Finite Group Databasebeta

← C2×C31×#2000 #21480143

Subgroups — C2×C31×#2000 #21480143

Order 7936.

2526 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×SD16×C31C211yesmaximal, characteristic, complemented
2C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
3C22×C31×#121C211yesmaximal, characteristic
4C22×C31×#103C211yesmaximal, characteristic, complemented
5C22×C31×#102C211yesmaximal, characteristic, complemented
6C22×C31×C22⋊C8C211yesmaximal, characteristic, complemented
7C31×#2000C218yesmaximal, direct product factor
8C2×C31×#340C211yesmaximal, characteristic, complemented
9C23×Q8×C31C2211yescharacteristic
10C23×D4×C31—21no—
11C23×D4×C31C2211yescharacteristic
12C24×C4×C31C2211yescharacteristic
13C22×SD16×C31—24no—
14C22×SD16×C31—24no—
15C22×SD16×C31—24no—
16C22×SD16×C31C2214yescomplemented
17C23×C8×C31C2211yescharacteristic
18C23×C8×C31C2211yescharacteristic
19C2×C31×C22⋊Q8—24no—
20C2×C31×C22⋊Q8—22no—
21C2×C31×C22⋊Q8—24no—
22C2×C31×C22⋊Q8C2214yescomplemented
23C2×C31×#121—24no—
24C2×C31×#121—22no—
25C2×C31×#121—24no—
26C2×C31×#121C2214yes—
27C22×C4⋊C4×C31—21no—
28C22×C4⋊C4×C31C2211yescharacteristic
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31—21no—
31C22×C22⋊C4×C31—21no—
32C2×C31×#103—24no—
33C2×C31×#103C2214yescomplemented
34C2×C31×#102—24no—
35C2×C31×#102C2214yescomplemented
36C2×C31×C22⋊C8—24no—
37C2×C31×C22⋊C8C2214yescomplemented
38C31×#340C2214yescomplemented
39C25×C31—21no—
40C25×C31D411yescharacteristic
41C22×Q8×C31—22no—
42C22×Q8×C31—21no—
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31—22no—
47C22×Q8×C31D414yescomplemented
48C22×Q8×C31C2312yes—
49C22×D4×C31—28no—
50C22×D4×C31—24no—
51C22×D4×C31—22no—
52C22×D4×C31—22no—
53C22×D4×C31—22no—
54C22×D4×C31—21no—
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—44no—
58C22×D4×C31—44no—
59C22×D4×C31D414yes—
60C22×D4×C31C2312yes—
61C23×C4×C31—21no—
62C23×C4×C31—21no—
63C23×C4×C31—21no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31—22no—
68C23×C4×C31—22no—
69C23×C4×C31—22no—
70C23×C4×C31D412yes—
71C23×C4×C31D411yescharacteristic
72C23×C4×C31C2312yes—
73C23×C4×C31C2311yescharacteristic
74C2×SD16×C31—232no—
75C2×SD16×C31—28no—
76C2×SD16×C31—28no—
77C2×SD16×C31—28no—
78C22×C8×C31—22no—
79C22×C8×C31—22no—
80C22×C8×C31—22no—
81C22×C8×C31—22no—
82C22×C8×C31—22no—
83C22×C8×C31D414yescomplemented
84C22×C8×C31C2312yes—
85C22×C8×C31C2312yes—
86C31×C22⋊Q8—216no—
87C31×C22⋊Q8—28no—
88C31×C22⋊Q8—28no—
89C31×#121—216no—
90C31×#121—28no—
91C31×#121—28no—
92C2×C4⋊C4×C31—28no—
93C2×C4⋊C4×C31—24no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31D414yes—
99C2×C4⋊C4×C31D414yescomplemented
100C2×C4⋊C4×C31C2312yes—
101C2×C4⋊C4×C31C2312yes—
102C2×C22⋊C4×C31—28no—
103C2×C22⋊C4×C31—28no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—24no—
106C31×#103—28no—
107C31×#102—28no—
108C31×C22⋊C8—28no—
109C24×C31—22no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—22no—
113C24×C31—22no—
114C24×C31—22no—
115C24×C31—24no—
116C24×C31—22no—
117C24×C31—42no—
118C24×C31—42no—
119C24×C31—42no—
120C24×C31—42no—
121C24×C31—42no—
122C24×C31—42no—
123C24×C31SD1614yescomplemented
124C24×C31C2×D412yes—
125C24×C31C2×D411yescharacteristic
126C2×Q8×C31—24no—
127C2×Q8×C31—22no—
128C2×Q8×C31—28no—
129C2×Q8×C31—28no—
130C2×Q8×C31—22no—
131C2×Q8×C31—22no—
132C2×Q8×C31—22no—
133C2×Q8×C31—22no—
134C2×Q8×C31—42no—
135C2×Q8×C31—42no—
136C2×Q8×C31—44no—
137C2×Q8×C31—44no—
138C2×Q8×C31C2×D414yescomplemented
139C2×D4×C31—216no—
140C2×D4×C31—28no—
141C2×D4×C31—24no—
142C2×D4×C31—28no—
143C2×D4×C31—22no—
144C2×D4×C31—22no—
145C2×D4×C31—22no—
146C2×D4×C31—22no—
147C2×D4×C31—22no—
148C2×D4×C31—48no—
149C2×D4×C31—432no—
150C2×D4×C31—48no—
151C2×D4×C31—42no—
152C2×D4×C31—44no—
153C2×D4×C31—42no—
154C2×D4×C31—44no—
155C2×D4×C31C2×D414yes—
156C22×C4×C31—22no—
157C22×C4×C31—24no—
158C22×C4×C31—24no—
159C22×C4×C31—24no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—24no—
166C22×C4×C31—24no—
167C22×C4×C31—24no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—42no—
175C22×C4×C31—42no—
176C22×C4×C31—42no—
177C22×C4×C31—42no—
178C22×C4×C31—42no—
179C22×C4×C31—42no—
180C22×C4×C31—44no—
181C22×C4×C31—44no—
182C22×C4×C31—44no—
183C22×C4×C31—44no—
184C22×C4×C31C2×D412yes—
185C22×C4×C31C2×D411yescharacteristic
186C22×C4×C31C2×D412yes—
187C22×C4×C31C2×D412yes—
188C22×C4×C31C2×D412yes—
189C22×C4×C31C2×D412yes—
190C22×C4×C31C2×D412yes—
191C22×C4×C31#4112yes—
192C22×C4×C31C2411yescharacteristic
193SD16×C31—232no—
194C2×C8×C31—28no—
195C2×C8×C31—22no—
196C2×C8×C31—22no—
197C2×C8×C31—22no—
198C2×C8×C31—22no—
199C2×C8×C31—22no—
200C2×C8×C31—44no—
201C2×C8×C31C2×D414yescomplemented
202C4⋊C4×C31—216no—
203C4⋊C4×C31—24no—
204C4⋊C4×C31—24no—
205C4⋊C4×C31—22no—
206C4⋊C4×C31—22no—
207C4⋊C4×C31C2×D414yes—
208C4⋊C4×C31C2×D414yescomplemented
209C22⋊C4×C31—216no—
210C22⋊C4×C31—216no—
211C2×#2000C3111yesmaximal, characteristic, direct product factor, Sylow
212C23×C31—22no—
213C23×C31—22no—
214C23×C31—22no—
215C23×C31—22no—
216C23×C31—22no—
217C23×C31—22no—
218C23×C31—28no—
219C23×C31—28no—
220C23×C31—28no—
221C23×C31—24no—
222C23×C31—44no—
223C23×C31—44no—
224C23×C31—44no—
225C23×C31—44no—
226C23×C31—42no—
227C23×C31—42no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31—42no—
231C23×C31—42no—
232C23×C31—48no—
233C23×C31—48no—
234C23×C31—48no—
235C23×C31—84no—
236C23×C31—84no—
237C23×C31—84no—
238C23×C31—84no—
239C23×C31#12012yes—
240C23×C31#12012yes—
241C23×C31#12112yes—
242C23×C31C2×SD1612yes—
243C23×C31C2×SD1614yescomplemented
244C23×C31#13512yes—
245C23×C31AGL(1,ℤ/8)12yes—
246C23×C31#13712yes—
247C23×C31C22×D411yescharacteristic
248Q8×C31—24no—
249Q8×C31—24no—
250Q8×C31—42no—
251Q8×C31—42no—
252Q8×C31—48no—
253D4×C31—24no—
254D4×C31—24no—
255D4×C31—432no—
256D4×C31—42no—
257D4×C31—42no—
258D4×C31—48no—
259C2×C4×C31—22no—
260C2×C4×C31—24no—
261C2×C4×C31—24no—
262C2×C4×C31—24no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—42no—
266C2×C4×C31—42no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—42no—
270C2×C4×C31—42no—
271C2×C4×C31—44no—
272C2×C4×C31—48no—
273C2×C4×C31—48no—
274C2×C4×C31—48no—
275C2×C4×C31—42no—
276C2×C4×C31—42no—
277C2×C4×C31—42no—
278C2×C4×C31—42no—
279C2×C4×C31—48no—
280C2×C4×C31#12014yes—
281C2×C4×C31#12012yes—
282C2×C4×C31#12012yes—
283C2×C4×C31#12114yes—
284C2×C4×C31#12114yes—
285C2×C4×C31#12112yes—
286C2×C4×C31#12714yes—
287C2×C4×C31C22×D411yescharacteristic
288C2×C4×C31C22×D411yescharacteristic
289C2×C4×C31C22×D411yescharacteristic
290C2×C4×C31C22×D411yescharacteristic
291C2×C4×C31C22×D411yescharacteristic
292C2×C4×C31C2×#4111yescharacteristic
293C8×C31—24no—
294C8×C31—42no—
295C23×SD16C2×C3111yescharacteristic, complemented
296C22×C22⋊Q8C2×C3111yescharacteristic, complemented
297C22×#121C2×C3111yescharacteristic
298C22×#103C2×C3111yescharacteristic, complemented
299C22×#102C2×C3111yescharacteristic, complemented
300C22×C22⋊C8C2×C3111yescharacteristic, complemented
301#2000C2×C3118yesdirect product factor
302C2×#340C2×C3111yescharacteristic, complemented
303C22×C31—24no—
304C22×C31—24no—
305C22×C31—24no—
306C22×C31—42no—
307C22×C31—42no—
308C22×C31—42no—
309C22×C31—416no—
310C22×C31—42no—
311C22×C31—44no—
312C22×C31—44no—
313C22×C31—44no—
314C22×C31—82no—
315C22×C31—82no—
316C22×C31—816no—
317C22×C31—82no—
318C22×C31—82no—
319C22×C31#39214yes—
320C22×C31#44814yes—
321C22×C31#44914yes—
322C22×C31#45014yes—
323C22×C31#45214yes—
324C22×C31#46514yes—
325C22×C31#46814yes—
326C22×C31C2×#12011yescharacteristic
327C22×C31C2×#12011yescharacteristic
328C22×C31C2×#12111yescharacteristic
329C22×C31C22×SD1611yescharacteristic
330C22×C31C2×#13511yescharacteristic
331C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C31C2×#13711yescharacteristic
333C4×C31—42no—
334C4×C31—44no—
335C4×C31—44no—
336C4×C31—44no—
337C4×C31#39214yes—
338C4×C31C2×#12011yescharacteristic
339C4×C31C2×#12111yescharacteristic
340C4×C31C2×#12111yescharacteristic
341C4×C31C2×#12711yescharacteristic
342C23×Q8C22×C3111yescharacteristic
343C23×D4—21no—
344C23×D4C22×C3111yescharacteristic
345C24×C4C22×C3111yescharacteristic
346C22×SD16—24no—
347C22×SD16—24no—
348C22×SD16—24no—
349C22×SD16C22×C3114yescomplemented
350C23×C8C22×C3111yescharacteristic
351C23×C8C22×C3111yescharacteristic
352C2×C22⋊Q8—24no—
353C2×C22⋊Q8—22no—
354C2×C22⋊Q8—24no—
355C2×C22⋊Q8C22×C3114yescomplemented
356C2×#121—24no—
357C2×#121—22no—
358C2×#121—24no—
359C2×#121C22×C3114yes—
360C22×C4⋊C4—21no—
361C22×C4⋊C4C22×C3111yescharacteristic
362C22×C4⋊C4C22×C3111yescharacteristic
363C22×C22⋊C4—21no—
364C22×C22⋊C4—21no—
365C2×#103—24no—
366C2×#103C22×C3114yescomplemented
367C2×#102—24no—
368C2×#102C22×C3114yescomplemented
369C2×C22⋊C8—24no—
370C2×C22⋊C8C22×C3114yescomplemented
371#340C22×C3114yescomplemented
372C2×C31—44no—
373C2×C31—84no—
374C2×C31#200018yesdirect product factor
375C2×C31C2×#39211yescharacteristic
376C2×C31C2×#45011yescharacteristic
377C2×C31C2×#44811yescharacteristic
378C2×C31C2×#44911yescharacteristic
379C2×C31C2×#45211yescharacteristic
380C2×C31C2×#46511yescharacteristic
381C2×C31C2×#46811yescharacteristic
382C25—21no—
383C25D4×C3111yescharacteristic
384C22×Q8—22no—
385C22×Q8—21no—
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8D4×C3114yescomplemented
391C22×Q8C23×C3112yes—
392C22×D4—28no—
393C22×D4—24no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—21no—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—44no—
401C22×D4—44no—
402C22×D4D4×C3114yes—
403C22×D4C23×C3112yes—
404C23×C4—21no—
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4D4×C3111yescharacteristic
414C23×C4D4×C3112yes—
415C23×C4C23×C3112yes—
416C23×C4C23×C3111yescharacteristic
417C2×SD16—232no—
418C2×SD16—28no—
419C2×SD16—28no—
420C2×SD16—28no—
421C22×C8—22no—
422C22×C8—22no—
423C22×C8—22no—
424C22×C8—22no—
425C22×C8—22no—
426C22×C8D4×C3114yescomplemented
427C22×C8C23×C3112yes—
428C22×C8C23×C3112yes—
429C22⋊Q8—216no—
430C22⋊Q8—28no—
431C22⋊Q8—28no—
432#121—216no—
433#121—28no—
434#121—28no—
435C2×C4⋊C4—28no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4D4×C3114yes—
442C2×C4⋊C4D4×C3114yescomplemented
443C2×C4⋊C4C23×C3112yes—
444C2×C4⋊C4C23×C3112yes—
445C2×C22⋊C4—28no—
446C2×C22⋊C4—28no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449#103—28no—
450#102—28no—
451C22⋊C8—28no—
452C31C2×#200011yescharacteristic, direct product factor, Sylow
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—22no—
461C24—42no—
462C24—42no—
463C24—42no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24SD16×C3114yescomplemented
468C24C2×D4×C3112yes—
469C24C2×D4×C3111yescharacteristic
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—28no—
473C2×Q8—28no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8C2×D4×C3114yescomplemented
483C2×D4—216no—
484C2×D4—28no—
485C2×D4—24no—
486C2×D4—28no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—432no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—42no—
496C2×D4—44no—
497C2×D4—42no—
498C2×D4—44no—
499C2×D4C2×D4×C3114yes—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4C2×D4×C3112yes—
529C22×C4C2×D4×C3111yescharacteristic
530C22×C4C2×D4×C3112yes—
531C22×C4C2×D4×C3112yes—
532C22×C4C2×D4×C3112yes—
533C22×C4C2×D4×C3112yes—
534C22×C4C2×D4×C3112yes—
535C22×C4#41×C3112yes—
536C22×C4C24×C3111yescharacteristic
537SD16—232no—
538C2×C8—28no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—44no—
545C2×C8C2×D4×C3114yescomplemented
546C4⋊C4—216no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4C2×D4×C3114yes—
552C4⋊C4C2×D4×C3114yescomplemented
553C22⋊C4—216no—
554C22⋊C4—216no—
555C23—28no—
556C23—28no—
557C23—28no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—24no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—48no—
570C23—48no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—48no—
578C23—84no—
579C23—84no—
580C23—84no—
581C23—84no—
582C23C31×#12012yes—
583C23C31×#12012yes—
584C23C31×#12112yes—
585C23C2×SD16×C3112yes—
586C23C2×SD16×C3114yescomplemented
587C23C31×#13512yes—
588C23C31×AGL(1,ℤ/8)12yes—
589C23C31×#13712yes—
590C23C22×D4×C3111yescharacteristic
591Q8—24no—
592Q8—24no—
593Q8—42no—
594Q8—42no—
595Q8—48no—
596D4—24no—
597D4—24no—
598D4—432no—
599D4—42no—
600D4—42no—
601D4—48no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—48no—
609C2×C4—48no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—44no—
617C2×C4—48no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—48no—
623C2×C4C31×#12014yes—
624C2×C4C31×#12012yes—
625C2×C4C31×#12012yes—
626C2×C4C31×#12114yes—
627C2×C4C31×#12114yes—
628C2×C4C31×#12112yes—
629C2×C4C31×#12714yes—
630C2×C4C22×D4×C3111yescharacteristic
631C2×C4C22×D4×C3111yescharacteristic
632C2×C4C22×D4×C3111yescharacteristic
633C2×C4C22×D4×C3111yescharacteristic
634C2×C4C22×D4×C3111yescharacteristic
635C2×C4C2×#41×C3111yescharacteristic
636C8—24no—
637C8—42no—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—416no—
645C22—42no—
646C22—44no—
647C22—44no—
648C22—44no—
649C22—82no—
650C22—82no—
651C22—816no—
652C22—82no—
653C22—82no—
654C22C31×#39214yes—
655C22C31×#44814yes—
656C22C31×#44914yes—
657C22C31×#45014yes—
658C22C31×#45214yes—
659C22C31×#46514yes—
660C22C31×#46814yes—
661C22C2×C31×#12011yescharacteristic
662C22C2×C31×#12011yescharacteristic
663C22C2×C31×#12111yescharacteristic
664C22C22×SD16×C3111yescharacteristic
665C22C2×C31×#13511yescharacteristic
666C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
667C22C2×C31×#13711yescharacteristic
668C4—42no—
669C4—44no—
670C4—44no—
671C4—44no—
672C4C31×#39214yes—
673C4C2×C31×#12011yescharacteristic
674C4C2×C31×#12111yescharacteristic
675C4C2×C31×#12111yescharacteristic
676C4C2×C31×#12711yescharacteristic
677C2—44no—
678C2—84no—
679C2C31×#200018yesdirect product factor
680C2C2×C31×#39211yescharacteristic
681C2C2×C31×#45011yescharacteristic
682C2C2×C31×#44811yescharacteristic
683C2C2×C31×#44911yescharacteristic
684C2C2×C31×#45211yescharacteristic
685C2C2×C31×#46511yescharacteristic
686C2C2×C31×#46811yescharacteristic
subgroupG/H
center, socleC24×C31C2×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×SD16×C31C2semidirect
2. C22×C31×C22⋊Q8C2semidirect
4. C22×C31×#103C2semidirect
5. C22×C31×#102C2semidirect
6. C22×C31×C22⋊C8C2semidirect
7. C31×#2000C2direct (N × H)
8. C2×C31×#340C2semidirect
16. C22×SD16×C31C22semidirect
22. C2×C31×C22⋊Q8C22semidirect
33. C2×C31×#103C22semidirect
35. C2×C31×#102C22semidirect
37. C2×C31×C22⋊C8C22semidirect
38. C31×#340C22semidirect
47. C22×Q8×C31D4semidirect
83. C22×C8×C31D4semidirect
99. C2×C4⋊C4×C31D4semidirect
123. C24×C31SD16semidirect
138. C2×Q8×C31C2×D4semidirect
201. C2×C8×C31C2×D4semidirect
208. C4⋊C4×C31C2×D4semidirect
211. C2×#2000C31direct (N × H)
243. C23×C31C2×SD16semidirect
295. C23×SD16C2×C31semidirect
296. C22×C22⋊Q8C2×C31semidirect
298. C22×#103C2×C31semidirect
299. C22×#102C2×C31semidirect
300. C22×C22⋊C8C2×C31semidirect
301. #2000C2×C31direct (N × H)
302. C2×#340C2×C31semidirect
349. C22×SD16C22×C31semidirect
355. C2×C22⋊Q8C22×C31semidirect
366. C2×#103C22×C31semidirect
368. C2×#102C22×C31semidirect
370. C2×C22⋊C8C22×C31semidirect
371. #340C22×C31semidirect
374. C2×C31#2000direct (N × H)
390. C22×Q8D4×C31semidirect
426. C22×C8D4×C31semidirect
442. C2×C4⋊C4D4×C31semidirect
452. C31C2×#2000direct (N × H)
467. C24SD16×C31semidirect
482. C2×Q8C2×D4×C31semidirect
545. C2×C8C2×D4×C31semidirect
552. C4⋊C4C2×D4×C31semidirect
586. C23C2×SD16×C31semidirect
679. C2C31×#2000direct (N × H)

Maximal subgroups

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

subgroupindex
C23×SD16×C312
C22×C31×C22⋊Q82
C22×C31×#1212
C22×C31×#1032
C22×C31×#1022
C22×C31×C22⋊C82
C31×#20002
C2×C31×#3402
C2×#200031