Finite Group Databasebeta

← C31×#24367 #21481126

Subgroups — C31×#24367 #21481126

Order 7936.

1604 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#461C211yesmaximal, characteristic, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C31×#2432C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2055C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2013C211yesmaximal, characteristic, complemented
10C31×#2012C211yesmaximal, characteristic, complemented
11C31×#1894C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1877C211yesmaximal, characteristic, complemented
14C31×#1851C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C2×C31×AGL(1,ℤ/8)—24no—
19C2×C31×AGL(1,ℤ/8)—24no—
20C2×C31×AGL(1,ℤ/8)—24no—
21C22×SD16×C31C2211yescharacteristic
22C22×SD16×C31C2211yescharacteristic
23C22×SD16×C31C2211yescharacteristic
24C22×SD16×C31C2211yescharacteristic
25C22×D8×C31C2211yescharacteristic
26C22×D8×C31C2211yescharacteristic
27C22×M16×C31C2211yescharacteristic
28C2×C31×C4⋊Q8C2211yescharacteristic, complemented
29C2×C31×#124C2211yescharacteristic, complemented
30C2×C31×C22⋊Q8C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C4×D4×C31C2211yescharacteristic
33C22×C22⋊C4×C31—21no—
34C31×#463—24no—
35C31×#461—24no—
36C31×#450—24no—
37C2×C31×C4⋊C8C2211yescharacteristic, complemented
38C2×C31×C4⋊C8C2211yescharacteristic, complemented
39C2×C31×#103C2211yescharacteristic, complemented
40C2×C31×#103C2211yescharacteristic, complemented
41C2×C31×#103C2211yescharacteristic, complemented
42C2×C31×#103C2211yescharacteristic, complemented
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×C22⋊C8C2211yescharacteristic
48C31×#394—21no—
49C31×#394—21no—
50C31×#391C2211yescharacteristic, complemented
51C31×#390C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#390C2211yescharacteristic, complemented
54C31×#386—21no—
55C31×#386—21no—
56C31×#385—21no—
57C31×#385—21no—
58C31×#380C2211yescharacteristic
59C31×#379—21no—
60C4×C22⋊C4×C31C2211yescharacteristic
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C31×#336C2211yescharacteristic, complemented
65C25×C31—21no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—41no—
71C2×#41×C31—41no—
72C22×Q8×C31C2311yescharacteristic
73C22×Q8×C31C2311yescharacteristic
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—22no—
79C22×D4×C31—41no—
80C22×D4×C31—41no—
81C22×D4×C31D414yes—
82C22×D4×C31C2311yescharacteristic
83C22×D4×C31C2311yescharacteristic
84C22×D4×C31C2311yescharacteristic
85C23×C4×C31—21no—
86C23×C4×C31—21no—
87C23×C4×C31—21no—
88C23×C4×C31C2311yescharacteristic
89C31×AGL(1,ℤ/8)—232no—
90C2×SD16×C31—22no—
91C2×SD16×C31—22no—
92C2×SD16×C31—22no—
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—41no—
100C2×SD16×C31—41no—
101C2×SD16×C31D414yes—
102C2×D8×C31—22no—
103C2×D8×C31—22no—
104C2×D8×C31—22no—
105C2×D8×C31—22no—
106C2×D8×C31—22no—
107C2×D8×C31D414yes—
108C2×M16×C31—22no—
109C2×M16×C31—22no—
110C2×M16×C31—22no—
111C22×C8×C31C2311yescharacteristic
112C22×C8×C31C2311yescharacteristic
113C22×C8×C31C2311yescharacteristic
114C22×C8×C31C2311yescharacteristic
115C31×C4⋊Q8—22no—
116C31×C4⋊Q8—41no—
117C31×#124—22no—
118C31×#124—41no—
119C31×C22⋊Q8—22no—
120C31×C22⋊Q8—22no—
121C4×D4×C31—22no—
122C4×D4×C31—22no—
123C4×D4×C31—41no—
124C4×D4×C31—41no—
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31C2311yescharacteristic
129C2×C4⋊C4×C31C2311yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—44no—
144C2×C22⋊C4×C31D411yescharacteristic
145C2×C22⋊C4×C31D411yescharacteristic
146C2×C42×C31C2311yescharacteristic
147C2×C42×C31C2311yescharacteristic
148C31×C4⋊C8—22no—
149C31×C4⋊C8—22no—
150C31×#103—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#103—41no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—41no—
158C31×C22⋊C8—22no—
159C31×#95—21no—
160C31×#95—21no—
161C31×#95—21no—
162C31×#95D411yescharacteristic
163C31×#95D411yescharacteristic
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—24no—
168C24×C31—42no—
169C24×C31—42no—
170C24×C31—42no—
171C24×C31—42no—
172C24×C31—81no—
173C24×C31—81no—
174C24×C31C2×D411yescharacteristic
175#41×C31—28no—
176#41×C31—44no—
177#41×C31—44no—
178#41×C31—44no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31—21no—
188C2×Q8×C31—21no—
189C2×Q8×C31—21no—
190C2×Q8×C31C2×D412yes—
191C2×D4×C31—28no—
192C2×D4×C31—24no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—44no—
207C2×D4×C31—44no—
208C2×D4×C31—44no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31C2×D412yes—
215C2×D4×C31C2×D412yes—
216C2×D4×C31C2×D412yes—
217C2×D4×C31C2×D412yes—
218C2×D4×C31C2×D412yes—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—42no—
229C22×C4×C31—42no—
230C22×C4×C31—42no—
231C22×C4×C31—42no—
232C22×C4×C31—42no—
233C22×C4×C31—42no—
234C22×C4×C31—42no—
235C22×C4×C31—81no—
236C22×C4×C31—81no—
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31C2×D411yescharacteristic
239C22×C4×C31C2×D411yescharacteristic
240C22×C4×C31C2×D411yescharacteristic
241C22×C4×C31C2×D412yes—
242C22×C4×C31C2×D411yescharacteristic
243C22×C4×C31#4112yes—
244C22×C4×C31C2411yescharacteristic
245SD16×C31—28no—
246SD16×C31—28no—
247SD16×C31—44no—
248SD16×C31—44no—
249D8×C31—28no—
250D8×C31—28no—
251M16×C31—28no—
252C2×C8×C31—21no—
253C2×C8×C31—21no—
254C2×C8×C31—21no—
255C2×C8×C31—21no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C2×C8×C31—21no—
262C2×C8×C31C2×D412yes—
263C2×C8×C31C2×D412yes—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—21no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—21no—
270C4⋊C4×C31—42no—
271C4⋊C4×C31—42no—
272C4⋊C4×C31—42no—
273C22⋊C4×C31—22no—
274C22⋊C4×C31—41no—
275C22⋊C4×C31—42no—
276C22⋊C4×C31—42no—
277C22⋊C4×C31—42no—
278C22⋊C4×C31—42no—
279C22⋊C4×C31—42no—
280C22⋊C4×C31—42no—
281C22⋊C4×C31—42no—
282C22⋊C4×C31—42no—
283C22⋊C4×C31—42no—
284C22⋊C4×C31—42no—
285C22⋊C4×C31—81no—
286C22⋊C4×C31—81no—
287C42×C31—21no—
288C42×C31—21no—
289C42×C31—21no—
290C42×C31—21no—
291#24367C3111yesmaximal, characteristic, direct product factor, Sylow
292C23×C31—22no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—48no—
304C23×C31—48no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—84no—
322C23×C31—84no—
323C23×C31—84no—
324C23×C31—84no—
325C23×C31—84no—
326C23×C31#12112yes—
327C23×C31C22×D411yescharacteristic
328Q8×C31—22no—
329Q8×C31—22no—
330Q8×C31—41no—
331Q8×C31—41no—
332Q8×C31—41no—
333Q8×C31—41no—
334Q8×C31—41no—
335Q8×C31—41no—
336D4×C31—22no—
337D4×C31—22no—
338D4×C31—22no—
339D4×C31—22no—
340D4×C31—22no—
341D4×C31—22no—
342D4×C31—22no—
343D4×C31—48no—
344D4×C31—48no—
345D4×C31—41no—
346D4×C31—41no—
347D4×C31—41no—
348D4×C31—41no—
349D4×C31#12014yes—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—21no—
353C2×C4×C31—21no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—21no—
361C2×C4×C31—22no—
362C2×C4×C31—21no—
363C2×C4×C31—21no—
364C2×C4×C31—21no—
365C2×C4×C31—21no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—48no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—84no—
384C2×C4×C31—84no—
385C2×C4×C31#12112yes—
386C2×C4×C31AGL(1,ℤ/8)12yescomplemented
387C2×C4×C31C22×D411yescharacteristic
388C2×C4×C31C22×D411yescharacteristic
389C2×C4×C31C22×D411yescharacteristic
390C2×C4×C31C2×#4111yescharacteristic
391C2×C4×C31H(5,𝔽2)11yescharacteristic
392C2×C4×C31H(5,𝔽2)11yescharacteristic
393C8×C31—22no—
394C8×C31—22no—
395C8×C31—41no—
396C8×C31—41no—
397C22×AGL(1,ℤ/8)C2×C3111yescharacteristic
398C2×#463C2×C3111yescharacteristic, complemented
399C2×#461C2×C3111yescharacteristic, complemented
400C2×#450C2×C3111yescharacteristic, complemented
401#2432C2×C3111yescharacteristic, complemented
402D4×C22⋊C4C2×C3111yescharacteristic, complemented
403#2055C2×C3111yescharacteristic, complemented
404#2054C2×C3111yescharacteristic, complemented
405#2013C2×C3111yescharacteristic, complemented
406#2012C2×C3111yescharacteristic, complemented
407#1894C2×C3111yescharacteristic, complemented
408#1879C2×C3111yescharacteristic, complemented
409#1877C2×C3111yescharacteristic, complemented
410#1851C2×C3111yescharacteristic, complemented
411#1788C2×C3111yescharacteristic, complemented
412C22×C31—22no—
413C22×C31—24no—
414C22×C31—22no—
415C22×C31—22no—
416C22×C31—42no—
417C22×C31—41no—
418C22×C31—41no—
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—41no—
422C22×C31—41no—
423C22×C31—42no—
424C22×C31—42no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—42no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—42no—
431C22×C31—42no—
432C22×C31—816no—
433C22×C31—81no—
434C22×C31—81no—
435C22×C31—81no—
436C22×C31—81no—
437C22×C31—81no—
438C22×C31—81no—
439C22×C31—81no—
440C22×C31—81no—
441C22×C31C2×#12111yescharacteristic
442C22×C31D4211yescharacteristic
443C22×C31D4211yescharacteristic
444C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
445C22×C31#57511yescharacteristic
446C22×C31#57711yescharacteristic
447C22×C31#57711yescharacteristic
448C4×C31—22no—
449C4×C31—22no—
450C4×C31—42no—
451C4×C31—41no—
452C4×C31—41no—
453C4×C31—41no—
454C4×C31—81no—
455C4×C31—81no—
456C4×C31—81no—
457C4×C31—81no—
458C4×C31C2×#12011yescharacteristic
459C4×C31#53411yescharacteristic
460C4×C31#54611yescharacteristic
461C4×C31#54611yescharacteristic
462C22×#41C22×C3111yescharacteristic
463C23×D4C22×C3111yescharacteristic
464C2×AGL(1,ℤ/8)—24no—
465C2×AGL(1,ℤ/8)—24no—
466C2×AGL(1,ℤ/8)—24no—
467C22×SD16C22×C3111yescharacteristic
468C22×SD16C22×C3111yescharacteristic
469C22×SD16C22×C3111yescharacteristic
470C22×SD16C22×C3111yescharacteristic
471C22×D8C22×C3111yescharacteristic
472C22×D8C22×C3111yescharacteristic
473C22×M16C22×C3111yescharacteristic
474C2×C4⋊Q8C22×C3111yescharacteristic, complemented
475C2×#124C22×C3111yescharacteristic, complemented
476C2×C22⋊Q8C22×C3111yescharacteristic
477C2×C4×D4C22×C3111yescharacteristic
478C2×C4×D4C22×C3111yescharacteristic
479C22×C22⋊C4—21no—
480#463—24no—
481#461—24no—
482#450—24no—
483C2×C4⋊C8C22×C3111yescharacteristic, complemented
484C2×C4⋊C8C22×C3111yescharacteristic, complemented
485C2×#103C22×C3111yescharacteristic, complemented
486C2×#103C22×C3111yescharacteristic, complemented
487C2×#103C22×C3111yescharacteristic, complemented
488C2×#103C22×C3111yescharacteristic, complemented
489C2×#102C22×C3111yescharacteristic
490C2×#102C22×C3111yescharacteristic
491C2×#102C22×C3111yescharacteristic, complemented
492C2×#102C22×C3111yescharacteristic, complemented
493C2×C22⋊C8C22×C3111yescharacteristic
494#394—21no—
495#394—21no—
496#391C22×C3111yescharacteristic, complemented
497#390C22×C3111yescharacteristic
498#390C22×C3111yescharacteristic
499#390C22×C3111yescharacteristic, complemented
500#386—21no—
501#386—21no—
502#385—21no—
503#385—21no—
504#380C22×C3111yescharacteristic
505#379—21no—
506C4×C22⋊C4C22×C3111yescharacteristic
507#340C22×C3111yescharacteristic, complemented
508#340C22×C3111yescharacteristic, complemented
509#336C22×C3111yescharacteristic, complemented
510#336C22×C3111yescharacteristic, complemented
511C2×C31—42no—
512C2×C31—44no—
513C2×C31—82no—
514C2×C31—82no—
515C2×C31#241011yescharacteristic
516C2×C31#303611yescharacteristic
517C2×C31#304211yescharacteristic
518C2×C31#326511yescharacteristic
519C2×C31#326711yescharacteristic
520C2×C31#327211yescharacteristic
521C2×C31#327511yescharacteristic
522C25—21no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C22×Q8C23×C3111yescharacteristic
530C22×Q8C23×C3111yescharacteristic
531C22×D4—22no—
532C22×D4—22no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—41no—
537C22×D4—41no—
538C22×D4D4×C3114yes—
539C22×D4C23×C3111yescharacteristic
540C22×D4C23×C3111yescharacteristic
541C22×D4C23×C3111yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C23×C3111yescharacteristic
546AGL(1,ℤ/8)—232no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16D4×C3114yes—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8D4×C3114yes—
565C2×M16—22no—
566C2×M16—22no—
567C2×M16—22no—
568C22×C8C23×C3111yescharacteristic
569C22×C8C23×C3111yescharacteristic
570C22×C8C23×C3111yescharacteristic
571C22×C8C23×C3111yescharacteristic
572C4⋊Q8—22no—
573C4⋊Q8—41no—
574#124—22no—
575#124—41no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—41no—
581C4×D4—41no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4C23×C3111yescharacteristic
586C2×C4⋊C4C23×C3111yescharacteristic
587C2×C4⋊C4C23×C3111yescharacteristic
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—44no—
601C2×C22⋊C4D4×C3111yescharacteristic
602C2×C22⋊C4D4×C3111yescharacteristic
603C2×C42C23×C3111yescharacteristic
604C2×C42C23×C3111yescharacteristic
605C4⋊C8—22no—
606C4⋊C8—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—41no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—41no—
615C22⋊C8—22no—
616#95—21no—
617#95—21no—
618#95—21no—
619#95D4×C3111yescharacteristic
620#95D4×C3111yescharacteristic
621C31#2436711yescharacteristic, direct product factor, Sylow
622C24—21no—
623C24—21no—
624C24—21no—
625C24—24no—
626C24—42no—
627C24—42no—
628C24—42no—
629C24—42no—
630C24—81no—
631C24—81no—
632C24C2×D4×C3111yescharacteristic
633#41—28no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×D4×C3112yes—
649C2×D4—28no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C3112yes—
673C2×D4C2×D4×C3112yes—
674C2×D4C2×D4×C3112yes—
675C2×D4C2×D4×C3112yes—
676C2×D4C2×D4×C3112yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—81no—
694C22×C4—81no—
695C22×C4C2×D4×C3111yescharacteristic
696C22×C4C2×D4×C3111yescharacteristic
697C22×C4C2×D4×C3111yescharacteristic
698C22×C4C2×D4×C3111yescharacteristic
699C22×C4C2×D4×C3112yes—
700C22×C4C2×D4×C3111yescharacteristic
701C22×C4#41×C3112yes—
702C22×C4C24×C3111yescharacteristic
703SD16—28no—
704SD16—28no—
705SD16—44no—
706SD16—44no—
707D8—28no—
708D8—28no—
709M16—28no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8C2×D4×C3112yes—
721C2×C8C2×D4×C3112yes—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C22⋊C4—22no—
732C22⋊C4—41no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C42—21no—
746C42—21no—
747C42—21no—
748C42—21no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—22no—
760C23—48no—
761C23—48no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—84no—
779C23—84no—
780C23—84no—
781C23—84no—
782C23—84no—
783C23C31×#12112yes—
784C23C22×D4×C3111yescharacteristic
785Q8—22no—
786Q8—22no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793D4—22no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—48no—
801D4—48no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4C31×#12014yes—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4C31×#12112yes—
843C2×C4C31×AGL(1,ℤ/8)12yescomplemented
844C2×C4C22×D4×C3111yescharacteristic
845C2×C4C22×D4×C3111yescharacteristic
846C2×C4C22×D4×C3111yescharacteristic
847C2×C4C2×#41×C3111yescharacteristic
848C2×C4C31×H(5,𝔽2)11yescharacteristic
849C2×C4C31×H(5,𝔽2)11yescharacteristic
850C8—22no—
851C8—22no—
852C8—41no—
853C8—41no—
854C22—22no—
855C22—24no—
856C22—22no—
857C22—22no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—816no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×C31×#12111yescharacteristic
884C22D42×C3111yescharacteristic
885C22D42×C3111yescharacteristic
886C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
887C22C31×#57511yescharacteristic
888C22C31×#57711yescharacteristic
889C22C31×#57711yescharacteristic
890C4—22no—
891C4—22no—
892C4—42no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×C31×#12011yescharacteristic
901C4C31×#53411yescharacteristic
902C4C31×#54611yescharacteristic
903C4C31×#54611yescharacteristic
904C2—42no—
905C2—44no—
906C2—82no—
907C2—82no—
908C2C31×#241011yescharacteristic
909C2C31×#303611yescharacteristic
910C2C31×#304211yescharacteristic
911C2C31×#326511yescharacteristic
912C2C31×#326711yescharacteristic
913C2C31×#327211yescharacteristic
914C2C31×#327511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×C31×AGL(1,ℤ/8)C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#463C2semidirect
3. C2×C31×#461C2semidirect
4. C2×C31×#450C2semidirect
5. C31×#2432C2semidirect
6. D4×C22⋊C4×C31C2semidirect
7. C31×#2055C2semidirect
8. C31×#2054C2semidirect
9. C31×#2013C2semidirect
10. C31×#2012C2semidirect
11. C31×#1894C2semidirect
12. C31×#1879C2semidirect
13. C31×#1877C2semidirect
14. C31×#1851C2semidirect
15. C31×#1788C2semidirect
28. C2×C31×C4⋊Q8C22semidirect
29. C2×C31×#124C22semidirect
37. C2×C31×C4⋊C8C22semidirect
38. C2×C31×C4⋊C8C22semidirect
39. C2×C31×#103C22semidirect
40. C2×C31×#103C22semidirect
41. C2×C31×#103C22semidirect
42. C2×C31×#103C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
50. C31×#391C22semidirect
53. C31×#390C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#336C22semidirect
64. C31×#336C22semidirect
291. #24367C31direct (N × H)
386. C2×C4×C31AGL(1,ℤ/8)semidirect
398. C2×#463C2×C31semidirect
399. C2×#461C2×C31semidirect
400. C2×#450C2×C31semidirect
401. #2432C2×C31semidirect
402. D4×C22⋊C4C2×C31semidirect
403. #2055C2×C31semidirect
404. #2054C2×C31semidirect
405. #2013C2×C31semidirect
406. #2012C2×C31semidirect
407. #1894C2×C31semidirect
408. #1879C2×C31semidirect
409. #1877C2×C31semidirect
410. #1851C2×C31semidirect
411. #1788C2×C31semidirect
474. C2×C4⋊Q8C22×C31semidirect
475. C2×#124C22×C31semidirect
483. C2×C4⋊C8C22×C31semidirect
484. C2×C4⋊C8C22×C31semidirect
485. C2×#103C22×C31semidirect
486. C2×#103C22×C31semidirect
487. C2×#103C22×C31semidirect
488. C2×#103C22×C31semidirect
491. C2×#102C22×C31semidirect
492. C2×#102C22×C31semidirect
496. #391C22×C31semidirect
499. #390C22×C31semidirect
507. #340C22×C31semidirect
508. #340C22×C31semidirect
509. #336C22×C31semidirect
510. #336C22×C31semidirect
621. C31#24367direct (N × H)
843. 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×#4632
C2×C31×#4612
C2×C31×#4502
C31×#24322
D4×C22⋊C4×C312
C31×#20552
C31×#20542
C31×#20132
C31×#20122
C31×#18942
C31×#18792
C31×#18772
C31×#18512
C31×#17882
#2436731