Finite Group Databasebeta

← C31×#23955 #21480714

Subgroups — C31×#23955 #21480714

Order 7936.

1234 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3494C211yesmaximal, characteristic
2C31×#3004C211yesmaximal, characteristic, complemented
3C2×C31×#419C211yesmaximal, characteristic, complemented
4C31×#2436C211yesmaximal, characteristic, complemented
5C31×#2028C212yesmaximal, complemented
6C31×#2004C212yesmaximal, complemented
7C31×#1900C211yesmaximal, characteristic, complemented
8C31×#1885C212yesmaximal, complemented
9C31×#1882C212yesmaximal, complemented
10C31×#1871C211yesmaximal, characteristic, complemented
11C31×#1826C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic
13C2×C31×#137C2212yes—
14C22×M16×C31C2211yescharacteristic
15C31×#555—21no—
16C31×#553—21no—
17C31×#553—21no—
18C31×#551—22no—
19C31×#547—21no—
20C31×#546—22no—
21C31×#544C2211yescharacteristic
22C31×#542—21no—
23C31×#540—21no—
24C31×#535C2211yescharacteristic
25C31×#532—21no—
26C31×#529—21no—
27C2×C31×#124C2212yes—
28C31×#525C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C31×#520C2211yescharacteristic
31C31×#518C2211yescharacteristic
32C2×C31×#117C2211yescharacteristic
33C31×#451—21no—
34C31×#451—21no—
35C31×#448—21no—
36C31×#448—21no—
37C2×C31×#104C2212yes—
38C31×#419—21no—
39C31×#419—21no—
40C31×#419C2212yes—
41C31×#419C2212yes—
42C31×#419C2212yes—
43C2×C31×#103—21no—
44C2×C31×#103—21no—
45C2×C31×#100C2212yes—
46C31×#407C2211yescharacteristic
47C31×#393—22no—
48C31×#391C2212yes—
49C31×#386—22no—
50C4×C22⋊C4×C31C2211yescharacteristic
51C31×#343C2212yes—
52C31×#339C2212yes—
53C31×#339C2212yes—
54C31×#339C2212yes—
55C2×#41×C31—22no—
56C2×#41×C31C2311yescharacteristic
57C22×Q8×C31—21no—
58C22×Q8×C31—24no—
59C22×Q8×C31—21no—
60C22×Q8×C31—21no—
61C22×Q8×C31—21no—
62C22×Q8×C31—21no—
63C22×Q8×C31—42no—
64C22×Q8×C31C2312yes—
65C22×D4×C31D412yes—
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C31×#137—24no—
70C31×#137—42no—
71C2×Q16×C31—22no—
72C2×SD16×C31—22no—
73C2×M16×C31—21no—
74C2×M16×C31—42no—
75C2×M16×C31C2312yes—
76C2×M16×C31C2312yes—
77C22×C8×C31—21no—
78C31×C4⋊Q8—21no—
79C31×C4⋊Q8—21no—
80C31×#127—21no—
81C31×#126—22no—
82C31×#126—22no—
83C31×#125—21no—
84C31×#125—21no—
85C31×#124—22no—
86C31×#124—22no—
87C31×#124—21no—
88C31×#124—24no—
89C31×#124—42no—
90C31×#123—22no—
91C31×#123—22no—
92C31×#123—22no—
93C31×#123—22no—
94C31×#123—21no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8D411yescharacteristic
98C31×C22⋊Q8D411yescharacteristic
99C31×#121—22no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—21no—
103C31×#121—21no—
104C31×#121—21no—
105C31×#121—21no—
106C31×#121—21no—
107C31×#121—21no—
108C31×#121D411yescharacteristic
109C31×#121D411yescharacteristic
110C31×#120—21no—
111C31×#120—22no—
112C4×Q8×C31—21no—
113C4×D4×C31—22no—
114C4×D4×C31—22no—
115C4×D4×C31—21no—
116C4×D4×C31—22no—
117C4×D4×C31—21no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31—21no—
122C4×D4×C31—21no—
123C31×#117—22no—
124C31×#117—21no—
125C31×#117—21no—
126C31×#117—21no—
127C31×#117D411yescharacteristic
128C31×#117D411yescharacteristic
129C31×#117C2311yescharacteristic
130C31×#117C2311yescharacteristic
131C31×#117C2311yescharacteristic
132C2×C4⋊C4×C31—21no—
133C2×C4⋊C4×C31D411yescharacteristic
134C2×C4⋊C4×C31D411yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31—24no—
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31D412yes—
141C2×C42×C31—21no—
142C2×C42×C31C2312yes—
143C31×#104—42no—
144C31×#103—22no—
145C31×#103—22no—
146C31×#103—22no—
147C31×#103—22no—
148C31×#103—22no—
149C31×#103—22no—
150C31×#100—42no—
151C31×C22⋊C8—21no—
152C31×C22⋊C8—21no—
153C31×#95—21no—
154C31×#95—24no—
155C24×C31C2×D411yescharacteristic
156C24×C31C2×D412yes—
157#41×C31—22no—
158#41×C31—22no—
159#41×C31—84no—
160C2×Q8×C31—22no—
161C2×Q8×C31—22no—
162C2×Q8×C31—24no—
163C2×Q8×C31—24no—
164C2×Q8×C31—22no—
165C2×Q8×C31—22no—
166C2×Q8×C31—22no—
167C2×Q8×C31—22no—
168C2×Q8×C31—44no—
169C2×Q8×C31—44no—
170C2×Q8×C31—44no—
171C2×Q8×C31—42no—
172C2×Q8×C31—42no—
173C2×Q8×C31—41no—
174C2×Q8×C31—41no—
175C2×Q8×C31C2×D411yescharacteristic
176C2×Q8×C31#4114yescomplemented
177C2×D4×C31—21no—
178C2×D4×C31—22no—
179C2×D4×C31—21no—
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—21no—
183C2×D4×C31—22no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—22no—
187C2×D4×C31—22no—
188C2×D4×C31—44no—
189C2×D4×C31C2×D411yescharacteristic
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—21no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—22no—
200C22×C4×C31—44no—
201C22×C4×C31—41no—
202C22×C4×C31—41no—
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D412yes—
209C22×C4×C31C2411yescharacteristic
210Q16×C31—44no—
211SD16×C31—44no—
212M16×C31—22no—
213M16×C31—22no—
214M16×C31—22no—
215M16×C31—22no—
216M16×C31—42no—
217C2×C8×C31—22no—
218C2×C8×C31—22no—
219C2×C8×C31—42no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—22no—
223C4⋊C4×C31—22no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31C2×D411yescharacteristic
231C4⋊C4×C31C2×D411yescharacteristic
232C4⋊C4×C31C2×D411yescharacteristic
233C4⋊C4×C31C2×D411yescharacteristic
234C4⋊C4×C31C2×D411yescharacteristic
235C4⋊C4×C31C2×D411yescharacteristic
236C22⋊C4×C31—22no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—21no—
242C22⋊C4×C31—21no—
243C22⋊C4×C31—21no—
244C22⋊C4×C31—21no—
245C22⋊C4×C31—21no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—21no—
251C22⋊C4×C31—21no—
252C22⋊C4×C31—48no—
253C22⋊C4×C31—42no—
254C42×C31—22no—
255C42×C31—21no—
256C42×C31—21no—
257C42×C31—21no—
258C42×C31—21no—
259C42×C31—21no—
260C42×C31—22no—
261C42×C31—22no—
262#23955C3111yesmaximal, characteristic, direct product factor, Sylow
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—21no—
267C23×C31—24no—
268C23×C31—41no—
269C23×C31—42no—
270C23×C31—42no—
271C23×C31#12011yescharacteristic
272C23×C31#12011yescharacteristic
273C23×C31C22×D411yescharacteristic
274Q8×C31—24no—
275Q8×C31—24no—
276Q8×C31—22no—
277Q8×C31—44no—
278Q8×C31—44no—
279Q8×C31—42no—
280Q8×C31—42no—
281Q8×C31—82no—
282D4×C31—22no—
283D4×C31—42no—
284D4×C31—44no—
285D4×C31—42no—
286D4×C31—41no—
287D4×C31—41no—
288D4×C31—42no—
289D4×C31—81no—
290D4×C31—82no—
291D4×C31—82no—
292D4×C31—82no—
293C2×C4×C31—22no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—22no—
308C2×C4×C31—24no—
309C2×C4×C31—44no—
310C2×C4×C31—44no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—81no—
321C2×C4×C31—82no—
322C2×C4×C31—82no—
323C2×C4×C31—82no—
324C2×C4×C31#12011yescharacteristic
325C2×C4×C31#12011yescharacteristic
326C2×C4×C31C22×D411yescharacteristic
327C2×C4×C31C22×D411yescharacteristic
328C2×C4×C31C2×#4112yes—
329C2×C4×C31H(5,𝔽2)12yes—
330C8×C31—42no—
331C8×C31—42no—
332#3494C2×C3111yescharacteristic
333#3004C2×C3111yescharacteristic, complemented
334C2×#419C2×C3111yescharacteristic, complemented
335#2436C2×C3111yescharacteristic, complemented
336#2028C2×C3112yescomplemented
337#2004C2×C3112yescomplemented
338#1900C2×C3111yescharacteristic, complemented
339#1885C2×C3112yescomplemented
340#1882C2×C3112yescomplemented
341#1871C2×C3111yescharacteristic, complemented
342#1826C2×C3111yescharacteristic, complemented
343C22×C31—21no—
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—21no—
349C22×C31—21no—
350C22×C31—44no—
351C22×C31—41no—
352C22×C31—42no—
353C22×C31—41no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—41no—
357C22×C31—84no—
358C22×C31#45512yes—
359C22×C31C2×#12011yescharacteristic
360C22×C31#54612yes—
361C4×C31—21no—
362C4×C31—21no—
363C4×C31—44no—
364C4×C31—41no—
365C4×C31—41no—
366C4×C31—41no—
367C4×C31—42no—
368C4×C31—41no—
369C4×C31—41no—
370C4×C31—41no—
371C4×C31—41no—
372C4×C31—82no—
373C4×C31#52511yescharacteristic
374C4×C31#53511yescharacteristic
375C4×C31#54612yes—
376C23×Q8C22×C3111yescharacteristic
377C2×#137C22×C3112yes—
378C22×M16C22×C3111yescharacteristic
379#555—21no—
380#553—21no—
381#553—21no—
382#551—22no—
383#547—21no—
384#546—22no—
385#544C22×C3111yescharacteristic
386#542—21no—
387#540—21no—
388#535C22×C3111yescharacteristic
389#532—21no—
390#529—21no—
391C2×#124C22×C3112yes—
392#525C22×C3111yescharacteristic
393C2×#121C22×C3111yescharacteristic
394#520C22×C3111yescharacteristic
395#518C22×C3111yescharacteristic
396C2×#117C22×C3111yescharacteristic
397#451—21no—
398#451—21no—
399#448—21no—
400#448—21no—
401C2×#104C22×C3112yes—
402#419—21no—
403#419—21no—
404#419C22×C3112yes—
405#419C22×C3112yes—
406#419C22×C3112yes—
407C2×#103—21no—
408C2×#103—21no—
409C2×#100C22×C3112yes—
410#407C22×C3111yescharacteristic
411#393—22no—
412#391C22×C3112yes—
413#386—22no—
414C4×C22⋊C4C22×C3111yescharacteristic
415#343C22×C3112yes—
416#339C22×C3112yes—
417#339C22×C3112yes—
418#339C22×C3112yes—
419C2×C31—22no—
420C2×C31—22no—
421C2×C31—41no—
422C2×C31—81no—
423C2×C31—82no—
424C2×C31#240411yescharacteristic
425C2×C31C2×#45511yescharacteristic
426C2×C31#302211yescharacteristic
427C2×#41—22no—
428C2×#41C23×C3111yescharacteristic
429C22×Q8—21no—
430C22×Q8—24no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—42no—
436C22×Q8C23×C3112yes—
437C22×D4D4×C3112yes—
438C22×D4C23×C3111yescharacteristic
439C23×C4—21no—
440C23×C4C23×C3111yescharacteristic
441#137—24no—
442#137—42no—
443C2×Q16—22no—
444C2×SD16—22no—
445C2×M16—21no—
446C2×M16—42no—
447C2×M16C23×C3112yes—
448C2×M16C23×C3112yes—
449C22×C8—21no—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452#127—21no—
453#126—22no—
454#126—22no—
455#125—21no—
456#125—21no—
457#124—22no—
458#124—22no—
459#124—21no—
460#124—24no—
461#124—42no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—22no—
466#123—21no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8D4×C3111yescharacteristic
470C22⋊Q8D4×C3111yescharacteristic
471#121—22no—
472#121—22no—
473#121—22no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121D4×C3111yescharacteristic
481#121D4×C3111yescharacteristic
482#120—21no—
483#120—22no—
484C4×Q8—21no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—21no—
488C4×D4—22no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495#117—22no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117D4×C3111yescharacteristic
500#117D4×C3111yescharacteristic
501#117C23×C3111yescharacteristic
502#117C23×C3111yescharacteristic
503#117C23×C3111yescharacteristic
504C2×C4⋊C4—21no—
505C2×C4⋊C4D4×C3111yescharacteristic
506C2×C4⋊C4D4×C3111yescharacteristic
507C2×C4⋊C4C23×C3111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4D4×C3112yes—
513C2×C42—21no—
514C2×C42C23×C3112yes—
515#104—42no—
516#103—22no—
517#103—22no—
518#103—22no—
519#103—22no—
520#103—22no—
521#103—22no—
522#100—42no—
523C22⋊C8—21no—
524C22⋊C8—21no—
525#95—21no—
526#95—24no—
527C31#2395511yescharacteristic, direct product factor, Sylow
528C24C2×D4×C3111yescharacteristic
529C24C2×D4×C3112yes—
530#41—22no—
531#41—22no—
532#41—84no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—24no—
536C2×Q8—24no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—44no—
542C2×Q8—44no—
543C2×Q8—44no—
544C2×Q8—42no—
545C2×Q8—42no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8C2×D4×C3111yescharacteristic
549C2×Q8#41×C3114yescomplemented
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—44no—
562C2×D4C2×D4×C3111yescharacteristic
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—44no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4C2×D4×C3111yescharacteristic
577C22×C4C2×D4×C3111yescharacteristic
578C22×C4C2×D4×C3111yescharacteristic
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4C2×D4×C3112yes—
582C22×C4C24×C3111yescharacteristic
583Q16—44no—
584SD16—44no—
585M16—22no—
586M16—22no—
587M16—22no—
588M16—22no—
589M16—42no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—42no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4C2×D4×C3111yescharacteristic
604C4⋊C4C2×D4×C3111yescharacteristic
605C4⋊C4C2×D4×C3111yescharacteristic
606C4⋊C4C2×D4×C3111yescharacteristic
607C4⋊C4C2×D4×C3111yescharacteristic
608C4⋊C4C2×D4×C3111yescharacteristic
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—48no—
626C22⋊C4—42no—
627C42—22no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—22no—
634C42—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—24no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23C31×#12011yescharacteristic
644C23C31×#12011yescharacteristic
645C23C22×D4×C3111yescharacteristic
646Q8—24no—
647Q8—24no—
648Q8—22no—
649Q8—44no—
650Q8—44no—
651Q8—42no—
652Q8—42no—
653Q8—82no—
654D4—22no—
655D4—44no—
656D4—42no—
657D4—42no—
658D4—41no—
659D4—41no—
660D4—42no—
661D4—81no—
662D4—82no—
663D4—82no—
664D4—82no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—81no—
693C2×C4—82no—
694C2×C4—82no—
695C2×C4—82no—
696C2×C4C31×#12011yescharacteristic
697C2×C4C31×#12011yescharacteristic
698C2×C4C22×D4×C3111yescharacteristic
699C2×C4C22×D4×C3111yescharacteristic
700C2×C4C2×#41×C3112yes—
701C2×C4C31×H(5,𝔽2)12yes—
702C8—42no—
703C8—42no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—44no—
712C22—41no—
713C22—42no—
714C22—41no—
715C22—42no—
716C22—42no—
717C22—41no—
718C22—84no—
719C22C31×#45512yes—
720C22C2×C31×#12011yescharacteristic
721C22C31×#54612yes—
722C4—21no—
723C4—21no—
724C4—44no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—82no—
734C4C31×#52511yescharacteristic
735C4C31×#53511yescharacteristic
736C4C31×#54612yes—
737C2—22no—
738C2—22no—
739C2—41no—
740C2—82no—
741C2—81no—
742C2C31×#240411yescharacteristic
743C2C2×C31×#45511yescharacteristic
744C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3494C2
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
2. C31×#3004C2semidirect
3. C2×C31×#419C2semidirect
4. C31×#2436C2semidirect
5. C31×#2028C2semidirect
6. C31×#2004C2semidirect
7. C31×#1900C2semidirect
8. C31×#1885C2semidirect
9. C31×#1882C2semidirect
10. C31×#1871C2semidirect
11. C31×#1826C2semidirect
176. C2×Q8×C31#41semidirect
262. #23955C31direct (N × H)
333. #3004C2×C31semidirect
334. C2×#419C2×C31semidirect
335. #2436C2×C31semidirect
336. #2028C2×C31semidirect
337. #2004C2×C31semidirect
338. #1900C2×C31semidirect
339. #1885C2×C31semidirect
340. #1882C2×C31semidirect
341. #1871C2×C31semidirect
342. #1826C2×C31semidirect
527. C31#23955direct (N × H)
549. C2×Q8#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34942
C31×#30042
C2×C31×#4192
C31×#24362
C31×#20282
C31×#20042
C31×#19002
C31×#18852
C31×#18822
C31×#18712
C31×#18262
#2395531