Finite Group Databasebeta

← C31×#14763 #21471522

Subgroups — C31×#14763 #21471522

Order 7936.

1982 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic
2C2×C31×#395C211yesmaximal, characteristic, complemented
3C2×C31×#389C212yesmaximal, complemented
4C2×C31×#385C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
6C31×#1446C211yesmaximal, characteristic, complemented
7C31×#1444C211yesmaximal, characteristic, complemented
8C31×#1441C211yesmaximal, characteristic, complemented
9C31×#1439C212yesmaximal
10C31×#1439C212yesmaximal
11C31×#1436C212yesmaximal, complemented
12C23×Q8×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C2×C31×C22⋊Q8—24no—
15C2×C31×C22⋊Q8—28no—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2212yes—
21C22×C4⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C42×C31C2212yes—
27C31×#395—24no—
28C31×#389—28no—
29C31×#385—24no—
30C4×C22⋊C4×C31—24no—
31C2×C31×#95C2212yes—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2212yes—
40C2×C31×#95C2211yescharacteristic
41C25×C31C2311yescharacteristic
42C22×Q8×C31—24no—
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31—42no—
47C23×C4×C31—24no—
48C23×C4×C31—22no—
49C23×C4×C31—22no—
50C23×C4×C31—42no—
51C23×C4×C31D414yes—
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2312yes—
55C23×C4×C31C2312yes—
56C23×C4×C31C2312yes—
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2312yes—
62C31×C22⋊Q8—232no—
63C2×C4⋊C4×C31—24no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—24no—
66C2×C4⋊C4×C31—24no—
67C2×C4⋊C4×C31—24no—
68C2×C4⋊C4×C31—24no—
69C2×C4⋊C4×C31—24no—
70C2×C4⋊C4×C31—24no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—24no—
75C2×C4⋊C4×C31—24no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—42no—
78C2×C4⋊C4×C31D418yes—
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—24no—
82C2×C22⋊C4×C31—24no—
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—42no—
89C2×C22⋊C4×C31Q818yescomplemented
90C2×C42×C31—24no—
91C2×C42×C31—24no—
92C2×C42×C31—42no—
93C31×#95—24no—
94C31×#95—22no—
95C31×#95—22no—
96C31×#95—22no—
97C31×#95—24no—
98C31×#95—24no—
99C31×#95—24no—
100C31×#95—24no—
101C31×#95—42no—
102C31×#95D414yes—
103C24×C31—22no—
104C24×C31—21no—
105C24×C31—22no—
106C24×C31—21no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—22no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31C2×D412yes—
113C24×C31C2×Q814yes—
114C24×C31C2411yescharacteristic
115C2×Q8×C31—28no—
116C2×Q8×C31—48no—
117C2×Q8×C31—48no—
118C2×Q8×C31—44no—
119C2×Q8×C31—44no—
120C22×C4×C31—21no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—21no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—21no—
131C22×C4×C31—22no—
132C22×C4×C31—21no—
133C22×C4×C31—21no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—21no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—21no—
155C22×C4×C31—22no—
156C22×C4×C31—21no—
157C22×C4×C31—28no—
158C22×C4×C31—28no—
159C22×C4×C31—21no—
160C22×C4×C31—22no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—22no—
164C22×C4×C31—21no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—44no—
170C22×C4×C31—48no—
171C22×C4×C31—48no—
172C22×C4×C31C2×D414yes—
173C22×C4×C31C2×D414yes—
174C22×C4×C31C2×D412yes—
175C22×C4×C31C2×D414yes—
176C22×C4×C31C2×D412yes—
177C22×C4×C31C2×D412yes—
178C22×C4×C31C2×D414yes—
179C22×C4×C31C2×Q814yes—
180C22×C4×C31C2×Q814yes—
181C22×C4×C31#4112yes—
182C22×C4×C31#4112yes—
183C22×C4×C31#4112yes—
184C22×C4×C31#4114yes—
185C4⋊C4×C31—216no—
186C4⋊C4×C31—28no—
187C4⋊C4×C31—216no—
188C4⋊C4×C31—48no—
189C4⋊C4×C31—44no—
190C4⋊C4×C31—44no—
191C22⋊C4×C31—28no—
192C22⋊C4×C31—216no—
193C22⋊C4×C31—216no—
194C22⋊C4×C31—44no—
195C42×C31—48no—
196#14763C3111yesmaximal, characteristic, direct product factor, Sylow
197C23×C31—22no—
198C23×C31—22no—
199C23×C31—24no—
200C23×C31—22no—
201C23×C31—22no—
202C23×C31—24no—
203C23×C31—22no—
204C23×C31—22no—
205C23×C31—24no—
206C23×C31—24no—
207C23×C31—24no—
208C23×C31—24no—
209C23×C31—42no—
210C23×C31—42no—
211C23×C31—42no—
212C23×C31—42no—
213C23×C31—42no—
214C23×C31—42no—
215C23×C31—41no—
216C23×C31—41no—
217C23×C31—41no—
218C23×C31—41no—
219C23×C31C4⋊Q814yes—
220C23×C31C22×D411yescharacteristic
221C23×C31C22×D412yes—
222C23×C31C22×D411yescharacteristic
223C23×C31C22×Q812yes—
224C23×C31C2×#4111yescharacteristic
225C23×C31C2×#4112yes—
226C23×C31C2×#4111yescharacteristic
227C23×C31C2×#4111yescharacteristic
228C23×C31H(5,𝔽2)12yes—
229C23×C312−1+411yescharacteristic
230C23×C312−1+411yescharacteristic
231Q8×C31—416no—
232C2×C4×C31—22no—
233C2×C4×C31—22no—
234C2×C4×C31—24no—
235C2×C4×C31—22no—
236C2×C4×C31—22no—
237C2×C4×C31—24no—
238C2×C4×C31—24no—
239C2×C4×C31—24no—
240C2×C4×C31—24no—
241C2×C4×C31—24no—
242C2×C4×C31—24no—
243C2×C4×C31—24no—
244C2×C4×C31—24no—
245C2×C4×C31—24no—
246C2×C4×C31—24no—
247C2×C4×C31—24no—
248C2×C4×C31—24no—
249C2×C4×C31—22no—
250C2×C4×C31—22no—
251C2×C4×C31—24no—
252C2×C4×C31—24no—
253C2×C4×C31—24no—
254C2×C4×C31—24no—
255C2×C4×C31—24no—
256C2×C4×C31—22no—
257C2×C4×C31—24no—
258C2×C4×C31—22no—
259C2×C4×C31—24no—
260C2×C4×C31—416no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—42no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—41no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—42no—
270C2×C4×C31—42no—
271C2×C4×C31—42no—
272C2×C4×C31—41no—
273C2×C4×C31—42no—
274C2×C4×C31—42no—
275C2×C4×C31—42no—
276C2×C4×C31—42no—
277C2×C4×C31—41no—
278C2×C4×C31—42no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—42no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
289C2×C4×C31—42no—
290C2×C4×C31#12014yes—
291C2×C4×C31#12114yes—
292C2×C4×C31C22⋊Q818yescomplemented
293C22×C22⋊Q8C2×C3111yescharacteristic
294C2×#395C2×C3111yescharacteristic, complemented
295C2×#389C2×C3112yescomplemented
296C2×#385C2×C3111yescharacteristic
297C2×C4×C22⋊C4C2×C3111yescharacteristic
298#1446C2×C3111yescharacteristic, complemented
299#1444C2×C3111yescharacteristic, complemented
300#1441C2×C3111yescharacteristic, complemented
301#1439C2×C3112yes—
302#1439C2×C3112yes—
303#1436C2×C3112yescomplemented
304C22×C31—24no—
305C22×C31—24no—
306C22×C31—24no—
307C22×C31—42no—
308C22×C31—42no—
309C22×C31—42no—
310C22×C31—42no—
311C22×C31—44no—
312C22×C31—44no—
313C22×C31—44no—
314C22×C31—44no—
315C22×C31C2×#12011yescharacteristic
316C22×C31C2×#12111yescharacteristic
317C22×C31C2×C22⋊Q812yes—
318C22×C31#52511yescharacteristic
319C22×C31#52512yes—
320C22×C31C2×C4⋊Q811yescharacteristic
321C22×C31#53211yescharacteristic
322C22×C31#53212yes—
323C22×C31#53312yes—
324C22×C31#53411yescharacteristic
325C22×C31#53611yescharacteristic
326C22×C31#53912yes—
327C22×C31#54212yes—
328C22×C31D4212yes—
329C22×C31#54612yes—
330C22×C31#54711yescharacteristic
331C22×C31#54811yescharacteristic
332C22×C31D4×Q812yes—
333C22×C31D4×Q812yes—
334C22×C31#55211yescharacteristic
335C22×C31#55412yes—
336C22×C31#55412yes—
337C22×C31#55611yescharacteristic
338C4×C31—24no—
339C4×C31—24no—
340C4×C31—28no—
341C4×C31—44no—
342C4×C31—42no—
343C4×C31—44no—
344C4×C31—42no—
345C4×C31—44no—
346C4×C31—81no—
347C4×C31—81no—
348C23×Q8C22×C3111yescharacteristic
349C24×C4C22×C3111yescharacteristic
350C2×C22⋊Q8—24no—
351C2×C22⋊Q8—28no—
352C22×C4⋊C4C22×C3111yescharacteristic
353C22×C4⋊C4C22×C3111yescharacteristic
354C22×C4⋊C4C22×C3112yes—
355C22×C4⋊C4C22×C3111yescharacteristic
356C22×C4⋊C4C22×C3112yes—
357C22×C4⋊C4C22×C3112yes—
358C22×C22⋊C4C22×C3112yes—
359C22×C22⋊C4C22×C3111yescharacteristic
360C22×C22⋊C4C22×C3112yes—
361C22×C22⋊C4C22×C3111yescharacteristic
362C22×C42C22×C3112yes—
363#395—24no—
364#389—28no—
365#385—24no—
366C4×C22⋊C4—24no—
367C2×#95C22×C3112yes—
368C2×#95C22×C3111yescharacteristic
369C2×#95C22×C3112yes—
370C2×#95C22×C3112yes—
371C2×#95C22×C3112yes—
372C2×#95C22×C3112yes—
373C2×#95C22×C3111yescharacteristic
374C2×#95C22×C3111yescharacteristic
375C2×#95C22×C3112yes—
376C2×#95C22×C3111yescharacteristic
377C2×C31—44no—
378C2×C31#238811yescharacteristic
379C2×C31#241011yescharacteristic
380C2×C31#241511yescharacteristic
381C2×C31#243411yescharacteristic
382C2×C31#244912yes—
383C2×C31#245212yes—
384C2×C31#246512yes—
385C2×C31#255612yes—
386C2×C31#258311yescharacteristic
387C2×C31#266311yescharacteristic
388C2×C31#285711yescharacteristic
389C25C23×C3111yescharacteristic
390C22×Q8—24no—
391C22×Q8—22no—
392C22×Q8—22no—
393C22×Q8—22no—
394C22×Q8—42no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—42no—
399C23×C4D4×C3114yes—
400C23×C4C23×C3111yescharacteristic
401C23×C4C23×C3111yescharacteristic
402C23×C4C23×C3112yes—
403C23×C4C23×C3112yes—
404C23×C4C23×C3112yes—
405C23×C4C23×C3111yescharacteristic
406C23×C4C23×C3111yescharacteristic
407C23×C4C23×C3111yescharacteristic
408C23×C4C23×C3111yescharacteristic
409C23×C4C23×C3112yes—
410C22⋊Q8—232no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4D4×C3118yes—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4Q8×C3118yescomplemented
438C2×C42—24no—
439C2×C42—24no—
440C2×C42—42no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—42no—
450#95D4×C3114yes—
451C31#1476311yescharacteristic, direct product factor, Sylow
452C24—22no—
453C24—21no—
454C24—22no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—21no—
460C24—21no—
461C24C2×D4×C3112yes—
462C24C2×Q8×C3114yes—
463C24C24×C3111yescharacteristic
464C2×Q8—28no—
465C2×Q8—48no—
466C2×Q8—48no—
467C2×Q8—44no—
468C2×Q8—44no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—44no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4C2×D4×C3114yes—
522C22×C4C2×D4×C3114yes—
523C22×C4C2×D4×C3112yes—
524C22×C4C2×D4×C3114yes—
525C22×C4C2×D4×C3112yes—
526C22×C4C2×D4×C3112yes—
527C22×C4C2×D4×C3114yes—
528C22×C4C2×Q8×C3114yes—
529C22×C4C2×Q8×C3114yes—
530C22×C4#41×C3112yes—
531C22×C4#41×C3112yes—
532C22×C4#41×C3112yes—
533C22×C4#41×C3114yes—
534C4⋊C4—216no—
535C4⋊C4—28no—
536C4⋊C4—216no—
537C4⋊C4—48no—
538C4⋊C4—44no—
539C4⋊C4—44no—
540C22⋊C4—28no—
541C22⋊C4—216no—
542C22⋊C4—216no—
543C22⋊C4—44no—
544C42—48no—
545C23—22no—
546C23—22no—
547C23—24no—
548C23—22no—
549C23—22no—
550C23—24no—
551C23—22no—
552C23—22no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23C31×C4⋊Q814yes—
568C23C22×D4×C3111yescharacteristic
569C23C22×D4×C3112yes—
570C23C22×D4×C3111yescharacteristic
571C23C22×Q8×C3112yes—
572C23C2×#41×C3111yescharacteristic
573C23C2×#41×C3112yes—
574C23C2×#41×C3111yescharacteristic
575C23C2×#41×C3111yescharacteristic
576C23C31×H(5,𝔽2)12yes—
577C23C31×2−1+411yescharacteristic
578C23C31×2−1+411yescharacteristic
579Q8—416no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—416no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4C31×#12014yes—
639C2×C4C31×#12114yes—
640C2×C4C31×C22⋊Q818yescomplemented
641C22—24no—
642C22—24no—
643C22—24no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—44no—
649C22—44no—
650C22—44no—
651C22—44no—
652C22C2×C31×#12011yescharacteristic
653C22C2×C31×#12111yescharacteristic
654C22C2×C31×C22⋊Q812yes—
655C22C31×#52511yescharacteristic
656C22C31×#52512yes—
657C22C2×C31×C4⋊Q811yescharacteristic
658C22C31×#53211yescharacteristic
659C22C31×#53212yes—
660C22C31×#53312yes—
661C22C31×#53411yescharacteristic
662C22C31×#53611yescharacteristic
663C22C31×#53912yes—
664C22C31×#54212yes—
665C22D42×C3112yes—
666C22C31×#54612yes—
667C22C31×#54711yescharacteristic
668C22C31×#54811yescharacteristic
669C22D4×Q8×C3112yes—
670C22D4×Q8×C3112yes—
671C22C31×#55211yescharacteristic
672C22C31×#55412yes—
673C22C31×#55412yes—
674C22C31×#55611yescharacteristic
675C4—24no—
676C4—24no—
677C4—28no—
678C4—44no—
679C4—42no—
680C4—44no—
681C4—42no—
682C4—44no—
683C4—81no—
684C4—81no—
685C2—44no—
686C2C31×#238811yescharacteristic
687C2C31×#241011yescharacteristic
688C2C31×#241511yescharacteristic
689C2C31×#243411yescharacteristic
690C2C31×#244912yes—
691C2C31×#245212yes—
692C2C31×#246512yes—
693C2C31×#255612yes—
694C2C31×#258311yescharacteristic
695C2C31×#266311yescharacteristic
696C2C31×#285711yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#395C2semidirect
3. C2×C31×#389C2semidirect
6. C31×#1446C2semidirect
7. C31×#1444C2semidirect
8. C31×#1441C2semidirect
11. C31×#1436C2semidirect
89. C2×C22⋊C4×C31Q8semidirect
196. #14763C31direct (N × H)
292. C2×C4×C31C22⋊Q8semidirect
294. C2×#395C2×C31semidirect
295. C2×#389C2×C31semidirect
298. #1446C2×C31semidirect
299. #1444C2×C31semidirect
300. #1441C2×C31semidirect
303. #1436C2×C31semidirect
437. C2×C22⋊C4Q8×C31semidirect
451. C31#14763direct (N × H)
640. C2×C4C31×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#3952
C2×C31×#3892
C2×C31×#3852
C2×C4×C22⋊C4×C312
C31×#14462
C31×#14442
C31×#14412
C31×#14392
C31×#14362
#1476331