Finite Group Databasebeta

← C31×#20998 #21477757

Subgroups — C31×#20998 #21477757

Order 7936.

1704 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#575C211yesmaximal, characteristic
2C31×#3428C211yesmaximal, characteristic, complemented
3C2×C31×#421C211yesmaximal, characteristic, complemented
4C31×#2896C211yesmaximal, characteristic, complemented
5C2×C31×#410C211yesmaximal, characteristic, complemented
6C31×#1905C214yesmaximal, complemented
7C31×#1904C214yesmaximal, complemented
8C2×C31×#344C211yesmaximal, characteristic, complemented
9C2×C31×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
10C22×#41×C31C2211yescharacteristic
11C22×#41×C31C2211yescharacteristic
12C31×#575—22no—
13C31×#575—22no—
14C31×#575—22no—
15C31×#575—22no—
16C2×C31×#137C412yescomplemented
17C2×C31×#137C2212yes—
18C2×C31×AGL(1,ℤ/8)C412yescomplemented
19C2×C31×AGL(1,ℤ/8)C2212yes—
20C2×C31×#135C414yescomplemented
21C22×M16×C31C2211yescharacteristic
22C22×M16×C31C2211yescharacteristic
23C31×#520—22no—
24C31×#520—22no—
25C31×#519C2212yescomplemented
26C31×#518—22no—
27C31×#518C2212yescomplemented
28C4×#41×C31—22no—
29C4×#41×C31—22no—
30C2×C31×#117—22no—
31C2×C31×#117C2211yescharacteristic
32C2×C31×#117C2211yescharacteristic
33C2×C31×#117C2211yescharacteristic
34C31×#421—22no—
35C31×#421C2214yes—
36C2×C31×#104—22no—
37C31×#419C2212yescomplemented
38C31×#418C2212yescomplemented
39C31×#417—22no—
40C31×#416—22no—
41C31×#410—22no—
42C31×#410C2214yes—
43C2×C31×#99—22no—
44C31×#344C2214yescomplemented
45C31×H(3,ℤ/4)C2214yescomplemented
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×C31D412yes—
69C2×#41×C31C2312yes—
70C22×Q8×C31C2×C411yescharacteristic, complemented
71C22×Q8×C31C2311yescharacteristic
72C22×D4×C31—21no—
73C22×D4×C31—21no—
74C22×D4×C31C2×C411yescharacteristic, complemented
75C22×D4×C31C2311yescharacteristic
76C23×C4×C31—21no—
77C23×C4×C31—21no—
78C23×C4×C31C2311yescharacteristic
79C31×#137—24no—
80C31×#137—24no—
81C31×#137—24no—
82C31×#137—24no—
83C31×AGL(1,ℤ/8)—24no—
84C31×AGL(1,ℤ/8)—24no—
85C31×AGL(1,ℤ/8)—24no—
86C31×AGL(1,ℤ/8)—24no—
87C31×#135—28no—
88C31×#135—28no—
89C2×Q16×C31C2×C414yescomplemented
90C2×SD16×C31C2×C414yescomplemented
91C2×SD16×C31C2×C414yescomplemented
92C2×D8×C31C2×C414yescomplemented
93C2×M16×C31—21no—
94C2×M16×C31—21no—
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×C31C2×C412yescomplemented
103C2×M16×C31C2312yes—
104C2×M16×C31C2312yes—
105C22×C8×C31—21no—
106C22×C8×C31C2×C412yescomplemented
107C4×Q8×C31—24no—
108C4×Q8×C31—24no—
109C4×D4×C31—28no—
110C4×D4×C31—28no—
111C4×D4×C31—24no—
112C4×D4×C31—24no—
113C31×#117—24no—
114C31×#117—24no—
115C31×#117—21no—
116C31×#117—21no—
117C31×#117—21no—
118C31×#117—21no—
119C31×#117—24no—
120C31×#117—21no—
121C31×#117—21no—
122C31×#117—21no—
123C31×#117D412yes—
124C31×#117D412yes—
125C31×#117C2312yes—
126C31×#117C2312yes—
127C31×#117C2312yes—
128C2×C4⋊C4×C31—24no—
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—24no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31D412yes—
136C2×C42×C31—24no—
137C2×C42×C31—21no—
138C2×C42×C31—21no—
139C2×C42×C31D412yes—
140C31×#104—28no—
141C31×#103—24no—
142C31×#102—24no—
143C31×#99—28no—
144C24×C31—21no—
145C24×C31—21no—
146C24×C31C2×D411yescharacteristic
147#41×C31—22no—
148#41×C31—22no—
149#41×C31—22no—
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—41no—
168#41×C31—41no—
169#41×C31—41no—
170#41×C31—41no—
171#41×C31—41no—
172#41×C31—41no—
173#41×C31—41no—
174#41×C31—41no—
175#41×C31C22⋊C414yes—
176#41×C31C22⋊C414yes—
177#41×C31C22⋊C414yes—
178#41×C31C22⋊C414yes—
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×C31C22×C412yes—
188C2×Q8×C31C22×C412yes—
189C2×Q8×C31C2×D412yes—
190C2×Q8×C31C2×D412yes—
191C2×D4×C31—22no—
192C2×D4×C31—22no—
193C2×D4×C31—22no—
194C2×D4×C31—22no—
195C2×D4×C31—22no—
196C2×D4×C31—22no—
197C2×D4×C31—22no—
198C2×D4×C31—22no—
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—21no—
207C2×D4×C31—41no—
208C2×D4×C31—41no—
209C2×D4×C31—41no—
210C2×D4×C31—41no—
211C2×D4×C31C22×C412yes—
212C2×D4×C31C22×C412yes—
213C2×D4×C31C2×D412yes—
214C2×D4×C31C2×D412yes—
215C22×C4×C31—21no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—22no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—21no—
223C22×C4×C31—28no—
224C22×C4×C31—22no—
225C22×C4×C31—22no—
226C22×C4×C31—22no—
227C22×C4×C31—22no—
228C22×C4×C31—41no—
229C22×C4×C31—41no—
230C22×C4×C31—41no—
231C22×C4×C31—41no—
232C22×C4×C31—41no—
233C22×C4×C31C22×C411yescharacteristic
234C22×C4×C31C22×C411yescharacteristic
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D411yescharacteristic
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31C2×D411yescharacteristic
239C22×C4×C31C2×D411yescharacteristic
240C22×C4×C31C2×D411yescharacteristic
241C22×C4×C31C2×D411yescharacteristic
242C22×C4×C31#4111yescharacteristic
243C22×C4×C31#4111yescharacteristic
244C22×C4×C31#4111yescharacteristic
245C22×C4×C31#4111yescharacteristic
246C22×C4×C31C2411yescharacteristic
247Q16×C31—28no—
248SD16×C31—28no—
249SD16×C31—28no—
250D8×C31—28no—
251M16×C31—22no—
252M16×C31—22no—
253M16×C31—22no—
254M16×C31—22no—
255M16×C31—22no—
256M16×C31—22no—
257M16×C31—41no—
258M16×C31—41no—
259C2×C8×C31—22no—
260C2×C8×C31—22no—
261C2×C8×C31—22no—
262C2×C8×C31—41no—
263C2×C8×C31—41no—
264C2×C8×C31C22×C414yes—
265C4⋊C4×C31—28no—
266C4⋊C4×C31—22no—
267C4⋊C4×C31—22no—
268C4⋊C4×C31—22no—
269C4⋊C4×C31—22no—
270C4⋊C4×C31—22no—
271C4⋊C4×C31—41no—
272C22⋊C4×C31—28no—
273C22⋊C4×C31—22no—
274C22⋊C4×C31—22no—
275C22⋊C4×C31—22no—
276C22⋊C4×C31—22no—
277C22⋊C4×C31—41no—
278C22⋊C4×C31C2×D414yes—
279C42×C31—28no—
280C42×C31—22no—
281C42×C31—22no—
282C42×C31—22no—
283C42×C31—22no—
284C42×C31—41no—
285C42×C31C2×D414yes—
286#20998C3111yesmaximal, characteristic, direct product factor, Sylow
287C23×C31—22no—
288C23×C31—22no—
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—81no—
294C23×C31—82no—
295C23×C31—82no—
296C23×C31C4×D411yescharacteristic
297C23×C31C4×D411yescharacteristic
298C23×C31#12011yescharacteristic
299C23×C31#12011yescharacteristic
300C23×C31#12111yescharacteristic
301C23×C31#12111yescharacteristic
302C23×C31C22×D411yescharacteristic
303Q8×C31—22no—
304Q8×C31—22no—
305Q8×C31—22no—
306Q8×C31—22no—
307Q8×C31—22no—
308Q8×C31—41no—
309Q8×C31—41no—
310Q8×C31C2×C22⋊C414yes—
311D4×C31—24no—
312D4×C31—24no—
313D4×C31—24no—
314D4×C31—24no—
315D4×C31—22no—
316D4×C31—22no—
317D4×C31—22no—
318D4×C31—22no—
319D4×C31—22no—
320D4×C31—42no—
321D4×C31—42no—
322D4×C31—42no—
323D4×C31—42no—
324D4×C31—41no—
325D4×C31—41no—
326D4×C31C2×C22⋊C414yes—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—24no—
331C2×C4×C31—24no—
332C2×C4×C31—24no—
333C2×C4×C31—24no—
334C2×C4×C31—22no—
335C2×C4×C31—24no—
336C2×C4×C31—24no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—82no—
345C2×C4×C31—82no—
346C2×C4×C31—88no—
347C2×C4×C31—82no—
348C2×C4×C31C2×C22⋊C411yescharacteristic
349C2×C4×C31C2×C22⋊C411yescharacteristic
350C2×C4×C31C2×C22⋊C411yescharacteristic
351C2×C4×C31C2×C22⋊C411yescharacteristic
352C2×C4×C31C4×D411yescharacteristic
353C2×C4×C31C4×D411yescharacteristic
354C2×C4×C31C4×D411yescharacteristic
355C2×C4×C31C4×D411yescharacteristic
356C2×C4×C31C4×D411yescharacteristic
357C2×C4×C31C4×D411yescharacteristic
358C2×C4×C31#12011yescharacteristic
359C2×C4×C31#12011yescharacteristic
360C2×C4×C31#12111yescharacteristic
361C2×C4×C31#12111yescharacteristic
362C2×C4×C31#12111yescharacteristic
363C2×C4×C31#12111yescharacteristic
364C2×C4×C31#12111yescharacteristic
365C2×C4×C31#12111yescharacteristic
366C2×C4×C31#12311yescharacteristic
367C2×C4×C31#12311yescharacteristic
368C2×C4×C31#12311yescharacteristic
369C2×C4×C31#12311yescharacteristic
370C2×C4×C31C23×C411yescharacteristic
371C2×C4×C31C22×D411yescharacteristic
372C2×C4×C31C22×D411yescharacteristic
373C2×C4×C31C22×D411yescharacteristic
374C2×C4×C31C2×#4111yescharacteristic
375C2×C4×C31C2×#4111yescharacteristic
376C8×C31—24no—
377C8×C31—42no—
378C2×#575C2×C3111yescharacteristic
379#3428C2×C3111yescharacteristic, complemented
380C2×#421C2×C3111yescharacteristic, complemented
381#2896C2×C3111yescharacteristic, complemented
382C2×#410C2×C3111yescharacteristic, complemented
383#1905C2×C3114yescomplemented
384#1904C2×C3114yescomplemented
385C2×#344C2×C3111yescharacteristic, complemented
386C2×H(3,ℤ/4)C2×C3111yescharacteristic, complemented
387C22×C31—24no—
388C22×C31—41no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—41no—
394C22×C31—41no—
395C22×C31—44no—
396C22×C31—42no—
397C22×C31—82no—
398C22×C31—82no—
399C22×C31—82no—
400C22×C31—82no—
401C22×C31—82no—
402C22×C31#38611yescharacteristic
403C22×C31#38611yescharacteristic
404C22×C31#38611yescharacteristic
405C22×C31#38611yescharacteristic
406C22×C31C2×C4×D411yescharacteristic
407C22×C31C2×#12011yescharacteristic
408C22×C31C2×#12111yescharacteristic
409C4×C31—24no—
410C4×C31—44no—
411C4×C31—44no—
412C4×C31—42no—
413C4×C31—82no—
414C4×C31#38611yescharacteristic
415C4×C31#38611yescharacteristic
416C4×C31#38611yescharacteristic
417C4×C31#38611yescharacteristic
418C4×C31C22×C22⋊C411yescharacteristic
419C4×C31C2×C4×D411yescharacteristic
420C4×C31C2×#12111yescharacteristic
421C4×C31C2×#12311yescharacteristic
422C22×#41C22×C3111yescharacteristic
423C22×#41C22×C3111yescharacteristic
424#575—22no—
425#575—22no—
426#575—22no—
427#575—22no—
428C2×#137C4×C3112yescomplemented
429C2×#137C22×C3112yes—
430C2×AGL(1,ℤ/8)C4×C3112yescomplemented
431C2×AGL(1,ℤ/8)C22×C3112yes—
432C2×#135C4×C3114yescomplemented
433C22×M16C22×C3111yescharacteristic
434C22×M16C22×C3111yescharacteristic
435#520—22no—
436#520—22no—
437#519C22×C3112yescomplemented
438#518—22no—
439#518C22×C3112yescomplemented
440C4×#41—22no—
441C4×#41—22no—
442C2×#117—22no—
443C2×#117C22×C3111yescharacteristic
444C2×#117C22×C3111yescharacteristic
445C2×#117C22×C3111yescharacteristic
446#421—22no—
447#421C22×C3114yes—
448C2×#104—22no—
449#419C22×C3112yescomplemented
450#418C22×C3112yescomplemented
451#417—22no—
452#416—22no—
453#410—22no—
454#410C22×C3114yes—
455C2×#99—22no—
456#344C22×C3114yescomplemented
457H(3,ℤ/4)C22×C3114yescomplemented
458C2×C31—21no—
459C2×C31—21no—
460C2×C31—21no—
461C2×C31—21no—
462C2×C31—21no—
463C2×C31—21no—
464C2×C31—21no—
465C2×C31—44no—
466C2×C31—82no—
467C2×C31C2×#38611yescharacteristic
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41C2×C4×C3112yes—
485C2×#41C2×C4×C3112yes—
486C2×#41C2×C4×C3112yescomplemented
487C2×#41D4×C3112yes—
488C2×#41D4×C3112yes—
489C2×#41D4×C3112yes—
490C2×#41D4×C3112yes—
491C2×#41C23×C3112yes—
492C22×Q8C2×C4×C3111yescharacteristic, complemented
493C22×Q8C23×C3111yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4C2×C4×C3111yescharacteristic, complemented
497C22×D4C23×C3111yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C3111yescharacteristic
501#137—24no—
502#137—24no—
503#137—24no—
504#137—24no—
505AGL(1,ℤ/8)—24no—
506AGL(1,ℤ/8)—24no—
507AGL(1,ℤ/8)—24no—
508AGL(1,ℤ/8)—24no—
509#135—28no—
510#135—28no—
511C2×Q16C2×C4×C3114yescomplemented
512C2×SD16C2×C4×C3114yescomplemented
513C2×SD16C2×C4×C3114yescomplemented
514C2×D8C2×C4×C3114yescomplemented
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—21no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—21no—
524C2×M16C2×C4×C3112yescomplemented
525C2×M16C23×C3112yes—
526C2×M16C23×C3112yes—
527C22×C8—21no—
528C22×C8C2×C4×C3112yescomplemented
529C4×Q8—24no—
530C4×Q8—24no—
531C4×D4—28no—
532C4×D4—28no—
533C4×D4—24no—
534C4×D4—24no—
535#117—24no—
536#117—24no—
537#117—21no—
538#117—21no—
539#117—21no—
540#117—21no—
541#117—24no—
542#117—21no—
543#117—21no—
544#117—21no—
545#117D4×C3112yes—
546#117D4×C3112yes—
547#117C23×C3112yes—
548#117C23×C3112yes—
549#117C23×C3112yes—
550C2×C4⋊C4—24no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4D4×C3112yes—
558C2×C42—24no—
559C2×C42—21no—
560C2×C42—21no—
561C2×C42D4×C3112yes—
562#104—28no—
563#103—24no—
564#102—24no—
565#99—28no—
566C31#2099811yescharacteristic, direct product factor, Sylow
567C24—21no—
568C24—21no—
569C24C2×D4×C3111yescharacteristic
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—22no—
579#41—22no—
580#41—22no—
581#41—22no—
582#41—22no—
583#41—22no—
584#41—22no—
585#41—22no—
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41C22⋊C4×C3114yes—
599#41C22⋊C4×C3114yes—
600#41C22⋊C4×C3114yes—
601#41C22⋊C4×C3114yes—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C22×C4×C3112yes—
611C2×Q8C22×C4×C3112yes—
612C2×Q8C2×D4×C3112yes—
613C2×Q8C2×D4×C3112yes—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4C22×C4×C3112yes—
635C2×D4C22×C4×C3112yes—
636C2×D4C2×D4×C3112yes—
637C2×D4C2×D4×C3112yes—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—21no—
646C22×C4—28no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4C22×C4×C3111yescharacteristic
657C22×C4C22×C4×C3111yescharacteristic
658C22×C4C2×D4×C3111yescharacteristic
659C22×C4C2×D4×C3111yescharacteristic
660C22×C4C2×D4×C3111yescharacteristic
661C22×C4C2×D4×C3111yescharacteristic
662C22×C4C2×D4×C3111yescharacteristic
663C22×C4C2×D4×C3111yescharacteristic
664C22×C4C2×D4×C3111yescharacteristic
665C22×C4#41×C3111yescharacteristic
666C22×C4#41×C3111yescharacteristic
667C22×C4#41×C3111yescharacteristic
668C22×C4#41×C3111yescharacteristic
669C22×C4C24×C3111yescharacteristic
670Q16—28no—
671SD16—28no—
672SD16—28no—
673D8—28no—
674M16—22no—
675M16—22no—
676M16—22no—
677M16—22no—
678M16—22no—
679M16—22no—
680M16—41no—
681M16—41no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—41no—
686C2×C8—41no—
687C2×C8C22×C4×C3114yes—
688C4⋊C4—28no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—41no—
695C22⋊C4—28no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—41no—
701C22⋊C4C2×D4×C3114yes—
702C42—28no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—41no—
708C42C2×D4×C3114yes—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—82no—
717C23—82no—
718C23C4×D4×C3111yescharacteristic
719C23C4×D4×C3111yescharacteristic
720C23C31×#12011yescharacteristic
721C23C31×#12011yescharacteristic
722C23C31×#12111yescharacteristic
723C23C31×#12111yescharacteristic
724C23C22×D4×C3111yescharacteristic
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8C2×C22⋊C4×C3114yes—
733D4—24no—
734D4—24no—
735D4—24no—
736D4—24no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—42no—
746D4—41no—
747D4—41no—
748D4C2×C22⋊C4×C3114yes—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—82no—
767C2×C4—82no—
768C2×C4—88no—
769C2×C4—82no—
770C2×C4C2×C22⋊C4×C3111yescharacteristic
771C2×C4C2×C22⋊C4×C3111yescharacteristic
772C2×C4C2×C22⋊C4×C3111yescharacteristic
773C2×C4C2×C22⋊C4×C3111yescharacteristic
774C2×C4C4×D4×C3111yescharacteristic
775C2×C4C4×D4×C3111yescharacteristic
776C2×C4C4×D4×C3111yescharacteristic
777C2×C4C4×D4×C3111yescharacteristic
778C2×C4C4×D4×C3111yescharacteristic
779C2×C4C4×D4×C3111yescharacteristic
780C2×C4C31×#12011yescharacteristic
781C2×C4C31×#12011yescharacteristic
782C2×C4C31×#12111yescharacteristic
783C2×C4C31×#12111yescharacteristic
784C2×C4C31×#12111yescharacteristic
785C2×C4C31×#12111yescharacteristic
786C2×C4C31×#12111yescharacteristic
787C2×C4C31×#12111yescharacteristic
788C2×C4C31×#12311yescharacteristic
789C2×C4C31×#12311yescharacteristic
790C2×C4C31×#12311yescharacteristic
791C2×C4C31×#12311yescharacteristic
792C2×C4C23×C4×C3111yescharacteristic
793C2×C4C22×D4×C3111yescharacteristic
794C2×C4C22×D4×C3111yescharacteristic
795C2×C4C22×D4×C3111yescharacteristic
796C2×C4C2×#41×C3111yescharacteristic
797C2×C4C2×#41×C3111yescharacteristic
798C8—24no—
799C8—42no—
800C22—24no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—44no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22C31×#38611yescharacteristic
816C22C31×#38611yescharacteristic
817C22C31×#38611yescharacteristic
818C22C31×#38611yescharacteristic
819C22C2×C4×D4×C3111yescharacteristic
820C22C2×C31×#12011yescharacteristic
821C22C2×C31×#12111yescharacteristic
822C4—24no—
823C4—44no—
824C4—44no—
825C4—42no—
826C4—82no—
827C4C31×#38611yescharacteristic
828C4C31×#38611yescharacteristic
829C4C31×#38611yescharacteristic
830C4C31×#38611yescharacteristic
831C4C22×C22⋊C4×C3111yescharacteristic
832C4C2×C4×D4×C3111yescharacteristic
833C4C2×C31×#12111yescharacteristic
834C4C2×C31×#12311yescharacteristic
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—44no—
843C2—82no—
844C2C2×C31×#38611yescharacteristic
subgroupG/H
centerC4×C31#386
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC2×C31C2×#386
prime radicalC2×C31×#575C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3428C2semidirect
3. C2×C31×#421C2semidirect
4. C31×#2896C2semidirect
5. C2×C31×#410C2semidirect
6. C31×#1905C2semidirect
7. C31×#1904C2semidirect
8. C2×C31×#344C2semidirect
9. C2×C31×H(3,ℤ/4)C2semidirect
16. C2×C31×#137C4semidirect
18. C2×C31×AGL(1,ℤ/8)C4semidirect
20. C2×C31×#135C4semidirect
25. C31×#519C22semidirect
27. C31×#518C22semidirect
37. C31×#419C22semidirect
38. C31×#418C22semidirect
44. C31×#344C22semidirect
45. C31×H(3,ℤ/4)C22semidirect
64. C2×#41×C31C2×C4semidirect
70. C22×Q8×C31C2×C4semidirect
74. C22×D4×C31C2×C4semidirect
89. C2×Q16×C31C2×C4semidirect
90. C2×SD16×C31C2×C4semidirect
91. C2×SD16×C31C2×C4semidirect
92. C2×D8×C31C2×C4semidirect
102. C2×M16×C31C2×C4semidirect
106. C22×C8×C31C2×C4semidirect
286. #20998C31direct (N × H)
379. #3428C2×C31semidirect
380. C2×#421C2×C31semidirect
381. #2896C2×C31semidirect
382. C2×#410C2×C31semidirect
383. #1905C2×C31semidirect
384. #1904C2×C31semidirect
385. C2×#344C2×C31semidirect
386. C2×H(3,ℤ/4)C2×C31semidirect
428. C2×#137C4×C31semidirect
430. C2×AGL(1,ℤ/8)C4×C31semidirect
432. C2×#135C4×C31semidirect
437. #519C22×C31semidirect
439. #518C22×C31semidirect
449. #419C22×C31semidirect
450. #418C22×C31semidirect
456. #344C22×C31semidirect
457. H(3,ℤ/4)C22×C31semidirect
486. C2×#41C2×C4×C31semidirect
492. C22×Q8C2×C4×C31semidirect
496. C22×D4C2×C4×C31semidirect
511. C2×Q16C2×C4×C31semidirect
512. C2×SD16C2×C4×C31semidirect
513. C2×SD16C2×C4×C31semidirect
514. C2×D8C2×C4×C31semidirect
524. C2×M16C2×C4×C31semidirect
528. C22×C8C2×C4×C31semidirect
566. C31#20998direct (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
C31×#34282
C2×C31×#4212
C31×#28962
C2×C31×#4102
C31×#19052
C31×#19042
C2×C31×#3442
C2×C31×H(3,ℤ/4)2
#2099831