Finite Group Databasebeta

← C4×C31×#463 #21478260

Subgroups — C4×C31×#463 #21478260

Order 7936.

1136 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#463C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C2×C4×D8×C31C211yesmaximal, characteristic
4C4×C31×#124C211yesmaximal, characteristic, complemented
5C42×D4×C31C211yesmaximal, characteristic, complemented
6C31×#1983C211yesmaximal, characteristic, complemented
7C31×#1949C211yesmaximal, characteristic, complemented
8C31×#1928C211yesmaximal, characteristic, complemented
9C31×#1926C211yesmaximal, characteristic, complemented
10C31×#1879C211yesmaximal, characteristic
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1804C211yesmaximal, characteristic, complemented
13C4×C31×C4⋊C8C211yesmaximal, characteristic, complemented
14C4×C31×#103C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C2×C31×#124C2211yescharacteristic
19C2×C4×Q8×C31C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C22×C42×C31—21no—
25C31×#463C418yesdirect product factor
26C4×SD16×C31—24no—
27C4×D8×C31—24no—
28C2×C31×#107C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C4×C8×C31C2211yescharacteristic
41C2×C4×C8×C31C2211yescharacteristic
42C31×#391C2211yescharacteristic
43C31×#390C2211yescharacteristic
44C31×#388—21no—
45C31×#388—21no—
46C31×#382C2211yescharacteristic
47C4×C4⋊C4×C31C2211yescharacteristic
48C4×C4⋊C4×C31C2211yescharacteristic
49C4×C4⋊C4×C31C2211yescharacteristic
50C4×C22⋊C4×C31—21no—
51C4×C22⋊C4×C31—21no—
52C4×C22⋊C4×C31—21no—
53C4×C22⋊C4×C31—21no—
54C4×C22⋊C4×C31—21no—
55C43×C31C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31C2311yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C2×SD16×C31—22no—
70C2×SD16×C31—22no—
71C2×SD16×C31C2×C414yescomplemented
72C2×D8×C31—22no—
73C2×D8×C31—22no—
74C2×D8×C31C2×C414yes—
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C31×#124—22no—
80C31×#124C2×C414yescomplemented
81C4×Q8×C31—22no—
82C4×Q8×C31—22no—
83C4×D4×C31—22no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C4×D4×C31—22no—
88C4×D4×C31—22no—
89C4×D4×C31C2×C414yescomplemented
90C4×D4×C31D414yes—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31—21no—
108C2×C42×C31—21no—
109C2×C42×C31—44no—
110C2×C42×C31D411yescharacteristic
111C2×C42×C31D411yescharacteristic
112C2×C42×C31D411yescharacteristic
113C2×C42×C31D411yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C2×C42×C31C2311yescharacteristic
117C31×#107—22no—
118C31×#106—22no—
119C31×C4⋊C8—22no—
120C31×C4⋊C8C2×C414yescomplemented
121C31×#103—22no—
122C31×#103—22no—
123C31×#103C2×C414yescomplemented
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102C2×C414yescomplemented
129C4×C8×C31—22no—
130C4×C8×C31—22no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C24×C31—21no—
139C24×C31—21no—
140C2×Q8×C31—21no—
141C2×Q8×C31—21no—
142C2×Q8×C31—21no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31C22×C412yes—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31C22×C412yes—
155C2×D4×C31C22×C412yes—
156C2×D4×C31C2×D412yes—
157C2×D4×C31#4112yes—
158C22×C4×C31—24no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—24no—
164C22×C4×C31—24no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—42no—
168C22×C4×C31—42no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—42no—
174C22×C4×C31—42no—
175C22×C4×C31—42no—
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2411yescharacteristic
183SD16×C31—28no—
184D8×C31—28no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31C22×C412yes—
196C2×C8×C31C22×C412yes—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31C22×C412yes—
206C4⋊C4×C31C2×D412yes—
207C4⋊C4×C31#4112yes—
208C22⋊C4×C31—24no—
209C22⋊C4×C31—24no—
210C22⋊C4×C31—24no—
211C22⋊C4×C31—24no—
212C22⋊C4×C31—24no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C42×C31—22no—
217C42×C31—22no—
218C42×C31—22no—
219C42×C31—21no—
220C42×C31—21no—
221C42×C31—41no—
222C42×C31—42no—
223C42×C31—42no—
224C42×C31—42no—
225C42×C31—42no—
226C42×C31C22×C412yes—
227C42×C31C2×D412yes—
228C42×C31#4112yes—
229C42×C31#4112yes—
230C4×#463C3111yesmaximal, characteristic, direct product factor, Sylow
231C23×C31—22no—
232C23×C31—22no—
233C23×C31—22no—
234C23×C31—22no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31C22×D411yescharacteristic
246Q8×C31—22no—
247Q8×C31—22no—
248Q8×C31—41no—
249Q8×C31—41no—
250D4×C31—22no—
251D4×C31—22no—
252D4×C31—22no—
253D4×C31—22no—
254D4×C31—22no—
255D4×C31—41no—
256D4×C31—41no—
257D4×C31C4×D414yes—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—22no—
267C2×C4×C31—22no—
268C2×C4×C31—22no—
269C2×C4×C31—21no—
270C2×C4×C31—22no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—48no—
274C2×C4×C31—48no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—48no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—84no—
291C2×C4×C31C4×D412yes—
292C2×C4×C31C4×D412yes—
293C2×C4×C31#12112yes—
294C2×C4×C31#12112yes—
295C2×C4×C31#13512yes—
296C2×C4×C31#13512yes—
297C2×C4×C31AGL(1,ℤ/8)12yes—
298C2×C4×C31C23×C411yescharacteristic
299C2×C4×C31C22×D411yescharacteristic
300C2×C4×C31C2×#4111yescharacteristic
301C2×C4×C31C2×#4111yescharacteristic
302C2×C4×C31C2×#4111yescharacteristic
303C2×C4×C31C2×#4111yescharacteristic
304C8×C31—22no—
305C8×C31—22no—
306C8×C31—41no—
307C8×C31—41no—
308C2×#463C2×C3111yescharacteristic
309C2×C4×SD16C2×C3111yescharacteristic, complemented
310C2×C4×D8C2×C3111yescharacteristic
311C4×#124C2×C3111yescharacteristic, complemented
312C42×D4C2×C3111yescharacteristic, complemented
313#1983C2×C3111yescharacteristic, complemented
314#1949C2×C3111yescharacteristic, complemented
315#1928C2×C3111yescharacteristic, complemented
316#1926C2×C3111yescharacteristic, complemented
317#1879C2×C3111yescharacteristic
318#1877C2×C3111yescharacteristic, complemented
319#1804C2×C3111yescharacteristic, complemented
320C4×C4⋊C8C2×C3111yescharacteristic, complemented
321C4×#103C2×C3111yescharacteristic, complemented
322C4×#102C2×C3111yescharacteristic, complemented
323C22×C31—24no—
324C22×C31—42no—
325C22×C31—42no—
326C22×C31—42no—
327C22×C31—42no—
328C22×C31—42no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31—42no—
332C22×C31—42no—
333C22×C31—81no—
334C22×C31—81no—
335C22×C31—81no—
336C22×C31—81no—
337C22×C31C2×C4×D411yescharacteristic
338C22×C31C2×#12111yescharacteristic
339C22×C31#52511yescharacteristic
340C22×C31C2×#13511yescharacteristic
341C22×C31C2×#13511yescharacteristic
342C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C31#57511yescharacteristic
344C4×C31—22no—
345C4×C31—22no—
346C4×C31—22no—
347C4×C31—22no—
348C4×C31—41no—
349C4×C31—42no—
350C4×C31—42no—
351C4×C31—42no—
352C4×C31—42no—
353C4×C31—81no—
354C4×C31—81no—
355C4×C31#46314yesdirect product factor
356C4×C31C2×C4×D411yescharacteristic
357C4×C31C4×#4111yescharacteristic
358C4×C31#52911yescharacteristic
359C4×C31#53211yescharacteristic
360C22×SD16C22×C3111yescharacteristic
361C22×D8C22×C3111yescharacteristic
362C2×#124C22×C3111yescharacteristic
363C2×C4×Q8C22×C3111yescharacteristic
364C2×C4×D4C22×C3111yescharacteristic
365C2×C4×D4C22×C3111yescharacteristic
366C2×C4×D4C22×C3111yescharacteristic
367C2×C4×D4C22×C3111yescharacteristic
368C22×C42—21no—
369#463C4×C3118yesdirect product factor
370C4×SD16—24no—
371C4×D8—24no—
372C2×#107C22×C3111yescharacteristic
373C2×#106C22×C3111yescharacteristic
374C2×C4⋊C8C22×C3111yescharacteristic
375C2×C4⋊C8C22×C3111yescharacteristic
376C2×#103C22×C3111yescharacteristic
377C2×#103C22×C3111yescharacteristic
378C2×#103C22×C3111yescharacteristic
379C2×#102C22×C3111yescharacteristic
380C2×#102C22×C3111yescharacteristic
381C2×#102C22×C3111yescharacteristic
382C2×#102C22×C3111yescharacteristic
383C2×#102C22×C3111yescharacteristic
384C2×C4×C8C22×C3111yescharacteristic
385C2×C4×C8C22×C3111yescharacteristic
386#391C22×C3111yescharacteristic
387#390C22×C3111yescharacteristic
388#388—21no—
389#388—21no—
390#382C22×C3111yescharacteristic
391C4×C4⋊C4C22×C3111yescharacteristic
392C4×C4⋊C4C22×C3111yescharacteristic
393C4×C4⋊C4C22×C3111yescharacteristic
394C4×C22⋊C4—21no—
395C4×C22⋊C4—21no—
396C4×C22⋊C4—21no—
397C4×C22⋊C4—21no—
398C4×C22⋊C4—21no—
399C43C22×C3111yescharacteristic
400#340C22×C3111yescharacteristic
401#340C22×C3111yescharacteristic
402#340C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#336C22×C3111yescharacteristic
405#336C22×C3111yescharacteristic
406C2×C31—44no—
407C2×C31—82no—
408C2×C31C4×#12111yescharacteristic
409C2×C31C4×#13511yescharacteristic
410C2×C31C4×AGL(1,ℤ/8)11yescharacteristic
411C2×C31C2×#46311yescharacteristic
412C2×C31#303511yescharacteristic
413C2×C31#310211yescharacteristic
414C2×C31#310511yescharacteristic
415C22×Q8C23×C3111yescharacteristic
416C22×D4C23×C3111yescharacteristic
417C22×D4C23×C3111yescharacteristic
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—21no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16C2×C4×C3114yescomplemented
425C2×D8—22no—
426C2×D8—22no—
427C2×D8C2×C4×C3114yes—
428C22×C8C23×C3111yescharacteristic
429C22×C8C23×C3111yescharacteristic
430C22×C8C23×C3111yescharacteristic
431C22×C8C23×C3111yescharacteristic
432#124—22no—
433#124C2×C4×C3114yescomplemented
434C4×Q8—22no—
435C4×Q8—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4C2×C4×C3114yescomplemented
443C4×D4D4×C3114yes—
444C2×C4⋊C4—21no—
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—44no—
463C2×C42D4×C3111yescharacteristic
464C2×C42D4×C3111yescharacteristic
465C2×C42D4×C3111yescharacteristic
466C2×C42D4×C3111yescharacteristic
467C2×C42C23×C3111yescharacteristic
468C2×C42C23×C3111yescharacteristic
469C2×C42C23×C3111yescharacteristic
470#107—22no—
471#106—22no—
472C4⋊C8—22no—
473C4⋊C8C2×C4×C3114yescomplemented
474#103—22no—
475#103—22no—
476#103C2×C4×C3114yescomplemented
477#102—22no—
478#102—22no—
479#102—22no—
480#102—22no—
481#102C2×C4×C3114yescomplemented
482C4×C8—22no—
483C4×C8—22no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491C31C4×#46311yescharacteristic, direct product factor, Sylow
492C24—21no—
493C24—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C22×C4×C3112yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C22×C4×C3112yes—
509C2×D4C22×C4×C3112yes—
510C2×D4C2×D4×C3112yes—
511C2×D4#41×C3112yes—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4C2×D4×C3111yescharacteristic
531C22×C4C2×D4×C3111yescharacteristic
532C22×C4C2×D4×C3111yescharacteristic
533C22×C4C2×D4×C3111yescharacteristic
534C22×C4C2×D4×C3111yescharacteristic
535C22×C4C2×D4×C3111yescharacteristic
536C22×C4C24×C3111yescharacteristic
537SD16—28no—
538D8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8C22×C4×C3112yes—
550C2×C8C22×C4×C3112yes—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4C22×C4×C3112yes—
560C4⋊C4C2×D4×C3112yes—
561C4⋊C4#41×C3112yes—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—24no—
566C22⋊C4—24no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—21no—
574C42—21no—
575C42—41no—
576C42—42no—
577C42—42no—
578C42—42no—
579C42—42no—
580C42C22×C4×C3112yes—
581C42C2×D4×C3112yes—
582C42#41×C3112yes—
583C42#41×C3112yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C22×D4×C3111yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4C4×D4×C3114yes—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—48no—
627C2×C4—48no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—48no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4C4×D4×C3112yes—
645C2×C4C4×D4×C3112yes—
646C2×C4C31×#12112yes—
647C2×C4C31×#12112yes—
648C2×C4C31×#13512yes—
649C2×C4C31×#13512yes—
650C2×C4C31×AGL(1,ℤ/8)12yes—
651C2×C4C23×C4×C3111yescharacteristic
652C2×C4C22×D4×C3111yescharacteristic
653C2×C4C2×#41×C3111yescharacteristic
654C2×C4C2×#41×C3111yescharacteristic
655C2×C4C2×#41×C3111yescharacteristic
656C2×C4C2×#41×C3111yescharacteristic
657C8—22no—
658C8—22no—
659C8—41no—
660C8—41no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×C4×D4×C3111yescharacteristic
676C22C2×C31×#12111yescharacteristic
677C22C31×#52511yescharacteristic
678C22C2×C31×#13511yescharacteristic
679C22C2×C31×#13511yescharacteristic
680C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
681C22C31×#57511yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—41no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4C31×#46314yesdirect product factor
694C4C2×C4×D4×C3111yescharacteristic
695C4C4×#41×C3111yescharacteristic
696C4C31×#52911yescharacteristic
697C4C31×#53211yescharacteristic
698C2—44no—
699C2—82no—
700C2C4×C31×#12111yescharacteristic
701C2C4×C31×#13511yescharacteristic
702C2C4×C31×AGL(1,ℤ/8)11yescharacteristic
703C2C2×C31×#46311yescharacteristic
704C2C31×#303511yescharacteristic
705C2C31×#310211yescharacteristic
706C2C31×#310511yescharacteristic
subgroupG/H
centerC22×C4×C31C2×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC23×C31C22×D4
prime radicalC22×D8×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C43×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C31C2semidirect
4. C4×C31×#124C2semidirect
5. C42×D4×C31C2semidirect
6. C31×#1983C2semidirect
7. C31×#1949C2semidirect
8. C31×#1928C2semidirect
9. C31×#1926C2semidirect
11. C31×#1877C2semidirect
12. C31×#1804C2semidirect
13. C4×C31×C4⋊C8C2semidirect
14. C4×C31×#103C2semidirect
15. C4×C31×#102C2semidirect
25. C31×#463C4direct (N × H)
71. C2×SD16×C31C2×C4semidirect
80. C31×#124C2×C4semidirect
89. C4×D4×C31C2×C4semidirect
120. C31×C4⋊C8C2×C4semidirect
123. C31×#103C2×C4semidirect
128. C31×#102C2×C4semidirect
230. C4×#463C31direct (N × H)
309. C2×C4×SD16C2×C31semidirect
311. C4×#124C2×C31semidirect
312. C42×D4C2×C31semidirect
313. #1983C2×C31semidirect
314. #1949C2×C31semidirect
315. #1928C2×C31semidirect
316. #1926C2×C31semidirect
318. #1877C2×C31semidirect
319. #1804C2×C31semidirect
320. C4×C4⋊C8C2×C31semidirect
321. C4×#103C2×C31semidirect
322. C4×#102C2×C31semidirect
355. C4×C31#463direct (N × H)
369. #463C4×C31direct (N × H)
424. C2×SD16C2×C4×C31semidirect
433. #124C2×C4×C31semidirect
442. C4×D4C2×C4×C31semidirect
473. C4⋊C8C2×C4×C31semidirect
476. #103C2×C4×C31semidirect
481. #102C2×C4×C31semidirect
491. C31C4×#463direct (N × H)
693. C4C31×#463direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4632
C2×C4×SD16×C312
C2×C4×D8×C312
C4×C31×#1242
C42×D4×C312
C31×#19832
C31×#19492
C31×#19282
C31×#19262
C31×#18792
C31×#18772
C31×#18042
C4×C31×C4⋊C82
C4×C31×#1032
C4×C31×#1022
C4×#46331