Finite Group Databasebeta

← C31×#15215 #21471974

Subgroups — C31×#15215 #21471974

Order 7936.

2878 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic, complemented
2C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
3C22×C31×#121C211yesmaximal, characteristic
4C2×C31×#391C211yesmaximal, characteristic, complemented
5C2×C31×#390C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#1439C214yesmaximal, complemented
8C31×#1438C214yesmaximal, complemented
9C31×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×Q8×C31C2211yescharacteristic
11C23×D4×C31C2211yescharacteristic
12C23×D4×C31C2212yes—
13C24×C4×C31C2211yescharacteristic
14C2×C31×#124—24no—
15C2×C31×#124—24no—
16C2×C31×#124—24no—
17C2×C31×C22⋊Q8—24no—
18C2×C31×C22⋊Q8—24no—
19C2×C31×C22⋊Q8—24no—
20C2×C31×#121—24no—
21C2×C31×#121—24no—
22C2×C31×#121—24no—
23C22×C4⋊C4×C31C2212yes—
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2212yes—
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2214yes—
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2214yes—
31C22×C42×C31C2211yescharacteristic
32C22×C42×C31C2211yescharacteristic
33C31×#391—24no—
34C31×#390—24no—
35C4×C22⋊C4×C31—24no—
36C2×C31×#95C2214yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2214yes—
39C25×C31C2312yes—
40C25×C31C2311yescharacteristic
41C22×Q8×C31—22no—
42C22×Q8×C31—22no—
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31—22no—
47C22×Q8×C31D414yescomplemented
48C22×D4×C31—24no—
49C22×D4×C31—24no—
50C22×D4×C31—28no—
51C22×D4×C31—24no—
52C22×D4×C31—22no—
53C22×D4×C31—22no—
54C22×D4×C31—22no—
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—22no—
58C22×D4×C31—44no—
59C22×D4×C31D414yes—
60C23×C4×C31—22no—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31D414yes—
67C23×C4×C31C2312yes—
68C23×C4×C31C2312yes—
69C23×C4×C31C2312yes—
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2312yes—
72C23×C4×C31C2312yes—
73C23×C4×C31C2311yescharacteristic
74C31×#124—232no—
75C31×C22⋊Q8—232no—
76C31×#121—232no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—24no—
81C2×C4⋊C4×C31—24no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31D414yes—
85C2×C4⋊C4×C31D414yescomplemented
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—28no—
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—28no—
95C2×C22⋊C4×C31—28no—
96C2×C22⋊C4×C31—24no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—28no—
99C2×C22⋊C4×C31—28no—
100C2×C22⋊C4×C31—44no—
101C2×C42×C31—22no—
102C2×C42×C31—22no—
103C2×C42×C31—22no—
104C2×C42×C31—22no—
105C2×C42×C31—22no—
106C2×C42×C31D414yescomplemented
107C31×#95—24no—
108C31×#95—28no—
109C31×#95—44no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—22no—
116C24×C31—21no—
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—24no—
125C24×C31—22no—
126C24×C31—24no—
127C24×C31—24no—
128C24×C31—24no—
129C24×C31C2×D414yes—
130C24×C31C2×D412yes—
131C24×C31#4114yes—
132C24×C31C2411yescharacteristic
133C2×Q8×C31—28no—
134C2×Q8×C31—28no—
135C2×Q8×C31—28no—
136C2×Q8×C31—44no—
137C2×Q8×C31—44no—
138C2×Q8×C31—44no—
139C2×Q8×C31—44no—
140C2×D4×C31—216no—
141C2×D4×C31—28no—
142C2×D4×C31—28no—
143C2×D4×C31—28no—
144C2×D4×C31—416no—
145C2×D4×C31—416no—
146C2×D4×C31—48no—
147C2×D4×C31—48no—
148C2×D4×C31—44no—
149C2×D4×C31—44no—
150C2×D4×C31—44no—
151C2×D4×C31—44no—
152C22×C4×C31—22no—
153C22×C4×C31—21no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—24no—
175C22×C4×C31—21no—
176C22×C4×C31—24no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—24no—
180C22×C4×C31—24no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—28no—
185C22×C4×C31—28no—
186C22×C4×C31—28no—
187C22×C4×C31—44no—
188C22×C4×C31—44no—
189C22×C4×C31—44no—
190C22×C4×C31—44no—
191C22×C4×C31C2×D414yes—
192C22×C4×C31C2×D414yes—
193C22×C4×C31C2×D414yes—
194C22×C4×C31C2×D414yes—
195C22×C4×C31C2×D412yes—
196C22×C4×C31C2×D412yes—
197C22×C4×C31C2×D412yes—
198C22×C4×C31C2×D412yes—
199C22×C4×C31C2×D412yes—
200C22×C4×C31C2×D412yes—
201C22×C4×C31C2×D412yes—
202C22×C4×C31#4114yes—
203C22×C4×C31#4112yes—
204C4⋊C4×C31—216no—
205C4⋊C4×C31—28no—
206C4⋊C4×C31—28no—
207C22⋊C4×C31—216no—
208C22⋊C4×C31—216no—
209C22⋊C4×C31—216no—
210C22⋊C4×C31—232no—
211C22⋊C4×C31—416no—
212C42×C31—28no—
213C42×C31—44no—
214#15215C3111yesmaximal, characteristic, direct product factor, Sylow
215C23×C31—22no—
216C23×C31—22no—
217C23×C31—22no—
218C23×C31—24no—
219C23×C31—24no—
220C23×C31—22no—
221C23×C31—22no—
222C23×C31—22no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—24no—
226C23×C31—24no—
227C23×C31—24no—
228C23×C31—24no—
229C23×C31—24no—
230C23×C31—28no—
231C23×C31—28no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—42no—
237C23×C31—42no—
238C23×C31—42no—
239C23×C31—42no—
240C23×C31—42no—
241C23×C31—42no—
242C23×C31—42no—
243C23×C31—42no—
244C23×C31—42no—
245C23×C31—44no—
246C23×C31—42no—
247C23×C31—44no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—44no—
253C23×C31—44no—
254C23×C31—44no—
255C23×C31—44no—
256C23×C31—44no—
257C23×C31—44no—
258C23×C31—44no—
259C23×C31—44no—
260C23×C31#12414yescomplemented
261C23×C31C22×D411yescharacteristic
262C23×C31C22×D411yescharacteristic
263C23×C31C22×D411yescharacteristic
264C23×C31C22×D411yescharacteristic
265C23×C31C22×D411yescharacteristic
266C23×C31C22×D411yescharacteristic
267C23×C31C2×#4111yescharacteristic
268C23×C31C2×#4112yes—
269C23×C31C2×#4112yes—
270C23×C31H(5,𝔽2)12yes—
271C23×C312−1+412yes—
272Q8×C31—416no—
273D4×C31—432no—
274D4×C31—416no—
275C2×C4×C31—24no—
276C2×C4×C31—22no—
277C2×C4×C31—24no—
278C2×C4×C31—24no—
279C2×C4×C31—24no—
280C2×C4×C31—24no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—24no—
284C2×C4×C31—24no—
285C2×C4×C31—24no—
286C2×C4×C31—24no—
287C2×C4×C31—24no—
288C2×C4×C31—28no—
289C2×C4×C31—28no—
290C2×C4×C31—24no—
291C2×C4×C31—41no—
292C2×C4×C31—42no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—41no—
300C2×C4×C31—42no—
301C2×C4×C31—42no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—44no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—44no—
313C2×C4×C31—416no—
314C2×C4×C31#12014yes—
315C2×C4×C31#12014yes—
316C2×C4×C31#12014yes—
317C2×C4×C31#12114yes—
318C2×C4×C31#12114yes—
319C2×C4×C31#12114yes—
320C2×C4×C31#12714yes—
321C22×#124C2×C3111yescharacteristic, complemented
322C22×C22⋊Q8C2×C3111yescharacteristic, complemented
323C22×#121C2×C3111yescharacteristic
324C2×#391C2×C3111yescharacteristic, complemented
325C2×#390C2×C3111yescharacteristic, complemented
326C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
327#1439C2×C3114yescomplemented
328#1438C2×C3114yescomplemented
329C4⋊#95C2×C3111yescharacteristic, complemented
330C22×C31—24no—
331C22×C31—24no—
332C22×C31—24no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31—44no—
336C22×C31—44no—
337C22×C31—44no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—44no—
341C22×C31—44no—
342C22×C31—48no—
343C22×C31—48no—
344C22×C31—44no—
345C22×C31—44no—
346C22×C31—82no—
347C22×C31—82no—
348C22×C31—84no—
349C22×C31—82no—
350C22×C31—82no—
351C22×C31—84no—
352C22×C31C2×#12011yescharacteristic
353C22×C31C2×#12011yescharacteristic
354C22×C31C2×#12011yescharacteristic
355C22×C31C2×#12111yescharacteristic
356C22×C31C2×#12111yescharacteristic
357C22×C31C2×#12111yescharacteristic
358C22×C31#52512yes—
359C22×C31C2×#12411yescharacteristic
360C22×C31#52912yes—
361C22×C31C2×#12711yescharacteristic
362C22×C31#53211yescharacteristic
363C22×C31#53511yescharacteristic
364C22×C31#53611yescharacteristic
365C22×C31#53712yes—
366C22×C31#54212yes—
367C22×C31#54612yes—
368C22×C31#54612yes—
369C22×C31#54612yes—
370C22×C31#54712yes—
371C22×C31#54812yes—
372C22×C31#54812yes—
373C22×C31#54812yes—
374C22×C31#55012yes—
375C4×C31—42no—
376C4×C31—44no—
377C4×C31—44no—
378C4×C31—44no—
379C4×C31—44no—
380C4×C31—44no—
381C4×C31#39218yes—
382C23×Q8C22×C3111yescharacteristic
383C23×D4C22×C3111yescharacteristic
384C23×D4C22×C3112yes—
385C24×C4C22×C3111yescharacteristic
386C2×#124—24no—
387C2×#124—24no—
388C2×#124—24no—
389C2×C22⋊Q8—24no—
390C2×C22⋊Q8—24no—
391C2×C22⋊Q8—24no—
392C2×#121—24no—
393C2×#121—24no—
394C2×#121—24no—
395C22×C4⋊C4C22×C3112yes—
396C22×C4⋊C4C22×C3111yescharacteristic
397C22×C4⋊C4C22×C3111yescharacteristic
398C22×C22⋊C4C22×C3112yes—
399C22×C22⋊C4C22×C3112yes—
400C22×C22⋊C4C22×C3114yes—
401C22×C22⋊C4C22×C3112yes—
402C22×C22⋊C4C22×C3114yes—
403C22×C42C22×C3111yescharacteristic
404C22×C42C22×C3111yescharacteristic
405#391—24no—
406#390—24no—
407C4×C22⋊C4—24no—
408C2×#95C22×C3114yes—
409C2×#95C22×C3112yes—
410C2×#95C22×C3114yes—
411C2×C31—44no—
412C2×C31—84no—
413C2×C31C2×#39211yescharacteristic
414C2×C31#240712yes—
415C2×C31#242612yes—
416C2×C31#242712yes—
417C2×C31#243111yescharacteristic
418C2×C31#243211yescharacteristic
419C2×C31#243511yescharacteristic
420C2×C31#243611yescharacteristic
421C2×C31#254012yes—
422C2×C31#262011yescharacteristic
423C2×C31#285011yescharacteristic
424C25C23×C3112yes—
425C25C23×C3111yescharacteristic
426C22×Q8—22no—
427C22×Q8—22no—
428C22×Q8—22no—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—22no—
432C22×Q8D4×C3114yescomplemented
433C22×D4—24no—
434C22×D4—24no—
435C22×D4—28no—
436C22×D4—24no—
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—44no—
444C22×D4D4×C3114yes—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—22no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4D4×C3114yes—
452C23×C4C23×C3112yes—
453C23×C4C23×C3112yes—
454C23×C4C23×C3112yes—
455C23×C4C23×C3111yescharacteristic
456C23×C4C23×C3112yes—
457C23×C4C23×C3112yes—
458C23×C4C23×C3111yescharacteristic
459#124—232no—
460C22⋊Q8—232no—
461#121—232no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4D4×C3114yes—
470C2×C4⋊C4D4×C3114yescomplemented
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—28no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—28no—
480C2×C22⋊C4—28no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—28no—
484C2×C22⋊C4—28no—
485C2×C22⋊C4—44no—
486C2×C42—22no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42D4×C3114yescomplemented
492#95—24no—
493#95—28no—
494#95—44no—
495C31#1521511yescharacteristic, direct product factor, Sylow
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—22no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—24no—
511C24—22no—
512C24—24no—
513C24—24no—
514C24—24no—
515C24C2×D4×C3114yes—
516C24C2×D4×C3112yes—
517C24#41×C3114yes—
518C24C24×C3111yescharacteristic
519C2×Q8—28no—
520C2×Q8—28no—
521C2×Q8—28no—
522C2×Q8—44no—
523C2×Q8—44no—
524C2×Q8—44no—
525C2×Q8—44no—
526C2×D4—216no—
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—416no—
531C2×D4—416no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4C2×D4×C3114yes—
578C22×C4C2×D4×C3114yes—
579C22×C4C2×D4×C3114yes—
580C22×C4C2×D4×C3114yes—
581C22×C4C2×D4×C3112yes—
582C22×C4C2×D4×C3112yes—
583C22×C4C2×D4×C3112yes—
584C22×C4C2×D4×C3112yes—
585C22×C4C2×D4×C3112yes—
586C22×C4C2×D4×C3112yes—
587C22×C4C2×D4×C3112yes—
588C22×C4#41×C3114yes—
589C22×C4#41×C3112yes—
590C4⋊C4—216no—
591C4⋊C4—28no—
592C4⋊C4—28no—
593C22⋊C4—216no—
594C22⋊C4—216no—
595C22⋊C4—216no—
596C22⋊C4—232no—
597C22⋊C4—416no—
598C42—28no—
599C42—44no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—28no—
616C23—28no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—44no—
631C23—42no—
632C23—44no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23C31×#12414yescomplemented
646C23C22×D4×C3111yescharacteristic
647C23C22×D4×C3111yescharacteristic
648C23C22×D4×C3111yescharacteristic
649C23C22×D4×C3111yescharacteristic
650C23C22×D4×C3111yescharacteristic
651C23C22×D4×C3111yescharacteristic
652C23C2×#41×C3111yescharacteristic
653C23C2×#41×C3112yes—
654C23C2×#41×C3112yes—
655C23C31×H(5,𝔽2)12yes—
656C23C31×2−1+412yes—
657Q8—416no—
658D4—432no—
659D4—416no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—24no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—416no—
699C2×C4C31×#12014yes—
700C2×C4C31×#12014yes—
701C2×C4C31×#12014yes—
702C2×C4C31×#12114yes—
703C2×C4C31×#12114yes—
704C2×C4C31×#12114yes—
705C2×C4C31×#12714yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—44no—
718C22—48no—
719C22—48no—
720C22—44no—
721C22—44no—
722C22—82no—
723C22—82no—
724C22—84no—
725C22—82no—
726C22—82no—
727C22—84no—
728C22C2×C31×#12011yescharacteristic
729C22C2×C31×#12011yescharacteristic
730C22C2×C31×#12011yescharacteristic
731C22C2×C31×#12111yescharacteristic
732C22C2×C31×#12111yescharacteristic
733C22C2×C31×#12111yescharacteristic
734C22C31×#52512yes—
735C22C2×C31×#12411yescharacteristic
736C22C31×#52912yes—
737C22C2×C31×#12711yescharacteristic
738C22C31×#53211yescharacteristic
739C22C31×#53511yescharacteristic
740C22C31×#53611yescharacteristic
741C22C31×#53712yes—
742C22C31×#54212yes—
743C22C31×#54612yes—
744C22C31×#54612yes—
745C22C31×#54612yes—
746C22C31×#54712yes—
747C22C31×#54812yes—
748C22C31×#54812yes—
749C22C31×#54812yes—
750C22C31×#55012yes—
751C4—42no—
752C4—44no—
753C4—44no—
754C4—44no—
755C4—44no—
756C4—44no—
757C4C31×#39218yes—
758C2—44no—
759C2—84no—
760C2C2×C31×#39211yescharacteristic
761C2C31×#240712yes—
762C2C31×#242612yes—
763C2C31×#242712yes—
764C2C31×#243111yescharacteristic
765C2C31×#243211yescharacteristic
766C2C31×#243511yescharacteristic
767C2C31×#243611yescharacteristic
768C2C31×#254012yes—
769C2C31×#262011yescharacteristic
770C2C31×#285011yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#121C2
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. C22×C31×C22⋊Q8C2semidirect
4. C2×C31×#391C2semidirect
5. C2×C31×#390C2semidirect
6. C2×C4×C22⋊C4×C31C2semidirect
7. C31×#1439C2semidirect
8. C31×#1438C2semidirect
9. C31×C4⋊#95C2semidirect
47. C22×Q8×C31D4semidirect
85. C2×C4⋊C4×C31D4semidirect
106. C2×C42×C31D4semidirect
214. #15215C31direct (N × H)
260. C23×C31#124semidirect
321. C22×#124C2×C31semidirect
322. C22×C22⋊Q8C2×C31semidirect
324. C2×#391C2×C31semidirect
325. C2×#390C2×C31semidirect
326. C2×C4×C22⋊C4C2×C31semidirect
327. #1439C2×C31semidirect
328. #1438C2×C31semidirect
329. C4⋊#95C2×C31semidirect
432. C22×Q8D4×C31semidirect
470. C2×C4⋊C4D4×C31semidirect
491. C2×C42D4×C31semidirect
495. C31#15215direct (N × H)
645. C23C31×#124semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C22×C31×C22⋊Q82
C22×C31×#1212
C2×C31×#3912
C2×C31×#3902
C2×C4×C22⋊C4×C312
C31×#14392
C31×#14382
C31×C4⋊#952
#1521531