Finite Group Databasebeta

← C31×#23900 #21480659

Subgroups — C31×#23900 #21480659

Order 7936.

3520 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3484C211yesmaximal, characteristic, complemented
2C22×C31×#120C211yesmaximal, characteristic, complemented
3C2×C31×B(4,𝔽2)C212yesmaximal, complemented
4C31×#2846C212yesmaximal, complemented
5C31×#2021C214yesmaximal, complemented
6C31×#1898C212yesmaximal, complemented
7C31×#1889C212yesmaximal, complemented
8C31×#1781C211yesmaximal, characteristic, complemented
9C26×C31C2211yescharacteristic, complemented
10C2×C31×H(5,𝔽2)C2211yescharacteristic, complemented
11C23×D4×C31—21no—
12C23×D4×C31C2211yescharacteristic
13C31×#546—24no—
14D42×C31—24no—
15C31×#535—21no—
16C31×#534—21no—
17C31×#534C2212yescomplemented
18C31×#525—21no—
19C2×C31×#120—21no—
20C2×C31×#120—21no—
21C2×C31×#120—21no—
22C2×C31×#120—28no—
23C2×C31×#120—24no—
24C2×C31×#120C2212yes—
25C2×C31×#120C2212yes—
26C2×C31×#120C2212yescomplemented
27C2×C31×#120C2214yescomplemented
28C31×#518C2211yescharacteristic, complemented
29C22×C22⋊C4×C31—21no—
30C22×C22⋊C4×C31C2211yescharacteristic, complemented
31C31×B(4,𝔽2)—28no—
32C2×C31×#99C2212yescomplemented
33C2×C31×#99C2214yescomplemented
34C2×C31×#99C2212yescomplemented
35C31×#379—24no—
36C31×#379C2214yescomplemented
37C31×#379C2212yescomplemented
38C31×#342C2214yescomplemented
39C25×C31—21no—
40C25×C31—21no—
41C25×C31—24no—
42C25×C31—24no—
43C25×C31—48no—
44C25×C31—42no—
45C25×C31D411yescharacteristic, complemented
46C25×C31C2312yes—
47C25×C31C2311yescharacteristic
48C31×H(5,𝔽2)—24no—
49C31×H(5,𝔽2)—42no—
50C2×#41×C31—21no—
51C2×#41×C31—22no—
52C22×D4×C31—28no—
53C22×D4×C31—22no—
54C22×D4×C31—22no—
55C22×D4×C31—21no—
56C22×D4×C31—24no—
57C22×D4×C31—22no—
58C22×D4×C31—22no—
59C22×D4×C31—24no—
60C22×D4×C31—24no—
61C22×D4×C31—42no—
62C22×D4×C31—48no—
63C22×D4×C31D411yescharacteristic, complemented
64C22×D4×C31D411yescharacteristic, complemented
65C22×D4×C31D414yescomplemented
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2312yes—
69C23×C4×C31—21no—
70C23×C4×C31D411yescharacteristic, complemented
71C31×#127—22no—
72C31×#124—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×C22⋊Q8—22no—
77C31×#121—22no—
78C31×#121—24no—
79C31×#121—24no—
80C31×#121—24no—
81C31×#120—28no—
82C31×#120—28no—
83C31×#120—24no—
84C31×#120—22no—
85C31×#120—22no—
86C31×#120—22no—
87C31×#120—22no—
88C31×#120—24no—
89C31×#120—24no—
90C31×#120—22no—
91C31×#120—24no—
92C31×#120—24no—
93C31×#120—28no—
94C31×#120—44no—
95C31×#120—416no—
96C31×#120D418yescomplemented
97C4×D4×C31—24no—
98C4×D4×C31—24no—
99C31×#117—21no—
100C2×C22⋊C4×C31—28no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—24no—
107C2×C22⋊C4×C31—24no—
108C2×C22⋊C4×C31—28no—
109C2×C22⋊C4×C31—24no—
110C2×C22⋊C4×C31D414yescomplemented
111C2×C22⋊C4×C31C2314yes—
112C2×C22⋊C4×C31C2312yes—
113C2×C22⋊C4×C31C2312yes—
114C31×#99—24no—
115C31×#99—28no—
116C31×#99—42no—
117C24×C31—24no—
118C24×C31—28no—
119C24×C31—24no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—24no—
124C24×C31—216no—
125C24×C31—21no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—24no—
129C24×C31—22no—
130C24×C31—48no—
131C24×C31—44no—
132C24×C31—41no—
133C24×C31—416no—
134C24×C31—42no—
135C24×C31—44no—
136C24×C31—416no—
137C24×C31—48no—
138C24×C31—432no—
139C24×C31—42no—
140C24×C31—48no—
141C24×C31—44no—
142C24×C31—432no—
143C24×C31—42no—
144C24×C31—42no—
145C24×C31C2×D411yescharacteristic
146C24×C31C2×D414yes—
147C24×C31C2×D411yescharacteristic
148C24×C31C2×D411yescharacteristic
149C24×C31C2×D411yescharacteristic
150C24×C31C2×D414yescomplemented
151C24×C31C2×D412yescomplemented
152C24×C31C2411yescharacteristic
153#41×C31—48no—
154#41×C31—42no—
155#41×C31—42no—
156C2×Q8×C31—21no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—28no—
160C2×D4×C31—22no—
161C2×D4×C31—21no—
162C2×D4×C31—24no—
163C2×D4×C31—22no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—28no—
167C2×D4×C31—24no—
168C2×D4×C31—22no—
169C2×D4×C31—22no—
170C2×D4×C31—22no—
171C2×D4×C31—22no—
172C2×D4×C31—22no—
173C2×D4×C31—24no—
174C2×D4×C31—24no—
175C2×D4×C31—24no—
176C2×D4×C31—22no—
177C2×D4×C31—41no—
178C2×D4×C31—41no—
179C2×D4×C31—416no—
180C2×D4×C31—48no—
181C2×D4×C31—48no—
182C2×D4×C31—48no—
183C2×D4×C31—432no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—48no—
187C2×D4×C31—48no—
188C2×D4×C31—416no—
189C2×D4×C31—84no—
190C2×D4×C31C2×D414yes—
191C22×C4×C31—24no—
192C22×C4×C31—21no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—24no—
199C22×C4×C31—41no—
200C22×C4×C31—44no—
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D412yescomplemented
204C22×C4×C31C2×D414yescomplemented
205C4⋊C4×C31—22no—
206C4⋊C4×C31—24no—
207C22⋊C4×C31—28no—
208C22⋊C4×C31—24no—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—24no—
211C22⋊C4×C31—24no—
212C22⋊C4×C31—24no—
213C22⋊C4×C31—24no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—28no—
218C22⋊C4×C31—24no—
219C22⋊C4×C31—24no—
220C22⋊C4×C31—48no—
221C22⋊C4×C31—416no—
222C22⋊C4×C31—48no—
223C22⋊C4×C31C2×D414yescomplemented
224C42×C31—22no—
225#23900C3111yesmaximal, characteristic, direct product factor, Sylow
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—24no—
229C23×C31—216no—
230C23×C31—216no—
231C23×C31—28no—
232C23×C31—21no—
233C23×C31—24no—
234C23×C31—21no—
235C23×C31—21no—
236C23×C31—28no—
237C23×C31—28no—
238C23×C31—28no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—21no—
242C23×C31—22no—
243C23×C31—21no—
244C23×C31—24no—
245C23×C31—44no—
246C23×C31—42no—
247C23×C31—48no—
248C23×C31—42no—
249C23×C31—44no—
250C23×C31—48no—
251C23×C31—48no—
252C23×C31—48no—
253C23×C31—416no—
254C23×C31—48no—
255C23×C31—48no—
256C23×C31—44no—
257C23×C31—48no—
258C23×C31—48no—
259C23×C31—416no—
260C23×C31—416no—
261C23×C31—464no—
262C23×C31—48no—
263C23×C31—416no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—48no—
267C23×C31—42no—
268C23×C31—44no—
269C23×C31—464no—
270C23×C31—416no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—44no—
274C23×C31—48no—
275C23×C31—44no—
276C23×C31—82no—
277C23×C31—84no—
278C23×C31—82no—
279C23×C31#12012yes—
280C23×C31#12012yes—
281C23×C31#12012yescomplemented
282C23×C31C22×D411yescharacteristic
283C23×C31C22×D412yes—
284C23×C31C22×D412yes—
285C23×C31H(5,𝔽2)12yes—
286Q8×C31—42no—
287D4×C31—28no—
288D4×C31—44no—
289D4×C31—42no—
290D4×C31—44no—
291D4×C31—416no—
292D4×C31—416no—
293D4×C31—44no—
294D4×C31—42no—
295D4×C31—42no—
296D4×C31—44no—
297D4×C31—44no—
298D4×C31—48no—
299D4×C31—84no—
300D4×C31—84no—
301D4×C31—816no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—24no—
306C2×C4×C31—24no—
307C2×C4×C31—22no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—24no—
311C2×C4×C31—44no—
312C2×C4×C31—44no—
313C2×C4×C31—48no—
314C2×C4×C31—44no—
315C2×C4×C31—42no—
316C2×C4×C31—44no—
317C2×C4×C31—48no—
318C2×C4×C31—44no—
319C2×C4×C31—82no—
320C2×C4×C31#12012yescomplemented
321#3484C2×C3111yescharacteristic, complemented
322C22×#120C2×C3111yescharacteristic, complemented
323C2×B(4,𝔽2)C2×C3112yescomplemented
324#2846C2×C3112yescomplemented
325#2021C2×C3114yescomplemented
326#1898C2×C3112yescomplemented
327#1889C2×C3112yescomplemented
328#1781C2×C3111yescharacteristic, complemented
329C22×C31—24no—
330C22×C31—24no—
331C22×C31—22no—
332C22×C31—24no—
333C22×C31—22no—
334C22×C31—22no—
335C22×C31—28no—
336C22×C31—216no—
337C22×C31—22no—
338C22×C31—22no—
339C22×C31—24no—
340C22×C31—42no—
341C22×C31—42no—
342C22×C31—416no—
343C22×C31—42no—
344C22×C31—42no—
345C22×C31—44no—
346C22×C31—416no—
347C22×C31—48no—
348C22×C31—48no—
349C22×C31—42no—
350C22×C31—432no—
351C22×C31—42no—
352C22×C31—432no—
353C22×C31—44no—
354C22×C31—42no—
355C22×C31—48no—
356C22×C31—42no—
357C22×C31—41no—
358C22×C31—44no—
359C22×C31—42no—
360C22×C31—81no—
361C22×C31—88no—
362C22×C31—84no—
363C22×C31—81no—
364C22×C31—162no—
365C22×C31B(4,𝔽2)14yescomplemented
366C22×C31C2×#12011yescharacteristic
367C22×C31C2×#12011yescharacteristic
368C22×C31#53411yescharacteristic
369C22×C31D4214yes—
370C4×C31—22no—
371C4×C31—44no—
372C4×C31—41no—
373C4×C31—42no—
374C4×C31—44no—
375C4×C31—84no—
376C26C22×C3111yescharacteristic, complemented
377C2×H(5,𝔽2)C22×C3111yescharacteristic, complemented
378C23×D4—21no—
379C23×D4C22×C3111yescharacteristic
380#546—24no—
381D42—24no—
382#535—21no—
383#534—21no—
384#534C22×C3112yescomplemented
385#525—21no—
386C2×#120—21no—
387C2×#120—21no—
388C2×#120—21no—
389C2×#120—28no—
390C2×#120—24no—
391C2×#120C22×C3112yes—
392C2×#120C22×C3112yes—
393C2×#120C22×C3112yescomplemented
394C2×#120C22×C3114yescomplemented
395#518C22×C3111yescharacteristic, complemented
396C22×C22⋊C4—21no—
397C22×C22⋊C4C22×C3111yescharacteristic, complemented
398B(4,𝔽2)—28no—
399C2×#99C22×C3112yescomplemented
400C2×#99C22×C3114yescomplemented
401C2×#99C22×C3112yescomplemented
402#379—24no—
403#379C22×C3114yescomplemented
404#379C22×C3112yescomplemented
405#342C22×C3114yescomplemented
406C2×C31—21no—
407C2×C31—24no—
408C2×C31—21no—
409C2×C31—24no—
410C2×C31—48no—
411C2×C31—42no—
412C2×C31—42no—
413C2×C31—81no—
414C2×C31—82no—
415C2×C31#240311yescharacteristic
416C2×C31C2×B(4,𝔽2)12yes—
417C25—21no—
418C25—21no—
419C25—24no—
420C25—24no—
421C25—48no—
422C25—42no—
423C25D4×C3111yescharacteristic, complemented
424C25C23×C3112yes—
425C25C23×C3111yescharacteristic
426H(5,𝔽2)—24no—
427H(5,𝔽2)—42no—
428C2×#41—21no—
429C2×#41—22no—
430C22×D4—28no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—21no—
434C22×D4—24no—
435C22×D4—22no—
436C22×D4—22no—
437C22×D4—24no—
438C22×D4—24no—
439C22×D4—42no—
440C22×D4—48no—
441C22×D4D4×C3111yescharacteristic, complemented
442C22×D4D4×C3111yescharacteristic, complemented
443C22×D4D4×C3114yescomplemented
444C22×D4C23×C3111yescharacteristic
445C22×D4C23×C3111yescharacteristic
446C22×D4C23×C3112yes—
447C23×C4—21no—
448C23×C4D4×C3111yescharacteristic, complemented
449#127—22no—
450#124—22no—
451#123—22no—
452#123—22no—
453#123—22no—
454C22⋊Q8—22no—
455#121—22no—
456#121—24no—
457#121—24no—
458#121—24no—
459#120—28no—
460#120—28no—
461#120—24no—
462#120—22no—
463#120—22no—
464#120—22no—
465#120—22no—
466#120—24no—
467#120—24no—
468#120—22no—
469#120—24no—
470#120—24no—
471#120—28no—
472#120—44no—
473#120—416no—
474#120D4×C3118yescomplemented
475C4×D4—24no—
476C4×D4—24no—
477#117—21no—
478C2×C22⋊C4—28no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—28no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4D4×C3114yescomplemented
489C2×C22⋊C4C23×C3114yes—
490C2×C22⋊C4C23×C3112yes—
491C2×C22⋊C4C23×C3112yes—
492#99—24no—
493#99—28no—
494#99—42no—
495C31#2390011yescharacteristic, direct product factor, Sylow
496C24—24no—
497C24—28no—
498C24—24no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—24no—
503C24—216no—
504C24—21no—
505C24—22no—
506C24—22no—
507C24—24no—
508C24—22no—
509C24—44no—
510C24—48no—
511C24—41no—
512C24—416no—
513C24—44no—
514C24—42no—
515C24—416no—
516C24—48no—
517C24—432no—
518C24—48no—
519C24—42no—
520C24—44no—
521C24—432no—
522C24—42no—
523C24—42no—
524C24C2×D4×C3111yescharacteristic
525C24C2×D4×C3114yes—
526C24C2×D4×C3111yescharacteristic
527C24C2×D4×C3111yescharacteristic
528C24C2×D4×C3111yescharacteristic
529C24C2×D4×C3114yescomplemented
530C24C2×D4×C3112yescomplemented
531C24C24×C3111yescharacteristic
532#41—48no—
533#41—42no—
534#41—42no—
535C2×Q8—21no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—28no—
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—24no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—28no—
546C2×D4—24no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—22no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—416no—
559C2×D4—48no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—432no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—416no—
568C2×D4—84no—
569C2×D4C2×D4×C3114yes—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—41no—
579C22×C4—44no—
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3112yescomplemented
583C22×C4C2×D4×C3114yescomplemented
584C4⋊C4—22no—
585C4⋊C4—24no—
586C22⋊C4—28no—
587C22⋊C4—24no—
588C22⋊C4—22no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—28no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—48no—
600C22⋊C4—416no—
601C22⋊C4—48no—
602C22⋊C4C2×D4×C3114yescomplemented
603C42—22no—
604C23—24no—
605C23—21no—
606C23—21no—
607C23—216no—
608C23—216no—
609C23—28no—
610C23—28no—
611C23—21no—
612C23—24no—
613C23—21no—
614C23—21no—
615C23—28no—
616C23—28no—
617C23—21no—
618C23—21no—
619C23—22no—
620C23—21no—
621C23—21no—
622C23—24no—
623C23—44no—
624C23—42no—
625C23—48no—
626C23—42no—
627C23—44no—
628C23—48no—
629C23—48no—
630C23—48no—
631C23—416no—
632C23—48no—
633C23—48no—
634C23—44no—
635C23—48no—
636C23—48no—
637C23—416no—
638C23—416no—
639C23—464no—
640C23—48no—
641C23—416no—
642C23—42no—
643C23—42no—
644C23—48no—
645C23—42no—
646C23—44no—
647C23—464no—
648C23—416no—
649C23—48no—
650C23—42no—
651C23—42no—
652C23—44no—
653C23—44no—
654C23—82no—
655C23—84no—
656C23—82no—
657C23C31×#12012yes—
658C23C31×#12012yes—
659C23C31×#12012yescomplemented
660C23C22×D4×C3111yescharacteristic
661C23C22×D4×C3112yes—
662C23C22×D4×C3112yes—
663C23C31×H(5,𝔽2)12yes—
664Q8—42no—
665D4—28no—
666D4—44no—
667D4—42no—
668D4—44no—
669D4—416no—
670D4—416no—
671D4—44no—
672D4—48no—
673D4—42no—
674D4—42no—
675D4—44no—
676D4—44no—
677D4—84no—
678D4—84no—
679D4—816no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—24no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—24no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—48no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—48no—
696C2×C4—44no—
697C2×C4—82no—
698C2×C4C31×#12012yescomplemented
699C22—24no—
700C22—24no—
701C22—22no—
702C22—24no—
703C22—22no—
704C22—22no—
705C22—28no—
706C22—216no—
707C22—22no—
708C22—22no—
709C22—24no—
710C22—42no—
711C22—42no—
712C22—416no—
713C22—42no—
714C22—42no—
715C22—44no—
716C22—416no—
717C22—48no—
718C22—432no—
719C22—48no—
720C22—42no—
721C22—42no—
722C22—432no—
723C22—44no—
724C22—42no—
725C22—48no—
726C22—42no—
727C22—41no—
728C22—44no—
729C22—42no—
730C22—81no—
731C22—88no—
732C22—84no—
733C22—81no—
734C22—162no—
735C22C31×B(4,𝔽2)14yescomplemented
736C22C2×C31×#12011yescharacteristic
737C22C2×C31×#12011yescharacteristic
738C22C31×#53411yescharacteristic
739C22D42×C3114yes—
740C4—22no—
741C4—44no—
742C4—41no—
743C4—42no—
744C4—44no—
745C4—84no—
746C2—21no—
747C2—24no—
748C2—24no—
749C2—21no—
750C2—48no—
751C2—42no—
752C2—42no—
753C2—81no—
754C2—82no—
755C2C31×#240311yescharacteristic
756C2C2×C31×B(4,𝔽2)12yes—
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3484C2semidirect
2. C22×C31×#120C2semidirect
3. C2×C31×B(4,𝔽2)C2semidirect
4. C31×#2846C2semidirect
5. C31×#2021C2semidirect
6. C31×#1898C2semidirect
7. C31×#1889C2semidirect
8. C31×#1781C2semidirect
9. C26×C31C22semidirect
10. C2×C31×H(5,𝔽2)C22semidirect
17. C31×#534C22semidirect
26. C2×C31×#120C22semidirect
27. C2×C31×#120C22semidirect
28. C31×#518C22semidirect
30. C22×C22⋊C4×C31C22semidirect
32. C2×C31×#99C22semidirect
33. C2×C31×#99C22semidirect
34. C2×C31×#99C22semidirect
36. C31×#379C22semidirect
37. C31×#379C22semidirect
38. C31×#342C22semidirect
45. C25×C31D4semidirect
63. C22×D4×C31D4semidirect
64. C22×D4×C31D4semidirect
65. C22×D4×C31D4semidirect
70. C23×C4×C31D4semidirect
96. C31×#120D4semidirect
110. C2×C22⋊C4×C31D4semidirect
150. C24×C31C2×D4semidirect
151. C24×C31C2×D4semidirect
203. C22×C4×C31C2×D4semidirect
204. C22×C4×C31C2×D4semidirect
223. C22⋊C4×C31C2×D4semidirect
225. #23900C31direct (N × H)
281. C23×C31#120semidirect
320. C2×C4×C31#120semidirect
321. #3484C2×C31semidirect
322. C22×#120C2×C31semidirect
323. C2×B(4,𝔽2)C2×C31semidirect
324. #2846C2×C31semidirect
325. #2021C2×C31semidirect
326. #1898C2×C31semidirect
327. #1889C2×C31semidirect
328. #1781C2×C31semidirect
365. C22×C31B(4,𝔽2)semidirect
376. C26C22×C31semidirect
377. C2×H(5,𝔽2)C22×C31semidirect
384. #534C22×C31semidirect
393. C2×#120C22×C31semidirect
394. C2×#120C22×C31semidirect
395. #518C22×C31semidirect
397. C22×C22⋊C4C22×C31semidirect
399. C2×#99C22×C31semidirect
400. C2×#99C22×C31semidirect
401. C2×#99C22×C31semidirect
403. #379C22×C31semidirect
404. #379C22×C31semidirect
405. #342C22×C31semidirect
423. C25D4×C31semidirect
441. C22×D4D4×C31semidirect
442. C22×D4D4×C31semidirect
443. C22×D4D4×C31semidirect
448. C23×C4D4×C31semidirect
474. #120D4×C31semidirect
488. C2×C22⋊C4D4×C31semidirect
495. C31#23900direct (N × H)
529. C24C2×D4×C31semidirect
530. C24C2×D4×C31semidirect
582. C22×C4C2×D4×C31semidirect
583. C22×C4C2×D4×C31semidirect
602. C22⋊C4C2×D4×C31semidirect
659. C23C31×#120semidirect
698. C2×C4C31×#120semidirect
735. C22C31×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C31×#34842
C22×C31×#1202
C2×C31×B(4,𝔽2)2
C31×#28462
C31×#20212
C31×#18982
C31×#18892
C31×#17812
#2390031