Finite Group Databasebeta

← C2×C31×#1906 #21477758

Subgroups — C2×C31×#1906 #21477758

Order 7936.

1798 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic
2C2×C4×#41×C31C211yesmaximal, characteristic, complemented
3C2×C31×#421C211yesmaximal, characteristic, complemented
4C22×C31×#104C211yesmaximal, characteristic, complemented
5C2×C31×#410C211yesmaximal, characteristic, complemented
6C31×#1906C218yesmaximal, direct product factor
7C2×C31×#344C211yesmaximal, characteristic, complemented
8C2×C31×#339C211yesmaximal, characteristic, complemented
9C22×#41×C31C2211yescharacteristic
10C22×#41×C31C2211yescharacteristic
11C31×#575—22no—
12C31×#575—22no—
13C31×#575C414yescomplemented
14C31×#575C2214yes—
15C2×C31×#137—21no—
16C2×C31×#137C412yescomplemented
17C2×C31×AGL(1,ℤ/8)—21no—
18C2×C31×AGL(1,ℤ/8)C412yescomplemented
19C2×C31×#135—22no—
20C22×M16×C31C2211yescharacteristic
21C22×M16×C31C2211yescharacteristic
22C4×#41×C31—22no—
23C4×#41×C31—22no—
24C4×#41×C31—22no—
25C4×#41×C31C2214yescomplemented
26C2×C4×Q8×C31—21no—
27C2×C4×D4×C31—21no—
28C2×C4×D4×C31—22no—
29C2×C31×#117—21no—
30C2×C31×#117C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic
32C22×C42×C31—21no—
33C22×C42×C31C2211yescharacteristic
34C31×#421—22no—
35C31×#421C2214yescomplemented
36C2×C31×#104—22no—
37C2×C31×#104—21no—
38C2×C31×#104—21no—
39C2×C31×#104—22no—
40C2×C31×#104C2214yescomplemented
41C31×#410—22no—
42C31×#410C2214yescomplemented
43C2×C31×#99—22no—
44C31×#344C2214yescomplemented
45C31×#339C2214yescomplemented
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31—21no—
49C2×#41×C31—21no—
50C2×#41×C31—21no—
51C2×#41×C31—21no—
52C2×#41×C31—21no—
53C2×#41×C31—21no—
54C2×#41×C31—21no—
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31—21no—
60C2×#41×C31—21no—
61C2×#41×C31—21no—
62C2×#41×C31C2×C412yes—
63C2×#41×C31C2×C412yes—
64C2×#41×C31C2×C412yescomplemented
65C2×#41×C31D412yes—
66C2×#41×C31D412yes—
67C2×#41×C31D412yes—
68C2×#41×C31C2312yes—
69C2×#41×C31C2312yes—
70C22×Q8×C31C2×C411yescharacteristic, complemented
71C22×Q8×C31D411yescharacteristic
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31C2×C411yescharacteristic, complemented
75C22×D4×C31D411yescharacteristic
76C23×C4×C31—21no—
77C23×C4×C31—22no—
78C23×C4×C31—21no—
79C23×C4×C31—21no—
80C23×C4×C31C2311yescharacteristic
81C31×#137—24no—
82C31×#137—24no—
83C31×#137—24no—
84C31×#137C2×C418yescomplemented
85C31×AGL(1,ℤ/8)—24no—
86C31×AGL(1,ℤ/8)—24no—
87C31×AGL(1,ℤ/8)—24no—
88C31×AGL(1,ℤ/8)C2×C418yescomplemented
89C31×#135—28no—
90C31×#135—28no—
91C2×Q16×C31—22no—
92C2×SD16×C31—22no—
93C2×SD16×C31—22no—
94C2×D8×C31—22no—
95C2×M16×C31—21no—
96C2×M16×C31—21no—
97C2×M16×C31—21no—
98C2×M16×C31—21no—
99C2×M16×C31—21no—
100C2×M16×C31—21no—
101C2×M16×C31—21no—
102C2×M16×C31—21no—
103C2×M16×C31C2×C412yescomplemented
104C2×M16×C31C2×C412yescomplemented
105C2×M16×C31C2312yes—
106C2×M16×C31C2312yes—
107C22×C8×C31—21no—
108C22×C8×C31—21no—
109C4×Q8×C31—24no—
110C4×Q8×C31—24no—
111C4×D4×C31—28no—
112C4×D4×C31—24no—
113C4×D4×C31—24no—
114C4×D4×C31—28no—
115C31×#117—24no—
116C31×#117—21no—
117C31×#117—21no—
118C31×#117—21no—
119C31×#117—24no—
120C31×#117—21no—
121C31×#117—21no—
122C31×#117D412yes—
123C31×#117C2312yes—
124C31×#117C2312yes—
125C2×C4⋊C4×C31—22no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31D412yes—
131C2×C42×C31—22no—
132C2×C42×C31—24no—
133C2×C42×C31—21no—
134C2×C42×C31—21no—
135C2×C42×C31—21no—
136C2×C42×C31—21no—
137C2×C42×C31—24no—
138C2×C42×C31—21no—
139C2×C42×C31D411yescharacteristic
140C2×C42×C31D411yescharacteristic
141C2×C42×C31D412yes—
142C2×C42×C31C2312yes—
143C31×#104—28no—
144C31×#104—24no—
145C31×#104—24no—
146C31×#99—28no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31C2×D411yescharacteristic
150#41×C31—22no—
151#41×C31—22no—
152#41×C31—22no—
153#41×C31—22no—
154#41×C31—22no—
155#41×C31—22no—
156#41×C31—22no—
157#41×C31—22no—
158#41×C31—22no—
159#41×C31—22no—
160#41×C31—22no—
161#41×C31—22no—
162#41×C31—22no—
163#41×C31—22no—
164#41×C31—22no—
165#41×C31—22no—
166#41×C31—22no—
167#41×C31—22no—
168#41×C31—22no—
169#41×C31—22no—
170#41×C31—41no—
171#41×C31—41no—
172#41×C31—41no—
173#41×C31—41no—
174#41×C31—41no—
175#41×C31—41no—
176#41×C31—41no—
177#41×C31—41no—
178#41×C31C22⋊C414yes—
179#41×C31C22⋊C414yes—
180#41×C31C22×C414yes—
181#41×C31C2×D414yes—
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×C31C22⋊C412yes—
191C2×Q8×C31C22⋊C412yes—
192C2×Q8×C31C22×C412yescomplemented
193C2×Q8×C31C2×D412yes—
194C2×D4×C31—22no—
195C2×D4×C31—22no—
196C2×D4×C31—22no—
197C2×D4×C31—22no—
198C2×D4×C31—22no—
199C2×D4×C31—22no—
200C2×D4×C31—22no—
201C2×D4×C31—22no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—21no—
209C2×D4×C31—21no—
210C2×D4×C31—41no—
211C2×D4×C31—41no—
212C2×D4×C31—41no—
213C2×D4×C31—41no—
214C2×D4×C31C22⋊C412yes—
215C2×D4×C31C22⋊C412yes—
216C2×D4×C31C22×C412yescomplemented
217C2×D4×C31C2×D412yes—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—22no—
226C22×C4×C31—28no—
227C22×C4×C31—21no—
228C22×C4×C31—22no—
229C22×C4×C31—21no—
230C22×C4×C31—22no—
231C22×C4×C31—22no—
232C22×C4×C31—22no—
233C22×C4×C31—22no—
234C22×C4×C31—44no—
235C22×C4×C31—48no—
236C22×C4×C31—41no—
237C22×C4×C31—41no—
238C22×C4×C31—41no—
239C22×C4×C31—41no—
240C22×C4×C31—41no—
241C22×C4×C31C22×C411yescharacteristic
242C22×C4×C31C22×C411yescharacteristic
243C22×C4×C31C2×D411yescharacteristic
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2×D411yescharacteristic
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31C2×D411yescharacteristic
248C22×C4×C31C2×D411yescharacteristic
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31#4111yescharacteristic
251C22×C4×C31#4111yescharacteristic
252C22×C4×C31#4111yescharacteristic
253C22×C4×C31#4111yescharacteristic
254C22×C4×C31C2411yescharacteristic
255Q16×C31—28no—
256SD16×C31—28no—
257SD16×C31—28no—
258D8×C31—28no—
259M16×C31—22no—
260M16×C31—22no—
261M16×C31—22no—
262M16×C31—22no—
263M16×C31—22no—
264M16×C31—41no—
265M16×C31—41no—
266M16×C31C22×C414yescomplemented
267C2×C8×C31—22no—
268C2×C8×C31—22no—
269C2×C8×C31—22no—
270C2×C8×C31—22no—
271C2×C8×C31—41no—
272C2×C8×C31—41no—
273C4⋊C4×C31—28no—
274C4⋊C4×C31—22no—
275C4⋊C4×C31—22no—
276C4⋊C4×C31—22no—
277C4⋊C4×C31—41no—
278C22⋊C4×C31—28no—
279C22⋊C4×C31—22no—
280C22⋊C4×C31—22no—
281C22⋊C4×C31—41no—
282C22⋊C4×C31C2×D414yes—
283C42×C31—28no—
284C42×C31—21no—
285C42×C31—22no—
286C42×C31—21no—
287C42×C31—22no—
288C42×C31—22no—
289C42×C31—22no—
290C42×C31—22no—
291C42×C31—41no—
292C42×C31C2×D412yes—
293C42×C31C2×D412yes—
294C2×#1906C3111yesmaximal, characteristic, direct product factor, Sylow
295C23×C31—22no—
296C23×C31—22no—
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—42no—
300C23×C31—44no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—82no—
304C23×C31C4×D411yescharacteristic
305C23×C31C4×D411yescharacteristic
306C23×C31#12011yescharacteristic
307C23×C31#12011yescharacteristic
308C23×C31#12111yescharacteristic
309C23×C31#12111yescharacteristic
310C23×C31C22×D411yescharacteristic
311Q8×C31—22no—
312Q8×C31—22no—
313Q8×C31—22no—
314Q8×C31—22no—
315Q8×C31—22no—
316Q8×C31—41no—
317Q8×C31—41no—
318Q8×C31C2×C22⋊C414yes—
319D4×C31—24no—
320D4×C31—24no—
321D4×C31—24no—
322D4×C31—24no—
323D4×C31—22no—
324D4×C31—22no—
325D4×C31—22no—
326D4×C31—22no—
327D4×C31—22no—
328D4×C31—42no—
329D4×C31—42no—
330D4×C31—42no—
331D4×C31—42no—
332D4×C31—41no—
333D4×C31—41no—
334D4×C31C2×C22⋊C414yes—
335C2×C4×C31—24no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—24no—
341C2×C4×C31—24no—
342C2×C4×C31—24no—
343C2×C4×C31—24no—
344C2×C4×C31—22no—
345C2×C4×C31—24no—
346C2×C4×C31—22no—
347C2×C4×C31—44no—
348C2×C4×C31—44no—
349C2×C4×C31—416no—
350C2×C4×C31—44no—
351C2×C4×C31—42no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—42no—
355C2×C4×C31—42no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—42no—
359C2×C4×C31—82no—
360C2×C4×C31C2×C22⋊C411yescharacteristic
361C2×C4×C31C2×C22⋊C411yescharacteristic
362C2×C4×C31C2×C22⋊C411yescharacteristic
363C2×C4×C31C2×C22⋊C411yescharacteristic
364C2×C4×C31C4×D411yescharacteristic
365C2×C4×C31C4×D411yescharacteristic
366C2×C4×C31C4×D411yescharacteristic
367C2×C4×C31C4×D411yescharacteristic
368C2×C4×C31C4×D411yescharacteristic
369C2×C4×C31C4×D411yescharacteristic
370C2×C4×C31#12011yescharacteristic
371C2×C4×C31#12011yescharacteristic
372C2×C4×C31#12111yescharacteristic
373C2×C4×C31#12111yescharacteristic
374C2×C4×C31#12111yescharacteristic
375C2×C4×C31#12111yescharacteristic
376C2×C4×C31#12111yescharacteristic
377C2×C4×C31#12111yescharacteristic
378C2×C4×C31#12311yescharacteristic
379C2×C4×C31#12311yescharacteristic
380C2×C4×C31#12311yescharacteristic
381C2×C4×C31#12311yescharacteristic
382C2×C4×C31C23×C411yescharacteristic
383C2×C4×C31C22×D411yescharacteristic
384C2×C4×C31C22×D411yescharacteristic
385C2×C4×C31C22×D411yescharacteristic
386C2×C4×C31C2×#4111yescharacteristic
387C2×C4×C31C2×#4111yescharacteristic
388C8×C31—24no—
389C8×C31—42no—
390C2×#575C2×C3111yescharacteristic
391C2×C4×#41C2×C3111yescharacteristic, complemented
392C2×#421C2×C3111yescharacteristic, complemented
393C22×#104C2×C3111yescharacteristic, complemented
394C2×#410C2×C3111yescharacteristic, complemented
395#1906C2×C3118yesdirect product factor
396C2×#344C2×C3111yescharacteristic, complemented
397C2×#339C2×C3111yescharacteristic, complemented
398C22×C31—22no—
399C22×C31—22no—
400C22×C31—22no—
401C22×C31—24no—
402C22×C31—41no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—44no—
407C22×C31—44no—
408C22×C31—44no—
409C22×C31—42no—
410C22×C31—82no—
411C22×C31—82no—
412C22×C31—82no—
413C22×C31#38611yescharacteristic
414C22×C31#38611yescharacteristic
415C22×C31#38611yescharacteristic
416C22×C31#38611yescharacteristic
417C22×C31C2×C4×D411yescharacteristic
418C22×C31C2×#12011yescharacteristic
419C22×C31C2×#12111yescharacteristic
420C4×C31—24no—
421C4×C31—24no—
422C4×C31—44no—
423C4×C31—42no—
424C4×C31—42no—
425C4×C31—82no—
426C4×C31#38611yescharacteristic
427C4×C31#38611yescharacteristic
428C4×C31#38611yescharacteristic
429C4×C31#38611yescharacteristic
430C4×C31C22×C22⋊C411yescharacteristic
431C4×C31C2×C4×D411yescharacteristic
432C4×C31C2×#12111yescharacteristic
433C4×C31C2×#12311yescharacteristic
434C22×#41C22×C3111yescharacteristic
435C22×#41C22×C3111yescharacteristic
436#575—22no—
437#575—22no—
438#575C4×C3114yescomplemented
439#575C22×C3114yes—
440C2×#137—21no—
441C2×#137C4×C3112yescomplemented
442C2×AGL(1,ℤ/8)—21no—
443C2×AGL(1,ℤ/8)C4×C3112yescomplemented
444C2×#135—22no—
445C22×M16C22×C3111yescharacteristic
446C22×M16C22×C3111yescharacteristic
447C4×#41—22no—
448C4×#41—22no—
449C4×#41—22no—
450C4×#41C22×C3114yescomplemented
451C2×C4×Q8—21no—
452C2×C4×D4—21no—
453C2×C4×D4—22no—
454C2×#117—21no—
455C2×#117C22×C3111yescharacteristic
456C2×#117C22×C3111yescharacteristic
457C22×C42—21no—
458C22×C42C22×C3111yescharacteristic
459#421—22no—
460#421C22×C3114yescomplemented
461C2×#104—22no—
462C2×#104—21no—
463C2×#104—22no—
464C2×#104—21no—
465C2×#104C22×C3114yescomplemented
466#410—22no—
467#410C22×C3114yescomplemented
468C2×#99—22no—
469#344C22×C3114yescomplemented
470#339C22×C3114yescomplemented
471C2×C31—21no—
472C2×C31—21no—
473C2×C31—21no—
474C2×C31—21no—
475C2×C31—21no—
476C2×C31—21no—
477C2×C31—44no—
478C2×C31—82no—
479C2×C31#190612yesdirect product factor
480C2×C31C2×#38611yescharacteristic
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—21no—
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41C2×C4×C3112yes—
498C2×#41C2×C4×C3112yes—
499C2×#41C2×C4×C3112yescomplemented
500C2×#41D4×C3112yes—
501C2×#41D4×C3112yes—
502C2×#41D4×C3112yes—
503C2×#41C23×C3112yes—
504C2×#41C23×C3112yes—
505C22×Q8C2×C4×C3111yescharacteristic, complemented
506C22×Q8D4×C3111yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4C2×C4×C3111yescharacteristic, complemented
510C22×D4D4×C3111yescharacteristic
511C23×C4—21no—
512C23×C4—22no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C23×C3111yescharacteristic
516#137—24no—
517#137—24no—
518#137—24no—
519#137C2×C4×C3118yescomplemented
520AGL(1,ℤ/8)—24no—
521AGL(1,ℤ/8)—24no—
522AGL(1,ℤ/8)—24no—
523AGL(1,ℤ/8)C2×C4×C3118yescomplemented
524#135—28no—
525#135—28no—
526C2×Q16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×D8—22no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—21no—
533C2×M16—21no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16C2×C4×C3112yescomplemented
539C2×M16C2×C4×C3112yescomplemented
540C2×M16C23×C3112yes—
541C2×M16C23×C3112yes—
542C22×C8—21no—
543C22×C8—21no—
544C4×Q8—24no—
545C4×Q8—24no—
546C4×D4—28no—
547C4×D4—24no—
548C4×D4—24no—
549C4×D4—28no—
550#117—24no—
551#117—21no—
552#117—21no—
553#117—21no—
554#117—24no—
555#117—21no—
556#117—21no—
557#117D4×C3112yes—
558#117C23×C3112yes—
559#117C23×C3112yes—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C3112yes—
566C2×C42—22no—
567C2×C42—24no—
568C2×C42—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572C2×C42—24no—
573C2×C42—21no—
574C2×C42D4×C3111yescharacteristic
575C2×C42D4×C3112yes—
576C2×C42D4×C3111yescharacteristic
577C2×C42C23×C3112yes—
578#104—28no—
579#104—24no—
580#104—24no—
581#99—28no—
582C31C2×#190611yescharacteristic, direct product factor, Sylow
583C24—21no—
584C24—21no—
585C24C2×D4×C3111yescharacteristic
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—22no—
592#41—22no—
593#41—22no—
594#41—22no—
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—22no—
604#41—22no—
605#41—22no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—41no—
611#41—41no—
612#41—41no—
613#41—41no—
614#41C22⋊C4×C3114yes—
615#41C22⋊C4×C3114yes—
616#41C22×C4×C3114yes—
617#41C2×D4×C3114yes—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8C22⋊C4×C3112yes—
627C2×Q8C22⋊C4×C3112yes—
628C2×Q8C22×C4×C3112yescomplemented
629C2×Q8C2×D4×C3112yes—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4—41no—
649C2×D4—41no—
650C2×D4C22⋊C4×C3112yes—
651C2×D4C22⋊C4×C3112yes—
652C2×D4C22×C4×C3112yescomplemented
653C2×D4C2×D4×C3112yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—28no—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—44no—
671C22×C4—48no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4C22×C4×C3111yescharacteristic
678C22×C4C22×C4×C3111yescharacteristic
679C22×C4C2×D4×C3111yescharacteristic
680C22×C4C2×D4×C3111yescharacteristic
681C22×C4C2×D4×C3111yescharacteristic
682C22×C4C2×D4×C3111yescharacteristic
683C22×C4C2×D4×C3111yescharacteristic
684C22×C4C2×D4×C3111yescharacteristic
685C22×C4C2×D4×C3111yescharacteristic
686C22×C4#41×C3111yescharacteristic
687C22×C4#41×C3111yescharacteristic
688C22×C4#41×C3111yescharacteristic
689C22×C4#41×C3111yescharacteristic
690C22×C4C24×C3111yescharacteristic
691Q16—28no—
692SD16—28no—
693SD16—28no—
694D8—28no—
695M16—22no—
696M16—22no—
697M16—22no—
698M16—22no—
699M16—22no—
700M16—41no—
701M16—41no—
702M16C22×C4×C3114yescomplemented
703C2×C8—22no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—41no—
708C2×C8—41no—
709C4⋊C4—28no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—41no—
714C22⋊C4—28no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—41no—
718C22⋊C4C2×D4×C3114yes—
719C42—28no—
720C42—21no—
721C42—22no—
722C42—21no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—41no—
728C42C2×D4×C3112yes—
729C42C2×D4×C3112yes—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—42no—
735C23—44no—
736C23—41no—
737C23—41no—
738C23—82no—
739C23C4×D4×C3111yescharacteristic
740C23C4×D4×C3111yescharacteristic
741C23C31×#12011yescharacteristic
742C23C31×#12011yescharacteristic
743C23C31×#12111yescharacteristic
744C23C31×#12111yescharacteristic
745C23C22×D4×C3111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—41no—
752Q8—41no—
753Q8C2×C22⋊C4×C3114yes—
754D4—24no—
755D4—24no—
756D4—24no—
757D4—24no—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—41no—
768D4—41no—
769D4C2×C22⋊C4×C3114yes—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—416no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—82no—
795C2×C4C2×C22⋊C4×C3111yescharacteristic
796C2×C4C2×C22⋊C4×C3111yescharacteristic
797C2×C4C2×C22⋊C4×C3111yescharacteristic
798C2×C4C2×C22⋊C4×C3111yescharacteristic
799C2×C4C4×D4×C3111yescharacteristic
800C2×C4C4×D4×C3111yescharacteristic
801C2×C4C4×D4×C3111yescharacteristic
802C2×C4C4×D4×C3111yescharacteristic
803C2×C4C4×D4×C3111yescharacteristic
804C2×C4C4×D4×C3111yescharacteristic
805C2×C4C31×#12011yescharacteristic
806C2×C4C31×#12011yescharacteristic
807C2×C4C31×#12111yescharacteristic
808C2×C4C31×#12111yescharacteristic
809C2×C4C31×#12111yescharacteristic
810C2×C4C31×#12111yescharacteristic
811C2×C4C31×#12111yescharacteristic
812C2×C4C31×#12111yescharacteristic
813C2×C4C31×#12311yescharacteristic
814C2×C4C31×#12311yescharacteristic
815C2×C4C31×#12311yescharacteristic
816C2×C4C31×#12311yescharacteristic
817C2×C4C23×C4×C3111yescharacteristic
818C2×C4C22×D4×C3111yescharacteristic
819C2×C4C22×D4×C3111yescharacteristic
820C2×C4C22×D4×C3111yescharacteristic
821C2×C4C2×#41×C3111yescharacteristic
822C2×C4C2×#41×C3111yescharacteristic
823C8—24no—
824C8—42no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—24no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22C31×#38611yescharacteristic
841C22C31×#38611yescharacteristic
842C22C31×#38611yescharacteristic
843C22C31×#38611yescharacteristic
844C22C2×C4×D4×C3111yescharacteristic
845C22C2×C31×#12011yescharacteristic
846C22C2×C31×#12111yescharacteristic
847C4—24no—
848C4—24no—
849C4—44no—
850C4—42no—
851C4—42no—
852C4—82no—
853C4C31×#38611yescharacteristic
854C4C31×#38611yescharacteristic
855C4C31×#38611yescharacteristic
856C4C31×#38611yescharacteristic
857C4C22×C22⋊C4×C3111yescharacteristic
858C4C2×C4×D4×C3111yescharacteristic
859C4C2×C31×#12111yescharacteristic
860C4C2×C31×#12311yescharacteristic
861C2—21no—
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—21no—
867C2—44no—
868C2—82no—
869C2C31×#190612yesdirect product factor
870C2C2×C31×#38611yescharacteristic
subgroupG/H
centerC2×C4×C31#121
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC22×C31#386
prime radicalC2×C31×#575C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×#41×C31C2semidirect
3. C2×C31×#421C2semidirect
4. C22×C31×#104C2semidirect
5. C2×C31×#410C2semidirect
6. C31×#1906C2direct (N × H)
7. C2×C31×#344C2semidirect
8. C2×C31×#339C2semidirect
13. C31×#575C4semidirect
16. C2×C31×#137C4semidirect
18. C2×C31×AGL(1,ℤ/8)C4semidirect
25. C4×#41×C31C22semidirect
35. C31×#421C22semidirect
40. C2×C31×#104C22semidirect
42. C31×#410C22semidirect
44. C31×#344C22semidirect
45. C31×#339C22semidirect
64. C2×#41×C31C2×C4semidirect
70. C22×Q8×C31C2×C4semidirect
74. C22×D4×C31C2×C4semidirect
84. C31×#137C2×C4semidirect
88. C31×AGL(1,ℤ/8)C2×C4semidirect
103. C2×M16×C31C2×C4semidirect
104. C2×M16×C31C2×C4semidirect
192. C2×Q8×C31C22×C4semidirect
216. C2×D4×C31C22×C4semidirect
266. M16×C31C22×C4semidirect
294. C2×#1906C31direct (N × H)
391. C2×C4×#41C2×C31semidirect
392. C2×#421C2×C31semidirect
393. C22×#104C2×C31semidirect
394. C2×#410C2×C31semidirect
395. #1906C2×C31direct (N × H)
396. C2×#344C2×C31semidirect
397. C2×#339C2×C31semidirect
438. #575C4×C31semidirect
441. C2×#137C4×C31semidirect
443. C2×AGL(1,ℤ/8)C4×C31semidirect
450. C4×#41C22×C31semidirect
460. #421C22×C31semidirect
465. C2×#104C22×C31semidirect
467. #410C22×C31semidirect
469. #344C22×C31semidirect
470. #339C22×C31semidirect
479. C2×C31#1906direct (N × H)
499. C2×#41C2×C4×C31semidirect
505. C22×Q8C2×C4×C31semidirect
509. C22×D4C2×C4×C31semidirect
519. #137C2×C4×C31semidirect
523. AGL(1,ℤ/8)C2×C4×C31semidirect
538. C2×M16C2×C4×C31semidirect
539. C2×M16C2×C4×C31semidirect
582. C31C2×#1906direct (N × H)
628. C2×Q8C22×C4×C31semidirect
652. C2×D4C22×C4×C31semidirect
702. M16C22×C4×C31semidirect
869. C2C31×#1906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5752
C2×C4×#41×C312
C2×C31×#4212
C22×C31×#1042
C2×C31×#4102
C31×#19062
C2×C31×#3442
C2×C31×#3392
C2×#190631