Finite Group Databasebeta

← C31×#24275 #21481034

Subgroups — C31×#24275 #21481034

Order 7936.

1614 conjugacy classes of subgroups.

The subgroup lattice has 950 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×#466C211yesmaximal, characteristic, complemented
3C2×C31×#465C211yesmaximal, characteristic, complemented
4C2×C31×#435C211yesmaximal, characteristic, complemented
5C31×#2408C211yesmaximal, characteristic, complemented
6C31×#2407C211yesmaximal, characteristic, complemented
7C31×#2055C211yesmaximal, characteristic, complemented
8C31×#2054C211yesmaximal, characteristic, complemented
9C31×#2000C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1973C211yesmaximal, characteristic, complemented
12C31×#1972C211yesmaximal, characteristic, complemented
13C31×#1809C211yesmaximal, characteristic, complemented
14C31×#1788C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, 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×D8×C31C2211yescharacteristic
24C22×D8×C31C2211yescharacteristic
25C22×M16×C31C2211yescharacteristic
26C23×C8×C31C2211yescharacteristic, complemented
27C2×C31×C22⋊Q8C2211yescharacteristic, complemented
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic, complemented
31C2×C31×#120—21no—
32C2×C4×D4×C31C2211yescharacteristic
33C31×#466—24no—
34C31×#465—24no—
35C31×#435—24no—
36C2×C31×#107C2211yescharacteristic, complemented
37C2×C31×#106C2211yescharacteristic, complemented
38C2×C31×C4⋊C8C2211yescharacteristic, complemented
39C2×C31×#103C2211yescharacteristic, complemented
40C2×C31×#103C2211yescharacteristic, complemented
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×C22⋊C8C2211yescharacteristic, complemented
49C2×C31×#97C2211yescharacteristic, complemented
50C31×#394—21no—
51C31×#394—21no—
52C31×#392—21no—
53C31×#392—21no—
54C31×#391C2211yescharacteristic, complemented
55C31×#390C2211yescharacteristic
56C31×#390C2211yescharacteristic
57C31×#390C2211yescharacteristic, complemented
58C31×#386—21no—
59C31×#385—21no—
60C31×#380C2211yescharacteristic
61C31×#380C2211yescharacteristic
62C31×#379—21no—
63C31×#340C2211yescharacteristic, complemented
64C31×#340C2211yescharacteristic, 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×D4×C31—22no—
74C22×D4×C31—22no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—22no—
80C22×D4×C31—21no—
81C22×D4×C31—22no—
82C22×D4×C31—41no—
83C22×D4×C31—41no—
84C22×D4×C31D411yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C22×D4×C31C2311yescharacteristic
88C23×C4×C31—21no—
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C31×AGL(1,ℤ/8)—232no—
92C2×SD16×C31—22no—
93C2×SD16×C31—22no—
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31D414yescomplemented
98C2×D8×C31—22no—
99C2×D8×C31—22no—
100C2×D8×C31—22no—
101C2×D8×C31—22no—
102C2×D8×C31—22no—
103C2×D8×C31D414yescomplemented
104C2×M16×C31—22no—
105C2×M16×C31—22no—
106C2×M16×C31D414yescomplemented
107C22×C8×C31—22no—
108C22×C8×C31—22no—
109C22×C8×C31—22no—
110C22×C8×C31C2311yescharacteristic
111C22×C8×C31C2311yescharacteristic
112C22×C8×C31C2311yescharacteristic
113C22×C8×C31C2311yescharacteristic
114C31×C22⋊Q8—22no—
115C31×C22⋊Q8—41no—
116C31×#121—22no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#121—41no—
120C31×#121—41no—
121C31×#121—41no—
122C31×#120—44no—
123C4×D4×C31—22no—
124C4×D4×C31—22no—
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31D411yescharacteristic
127C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
144C2×C22⋊C4×C31D411yescharacteristic
145C2×C42×C31C2311yescharacteristic
146C31×#107—22no—
147C31×#106—22no—
148C31×C4⋊C8—22no—
149C31×#103—22no—
150C31×#103—41no—
151C31×#102—22no—
152C31×#102—22no—
153C31×#102—22no—
154C31×#102—41no—
155C31×#102—41no—
156C31×#102—41no—
157C31×C22⋊C8—22no—
158C31×C22⋊C8—22no—
159C31×#97—22no—
160C31×#95—21no—
161C31×#95—21no—
162C31×#95—21no—
163C31×#95—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—42no—
168C24×C31—42no—
169C24×C31—42no—
170C24×C31—42no—
171C24×C31—42no—
172C24×C31—81no—
173C24×C31—81no—
174C24×C31C2×D411yescharacteristic
175C24×C31C2×D411yescharacteristic
176#41×C31—28no—
177#41×C31—44no—
178#41×C31—44no—
179#41×C31—44no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31C2×D412yes—
186C2×D4×C31—28no—
187C2×D4×C31—22no—
188C2×D4×C31—22no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
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—44no—
205C2×D4×C31—44no—
206C2×D4×C31—41no—
207C2×D4×C31—42no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31—44no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—42no—
216C2×D4×C31—42no—
217C2×D4×C31—42no—
218C2×D4×C31—42no—
219C2×D4×C31—42no—
220C2×D4×C31—81no—
221C2×D4×C31—81no—
222C2×D4×C31—81no—
223C2×D4×C31C2×D412yes—
224C2×D4×C31C2×D412yes—
225C2×D4×C31C2×D412yes—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—42no—
242C22×C4×C31—42no—
243C22×C4×C31—42no—
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2×D411yescharacteristic
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2×D411yescharacteristic
248C22×C4×C31C2×D412yes—
249C22×C4×C31#4112yes—
250C22×C4×C31C2411yescharacteristic
251SD16×C31—28no—
252SD16×C31—28no—
253D8×C31—28no—
254D8×C31—28no—
255M16×C31—28no—
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×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—44no—
265C2×C8×C31C2×D412yes—
266C2×C8×C31C2×D412yes—
267C2×C8×C31C2×D412yes—
268C2×C8×C31C2×D412yes—
269C4⋊C4×C31—22no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—42no—
279C22⋊C4×C31—22no—
280C22⋊C4×C31—22no—
281C22⋊C4×C31—42no—
282C22⋊C4×C31—42no—
283C22⋊C4×C31—42no—
284C22⋊C4×C31—42no—
285C22⋊C4×C31—42no—
286C22⋊C4×C31—42no—
287C22⋊C4×C31—42no—
288C22⋊C4×C31—42no—
289C22⋊C4×C31—81no—
290C22⋊C4×C31—81no—
291C22⋊C4×C31—81no—
292C22⋊C4×C31—81no—
293C42×C31—21no—
294C42×C31—21no—
295#24275C3111yesmaximal, characteristic, direct product factor, Sylow
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—21no—
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—48no—
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—41no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—84no—
331C23×C31—84no—
332C23×C31—84no—
333C23×C31—84no—
334C23×C31—84no—
335C23×C31—84no—
336C23×C31#12112yes—
337C23×C31AGL(1,ℤ/8)12yescomplemented
338C23×C31C22×D411yescharacteristic
339Q8×C31—22no—
340Q8×C31—22no—
341Q8×C31—41no—
342Q8×C31—41no—
343D4×C31—22no—
344D4×C31—22no—
345D4×C31—22no—
346D4×C31—22no—
347D4×C31—22no—
348D4×C31—22no—
349D4×C31—48no—
350D4×C31—44no—
351D4×C31—48no—
352D4×C31—41no—
353D4×C31—41no—
354D4×C31—41no—
355D4×C31—41no—
356D4×C31—41no—
357D4×C31—41no—
358D4×C31—84no—
359D4×C31—84no—
360D4×C31—84no—
361C2×C4×C31—21no—
362C2×C4×C31—21no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—21no—
370C2×C4×C31—21no—
371C2×C4×C31—21no—
372C2×C4×C31—22no—
373C2×C4×C31—21no—
374C2×C4×C31—21no—
375C2×C4×C31—21no—
376C2×C4×C31—21no—
377C2×C4×C31—48no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31#12112yes—
397C2×C4×C31C22×D411yescharacteristic
398C2×C4×C31C22×D411yescharacteristic
399C2×C4×C31C22×D411yescharacteristic
400C2×C4×C31C2×#4111yescharacteristic
401C2×C4×C31H(5,𝔽2)11yescharacteristic
402C2×C4×C31H(5,𝔽2)11yescharacteristic
403C8×C31—22no—
404C8×C31—41no—
405C8×C31—41no—
406C8×C31#12014yescomplemented
407C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
408C2×#466C2×C3111yescharacteristic, complemented
409C2×#465C2×C3111yescharacteristic, complemented
410C2×#435C2×C3111yescharacteristic, complemented
411#2408C2×C3111yescharacteristic, complemented
412#2407C2×C3111yescharacteristic, complemented
413#2055C2×C3111yescharacteristic, complemented
414#2054C2×C3111yescharacteristic, complemented
415#2000C2×C3111yescharacteristic, complemented
416#1999C2×C3111yescharacteristic, complemented
417#1973C2×C3111yescharacteristic, complemented
418#1972C2×C3111yescharacteristic, complemented
419#1809C2×C3111yescharacteristic, complemented
420#1788C2×C3111yescharacteristic, complemented
421#1786C2×C3111yescharacteristic, complemented
422C22×C31—22no—
423C22×C31—22no—
424C22×C31—22no—
425C22×C31—22no—
426C22×C31—22no—
427C22×C31—22no—
428C22×C31—41no—
429C22×C31—41no—
430C22×C31—41no—
431C22×C31—41no—
432C22×C31—41no—
433C22×C31—41no—
434C22×C31—41no—
435C22×C31—41no—
436C22×C31—42no—
437C22×C31—42no—
438C22×C31—42no—
439C22×C31—42no—
440C22×C31—42no—
441C22×C31—42no—
442C22×C31—42no—
443C22×C31—42no—
444C22×C31—42no—
445C22×C31—816no—
446C22×C31—81no—
447C22×C31—81no—
448C22×C31—81no—
449C22×C31—81no—
450C22×C31—81no—
451C22×C31—81no—
452C22×C31—81no—
453C22×C31—81no—
454C22×C31—81no—
455C22×C31—81no—
456C22×C31—81no—
457C22×C31—81no—
458C22×C31C2×#12111yescharacteristic
459C22×C31D4211yescharacteristic
460C22×C31D4211yescharacteristic
461C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C31#57511yescharacteristic
463C22×C31#57611yescharacteristic
464C22×C31#57711yescharacteristic
465C4×C31—22no—
466C4×C31—41no—
467C4×C31—42no—
468C4×C31—41no—
469C4×C31—41no—
470C4×C31—81no—
471C4×C31—81no—
472C4×C31—81no—
473C4×C31—81no—
474C4×C31C2×#12011yescharacteristic
475C4×C31#53511yescharacteristic
476C4×C31#54611yescharacteristic
477C4×C31#54611yescharacteristic
478C22×#41C22×C3111yescharacteristic
479C23×D4C22×C3111yescharacteristic
480C2×AGL(1,ℤ/8)—24no—
481C2×AGL(1,ℤ/8)—24no—
482C2×AGL(1,ℤ/8)—24no—
483C22×SD16C22×C3111yescharacteristic
484C22×SD16C22×C3111yescharacteristic
485C22×D8C22×C3111yescharacteristic
486C22×D8C22×C3111yescharacteristic
487C22×M16C22×C3111yescharacteristic
488C23×C8C22×C3111yescharacteristic, complemented
489C2×C22⋊Q8C22×C3111yescharacteristic, complemented
490C2×#121C22×C3111yescharacteristic
491C2×#121C22×C3111yescharacteristic
492C2×#121C22×C3111yescharacteristic, complemented
493C2×#120—21no—
494C2×C4×D4C22×C3111yescharacteristic
495#466—24no—
496#465—24no—
497#435—24no—
498C2×#107C22×C3111yescharacteristic, complemented
499C2×#106C22×C3111yescharacteristic, complemented
500C2×C4⋊C8C22×C3111yescharacteristic, complemented
501C2×#103C22×C3111yescharacteristic, complemented
502C2×#103C22×C3111yescharacteristic, complemented
503C2×#102C22×C3111yescharacteristic
504C2×#102C22×C3111yescharacteristic
505C2×#102C22×C3111yescharacteristic
506C2×#102C22×C3111yescharacteristic
507C2×#102C22×C3111yescharacteristic, complemented
508C2×#102C22×C3111yescharacteristic, complemented
509C2×C22⋊C8C22×C3111yescharacteristic
510C2×C22⋊C8C22×C3111yescharacteristic, complemented
511C2×#97C22×C3111yescharacteristic, complemented
512#394—21no—
513#394—21no—
514#392—21no—
515#392—21no—
516#391C22×C3111yescharacteristic, complemented
517#390C22×C3111yescharacteristic
518#390C22×C3111yescharacteristic
519#390C22×C3111yescharacteristic, complemented
520#386—21no—
521#385—21no—
522#380C22×C3111yescharacteristic
523#380C22×C3111yescharacteristic
524#379—21no—
525#340C22×C3111yescharacteristic, complemented
526#340C22×C3111yescharacteristic, complemented
527C2×C31—42no—
528C2×C31—42no—
529C2×C31—82no—
530C2×C31—82no—
531C2×C31—82no—
532C2×C31#240811yescharacteristic
533C2×C31#305511yescharacteristic
534C2×C31#306211yescharacteristic
535C2×C31#326411yescharacteristic
536C2×C31#326511yescharacteristic
537C2×C31#326711yescharacteristic
538C2×C31#326811yescharacteristic
539C25—21no—
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—41no—
545C2×#41—41no—
546C22×Q8C23×C3111yescharacteristic
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—22no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—41no—
557C22×D4—41no—
558C22×D4D4×C3111yescharacteristic
559C22×D4C23×C3111yescharacteristic
560C22×D4C23×C3111yescharacteristic
561C22×D4C23×C3111yescharacteristic
562C23×C4—21no—
563C23×C4C23×C3111yescharacteristic
564C23×C4C23×C3111yescharacteristic
565AGL(1,ℤ/8)—232no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16D4×C3114yescomplemented
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8D4×C3114yescomplemented
578C2×M16—22no—
579C2×M16—22no—
580C2×M16D4×C3114yescomplemented
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—22no—
584C22×C8C23×C3111yescharacteristic
585C22×C8C23×C3111yescharacteristic
586C22×C8C23×C3111yescharacteristic
587C22×C8C23×C3111yescharacteristic
588C22⋊Q8—22no—
589C22⋊Q8—41no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—41no—
594#121—41no—
595#121—41no—
596#120—44no—
597C4×D4—22no—
598C4×D4—22no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4D4×C3111yescharacteristic
601C2×C4⋊C4C23×C3111yescharacteristic
602C2×C4⋊C4C23×C3111yescharacteristic
603C2×C4⋊C4C23×C3111yescharacteristic
604C2×C4⋊C4C23×C3111yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4D4×C3111yescharacteristic
618C2×C22⋊C4D4×C3111yescharacteristic
619C2×C42C23×C3111yescharacteristic
620#107—22no—
621#106—22no—
622C4⋊C8—22no—
623#103—22no—
624#103—41no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630#102—41no—
631C22⋊C8—22no—
632C22⋊C8—22no—
633#97—22no—
634#95—21no—
635#95—21no—
636#95—21no—
637#95—21no—
638C31#2427511yescharacteristic, direct product factor, Sylow
639C24—21no—
640C24—21no—
641C24—21no—
642C24—42no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24C2×D4×C3111yescharacteristic
650C24C2×D4×C3111yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C3112yes—
661C2×D4—28no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4C2×D4×C3112yes—
699C2×D4C2×D4×C3112yes—
700C2×D4C2×D4×C3112yes—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4C2×D4×C3111yescharacteristic
720C22×C4C2×D4×C3111yescharacteristic
721C22×C4C2×D4×C3111yescharacteristic
722C22×C4C2×D4×C3111yescharacteristic
723C22×C4C2×D4×C3112yes—
724C22×C4#41×C3112yes—
725C22×C4C24×C3111yescharacteristic
726SD16—28no—
727SD16—28no—
728D8—28no—
729D8—28no—
730M16—28no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—44no—
740C2×C8C2×D4×C3112yes—
741C2×C8C2×D4×C3112yes—
742C2×C8C2×D4×C3112yes—
743C2×C8C2×D4×C3112yes—
744C4⋊C4—22no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—42no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C22⋊C4—81no—
766C22⋊C4—81no—
767C22⋊C4—81no—
768C42—21no—
769C42—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—48no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—84no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23C31×#12112yes—
811C23C31×AGL(1,ℤ/8)12yescomplemented
812C23C22×D4×C3111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—41no—
816Q8—41no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—48no—
824D4—44no—
825D4—48no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—48no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C31×#12112yes—
871C2×C4C22×D4×C3111yescharacteristic
872C2×C4C22×D4×C3111yescharacteristic
873C2×C4C22×D4×C3111yescharacteristic
874C2×C4C2×#41×C3111yescharacteristic
875C2×C4C31×H(5,𝔽2)11yescharacteristic
876C2×C4C31×H(5,𝔽2)11yescharacteristic
877C8—22no—
878C8—41no—
879C8—41no—
880C8C31×#12014yescomplemented
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—816no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×C31×#12111yescharacteristic
918C22D42×C3111yescharacteristic
919C22D42×C3111yescharacteristic
920C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
921C22C31×#57511yescharacteristic
922C22C31×#57611yescharacteristic
923C22C31×#57711yescharacteristic
924C4—22no—
925C4—41no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—81no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4C2×C31×#12011yescharacteristic
934C4C31×#53511yescharacteristic
935C4C31×#54611yescharacteristic
936C4C31×#54611yescharacteristic
937C2—42no—
938C2—42no—
939C2—82no—
940C2—82no—
941C2—82no—
942C2C31×#240811yescharacteristic
943C2C31×#305511yescharacteristic
944C2C31×#306211yescharacteristic
945C2C31×#326411yescharacteristic
946C2C31×#326511yescharacteristic
947C2C31×#326711yescharacteristic
948C2C31×#326811yescharacteristic
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×#466C2semidirect
3. C2×C31×#465C2semidirect
4. C2×C31×#435C2semidirect
5. C31×#2408C2semidirect
6. C31×#2407C2semidirect
7. C31×#2055C2semidirect
8. C31×#2054C2semidirect
9. C31×#2000C2semidirect
10. C31×#1999C2semidirect
11. C31×#1973C2semidirect
12. C31×#1972C2semidirect
13. C31×#1809C2semidirect
14. C31×#1788C2semidirect
15. C31×#1786C2semidirect
26. C23×C8×C31C22semidirect
27. C2×C31×C22⋊Q8C22semidirect
30. C2×C31×#121C22semidirect
36. C2×C31×#107C22semidirect
37. C2×C31×#106C22semidirect
38. C2×C31×C4⋊C8C22semidirect
39. C2×C31×#103C22semidirect
40. C2×C31×#103C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
48. C2×C31×C22⋊C8C22semidirect
49. C2×C31×#97C22semidirect
54. C31×#391C22semidirect
57. C31×#390C22semidirect
63. C31×#340C22semidirect
64. C31×#340C22semidirect
97. C2×SD16×C31D4semidirect
103. C2×D8×C31D4semidirect
106. C2×M16×C31D4semidirect
295. #24275C31direct (N × H)
337. C23×C31AGL(1,ℤ/8)semidirect
406. C8×C31#120semidirect
407. C22×AGL(1,ℤ/8)C2×C31semidirect
408. C2×#466C2×C31semidirect
409. C2×#465C2×C31semidirect
410. C2×#435C2×C31semidirect
411. #2408C2×C31semidirect
412. #2407C2×C31semidirect
413. #2055C2×C31semidirect
414. #2054C2×C31semidirect
415. #2000C2×C31semidirect
416. #1999C2×C31semidirect
417. #1973C2×C31semidirect
418. #1972C2×C31semidirect
419. #1809C2×C31semidirect
420. #1788C2×C31semidirect
421. #1786C2×C31semidirect
488. C23×C8C22×C31semidirect
489. C2×C22⋊Q8C22×C31semidirect
492. C2×#121C22×C31semidirect
498. C2×#107C22×C31semidirect
499. C2×#106C22×C31semidirect
500. C2×C4⋊C8C22×C31semidirect
501. C2×#103C22×C31semidirect
502. C2×#103C22×C31semidirect
507. C2×#102C22×C31semidirect
508. C2×#102C22×C31semidirect
510. C2×C22⋊C8C22×C31semidirect
511. C2×#97C22×C31semidirect
516. #391C22×C31semidirect
519. #390C22×C31semidirect
525. #340C22×C31semidirect
526. #340C22×C31semidirect
571. C2×SD16D4×C31semidirect
577. C2×D8D4×C31semidirect
580. C2×M16D4×C31semidirect
638. C31#24275direct (N × H)
811. C23C31×AGL(1,ℤ/8)semidirect
880. C8C31×#120semidirect

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×#4662
C2×C31×#4652
C2×C31×#4352
C31×#24082
C31×#24072
C31×#20552
C31×#20542
C31×#20002
C31×#19992
C31×#19732
C31×#19722
C31×#18092
C31×#17882
C31×#17862
#2427531