C31C2×D412yes—
205C22×C4×C31#4114yes—
206C22×C4×C31#4112yes—
207C4⋊C4×C31—44no—
208C22⋊C4×C31—28no—
209C22⋊C4×C31—216no—
210C22⋊C4×C31—216no—
211C22⋊C4×C31—48no—
212C22⋊C4×C31—48no—
213C22⋊C4×C31—44no—
214C22⋊C4×C31—48no—
215C22⋊C4×C31—48no—
216C22⋊C4×C31—44no—
217C42×C31—28no—
218#16680C3111yesmaximal, characteristic, direct product factor, Sylow
219C23×C31—24no—
220C23×C31—22no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—22no—
226C23×C31—24no—
227C23×C31—24no—
228C23×C31—24no—
229C23×C31—22no—
230C23×C31—24no—
231C23×C31—41no—
232C23×C31—42no—
233C23×C31—41no—
234C23×C31—42no—
235C23×C31—42no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—41no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—42no—
245C23×C31—41no—
246C23×C31—42no—
247C23×C31—42no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—41no—
260C23×C31—42no—
261C23×C31—41no—
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—42no—
276C23×C31—42no—
277C23×C31C22×D411yescharacteristic
278C23×C31C22×D411yescharacteristic
279C23×C31C22×D411yescharacteristic
280C23×C31C2×#4111yescharacteristic
281C23×C31C2×#4111yescharacteristic
282C23×C31C2×#4112yes—
283C23×C31H(5,𝔽2)12yes—
284C23×C31H(5,𝔽2)12yes—
285C23×C31H(5,𝔽2)12yes—
286C23×C31H(5,𝔽2)11yescharacteristic
287C23×C312−1+411yescharacteristic
288Q8×C31—416no—
289D4×C31—416no—
290D4×C31—432no—
291C2×C4×C31—24no—
292C2×C4×C31—24no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—24no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—24no—
302C2×C4×C31—24no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—24no—
306C2×C4×C31—24no—
307C2×C4×C31—24no—
308C2×C4×C31—24no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—41no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—42no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
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#12014yes—
344C22×#124C2×C3111yescharacteristic, complemented
345C2×#393C2×C3111yescharacteristic, complemented
346C2×#392C2×C3111yescharacteristic
347C2×#388C2×C3111yescharacteristic, complemented
348#1446C2×C3111yescharacteristic, complemented
349#1440C2×C3112yescomplemented
350#1439C2×C3112yescomplemented
351#1438C2×C3112yescomplemented
352#1438C2×C3112yescomplemented
353#1438C2×C3111yescharacteristic, complemented
354#1434C2×C3111yescharacteristic, complemented
355C22×C31—42no—
356C22×C31—44no—
357C22×C31—42no—
358C22×C31—44no—
359C22×C31—42no—
360C22×C31—44no—
361C22×C31—44no—
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—44no—
365C22×C31—44no—
366C22×C31—44no—
367C22×C31—81no—
368C22×C31—82no—
369C22×C31—82no—
370C22×C31—81no—
371C22×C31—82no—
372C22×C31—82no—
373C22×C31—81no—
374C22×C31—82no—
375C22×C31—81no—
376C22×C31—82no—
377C22×C31—82no—
378C22×C31—82no—
379C22×C31—82no—
380C22×C31—82no—
381C22×C31C2×#12011yescharacteristic
382C22×C31#52511yescharacteristic
383C22×C31#53211yescharacteristic
384C22×C31#53412yes—
385C22×C31#53412yes—
386C22×C31#53511yescharacteristic
387C22×C31#53511yescharacteristic
388C22×C31#53511yescharacteristic
389C22×C31#53711yescharacteristic
390C22×C31#53812yes—
391C22×C31#53812yes—
392C22×C31#53812yes—
393C22×C31#54212yes—
394C22×C31#54611yescharacteristic
395C22×C31#54612yes—
396C22×C31#54711yescharacteristic
397C22×C31#54811yescharacteristic
398C22×C31#55011yescharacteristic
399C22×C31#55012yes—
400C22×C31#55112yes—
401C22×C31#55512yes—
402C22×C31H(3,𝔽4)12yes—
403C22×C31#56212yes—
404C4×C31—24no—
405C4×C31—44no—
406C4×C31—42no—
407C4×C31—42no—
408C4×C31—44no—
409C4×C31—42no—
410C4×C31—81no—
411C4×C31—81no—
412C4×C31—82no—
413C23×Q8C22×C3111yescharacteristic
414C23×D4C22×C3112yes—
415C23×D4C22×C3111yescharacteristic
416C2×#124—24no—
417C2×#124—24no—
418C2×#124—24no—
419C22×C4⋊C4C22×C3111yescharacteristic
420C22×C22⋊C4C22×C3111yescharacteristic
421C22×C22⋊C4C22×C3112yes—
422C22×C22⋊C4C22×C3112yes—
423C22×C22⋊C4C22×C3111yescharacteristic
424C22×C22⋊C4C22×C3112yes—
425C22×C22⋊C4C22×C3112yes—
426C22×C22⋊C4C22×C3112yes—
427C22×C22⋊C4C22×C3111yescharacteristic
428C22×C22⋊C4C22×C3112yes—
429C22×C42C22×C3111yescharacteristic
430#393—24no—
431#392—24no—
432#388—24no—
433C2×#95C22×C3111yescharacteristic
434C2×#95C22×C3111yescharacteristic
435C2×#95C22×C3112yes—
436C2×#95C22×C3112yes—
437C2×#95C22×C3111yescharacteristic
438C2×#95C22×C3111yescharacteristic
439C2×#95C22×C3112yes—
440C2×#95C22×C3112yes—
441C2×#95C22×C3112yes—
442C2×C31—82no—
443C2×C31—84no—
444C2×C31#240711yescharacteristic
445C2×C31#243111yescharacteristic
446C2×C31#261011yescharacteristic
447C2×C31#261311yescharacteristic
448C2×C31#263111yescharacteristic
449C2×C31#266211yescharacteristic
450C2×C31#268412yes—
451C2×C31#268612yes—
452C2×C31#273012yes—
453C2×C31#273312yes—
454C2×C31#281911yescharacteristic
455C25C23×C3112yes—
456C25C23×C3111yescharacteristic
457C22×Q8—22no—
458C22×Q8—22no—
459C22×Q8—42no—
460C22×Q8—42no—
461C22×Q8D4×C3114yescomplemented
462C22×D4—24no—
463C22×D4—24no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—24no—
467C22×D4—42no—
468C22×D4—42no—
469C22×D4—42no—
470C22×D4—42no—
471C22×D4—42no—
472C22×D4—42no—
473C22×D4D4×C3114yes—
474C23×C4C23×C3111yescharacteristic
475C23×C4C23×C3112yes—
476C23×C4C23×C3111yescharacteristic
477C23×C4C23×C3111yescharacteristic
478C23×C4C23×C3112yes—
479C23×C4C23×C3111yescharacteristic
480C23×C4C23×C3111yescharacteristic
481C23×C4C23×C3112yes—
482C23×C4C23×C3111yescharacteristic
483#124—232no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—42no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42D4×C3114yescomplemented
515#95—22no—
516#95—22no—
517#95—22no—
518#95—24no—
519#95—22no—
520#95—24no—
521#95—42no—
522#95—42no—
523#95—42no—
524C31#1668011yescharacteristic, direct product factor, Sylow
525C24—21no—
526C24—21no—
527C24—22no—
528C24—22no—
529C24—21no—
530C24—21no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—21no—
547C24—22no—
548C24—21no—
549C24C2×D4×C3114yes—
550C24#41×C3112yes—
551C24C24×C3111yescharacteristic
552C2×Q8—28no—
553C2×Q8—48no—
554C2×Q8—48no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×D4—28no—
558C2×D4—48no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4—48no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—48no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4C2×D4×C3112yes—
615C22×C4C2×D4×C3114yes—
616C22×C4C2×D4×C3112yes—
617C22×C4C2×D4×C3112yes—
618C22×C4C2×D4×C3112yes—
619C22×C4C2×D4×C3112yes—
620C22×C4#41×C3114yes—
621C22×C4#41×C3112yes—
622C4⋊C4—44no—
623C22⋊C4—28no—
624C22⋊C4—216no—
625C22⋊C4—216no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C42—28no—
633C23—24no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—24no—
645C23—41no—
646C23—42no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—41no—
654C23—42no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—42no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—42no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23C22×D4×C3111yescharacteristic
692C23C22×D4×C3111yescharacteristic
693C23C22×D4×C3111yescharacteristic
694C23C2×#41×C3111yescharacteristic
695C23C2×#41×C3111yescharacteristic
696C23C2×#41×C3112yes—
697C23C31×H(5,𝔽2)12yes—
698C23C31×H(5,𝔽2)12yes—
699C23C31×H(5,𝔽2)12yes—
700C23C31×H(5,𝔽2)11yescharacteristic
701C23C31×2−1+411yescharacteristic
702Q8—416no—
703D4—416no—
704D4—432no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4C31×#12014yes—
758C22—42no—
759C22—44no—
760C22—42no—
761C22—44no—
762C22—42no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—81no—
771C22—82no—
772C22—82no—
773C22—81no—
774C22—82no—
775C22—82no—
776C22—81no—
777C22—82no—
778C22—81no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22C2×C31×#12011yescharacteristic
785C22C31×#52511yescharacteristic
786C22C31×#53211yescharacteristic
787C22C31×#53412yes—
788C22C31×#53412yes—
789C22C31×#53511yescharacteristic
790C22C31×#53511yescharacteristic
791C22C31×#53511yescharacteristic
792C22C31×#53711yescharacteristic
793C22C31×#53812yes—
794C22C31×#53812yes—
795C22C31×#53812yes—
796C22C31×#54212yes—
797C22C31×#54611yescharacteristic
798C22C31×#54612yes—
799C22C31×#54711yescharacteristic
800C22C31×#54811yescharacteristic
801C22C31×#55011yescharacteristic
802C22C31×#55012yes—
803C22C31×#55112yes—
804C22C31×#55512yes—
805C22C31×H(3,𝔽4)12yes—
806C22C31×#56212yes—
807C4—24no—
808C4—44no—
809C4—42no—
810C4—42no—
811C4—44no—
812C4—42no—
813C4—81no—
814C4—81no—
815C4—82no—
816C2—82no—
817C2—84no—
818C2C31×#240711yescharacteristic
819C2C31×#243111yescharacteristic
820C2C31×#261011yescharacteristic
821C2C31×#261311yescharacteristic
822C2C31×#263111yescharacteristic
823C2C31×#266211yescharacteristic
824C2C31×#268412yes—
825C2C31×#268612yes—
826C2C31×#273012yes—
827C2C31×#273312yes—
828C2C31×#281911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#124C2semidirect
2. C2×C31×#393C2semidirect
4. C2×C31×#388C2semidirect
5. C31×#1446C2semidirect
6. C31×#1440C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×#1434C2semidirect
47. C22×Q8×C31D4semidirect
100. C2×C42×C31D4semidirect
218. #16680C31direct (N × H)
344. C22×#124C2×C31semidirect
345. C2×#393C2×C31semidirect
347. C2×#388C2×C31semidirect
348. #1446C2×C31semidirect
349. #1440C2×C31semidirect
350. #1439C2×C31semidirect
351. #1438C2×C31semidirect
352. #1438C2×C31semidirect
353. #1438C2×C31semidirect
354. #1434C2×C31semidirect
461. C22×Q8D4×C31semidirect
514. C2×C42D4×C31semidirect
524. C31#16680direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C2×C31×#3932
C2×C31×#3922
C2×C31×#3882
C31×#14462
C31×#14402
C31×#14392
C31×#14382
C31×#14342
#1668031