Finite Group Databasebeta

← C2×C31×#2008 #21480169

Subgroups — C2×C31×#2008 #21480169

Order 7936.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic, complemented
2C22×C31×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C2×C31×#535C211yesmaximal, characteristic, complemented
4C2×C31×#421C211yesmaximal, characteristic, complemented
5C2×C31×#418C211yesmaximal, characteristic, complemented
6C2×C31×#410C211yesmaximal, characteristic, complemented
7C31×#2008C218yesmaximal, direct product factor
8C2×C31×#344C211yesmaximal, characteristic, complemented
9C22×#41×C31C2211yescharacteristic
10C22×#41×C31C2211yescharacteristic
11C23×D4×C31C2211yescharacteristic
12C31×#575—22no—
13C31×#575—22no—
14C31×#575—22no—
15C31×#575C2214yescomplemented
16C2×C31×#137—21no—
17C2×C31×#137—21no—
18C2×C31×AGL(1,ℤ/8)—22no—
19C2×C31×AGL(1,ℤ/8)—22no—
20C2×C31×AGL(1,ℤ/8)—22no—
21C2×C31×AGL(1,ℤ/8)—21no—
22C2×C31×AGL(1,ℤ/8)—21no—
23C2×C31×AGL(1,ℤ/8)—22no—
24C2×C31×AGL(1,ℤ/8)—22no—
25C2×C31×AGL(1,ℤ/8)C2214yescomplemented
26C2×C31×#135—22no—
27C22×SD16×C31—21no—
28C22×D8×C31—21no—
29C22×M16×C31C2211yescharacteristic
30C22×M16×C31C2211yescharacteristic
31C31×#535—22no—
32C31×#535—22no—
33C31×#535—22no—
34C31×#535C2214yescomplemented
35C2×C31×#127—21no—
36C2×C31×#124—21no—
37C2×C31×#121—22no—
38C2×C31×#120—22no—
39C2×C31×#117C2211yescharacteristic
40C2×C31×#117C2211yescharacteristic
41C31×#421—22no—
42C31×#421C2214yescomplemented
43C2×C31×#104—22no—
44C31×#418—22no—
45C31×#418C2214yescomplemented
46C2×C31×#102—22no—
47C31×#410—22no—
48C31×#410C2214yescomplemented
49C2×C31×#99—22no—
50C31×#344C2214yescomplemented
51C25×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×C31—21no—
63C2×#41×C31—21no—
64C2×#41×C31—21no—
65C2×#41×C31—21no—
66C2×#41×C31—21no—
67C2×#41×C31—21no—
68C2×#41×C31—21no—
69C2×#41×C31—21no—
70C2×#41×C31—21no—
71C2×#41×C31—21no—
72C2×#41×C31D412yes—
73C2×#41×C31D412yescomplemented
74C2×#41×C31C2312yes—
75C2×#41×C31C2312yes—
76C22×Q8×C31D411yescharacteristic
77C22×Q8×C31D411yescharacteristic, complemented
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—24no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31—21no—
85C22×D4×C31—21no—
86C22×D4×C31—21no—
87C22×D4×C31—21no—
88C22×D4×C31—21no—
89C22×D4×C31—21no—
90C22×D4×C31—21no—
91C22×D4×C31—21no—
92C22×D4×C31D412yes—
93C22×D4×C31D411yescharacteristic
94C22×D4×C31D412yes—
95C22×D4×C31D411yescharacteristic, complemented
96C22×D4×C31C2312yes—
97C23×C4×C31—21no—
98C23×C4×C31—21no—
99C23×C4×C31C2311yescharacteristic
100C31×#137—24no—
101C31×#137—24no—
102C31×#137—24no—
103C31×#137—24no—
104C31×AGL(1,ℤ/8)—28no—
105C31×AGL(1,ℤ/8)—28no—
106C31×AGL(1,ℤ/8)—24no—
107C31×AGL(1,ℤ/8)—24no—
108C31×AGL(1,ℤ/8)—28no—
109C31×AGL(1,ℤ/8)—24no—
110C31×AGL(1,ℤ/8)—24no—
111C31×AGL(1,ℤ/8)—28no—
112C31×#135—28no—
113C31×#135—28no—
114C2×Q16×C31—22no—
115C2×SD16×C31—24no—
116C2×SD16×C31—24no—
117C2×SD16×C31—22no—
118C2×SD16×C31—22no—
119C2×SD16×C31—24no—
120C2×D8×C31—24no—
121C2×D8×C31—24no—
122C2×D8×C31—22no—
123C2×D8×C31—24no—
124C2×M16×C31—21no—
125C2×M16×C31—21no—
126C2×M16×C31—21no—
127C2×M16×C31—21no—
128C2×M16×C31—21no—
129C2×M16×C31—21no—
130C2×M16×C31—21no—
131C2×M16×C31D412yescomplemented
132C2×M16×C31D412yescomplemented
133C2×M16×C31D412yescomplemented
134C2×M16×C31C2312yes—
135C2×M16×C31C2312yes—
136C22×C8×C31—21no—
137C22×C8×C31D412yescomplemented
138C31×#127—24no—
139C31×#127—24no—
140C31×#124—24no—
141C31×#124—24no—
142C31×#121—28no—
143C31×#121—28no—
144C31×#120—28no—
145C31×#120—28no—
146C31×#117—21no—
147C31×#117—21no—
148C31×#117—21no—
149C31×#117—21no—
150C31×#117—21no—
151C31×#117D412yes—
152C31×#117C2312yes—
153C31×#117C2312yes—
154C2×C4⋊C4×C31—21no—
155C2×C4⋊C4×C31—21no—
156C2×C22⋊C4×C31—24no—
157C2×C22⋊C4×C31—21no—
158C2×C22⋊C4×C31D412yes—
159C2×C42×C31—21no—
160C2×C42×C31—21no—
161C31×#104—28no—
162C31×#102—28no—
163C31×#99—28no—
164C24×C31—22no—
165C24×C31—21no—
166C24×C31—22no—
167C24×C31—21no—
168C24×C31—22no—
169C24×C31—41no—
170C24×C31—41no—
171C24×C31—41no—
172C24×C31—41no—
173C24×C31—84no—
174C24×C31C2×D411yescharacteristic
175#41×C31—22no—
176#41×C31—22no—
177#41×C31—22no—
178#41×C31—22no—
179#41×C31—22no—
180#41×C31—22no—
181#41×C31—22no—
182#41×C31—22no—
183#41×C31—22no—
184#41×C31—22no—
185#41×C31—22no—
186#41×C31—22no—
187#41×C31—22no—
188#41×C31—22no—
189#41×C31—22no—
190#41×C31—22no—
191#41×C31—41no—
192#41×C31—41no—
193#41×C31—41no—
194#41×C31—41no—
195#41×C31—41no—
196#41×C31—41no—
197#41×C31—41no—
198#41×C31—41no—
199#41×C31—41no—
200#41×C31—41no—
201#41×C31—41no—
202#41×C31—41no—
203#41×C31—41no—
204#41×C31—41no—
205#41×C31—41no—
206#41×C31—41no—
207C2×Q8×C31—21no—
208C2×Q8×C31—21no—
209C2×Q8×C31—21no—
210C2×Q8×C31—21no—
211C2×Q8×C31—21no—
212C2×Q8×C31—21no—
213C2×Q8×C31—21no—
214C2×Q8×C31—21no—
215C2×Q8×C31—21no—
216C2×Q8×C31—21no—
217C2×Q8×C31C2×D412yes—
218C2×Q8×C31C2×D412yescomplemented
219C2×D4×C31—22no—
220C2×D4×C31—22no—
221C2×D4×C31—22no—
222C2×D4×C31—22no—
223C2×D4×C31—216no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—22no—
227C2×D4×C31—22no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—22no—
231C2×D4×C31—22no—
232C2×D4×C31—21no—
233C2×D4×C31—21no—
234C2×D4×C31—22no—
235C2×D4×C31—22no—
236C2×D4×C31—21no—
237C2×D4×C31—22no—
238C2×D4×C31—22no—
239C2×D4×C31—22no—
240C2×D4×C31—22no—
241C2×D4×C31—21no—
242C2×D4×C31—21no—
243C2×D4×C31—21no—
244C2×D4×C31—22no—
245C2×D4×C31—22no—
246C2×D4×C31—22no—
247C2×D4×C31—22no—
248C2×D4×C31—22no—
249C2×D4×C31—41no—
250C2×D4×C31—41no—
251C2×D4×C31—41no—
252C2×D4×C31—41no—
253C2×D4×C31—41no—
254C2×D4×C31—41no—
255C2×D4×C31—41no—
256C2×D4×C31—41no—
257C2×D4×C31—41no—
258C2×D4×C31—41no—
259C2×D4×C31—41no—
260C2×D4×C31—41no—
261C2×D4×C31—41no—
262C2×D4×C31—41no—
263C2×D4×C31—41no—
264C2×D4×C31—41no—
265C2×D4×C31—41no—
266C2×D4×C31—41no—
267C2×D4×C31—41no—
268C2×D4×C31—41no—
269C2×D4×C31—88no—
270C2×D4×C31C2×D414yes—
271C2×D4×C31C2×D412yes—
272C2×D4×C31C2×D412yescomplemented
273C22×C4×C31—22no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—22no—
277C22×C4×C31—22no—
278C22×C4×C31—22no—
279C22×C4×C31—22no—
280C22×C4×C31—41no—
281C22×C4×C31—41no—
282C22×C4×C31—41no—
283C22×C4×C31—41no—
284C22×C4×C31—41no—
285C22×C4×C31—41no—
286C22×C4×C31—41no—
287C22×C4×C31—41no—
288C22×C4×C31—41no—
289C22×C4×C31C2×D411yescharacteristic
290C22×C4×C31C2×D411yescharacteristic
291C22×C4×C31C2×D411yescharacteristic
292C22×C4×C31C2×D411yescharacteristic
293C22×C4×C31C2×D411yescharacteristic
294C22×C4×C31C2×D411yescharacteristic
295C22×C4×C31C2×D411yescharacteristic
296C22×C4×C31C2×D411yescharacteristic
297C22×C4×C31C2×D411yescharacteristic
298C22×C4×C31C2×D411yescharacteristic
299C22×C4×C31C2×D411yescharacteristic
300C22×C4×C31#4111yescharacteristic
301C22×C4×C31#4111yescharacteristic
302C22×C4×C31C2411yescharacteristic
303Q16×C31—28no—
304SD16×C31—216no—
305SD16×C31—28no—
306SD16×C31—28no—
307D8×C31—216no—
308D8×C31—28no—
309M16×C31—22no—
310M16×C31—22no—
311M16×C31—22no—
312M16×C31—22no—
313M16×C31—22no—
314M16×C31—22no—
315M16×C31—22no—
316M16×C31C2×D414yescomplemented
317C2×C8×C31—22no—
318C2×C8×C31—22no—
319C2×C8×C31—22no—
320C2×C8×C31—22no—
321C2×C8×C31—22no—
322C2×C8×C31C2×D414yescomplemented
323C4⋊C4×C31—22no—
324C4⋊C4×C31—22no—
325C4⋊C4×C31—22no—
326C4⋊C4×C31—41no—
327C22⋊C4×C31—216no—
328C22⋊C4×C31—22no—
329C22⋊C4×C31—22no—
330C22⋊C4×C31—41no—
331C22⋊C4×C31C2×D414yes—
332C42×C31—22no—
333C42×C31—22no—
334C42×C31—22no—
335C42×C31—41no—
336C2×#2008C3111yesmaximal, characteristic, direct product factor, Sylow
337C23×C31—24no—
338C23×C31—22no—
339C23×C31—22no—
340C23×C31—42no—
341C23×C31—44no—
342C23×C31—48no—
343C23×C31—42no—
344C23×C31—42no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—42no—
348C23×C31—42no—
349C23×C31—42no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—42no—
353C23×C31—82no—
354C23×C31—84no—
355C23×C31—84no—
356C23×C31—84no—
357C23×C31—84no—
358C23×C31—84no—
359C23×C31—84no—
360C23×C31#12011yescharacteristic
361C23×C31#12011yescharacteristic
362C23×C31#12111yescharacteristic
363C23×C31#12111yescharacteristic
364C23×C31#12711yescharacteristic
365C23×C31#12711yescharacteristic
366C23×C31C22×D411yescharacteristic
367Q8×C31—22no—
368Q8×C31—22no—
369Q8×C31—22no—
370Q8×C31—22no—
371Q8×C31—41no—
372Q8×C31—41no—
373Q8×C31—41no—
374Q8×C31—41no—
375D4×C31—22no—
376D4×C31—24no—
377D4×C31—22no—
378D4×C31—22no—
379D4×C31—24no—
380D4×C31—22no—
381D4×C31—42no—
382D4×C31—42no—
383D4×C31—42no—
384D4×C31—42no—
385D4×C31—42no—
386D4×C31—42no—
387D4×C31—42no—
388D4×C31—42no—
389D4×C31—42no—
390D4×C31—42no—
391D4×C31—42no—
392D4×C31—42no—
393D4×C31—42no—
394D4×C31—42no—
395D4×C31—41no—
396D4×C31—41no—
397D4×C31—41no—
398D4×C31—41no—
399D4×C31—816no—
400C2×C4×C31—24no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—44no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—42no—
409C2×C4×C31—42no—
410C2×C4×C31—42no—
411C2×C4×C31—42no—
412C2×C4×C31—42no—
413C2×C4×C31—42no—
414C2×C4×C31—42no—
415C2×C4×C31—42no—
416C2×C4×C31—42no—
417C2×C4×C31—82no—
418C2×C4×C31#12011yescharacteristic
419C2×C4×C31#12011yescharacteristic
420C2×C4×C31#12011yescharacteristic
421C2×C4×C31#12011yescharacteristic
422C2×C4×C31#12011yescharacteristic
423C2×C4×C31#12011yescharacteristic
424C2×C4×C31#12011yescharacteristic
425C2×C4×C31#12011yescharacteristic
426C2×C4×C31#12011yescharacteristic
427C2×C4×C31#12011yescharacteristic
428C2×C4×C31#12111yescharacteristic
429C2×C4×C31#12111yescharacteristic
430C2×C4×C31#12111yescharacteristic
431C2×C4×C31#12111yescharacteristic
432C2×C4×C31#12111yescharacteristic
433C2×C4×C31#12111yescharacteristic
434C2×C4×C31#12111yescharacteristic
435C2×C4×C31#12111yescharacteristic
436C2×C4×C31#12111yescharacteristic
437C2×C4×C31#12111yescharacteristic
438C2×C4×C31#12711yescharacteristic
439C2×C4×C31#12711yescharacteristic
440C2×C4×C31C22×D411yescharacteristic
441C2×C4×C31C22×D411yescharacteristic
442C2×C4×C31C22×D411yescharacteristic
443C2×C4×C31C22×D411yescharacteristic
444C2×C4×C31C22×D411yescharacteristic
445C2×C4×C31C2×#4111yescharacteristic
446C8×C31—24no—
447C8×C31—24no—
448C2×#575C2×C3111yescharacteristic, complemented
449C22×AGL(1,ℤ/8)C2×C3111yescharacteristic, complemented
450C2×#535C2×C3111yescharacteristic, complemented
451C2×#421C2×C3111yescharacteristic, complemented
452C2×#418C2×C3111yescharacteristic, complemented
453C2×#410C2×C3111yescharacteristic, complemented
454#2008C2×C3118yesdirect product factor
455C2×#344C2×C3111yescharacteristic, complemented
456C22×C31—22no—
457C22×C31—22no—
458C22×C31—22no—
459C22×C31—41no—
460C22×C31—41no—
461C22×C31—41no—
462C22×C31—41no—
463C22×C31—44no—
464C22×C31—48no—
465C22×C31—42no—
466C22×C31—42no—
467C22×C31—44no—
468C22×C31—82no—
469C22×C31—82no—
470C22×C31—84no—
471C22×C31—82no—
472C22×C31—84no—
473C22×C31—84no—
474C22×C31—84no—
475C22×C31—84no—
476C22×C31—82no—
477C22×C31—84no—
478C22×C31—82no—
479C22×C31#39211yescharacteristic
480C22×C31#39211yescharacteristic
481C22×C31#39211yescharacteristic
482C22×C31#39211yescharacteristic
483C22×C31C2×#12011yescharacteristic
484C22×C31C2×#12111yescharacteristic
485C22×C31C2×#12711yescharacteristic
486C4×C31—44no—
487C4×C31—42no—
488C4×C31—42no—
489C4×C31—82no—
490C4×C31#39211yescharacteristic
491C4×C31#39211yescharacteristic
492C4×C31#39211yescharacteristic
493C4×C31#39211yescharacteristic
494C4×C31C2×#12011yescharacteristic
495C4×C31C2×#12011yescharacteristic
496C4×C31C2×#12111yescharacteristic
497C4×C31C2×#12111yescharacteristic
498C22×#41C22×C3111yescharacteristic
499C22×#41C22×C3111yescharacteristic
500C23×D4C22×C3111yescharacteristic
501#575—22no—
502#575—22no—
503#575—22no—
504#575C22×C3114yescomplemented
505C2×#137—21no—
506C2×#137—21no—
507C2×AGL(1,ℤ/8)—22no—
508C2×AGL(1,ℤ/8)—22no—
509C2×AGL(1,ℤ/8)—22no—
510C2×AGL(1,ℤ/8)—21no—
511C2×AGL(1,ℤ/8)—21no—
512C2×AGL(1,ℤ/8)—22no—
513C2×AGL(1,ℤ/8)—22no—
514C2×AGL(1,ℤ/8)C22×C3114yescomplemented
515C2×#135—22no—
516C22×SD16—21no—
517C22×D8—21no—
518C22×M16C22×C3111yescharacteristic
519C22×M16C22×C3111yescharacteristic
520#535—22no—
521#535—22no—
522#535—22no—
523#535C22×C3114yescomplemented
524C2×#127—21no—
525C2×#124—21no—
526C2×#121—22no—
527C2×#120—22no—
528C2×#117C22×C3111yescharacteristic
529C2×#117C22×C3111yescharacteristic
530#421—22no—
531#421C22×C3114yescomplemented
532C2×#104—22no—
533#418—22no—
534#418C22×C3114yescomplemented
535C2×#102—22no—
536#410—22no—
537#410C22×C3114yescomplemented
538C2×#99—22no—
539#344C22×C3114yescomplemented
540C2×C31—21no—
541C2×C31—21no—
542C2×C31—21no—
543C2×C31—21no—
544C2×C31—21no—
545C2×C31—21no—
546C2×C31—82no—
547C2×C31—84no—
548C2×C31—82no—
549C2×C31#200812yesdirect product factor
550C2×C31C2×#39211yescharacteristic
551C25—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41D4×C3112yes—
573C2×#41D4×C3112yescomplemented
574C2×#41C23×C3112yes—
575C2×#41C23×C3112yes—
576C22×Q8D4×C3111yescharacteristic
577C22×Q8D4×C3111yescharacteristic, complemented
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—24no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4D4×C3112yes—
593C22×D4D4×C3111yescharacteristic
594C22×D4D4×C3112yes—
595C22×D4D4×C3111yescharacteristic, complemented
596C22×D4C23×C3112yes—
597C23×C4—21no—
598C23×C4—21no—
599C23×C4C23×C3111yescharacteristic
600#137—24no—
601#137—24no—
602#137—24no—
603#137—24no—
604AGL(1,ℤ/8)—28no—
605AGL(1,ℤ/8)—28no—
606AGL(1,ℤ/8)—24no—
607AGL(1,ℤ/8)—24no—
608AGL(1,ℤ/8)—28no—
609AGL(1,ℤ/8)—24no—
610AGL(1,ℤ/8)—24no—
611AGL(1,ℤ/8)—28no—
612#135—28no—
613#135—28no—
614C2×Q16—22no—
615C2×SD16—24no—
616C2×SD16—24no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—24no—
620C2×D8—24no—
621C2×D8—24no—
622C2×D8—22no—
623C2×D8—24no—
624C2×M16—21no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16—21no—
630C2×M16—21no—
631C2×M16D4×C3112yescomplemented
632C2×M16D4×C3112yescomplemented
633C2×M16D4×C3112yescomplemented
634C2×M16C23×C3112yes—
635C2×M16C23×C3112yes—
636C22×C8—21no—
637C22×C8D4×C3112yescomplemented
638#127—24no—
639#127—24no—
640#124—24no—
641#124—24no—
642#121—28no—
643#121—28no—
644#120—28no—
645#120—28no—
646#117—21no—
647#117—21no—
648#117—21no—
649#117—21no—
650#117—21no—
651#117D4×C3112yes—
652#117C23×C3112yes—
653#117C23×C3112yes—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4D4×C3112yes—
659C2×C42—21no—
660C2×C42—21no—
661#104—28no—
662#102—28no—
663#99—28no—
664C31C2×#200811yescharacteristic, direct product factor, Sylow
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—41no—
674C24—84no—
675C24C2×D4×C3111yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—22no—
685#41—22no—
686#41—22no—
687#41—22no—
688#41—22no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696#41—41no—
697#41—41no—
698#41—41no—
699#41—41no—
700#41—41no—
701#41—41no—
702#41—41no—
703#41—41no—
704#41—41no—
705#41—41no—
706#41—41no—
707#41—41no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8C2×D4×C3112yes—
719C2×Q8C2×D4×C3112yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—216no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—41no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—41no—
770C2×D4—88no—
771C2×D4C2×D4×C3114yes—
772C2×D4C2×D4×C3112yes—
773C2×D4C2×D4×C3112yescomplemented
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4C2×D4×C3111yescharacteristic
791C22×C4C2×D4×C3111yescharacteristic
792C22×C4C2×D4×C3111yescharacteristic
793C22×C4C2×D4×C3111yescharacteristic
794C22×C4C2×D4×C3111yescharacteristic
795C22×C4C2×D4×C3111yescharacteristic
796C22×C4C2×D4×C3111yescharacteristic
797C22×C4C2×D4×C3111yescharacteristic
798C22×C4C2×D4×C3111yescharacteristic
799C22×C4C2×D4×C3111yescharacteristic
800C22×C4C2×D4×C3111yescharacteristic
801C22×C4#41×C3111yescharacteristic
802C22×C4#41×C3111yescharacteristic
803C22×C4C24×C3111yescharacteristic
804Q16—28no—
805SD16—216no—
806SD16—28no—
807SD16—28no—
808D8—216no—
809D8—28no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—22no—
814M16—22no—
815M16—22no—
816M16—22no—
817M16C2×D4×C3114yescomplemented
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—22no—
822C2×C8—22no—
823C2×C8C2×D4×C3114yescomplemented
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—41no—
828C22⋊C4—216no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—41no—
832C22⋊C4C2×D4×C3114yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—41no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—42no—
841C23—44no—
842C23—48no—
843C23—42no—
844C23—42no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—82no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23C31×#12011yescharacteristic
861C23C31×#12011yescharacteristic
862C23C31×#12111yescharacteristic
863C23C31×#12111yescharacteristic
864C23C31×#12711yescharacteristic
865C23C31×#12711yescharacteristic
866C23C22×D4×C3111yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875D4—22no—
876D4—24no—
877D4—22no—
878D4—22no—
879D4—24no—
880D4—22no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—42no—
894D4—42no—
895D4—41no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—816no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—82no—
918C2×C4C31×#12011yescharacteristic
919C2×C4C31×#12011yescharacteristic
920C2×C4C31×#12011yescharacteristic
921C2×C4C31×#12011yescharacteristic
922C2×C4C31×#12011yescharacteristic
923C2×C4C31×#12011yescharacteristic
924C2×C4C31×#12011yescharacteristic
925C2×C4C31×#12011yescharacteristic
926C2×C4C31×#12011yescharacteristic
927C2×C4C31×#12011yescharacteristic
928C2×C4C31×#12111yescharacteristic
929C2×C4C31×#12111yescharacteristic
930C2×C4C31×#12111yescharacteristic
931C2×C4C31×#12111yescharacteristic
932C2×C4C31×#12111yescharacteristic
933C2×C4C31×#12111yescharacteristic
934C2×C4C31×#12111yescharacteristic
935C2×C4C31×#12111yescharacteristic
936C2×C4C31×#12111yescharacteristic
937C2×C4C31×#12111yescharacteristic
938C2×C4C31×#12711yescharacteristic
939C2×C4C31×#12711yescharacteristic
940C2×C4C22×D4×C3111yescharacteristic
941C2×C4C22×D4×C3111yescharacteristic
942C2×C4C22×D4×C3111yescharacteristic
943C2×C4C22×D4×C3111yescharacteristic
944C2×C4C22×D4×C3111yescharacteristic
945C2×C4C2×#41×C3111yescharacteristic
946C8—24no—
947C8—24no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—48no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—82no—
961C22—84no—
962C22—82no—
963C22—84no—
964C22—84no—
965C22—84no—
966C22—84no—
967C22—82no—
968C22—84no—
969C22—82no—
970C22—82no—
971C22C31×#39211yescharacteristic
972C22C31×#39211yescharacteristic
973C22C31×#39211yescharacteristic
974C22C31×#39211yescharacteristic
975C22C2×C31×#12011yescharacteristic
976C22C2×C31×#12111yescharacteristic
977C22C2×C31×#12711yescharacteristic
978C4—44no—
979C4—42no—
980C4—42no—
981C4—82no—
982C4C31×#39211yescharacteristic
983C4C31×#39211yescharacteristic
984C4C31×#39211yescharacteristic
985C4C31×#39211yescharacteristic
986C4C2×C31×#12011yescharacteristic
987C4C2×C31×#12011yescharacteristic
988C4C2×C31×#12111yescharacteristic
989C4C2×C31×#12111yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—82no—
999C2C31×#200812yesdirect product factor
1000C2C2×C31×#39211yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#575C2semidirect
2. C22×C31×AGL(1,ℤ/8)C2semidirect
3. C2×C31×#535C2semidirect
4. C2×C31×#421C2semidirect
5. C2×C31×#418C2semidirect
6. C2×C31×#410C2semidirect
7. C31×#2008C2direct (N × H)
8. C2×C31×#344C2semidirect
15. C31×#575C22semidirect
25. C2×C31×AGL(1,ℤ/8)C22semidirect
34. C31×#535C22semidirect
42. C31×#421C22semidirect
45. C31×#418C22semidirect
48. C31×#410C22semidirect
50. C31×#344C22semidirect
73. C2×#41×C31D4semidirect
77. C22×Q8×C31D4semidirect
95. C22×D4×C31D4semidirect
131. C2×M16×C31D4semidirect
132. C2×M16×C31D4semidirect
133. C2×M16×C31D4semidirect
137. C22×C8×C31D4semidirect
218. C2×Q8×C31C2×D4semidirect
272. C2×D4×C31C2×D4semidirect
316. M16×C31C2×D4semidirect
322. C2×C8×C31C2×D4semidirect
336. C2×#2008C31direct (N × H)
448. C2×#575C2×C31semidirect
449. C22×AGL(1,ℤ/8)C2×C31semidirect
450. C2×#535C2×C31semidirect
451. C2×#421C2×C31semidirect
452. C2×#418C2×C31semidirect
453. C2×#410C2×C31semidirect
454. #2008C2×C31direct (N × H)
455. C2×#344C2×C31semidirect
504. #575C22×C31semidirect
514. C2×AGL(1,ℤ/8)C22×C31semidirect
523. #535C22×C31semidirect
531. #421C22×C31semidirect
534. #418C22×C31semidirect
537. #410C22×C31semidirect
539. #344C22×C31semidirect
549. C2×C31#2008direct (N × H)
573. C2×#41D4×C31semidirect
577. C22×Q8D4×C31semidirect
595. C22×D4D4×C31semidirect
631. C2×M16D4×C31semidirect
632. C2×M16D4×C31semidirect
633. C2×M16D4×C31semidirect
637. C22×C8D4×C31semidirect
664. C31C2×#2008direct (N × H)
719. C2×Q8C2×D4×C31semidirect
773. C2×D4C2×D4×C31semidirect
817. M16C2×D4×C31semidirect
823. C2×C8C2×D4×C31semidirect
999. C2C31×#2008direct (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
C22×C31×AGL(1,ℤ/8)2
C2×C31×#5352
C2×C31×#4212
C2×C31×#4182
C2×C31×#4102
C31×#20082
C2×C31×#3442
C2×#200831