Finite Group Databasebeta

← C31×#20748 #21477507

Subgroups — C31×#20748 #21477507

Order 7936.

1336 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C31C211yesmaximal, characteristic
2C31×#2920C211yesmaximal, characteristic, complemented
3C31×#2283C211yesmaximal, characteristic, complemented
4C31×#1826C212yesmaximal, complemented
5C31×#1806C214yesmaximal, complemented
6C31×#1789C212yesmaximal
7C31×#1759C214yesmaximal, complemented
8C22×#41×C31C2211yescharacteristic
9C4×#41×C31—21no—
10C4×#41×C31—21no—
11C4×#41×C31—21no—
12C4×#41×C31—21no—
13C4×#41×C31C412yescomplemented
14C4×#41×C31C412yescomplemented
15C4×#41×C31C2212yes—
16C4×#41×C31C2212yes—
17C2×C4×Q8×C31C411yescharacteristic, complemented
18C2×C4×Q8×C31C411yescharacteristic, complemented
19C2×C4×D4×C31—21no—
20C2×C4×D4×C31—21no—
21C2×C4×D4×C31C411yescharacteristic, complemented
22C2×C4×D4×C31C411yescharacteristic, complemented
23C2×C31×#117—21no—
24C2×C31×#117C2211yescharacteristic
25C22×C42×C31—21no—
26C22×C42×C31C2211yescharacteristic
27C31×#432—21no—
28C31×#432—21no—
29C31×#431—21no—
30C31×#431—21no—
31C31×#423C2212yescomplemented
32C2×C31×#104C2218yes—
33C31×#407C2212yes—
34C4×M16×C31C2212yescomplemented
35C31×#383—21no—
36C31×#382—21no—
37C31×#381—21no—
38C31×#380—21no—
39C4×C4⋊C4×C31C2212yescomplemented
40C4×C22⋊C4×C31C2212yes—
41C31×#376C2212yescomplemented
42C31×#339C2218yescomplemented
43C2×#41×C31—28no—
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31C2×C412yes—
47C2×#41×C31C2312yes—
48C22×Q8×C31C2×C411yescharacteristic
49C22×D4×C31—21no—
50C22×D4×C31C2×C411yescharacteristic
51C23×C4×C31—21no—
52C23×C4×C31—21no—
53C23×C4×C31—21no—
54C23×C4×C31D411yescharacteristic
55C23×C4×C31D411yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C2×M16×C31C2314yes—
58C4×Q8×C31—21no—
59C4×Q8×C31—21no—
60C4×Q8×C31—21no—
61C4×Q8×C31—21no—
62C4×Q8×C31C2×C412yes—
63C4×Q8×C31C2×C412yes—
64C4×Q8×C31C2×C412yes—
65C4×Q8×C31C2×C412yes—
66C4×D4×C31—22no—
67C4×D4×C31—22no—
68C4×D4×C31—22no—
69C4×D4×C31—22no—
70C4×D4×C31—22no—
71C4×D4×C31—22no—
72C4×D4×C31—22no—
73C4×D4×C31—22no—
74C4×D4×C31—21no—
75C4×D4×C31—21no—
76C4×D4×C31—21no—
77C4×D4×C31—21no—
78C4×D4×C31C2×C412yes—
79C4×D4×C31C2×C412yes—
80C4×D4×C31C2×C412yes—
81C4×D4×C31C2×C412yes—
82C31×#117—21no—
83C31×#117—21no—
84C31×#117—22no—
85C31×#117—22no—
86C31×#117—22no—
87C31×#117—22no—
88C31×#117C2×C412yes—
89C31×#117C2312yes—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31C2×C411yescharacteristic
94C2×C4⋊C4×C31C2×C411yescharacteristic
95C2×C22⋊C4×C31—21no—
96C2×C22⋊C4×C31—21no—
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—22no—
99C2×C42×C31—21no—
100C2×C42×C31—21no—
101C2×C42×C31—21no—
102C2×C42×C31—22no—
103C2×C42×C31—22no—
104C2×C42×C31—22no—
105C2×C42×C31—22no—
106C2×C42×C31C2×C411yescharacteristic
107C2×C42×C31C2×C411yescharacteristic
108C2×C42×C31C2×C411yescharacteristic
109C2×C42×C31C2×C411yescharacteristic
110C2×C42×C31D411yescharacteristic
111C2×C42×C31D411yescharacteristic
112C2×C42×C31D411yescharacteristic
113C2×C42×C31D411yescharacteristic
114C2×C42×C31D411yescharacteristic
115C2×C42×C31D411yescharacteristic
116C2×C42×C31C2314yes—
117C2×C42×C31C2311yescharacteristic
118C2×C42×C31C2311yescharacteristic
119C31×C4⋊C8—22no—
120C31×C4⋊C8—22no—
121C31×#104—216no—
122C31×C22⋊C8—22no—
123C31×C22⋊C8—22no—
124C31×#97—22no—
125C4×C8×C31—22no—
126C31×#95—22no—
127C31×#95—22no—
128C31×#95—22no—
129C31×#95—22no—
130C24×C31—21no—
131C24×C31C2×D411yescharacteristic
132#41×C31—28no—
133#41×C31—28no—
134#41×C31—24no—
135#41×C31—24no—
136#41×C31—24no—
137#41×C31#4118yes—
138C2×Q8×C31—24no—
139C2×Q8×C31—21no—
140C2×Q8×C31C22×C412yes—
141C2×D4×C31—28no—
142C2×D4×C31—22no—
143C2×D4×C31—22no—
144C2×D4×C31—24no—
145C2×D4×C31—21no—
146C2×D4×C31C22×C412yes—
147C22×C4×C31—28no—
148C22×C4×C31—21no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—24no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—24no—
159C22×C4×C31—42no—
160C22×C4×C31—42no—
161C22×C4×C31—44no—
162C22×C4×C31—44no—
163C22×C4×C31C22⋊C411yescharacteristic
164C22×C4×C31C22⋊C411yescharacteristic
165C22×C4×C31C22⋊C411yescharacteristic
166C22×C4×C31C22⋊C411yescharacteristic
167C22×C4×C31C22⋊C411yescharacteristic
168C22×C4×C31C22⋊C411yescharacteristic
169C22×C4×C31C22⋊C411yescharacteristic
170C22×C4×C31C22⋊C411yescharacteristic
171C22×C4×C31C22×C411yescharacteristic
172C22×C4×C31C22×C411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2411yescharacteristic
181M16×C31—28no—
182C2×C8×C31—24no—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—22no—
186C4⋊C4×C31—22no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—44no—
190C4⋊C4×C31C22×C412yes—
191C4⋊C4×C31C22×C412yes—
192C22⋊C4×C31—22no—
193C22⋊C4×C31—22no—
194C22⋊C4×C31—22no—
195C22⋊C4×C31—22no—
196C22⋊C4×C31—22no—
197C22⋊C4×C31—22no—
198C22⋊C4×C31—44no—
199C42×C31—22no—
200C42×C31—22no—
201C42×C31—22no—
202C42×C31—22no—
203C42×C31—22no—
204C42×C31—22no—
205C42×C31—28no—
206C42×C31C22⋊C411yescharacteristic
207C42×C31C22⋊C411yescharacteristic
208C42×C31C22⋊C411yescharacteristic
209C42×C31C22⋊C411yescharacteristic
210C42×C31C22⋊C411yescharacteristic
211C42×C31C22⋊C411yescharacteristic
212C42×C31C22⋊C411yescharacteristic
213C42×C31C22⋊C411yescharacteristic
214C42×C31C22×C411yescharacteristic
215C42×C31C22×C411yescharacteristic
216C42×C31C22×C411yescharacteristic
217C42×C31C22×C411yescharacteristic
218C42×C31C2×D411yescharacteristic
219C42×C31C2×D411yescharacteristic
220C42×C31C2×D411yescharacteristic
221C42×C31C2×D411yescharacteristic
222#20748C3111yesmaximal, characteristic, direct product factor, Sylow
223C23×C31—24no—
224C23×C31—22no—
225C23×C31—22no—
226C23×C31—22no—
227C23×C31—41no—
228C23×C31—42no—
229C23×C31—42no—
230C23×C31C2×C22⋊C411yescharacteristic
231C23×C31C2×C22⋊C411yescharacteristic
232C23×C31C22×D411yescharacteristic
233Q8×C31—24no—
234Q8×C31—22no—
235Q8×C31#11714yes—
236D4×C31—28no—
237D4×C31—24no—
238D4×C31—28no—
239D4×C31—22no—
240D4×C31#11714yes—
241C2×C4×C31—24no—
242C2×C4×C31—28no—
243C2×C4×C31—22no—
244C2×C4×C31—22no—
245C2×C4×C31—22no—
246C2×C4×C31—22no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—22no—
250C2×C4×C31—28no—
251C2×C4×C31—22no—
252C2×C4×C31—22no—
253C2×C4×C31—22no—
254C2×C4×C31—22no—
255C2×C4×C31—22no—
256C2×C4×C31—22no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—44no—
265C2×C4×C31—44no—
266C2×C4×C31—44no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—44no—
270C2×C4×C31—44no—
271C2×C4×C31—44no—
272C2×C4×C31—44no—
273C2×C4×C31C2×C22⋊C411yescharacteristic
274C2×C4×C31C2×C22⋊C411yescharacteristic
275C2×C4×C31C2×C22⋊C411yescharacteristic
276C2×C4×C31C2×C22⋊C411yescharacteristic
277C2×C4×C31C2×C22⋊C411yescharacteristic
278C2×C4×C31C2×C22⋊C411yescharacteristic
279C2×C4×C31C2×C22⋊C411yescharacteristic
280C2×C4×C31C2×C22⋊C411yescharacteristic
281C2×C4×C31C2×C22⋊C411yescharacteristic
282C2×C4×C31C2×C22⋊C411yescharacteristic
283C2×C4×C31C23×C411yescharacteristic
284C2×C4×C31C22×D411yescharacteristic
285C2×C4×C31C2×#4114yes—
286C8×C31—44no—
287C2×C4×#41C2×C3111yescharacteristic
288#2920C2×C3111yescharacteristic, complemented
289#2283C2×C3111yescharacteristic, complemented
290#1826C2×C3112yescomplemented
291#1806C2×C3114yescomplemented
292#1789C2×C3112yes—
293#1759C2×C3114yescomplemented
294C22×C31—21no—
295C22×C31—21no—
296C22×C31—21no—
297C22×C31—21no—
298C22×C31—21no—
299C22×C31—21no—
300C22×C31—21no—
301C22×C31—24no—
302C22×C31—44no—
303C22×C31—48no—
304C22×C31—42no—
305C22×C31—42no—
306C22×C31#42112yes—
307C22×C31C22×C22⋊C411yescharacteristic
308C22×C31#52512yes—
309C4×C31—21no—
310C4×C31—21no—
311C4×C31—21no—
312C4×C31—21no—
313C4×C31—21no—
314C4×C31—21no—
315C4×C31—21no—
316C4×C31—21no—
317C4×C31—24no—
318C4×C31—21no—
319C4×C31—42no—
320C4×C31—42no—
321C4×C31—84no—
322C4×C31#42112yes—
323C4×C31C2×#11712yes—
324C4×C31#52512yes—
325C22×#41C22×C3111yescharacteristic
326C4×#41—21no—
327C4×#41—21no—
328C4×#41—21no—
329C4×#41—21no—
330C4×#41C4×C3112yescomplemented
331C4×#41C4×C3112yescomplemented
332C4×#41C22×C3112yes—
333C4×#41C22×C3112yes—
334C2×C4×Q8C4×C3111yescharacteristic, complemented
335C2×C4×Q8C4×C3111yescharacteristic, complemented
336C2×C4×D4—21no—
337C2×C4×D4—21no—
338C2×C4×D4C4×C3111yescharacteristic, complemented
339C2×C4×D4C4×C3111yescharacteristic, complemented
340C2×#117—21no—
341C2×#117C22×C3111yescharacteristic
342C22×C42—21no—
343C22×C42C22×C3111yescharacteristic
344#432—21no—
345#432—21no—
346#431—21no—
347#431—21no—
348#423C22×C3112yescomplemented
349C2×#104C22×C3118yes—
350#407C22×C3112yes—
351C4×M16C22×C3112yescomplemented
352#383—21no—
353#382—21no—
354#381—21no—
355#380—21no—
356C4×C4⋊C4C22×C3112yescomplemented
357C4×C22⋊C4C22×C3112yes—
358#376C22×C3112yescomplemented
359#339C22×C3118yescomplemented
360C2×C31—22no—
361C2×C31—22no—
362C2×C31—41no—
363C2×C31—44no—
364C2×C31#228011yescharacteristic
365C2×C31C2×#42111yescharacteristic
366C2×C31C2×#42111yescharacteristic
367C2×#41—28no—
368C2×#41—21no—
369C2×#41—21no—
370C2×#41C2×C4×C3112yes—
371C2×#41C23×C3112yes—
372C22×Q8C2×C4×C3111yescharacteristic
373C22×D4—21no—
374C22×D4C2×C4×C3111yescharacteristic
375C23×C4—21no—
376C23×C4—21no—
377C23×C4—21no—
378C23×C4D4×C3111yescharacteristic
379C23×C4D4×C3111yescharacteristic
380C23×C4C23×C3111yescharacteristic
381C2×M16C23×C3114yes—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8C2×C4×C3112yes—
387C4×Q8C2×C4×C3112yes—
388C4×Q8C2×C4×C3112yes—
389C4×Q8C2×C4×C3112yes—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C2×C4×C3112yes—
403C4×D4C2×C4×C3112yes—
404C4×D4C2×C4×C3112yes—
405C4×D4C2×C4×C3112yes—
406#117—21no—
407#117—21no—
408#117—22no—
409#117—22no—
410#117—22no—
411#117—22no—
412#117C2×C4×C3112yes—
413#117C23×C3112yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4C2×C4×C3111yescharacteristic
418C2×C4⋊C4C2×C4×C3111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—22no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42C2×C4×C3111yescharacteristic
431C2×C42C2×C4×C3111yescharacteristic
432C2×C42C2×C4×C3111yescharacteristic
433C2×C42C2×C4×C3111yescharacteristic
434C2×C42D4×C3111yescharacteristic
435C2×C42D4×C3111yescharacteristic
436C2×C42D4×C3111yescharacteristic
437C2×C42D4×C3111yescharacteristic
438C2×C42D4×C3111yescharacteristic
439C2×C42D4×C3111yescharacteristic
440C2×C42C23×C3114yes—
441C2×C42C23×C3111yescharacteristic
442C2×C42C23×C3111yescharacteristic
443C4⋊C8—22no—
444C4⋊C8—22no—
445#104—216no—
446C22⋊C8—22no—
447C22⋊C8—22no—
448#97—22no—
449C4×C8—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454C31#2074811yescharacteristic, direct product factor, Sylow
455C24—21no—
456C24C2×D4×C3111yescharacteristic
457#41—28no—
458#41—28no—
459#41—24no—
460#41—24no—
461#41—24no—
462#41#41×C3118yes—
463C2×Q8—24no—
464C2×Q8—21no—
465C2×Q8C22×C4×C3112yes—
466C2×D4—28no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—24no—
470C2×D4—21no—
471C2×D4C22×C4×C3112yes—
472C22×C4—28no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4C22⋊C4×C3111yescharacteristic
489C22×C4C22⋊C4×C3111yescharacteristic
490C22×C4C22⋊C4×C3111yescharacteristic
491C22×C4C22⋊C4×C3111yescharacteristic
492C22×C4C22⋊C4×C3111yescharacteristic
493C22×C4C22⋊C4×C3111yescharacteristic
494C22×C4C22⋊C4×C3111yescharacteristic
495C22×C4C22⋊C4×C3111yescharacteristic
496C22×C4C22×C4×C3111yescharacteristic
497C22×C4C22×C4×C3111yescharacteristic
498C22×C4C2×D4×C3111yescharacteristic
499C22×C4C2×D4×C3111yescharacteristic
500C22×C4C2×D4×C3111yescharacteristic
501C22×C4C2×D4×C3111yescharacteristic
502C22×C4C2×D4×C3111yescharacteristic
503C22×C4C2×D4×C3111yescharacteristic
504C22×C4C2×D4×C3111yescharacteristic
505C22×C4C24×C3111yescharacteristic
506M16—28no—
507C2×C8—24no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—44no—
515C4⋊C4C22×C4×C3112yes—
516C4⋊C4C22×C4×C3112yes—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—44no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—28no—
531C42C22⋊C4×C3111yescharacteristic
532C42C22⋊C4×C3111yescharacteristic
533C42C22⋊C4×C3111yescharacteristic
534C42C22⋊C4×C3111yescharacteristic
535C42C22⋊C4×C3111yescharacteristic
536C42C22⋊C4×C3111yescharacteristic
537C42C22⋊C4×C3111yescharacteristic
538C42C22⋊C4×C3111yescharacteristic
539C42C22×C4×C3111yescharacteristic
540C42C22×C4×C3111yescharacteristic
541C42C22×C4×C3111yescharacteristic
542C42C22×C4×C3111yescharacteristic
543C42C2×D4×C3111yescharacteristic
544C42C2×D4×C3111yescharacteristic
545C42C2×D4×C3111yescharacteristic
546C42C2×D4×C3111yescharacteristic
547C23—24no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—41no—
552C23—42no—
553C23—42no—
554C23C2×C22⋊C4×C3111yescharacteristic
555C23C2×C22⋊C4×C3111yescharacteristic
556C23C22×D4×C3111yescharacteristic
557Q8—24no—
558Q8—22no—
559Q8C31×#11714yes—
560D4—28no—
561D4—24no—
562D4—28no—
563D4—22no—
564D4C31×#11714yes—
565C2×C4—24no—
566C2×C4—28no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—28no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4C2×C22⋊C4×C3111yescharacteristic
598C2×C4C2×C22⋊C4×C3111yescharacteristic
599C2×C4C2×C22⋊C4×C3111yescharacteristic
600C2×C4C2×C22⋊C4×C3111yescharacteristic
601C2×C4C2×C22⋊C4×C3111yescharacteristic
602C2×C4C2×C22⋊C4×C3111yescharacteristic
603C2×C4C2×C22⋊C4×C3111yescharacteristic
604C2×C4C2×C22⋊C4×C3111yescharacteristic
605C2×C4C2×C22⋊C4×C3111yescharacteristic
606C2×C4C2×C22⋊C4×C3111yescharacteristic
607C2×C4C23×C4×C3111yescharacteristic
608C2×C4C22×D4×C3111yescharacteristic
609C2×C4C2×#41×C3114yes—
610C8—44no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—24no—
619C22—44no—
620C22—48no—
621C22—42no—
622C22—42no—
623C22C31×#42112yes—
624C22C22×C22⋊C4×C3111yescharacteristic
625C22C31×#52512yes—
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—24no—
635C4—21no—
636C4—42no—
637C4—42no—
638C4—84no—
639C4C31×#42112yes—
640C4C2×C31×#11712yes—
641C4C31×#52512yes—
642C2—22no—
643C2—22no—
644C2—41no—
645C2—44no—
646C2C31×#228011yescharacteristic
647C2C2×C31×#42111yescharacteristic
648C2C2×C31×#42111yescharacteristic
subgroupG/H
centerC2×C4×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC22×C31C22×C22⋊C4
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2920C2semidirect
3. C31×#2283C2semidirect
4. C31×#1826C2semidirect
5. C31×#1806C2semidirect
7. C31×#1759C2semidirect
13. C4×#41×C31C4semidirect
14. C4×#41×C31C4semidirect
17. C2×C4×Q8×C31C4semidirect
18. C2×C4×Q8×C31C4semidirect
21. C2×C4×D4×C31C4semidirect
22. C2×C4×D4×C31C4semidirect
31. C31×#423C22semidirect
34. C4×M16×C31C22semidirect
39. C4×C4⋊C4×C31C22semidirect
41. C31×#376C22semidirect
42. C31×#339C22semidirect
222. #20748C31direct (N × H)
288. #2920C2×C31semidirect
289. #2283C2×C31semidirect
290. #1826C2×C31semidirect
291. #1806C2×C31semidirect
293. #1759C2×C31semidirect
330. C4×#41C4×C31semidirect
331. C4×#41C4×C31semidirect
334. C2×C4×Q8C4×C31semidirect
335. C2×C4×Q8C4×C31semidirect
338. C2×C4×D4C4×C31semidirect
339. C2×C4×D4C4×C31semidirect
348. #423C22×C31semidirect
351. C4×M16C22×C31semidirect
356. C4×C4⋊C4C22×C31semidirect
358. #376C22×C31semidirect
359. #339C22×C31semidirect
454. C31#20748direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#41×C312
C31×#29202
C31×#22832
C31×#18262
C31×#18062
C31×#17892
C31×#17592
#2074831