Finite Group Databasebeta

← C31×#23864 #21480623

Subgroups — C31×#23864 #21480623

Order 7936.

1950 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C31×#547C211yesmaximal, characteristic, complemented
3C2×C31×#449C212yesmaximal, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C31×#2408C211yesmaximal, characteristic, complemented
6C31×#2013C212yesmaximal, complemented
7C31×#2000C212yesmaximal, complemented
8C31×#1894C211yesmaximal, characteristic, complemented
9C31×#1879C212yesmaximal, complemented
10C31×#1870C211yesmaximal, characteristic, complemented
11C31×#1788C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C22×#41×C31C2211yescharacteristic, complemented
14C23×D4×C31C2211yescharacteristic
15C2×C31×AGL(1,ℤ/8)—24no—
16C2×C31×AGL(1,ℤ/8)—28no—
17C22×SD16×C31C2212yes—
18C22×SD16×C31C2212yes—
19C22×D8×C31C2212yes—
20C22×M16×C31C2211yescharacteristic
21C31×#547—24no—
22C31×#547—24no—
23C2×C31×C4⋊Q8C2211yescharacteristic, complemented
24C2×C31×#123—21no—
25C2×C31×#123—21no—
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×C22⋊Q8C2211yescharacteristic, complemented
28C2×C31×#121—21no—
29C2×C31×#121C2212yes—
30C2×C31×#120—21no—
31C2×C4×D4×C31C2211yescharacteristic
32C2×C4×D4×C31C2211yescharacteristic, complemented
33C22×C4⋊C4×C31—21no—
34C31×#450—24no—
35C31×#449—28no—
36C2×C31×#103C2212yescomplemented
37C2×C31×#103C2212yescomplemented
38C2×C31×#102C2212yes—
39C2×C31×#102C2212yescomplemented
40C2×C31×C22⋊C8C2211yescharacteristic
41C2×C31×C22⋊C8C2212yescomplemented
42C31×#394—21no—
43C31×#392—21no—
44C31×#390C2212yes—
45C31×#380C2211yescharacteristic
46C31×#379—21no—
47C31×#340C2212yescomplemented
48C31×#336C2212yescomplemented
49C25×C31—21no—
50C2×#41×C31—22no—
51C2×#41×C31—22no—
52C2×#41×C31—22no—
53C2×#41×C31—24no—
54C2×#41×C31—24no—
55C2×#41×C31—42no—
56C2×#41×C31—42no—
57C2×#41×C31D414yescomplemented
58C22×Q8×C31C2311yescharacteristic
59C22×Q8×C31C2311yescharacteristic
60C22×D4×C31—24no—
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—42no—
68C22×D4×C31D411yescharacteristic
69C22×D4×C31C2312yes—
70C22×D4×C31C2311yescharacteristic
71C23×C4×C31—21no—
72C23×C4×C31—21no—
73C23×C4×C31—21no—
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C31×AGL(1,ℤ/8)—232no—
77C2×SD16×C31—24no—
78C2×SD16×C31—24no—
79C2×SD16×C31—24no—
80C2×SD16×C31—24no—
81C2×SD16×C31—24no—
82C2×SD16×C31—42no—
83C2×D8×C31—24no—
84C2×D8×C31—24no—
85C2×D8×C31D418yescomplemented
86C2×M16×C31—22no—
87C2×M16×C31—24no—
88C22×C8×C31C2312yes—
89C22×C8×C31C2312yes—
90C31×C4⋊Q8—22no—
91C31×C4⋊Q8—22no—
92C31×#123—28no—
93C31×#123—28no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8D414yescomplemented
98C31×#121—28no—
99C31×#121—24no—
100C31×#121—42no—
101C31×#120—44no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C2×C4⋊C4×C31—28no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31C2312yes—
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31D411yescharacteristic
122C2×C22⋊C4×C31D411yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C31×#103—24no—
125C31×#103—42no—
126C31×#102—24no—
127C31×#102—24no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—24no—
130C31×#95—21no—
131C24×C31—21no—
132C24×C31—22no—
133C24×C31—44no—
134C24×C31—42no—
135C24×C31—42no—
136C24×C31—42no—
137C24×C31—82no—
138C24×C31C2×D411yescharacteristic
139C24×C31C2×D411yescharacteristic
140#41×C31—28no—
141#41×C31—44no—
142#41×C31—48no—
143#41×C31—48no—
144#41×C31—44no—
145#41×C31—44no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—22no—
149C2×Q8×C31—22no—
150C2×Q8×C31—22no—
151C2×Q8×C31—22no—
152C2×Q8×C31C2×D412yes—
153C2×Q8×C31C2×D412yes—
154C2×D4×C31—28no—
155C2×D4×C31—24no—
156C2×D4×C31—22no—
157C2×D4×C31—24no—
158C2×D4×C31—22no—
159C2×D4×C31—21no—
160C2×D4×C31—22no—
161C2×D4×C31—22no—
162C2×D4×C31—22no—
163C2×D4×C31—22no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—48no—
167C2×D4×C31—41no—
168C2×D4×C31—44no—
169C2×D4×C31—44no—
170C2×D4×C31—44no—
171C2×D4×C31—44no—
172C2×D4×C31—44no—
173C2×D4×C31—44no—
174C2×D4×C31—42no—
175C2×D4×C31—82no—
176C2×D4×C31C2×D414yes—
177C2×D4×C31C2×D414yes—
178C2×D4×C31C2×D412yes—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—24no—
182C22×C4×C31—24no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—24no—
187C22×C4×C31—22no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—44no—
193C22×C4×C31—44no—
194C22×C4×C31—42no—
195C22×C4×C31—42no—
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D412yes—
200C22×C4×C31C2×D412yes—
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2411yescharacteristic
203SD16×C31—216no—
204SD16×C31—48no—
205D8×C31—216no—
206M16×C31—28no—
207C2×C8×C31—22no—
208C2×C8×C31—22no—
209C2×C8×C31—22no—
210C2×C8×C31—22no—
211C2×C8×C31—22no—
212C2×C8×C31C2×D414yes—
213C4⋊C4×C31—24no—
214C4⋊C4×C31—24no—
215C4⋊C4×C31—24no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—24no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31C2×D412yes—
222C22⋊C4×C31—24no—
223C22⋊C4×C31—24no—
224C22⋊C4×C31—24no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—44no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—44no—
230C22⋊C4×C31—82no—
231C42×C31—21no—
232C42×C31—21no—
233#23864C3111yesmaximal, characteristic, direct product factor, Sylow
234C23×C31—22no—
235C23×C31—22no—
236C23×C31—24no—
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—22no—
240C23×C31—21no—
241C23×C31—24no—
242C23×C31—22no—
243C23×C31—21no—
244C23×C31—21no—
245C23×C31—22no—
246C23×C31—48no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31—84no—
257C23×C31—84no—
258C23×C31—88no—
259C23×C31—88no—
260C23×C31#12012yes—
261C23×C31C22×D411yescharacteristic
262Q8×C31—22no—
263Q8×C31—22no—
264Q8×C31—24no—
265Q8×C31—41no—
266Q8×C31—41no—
267Q8×C31—42no—
268D4×C31—24no—
269D4×C31—22no—
270D4×C31—24no—
271D4×C31—24no—
272D4×C31—44no—
273D4×C31—48no—
274D4×C31—48no—
275D4×C31—48no—
276D4×C31—42no—
277D4×C31—42no—
278D4×C31—88no—
279D4×C31#12014yescomplemented
280C2×C4×C31—21no—
281C2×C4×C31—22no—
282C2×C4×C31—21no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—24no—
286C2×C4×C31—21no—
287C2×C4×C31—22no—
288C2×C4×C31—21no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—48no—
294C2×C4×C31—48no—
295C2×C4×C31—48no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31#12012yes—
307C2×C4×C31AGL(1,ℤ/8)12yescomplemented
308C2×C4×C31C22×D411yescharacteristic
309C2×C4×C31C22×D412yes—
310C2×C4×C31C22×D411yescharacteristic
311C2×C4×C31H(5,𝔽2)12yes—
312C8×C31—24no—
313C8×C31—42no—
314C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
315C2×#547C2×C3111yescharacteristic, complemented
316C2×#449C2×C3112yescomplemented
317C2×#450C2×C3111yescharacteristic, complemented
318#2408C2×C3111yescharacteristic, complemented
319#2013C2×C3112yescomplemented
320#2000C2×C3112yescomplemented
321#1894C2×C3111yescharacteristic, complemented
322#1879C2×C3112yescomplemented
323#1870C2×C3111yescharacteristic, complemented
324#1788C2×C3111yescharacteristic, complemented
325C22×C31—22no—
326C22×C31—24no—
327C22×C31—22no—
328C22×C31—22no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31—42no—
332C22×C31—44no—
333C22×C31—42no—
334C22×C31—44no—
335C22×C31—41no—
336C22×C31—44no—
337C22×C31—41no—
338C22×C31—41no—
339C22×C31—42no—
340C22×C31—44no—
341C22×C31—42no—
342C22×C31—44no—
343C22×C31—816no—
344C22×C31—82no—
345C22×C31—82no—
346C22×C31—82no—
347C22×C31—82no—
348C22×C31C2×#12011yescharacteristic
349C22×C31D4212yes—
350C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C31#57511yescharacteristic
352C22×C31#57712yes—
353C4×C31—22no—
354C4×C31—22no—
355C4×C31—41no—
356C4×C31—42no—
357C4×C31—42no—
358C4×C31—42no—
359C4×C31—41no—
360C4×C31—82no—
361C4×C31C2×#12011yescharacteristic
362C4×C31#53411yescharacteristic
363C4×C31D4212yes—
364C22×#41C22×C3111yescharacteristic
365C22×#41C22×C3111yescharacteristic, complemented
366C23×D4C22×C3111yescharacteristic
367C2×AGL(1,ℤ/8)—24no—
368C2×AGL(1,ℤ/8)—28no—
369C22×SD16C22×C3112yes—
370C22×SD16C22×C3112yes—
371C22×D8C22×C3112yes—
372C22×M16C22×C3111yescharacteristic
373#547—24no—
374#547—24no—
375C2×C4⋊Q8C22×C3111yescharacteristic, complemented
376C2×#123—21no—
377C2×#123—21no—
378C2×C22⋊Q8C22×C3111yescharacteristic
379C2×C22⋊Q8C22×C3111yescharacteristic, complemented
380C2×#121—21no—
381C2×#121C22×C3112yes—
382C2×#120—21no—
383C2×C4×D4C22×C3111yescharacteristic
384C2×C4×D4C22×C3111yescharacteristic, complemented
385C22×C4⋊C4—21no—
386#450—24no—
387#449—28no—
388C2×#103C22×C3112yescomplemented
389C2×#103C22×C3112yescomplemented
390C2×#102C22×C3112yes—
391C2×#102C22×C3112yescomplemented
392C2×C22⋊C8C22×C3111yescharacteristic
393C2×C22⋊C8C22×C3112yescomplemented
394#394—21no—
395#392—21no—
396#390C22×C3112yes—
397#380C22×C3111yescharacteristic
398#379—21no—
399#340C22×C3112yescomplemented
400#336C22×C3112yescomplemented
401C2×C31—42no—
402C2×C31—44no—
403C2×C31—81no—
404C2×C31—84no—
405C2×C31#240311yescharacteristic
406C2×C31#300611yescharacteristic
407C2×C31#301011yescharacteristic
408C2×C31#326712yes—
409C2×C31#327212yes—
410C25—21no—
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—24no—
415C2×#41—24no—
416C2×#41—42no—
417C2×#41—42no—
418C2×#41D4×C3114yescomplemented
419C22×Q8C23×C3111yescharacteristic
420C22×Q8C23×C3111yescharacteristic
421C22×D4—24no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—22no—
425C22×D4—22no—
426C22×D4—22no—
427C22×D4—21no—
428C22×D4—42no—
429C22×D4D4×C3111yescharacteristic
430C22×D4C23×C3112yes—
431C22×D4C23×C3111yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4C23×C3111yescharacteristic
436C23×C4C23×C3111yescharacteristic
437AGL(1,ℤ/8)—232no—
438C2×SD16—24no—
439C2×SD16—24no—
440C2×SD16—24no—
441C2×SD16—24no—
442C2×SD16—24no—
443C2×SD16—42no—
444C2×D8—24no—
445C2×D8—24no—
446C2×D8D4×C3118yescomplemented
447C2×M16—22no—
448C2×M16—24no—
449C22×C8C23×C3112yes—
450C22×C8C23×C3112yes—
451C4⋊Q8—22no—
452C4⋊Q8—22no—
453#123—28no—
454#123—28no—
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—22no—
458C22⋊Q8D4×C3114yescomplemented
459#121—28no—
460#121—24no—
461#121—42no—
462#120—44no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—22no—
466C4×D4—22no—
467C2×C4⋊C4—28no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4D4×C3111yescharacteristic
473C2×C4⋊C4C23×C3112yes—
474C2×C4⋊C4C23×C3111yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4D4×C3111yescharacteristic
483C2×C22⋊C4D4×C3111yescharacteristic
484C2×C42C23×C3111yescharacteristic
485#103—24no—
486#103—42no—
487#102—24no—
488#102—24no—
489C22⋊C8—22no—
490C22⋊C8—24no—
491#95—21no—
492C31#2386411yescharacteristic, direct product factor, Sylow
493C24—21no—
494C24—22no—
495C24—44no—
496C24—42no—
497C24—42no—
498C24—42no—
499C24—82no—
500C24C2×D4×C3111yescharacteristic
501C24C2×D4×C3111yescharacteristic
502#41—28no—
503#41—44no—
504#41—48no—
505#41—48no—
506#41—44no—
507#41—44no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8C2×D4×C3112yes—
515C2×Q8C2×D4×C3112yes—
516C2×D4—28no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—24no—
520C2×D4—22no—
521C2×D4—21no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—48no—
529C2×D4—41no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—42no—
537C2×D4—82no—
538C2×D4C2×D4×C3114yes—
539C2×D4C2×D4×C3114yes—
540C2×D4C2×D4×C3112yes—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4C2×D4×C3111yescharacteristic
559C22×C4C2×D4×C3111yescharacteristic
560C22×C4C2×D4×C3111yescharacteristic
561C22×C4C2×D4×C3112yes—
562C22×C4C2×D4×C3112yes—
563C22×C4C2×D4×C3111yescharacteristic
564C22×C4C24×C3111yescharacteristic
565SD16—216no—
566SD16—48no—
567D8—216no—
568M16—28no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8C2×D4×C3114yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4C2×D4×C3112yes—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—44no—
590C22⋊C4—42no—
591C22⋊C4—44no—
592C22⋊C4—82no—
593C42—21no—
594C42—21no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—21no—
599C23—21no—
600C23—22no—
601C23—21no—
602C23—24no—
603C23—22no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—48no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—84no—
618C23—84no—
619C23—88no—
620C23—88no—
621C23C31×#12012yes—
622C23C22×D4×C3111yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—24no—
626Q8—41no—
627Q8—41no—
628Q8—42no—
629D4—24no—
630D4—22no—
631D4—24no—
632D4—24no—
633D4—44no—
634D4—48no—
635D4—48no—
636D4—48no—
637D4—42no—
638D4—42no—
639D4—88no—
640D4C31×#12014yescomplemented
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—48no—
655C2×C4—48no—
656C2×C4—48no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4C31×#12012yes—
668C2×C4C31×AGL(1,ℤ/8)12yescomplemented
669C2×C4C22×D4×C3111yescharacteristic
670C2×C4C22×D4×C3112yes—
671C2×C4C22×D4×C3111yescharacteristic
672C2×C4C31×H(5,𝔽2)12yes—
673C8—24no—
674C8—42no—
675C22—22no—
676C22—24no—
677C22—22no—
678C22—22no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—44no—
683C22—42no—
684C22—44no—
685C22—41no—
686C22—44no—
687C22—41no—
688C22—41no—
689C22—42no—
690C22—44no—
691C22—42no—
692C22—44no—
693C22—816no—
694C22—82no—
695C22—82no—
696C22—82no—
697C22—82no—
698C22C2×C31×#12011yescharacteristic
699C22D42×C3112yes—
700C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
701C22C31×#57511yescharacteristic
702C22C31×#57712yes—
703C4—22no—
704C4—22no—
705C4—41no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—41no—
710C4—82no—
711C4C2×C31×#12011yescharacteristic
712C4C31×#53411yescharacteristic
713C4D42×C3112yes—
714C2—42no—
715C2—44no—
716C2—81no—
717C2—84no—
718C2C31×#240311yescharacteristic
719C2C31×#300611yescharacteristic
720C2C31×#301011yescharacteristic
721C2C31×#326712yes—
722C2C31×#327212yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×AGL(1,ℤ/8)C2semidirect
2. C2×C31×#547C2semidirect
3. C2×C31×#449C2semidirect
4. C2×C31×#450C2semidirect
5. C31×#2408C2semidirect
6. C31×#2013C2semidirect
7. C31×#2000C2semidirect
8. C31×#1894C2semidirect
9. C31×#1879C2semidirect
10. C31×#1870C2semidirect
11. C31×#1788C2semidirect
13. C22×#41×C31C22semidirect
23. C2×C31×C4⋊Q8C22semidirect
27. C2×C31×C22⋊Q8C22semidirect
32. C2×C4×D4×C31C22semidirect
36. C2×C31×#103C22semidirect
37. C2×C31×#103C22semidirect
39. C2×C31×#102C22semidirect
41. C2×C31×C22⋊C8C22semidirect
47. C31×#340C22semidirect
48. C31×#336C22semidirect
57. C2×#41×C31D4semidirect
85. C2×D8×C31D4semidirect
97. C31×C22⋊Q8D4semidirect
233. #23864C31direct (N × H)
279. D4×C31#120semidirect
307. C2×C4×C31AGL(1,ℤ/8)semidirect
314. C22×AGL(1,ℤ/8)C2×C31semidirect
315. C2×#547C2×C31semidirect
316. C2×#449C2×C31semidirect
317. C2×#450C2×C31semidirect
318. #2408C2×C31semidirect
319. #2013C2×C31semidirect
320. #2000C2×C31semidirect
321. #1894C2×C31semidirect
322. #1879C2×C31semidirect
323. #1870C2×C31semidirect
324. #1788C2×C31semidirect
365. C22×#41C22×C31semidirect
375. C2×C4⋊Q8C22×C31semidirect
379. C2×C22⋊Q8C22×C31semidirect
384. C2×C4×D4C22×C31semidirect
388. C2×#103C22×C31semidirect
389. C2×#103C22×C31semidirect
391. C2×#102C22×C31semidirect
393. C2×C22⋊C8C22×C31semidirect
399. #340C22×C31semidirect
400. #336C22×C31semidirect
418. C2×#41D4×C31semidirect
446. C2×D8D4×C31semidirect
458. C22⋊Q8D4×C31semidirect
492. C31#23864direct (N × H)
640. D4C31×#120semidirect
668. C2×C4C31×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C22×C31×AGL(1,ℤ/8)2
C2×C31×#5472
C2×C31×#4492
C2×C31×#4502
C31×#24082
C31×#20132
C31×#20002
C31×#18942
C31×#18792
C31×#18702
C31×#17882
#2386431