Finite Group Databasebeta

← C31×#23920 #21480679

Subgroups — C31×#23920 #21480679

Order 7936.

2272 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic, complemented
2C22×C31×#121C211yesmaximal, characteristic, complemented
3C2×C31×#449C212yesmaximal, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C2×C31×#447C211yesmaximal, characteristic, complemented
6C31×#2000C212yesmaximal, complemented
7C31×#1999C212yesmaximal, complemented
8C31×#1875C212yesmaximal, complemented
9C31×#1874C211yesmaximal, characteristic, complemented
10C31×#1872C211yesmaximal, characteristic, complemented
11C31×#1779C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic, complemented
13C23×D4×C31—21no—
14C23×D4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C22×SD16×C31C2212yescomplemented
17C22×D8×C31C2212yescomplemented
18C31×#525—24no—
19C31×#525—24no—
20C2×C31×#123—21no—
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic, complemented
23C2×C31×#121—21no—
24C2×C31×#121—21no—
25C2×C31×#121—28no—
26C2×C31×#121C2212yes—
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2212yes—
29C2×C31×#121C2211yescharacteristic, complemented
30C2×C31×#120—21no—
31C2×C4×D4×C31—21no—
32C2×C4×D4×C31—21no—
33C2×C31×#117C2211yescharacteristic, complemented
34C22×C4⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31—21no—
36C31×#450—24no—
37C31×#449—28no—
38C31×#447—24no—
39C2×C31×#103C2212yescomplemented
40C2×C31×#102C2212yescomplemented
41C2×C31×#102C2212yescomplemented
42C2×C31×#102C2212yescomplemented
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C31×C22⋊C8C2212yescomplemented
46C2×C31×C22⋊C8C2212yescomplemented
47C31×#340C2212yescomplemented
48C31×#340C2212yescomplemented
49C25×C31—21no—
50C25×C31D411yescharacteristic
51C2×#41×C31—22no—
52C2×#41×C31—22no—
53C2×#41×C31—24no—
54C2×#41×C31—42no—
55C22×Q8×C31C2311yescharacteristic
56C22×D4×C31—28no—
57C22×D4×C31—21no—
58C22×D4×C31—21no—
59C22×D4×C31—21no—
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—24no—
63C22×D4×C31—21no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—42no—
67C22×D4×C31—44no—
68C22×D4×C31—44no—
69C22×D4×C31C2312yes—
70C22×D4×C31C2311yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31—24no—
74C23×C4×C31—22no—
75C23×C4×C31—22no—
76C23×C4×C31—42no—
77C23×C4×C31D411yescharacteristic
78C23×C4×C31D411yescharacteristic
79C23×C4×C31D411yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C2×SD16×C31—24no—
84C2×SD16×C31—24no—
85C2×SD16×C31—42no—
86C2×D8×C31—24no—
87C2×D8×C31—24no—
88C2×D8×C31—42no—
89C22×C8×C31C2312yes—
90C22×C8×C31C2312yes—
91C31×#123—28no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8D414yescomplemented
96C31×#121—28no—
97C31×#121—28no—
98C31×#121—24no—
99C31×#121—22no—
100C31×#121—24no—
101C31×#121—22no—
102C31×#121—24no—
103C31×#121—22no—
104C31×#121D418yescomplemented
105C31×#121D414yescomplemented
106C31×#120—28no—
107C4×D4×C31—28no—
108C4×D4×C31—28no—
109C31×#117—22no—
110C31×#117—22no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31—24no—
115C2×C4⋊C4×C31C2312yes—
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C22⋊C4×C31—28no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C42×C31—21no—
127C31×#103—24no—
128C31×#102—24no—
129C31×#102—24no—
130C31×#102—24no—
131C31×C22⋊C8—22no—
132C31×C22⋊C8—22no—
133C31×C22⋊C8—24no—
134C31×C22⋊C8—42no—
135C24×C31—22no—
136C24×C31—22no—
137C24×C31—22no—
138C24×C31—24no—
139C24×C31—22no—
140C24×C31—22no—
141C24×C31—21no—
142C24×C31—22no—
143C24×C31—41no—
144C24×C31—41no—
145C24×C31—42no—
146C24×C31—42no—
147C24×C31—42no—
148C24×C31—42no—
149C24×C31—42no—
150C24×C31—42no—
151C24×C31C2×D411yescharacteristic
152C24×C31C2×D411yescharacteristic
153C24×C31C2×D411yescharacteristic
154#41×C31—48no—
155#41×C31—48no—
156C2×Q8×C31—21no—
157C2×Q8×C31—22no—
158C2×Q8×C31—22no—
159C2×Q8×C31C2×D412yescomplemented
160C2×D4×C31—24no—
161C2×D4×C31—24no—
162C2×D4×C31—24no—
163C2×D4×C31—28no—
164C2×D4×C31—24no—
165C2×D4×C31—28no—
166C2×D4×C31—22no—
167C2×D4×C31—22no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—21no—
171C2×D4×C31—22no—
172C2×D4×C31—22no—
173C2×D4×C31—22no—
174C2×D4×C31—48no—
175C2×D4×C31—48no—
176C2×D4×C31—42no—
177C2×D4×C31—42no—
178C2×D4×C31—432no—
179C2×D4×C31—44no—
180C2×D4×C31—44no—
181C2×D4×C31—44no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—44no—
188C2×D4×C31—42no—
189C2×D4×C31C2×D414yes—
190C2×D4×C31C2×D412yescomplemented
191C22×C4×C31—22no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—24no—
197C22×C4×C31—24no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
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—21no—
210C22×C4×C31—21no—
211C22×C4×C31—22no—
212C22×C4×C31—41no—
213C22×C4×C31—41no—
214C22×C4×C31—41no—
215C22×C4×C31—48no—
216C22×C4×C31—48no—
217C22×C4×C31—42no—
218C22×C4×C31—42no—
219C22×C4×C31—42no—
220C22×C4×C31—42no—
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D414yes—
225C22×C4×C31C2×D412yes—
226C22×C4×C31C2×D412yes—
227C22×C4×C31C2411yescharacteristic
228SD16×C31—48no—
229D8×C31—48no—
230C2×C8×C31—22no—
231C2×C8×C31—22no—
232C2×C8×C31—22no—
233C2×C8×C31—22no—
234C2×C8×C31—22no—
235C2×C8×C31—22no—
236C4⋊C4×C31—24no—
237C4⋊C4×C31—24no—
238C4⋊C4×C31—24no—
239C4⋊C4×C31—22no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31C2×D414yes—
243C4⋊C4×C31C2×D412yescomplemented
244C4⋊C4×C31C2×D412yescomplemented
245C22⋊C4×C31—28no—
246C22⋊C4×C31—24no—
247C22⋊C4×C31—24no—
248C22⋊C4×C31—24no—
249C22⋊C4×C31—24no—
250C22⋊C4×C31—28no—
251C22⋊C4×C31—24no—
252C42×C31—24no—
253#23920C3111yesmaximal, characteristic, direct product factor, Sylow
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—28no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—21no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—22no—
272C23×C31—24no—
273C23×C31—44no—
274C23×C31—44no—
275C23×C31—44no—
276C23×C31—44no—
277C23×C31—44no—
278C23×C31—48no—
279C23×C31—48no—
280C23×C31—48no—
281C23×C31—44no—
282C23×C31—41no—
283C23×C31—42no—
284C23×C31—41no—
285C23×C31—42no—
286C23×C31—41no—
287C23×C31—42no—
288C23×C31—42no—
289C23×C31—42no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—42no—
294C23×C31—84no—
295C23×C31—84no—
296C23×C31—84no—
297C23×C31—84no—
298C23×C31#12012yes—
299C23×C31#12012yes—
300C23×C31#13512yes—
301C23×C31AGL(1,ℤ/8)12yes—
302C23×C31AGL(1,ℤ/8)12yes—
303C23×C31C22×D411yescharacteristic
304Q8×C31—24no—
305Q8×C31—42no—
306D4×C31—24no—
307D4×C31—24no—
308D4×C31—24no—
309D4×C31—48no—
310D4×C31—48no—
311D4×C31—416no—
312D4×C31—416no—
313D4×C31—48no—
314D4×C31—48no—
315D4×C31—42no—
316D4×C31—42no—
317D4×C31—42no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—24no—
323C2×C4×C31—24no—
324C2×C4×C31—24no—
325C2×C4×C31—24no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—21no—
330C2×C4×C31—22no—
331C2×C4×C31—24no—
332C2×C4×C31—21no—
333C2×C4×C31—44no—
334C2×C4×C31—44no—
335C2×C4×C31—44no—
336C2×C4×C31—48no—
337C2×C4×C31—48no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—42no—
347C2×C4×C31—42no—
348C2×C4×C31#12012yes—
349C2×C4×C31#12012yes—
350C2×C4×C31C22×D412yes—
351C2×C4×C31C22×D411yescharacteristic
352C2×C4×C31C22×D411yescharacteristic
353C2×C4×C31H(5,𝔽2)12yes—
354C8×C31—42no—
355C8×C31—42no—
356C2×#525C2×C3111yescharacteristic, complemented
357C22×#121C2×C3111yescharacteristic, complemented
358C2×#449C2×C3112yescomplemented
359C2×#450C2×C3111yescharacteristic, complemented
360C2×#447C2×C3111yescharacteristic, complemented
361#2000C2×C3112yescomplemented
362#1999C2×C3112yescomplemented
363#1875C2×C3112yescomplemented
364#1874C2×C3111yescharacteristic, complemented
365#1872C2×C3111yescharacteristic, complemented
366#1779C2×C3111yescharacteristic, complemented
367C22×C31—22no—
368C22×C31—22no—
369C22×C31—22no—
370C22×C31—22no—
371C22×C31—22no—
372C22×C31—22no—
373C22×C31—22no—
374C22×C31—22no—
375C22×C31—22no—
376C22×C31—22no—
377C22×C31—22no—
378C22×C31—22no—
379C22×C31—416no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—41no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—41no—
387C22×C31—41no—
388C22×C31—42no—
389C22×C31—44no—
390C22×C31—42no—
391C22×C31—44no—
392C22×C31—44no—
393C22×C31—42no—
394C22×C31—816no—
395C22×C31—81no—
396C22×C31—82no—
397C22×C31—81no—
398C22×C31—82no—
399C22×C31—82no—
400C22×C31—81no—
401C22×C31—81no—
402C22×C31—82no—
403C22×C31#44914yescomplemented
404C22×C31C2×#12011yescharacteristic
405C22×C31C2×#12011yescharacteristic
406C22×C31#53411yescharacteristic
407C22×C31C2×#13511yescharacteristic
408C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C31#57511yescharacteristic
411C4×C31—22no—
412C4×C31—22no—
413C4×C31—41no—
414C4×C31—42no—
415C4×C31—42no—
416C4×C31—44no—
417C4×C31—42no—
418C4×C31D4212yes—
419C4×C31D4212yes—
420C22×#41C22×C3111yescharacteristic, complemented
421C23×D4—21no—
422C23×D4C22×C3111yescharacteristic
423C24×C4C22×C3111yescharacteristic
424C22×SD16C22×C3112yescomplemented
425C22×D8C22×C3112yescomplemented
426#525—24no—
427#525—24no—
428C2×#123—21no—
429C2×C22⋊Q8C22×C3111yescharacteristic
430C2×C22⋊Q8C22×C3111yescharacteristic, complemented
431C2×#121—21no—
432C2×#121—21no—
433C2×#121—28no—
434C2×#121C22×C3112yes—
435C2×#121C22×C3111yescharacteristic
436C2×#121C22×C3112yes—
437C2×#121C22×C3111yescharacteristic, complemented
438C2×#120—21no—
439C2×C4×D4—21no—
440C2×C4×D4—21no—
441C2×#117C22×C3111yescharacteristic, complemented
442C22×C4⋊C4C22×C3111yescharacteristic
443C22×C22⋊C4—21no—
444#450—24no—
445#449—28no—
446#447—24no—
447C2×#103C22×C3112yescomplemented
448C2×#102C22×C3112yescomplemented
449C2×#102C22×C3112yescomplemented
450C2×#102C22×C3112yescomplemented
451C2×C22⋊C8C22×C3111yescharacteristic
452C2×C22⋊C8C22×C3111yescharacteristic
453C2×C22⋊C8C22×C3112yescomplemented
454C2×C22⋊C8C22×C3112yescomplemented
455#340C22×C3112yescomplemented
456#340C22×C3112yescomplemented
457C2×C31—24no—
458C2×C31—42no—
459C2×C31—42no—
460C2×C31—82no—
461C2×C31—84no—
462C2×C31#240311yescharacteristic
463C2×C31C2×#44911yescharacteristic
464C2×C31#300211yescharacteristic
465C2×C31#300311yescharacteristic
466C2×C31#300611yescharacteristic
467C2×C31#318811yescharacteristic
468C2×C31#319411yescharacteristic
469C25—21no—
470C25D4×C3111yescharacteristic
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—24no—
474C2×#41—42no—
475C22×Q8C23×C3111yescharacteristic
476C22×D4—28no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—24no—
483C22×D4—21no—
484C22×D4—22no—
485C22×D4—22no—
486C22×D4—42no—
487C22×D4—44no—
488C22×D4—44no—
489C22×D4C23×C3112yes—
490C22×D4C23×C3111yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—24no—
494C23×C4—22no—
495C23×C4—22no—
496C23×C4—42no—
497C23×C4D4×C3111yescharacteristic
498C23×C4D4×C3111yescharacteristic
499C23×C4D4×C3111yescharacteristic
500C23×C4C23×C3111yescharacteristic
501C23×C4C23×C3111yescharacteristic
502C23×C4C23×C3111yescharacteristic
503C2×SD16—24no—
504C2×SD16—24no—
505C2×SD16—42no—
506C2×D8—24no—
507C2×D8—24no—
508C2×D8—42no—
509C22×C8C23×C3112yes—
510C22×C8C23×C3112yes—
511#123—28no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8D4×C3114yescomplemented
516#121—28no—
517#121—28no—
518#121—24no—
519#121—22no—
520#121—24no—
521#121—22no—
522#121—24no—
523#121—22no—
524#121D4×C3118yescomplemented
525#121D4×C3114yescomplemented
526#120—28no—
527C4×D4—28no—
528C4×D4—28no—
529#117—22no—
530#117—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4C23×C3112yes—
536C2×C4⋊C4C23×C3111yescharacteristic
537C2×C4⋊C4C23×C3111yescharacteristic
538C2×C22⋊C4—28no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C42—21no—
547#103—24no—
548#102—24no—
549#102—24no—
550#102—24no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—24no—
554C22⋊C8—42no—
555C31#2392011yescharacteristic, direct product factor, Sylow
556C24—22no—
557C24—22no—
558C24—22no—
559C24—24no—
560C24—22no—
561C24—22no—
562C24—21no—
563C24—22no—
564C24—41no—
565C24—41no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—42no—
572C24C2×D4×C3111yescharacteristic
573C24C2×D4×C3111yescharacteristic
574C24C2×D4×C3111yescharacteristic
575#41—48no—
576#41—48no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8C2×D4×C3112yescomplemented
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—28no—
585C2×D4—24no—
586C2×D4—28no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—48no—
596C2×D4—48no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—432no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4—44no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—44no—
609C2×D4—42no—
610C2×D4C2×D4×C3114yes—
611C2×D4C2×D4×C3112yescomplemented
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3111yescharacteristic
644C22×C4C2×D4×C3111yescharacteristic
645C22×C4C2×D4×C3114yes—
646C22×C4C2×D4×C3112yes—
647C22×C4C2×D4×C3112yes—
648C22×C4C24×C3111yescharacteristic
649SD16—48no—
650D8—48no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4C2×D4×C3114yes—
664C4⋊C4C2×D4×C3112yescomplemented
665C4⋊C4C2×D4×C3112yescomplemented
666C22⋊C4—28no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—28no—
672C22⋊C4—24no—
673C42—24no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—28no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—22no—
692C23—24no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—48no—
699C23—48no—
700C23—48no—
701C23—44no—
702C23—41no—
703C23—42no—
704C23—41no—
705C23—42no—
706C23—41no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—84no—
715C23—84no—
716C23—84no—
717C23—84no—
718C23C31×#12012yes—
719C23C31×#12012yes—
720C23C31×#13512yes—
721C23C31×AGL(1,ℤ/8)12yes—
722C23C31×AGL(1,ℤ/8)12yes—
723C23C22×D4×C3111yescharacteristic
724Q8—24no—
725Q8—42no—
726D4—24no—
727D4—24no—
728D4—24no—
729D4—48no—
730D4—48no—
731D4—416no—
732D4—416no—
733D4—48no—
734D4—48no—
735D4—42no—
736D4—42no—
737D4—42no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—21no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—48no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4C31×#12012yes—
769C2×C4C31×#12012yes—
770C2×C4C22×D4×C3112yes—
771C2×C4C22×D4×C3111yescharacteristic
772C2×C4C22×D4×C3111yescharacteristic
773C2×C4C31×H(5,𝔽2)12yes—
774C8—42no—
775C8—42no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—416no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22—816no—
804C22—82no—
805C22—81no—
806C22—82no—
807C22—81no—
808C22—82no—
809C22—81no—
810C22—81no—
811C22—82no—
812C22C31×#44914yescomplemented
813C22C2×C31×#12011yescharacteristic
814C22C2×C31×#12011yescharacteristic
815C22C31×#53411yescharacteristic
816C22C2×C31×#13511yescharacteristic
817C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
818C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
819C22C31×#57511yescharacteristic
820C4—22no—
821C4—22no—
822C4—41no—
823C4—42no—
824C4—42no—
825C4—44no—
826C4—42no—
827C4D42×C3112yes—
828C4D42×C3112yes—
829C2—24no—
830C2—42no—
831C2—42no—
832C2—84no—
833C2—82no—
834C2C31×#240311yescharacteristic
835C2C2×C31×#44911yescharacteristic
836C2C31×#300211yescharacteristic
837C2C31×#300311yescharacteristic
838C2C31×#300611yescharacteristic
839C2C31×#318811yescharacteristic
840C2C31×#319411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#525C2semidirect
2. C22×C31×#121C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#450C2semidirect
5. C2×C31×#447C2semidirect
6. C31×#2000C2semidirect
7. C31×#1999C2semidirect
8. C31×#1875C2semidirect
9. C31×#1874C2semidirect
10. C31×#1872C2semidirect
11. C31×#1779C2semidirect
12. C22×#41×C31C22semidirect
16. C22×SD16×C31C22semidirect
17. C22×D8×C31C22semidirect
22. C2×C31×C22⋊Q8C22semidirect
29. C2×C31×#121C22semidirect
33. C2×C31×#117C22semidirect
39. C2×C31×#103C22semidirect
40. C2×C31×#102C22semidirect
41. C2×C31×#102C22semidirect
42. C2×C31×#102C22semidirect
45. C2×C31×C22⋊C8C22semidirect
46. C2×C31×C22⋊C8C22semidirect
47. C31×#340C22semidirect
48. C31×#340C22semidirect
95. C31×C22⋊Q8D4semidirect
104. C31×#121D4semidirect
105. C31×#121D4semidirect
159. C2×Q8×C31C2×D4semidirect
190. C2×D4×C31C2×D4semidirect
243. C4⋊C4×C31C2×D4semidirect
244. C4⋊C4×C31C2×D4semidirect
253. #23920C31direct (N × H)
356. C2×#525C2×C31semidirect
357. C22×#121C2×C31semidirect
358. C2×#449C2×C31semidirect
359. C2×#450C2×C31semidirect
360. C2×#447C2×C31semidirect
361. #2000C2×C31semidirect
362. #1999C2×C31semidirect
363. #1875C2×C31semidirect
364. #1874C2×C31semidirect
365. #1872C2×C31semidirect
366. #1779C2×C31semidirect
403. C22×C31#449semidirect
420. C22×#41C22×C31semidirect
424. C22×SD16C22×C31semidirect
425. C22×D8C22×C31semidirect
430. C2×C22⋊Q8C22×C31semidirect
437. C2×#121C22×C31semidirect
441. C2×#117C22×C31semidirect
447. C2×#103C22×C31semidirect
448. C2×#102C22×C31semidirect
449. C2×#102C22×C31semidirect
450. C2×#102C22×C31semidirect
453. C2×C22⋊C8C22×C31semidirect
454. C2×C22⋊C8C22×C31semidirect
455. #340C22×C31semidirect
456. #340C22×C31semidirect
515. C22⋊Q8D4×C31semidirect
524. #121D4×C31semidirect
525. #121D4×C31semidirect
555. C31#23920direct (N × H)
580. C2×Q8C2×D4×C31semidirect
611. C2×D4C2×D4×C31semidirect
664. C4⋊C4C2×D4×C31semidirect
665. C4⋊C4C2×D4×C31semidirect
812. C22C31×#449semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C22×C31×#1212
C2×C31×#4492
C2×C31×#4502
C2×C31×#4472
C31×#20002
C31×#19992
C31×#18752
C31×#18742
C31×#18722
C31×#17792
#2392031